TSTP Solution File: SWW337+1 by CSE---1.6
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%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : SWW337+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 1 00:13:51 EDT 2023
% Result : Theorem 109.13s 108.82s
% Output : CNFRefutation 109.25s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWW337+1 : TPTP v8.1.2. Released v5.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.13/0.34 % Computer : n022.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 19:56:09 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.55 start to proof:theBenchmark
% 108.59/108.65 %-------------------------------------------
% 108.59/108.65 % File :CSE---1.6
% 108.59/108.65 % Problem :theBenchmark
% 108.59/108.65 % Transform :cnf
% 108.59/108.65 % Format :tptp:raw
% 108.59/108.65 % Command :java -jar mcs_scs.jar %d %s
% 108.59/108.65
% 108.59/108.65 % Result :Theorem 105.360000s
% 108.59/108.65 % Output :CNFRefutation 105.360000s
% 108.59/108.65 %-------------------------------------------
% 108.59/108.66 %------------------------------------------------------------------------------
% 108.59/108.66 % File : SWW337+1 : TPTP v8.1.2. Released v5.2.0.
% 108.59/108.66 % Domain : Software Verification
% 108.59/108.66 % Problem : Hoare's Logic with Procedures 435184, 5000 axioms selected
% 108.59/108.66 % Version : Especial.
% 108.59/108.66 % English :
% 108.59/108.66
% 108.59/108.66 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 108.59/108.66 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 108.59/108.66 % Source : [Bla11]
% 108.59/108.66 % Names : hoare_435184.5000.p [Bla11]
% 108.59/108.66
% 108.59/108.66 % Status : Theorem
% 108.59/108.66 % Rating : 0.53 v8.1.0, 0.61 v7.5.0, 0.62 v7.4.0, 0.70 v7.3.0, 0.66 v7.1.0, 0.74 v7.0.0, 0.73 v6.4.0, 0.69 v6.3.0, 0.75 v6.2.0, 0.84 v6.1.0, 0.87 v6.0.0, 0.78 v5.5.0, 0.81 v5.4.0, 0.82 v5.3.0, 0.85 v5.2.0
% 108.59/108.66 % Syntax : Number of formulae : 5226 (1637 unt; 0 def)
% 108.59/108.66 % Number of atoms : 12842 (4415 equ)
% 108.59/108.66 % Maximal formula atoms : 13 ( 2 avg)
% 108.59/108.66 % Number of connectives : 8580 ( 964 ~; 148 |; 713 &)
% 108.59/108.66 % ( 900 <=>;5855 =>; 0 <=; 0 <~>)
% 108.59/108.66 % Maximal formula depth : 22 ( 6 avg)
% 108.59/108.66 % Maximal term depth : 19 ( 2 avg)
% 108.59/108.66 % Number of predicates : 152 ( 151 usr; 0 prp; 1-6 aty)
% 108.59/108.66 % Number of functors : 374 ( 374 usr; 46 con; 0-7 aty)
% 108.59/108.66 % Number of variables : 16635 (16480 !; 155 ?)
% 108.59/108.66 % SPC : FOF_THM_RFO_SEQ
% 108.59/108.66
% 108.59/108.66 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 108.59/108.66 % 2011-03-01 12:08:43
% 108.59/108.66 %------------------------------------------------------------------------------
% 108.59/108.66 %----Relevant facts (4984)
% 108.59/108.66 fof(fact_ext,axiom,
% 108.59/108.66 ! [V_g_2,V_f_2] :
% 108.59/108.66 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 108.59/108.66 => V_f_2 = V_g_2 ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_equalityI,axiom,
% 108.59/108.66 ! [V_B_2,V_A_2,T_b] :
% 108.59/108.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.59/108.66 => V_A_2 = V_B_2 ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_order__refl,axiom,
% 108.59/108.66 ! [V_x,T_a] :
% 108.59/108.66 ( class_Orderings_Opreorder(T_a)
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_hoare__valids__def,axiom,
% 108.59/108.66 ! [V_tsa_2,V_Ga_2,T_b] :
% 108.59/108.66 ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_tsa_2)
% 108.59/108.66 <=> ! [B_n] :
% 108.59/108.66 ( ! [B_x] :
% 108.59/108.66 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_Ga_2))
% 108.59/108.66 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) )
% 108.59/108.66 => ! [B_x] :
% 108.59/108.66 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 108.59/108.66 => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_le__fun__def,axiom,
% 108.59/108.66 ! [V_g_2,V_f_2,T_b,T_c] :
% 108.59/108.66 ( class_Orderings_Oord(T_c)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 108.59/108.66 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_le__funD,axiom,
% 108.59/108.66 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 108.59/108.66 ( class_Orderings_Oord(T_c)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_le__funE,axiom,
% 108.59/108.66 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 108.59/108.66 ( class_Orderings_Oord(T_c)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2))) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_subset__refl,axiom,
% 108.59/108.66 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2)) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_set__eq__subset,axiom,
% 108.59/108.66 ! [T_b,V_B_2,V_A_2] :
% 108.59/108.66 ( V_A_2 = V_B_2
% 108.59/108.66 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.59/108.66 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_rev__predicate1D,axiom,
% 108.59/108.66 ! [V_Q_2,T_b,V_x_2,V_P_2] :
% 108.59/108.66 ( hBOOL(hAPP(V_P_2,V_x_2))
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 108.59/108.66 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_equalityD1,axiom,
% 108.59/108.66 ! [T_b,V_B_2,V_A_2] :
% 108.59/108.66 ( V_A_2 = V_B_2
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_equalityD2,axiom,
% 108.59/108.66 ! [T_b,V_B_2,V_A_2] :
% 108.59/108.66 ( V_A_2 = V_B_2
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_predicate1D,axiom,
% 108.59/108.66 ! [V_x_2,V_Q_2,V_P_2,T_b] :
% 108.59/108.66 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 108.59/108.66 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 108.59/108.66 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_linorder__le__cases,axiom,
% 108.59/108.66 ! [V_y,V_x,T_a] :
% 108.59/108.66 ( class_Orderings_Olinorder(T_a)
% 108.59/108.66 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_xt1_I6_J,axiom,
% 108.59/108.66 ! [V_z,V_x,V_y,T_a] :
% 108.59/108.66 ( class_Orderings_Oorder(T_a)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_xt1_I5_J,axiom,
% 108.59/108.66 ! [V_x,V_y,T_a] :
% 108.59/108.66 ( class_Orderings_Oorder(T_a)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.59/108.66 => V_x = V_y ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_order__trans,axiom,
% 108.59/108.66 ! [V_z,V_y,V_x,T_a] :
% 108.59/108.66 ( class_Orderings_Opreorder(T_a)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_order__antisym,axiom,
% 108.59/108.66 ! [V_y,V_x,T_a] :
% 108.59/108.66 ( class_Orderings_Oorder(T_a)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.59/108.66 => V_x = V_y ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_xt1_I4_J,axiom,
% 108.59/108.66 ! [V_c,V_a,V_b,T_a] :
% 108.59/108.66 ( class_Orderings_Oorder(T_a)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 108.59/108.66 => ( V_b = V_c
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_ord__le__eq__trans,axiom,
% 108.59/108.66 ! [V_c,V_b,V_a,T_a] :
% 108.59/108.66 ( class_Orderings_Oord(T_a)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.59/108.66 => ( V_b = V_c
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_xt1_I3_J,axiom,
% 108.59/108.66 ! [V_c,V_b,V_a,T_a] :
% 108.59/108.66 ( class_Orderings_Oorder(T_a)
% 108.59/108.66 => ( V_a = V_b
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_ord__eq__le__trans,axiom,
% 108.59/108.66 ! [V_c,V_b,V_a,T_a] :
% 108.59/108.66 ( class_Orderings_Oord(T_a)
% 108.59/108.66 => ( V_a = V_b
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_order__antisym__conv,axiom,
% 108.59/108.66 ! [V_x_2,V_y_2,T_b] :
% 108.59/108.66 ( class_Orderings_Oorder(T_b)
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 108.59/108.66 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.59/108.66 <=> V_x_2 = V_y_2 ) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_order__eq__refl,axiom,
% 108.59/108.66 ! [V_y,V_x,T_a] :
% 108.59/108.66 ( class_Orderings_Opreorder(T_a)
% 108.59/108.66 => ( V_x = V_y
% 108.59/108.66 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 108.59/108.66
% 108.59/108.66 fof(fact_order__eq__iff,axiom,
% 108.59/108.66 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.67 ( class_Orderings_Oorder(T_b)
% 108.59/108.67 => ( V_x_2 = V_y_2
% 108.59/108.67 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.59/108.67 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_linorder__linear,axiom,
% 108.59/108.67 ! [V_y,V_x,T_a] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_a)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.59/108.67 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_equalityE,axiom,
% 108.59/108.67 ! [T_b,V_B_2,V_A_2] :
% 108.59/108.67 ( V_A_2 = V_B_2
% 108.59/108.67 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.59/108.67 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_subset__trans,axiom,
% 108.59/108.67 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Powp__mono,axiom,
% 108.59/108.67 ! [V_B_2,V_A_2,T_b] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_triples__valid__Suc,axiom,
% 108.59/108.67 ! [V_n_2,V_tsa_2,T_b] :
% 108.59/108.67 ( ! [B_x] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 108.59/108.67 => c_Hoare__Mirabelle_Otriple__valid(T_b,hAPP(c_Nat_OSuc,V_n_2),B_x) )
% 108.59/108.67 => ! [B_x] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_tsa_2))
% 108.59/108.67 => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_le__funI,axiom,
% 108.59/108.67 ! [T_b,V_g_2,V_f_2,T_c] :
% 108.59/108.67 ( class_Orderings_Oord(T_c)
% 108.59/108.67 => ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x)))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_strict__mono__less__eq,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 108.59/108.67 ( ( class_Orderings_Oorder(T_c)
% 108.59/108.67 & class_Orderings_Olinorder(T_b) )
% 108.59/108.67 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 108.59/108.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_thin,axiom,
% 108.59/108.67 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 108.59/108.67 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_G_H_2),V_Ga_2))
% 108.59/108.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_weaken,axiom,
% 108.59/108.67 ! [V_tsa_2,V_ts_H_2,V_Ga_2,T_b] :
% 108.59/108.67 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_H_2)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_ts_H_2))
% 108.59/108.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_asm,axiom,
% 108.59/108.67 ! [V_Ga_2,V_tsa_2,T_b] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_Ga_2))
% 108.59/108.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_greaterThan__subset__iff,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_b)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
% 108.59/108.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_lessThan__subset__iff,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_b)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)))
% 108.59/108.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_atLeast__subset__iff,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.67 ( class_Orderings_Oorder(T_b)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)))
% 108.59/108.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_atMost__subset__iff,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.67 ( class_Orderings_Oorder(T_b)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)))
% 108.59/108.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_SUP__subset,axiom,
% 108.59/108.67 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 108.59/108.67 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_B_2),V_f_2))) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_cut,axiom,
% 108.59/108.67 ! [V_Ga_2,V_tsa_2,V_G_H_2,T_b] :
% 108.59/108.67 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_tsa_2)
% 108.59/108.67 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_G_H_2)
% 108.59/108.67 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_greaterThan__eq__iff,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_b)
% 108.59/108.67 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 108.59/108.67 <=> V_x_2 = V_y_2 ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_lessThan__eq__iff,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_b)
% 108.59/108.67 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 108.59/108.67 <=> V_x_2 = V_y_2 ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_atLeast__eq__iff,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_b)
% 108.59/108.67 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 108.59/108.67 <=> V_x_2 = V_y_2 ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_atMost__eq__iff,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_b)
% 108.59/108.67 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 108.59/108.67 <=> V_x_2 = V_y_2 ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_lessThan__Suc__atMost,axiom,
% 108.59/108.67 ! [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) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_atLeast__Suc__greaterThan,axiom,
% 108.59/108.67 ! [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) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_strict__mono__eq,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 108.59/108.67 ( ( class_Orderings_Oorder(T_c)
% 108.59/108.67 & class_Orderings_Olinorder(T_b) )
% 108.59/108.67 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 108.59/108.67 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 108.59/108.67 <=> V_x_2 = V_y_2 ) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_triple__valid__Suc,axiom,
% 108.59/108.67 ! [V_t,V_n,T_a] :
% 108.59/108.67 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t)
% 108.59/108.67 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Suc__n__not__le__n,axiom,
% 108.59/108.67 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_not__less__eq__eq,axiom,
% 108.59/108.67 ! [V_n_2,V_m_2] :
% 108.59/108.67 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.59/108.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_le__Suc__eq,axiom,
% 108.59/108.67 ! [V_n_2,V_m_2] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 108.59/108.67 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.59/108.67 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Suc__le__mono,axiom,
% 108.59/108.67 ! [V_m_2,V_n_2] :
% 108.59/108.67 ( 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)))
% 108.59/108.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_le__SucI,axiom,
% 108.59/108.67 ! [V_n,V_m] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_le__SucE,axiom,
% 108.59/108.67 ! [V_n,V_m] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 108.59/108.67 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.59/108.67 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Suc__leD,axiom,
% 108.59/108.67 ! [V_n,V_m] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Suc__inject,axiom,
% 108.59/108.67 ! [V_y,V_x] :
% 108.59/108.67 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 108.59/108.67 => V_x = V_y ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_nat_Oinject,axiom,
% 108.59/108.67 ! [V_nat_H_2,V_nat_2] :
% 108.59/108.67 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 108.59/108.67 <=> V_nat_2 = V_nat_H_2 ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Suc__n__not__n,axiom,
% 108.59/108.67 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 108.59/108.67
% 108.59/108.67 fof(fact_n__not__Suc__n,axiom,
% 108.59/108.67 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_le__refl,axiom,
% 108.59/108.67 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_nat__le__linear,axiom,
% 108.59/108.67 ! [V_n,V_m] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.59/108.67 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_eq__imp__le,axiom,
% 108.59/108.67 ! [V_n,V_m] :
% 108.59/108.67 ( V_m = V_n
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_le__trans,axiom,
% 108.59/108.67 ! [V_k,V_j,V_i] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_le__antisym,axiom,
% 108.59/108.67 ! [V_n,V_m] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 108.59/108.67 => V_m = V_n ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_lift__Suc__mono__le,axiom,
% 108.59/108.67 ! [V_n_H_2,V_n_2,V_f_2,T_b] :
% 108.59/108.67 ( class_Orderings_Oorder(T_b)
% 108.59/108.67 => ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_n_H_2))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_n_H_2))) ) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 108.59/108.67 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 108.59/108.67 ( class_Rings_Osemiring__1(T_b)
% 108.59/108.67 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,hAPP(c_Nat_OSuc,V_n_2),V_i_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,V_n_2,hAPP(V_inc_2,V_i_2)) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_INF__subset,axiom,
% 108.59/108.67 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 108.59/108.67 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_B_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2))) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Pow__mono,axiom,
% 108.59/108.67 ! [V_B_2,V_A_2,T_b] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_mono__iff__le__Suc,axiom,
% 108.59/108.67 ! [V_f_2,T_b] :
% 108.59/108.67 ( class_Orderings_Oorder(T_b)
% 108.59/108.67 => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
% 108.59/108.67 <=> ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Suc__le__D,axiom,
% 108.59/108.67 ! [V_m_H,V_n] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_m_H))
% 108.59/108.67 => ? [B_m] : V_m_H = hAPP(c_Nat_OSuc,B_m) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Inter__anti__mono,axiom,
% 108.59/108.67 ! [V_A_2,V_B_2,T_b] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_B_2),V_A_2))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_nat__case__Suc,axiom,
% 108.59/108.67 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_atLeastLessThan__subset__iff,axiom,
% 108.59/108.67 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_b)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 108.59/108.67 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 108.59/108.67 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Compl__atMost,axiom,
% 108.59/108.67 ! [V_k_2,T_b] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_b)
% 108.59/108.67 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Compl__greaterThan,axiom,
% 108.59/108.67 ! [V_k_2,T_b] :
% 108.59/108.67 ( class_Orderings_Olinorder(T_b)
% 108.59/108.67 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_atLeastatMost__subset__iff,axiom,
% 108.59/108.67 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.59/108.67 ( class_Orderings_Oorder(T_b)
% 108.59/108.67 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 108.59/108.67 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 108.59/108.67 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 108.59/108.67 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_double__complement,axiom,
% 108.59/108.67 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = V_A_2 ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Compl__eq__Compl__iff,axiom,
% 108.59/108.67 ! [V_B_2,V_A_2,T_b] :
% 108.59/108.67 ( 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_b,tc_HOL_Obool)),V_B_2)
% 108.59/108.67 <=> V_A_2 = V_B_2 ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 108.59/108.67 ! [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) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Compl__subset__Compl__iff,axiom,
% 108.59/108.67 ! [V_B_2,V_A_2,T_b] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2)))
% 108.59/108.67 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_Compl__anti__mono,axiom,
% 108.59/108.67 ! [V_B_2,V_A_2,T_b] :
% 108.59/108.67 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.59/108.67 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 108.59/108.67
% 108.59/108.67 fof(fact_monoD,axiom,
% 108.59/108.67 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 108.59/108.67 ( ( class_Orderings_Oorder(T_c)
% 108.59/108.68 & class_Orderings_Oorder(T_b) )
% 108.59/108.68 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.59/108.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_mono__Suc,axiom,
% 108.59/108.68 c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_le__Inf__iff,axiom,
% 108.59/108.68 ! [V_A_2,V_b_2,T_b] :
% 108.59/108.68 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)))
% 108.59/108.68 <=> ! [B_x] :
% 108.59/108.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.59/108.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_INFI__bool__eq,axiom,
% 108.59/108.68 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_strict__mono__mono,axiom,
% 108.59/108.68 ! [V_f_2,T_b,T_c] :
% 108.59/108.68 ( ( class_Orderings_Oorder(T_c)
% 108.59/108.68 & class_Orderings_Oorder(T_b) )
% 108.59/108.68 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 108.59/108.68 => c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_Compl__lessThan,axiom,
% 108.59/108.68 ! [V_k_2,T_b] :
% 108.59/108.68 ( class_Orderings_Olinorder(T_b)
% 108.59/108.68 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_Compl__atLeast,axiom,
% 108.59/108.68 ! [V_k_2,T_b] :
% 108.59/108.68 ( class_Orderings_Olinorder(T_b)
% 108.59/108.68 => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_uminus__apply,axiom,
% 108.59/108.68 ! [V_x_2,V_A_2,T_c,T_b] :
% 108.59/108.68 ( class_Groups_Ouminus(T_b)
% 108.59/108.68 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_le__minus__iff,axiom,
% 108.59/108.68 ! [V_b_2,V_a_2,T_b] :
% 108.59/108.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 108.59/108.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_minus__le__iff,axiom,
% 108.59/108.68 ! [V_b_2,V_a_2,T_b] :
% 108.59/108.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 108.59/108.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_neg__le__iff__le,axiom,
% 108.59/108.68 ! [V_a_2,V_b_2,T_b] :
% 108.59/108.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 108.59/108.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_compl__le__compl__iff,axiom,
% 108.59/108.68 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.68 ( class_Lattices_Oboolean__algebra(T_b)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 108.59/108.68 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_le__imp__neg__le,axiom,
% 108.59/108.68 ! [V_b,V_a,T_a] :
% 108.59/108.68 ( class_Groups_Oordered__ab__group__add(T_a)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.59/108.68 => 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))) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_compl__mono,axiom,
% 108.59/108.68 ! [V_y,V_x,T_a] :
% 108.59/108.68 ( class_Lattices_Oboolean__algebra(T_a)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.59/108.68 => 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))) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_ivl__disj__un_I13_J,axiom,
% 108.59/108.68 ! [V_u_2,V_l_2,T_b] :
% 108.59/108.68 ( class_Orderings_Olinorder(T_b)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 108.59/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_ivl__disj__un_I10_J,axiom,
% 108.59/108.68 ! [V_u_2,V_l_2,T_b] :
% 108.59/108.68 ( class_Orderings_Olinorder(T_b)
% 108.59/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 108.59/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_compl__eq__compl__iff,axiom,
% 108.59/108.68 ! [V_y_2,V_x_2,T_b] :
% 108.59/108.68 ( class_Lattices_Oboolean__algebra(T_b)
% 108.59/108.68 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 108.59/108.68 <=> V_x_2 = V_y_2 ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_neg__equal__iff__equal,axiom,
% 108.59/108.68 ! [V_b_2,V_a_2,T_b] :
% 108.59/108.68 ( class_Groups_Ogroup__add(T_b)
% 108.59/108.68 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 108.59/108.68 <=> V_a_2 = V_b_2 ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_minus__equation__iff,axiom,
% 108.59/108.68 ! [V_b_2,V_a_2,T_b] :
% 108.59/108.68 ( class_Groups_Ogroup__add(T_b)
% 108.59/108.68 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 108.59/108.68 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_sup1CI,axiom,
% 108.59/108.68 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 108.59/108.68 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 108.59/108.68 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 108.59/108.68 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_sup1E,axiom,
% 108.59/108.68 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 108.59/108.68 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 108.59/108.68 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 108.59/108.68 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_sup_Oidem,axiom,
% 108.59/108.68 ! [V_a,T_a] :
% 108.59/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.59/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_sup__idem,axiom,
% 108.59/108.68 ! [V_x,T_a] :
% 108.59/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.59/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_sup_Ocommute,axiom,
% 108.59/108.68 ! [V_b,V_a,T_a] :
% 108.59/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.59/108.68 => 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) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_inf__sup__aci_I5_J,axiom,
% 108.59/108.68 ! [V_y,V_x,T_a] :
% 108.59/108.68 ( class_Lattices_Olattice(T_a)
% 108.59/108.68 => 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) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_sup__commute,axiom,
% 108.59/108.68 ! [V_y,V_x,T_a] :
% 108.59/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.59/108.68 => 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) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_sup_Oleft__idem,axiom,
% 108.59/108.68 ! [V_b,V_a,T_a] :
% 108.59/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.59/108.68 => 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) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_inf__sup__aci_I8_J,axiom,
% 108.59/108.68 ! [V_y,V_x,T_a] :
% 108.59/108.68 ( class_Lattices_Olattice(T_a)
% 108.59/108.68 => 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) ) ).
% 108.59/108.68
% 108.59/108.68 fof(fact_sup__left__idem,axiom,
% 108.59/108.68 ! [V_y,V_x,T_a] :
% 108.59/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => 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) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup_Oleft__commute,axiom,
% 108.69/108.68 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__sup__aci_I7_J,axiom,
% 108.69/108.68 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup__left__commute,axiom,
% 108.69/108.68 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup_Oassoc,axiom,
% 108.69/108.68 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__sup__aci_I6_J,axiom,
% 108.69/108.68 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup__assoc,axiom,
% 108.69/108.68 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup__apply,axiom,
% 108.69/108.68 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 108.69/108.68 ( class_Lattices_Olattice(T_b)
% 108.69/108.68 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup1I2,axiom,
% 108.69/108.68 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 108.69/108.68 ( hBOOL(hAPP(V_B_2,V_x_2))
% 108.69/108.68 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup1I1,axiom,
% 108.69/108.68 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 108.69/108.68 ( hBOOL(hAPP(V_A_2,V_x_2))
% 108.69/108.68 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_ball__Un,axiom,
% 108.69/108.68 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 108.69/108.68 ( ! [B_x] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.68 => hBOOL(hAPP(V_P_2,B_x)) )
% 108.69/108.68 <=> ( ! [B_x] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.68 => hBOOL(hAPP(V_P_2,B_x)) )
% 108.69/108.68 & ! [B_x] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 108.69/108.68 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_bex__Un,axiom,
% 108.69/108.68 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 108.69/108.68 ( ? [B_x] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.68 & hBOOL(hAPP(V_P_2,B_x)) )
% 108.69/108.68 <=> ( ? [B_x] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.68 & hBOOL(hAPP(V_P_2,B_x)) )
% 108.69/108.68 | ? [B_x] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 108.69/108.68 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__assoc,axiom,
% 108.69/108.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__left__commute,axiom,
% 108.69/108.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__left__absorb,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_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_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__commute,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,T_b] : 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_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__absorb,axiom,
% 108.69/108.68 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 108.69/108.68
% 108.69/108.68 fof(fact_le__supE,axiom,
% 108.69/108.68 ! [V_x,V_b,V_a,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => ( 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))
% 108.69/108.68 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 108.69/108.68 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup__mono,axiom,
% 108.69/108.68 ! [V_d,V_b,V_c,V_a,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 108.69/108.68 => 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))) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup__least,axiom,
% 108.69/108.68 ! [V_z,V_x,V_y,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 108.69/108.68 => 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)) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_le__supI,axiom,
% 108.69/108.68 ! [V_b,V_x,V_a,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 108.69/108.68 => 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)) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup__absorb1,axiom,
% 108.69/108.68 ! [V_x,V_y,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup__absorb2,axiom,
% 108.69/108.68 ! [V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_le__supI2,axiom,
% 108.69/108.68 ! [V_a,V_b,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 108.69/108.68 => 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))) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_le__supI1,axiom,
% 108.69/108.68 ! [V_b,V_a,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 108.69/108.68 => 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))) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_le__sup__iff,axiom,
% 108.69/108.68 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_b)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
% 108.69/108.68 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 108.69/108.68 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_le__iff__sup,axiom,
% 108.69/108.68 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_b)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.68 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup__ge2,axiom,
% 108.69/108.68 ! [V_x,V_y,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => 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))) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__sup__ord_I4_J,axiom,
% 108.69/108.68 ! [V_x,V_y,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => 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))) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_sup__ge1,axiom,
% 108.69/108.68 ! [V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.68 => 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))) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__sup__ord_I3_J,axiom,
% 108.69/108.68 ! [V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => 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))) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_mono__Un,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.68 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 108.69/108.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_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)))) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__mono,axiom,
% 108.69/108.68 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 108.69/108.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__least,axiom,
% 108.69/108.68 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 108.69/108.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,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_C_2)) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__absorb2,axiom,
% 108.69/108.68 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__absorb1,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_subset__Un__eq,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.68 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__upper2,axiom,
% 108.69/108.68 ! [V_A_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__upper1,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Un__Pow__subset,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_mono__sup,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 108.69/108.68 ( ( class_Lattices_Osemilattice__sup(T_c)
% 108.69/108.68 & class_Lattices_Osemilattice__sup(T_b) )
% 108.69/108.68 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 108.69/108.68 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_A_2),V_B_2)))) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_ivl__disj__un_I17_J,axiom,
% 108.69/108.68 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.68 ( class_Orderings_Olinorder(T_b)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_ivl__disj__un_I21_J,axiom,
% 108.69/108.68 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.68 ( class_Orderings_Olinorder(T_b)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_ivl__disj__un_I8_J,axiom,
% 108.69/108.68 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.68 ( class_Orderings_Olinorder(T_b)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_ivl__disj__un_I14_J,axiom,
% 108.69/108.68 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.68 ( class_Orderings_Olinorder(T_b)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_minus__minus,axiom,
% 108.69/108.68 ! [V_a,T_a] :
% 108.69/108.68 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.68 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_double__compl,axiom,
% 108.69/108.68 ! [V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.68 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_equation__minus__iff,axiom,
% 108.69/108.68 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.68 ( class_Groups_Ogroup__add(T_b)
% 108.69/108.68 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 108.69/108.68 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_ivl__disj__un_I11_J,axiom,
% 108.69/108.68 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.68 ( class_Orderings_Olinorder(T_b)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_ivl__disj__un_I9_J,axiom,
% 108.69/108.68 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.68 ( class_Orderings_Olinorder(T_b)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_ivl__disj__un_I22_J,axiom,
% 108.69/108.68 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.68 ( class_Orderings_Olinorder(T_b)
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 108.69/108.68 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Sup__fin_Oidem,axiom,
% 108.69/108.68 ! [V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Inter__Un__subset,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_atLeastAtMostSuc__conv,axiom,
% 108.69/108.68 ! [V_n_2,V_m_2] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_image__uminus__atMost,axiom,
% 108.69/108.68 ! [V_x_2,T_b] :
% 108.69/108.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.68 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_image__uminus__atLeast,axiom,
% 108.69/108.68 ! [V_x_2,T_b] :
% 108.69/108.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.68 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_image__uminus__lessThan,axiom,
% 108.69/108.68 ! [V_x_2,T_b] :
% 108.69/108.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.68 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_image__uminus__greaterThan,axiom,
% 108.69/108.68 ! [V_x_2,T_b] :
% 108.69/108.68 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.68 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_compl__sup__top,axiom,
% 108.69/108.68 ! [V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.68 => 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) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf1I,axiom,
% 108.69/108.68 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 108.69/108.68 ( hBOOL(hAPP(V_A_2,V_x_2))
% 108.69/108.68 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 108.69/108.68 => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf1E,axiom,
% 108.69/108.68 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 108.69/108.68 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 108.69/108.68 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__top__left,axiom,
% 108.69/108.68 ! [V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Obounded__lattice__top(T_a)
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__top__right,axiom,
% 108.69/108.68 ! [V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Obounded__lattice__top(T_a)
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf_Oidem,axiom,
% 108.69/108.68 ! [V_a,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__idem,axiom,
% 108.69/108.68 ! [V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf_Ocommute,axiom,
% 108.69/108.68 ! [V_b,V_a,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => 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) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__sup__aci_I1_J,axiom,
% 108.69/108.68 ! [V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => 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) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__commute,axiom,
% 108.69/108.68 ! [V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => 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) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf_Oleft__idem,axiom,
% 108.69/108.68 ! [V_b,V_a,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => 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) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__sup__aci_I4_J,axiom,
% 108.69/108.68 ! [V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => 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) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__left__idem,axiom,
% 108.69/108.68 ! [V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => 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) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf_Oleft__commute,axiom,
% 108.69/108.68 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__sup__aci_I3_J,axiom,
% 108.69/108.68 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__left__commute,axiom,
% 108.69/108.68 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__eq__top__iff,axiom,
% 108.69/108.68 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.68 ( class_Lattices_Obounded__lattice__top(T_b)
% 108.69/108.68 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 108.69/108.68 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 108.69/108.68 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf_Oassoc,axiom,
% 108.69/108.68 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__sup__aci_I2_J,axiom,
% 108.69/108.68 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__assoc,axiom,
% 108.69/108.68 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.68 => 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)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf__apply,axiom,
% 108.69/108.68 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 108.69/108.68 ( class_Lattices_Olattice(T_b)
% 108.69/108.68 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_top__apply,axiom,
% 108.69/108.68 ! [V_x_2,T_c,T_b] :
% 108.69/108.68 ( class_Orderings_Otop(T_b)
% 108.69/108.68 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Int__UNIV__left,axiom,
% 108.69/108.68 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Int__UNIV__right,axiom,
% 108.69/108.68 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Int__absorb,axiom,
% 108.69/108.68 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2 ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Int__commute,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,T_b] : 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_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_insert__absorb2,axiom,
% 108.69/108.68 ! [V_A_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Int__left__absorb,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_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_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_insert__commute,axiom,
% 108.69/108.68 ! [V_A_2,V_y_2,V_x_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Int__left__commute,axiom,
% 108.69/108.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_image__insert,axiom,
% 108.69/108.68 ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Int__assoc,axiom,
% 108.69/108.68 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_insert__inter__insert,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_insert__code,axiom,
% 108.69/108.68 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 108.69/108.68 <=> ( V_y_2 = V_x_2
% 108.69/108.68 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf1D1,axiom,
% 108.69/108.68 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 108.69/108.68 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_inf1D2,axiom,
% 108.69/108.68 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 108.69/108.68 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
% 108.69/108.68 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Inf__fin_Oidem,axiom,
% 108.69/108.68 ! [V_x,T_a] :
% 108.69/108.68 ( class_Lattices_Olattice(T_a)
% 108.69/108.68 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_image__Int__subset,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)))) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_image__Pow__surj,axiom,
% 108.69/108.68 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 108.69/108.68 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 108.69/108.68 => hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2)) = hAPP(c_Set_OPow(T_b),V_B_2) ) ).
% 108.69/108.68
% 108.69/108.68 fof(fact_Inf__insert,axiom,
% 108.69/108.68 ! [V_A_2,V_a_2,T_b] :
% 108.69/108.68 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Pow__insert,axiom,
% 108.69/108.69 ! [V_A_2,V_a_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_Oimage(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oinsert(T_b),V_a_2)),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Pow__Int__eq,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : hAPP(c_Set_OPow(T_b),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(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)),hAPP(c_Set_OPow(T_b),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Pow__UNIV,axiom,
% 108.69/108.69 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__sup__ord_I1_J,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Olattice(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__le1,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__sup__ord_I2_J,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Olattice(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__le2,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_le__iff__inf,axiom,
% 108.69/108.69 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.69 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_le__inf__iff,axiom,
% 108.69/108.69 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
% 108.69/108.69 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.69 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_le__infI1,axiom,
% 108.69/108.69 ! [V_b,V_x,V_a,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 108.69/108.69 => 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)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_le__infI2,axiom,
% 108.69/108.69 ! [V_a,V_x,V_b,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 108.69/108.69 => 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)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__absorb1,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__absorb2,axiom,
% 108.69/108.69 ! [V_x,V_y,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_le__infI,axiom,
% 108.69/108.69 ! [V_b,V_a,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 108.69/108.69 => 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))) ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__greatest,axiom,
% 108.69/108.69 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 108.69/108.69 => 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))) ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__mono,axiom,
% 108.69/108.69 ! [V_d,V_b,V_c,V_a,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 108.69/108.69 => 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))) ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_le__infE,axiom,
% 108.69/108.69 ! [V_b,V_a,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.69 => ( 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)))
% 108.69/108.69 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 108.69/108.69 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_subset__image__iff,axiom,
% 108.69/108.69 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 108.69/108.69 <=> ? [B_AA] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 108.69/108.69 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__mono,axiom,
% 108.69/108.69 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__Un,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_sup__inf__distrib2,axiom,
% 108.69/108.69 ! [V_x,V_z,V_y,T_a] :
% 108.69/108.69 ( class_Lattices_Odistrib__lattice(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__sup__distrib2,axiom,
% 108.69/108.69 ! [V_x,V_z,V_y,T_a] :
% 108.69/108.69 ( class_Lattices_Odistrib__lattice(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_sup__inf__distrib1,axiom,
% 108.69/108.69 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Odistrib__lattice(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__sup__distrib1,axiom,
% 108.69/108.69 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Odistrib__lattice(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_sup__inf__absorb,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Olattice(T_a)
% 108.69/108.69 => 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 ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__sup__absorb,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Olattice(T_a)
% 108.69/108.69 => 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 ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__uminus__atLeastLessThan,axiom,
% 108.69/108.69 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.69 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_x_2),V_y_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 108.69/108.69 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.69 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_x_2,V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_subset__insertI,axiom,
% 108.69/108.69 ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_subset__insertI2,axiom,
% 108.69/108.69 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_insert__mono,axiom,
% 108.69/108.69 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__lower1,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__lower2,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__absorb2,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__absorb1,axiom,
% 108.69/108.69 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__greatest,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__mono,axiom,
% 108.69/108.69 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_mono__Int,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.69 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),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(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__insert__right,axiom,
% 108.69/108.69 ! [V_B_2,V_a_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__insert__left,axiom,
% 108.69/108.69 ! [V_C_2,V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__Un__distrib,axiom,
% 108.69/108.69 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__Int__distrib,axiom,
% 108.69/108.69 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__Un__distrib2,axiom,
% 108.69/108.69 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__Int__distrib2,axiom,
% 108.69/108.69 ! [V_A_2,V_C_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__Int__crazy,axiom,
% 108.69/108.69 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2),V_C_2))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_subset__UNIV,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__UNIV__left,axiom,
% 108.69/108.69 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__UNIV__right,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Inter__Un__distrib,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__Pow__mono,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),V_B_2))
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Set_Oimage(T_c,T_b,V_f_2)),hAPP(c_Set_OPow(T_c),V_A_2))),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_top__greatest,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Orderings_Otop(T_a)
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_sup__top__right,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Obounded__lattice__top(T_a)
% 108.69/108.69 => 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) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_sup__top__left,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Obounded__lattice__top(T_a)
% 108.69/108.69 => 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) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_distrib__sup__le,axiom,
% 108.69/108.69 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Olattice(T_a)
% 108.69/108.69 => 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)))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_distrib__inf__le,axiom,
% 108.69/108.69 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Olattice(T_a)
% 108.69/108.69 => 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)))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_compl__inf,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_compl__sup,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.69 => 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)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__uminus__atLeastAtMost,axiom,
% 108.69/108.69 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.69 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__Suc__atLeastLessThan,axiom,
% 108.69/108.69 ! [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)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_mono__inf,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 108.69/108.69 ( ( class_Lattices_Osemilattice__inf(T_c)
% 108.69/108.69 & class_Lattices_Osemilattice__inf(T_b) )
% 108.69/108.69 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__Suc__atLeastAtMost,axiom,
% 108.69/108.69 ! [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)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__Int__assoc__eq,axiom,
% 108.69/108.69 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 108.69/108.69 ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 108.69/108.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Compl__Int,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Compl__Un,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Compl__partition,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Compl__partition2,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_lessThan__Suc,axiom,
% 108.69/108.69 ! [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)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atMost__Suc,axiom,
% 108.69/108.69 ! [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)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__un_I20_J,axiom,
% 108.69/108.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Olinorder(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 108.69/108.69 ! [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) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_sup__compl__top,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.69 => 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) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_surj__Compl__image__subset,axiom,
% 108.69/108.69 ! [V_A_2,V_f_2,T_b,T_c] :
% 108.69/108.69 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_compl__unique,axiom,
% 108.69/108.69 ! [V_y,V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 108.69/108.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 108.69/108.69 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__un_I5_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Olinorder(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__un_I6_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Olinorder(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__un_I1_J,axiom,
% 108.69/108.69 ! [V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Olinorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2)) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_l_2) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastLessThanSuc,axiom,
% 108.69/108.69 ! [V_n_2,V_m_2] :
% 108.69/108.69 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.69 => 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)) )
% 108.69/108.69 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.69 => 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)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atMost__Int__atLeast,axiom,
% 108.69/108.69 ! [V_n_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_n_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_n_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_n_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__un_I2_J,axiom,
% 108.69/108.69 ! [V_u_2,T_b] :
% 108.69/108.69 ( class_Orderings_Olinorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_u_2) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Cantors__paradox,axiom,
% 108.69/108.69 ! [V_A_2,T_b] :
% 108.69/108.69 ~ ? [B_f] : hAPP(c_Set_Oimage(T_b,tc_fun(T_b,tc_HOL_Obool),B_f),V_A_2) = hAPP(c_Set_OPow(T_b),V_A_2) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 108.69/108.69 ! [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))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Union__Int__subset,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_top1I,axiom,
% 108.69/108.69 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_empty__subsetI,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_le0,axiom,
% 108.69/108.69 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__eq__Union,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_UNIV__not__empty,axiom,
% 108.69/108.69 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Union__UNIV,axiom,
% 108.69/108.69 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Pow__empty,axiom,
% 108.69/108.69 ! [T_b] : hAPP(c_Set_OPow(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Union__empty,axiom,
% 108.69/108.69 ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Sup__empty,axiom,
% 108.69/108.69 ! [T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_bot__apply,axiom,
% 108.69/108.69 ! [V_x_2,T_c,T_b] :
% 108.69/108.69 ( class_Orderings_Obot(T_b)
% 108.69/108.69 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_bot__nat__def,axiom,
% 108.69/108.69 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_zero__reorient,axiom,
% 108.69/108.69 ! [V_x_2,T_b] :
% 108.69/108.69 ( class_Groups_Ozero(T_b)
% 108.69/108.69 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 108.69/108.69 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Union__insert,axiom,
% 108.69/108.69 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Union__disjoint,axiom,
% 108.69/108.69 ! [V_A_2,V_C_2,T_b] :
% 108.69/108.69 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.69 <=> ! [B_x] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_hoare__derivs_Oinsert,axiom,
% 108.69/108.69 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 108.69/108.69 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 108.69/108.69 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2)
% 108.69/108.69 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_derivs__insertD,axiom,
% 108.69/108.69 ! [V_tsa_2,V_t_2,V_Ga_2,T_b] :
% 108.69/108.69 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2))
% 108.69/108.69 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
% 108.69/108.69 & c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_tsa_2) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastLessThan0,axiom,
% 108.69/108.69 ! [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)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Sup__singleton,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_lessThan__0,axiom,
% 108.69/108.69 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)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__eq__Inter,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Sup__binary,axiom,
% 108.69/108.69 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_singleton__inject,axiom,
% 108.69/108.69 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( 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_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.69 => V_a_2 = V_b_2 ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_doubleton__eq__iff,axiom,
% 108.69/108.69 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.69 <=> ( ( V_a_2 = V_c_2
% 108.69/108.69 & V_b_2 = V_d_2 )
% 108.69/108.69 | ( V_a_2 = V_d_2
% 108.69/108.69 & V_b_2 = V_c_2 ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_insert__not__empty,axiom,
% 108.69/108.69 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_empty__not__insert,axiom,
% 108.69/108.69 ! [V_A_2,V_a_2,T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_subset__empty,axiom,
% 108.69/108.69 ! [V_A_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.69 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__is__empty,axiom,
% 108.69/108.69 ! [V_A_2,V_f_2,T_b,T_c] :
% 108.69/108.69 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.69 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_image__empty,axiom,
% 108.69/108.69 ! [V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_empty__is__image,axiom,
% 108.69/108.69 ! [V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.69 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)
% 108.69/108.69 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ball__empty,axiom,
% 108.69/108.69 ! [V_P_2,T_b,B_x] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.69 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_minus__zero,axiom,
% 108.69/108.69 ! [T_a] :
% 108.69/108.69 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.69 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_neg__0__equal__iff__equal,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Ogroup__add(T_b)
% 108.69/108.69 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 108.69/108.69 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_equal__neg__zero,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.69 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 108.69/108.69 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_neg__equal__0__iff__equal,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Ogroup__add(T_b)
% 108.69/108.69 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.69 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_neg__equal__zero,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.69 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 108.69/108.69 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__empty,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.69 ( hAPP(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))
% 108.69/108.69 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.69 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__empty__right,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Un__empty__left,axiom,
% 108.69/108.69 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = V_B_2 ).
% 108.69/108.69
% 108.69/108.69 fof(fact_disjoint__iff__not__equal,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.69 ( 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))
% 108.69/108.69 <=> ! [B_x] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.69 => ! [B_xa] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 108.69/108.69 => B_x != B_xa ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__empty__right,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_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)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Int__empty__left,axiom,
% 108.69/108.69 ! [V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Zero__not__Suc,axiom,
% 108.69/108.69 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_nat_Osimps_I2_J,axiom,
% 108.69/108.69 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Suc__not__Zero,axiom,
% 108.69/108.69 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_nat_Osimps_I3_J,axiom,
% 108.69/108.69 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Zero__neq__Suc,axiom,
% 108.69/108.69 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Suc__neq__Zero,axiom,
% 108.69/108.69 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 108.69/108.69 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_le__0__eq,axiom,
% 108.69/108.69 ! [V_n_2] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 108.69/108.69 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Union__Pow__eq,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OPow(T_b),V_A_2)) = V_A_2 ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Compl__UNIV__eq,axiom,
% 108.69/108.69 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Compl__empty__eq,axiom,
% 108.69/108.69 ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_empty,axiom,
% 108.69/108.69 ! [V_Ga_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 108.69/108.69 ! [V_a_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_a_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atMost__0,axiom,
% 108.69/108.69 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))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Pow__not__empty,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Inter__UNIV,axiom,
% 108.69/108.69 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Inter__empty,axiom,
% 108.69/108.69 ! [T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_nat__case__0,axiom,
% 108.69/108.69 ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Sup__le__iff,axiom,
% 108.69/108.69 ! [V_b_2,V_A_2,T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
% 108.69/108.69 <=> ! [B_x] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_bot__least,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Orderings_Obot(T_a)
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Sup__UNIV,axiom,
% 108.69/108.69 ! [T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OSup__class_OSup(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_sup__bot__left,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Obounded__lattice__bot(T_a)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_sup__bot__right,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Obounded__lattice__bot(T_a)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_sup__eq__bot__iff,axiom,
% 108.69/108.69 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.69 ( class_Lattices_Obounded__lattice__bot(T_b)
% 108.69/108.69 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 108.69/108.69 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 108.69/108.69 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__bot__right,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Obounded__lattice__bot(T_a)
% 108.69/108.69 => 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) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__bot__left,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Obounded__lattice__bot(T_a)
% 108.69/108.69 => 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) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Inf__UNIV,axiom,
% 108.69/108.69 ! [T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeast__0,axiom,
% 108.69/108.69 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)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 108.69/108.69 ! [V_i_2,V_inc_2,T_b] :
% 108.69/108.69 ( class_Rings_Osemiring__1(T_b)
% 108.69/108.69 => c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,V_inc_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2) = V_i_2 ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_minus__le__self__iff,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 108.69/108.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_neg__le__0__iff__le,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_le__minus__self__iff,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 108.69/108.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_neg__0__le__iff__le,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 108.69/108.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_subset__singletonD,axiom,
% 108.69/108.69 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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)))))
% 108.69/108.69 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.69 | 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))) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_insert__is__Un,axiom,
% 108.69/108.69 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_A_2) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastatMost__empty__iff,axiom,
% 108.69/108.69 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.69 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastatMost__empty__iff2,axiom,
% 108.69/108.69 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)
% 108.69/108.69 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastLessThan__empty,axiom,
% 108.69/108.69 ! [V_a_2,V_b_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 108.69/108.69 => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Inter__insert,axiom,
% 108.69/108.69 ! [V_B_2,V_a_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(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),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastAtMost__singleton_H,axiom,
% 108.69/108.69 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => ( V_a_2 = V_b_2
% 108.69/108.69 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_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))) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 108.69/108.69 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.69 <=> ( V_a_2 = V_b_2
% 108.69/108.69 & V_b_2 = V_c_2 ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastAtMost__singleton,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I11_J,axiom,
% 108.69/108.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_subset__Compl__self__eq,axiom,
% 108.69/108.69 ! [V_A_2,T_b] :
% 108.69/108.69 ( 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)),V_A_2)))
% 108.69/108.69 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Inf__singleton,axiom,
% 108.69/108.69 ! [V_a_2,T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Compl__disjoint2,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Compl__disjoint,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Union__mono,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.69 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_greaterThanAtMost__empty,axiom,
% 108.69/108.69 ! [V_k_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 108.69/108.69 => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Inf__empty,axiom,
% 108.69/108.69 ! [T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OInf__class_OInf(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I14_J,axiom,
% 108.69/108.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_subset__Pow__Union,axiom,
% 108.69/108.69 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Union__Un__distrib,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeast0LessThan,axiom,
% 108.69/108.69 ! [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) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeast0AtMost,axiom,
% 108.69/108.69 ! [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) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_greaterThan__0,axiom,
% 108.69/108.69 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))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Sup__insert,axiom,
% 108.69/108.69 ! [V_A_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_compl__inf__bot,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.69 => 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) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_inf__compl__bot,axiom,
% 108.69/108.69 ! [V_x,T_a] :
% 108.69/108.69 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.69 => 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) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_compl__bot__eq,axiom,
% 108.69/108.69 ! [T_a] :
% 108.69/108.69 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.69 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_compl__top__eq,axiom,
% 108.69/108.69 ! [T_a] :
% 108.69/108.69 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.69 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Inf__binary,axiom,
% 108.69/108.69 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.69 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_disjoint__eq__subset__Compl,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.69 ( 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))
% 108.69/108.69 <=> 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)),V_B_2))) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I15_J,axiom,
% 108.69/108.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I4_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I2_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_l_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I16_J,axiom,
% 108.69/108.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I8_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I7_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I3_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I5_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeastLessThan__singleton,axiom,
% 108.69/108.69 ! [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))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_all__nat__less,axiom,
% 108.69/108.69 ! [V_P_2,V_n_2] :
% 108.69/108.69 ( ! [B_m] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 108.69/108.69 => hBOOL(hAPP(V_P_2,B_m)) )
% 108.69/108.69 <=> ! [B_x] :
% 108.69/108.69 ( 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)))
% 108.69/108.69 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ex__nat__less,axiom,
% 108.69/108.69 ! [V_P_2,V_n_2] :
% 108.69/108.69 ( ? [B_m] :
% 108.69/108.69 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 108.69/108.69 & hBOOL(hAPP(V_P_2,B_m)) )
% 108.69/108.69 <=> ? [B_x] :
% 108.69/108.69 ( 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)))
% 108.69/108.69 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_the__elem__eq,axiom,
% 108.69/108.69 ! [V_x_2,T_b] : c_Set_Othe__elem(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ).
% 108.69/108.69
% 108.69/108.69 fof(fact_greaterThan__Suc,axiom,
% 108.69/108.69 ! [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)))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_atLeast__Suc,axiom,
% 108.69/108.69 ! [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)))) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I6_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I10_J,axiom,
% 108.69/108.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I1_J,axiom,
% 108.69/108.69 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I9_J,axiom,
% 108.69/108.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_ivl__disj__int_I13_J,axiom,
% 108.69/108.69 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.69 ( class_Orderings_Oorder(T_b)
% 108.69/108.69 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_minus__apply,axiom,
% 108.69/108.69 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 108.69/108.69 ( class_Groups_Ominus(T_b)
% 108.69/108.69 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_diff__eq__diff__eq,axiom,
% 108.69/108.69 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Oab__group__add(T_b)
% 108.69/108.69 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 108.69/108.69 => ( V_a_2 = V_b_2
% 108.69/108.69 <=> V_c_2 = V_d_2 ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_Diff__idemp,axiom,
% 108.69/108.69 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_diff__eq__diff__less__eq,axiom,
% 108.69/108.69 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.69 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 108.69/108.69 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 108.69/108.69 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_diff__0__right,axiom,
% 108.69/108.69 ! [V_a,T_a] :
% 108.69/108.69 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.69 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_diff__self,axiom,
% 108.69/108.69 ! [V_a,T_a] :
% 108.69/108.69 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.69 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_eq__iff__diff__eq__0,axiom,
% 108.69/108.69 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Oab__group__add(T_b)
% 108.69/108.69 => ( V_a_2 = V_b_2
% 108.69/108.69 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_right__minus__eq,axiom,
% 108.69/108.69 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.69 ( class_Groups_Ogroup__add(T_b)
% 108.69/108.69 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.69 <=> V_a_2 = V_b_2 ) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_minus__diff__eq,axiom,
% 108.69/108.69 ! [V_b,V_a,T_a] :
% 108.69/108.69 ( class_Groups_Oab__group__add(T_a)
% 108.69/108.69 => 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) ) ).
% 108.69/108.69
% 108.69/108.69 fof(fact_empty__Diff,axiom,
% 108.69/108.70 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__empty,axiom,
% 108.69/108.70 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__cancel,axiom,
% 108.69/108.70 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__subset,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_A_2)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__mono,axiom,
% 108.69/108.70 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_C_2),V_D_2))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_double__diff,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 108.69/108.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) = V_A_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Un__Diff__cancel,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Un__Diff__cancel2,axiom,
% 108.69/108.70 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Un__Diff,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,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_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__Int__distrib,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_C_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_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_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Int__Diff,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__Int__distrib2,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__Int2,axiom,
% 108.69/108.70 ! [V_B_2,V_C_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),V_B_2) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_le__iff__diff__le__0,axiom,
% 108.69/108.70 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__0,axiom,
% 108.69/108.70 ! [V_a,T_a] :
% 108.69/108.70 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.70 => 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) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__eq,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Lattices_Oboolean__algebra(T_a)
% 108.69/108.70 => 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)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__insert,axiom,
% 108.69/108.70 ! [V_B_2,V_a_2,V_A_2,T_b] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_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)))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__insert2,axiom,
% 108.69/108.70 ! [V_B_2,V_a_2,V_A_2,T_b] : 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_a_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_insert__Diff__single,axiom,
% 108.69/108.70 ! [V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__UNIV,axiom,
% 108.69/108.70 ! [V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__disjoint,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__triv,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( 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))
% 108.69/108.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_image__diff__subset,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2))),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__partition,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) = V_B_2 ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__subset__conv,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__Int,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__Un,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_HOL_Obool)),V_A_2),V_C_2)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Un__Diff__Int,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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),V_B_2)) = V_A_2 ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__diff,axiom,
% 108.69/108.70 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 108.69/108.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 108.69/108.70 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_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_A_2) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Compl__Diff__eq,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__eq,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(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(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Diff__Compl,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_greaterThanLessThan__empty,axiom,
% 108.69/108.70 ! [V_k_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 108.69/108.70 => c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 108.69/108.70 ! [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) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_x_2,V_y_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_single__Diff__lessThan,axiom,
% 108.69/108.70 ! [V_k_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_k_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__disj__int_I12_J,axiom,
% 108.69/108.70 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__disj__un_I19_J,axiom,
% 108.69/108.70 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__disj__un_I4_J,axiom,
% 108.69/108.70 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_u_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__disj__un_I18_J,axiom,
% 108.69/108.70 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__disj__un_I3_J,axiom,
% 108.69/108.70 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_l_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__disj__un_I12_J,axiom,
% 108.69/108.70 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_l_2) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__disj__un_I7_J,axiom,
% 108.69/108.70 ! [V_u_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_l_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_u_2) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__Un,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.70 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 108.69/108.70 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__disj__un_I16_J,axiom,
% 108.69/108.70 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ivl__disj__un_I15_J,axiom,
% 108.69/108.70 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 108.69/108.70 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_all__interval__nat__def,axiom,
% 108.69/108.70 ! [V_j_2,V_i_2,V_P_2] :
% 108.69/108.70 ( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
% 108.69/108.70 <=> ! [B_x] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)))
% 108.69/108.70 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__zeroE,axiom,
% 108.69/108.70 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_lessI,axiom,
% 108.69/108.70 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__mono,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_zero__less__Suc,axiom,
% 108.69/108.70 ! [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))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__empty,axiom,
% 108.69/108.70 ! [V_f_2,T_c,T_b] : c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__uminus,axiom,
% 108.69/108.70 ! [V_A_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_zero__less__diff,axiom,
% 108.69/108.70 ! [V_m_2,V_n_2] :
% 108.69/108.70 ( 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)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__less,axiom,
% 108.69/108.70 ! [V_m,V_n] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 108.69/108.70 => 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)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__less__Suc,axiom,
% 108.69/108.70 ! [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))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__diff__iff,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 108.69/108.70 => ( 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)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__less__mono,axiom,
% 108.69/108.70 ! [V_c,V_b,V_a] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 108.69/108.70 => 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))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__cases,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_a)
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => ( V_x != V_y
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__asym,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_xt1_I10_J,axiom,
% 108.69/108.70 ! [V_z,V_x,V_y,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__trans,axiom,
% 108.69/108.70 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_xt1_I2_J,axiom,
% 108.69/108.70 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 108.69/108.70 => ( V_b = V_c
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ord__less__eq__trans,axiom,
% 108.69/108.70 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.70 ( class_Orderings_Oord(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.70 => ( V_b = V_c
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_xt1_I1_J,axiom,
% 108.69/108.70 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( V_a = V_b
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ord__eq__less__trans,axiom,
% 108.69/108.70 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.70 ( class_Orderings_Oord(T_a)
% 108.69/108.70 => ( V_a = V_b
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_xt1_I9_J,axiom,
% 108.69/108.70 ! [V_a,V_b,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 108.69/108.70 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__asym_H,axiom,
% 108.69/108.70 ! [V_b,V_a,T_a] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.70 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__imp__not__eq2,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => V_y != V_x ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__imp__not__eq,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => V_x != V_y ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__imp__not__less,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__not__sym,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__imp__neq,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => V_x != V_y ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__neqE,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_a)
% 108.69/108.70 => ( V_x != V_y
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__antisym__conv3,axiom,
% 108.69/108.70 ! [V_x_2,V_y_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 <=> V_x_2 = V_y_2 ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__less__linear,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 | V_x = V_y
% 108.69/108.70 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_not__less__iff__gr__or__eq,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 108.69/108.70 | V_x_2 = V_y_2 ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__neq__iff,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( V_x_2 != V_y_2
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__irrefl,axiom,
% 108.69/108.70 ! [V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_a)
% 108.69/108.70 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__def,axiom,
% 108.69/108.70 ! [V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.70 <=> ! [B_x] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.70 => ! [B_xa] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 108.69/108.70 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 108.69/108.70 => B_x = B_xa ) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__strict__subset,axiom,
% 108.69/108.70 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_lessThan__strict__subset__iff,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_m_2)),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_n_2)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__pred,axiom,
% 108.69/108.70 ! [V_n] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.70 => 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 ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__Suc__less,axiom,
% 108.69/108.70 ! [V_i,V_n] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.70 => 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)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_atLeastatMost__psubset__iff,axiom,
% 108.69/108.70 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
% 108.69/108.70 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 108.69/108.70 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 108.69/108.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 108.69/108.70 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 108.69/108.70 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 108.69/108.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__Suc,axiom,
% 108.69/108.70 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_subset__inj__on,axiom,
% 108.69/108.70 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_injD,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.70 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 108.69/108.70 => V_x_2 = V_y_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__eq,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.70 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 108.69/108.70 <=> V_x_2 = V_y_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__Int,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.70 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 108.69/108.70 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__diff,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.70 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__fun__def,axiom,
% 108.69/108.70 ! [V_g_2,V_f_2,T_b,T_c] :
% 108.69/108.70 ( class_Orderings_Oord(T_c)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 108.69/108.70 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diffs0__imp__equal,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.70 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.70 => V_m = V_n ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__self__eq__0,axiom,
% 108.69/108.70 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_minus__nat_Odiff__0,axiom,
% 108.69/108.70 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__0__eq__0,axiom,
% 108.69/108.70 ! [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) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_xt1_I8_J,axiom,
% 108.69/108.70 ! [V_z,V_x,V_y,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__le__less__trans,axiom,
% 108.69/108.70 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_xt1_I7_J,axiom,
% 108.69/108.70 ! [V_z,V_x,V_y,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__le__trans,axiom,
% 108.69/108.70 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_xt1_I11_J,axiom,
% 108.69/108.70 ! [V_a,V_b,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 108.69/108.70 => ( V_a != V_b
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__le__neq__trans,axiom,
% 108.69/108.70 ! [V_b,V_a,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.70 => ( V_a != V_b
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__le__imp__less__or__eq,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 | V_x = V_y ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__antisym__conv2,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 <=> V_x_2 = V_y_2 ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__imp__le,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_leD,axiom,
% 108.69/108.70 ! [V_x,V_y,T_a] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.69/108.70 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_xt1_I12_J,axiom,
% 108.69/108.70 ! [V_b,V_a,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( V_a != V_b
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__neq__le__trans,axiom,
% 108.69/108.70 ! [V_b,V_a,T_a] :
% 108.69/108.70 ( class_Orderings_Oorder(T_a)
% 108.69/108.70 => ( V_a != V_b
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__antisym__conv1,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.70 <=> V_x_2 = V_y_2 ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_not__leE,axiom,
% 108.69/108.70 ! [V_x,V_y,T_a] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_a)
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_leI,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_a)
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__le__less,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 | V_x_2 = V_y_2 ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__le__not__le,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Orderings_Opreorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.70 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_order__less__le,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.70 & V_x_2 != V_y_2 ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__le__less__linear,axiom,
% 108.69/108.70 ! [V_y,V_x,T_a] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.70 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__not__le,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_linorder__not__less,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__Suc__Suc,axiom,
% 108.69/108.70 ! [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) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__diff__diff,axiom,
% 108.69/108.70 ! [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) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__le__self,axiom,
% 108.69/108.70 ! [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)) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__le__mono2,axiom,
% 108.69/108.70 ! [V_l,V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => 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))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__le__mono,axiom,
% 108.69/108.70 ! [V_l,V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => 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))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__diff__cancel,axiom,
% 108.69/108.70 ! [V_n,V_i] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 108.69/108.70 => 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 ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_eq__diff__iff,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 108.69/108.70 => ( 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)
% 108.69/108.70 <=> V_m_2 = V_n_2 ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Nat_Odiff__diff__eq,axiom,
% 108.69/108.70 ! [V_n,V_m,V_k] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 108.69/108.70 => 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) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_le__diff__iff,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 108.69/108.70 => ( 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)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_not__psubset__empty,axiom,
% 108.69/108.70 ! [V_A_2,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__eq__diff__less,axiom,
% 108.69/108.70 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_c_2),V_d_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__supI1,axiom,
% 108.69/108.70 ! [V_b,V_a,V_x,T_a] :
% 108.69/108.70 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 108.69/108.70 => 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))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__supI2,axiom,
% 108.69/108.70 ! [V_a,V_b,V_x,T_a] :
% 108.69/108.70 ( class_Lattices_Osemilattice__sup(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 108.69/108.70 => 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))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__infI2,axiom,
% 108.69/108.70 ! [V_a,V_x,V_b,T_a] :
% 108.69/108.70 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 108.69/108.70 => 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)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__infI1,axiom,
% 108.69/108.70 ! [V_b,V_x,V_a,T_a] :
% 108.69/108.70 ( class_Lattices_Osemilattice__inf(T_a)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 108.69/108.70 => 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)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__minus__iff,axiom,
% 108.69/108.70 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_minus__less__iff,axiom,
% 108.69/108.70 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_neg__less__iff__less,axiom,
% 108.69/108.70 ! [V_a_2,V_b_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_subset__psubset__trans,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_psubset__subset__trans,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_psubset__imp__subset,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_subset__iff__psubset__eq,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 | V_A_2 = V_B_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_psubset__eq,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 & V_A_2 != V_B_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_gr0I,axiom,
% 108.69/108.70 ! [V_n] :
% 108.69/108.70 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_gr__implies__not0,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__nat__zero__code,axiom,
% 108.69/108.70 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_neq0__conv,axiom,
% 108.69/108.70 ! [V_n_2] :
% 108.69/108.70 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_not__less0,axiom,
% 108.69/108.70 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_not__less__eq,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__Suc__eq,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.70 | V_m_2 = V_n_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__less__eq,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( 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)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_not__less__less__Suc__eq,axiom,
% 108.69/108.70 ! [V_m_2,V_n_2] :
% 108.69/108.70 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 108.69/108.70 <=> V_n_2 = V_m_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__antisym,axiom,
% 108.69/108.70 ! [V_m,V_n] :
% 108.69/108.70 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 108.69/108.70 => V_m = V_n ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__SucI,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__lessI,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__trans__Suc,axiom,
% 108.69/108.70 ! [V_k,V_j,V_i] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__SucE,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => V_m = V_n ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__lessD,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__less__SucD,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_nat__less__le,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.70 & V_m_2 != V_n_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_le__eq__less__or__eq,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.70 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.70 | V_m_2 = V_n_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__imp__le__nat,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_le__neq__implies__less,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => ( V_m != V_n
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__or__eq__imp__le,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 | V_m = V_n )
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 108.69/108.70 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 108.69/108.70 => V_b_2 = V_d_2 ) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 108.69/108.70 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 108.69/108.70 => V_a_2 = V_c_2 ) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_atLeastLessThan__eq__iff,axiom,
% 108.69/108.70 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Orderings_Olinorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 108.69/108.70 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
% 108.69/108.70 <=> ( V_a_2 = V_c_2
% 108.69/108.70 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__Sup__iff,axiom,
% 108.69/108.70 ! [V_S_2,V_a_2,T_b] :
% 108.69/108.70 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.70 & class_Orderings_Olinorder(T_b) )
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 108.69/108.70 <=> ? [B_x] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 108.69/108.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Inf__less__iff,axiom,
% 108.69/108.70 ! [V_a_2,V_S_2,T_b] :
% 108.69/108.70 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.70 & class_Orderings_Olinorder(T_b) )
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 108.69/108.70 <=> ? [B_x] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 108.69/108.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_strict__mono__imp__inj__on,axiom,
% 108.69/108.70 ! [V_A_2,V_f_2,T_b,T_c] :
% 108.69/108.70 ( ( class_Orderings_Oorder(T_c)
% 108.69/108.70 & class_Orderings_Olinorder(T_b) )
% 108.69/108.70 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 108.69/108.70 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_strict__monoD,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 108.69/108.70 ( ( class_Orderings_Oorder(T_c)
% 108.69/108.70 & class_Orderings_Oorder(T_b) )
% 108.69/108.70 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_strict__mono__less,axiom,
% 108.69/108.70 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 108.69/108.70 ( ( class_Orderings_Oorder(T_c)
% 108.69/108.70 & class_Orderings_Olinorder(T_b) )
% 108.69/108.70 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__image__eq__iff,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.70 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 108.69/108.70 <=> V_A_2 = V_B_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
% 108.69/108.70 <=> V_A_2 = V_B_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__iff__diff__less__0,axiom,
% 108.69/108.70 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__is__0__eq,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__is__0__eq_H,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__diff__le,axiom,
% 108.69/108.70 ! [V_m,V_n] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 108.69/108.70 => 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)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_neg__less__nonneg,axiom,
% 108.69/108.70 ! [V_a_2,T_b] :
% 108.69/108.70 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_neg__less__0__iff__less,axiom,
% 108.69/108.70 ! [V_a_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_neg__0__less__iff__less,axiom,
% 108.69/108.70 ! [V_a_2,T_b] :
% 108.69/108.70 ( class_Groups_Oordered__ab__group__add(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__Suc__eq__0__disj,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 108.69/108.70 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.70 | ? [B_j] :
% 108.69/108.70 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 108.69/108.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__Suc0,axiom,
% 108.69/108.70 ! [V_n_2] :
% 108.69/108.70 ( 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))))
% 108.69/108.70 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_gr0__conv__Suc,axiom,
% 108.69/108.70 ! [V_n_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 108.69/108.70 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_atLeastatMost__empty,axiom,
% 108.69/108.70 ! [V_a_2,V_b_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 108.69/108.70 => c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__le__lessD,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_le__less__Suc__eq,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 108.69/108.70 <=> V_n_2 = V_m_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__leI,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_le__imp__less__Suc,axiom,
% 108.69/108.70 ! [V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_Suc__le__eq,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__Suc__eq__le,axiom,
% 108.69/108.70 ! [V_n_2,V_m_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__eq__Suc__le,axiom,
% 108.69/108.70 ! [V_m_2,V_n_2] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_atLeastLessThan__empty__iff,axiom,
% 108.69/108.70 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.70 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 108.69/108.70 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
% 108.69/108.70 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 108.69/108.70 ! [V_l_2,V_k_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.70 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 108.69/108.70 ! [V_l_2,V_k_2,T_b] :
% 108.69/108.70 ( class_Orderings_Oorder(T_b)
% 108.69/108.70 => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
% 108.69/108.70 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ex__nat__less__eq,axiom,
% 108.69/108.70 ! [V_P_2,V_n_2] :
% 108.69/108.70 ( ? [B_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 108.69/108.70 & hBOOL(hAPP(V_P_2,B_m)) )
% 108.69/108.70 <=> ? [B_x] :
% 108.69/108.70 ( 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)))
% 108.69/108.70 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_all__nat__less__eq,axiom,
% 108.69/108.70 ! [V_P_2,V_n_2] :
% 108.69/108.70 ( ! [B_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 108.69/108.70 => hBOOL(hAPP(V_P_2,B_m)) )
% 108.69/108.70 <=> ! [B_x] :
% 108.69/108.70 ( 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)))
% 108.69/108.70 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__image__subset__iff,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__image__Int,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 108.69/108.70 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_image__Int,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.70 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__image__set__diff,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 108.69/108.70 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_image__set__diff,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.70 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__image__Compl__subset,axiom,
% 108.69/108.70 ! [V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__iff__surj,axiom,
% 108.69/108.70 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 108.69/108.70 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.70 => ( ? [B_f] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 108.69/108.70 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_A_H_2)) )
% 108.69/108.70 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__minus__self__iff,axiom,
% 108.69/108.70 ! [V_a_2,T_b] :
% 108.69/108.70 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 108.69/108.70 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__insert,axiom,
% 108.69/108.70 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 108.69/108.70 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.70 & ~ hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_psubset__insert__iff,axiom,
% 108.69/108.70 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 108.69/108.70 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 108.69/108.70 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 108.69/108.70 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),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))))),V_B_2)) )
% 108.69/108.70 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__single__insert,axiom,
% 108.69/108.70 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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))))),V_B_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_subset__insert__iff,axiom,
% 108.69/108.70 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 108.69/108.70 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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))))),V_B_2)) )
% 108.69/108.70 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_vimage__subsetI,axiom,
% 108.69/108.70 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 108.69/108.70 ! [V_k_2,V_f_2,T_b] :
% 108.69/108.70 ( class_Groups_Ocomm__monoid__add(T_b)
% 108.69/108.70 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.70 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_the__inv__into__onto,axiom,
% 108.69/108.70 ! [V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.70 => hAPP(c_Set_Oimage(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_inj__on__the__inv__into,axiom,
% 108.69/108.70 ! [V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.70 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.70 => c_Fun_Oinj__on(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_equalityCE,axiom,
% 108.69/108.70 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 108.69/108.70 ( V_A_2 = V_B_2
% 108.69/108.70 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.70 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 108.69/108.70 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_emptyE,axiom,
% 108.69/108.70 ! [V_a_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_insertE,axiom,
% 108.69/108.70 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 108.69/108.70 => ( V_a_2 != V_b_2
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_insertCI,axiom,
% 108.69/108.70 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 108.69/108.70 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 108.69/108.70 => V_a_2 = V_b_2 )
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_subsetD,axiom,
% 108.69/108.70 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_UNIV__I,axiom,
% 108.69/108.70 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_image__eqI,axiom,
% 108.69/108.70 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 108.69/108.70 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_UnE,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_UnCI,axiom,
% 108.69/108.70 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 108.69/108.70 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_IntI,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_IntE,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.70 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.70 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_DiffI,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.70 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_DiffE,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.70 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_ComplI,axiom,
% 108.69/108.70 ! [V_A_2,V_c_2,T_b] :
% 108.69/108.70 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_vimageI,axiom,
% 108.69/108.70 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 108.69/108.70 ( hAPP(V_f_2,V_a_2) = V_b_2
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_UnionI,axiom,
% 108.69/108.70 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_InterD,axiom,
% 108.69/108.70 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_InterE,axiom,
% 108.69/108.70 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_PowI,axiom,
% 108.69/108.70 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.70 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__commute,axiom,
% 108.69/108.70 ! [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) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_less__imp__diff__less,axiom,
% 108.69/108.70 ! [V_n,V_k,V_j] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 108.69/108.70 => 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)) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_diff__less__mono2,axiom,
% 108.69/108.70 ! [V_l,V_n,V_m] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.70 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 108.69/108.70 => 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))) ) ) ).
% 108.69/108.70
% 108.69/108.70 fof(fact_psubset__trans,axiom,
% 108.69/108.70 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 108.69/108.70 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_psubsetD,axiom,
% 108.69/108.71 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_nat__less__cases,axiom,
% 108.69/108.71 ! [V_P_2,V_n_2,V_m_2] :
% 108.69/108.71 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 108.69/108.71 => ( ( V_m_2 = V_n_2
% 108.69/108.71 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 108.69/108.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 108.69/108.71 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_less__not__refl3,axiom,
% 108.69/108.71 ! [V_t,V_s] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 108.69/108.71 => V_s != V_t ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_less__not__refl2,axiom,
% 108.69/108.71 ! [V_m,V_n] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 108.69/108.71 => V_m != V_n ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_less__irrefl__nat,axiom,
% 108.69/108.71 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_linorder__neqE__nat,axiom,
% 108.69/108.71 ! [V_y,V_x] :
% 108.69/108.71 ( V_x != V_y
% 108.69/108.71 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_nat__neq__iff,axiom,
% 108.69/108.71 ! [V_n_2,V_m_2] :
% 108.69/108.71 ( V_m_2 != V_n_2
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.71 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_less__not__refl,axiom,
% 108.69/108.71 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_mem__def,axiom,
% 108.69/108.71 ! [V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_eq__mem,axiom,
% 108.69/108.71 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 108.69/108.71 <=> V_x_2 = V_y_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__eq,axiom,
% 108.69/108.71 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__code,axiom,
% 108.69/108.71 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 108.69/108.71 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_eqset__imp__iff,axiom,
% 108.69/108.71 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 108.69/108.71 ( V_A_2 = V_B_2
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_eqelem__imp__iff,axiom,
% 108.69/108.71 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 108.69/108.71 ( V_x_2 = V_y_2
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_eq__mem__trans,axiom,
% 108.69/108.71 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 108.69/108.71 ( V_a_2 = V_b_2
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimageD,axiom,
% 108.69/108.71 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimageI2,axiom,
% 108.69/108.71 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_the__inv__into__f__f,axiom,
% 108.69/108.71 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_the__inv__into__f__eq,axiom,
% 108.69/108.71 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.71 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__singleton__eq,axiom,
% 108.69/108.71 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 108.69/108.71 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__empty,axiom,
% 108.69/108.71 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__mono,axiom,
% 108.69/108.71 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__UNIV,axiom,
% 108.69/108.71 ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__Un,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__Int,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__Diff,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,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_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_all__not__in__conv,axiom,
% 108.69/108.71 ! [V_A_2,T_b] :
% 108.69/108.71 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.71 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ex__in__conv,axiom,
% 108.69/108.71 ! [V_A_2,T_b] :
% 108.69/108.71 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.71 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_empty__iff,axiom,
% 108.69/108.71 ! [V_c_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_equals0D,axiom,
% 108.69/108.71 ! [V_a_2,T_b,V_A_2] :
% 108.69/108.71 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.71 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insertI1,axiom,
% 108.69/108.71 ! [V_B_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insert__iff,axiom,
% 108.69/108.71 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 108.69/108.71 <=> ( V_a_2 = V_b_2
% 108.69/108.71 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insert__ident,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 108.69/108.71 => ( hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)
% 108.69/108.71 <=> V_A_2 = V_B_2 ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insertI2,axiom,
% 108.69/108.71 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insert__absorb,axiom,
% 108.69/108.71 ! [V_A_2,V_a_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_in__mono,axiom,
% 108.69/108.71 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_set__rev__mp,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_set__mp,axiom,
% 108.69/108.71 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_image__iff,axiom,
% 108.69/108.71 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 108.69/108.71 <=> ? [B_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 108.69/108.71 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_imageI,axiom,
% 108.69/108.71 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_rev__image__eqI,axiom,
% 108.69/108.71 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Un__iff,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.71 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_UnI1,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_UnI2,axiom,
% 108.69/108.71 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Int__iff,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.71 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_IntD1,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_IntD2,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Diff__iff,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 108.69/108.71 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_DiffD1,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_DiffD2,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.71 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_inj__on__contraD,axiom,
% 108.69/108.71 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.71 => ( V_x_2 != V_y_2
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 108.69/108.71 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_inj__on__iff,axiom,
% 108.69/108.71 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 108.69/108.71 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 108.69/108.71 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_inj__onD,axiom,
% 108.69/108.71 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.71 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 108.69/108.71 => V_x_2 = V_y_2 ) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__Compl,axiom,
% 108.69/108.71 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_f__the__inv__into__f,axiom,
% 108.69/108.71 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 108.69/108.71 => hAPP(V_f_2,hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Compl__iff,axiom,
% 108.69/108.71 ! [V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 108.69/108.71 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ComplD,axiom,
% 108.69/108.71 ! [V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 108.69/108.71 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ComplE,axiom,
% 108.69/108.71 ! [V_A_2,V_c_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 108.69/108.71 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Pow__top,axiom,
% 108.69/108.71 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_A_2))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__empty,axiom,
% 108.69/108.71 ! [V_f_2,T_c,T_b] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum_Oempty,axiom,
% 108.69/108.71 ! [V_g_2,T_c,T_b] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_the__inv__into__into,axiom,
% 108.69/108.71 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2)),V_B_2)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_image__vimage__subset,axiom,
% 108.69/108.71 ! [V_A_2,V_f_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))),V_A_2)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_surj__image__vimage__eq,axiom,
% 108.69/108.71 ! [V_A_2,V_f_2,T_b,T_c] :
% 108.69/108.71 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.71 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = V_A_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_singleton__iff,axiom,
% 108.69/108.71 ! [V_a_2,V_b_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),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)))))
% 108.69/108.71 <=> V_b_2 = V_a_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_singletonE,axiom,
% 108.69/108.71 ! [V_a_2,V_b_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),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)))))
% 108.69/108.71 => V_b_2 = V_a_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_subset__insert,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insert__subset,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 108.69/108.71 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insert__image,axiom,
% 108.69/108.71 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Set_Oinsert(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Int__insert__right,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 108.69/108.71 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 108.69/108.71 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Int__insert__left,axiom,
% 108.69/108.71 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 108.69/108.71 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 108.69/108.71 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) )
% 108.69/108.71 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 108.69/108.71 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Int__insert__right__if0,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 108.69/108.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Int__insert__left__if0,axiom,
% 108.69/108.71 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 108.69/108.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 108.69/108.71 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Int__insert__right__if1,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Int__insert__left__if1,axiom,
% 108.69/108.71 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 108.69/108.71 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_rangeI,axiom,
% 108.69/108.71 ! [T_c,V_x_2,V_f_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_range__eqI,axiom,
% 108.69/108.71 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 108.69/108.71 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insert__Diff__if,axiom,
% 108.69/108.71 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 108.69/108.71 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 108.69/108.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) )
% 108.69/108.71 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 108.69/108.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insert__Diff1,axiom,
% 108.69/108.71 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 108.69/108.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Sup__upper,axiom,
% 108.69/108.71 ! [V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Inf__lower,axiom,
% 108.69/108.71 ! [V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)),V_x_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_lessThan__iff,axiom,
% 108.69/108.71 ! [V_k_2,V_i_2,T_b] :
% 108.69/108.71 ( class_Orderings_Oord(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_atMost__iff,axiom,
% 108.69/108.71 ! [V_k_2,V_i_2,T_b] :
% 108.69/108.71 ( class_Orderings_Oord(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Union__upper,axiom,
% 108.69/108.71 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Pow__bottom,axiom,
% 108.69/108.71 ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_atLeast__iff,axiom,
% 108.69/108.71 ! [V_k_2,V_i_2,T_b] :
% 108.69/108.71 ( class_Orderings_Oord(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_PowD,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Pow__iff,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_greaterThan__iff,axiom,
% 108.69/108.71 ! [V_k_2,V_i_2,T_b] :
% 108.69/108.71 ( class_Orderings_Oord(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Inter__lower,axiom,
% 108.69/108.71 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__diff__nat__ivl,axiom,
% 108.69/108.71 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 108.69/108.71 ( class_Groups_Oab__group__add(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 108.69/108.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),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_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_n_2),V_p_2)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 108.69/108.71 ! [V_k_2,V_f_2] :
% 108.69/108.71 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.71 => 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__insert,axiom,
% 108.69/108.71 ! [V_B_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_vimage__subsetD,axiom,
% 108.69/108.71 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 108.69/108.71 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2)),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_image__vimage__eq,axiom,
% 108.69/108.71 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_inj__vimage__image__eq,axiom,
% 108.69/108.71 ! [V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.71 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_insert__Diff,axiom,
% 108.69/108.71 ! [V_A_2,V_a_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = V_A_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Diff__insert__absorb,axiom,
% 108.69/108.71 ! [V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),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)))) = V_A_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_range__ex1__eq,axiom,
% 108.69/108.71 ! [V_b_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 108.69/108.71 <=> ? [B_x] :
% 108.69/108.71 ( V_b_2 = hAPP(V_f_2,B_x)
% 108.69/108.71 & ! [B_y] :
% 108.69/108.71 ( V_b_2 = hAPP(V_f_2,B_y)
% 108.69/108.71 => B_y = B_x ) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_inj__image__mem__iff,axiom,
% 108.69/108.71 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_linorder__neqE__linordered__idom,axiom,
% 108.69/108.71 ! [V_y,V_x,T_a] :
% 108.69/108.71 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.71 => ( V_x != V_y
% 108.69/108.71 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_the__inv__f__f,axiom,
% 108.69/108.71 ! [V_x_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.71 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ord_OatMost__iff,axiom,
% 108.69/108.71 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ord_OatLeast__iff,axiom,
% 108.69/108.71 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ord_OlessThan__iff,axiom,
% 108.69/108.71 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ord_OgreaterThan__iff,axiom,
% 108.69/108.71 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 108.69/108.71 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastAtMost(T_b,V_less__eq_2,V_l_2,V_u_2)))
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 108.69/108.71 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 108.69/108.71 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanLessThan(T_b,V_less_2,V_l_2,V_u_2)))
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 108.69/108.71 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 108.69/108.71 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeastLessThan(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 108.69/108.71 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 108.69/108.71 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThanAtMost(T_b,V_less__eq_2,V_less_2,V_l_2,V_u_2)))
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 108.69/108.71 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_termination__basic__simps_I5_J,axiom,
% 108.69/108.71 ! [V_y,V_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__diff1__nat,axiom,
% 108.69/108.71 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 108.69/108.71 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 108.69/108.71 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_iso__tuple__UNIV__I,axiom,
% 108.69/108.71 ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_fun__upd__image,axiom,
% 108.69/108.71 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 108.69/108.71 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,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)))))) )
% 108.69/108.71 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hAPP(c_Set_Oimage(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2)),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__diff1,axiom,
% 108.69/108.71 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Oab__group__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 108.69/108.71 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__diff1__ring,axiom,
% 108.69/108.71 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Rings_Oring(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_inj__on__Inter,axiom,
% 108.69/108.71 ! [V_f_2,T_c,T_b,V_S_2] :
% 108.69/108.71 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 108.69/108.71 => ( ! [B_A] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 108.69/108.71 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 108.69/108.71 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Inter__subset,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.71 ( ! [B_X] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 108.69/108.71 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2)),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__SucD,axiom,
% 108.69/108.71 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 108.69/108.71 ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
% 108.69/108.71 => ? [B_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.71 & 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))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__cl__ivl__Suc,axiom,
% 108.69/108.71 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 108.69/108.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b) )
% 108.69/108.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_fun__upd__triv,axiom,
% 108.69/108.71 ! [V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,hAPP(V_f_2,V_x_2)) = V_f_2 ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__atLeastLessThan,axiom,
% 108.69/108.71 ! [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))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__atLeastAtMost,axiom,
% 108.69/108.71 ! [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))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__lessThan,axiom,
% 108.69/108.71 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__atMost,axiom,
% 108.69/108.71 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__greaterThanAtMost,axiom,
% 108.69/108.71 ! [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))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__greaterThanLessThan,axiom,
% 108.69/108.71 ! [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))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_fun__upd__idem__iff,axiom,
% 108.69/108.71 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 108.69/108.71 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_fun__upd__upd,axiom,
% 108.69/108.71 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_x_2,V_z_2) = c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_z_2) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_fun__upd__same,axiom,
% 108.69/108.71 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2),V_x_2) = V_y_2 ).
% 108.69/108.71
% 108.69/108.71 fof(fact_fun__upd__apply,axiom,
% 108.69/108.71 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 108.69/108.71 ( ( V_z_2 = V_x_2
% 108.69/108.71 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 108.69/108.71 & ( V_z_2 != V_x_2
% 108.69/108.71 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_fun__upd__twist,axiom,
% 108.69/108.71 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 108.69/108.71 ( V_a_2 != V_c_2
% 108.69/108.71 => c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_a_2,V_b_2),V_c_2,V_d_2) = c_Fun_Ofun__upd(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_m_2,V_c_2,V_d_2),V_a_2,V_b_2) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_fun__upd__other,axiom,
% 108.69/108.71 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 108.69/108.71 ( V_z_2 != V_x_2
% 108.69/108.71 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_fun__upd__idem,axiom,
% 108.69/108.71 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 108.69/108.71 ( hAPP(V_f_2,V_x_2) = V_y_2
% 108.69/108.71 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oab__semigroup__add(T_a)
% 108.69/108.71 => 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__left__cancel,axiom,
% 108.69/108.71 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.71 ( class_Groups_Ocancel__semigroup__add(T_b)
% 108.69/108.71 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)
% 108.69/108.71 <=> V_b_2 = V_c_2 ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__right__cancel,axiom,
% 108.69/108.71 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 108.69/108.71 ( class_Groups_Ocancel__semigroup__add(T_b)
% 108.69/108.71 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)
% 108.69/108.71 <=> V_b_2 = V_c_2 ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__left__imp__eq,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ocancel__semigroup__add(T_a)
% 108.69/108.71 => ( 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)
% 108.69/108.71 => V_b = V_c ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__imp__eq,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 108.69/108.71 => ( 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)
% 108.69/108.71 => V_b = V_c ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__right__imp__eq,axiom,
% 108.69/108.71 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.71 ( class_Groups_Ocancel__semigroup__add(T_a)
% 108.69/108.71 => ( 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)
% 108.69/108.71 => V_b = V_c ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__le__cancel__right,axiom,
% 108.69/108.71 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__le__cancel__left,axiom,
% 108.69/108.71 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__right__mono,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.71 => 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))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__left__mono,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.71 => 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))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__mono,axiom,
% 108.69/108.71 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__le__imp__le__right,axiom,
% 108.69/108.71 ! [V_b,V_c,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 108.69/108.71 => ( 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)))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__le__imp__le__left,axiom,
% 108.69/108.71 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 108.69/108.71 => ( 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)))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__0__left,axiom,
% 108.69/108.71 ! [V_a,T_a] :
% 108.69/108.71 ( class_Groups_Omonoid__add(T_a)
% 108.69/108.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__0,axiom,
% 108.69/108.71 ! [V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_a)
% 108.69/108.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_double__zero__sym,axiom,
% 108.69/108.71 ! [V_a_2,T_b] :
% 108.69/108.71 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.71 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 108.69/108.71 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__0__right,axiom,
% 108.69/108.71 ! [V_a,T_a] :
% 108.69/108.71 ( class_Groups_Omonoid__add(T_a)
% 108.69/108.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add_Ocomm__neutral,axiom,
% 108.69/108.71 ! [V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_a)
% 108.69/108.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__less__cancel__right,axiom,
% 108.69/108.71 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_c_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__less__cancel__left,axiom,
% 108.69/108.71 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_c_2),V_b_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__strict__right__mono,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.71 => 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))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__strict__left__mono,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.71 => 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))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__strict__mono,axiom,
% 108.69/108.71 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__less__imp__less__right,axiom,
% 108.69/108.71 ! [V_b,V_c,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 108.69/108.71 => ( 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)))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__less__imp__less__left,axiom,
% 108.69/108.71 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 108.69/108.71 => ( 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)))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__add__cancel,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => 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 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__diff__cancel,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => 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 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_minus__add__cancel,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => 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 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__minus__cancel,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => 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 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_minus__add,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_minus__add__distrib,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oab__group__add(T_a)
% 108.69/108.71 => 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_plus__nat_Oadd__0,axiom,
% 108.69/108.71 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 108.69/108.71
% 108.69/108.71 fof(fact_Nat_Oadd__0__right,axiom,
% 108.69/108.71 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__is__0,axiom,
% 108.69/108.71 ! [V_n_2,V_m_2] :
% 108.69/108.71 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.71 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.71 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__eq__self__zero,axiom,
% 108.69/108.71 ! [V_n,V_m] :
% 108.69/108.71 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 108.69/108.71 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__Suc__shift,axiom,
% 108.69/108.71 ! [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)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__Suc,axiom,
% 108.69/108.71 ! [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)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__Suc__right,axiom,
% 108.69/108.71 ! [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)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__lessD1,axiom,
% 108.69/108.71 ! [V_k,V_j,V_i] :
% 108.69/108.71 ( 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))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_less__add__eq__less,axiom,
% 108.69/108.71 ! [V_n,V_m,V_l,V_k] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 108.69/108.71 => ( 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)
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__less__mono,axiom,
% 108.69/108.71 ! [V_l,V_k,V_j,V_i] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 108.69/108.71 => 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))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__less__mono1,axiom,
% 108.69/108.71 ! [V_k,V_j,V_i] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_trans__less__add2,axiom,
% 108.69/108.71 ! [V_m,V_j,V_i] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_trans__less__add1,axiom,
% 108.69/108.71 ! [V_m,V_j,V_i] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_nat__add__left__cancel__less,axiom,
% 108.69/108.71 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.71 ( 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)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_not__add__less2,axiom,
% 108.69/108.71 ! [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)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_not__add__less1,axiom,
% 108.69/108.71 ! [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)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_termination__basic__simps_I1_J,axiom,
% 108.69/108.71 ! [V_z,V_y,V_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_termination__basic__simps_I2_J,axiom,
% 108.69/108.71 ! [V_y,V_z,V_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__leE,axiom,
% 108.69/108.71 ! [V_n,V_k,V_m] :
% 108.69/108.71 ( 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))
% 108.69/108.71 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.69/108.71 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__leD1,axiom,
% 108.69/108.71 ! [V_n,V_k,V_m] :
% 108.69/108.71 ( 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))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__leD2,axiom,
% 108.69/108.71 ! [V_n,V_k,V_m] :
% 108.69/108.71 ( 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))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__le__mono,axiom,
% 108.69/108.71 ! [V_l,V_k,V_j,V_i] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 108.69/108.71 => 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))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__le__mono1,axiom,
% 108.69/108.71 ! [V_k,V_j,V_i] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_trans__le__add2,axiom,
% 108.69/108.71 ! [V_m,V_j,V_i] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_trans__le__add1,axiom,
% 108.69/108.71 ! [V_m,V_j,V_i] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_nat__add__left__cancel__le,axiom,
% 108.69/108.71 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.71 ( 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)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_le__iff__add,axiom,
% 108.69/108.71 ! [V_n_2,V_m_2] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.71 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_le__add1,axiom,
% 108.69/108.71 ! [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))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_le__add2,axiom,
% 108.69/108.71 ! [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))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_termination__basic__simps_I4_J,axiom,
% 108.69/108.71 ! [V_y,V_z,V_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_termination__basic__simps_I3_J,axiom,
% 108.69/108.71 ! [V_z,V_y,V_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__add__inverse2,axiom,
% 108.69/108.71 ! [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 ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__add__inverse,axiom,
% 108.69/108.71 ! [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 ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__diff__left,axiom,
% 108.69/108.71 ! [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)) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__cancel,axiom,
% 108.69/108.71 ! [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) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__cancel2,axiom,
% 108.69/108.71 ! [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) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__nat__set__iff__bounded,axiom,
% 108.69/108.71 ! [V_N_2] :
% 108.69/108.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 108.69/108.71 <=> ? [B_m] :
% 108.69/108.71 ! [B_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 108.69/108.71 ! [V_N_2] :
% 108.69/108.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 108.69/108.71 <=> ? [B_m] :
% 108.69/108.71 ! [B_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 108.69/108.71 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum_Oinsert,axiom,
% 108.69/108.71 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__insert,axiom,
% 108.69/108.71 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.71 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__Un__Int,axiom,
% 108.69/108.71 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum_Oinsert__remove,axiom,
% 108.69/108.71 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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)))))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__Un__disjoint,axiom,
% 108.69/108.71 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.71 => ( 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))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 108.69/108.71 ! [V_a_2,T_b] :
% 108.69/108.71 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 108.69/108.71 ! [V_a_2,T_b] :
% 108.69/108.71 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__nonneg__nonneg,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__nonneg__eq__0__iff,axiom,
% 108.69/108.71 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 108.69/108.71 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.71 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.71 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__increasing,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__increasing2,axiom,
% 108.69/108.71 ! [V_a,V_b,V_c,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__nonpos__nonpos,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__Un,axiom,
% 108.69/108.71 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Oab__group__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__le__less__mono,axiom,
% 108.69/108.71 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__less__le__mono,axiom,
% 108.69/108.71 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_pos__add__strict,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 108.69/108.71 ! [V_a_2,T_b] :
% 108.69/108.71 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 108.69/108.71 ! [V_a_2,T_b] :
% 108.69/108.71 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.71 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__pos__pos,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__neg__neg,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_right__minus,axiom,
% 108.69/108.71 ! [V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => 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) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 108.69/108.71 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_b)
% 108.69/108.71 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 108.69/108.71 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_left__minus,axiom,
% 108.69/108.71 ! [V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => 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) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ab__left__minus,axiom,
% 108.69/108.71 ! [V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oab__group__add(T_a)
% 108.69/108.71 => 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) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_minus__unique,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.71 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__minus__eq__add,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => 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) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_ab__diff__minus,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oab__group__add(T_a)
% 108.69/108.71 => 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__def,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Ogroup__add(T_a)
% 108.69/108.71 => 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_one__is__add,axiom,
% 108.69/108.71 ! [V_n_2,V_m_2] :
% 108.69/108.71 ( 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)
% 108.69/108.71 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 108.69/108.71 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 108.69/108.71 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.71 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__is__1,axiom,
% 108.69/108.71 ! [V_n_2,V_m_2] :
% 108.69/108.71 ( 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))
% 108.69/108.71 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 108.69/108.71 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 108.69/108.71 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.71 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__Un__nat,axiom,
% 108.69/108.71 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_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_b,tc_Nat_Onat),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__gr__0,axiom,
% 108.69/108.71 ! [V_n_2,V_m_2] :
% 108.69/108.71 ( 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)))
% 108.69/108.71 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 108.69/108.71 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_less__iff__Suc__add,axiom,
% 108.69/108.71 ! [V_n_2,V_m_2] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.71 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_less__add__Suc2,axiom,
% 108.69/108.71 ! [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)))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_less__add__Suc1,axiom,
% 108.69/108.71 ! [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)))) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__add__0,axiom,
% 108.69/108.71 ! [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) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_less__diff__conv,axiom,
% 108.69/108.71 ! [V_k_2,V_j_2,V_i_2] :
% 108.69/108.71 ( 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)))
% 108.69/108.71 <=> 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__diff__inverse,axiom,
% 108.69/108.71 ! [V_n,V_m] :
% 108.69/108.71 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.71 => 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 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__diff__right,axiom,
% 108.69/108.71 ! [V_i,V_j,V_k] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 108.69/108.71 => 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) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_le__diff__conv,axiom,
% 108.69/108.71 ! [V_i_2,V_k_2,V_j_2] :
% 108.69/108.71 ( 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))
% 108.69/108.71 <=> 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_le__add__diff,axiom,
% 108.69/108.71 ! [V_m,V_n,V_k] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_le__add__diff__inverse,axiom,
% 108.69/108.71 ! [V_m,V_n] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 108.69/108.71 => 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 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__diff__assoc,axiom,
% 108.69/108.71 ! [V_i,V_j,V_k] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 108.69/108.71 => 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) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_le__diff__conv2,axiom,
% 108.69/108.71 ! [V_i_2,V_j_2,V_k_2] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 108.69/108.71 => ( 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)))
% 108.69/108.71 <=> 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)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_le__add__diff__inverse2,axiom,
% 108.69/108.71 ! [V_m,V_n] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 108.69/108.71 => 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 ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_le__imp__diff__is__add,axiom,
% 108.69/108.71 ! [V_k_2,V_j_2,V_i_2] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 108.69/108.71 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 108.69/108.71 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__add__assoc,axiom,
% 108.69/108.71 ! [V_i,V_j,V_k] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 108.69/108.71 => 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__diff__assoc2,axiom,
% 108.69/108.71 ! [V_i,V_j,V_k] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 108.69/108.71 => 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) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__add__assoc2,axiom,
% 108.69/108.71 ! [V_i,V_j,V_k] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 108.69/108.71 => 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) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__infinite,axiom,
% 108.69/108.71 ! [V_f_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.71 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum_Oinfinite,axiom,
% 108.69/108.71 ! [V_g_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.71 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_atLeastLessThan__add__Un,axiom,
% 108.69/108.71 ! [V_k_2,V_j_2,V_i_2] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 108.69/108.71 => 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))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__eq__0__iff,axiom,
% 108.69/108.71 ! [V_f_2,V_F_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.71 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.71 <=> ! [B_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 108.69/108.71 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum_Oremove,axiom,
% 108.69/108.71 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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)))))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__diff1_H,axiom,
% 108.69/108.71 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__nonpos__neg,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__neg__nonpos,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__strict__increasing2,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__strict__increasing,axiom,
% 108.69/108.71 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__nonneg__pos,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_add__pos__nonneg,axiom,
% 108.69/108.71 ! [V_b,V_a,T_a] :
% 108.69/108.71 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.71 => 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))) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_nat__diff__split__asm,axiom,
% 108.69/108.71 ! [V_b_2,V_a_2,V_P_2] :
% 108.69/108.71 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 108.69/108.71 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 108.69/108.71 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 108.69/108.71 | ? [B_d] :
% 108.69/108.71 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 108.69/108.71 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_nat__diff__split,axiom,
% 108.69/108.71 ! [V_b_2,V_a_2,V_P_2] :
% 108.69/108.71 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 108.69/108.71 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 108.69/108.71 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 108.69/108.71 & ! [B_d] :
% 108.69/108.71 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 108.69/108.71 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__Suc__diff__eq2,axiom,
% 108.69/108.71 ! [V_m,V_j,V_k] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 108.69/108.71 => 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_diff__Suc__diff__eq1,axiom,
% 108.69/108.71 ! [V_m,V_j,V_k] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 108.69/108.71 => 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)) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__add__nat__ivl,axiom,
% 108.69/108.71 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 108.69/108.71 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),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_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_p_2)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__eq__Suc0__iff,axiom,
% 108.69/108.71 ! [V_f_2,V_A_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 108.69/108.71 <=> ? [B_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.71 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 108.69/108.71 & ! [B_xa] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 108.69/108.71 => ( B_x != B_xa
% 108.69/108.71 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_inj__on__fun__updI,axiom,
% 108.69/108.71 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.71 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.71 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 108.69/108.71 => c_Fun_Oinj__on(T_b,T_c,c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_A_2) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__head__upt__Suc,axiom,
% 108.69/108.71 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2)),V_n_2))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__head__Suc,axiom,
% 108.69/108.71 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(V_f_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m_2),V_n_2))) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__diff,axiom,
% 108.69/108.71 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.71 ( class_Groups_Oab__group__add(T_c)
% 108.69/108.71 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__diff__nat,axiom,
% 108.69/108.71 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.71 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),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_Nat_Onat),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,tc_Nat_Onat),V_f_2),V_B_2)) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_setsum__op__ivl__Suc,axiom,
% 108.69/108.71 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 108.69/108.71 ( class_Groups_Ocomm__monoid__add(T_b)
% 108.69/108.71 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b) )
% 108.69/108.71 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 108.69/108.71 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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)) ) ) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__Inter,axiom,
% 108.69/108.71 ! [V_M_2,T_b] :
% 108.69/108.71 ( ? [B_x] :
% 108.69/108.71 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 108.69/108.71 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 108.69/108.71 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__Diff,axiom,
% 108.69/108.71 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.71 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__Int,axiom,
% 108.69/108.71 ! [V_Ga_2,V_F_2,T_b] :
% 108.69/108.71 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.71 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) )
% 108.69/108.71 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite__imageI,axiom,
% 108.69/108.71 ! [V_h_2,T_c,V_F_2,T_b] :
% 108.69/108.71 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.71 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 108.69/108.71
% 108.69/108.71 fof(fact_finite_OinsertI,axiom,
% 108.69/108.71 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite_OemptyI,axiom,
% 108.69/108.72 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__vimageI,axiom,
% 108.69/108.72 ! [V_h_2,T_c,V_F_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.72 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__vimageD,axiom,
% 108.69/108.72 ! [V_F_2,V_h_2,T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 108.69/108.72 => ( hAPP(c_Set_Oimage(T_b,T_c,V_h_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))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_nat__add__commute,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_nat__add__left__commute,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_nat__add__assoc,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_nat__add__left__cancel,axiom,
% 108.69/108.72 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.72 ( 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)
% 108.69/108.72 <=> V_m_2 = V_n_2 ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_nat__add__right__cancel,axiom,
% 108.69/108.72 ! [V_n_2,V_k_2,V_m_2] :
% 108.69/108.72 ( 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)
% 108.69/108.72 <=> V_m_2 = V_n_2 ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__UN,axiom,
% 108.69/108.72 ! [V_B_2,T_c,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.72 <=> ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( class_Finite__Set_Ofinite(T_b)
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__code,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( class_Finite__Set_Ofinite(T_b)
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_infinite__UNIV__nat,axiom,
% 108.69/108.72 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite_Oequations_I1_J,axiom,
% 108.69/108.72 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__insert,axiom,
% 108.69/108.72 ! [V_A_2,V_a_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 108.69/108.72 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_rev__finite__subset,axiom,
% 108.69/108.72 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__subset,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__Prod__UNIV,axiom,
% 108.69/108.72 ! [T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__Plus__UNIV__iff,axiom,
% 108.69/108.72 ! [T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))))
% 108.69/108.72 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.72 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__option__UNIV,axiom,
% 108.69/108.72 ! [T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(T_b),tc_HOL_Obool))))
% 108.69/108.72 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__UNIV,axiom,
% 108.69/108.72 ! [T_b] :
% 108.69/108.72 ( class_Finite__Set_Ofinite(T_b)
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__UnI,axiom,
% 108.69/108.72 ! [V_Ga_2,V_F_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__Un,axiom,
% 108.69/108.72 ! [V_Ga_2,V_F_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_Ga_2)))
% 108.69/108.72 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.72 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Ga_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__Diff2,axiom,
% 108.69/108.72 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.72 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__UnionD,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__Pow__iff,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 108.69/108.72 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__surj,axiom,
% 108.69/108.72 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__Diff__insert,axiom,
% 108.69/108.72 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),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_a_2),V_B_2))))
% 108.69/108.72 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__imageD,axiom,
% 108.69/108.72 ! [V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 108.69/108.72 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__compl,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 108.69/108.72 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__fun__UNIVD2,axiom,
% 108.69/108.72 ! [T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_endo__inj__surj,axiom,
% 108.69/108.72 ! [V_f_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)),V_A_2))
% 108.69/108.72 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 108.69/108.72 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__surj__inj,axiom,
% 108.69/108.72 ! [V_f_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2)))
% 108.69/108.72 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__UNIV__surj__inj,axiom,
% 108.69/108.72 ! [V_f_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.72 => ( hAPP(c_Set_Oimage(T_b,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_b,tc_HOL_Obool))
% 108.69/108.72 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__UNIV__inj__surj,axiom,
% 108.69/108.72 ! [V_f_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.72 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.72 => hAPP(c_Set_Oimage(T_b,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_b,tc_HOL_Obool)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 108.69/108.72 ! [V_y,V_x,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__ring__1(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_even__less__0__iff,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one_Oremove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 108.69/108.72 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => 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_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)))))) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple_Oremove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 108.69/108.72 => 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_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__mono2,axiom,
% 108.69/108.72 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 108.69/108.72 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.72 => ( ! [B_b] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 108.69/108.72 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.72 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( ! [B_x] :
% 108.69/108.72 ( 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)))
% 108.69/108.72 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 108.69/108.72 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_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_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__Un__zero,axiom,
% 108.69/108.72 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 108.69/108.72 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 108.69/108.72 => ( ! [B_x] :
% 108.69/108.72 ( 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_S_2),V_T_2)))
% 108.69/108.72 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 108.69/108.72 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__mono3,axiom,
% 108.69/108.72 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 108.69/108.72 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.72 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.72 => ( ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_ball__UN,axiom,
% 108.69/108.72 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 108.69/108.72 ( ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.72 => hBOOL(hAPP(V_P_2,B_x)) )
% 108.69/108.72 <=> ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 108.69/108.72 => ! [B_xa] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 108.69/108.72 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple_Oempty,axiom,
% 108.69/108.72 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 108.69/108.72 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 108.69/108.72 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => 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) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 108.69/108.72 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 108.69/108.72 ! [V_d,V_c,V_a,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => 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) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 108.69/108.72 ! [V_d,V_c,V_a,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 108.69/108.72 ! [V_c,V_a,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => 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) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one_Osingleton,axiom,
% 108.69/108.72 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 108.69/108.72 => hAPP(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)))) = V_x_2 ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple_Oinsert,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 108.69/108.72 => hAPP(hAPP(V_f_2,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 108.69/108.72 ! [V_a,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 108.69/108.72 ! [V_a,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_add__0__iff,axiom,
% 108.69/108.72 ! [V_a_2,V_b_2,T_b] :
% 108.69/108.72 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 108.69/108.72 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 108.69/108.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_double__eq__0__iff,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.72 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one_Oinsert,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one_Oinsert__remove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 108.69/108.72 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),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_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)))))) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.72 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one_Ounion__inter,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( 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))
% 108.69/108.72 => 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)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one_Ounion__disjoint,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( 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))
% 108.69/108.72 => 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)) ) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 108.69/108.72 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 108.69/108.72 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__Union,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 108.69/108.72 => ( ! [B_M] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Oremove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 108.69/108.72 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,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)))))) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Oremove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 108.69/108.72 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,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)))))) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_insert__partition,axiom,
% 108.69/108.72 ! [V_F_2,V_x_2,T_b] :
% 108.69/108.72 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 108.69/108.72 => ( ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 108.69/108.72 => ! [B_xa] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_xa),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2)))
% 108.69/108.72 => ( B_x != B_xa
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),B_xa) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_x_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_F_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one_Oclosed,axiom,
% 108.69/108.72 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(V_f_2,B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__fun__UNIVD1,axiom,
% 108.69/108.72 ! [T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
% 108.69/108.72 => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__mono__zero__left,axiom,
% 108.69/108.72 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 108.69/108.72 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 108.69/108.72 => ( ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 108.69/108.72 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 108.69/108.72 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__mono__zero__right,axiom,
% 108.69/108.72 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 108.69/108.72 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 108.69/108.72 => ( ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 108.69/108.72 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 108.69/108.72 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__lessThan,axiom,
% 108.69/108.72 ! [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 ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__le__Sup,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card_Oempty,axiom,
% 108.69/108.72 ! [T_b] : hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__infinite,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.72 => ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 108.69/108.72 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__image,axiom,
% 108.69/108.72 ! [V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_subset__card__intvl__is__intvl,axiom,
% 108.69/108.72 ! [V_k_2,V_A_2] :
% 108.69/108.72 ( 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)))))
% 108.69/108.72 => 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__atLeastLessThan,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__atMost,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Osingleton,axiom,
% 108.69/108.72 ! [V_x_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Osingleton,axiom,
% 108.69/108.72 ! [V_x_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__greaterThanAtMost,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__eq__0__iff,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.72 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__ge__0__finite,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( 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_b),V_A_2)))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__insert__le,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__mono,axiom,
% 108.69/108.72 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__seteq,axiom,
% 108.69/108.72 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)))
% 108.69/108.72 => V_A_2 = V_B_2 ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__image__le,axiom,
% 108.69/108.72 ! [V_f_2,T_c,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_inj__on__iff__eq__card,axiom,
% 108.69/108.72 ! [V_f_2,T_c,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.72 <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_eq__card__imp__inj__on,axiom,
% 108.69/108.72 ! [V_f_2,T_c,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
% 108.69/108.72 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_pigeonhole,axiom,
% 108.69/108.72 ! [V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))),hAPP(c_Finite__Set_Ocard(T_c),V_A_2)))
% 108.69/108.72 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_psubset__card__mono,axiom,
% 108.69/108.72 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__atLeastAtMost,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sup__Inf__absorb,axiom,
% 108.69/108.72 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Oin__idem,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_inf__Sup__absorb,axiom,
% 108.69/108.72 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = V_a_2 ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Oin__idem,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__greaterThanLessThan,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin__Sup,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin__Inf,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__insert__if,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
% 108.69/108.72 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__insert__disjoint,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__gt__0__iff,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( 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_b),V_A_2)))
% 108.69/108.72 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__UNIV__card__ge__0,axiom,
% 108.69/108.72 ! [T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.72 => 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_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card_Ounion__inter,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Un__Int,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__bij__eq,axiom,
% 108.69/108.72 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 108.69/108.72 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Diff__subset,axiom,
% 108.69/108.72 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Diff__subset__Int,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),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_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_diff__card__le__card__Diff,axiom,
% 108.69/108.72 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => 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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__psubset,axiom,
% 108.69/108.72 ! [V_A_2,V_B_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Osubset__idem,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Osubset__idem,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Ounion__idem,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,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(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Ounion__idem,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,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__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__insert,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),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)))))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Un__disjoint,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( 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))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Diff1__le,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),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)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__inj__on__le,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_inj__on__iff__card__le,axiom,
% 108.69/108.72 ! [V_B_2,T_c,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 108.69/108.72 => ( ? [B_f] :
% 108.69/108.72 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 108.69/108.72 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,B_f),V_A_2)),V_B_2)) )
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Suc__Diff1,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(T_b),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)))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Diff2__less,axiom,
% 108.69/108.72 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),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))))),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Diff1__less,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),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)))))),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Oinsert,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Oinsert,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 108.69/108.72 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,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)))))) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 108.69/108.72 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,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)))))) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( 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))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,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(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Ounion__inter,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( 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))
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OSup__fin(T_b,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__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( 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))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,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__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Ounion__inter,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( 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))
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice__class_OInf__fin(T_b,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(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Oclosed,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Oclosed,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Suc__eq,axiom,
% 108.69/108.72 ! [V_k_2,V_A_2,T_b] :
% 108.69/108.72 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 108.69/108.72 <=> ? [B_b,B_B] :
% 108.69/108.72 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 108.69/108.72 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 108.69/108.72 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 108.69/108.72 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.72 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Diff__singleton__if,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 108.69/108.72 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),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))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Diff__singleton,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),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))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card_Oremove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),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_b),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)))))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Plus__conv__if,axiom,
% 108.69/108.72 ! [V_B_2,T_c,V_A_2,T_b] :
% 108.69/108.72 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) )
% 108.69/108.72 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__UNIV__unit,axiom,
% 108.69/108.72 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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_one__reorient,axiom,
% 108.69/108.72 ! [V_x_2,T_b] :
% 108.69/108.72 ( class_Groups_Oone(T_b)
% 108.69/108.72 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 108.69/108.72 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zero__neq__one,axiom,
% 108.69/108.72 ! [T_a] :
% 108.69/108.72 ( class_Rings_Ozero__neq__one(T_a)
% 108.69/108.72 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_one__neq__zero,axiom,
% 108.69/108.72 ! [T_a] :
% 108.69/108.72 ( class_Rings_Ozero__neq__one(T_a)
% 108.69/108.72 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_not__one__le__zero,axiom,
% 108.69/108.72 ! [T_a] :
% 108.69/108.72 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.72 => ~ 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zero__le__one,axiom,
% 108.69/108.72 ! [T_a] :
% 108.69/108.72 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.72 => 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zero__less__one,axiom,
% 108.69/108.72 ! [T_a] :
% 108.69/108.72 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_not__one__less__zero,axiom,
% 108.69/108.72 ! [T_a] :
% 108.69/108.72 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.72 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_less__add__one,axiom,
% 108.69/108.72 ! [V_a,T_a] :
% 108.69/108.72 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.72 => 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)))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_One__nat__def,axiom,
% 108.69/108.72 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Suc__eq__plus1,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Suc__eq__plus1__left,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_diff__Suc__1,axiom,
% 108.69/108.72 ! [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 ).
% 108.69/108.72
% 108.69/108.72 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zero__less__two,axiom,
% 108.69/108.72 ! [T_a] :
% 108.69/108.72 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.72 => 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)))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__eq__1__iff,axiom,
% 108.69/108.72 ! [V_f_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 108.69/108.72 <=> ? [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.72 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 108.69/108.72 & ! [B_xa] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 108.69/108.72 => ( B_x != B_xa
% 108.69/108.72 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Suc__diff__1,axiom,
% 108.69/108.72 ! [V_n] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.72 => 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 ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Suc__pred_H,axiom,
% 108.69/108.72 ! [V_n] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.72 => 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_add__eq__if,axiom,
% 108.69/108.72 ! [V_n,V_m] :
% 108.69/108.72 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 108.69/108.72 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.72 => 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)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__PlusD_I2_J,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__PlusD_I1_J,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__Plus,axiom,
% 108.69/108.72 ! [V_B_2,T_c,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 108.69/108.72 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__Plus__iff,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_c,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
% 108.69/108.72 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Plus,axiom,
% 108.69/108.72 ! [V_B_2,T_c,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card_Oinsert,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),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_b),V_A_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__ub__add__nat,axiom,
% 108.69/108.72 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 108.69/108.72 ( class_Groups_Ocomm__monoid__add(T_b)
% 108.69/108.72 => ( 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))))
% 108.69/108.72 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),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)))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Diff__insert,axiom,
% 108.69/108.72 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),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_a_2),V_B_2))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card_Oinsert__remove,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),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_b),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)))))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_UNIV__Plus__UNIV,axiom,
% 108.69/108.72 ! [T_c,T_b] : c_Sum__Type_OPlus(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card_Ounion__inter__neutral,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( ( ? [B_x] : 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)))
% 108.69/108.72 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Plus__eq__empty__conv,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_c,T_b] :
% 108.69/108.72 ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
% 108.69/108.72 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__odd__less__0,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Ohom__commute,axiom,
% 108.69/108.72 ! [V_N_2,V_h_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.72 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OInf__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Ohom__commute,axiom,
% 108.69/108.72 ! [V_N_2,V_h_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),B_x),B_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.72 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => hAPP(V_h_2,c_Big__Operators_Olattice__class_OSup__fin(T_b,V_N_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_ex__least__nat__less,axiom,
% 108.69/108.72 ! [V_n_2,V_P_2] :
% 108.69/108.72 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 108.69/108.72 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 108.69/108.72 => ? [B_k] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 108.69/108.72 & ! [B_i] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 108.69/108.72 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 108.69/108.72 & 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)))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__0,axiom,
% 108.69/108.72 ! [T_b] :
% 108.69/108.72 ( class_Rings_Oring__1(T_b)
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__add,axiom,
% 108.69/108.72 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Oring__1(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__diff,axiom,
% 108.69/108.72 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Oring__1(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__1,axiom,
% 108.69/108.72 ! [T_b] :
% 108.69/108.72 ( class_Rings_Oring__1(T_b)
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__minus,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Oring__1(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__double__eq__0__iff,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Int_Oring__char__0(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.72 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__odd__nonzero,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Int_Oring__char__0(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.72 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2)),V_a_2) != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__empty__induct,axiom,
% 108.69/108.72 ! [V_P_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 108.69/108.72 => ( ! [B_a,B_A] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 108.69/108.72 => ( hBOOL(hAPP(V_P_2,B_A))
% 108.69/108.72 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(hAPP(c_Set_Oinsert(T_b),B_a),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) )
% 108.69/108.72 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.72 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => 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)) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_finite__subset__induct,axiom,
% 108.69/108.72 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.72 => ( ! [B_a,B_F] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 108.69/108.72 => ( hBOOL(hAPP(V_P_2,B_F))
% 108.69/108.72 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 108.69/108.72 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.72 => 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) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__strict__mono,axiom,
% 108.69/108.72 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 108.69/108.72 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.72 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => ( ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,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_A_2))) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn__if,axiom,
% 108.69/108.72 ! [V_x,T_a] :
% 108.69/108.72 ( class_Groups_Osgn__if(T_a)
% 108.69/108.72 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.72 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 108.69/108.72 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.72 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.72 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 108.69/108.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.72 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one__idem_Oidem,axiom,
% 108.69/108.72 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 108.69/108.72 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn__sgn,axiom,
% 108.69/108.72 ! [V_a,T_a] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.72 => 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) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn__0__0,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.72 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.72 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn0,axiom,
% 108.69/108.72 ! [T_a] :
% 108.69/108.72 ( class_Groups_Osgn__if(T_a)
% 108.69/108.72 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn__less,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Osgn__class_Osgn(T_b,V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn__greater,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Groups_Osgn__class_Osgn(T_b,V_a_2)))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one__idem_Oin__idem,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn__pos,axiom,
% 108.69/108.72 ! [V_a,T_a] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.72 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn__1__pos,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.72 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn__1__neg,axiom,
% 108.69/108.72 ! [V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.72 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_sgn__neg,axiom,
% 108.69/108.72 ! [V_a,T_a] :
% 108.69/108.72 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.72 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 108.69/108.72 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 108.69/108.72 => ( ! [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))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.72 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.72 => hAPP(V_h_2,hAPP(V_F_2,V_N_2)) = hAPP(V_F_2,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 108.69/108.72 => ( ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)))
% 108.69/108.72 => hAPP(V_g_2,B_x) = V_z_2 )
% 108.69/108.72 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card_Oneutral,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.72 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_InterI,axiom,
% 108.69/108.72 ! [V_A_2,V_C_2,T_b] :
% 108.69/108.72 ( ! [B_X] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_C_2))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_expand__Suc,axiom,
% 108.69/108.72 ! [V_v] :
% 108.69/108.72 ( 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)))
% 108.69/108.72 => 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__reindex__cong,axiom,
% 108.69/108.72 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 108.69/108.72 ( class_Groups_Ocomm__monoid__add(T_d)
% 108.69/108.72 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 108.69/108.72 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 108.69/108.72 => ( ! [B_a] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 108.69/108.72 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 108.69/108.72 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_setsum__ivl__cong,axiom,
% 108.69/108.72 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 108.69/108.72 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.72 & class_Orderings_Oord(T_b) )
% 108.69/108.72 => ( V_a_2 = V_c_2
% 108.69/108.72 => ( V_b_2 = V_d_2
% 108.69/108.72 => ( ! [B_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 108.69/108.72 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 108.69/108.72 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_eq__number__of,axiom,
% 108.69/108.72 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.72 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.72 & class_Int_Oring__char__0(T_b) )
% 108.69/108.72 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 108.69/108.72 <=> V_x_2 = V_y_2 ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_number__of__reorient,axiom,
% 108.69/108.72 ! [V_x_2,V_w_2,T_b] :
% 108.69/108.72 ( class_Int_Onumber(T_b)
% 108.69/108.72 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 108.69/108.72 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_le__number__of,axiom,
% 108.69/108.72 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.72 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.72 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_less__number__of,axiom,
% 108.69/108.72 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.72 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.72 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_number__of__add,axiom,
% 108.69/108.72 ! [V_w,V_v,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_add__number__of__eq,axiom,
% 108.69/108.72 ! [V_w,V_v,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_add__number__of__left,axiom,
% 108.69/108.72 ! [V_z,V_w,V_v,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_number__of__diff,axiom,
% 108.69/108.72 ! [V_w,V_v,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_diff__number__of__eq,axiom,
% 108.69/108.72 ! [V_w,V_v,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_number__of__minus,axiom,
% 108.69/108.72 ! [V_w,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_arith__simps_I30_J,axiom,
% 108.69/108.72 ! [V_w,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_le__number__of__eq__not__less,axiom,
% 108.69/108.72 ! [V_w_2,V_v_2,T_b] :
% 108.69/108.72 ( ( class_Int_Onumber(T_b)
% 108.69/108.72 & class_Orderings_Olinorder(T_b) )
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.72 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_add__number__of__diff2,axiom,
% 108.69/108.72 ! [V_w,V_c,V_v,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_add__number__of__diff1,axiom,
% 108.69/108.72 ! [V_c,V_w,V_v,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__number__of,axiom,
% 108.69/108.72 ! [V_w_2,T_b] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_b)
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_number__of__pred,axiom,
% 108.69/108.72 ! [V_w,T_a] :
% 108.69/108.72 ( class_Int_Onumber__ring(T_a)
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 108.69/108.72 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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)) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_card__Pow,axiom,
% 108.69/108.72 ! [V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),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_b),V_A_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_UnionE,axiom,
% 108.69/108.72 ! [V_C_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 108.69/108.72 => ~ ! [B_X] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 108.69/108.72 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.72 => 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) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_x_2),V_A_2) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 108.69/108.72 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Olattice(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.72 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_x_2),V_A_2) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_less__eq__number__of__int__code,axiom,
% 108.69/108.72 ! [V_l_2,V_k_2] :
% 108.69/108.72 ( 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)))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_plus__numeral__code_I9_J,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_minus__numeral__code_I6_J,axiom,
% 108.69/108.72 ! [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))) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_minus__numeral__code_I5_J,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_less__number__of__int__code,axiom,
% 108.69/108.72 ! [V_l_2,V_k_2] :
% 108.69/108.72 ( 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)))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_int__0__less__1,axiom,
% 108.69/108.72 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))) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_int__one__le__iff__zero__less,axiom,
% 108.69/108.72 ! [V_z_2] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zle__diff1__eq,axiom,
% 108.69/108.72 ! [V_z_2,V_w_2] :
% 108.69/108.72 ( 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))))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_pred__def,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_odd__less__0,axiom,
% 108.69/108.72 ! [V_z_2] :
% 108.69/108.72 ( 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)))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_le__imp__0__less,axiom,
% 108.69/108.72 ! [V_z] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 108.69/108.72 => 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zless__add1__eq,axiom,
% 108.69/108.72 ! [V_z_2,V_w_2] :
% 108.69/108.72 ( 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))))
% 108.69/108.72 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 108.69/108.72 | V_w_2 = V_z_2 ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zless__imp__add1__zle,axiom,
% 108.69/108.72 ! [V_z,V_w] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 108.69/108.72 => 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)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_add1__zle__eq,axiom,
% 108.69/108.72 ! [V_z_2,V_w_2] :
% 108.69/108.72 ( 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))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zle__add1__eq__le,axiom,
% 108.69/108.72 ! [V_z_2,V_w_2] :
% 108.69/108.72 ( 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))))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_odd__nonzero,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 108.69/108.72 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.72 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.72 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_less__bin__lemma,axiom,
% 108.69/108.72 ! [V_l_2,V_k_2] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 108.69/108.72 <=> 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zless__linear,axiom,
% 108.69/108.72 ! [V_y,V_x] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 108.69/108.72 | V_x = V_y
% 108.69/108.72 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zminus__0,axiom,
% 108.69/108.72 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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zminus__zminus,axiom,
% 108.69/108.72 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 108.69/108.72
% 108.69/108.72 fof(fact_diff__int__def__symmetric,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_diff__int__def,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zadd__strict__right__mono,axiom,
% 108.69/108.72 ! [V_k,V_j,V_i] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 108.69/108.72 => 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zadd__0,axiom,
% 108.69/108.72 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zadd__0__right,axiom,
% 108.69/108.72 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zadd__zminus__inverse2,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zadd__commute,axiom,
% 108.69/108.72 ! [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) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zadd__left__commute,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zadd__assoc,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zminus__zadd__distrib,axiom,
% 108.69/108.72 ! [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)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zadd__left__mono,axiom,
% 108.69/108.72 ! [V_k,V_j,V_i] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 108.69/108.72 => 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))) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zadd__zless__mono,axiom,
% 108.69/108.72 ! [V_z,V_z_H,V_w,V_w_H] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 108.69/108.72 => 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))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zle__refl,axiom,
% 108.69/108.72 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zle__linear,axiom,
% 108.69/108.72 ! [V_w,V_z] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 108.69/108.72 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zle__trans,axiom,
% 108.69/108.72 ! [V_k,V_j,V_i] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zle__antisym,axiom,
% 108.69/108.72 ! [V_w,V_z] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 108.69/108.72 => V_z = V_w ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_le__iff__pred__less,axiom,
% 108.69/108.72 ! [V_l_2,V_k_2] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 108.69/108.72 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zless__le,axiom,
% 108.69/108.72 ! [V_w_2,V_z_2] :
% 108.69/108.72 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 108.69/108.72 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 108.69/108.72 & V_z_2 != V_w_2 ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_zsgn__def,axiom,
% 108.69/108.72 ! [V_i] :
% 108.69/108.72 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.72 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 108.69/108.72 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.72 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 108.69/108.72 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 108.69/108.72 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 108.69/108.72 => 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)) ) ) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_fold__empty,axiom,
% 108.69/108.72 ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 108.69/108.72 ! [V_x,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 108.69/108.72 ! [V_x,T_a] :
% 108.69/108.72 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.72 => 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) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_Ints__power,axiom,
% 108.69/108.72 ! [V_n_2,V_a_2,T_b] :
% 108.69/108.72 ( class_Rings_Oring__1(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.72 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_union__fold__insert,axiom,
% 108.69/108.72 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.72 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)),V_B_2),V_A_2) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_fold__sup__insert,axiom,
% 108.69/108.72 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 108.69/108.72 ( class_Lattices_Osemilattice__sup(T_b)
% 108.69/108.72 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.72 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2)) ) ) ).
% 108.69/108.72
% 108.69/108.72 fof(fact_fold__inf__insert,axiom,
% 108.69/108.72 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 108.69/108.73 ( class_Lattices_Osemilattice__inf(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_sup__Sup__fold__sup,axiom,
% 108.69/108.73 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_B_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_B_2),V_A_2) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_inf__Inf__fold__inf,axiom,
% 108.69/108.73 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_B_2),V_A_2) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 108.69/108.73 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_a_2),V_A_2) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_sup__le__fold__sup,axiom,
% 108.69/108.73 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 108.69/108.73 ( class_Lattices_Osemilattice__sup(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_fold__inf__le__inf,axiom,
% 108.69/108.73 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 108.69/108.73 ( class_Lattices_Osemilattice__inf(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_a_2),V_b_2))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Sup__fold__sup,axiom,
% 108.69/108.73 ! [V_A_2,T_b] :
% 108.69/108.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),c_Orderings_Obot__class_Obot(T_b)),V_A_2) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Inf__fold__inf,axiom,
% 108.69/108.73 ! [V_A_2,T_b] :
% 108.69/108.73 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),c_Orderings_Otop__class_Otop(T_b)),V_A_2) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 108.69/108.73 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.73 ( class_Lattices_Olattice(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_a_2),V_A_2) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 108.69/108.73 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.73 ( class_Lattices_Olattice(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_a_2),V_A_2) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_folding__one_Oeq__fold_H,axiom,
% 108.69/108.73 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.73 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,V_f_2),V_x_2),V_A_2) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 108.69/108.73 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 108.69/108.73 => 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) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 108.69/108.73 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.73 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_c),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)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__strict__mono,axiom,
% 108.69/108.73 ! [V_n,V_b,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.73 => 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))) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_one__less__power,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.73 => 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))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__increasing__iff,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__le__imp__le__exp,axiom,
% 108.69/108.73 ! [V_n,V_m,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 108.69/108.73 => ( 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)))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__decreasing,axiom,
% 108.69/108.73 ! [V_a,V_N,V_n,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 108.69/108.73 => 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))) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__strict__decreasing,axiom,
% 108.69/108.73 ! [V_a,V_N,V_n,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 108.69/108.73 => 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))) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__Suc__less__one,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 108.69/108.73 => 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))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_finite__atLeastAtMost__int,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_finite__atLeastLessThan__int,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_finite__greaterThanLessThan__int,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_finite__greaterThanAtMost__int,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_number__of__is__id,axiom,
% 108.69/108.73 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 108.69/108.73
% 108.69/108.73 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__0__neq__1,axiom,
% 108.69/108.73 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_field__power__not__zero,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 108.69/108.73 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__one,axiom,
% 108.69/108.73 ! [V_n,T_a] :
% 108.69/108.73 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__one__right,axiom,
% 108.69/108.73 ! [V_a,T_a] :
% 108.69/108.73 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.73 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__mono,axiom,
% 108.69/108.73 ! [V_n,V_b,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.73 => 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))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__le__power,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.73 => 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))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__less__power,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.73 => 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))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__eq__0__iff,axiom,
% 108.69/108.73 ! [V_n_2,V_a_2,T_b] :
% 108.69/108.73 ( ( class_Power_Opower(T_b)
% 108.69/108.73 & class_Rings_Omult__zero(T_b)
% 108.69/108.73 & class_Rings_Ono__zero__divisors(T_b)
% 108.69/108.73 & class_Rings_Ozero__neq__one(T_b) )
% 108.69/108.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.73 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.73 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_one__le__power,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 108.69/108.73 => 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))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__0__Suc,axiom,
% 108.69/108.73 ! [V_n,T_a] :
% 108.69/108.73 ( ( class_Power_Opower(T_a)
% 108.69/108.73 & class_Rings_Osemiring__0(T_a) )
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__inject__exp,axiom,
% 108.69/108.73 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 108.69/108.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
% 108.69/108.73 <=> V_m_2 = V_n_2 ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__0,axiom,
% 108.69/108.73 ! [V_a,T_a] :
% 108.69/108.73 ( class_Power_Opower(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 108.69/108.73 ! [V_m_2,V_x_2] :
% 108.69/108.73 ( 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))
% 108.69/108.73 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.73 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__Suc__0,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__zero__less__power__iff,axiom,
% 108.69/108.73 ! [V_n_2,V_x_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 108.69/108.73 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__power__less__imp__less,axiom,
% 108.69/108.73 ! [V_n,V_m,V_i] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 108.69/108.73 => ( 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)))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__less__imp__less__base,axiom,
% 108.69/108.73 ! [V_b,V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( 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)))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__inject__base,axiom,
% 108.69/108.73 ! [V_b,V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( 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))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.73 => V_a = V_b ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__le__imp__le__base,axiom,
% 108.69/108.73 ! [V_b,V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( 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))))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__0__left,axiom,
% 108.69/108.73 ! [V_n,T_a] :
% 108.69/108.73 ( ( class_Power_Opower(T_a)
% 108.69/108.73 & class_Rings_Osemiring__0(T_a) )
% 108.69/108.73 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.73 => 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) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__gt1,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 108.69/108.73 => 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)))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__strict__increasing__iff,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__less__imp__less__exp,axiom,
% 108.69/108.73 ! [V_n,V_m,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 108.69/108.73 => ( 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)))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__strict__increasing,axiom,
% 108.69/108.73 ! [V_a,V_N,V_n,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 108.69/108.73 => 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))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__increasing,axiom,
% 108.69/108.73 ! [V_a,V_N,V_n,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 108.69/108.73 => 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))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__one__le__power,axiom,
% 108.69/108.73 ! [V_n,V_i] :
% 108.69/108.73 ( 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))
% 108.69/108.73 => 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__eq__imp__eq__base,axiom,
% 108.69/108.73 ! [V_b,V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( 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)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.73 => V_a = V_b ) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_simp__from__to,axiom,
% 108.69/108.73 ! [V_i_2,V_j_2] :
% 108.69/108.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 108.69/108.73 => 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)) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 108.69/108.73 => 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)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 108.69/108.73 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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 108.69/108.73 ! [V_y,V_x] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.73 => 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))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 108.69/108.73 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.73 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_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)))))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 108.69/108.73 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_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)))))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 108.69/108.73 ! [V_n,V_x] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.73 => 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 108.69/108.73 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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_infinite__UNIV__int,axiom,
% 108.69/108.73 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 108.69/108.73 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 108.69/108.73 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 108.69/108.73 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.73 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 108.69/108.73 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.73 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.73 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.73 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.73 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_aset_I6_J,axiom,
% 108.69/108.73 ! [V_A_2,V_t_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ( 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))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 108.69/108.73 => 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)) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_bset_I8_J,axiom,
% 108.69/108.73 ! [V_B_2,V_t_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ( 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))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 108.69/108.73 => 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))) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_aset_I8_J,axiom,
% 108.69/108.73 ! [V_t_2,V_A_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 108.69/108.73 => 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))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_bset_I6_J,axiom,
% 108.69/108.73 ! [V_t_2,V_B_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 108.69/108.73 => 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)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_aset_I4_J,axiom,
% 108.69/108.73 ! [V_A_2,V_t_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( B_x != V_t_2
% 108.69/108.73 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_bset_I4_J,axiom,
% 108.69/108.73 ! [V_B_2,V_t_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( B_x != V_t_2
% 108.69/108.73 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_bset_I7_J,axiom,
% 108.69/108.73 ! [V_B_2,V_t_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 108.69/108.73 => 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))) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_bset_I3_J,axiom,
% 108.69/108.73 ! [V_B_2,V_t_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ( 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))
% 108.69/108.73 => ( ! [B_x] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xa] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 108.69/108.73 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 108.69/108.73 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_aset_I3_J,axiom,
% 108.69/108.73 ! [V_A_2,V_t_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ( 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))
% 108.69/108.73 => ( ! [B_x] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xa] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 108.69/108.73 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 108.69/108.73 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_aset_I5_J,axiom,
% 108.69/108.73 ! [V_A_2,V_t_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 108.69/108.73 => 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)) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_aset_I7_J,axiom,
% 108.69/108.73 ! [V_t_2,V_A_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 108.69/108.73 => 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))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_bset_I5_J,axiom,
% 108.69/108.73 ! [V_t_2,V_B_2,V_D_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 108.69/108.73 => ! [B_x] :
% 108.69/108.73 ( ! [B_xa] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ! [B_xb] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 108.69/108.73 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 108.69/108.73 => 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)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_tsub__def,axiom,
% 108.69/108.73 ! [V_x,V_y] :
% 108.69/108.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 108.69/108.73 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 108.69/108.73 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__number__of__diff__1,axiom,
% 108.69/108.73 ! [V_v] :
% 108.69/108.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.73 => 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)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Pls__def,axiom,
% 108.69/108.73 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I19_J,axiom,
% 108.69/108.73 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I2_J,axiom,
% 108.69/108.73 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__Pls,axiom,
% 108.69/108.73 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__Pls__right,axiom,
% 108.69/108.73 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 108.69/108.73
% 108.69/108.73 fof(fact_diff__bin__simps_I1_J,axiom,
% 108.69/108.73 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 108.69/108.73
% 108.69/108.73 fof(fact_minus__Pls,axiom,
% 108.69/108.73 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 108.69/108.73
% 108.69/108.73 fof(fact_semiring__norm_I112_J,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_number__of__Pls,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__numeral__0__right,axiom,
% 108.69/108.73 ! [V_a,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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 ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__numeral__0,axiom,
% 108.69/108.73 ! [V_a,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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 ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_bin__less__0__simps_I1_J,axiom,
% 108.69/108.73 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__number__of__Pls,axiom,
% 108.69/108.73 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_semiring__norm_I113_J,axiom,
% 108.69/108.73 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__is__num__zero,axiom,
% 108.69/108.73 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_eq__0__number__of,axiom,
% 108.69/108.73 ! [V_v_2] :
% 108.69/108.73 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_eq__number__of__0,axiom,
% 108.69/108.73 ! [V_v_2] :
% 108.69/108.73 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_number__of2,axiom,
% 108.69/108.73 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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__nat__number__of,axiom,
% 108.69/108.73 ! [V_v_H_2,V_v_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 108.69/108.73 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_le__nat__number__of,axiom,
% 108.69/108.73 ! [V_v_H_2,V_v_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_le__special_I3_J,axiom,
% 108.69/108.73 ! [V_x_2,T_b] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_le__special_I1_J,axiom,
% 108.69/108.73 ! [V_y_2,T_b] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__special_I1_J,axiom,
% 108.69/108.73 ! [V_y_2,T_b] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__special_I3_J,axiom,
% 108.69/108.73 ! [V_x_2,T_b] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__0__number__of,axiom,
% 108.69/108.73 ! [V_v_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__nat__number__of,axiom,
% 108.69/108.73 ! [V_v_H,V_v] :
% 108.69/108.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.73 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 108.69/108.73 => 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)) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 108.69/108.73 ! [V_y,V_x] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.73 => 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))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_tsub__eq,axiom,
% 108.69/108.73 ! [V_x,V_y] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 108.69/108.73 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Suc__diff__number__of,axiom,
% 108.69/108.73 ! [V_m,V_v] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 108.69/108.73 => 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_eq__special_I1_J,axiom,
% 108.69/108.73 ! [V_y_2,T_b] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 108.69/108.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_eq__special_I3_J,axiom,
% 108.69/108.73 ! [V_x_2,T_b] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__1__add__number__of,axiom,
% 108.69/108.73 ! [V_v] :
% 108.69/108.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.73 => 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)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__number__of__add__1,axiom,
% 108.69/108.73 ! [V_v] :
% 108.69/108.73 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.73 => 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)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nats__number__of,axiom,
% 108.69/108.73 ! [V_w_2,T_b] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__number__of__lemma,axiom,
% 108.69/108.73 ! [V_v,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => ( ( 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)))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ 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)))
% 108.69/108.73 => 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) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_diff__special_I2_J,axiom,
% 108.69/108.73 ! [V_v,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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)))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_negative__zle,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_negative__zless,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_succ__Pls,axiom,
% 108.69/108.73 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I51_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 108.69/108.73 <=> V_k_2 = V_l_2 ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__eq__iff,axiom,
% 108.69/108.73 ! [V_n_2,V_m_2,T_b] :
% 108.69/108.73 ( class_Nat_Osemiring__char__0(T_b)
% 108.69/108.73 => ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)
% 108.69/108.73 <=> V_m_2 = V_n_2 ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_iszero__number__of__Bit1,axiom,
% 108.69/108.73 ! [V_w,T_a] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 & class_Int_Oring__char__0(T_a) )
% 108.69/108.73 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__in__Nats,axiom,
% 108.69/108.73 ! [V_n_2,T_b] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_b)
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__eq__int__code_I16_J,axiom,
% 108.69/108.73 ! [V_k2_2,V_k1_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I34_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__int__code_I16_J,axiom,
% 108.69/108.73 ! [V_k2_2,V_k1_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I17_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I46_J,axiom,
% 108.69/108.73 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I39_J,axiom,
% 108.69/108.73 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__iszero__Numeral1,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_inj__int,axiom,
% 108.69/108.73 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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 108.69/108.73 ! [V_A_2,V_x_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 108.69/108.73 <=> 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 108.69/108.73 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)))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 108.69/108.73 ! [V_B_2,V_A_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.73 <=> 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_iszero__0,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_iszero__def,axiom,
% 108.69/108.73 ! [V_z_2,T_b] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_b)
% 108.69/108.73 => ( c_Int_Oiszero(T_b,V_z_2)
% 108.69/108.73 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__iszero__1,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__0,axiom,
% 108.69/108.73 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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__eq__0__conv,axiom,
% 108.69/108.73 ! [V_n_2] :
% 108.69/108.73 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.73 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 108.69/108.73 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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__zle__int,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 108.69/108.73 ! [V_P_2] :
% 108.69/108.73 ( ! [B_x] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 108.69/108.73 => hBOOL(hAPP(V_P_2,B_x)) )
% 108.69/108.73 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 108.69/108.73 ! [V_P_2] :
% 108.69/108.73 ( ? [B_x] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 108.69/108.73 & hBOOL(hAPP(V_P_2,B_x)) )
% 108.69/108.73 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__less__0__conv,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zless__int,axiom,
% 108.69/108.73 ! [V_n_2,V_m_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_bin__less__0__simps_I4_J,axiom,
% 108.69/108.73 ! [V_w_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zle__int,axiom,
% 108.69/108.73 ! [V_n_2,V_m_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zadd__int,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zadd__int__left,axiom,
% 108.69/108.73 ! [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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zle__iff__zadd,axiom,
% 108.69/108.73 ! [V_z_2,V_w_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 108.69/108.73 <=> ? [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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I22_J,axiom,
% 108.69/108.73 ! [V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I12_J,axiom,
% 108.69/108.73 ! [V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__le__imp__of__nat,axiom,
% 108.69/108.73 ! [V_m,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__0__le__iff,axiom,
% 108.69/108.73 ! [V_n,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_negative__eq__positive,axiom,
% 108.69/108.73 ! [V_m_2,V_n_2] :
% 108.69/108.73 ( 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)
% 108.69/108.73 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.73 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__less__0__iff,axiom,
% 108.69/108.73 ! [V_m,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ~ 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Bit1__def,axiom,
% 108.69/108.73 ! [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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__int__zless__negative,axiom,
% 108.69/108.73 ! [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)))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__0,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__less__imp__less,axiom,
% 108.69/108.73 ! [V_n,V_m,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( 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)))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__imp__of__nat__less,axiom,
% 108.69/108.73 ! [V_n,V_m,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.73 => 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))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__less__iff,axiom,
% 108.69/108.73 ! [V_n_2,V_m_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__1,axiom,
% 108.69/108.73 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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 108.69/108.73 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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__le__iff,axiom,
% 108.69/108.73 ! [V_n_2,V_m_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_m_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__add,axiom,
% 108.69/108.73 ! [V_n,V_m,T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_succ__pred,axiom,
% 108.69/108.73 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__1,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_minus__Bit1,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Ints__of__nat,axiom,
% 108.69/108.73 ! [V_n_2,T_b] :
% 108.69/108.73 ( class_Rings_Oring__1(T_b)
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__power,axiom,
% 108.69/108.73 ! [V_n,V_m,T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__power,axiom,
% 108.69/108.73 ! [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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zpower__int,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 108.69/108.73 ! [V_A_2] :
% 108.69/108.73 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 108.69/108.73 <=> 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_inj__of__nat,axiom,
% 108.69/108.73 ! [T_b] :
% 108.69/108.73 ( class_Nat_Osemiring__char__0(T_b)
% 108.69/108.73 => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 108.69/108.73 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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_number__of__Bit1,axiom,
% 108.69/108.73 ! [V_w,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__le__0__conv,axiom,
% 108.69/108.73 ! [V_n_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_numeral__1__eq__1,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_semiring__norm_I110_J,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__Suc0__eq__1,axiom,
% 108.69/108.73 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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zless__iff__Suc__zadd,axiom,
% 108.69/108.73 ! [V_z_2,V_w_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 108.69/108.73 <=> ? [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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I29_J,axiom,
% 108.69/108.73 ! [V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I5_J,axiom,
% 108.69/108.73 ! [V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__zle__neg,axiom,
% 108.69/108.73 ! [V_m_2,V_n_2] :
% 108.69/108.73 ( 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))))
% 108.69/108.73 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.73 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__Suc,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_negative__zle__0,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_eq__special_I2_J,axiom,
% 108.69/108.73 ! [V_y_2,T_b] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 108.69/108.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_eq__special_I4_J,axiom,
% 108.69/108.73 ! [V_x_2,T_b] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 108.69/108.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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))))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_one__is__num__one,axiom,
% 108.69/108.73 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zdiff__int,axiom,
% 108.69/108.73 ! [V_m,V_n] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__numeral__1__eq__1,axiom,
% 108.69/108.73 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Numeral1__eq1__nat,axiom,
% 108.69/108.73 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__Suc,axiom,
% 108.69/108.73 ! [V_m,T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__diff,axiom,
% 108.69/108.73 ! [V_m,V_n,T_a] :
% 108.69/108.73 ( class_Rings_Oring__1(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 108.69/108.73 => 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)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_succ__def,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_iszero__Numeral0,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nats__0,axiom,
% 108.69/108.73 ! [T_b] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_b)
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nats__add,axiom,
% 108.69/108.73 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nats__1,axiom,
% 108.69/108.73 ! [T_b] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_b)
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__less__int__conv,axiom,
% 108.69/108.73 ! [V_n_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_numeral__3__eq__3,axiom,
% 108.69/108.73 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)))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_numeral__1__eq__Suc__0,axiom,
% 108.69/108.73 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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__zle__0__negative,axiom,
% 108.69/108.73 ! [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))))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_negative__zless__0,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 108.69/108.73 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))))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Suc3__eq__add__3,axiom,
% 108.69/108.73 ! [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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__0__less__iff,axiom,
% 108.69/108.73 ! [V_n_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_le__special_I2_J,axiom,
% 108.69/108.73 ! [V_y_2,T_b] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_le__special_I4_J,axiom,
% 108.69/108.73 ! [V_x_2,T_b] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__special_I4_J,axiom,
% 108.69/108.73 ! [V_x_2,T_b] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__special_I2_J,axiom,
% 108.69/108.73 ! [V_y_2,T_b] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 & class_Rings_Olinordered__idom(T_b) )
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_number__of__succ,axiom,
% 108.69/108.73 ! [V_k,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__special_I3_J,axiom,
% 108.69/108.73 ! [V_v,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__special_I2_J,axiom,
% 108.69/108.73 ! [V_w,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 108.69/108.73 ! [V_m,V_n] :
% 108.69/108.73 ( 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))
% 108.69/108.73 => 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)))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zdiff__int__split,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2,V_P_2] :
% 108.69/108.73 ( 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))))
% 108.69/108.73 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 108.69/108.73 => 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)))) )
% 108.69/108.73 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 108.69/108.73 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_eq__number__of__eq,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 108.69/108.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),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)))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_diff__special_I1_J,axiom,
% 108.69/108.73 ! [V_w,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Suc__nat__number__of__add,axiom,
% 108.69/108.73 ! [V_n,V_v] :
% 108.69/108.73 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => 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) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_one__code__numeral__code,axiom,
% 108.69/108.73 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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_sum__power2__gt__zero__iff,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
% 108.69/108.73 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.73 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__sum__power2__lt__zero,axiom,
% 108.69/108.73 ! [V_y,V_x,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.73 => ~ 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_sum__power2__ge__zero,axiom,
% 108.69/108.73 ! [V_y,V_x,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.73 => 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))))))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_sum__power2__le__zero__iff,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b),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_b)))
% 108.69/108.73 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.73 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 108.69/108.73 ! [V_B_2,V_A_2] :
% 108.69/108.73 ( V_A_2 = V_B_2
% 108.69/108.73 <=> 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2] :
% 108.69/108.73 ( 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)
% 108.69/108.73 <=> V_x_2 = V_y_2 ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 108.69/108.73 ! [V_B_2,V_A_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.73 <=> 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__int__eq,axiom,
% 108.69/108.73 ! [V_n_2,V_m_2] :
% 108.69/108.73 ( 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)
% 108.69/108.73 <=> V_m_2 = V_n_2 ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__neg__int,axiom,
% 108.69/108.73 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_neg__number__of__Bit0,axiom,
% 108.69/108.73 ! [V_w_2] :
% 108.69/108.73 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 108.69/108.73 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_code__numeral__zero__minus__one,axiom,
% 108.69/108.73 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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I48_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 108.69/108.73 <=> V_k_2 = V_l_2 ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I31_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__eq__int__code_I13_J,axiom,
% 108.69/108.73 ! [V_k2_2,V_k1_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I14_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__int__code_I13_J,axiom,
% 108.69/108.73 ! [V_k2_2,V_k1_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Bit0__Pls,axiom,
% 108.69/108.73 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I38_J,axiom,
% 108.69/108.73 ! [V_l_2] :
% 108.69/108.73 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 108.69/108.73 <=> c_Int_OPls = V_l_2 ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I44_J,axiom,
% 108.69/108.73 ! [V_k_2] :
% 108.69/108.73 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 108.69/108.73 <=> V_k_2 = c_Int_OPls ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I49_J,axiom,
% 108.69/108.73 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I50_J,axiom,
% 108.69/108.73 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Bit0__def,axiom,
% 108.69/108.73 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__Bit0__Bit0,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_diff__bin__simps_I7_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_minus__Bit0,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__neg__0,axiom,
% 108.69/108.73 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__neg__1,axiom,
% 108.69/108.73 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_bin__less__0__simps_I3_J,axiom,
% 108.69/108.73 ! [V_w_2] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I27_J,axiom,
% 108.69/108.73 ! [V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I21_J,axiom,
% 108.69/108.73 ! [V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__eq__int__code_I14_J,axiom,
% 108.69/108.73 ! [V_k2_2,V_k1_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I32_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I10_J,axiom,
% 108.69/108.73 ! [V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I4_J,axiom,
% 108.69/108.73 ! [V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__int__code_I15_J,axiom,
% 108.69/108.73 ! [V_k2_2,V_k1_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I16_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__Bit1__Bit0,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__Bit0__Bit1,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_diff__bin__simps_I3_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_diff__bin__simps_I9_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_diff__bin__simps_I10_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_pred__Bit0,axiom,
% 108.69/108.73 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_pred__Bit1,axiom,
% 108.69/108.73 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_iszero__number__of__Bit0,axiom,
% 108.69/108.73 ! [V_w_2,T_b] :
% 108.69/108.73 ( ( class_Int_Onumber__ring(T_b)
% 108.69/108.73 & class_Int_Oring__char__0(T_b) )
% 108.69/108.73 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 108.69/108.73 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_succ__Bit0,axiom,
% 108.69/108.73 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_succ__Bit1,axiom,
% 108.69/108.73 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__neg__eq__ge__0,axiom,
% 108.69/108.73 ! [V_x_2] :
% 108.69/108.73 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_neg__def,axiom,
% 108.69/108.73 ! [V_Z_2] :
% 108.69/108.73 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_not__neg__number__of__Pls,axiom,
% 108.69/108.73 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_neg__number__of__Bit1,axiom,
% 108.69/108.73 ! [V_w_2] :
% 108.69/108.73 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 108.69/108.73 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_neg__zminus__int,axiom,
% 108.69/108.73 ! [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))))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_number__of__Bit0,axiom,
% 108.69/108.73 ! [V_w,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I15_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__int__code_I14_J,axiom,
% 108.69/108.73 ! [V_k2_2,V_k1_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_rel__simps_I33_J,axiom,
% 108.69/108.73 ! [V_l_2,V_k_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__eq__int__code_I15_J,axiom,
% 108.69/108.73 ! [V_k2_2,V_k1_2] :
% 108.69/108.73 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 108.69/108.73 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_card__UNIV__bool,axiom,
% 108.69/108.73 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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_diff__bin__simps_I8_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__Bit1__Bit1,axiom,
% 108.69/108.73 ! [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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__code__numeral__code,axiom,
% 108.69/108.73 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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_neg__imp__number__of__eq__0,axiom,
% 108.69/108.73 ! [V_v] :
% 108.69/108.73 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__nat__number__of,axiom,
% 108.69/108.73 ! [V_v] :
% 108.69/108.73 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => 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) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_number__of1,axiom,
% 108.69/108.73 ! [V_n] :
% 108.69/108.73 ( 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)))
% 108.69/108.73 => ( 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))))
% 108.69/108.73 & 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)))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 108.69/108.73 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)))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_eq__nat__number__of,axiom,
% 108.69/108.73 ! [V_v_H_2,V_v_2] :
% 108.69/108.73 ( 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)
% 108.69/108.73 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 108.69/108.73 => 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))) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 108.69/108.73 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 108.69/108.73 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 108.69/108.73 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__number__of__add__left,axiom,
% 108.69/108.73 ! [V_k,V_v_H,V_v] :
% 108.69/108.73 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 108.69/108.73 => 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) ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_one__add__one__is__two,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__eq__power2,axiom,
% 108.69/108.73 ! [V_a_2,T_b] :
% 108.69/108.73 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 108.69/108.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b)
% 108.69/108.73 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__power2,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_numeral__2__eq__2,axiom,
% 108.69/108.73 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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_semiring__norm_I115_J,axiom,
% 108.69/108.73 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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 108.69/108.73 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))))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__2__eq__Suc,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_add__2__eq__Suc_H,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_one__power2,axiom,
% 108.69/108.73 ! [T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power2__minus,axiom,
% 108.69/108.73 ! [V_a,T_a] :
% 108.69/108.73 ( class_Rings_Oring__1(T_a)
% 108.69/108.73 => 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)))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_neg__number__of__pred__iff__0,axiom,
% 108.69/108.73 ! [V_v_2] :
% 108.69/108.73 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 108.69/108.73 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__1__add__1,axiom,
% 108.69/108.73 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))) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__le__power2,axiom,
% 108.69/108.73 ! [V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.73 => 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)))))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power2__le__imp__le,axiom,
% 108.69/108.73 ! [V_y,V_x,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( 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))))))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power2__eq__imp__eq,axiom,
% 108.69/108.73 ! [V_y,V_x,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( 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))))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.73 => V_x = V_y ) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__less__power2,axiom,
% 108.69/108.73 ! [V_a_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 108.69/108.73 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power2__less__0,axiom,
% 108.69/108.73 ! [V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.73 => ~ 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_sum__power2__eq__zero__iff,axiom,
% 108.69/108.73 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.73 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b),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_b)
% 108.69/108.73 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.73 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_less__2__cases,axiom,
% 108.69/108.73 ! [V_n] :
% 108.69/108.73 ( 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)))))
% 108.69/108.73 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.73 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__number__of__eq,axiom,
% 108.69/108.73 ! [V_v,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => 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) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => 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) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power2__eq__1__iff,axiom,
% 108.69/108.73 ! [V_a_2,T_b] :
% 108.69/108.73 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 108.69/108.73 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b)
% 108.69/108.73 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 108.69/108.73 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Suc__nat__number__of,axiom,
% 108.69/108.73 ! [V_v] :
% 108.69/108.73 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 108.69/108.73 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.73 => 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)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power2__less__imp__less,axiom,
% 108.69/108.73 ! [V_y,V_x,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.73 => ( 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))))))
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__minus1__odd,axiom,
% 108.69/108.73 ! [V_n,T_a] :
% 108.69/108.73 ( class_Rings_Oring__1(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_odd__power__less__zero,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.73 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.73 => 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))) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.73 => ( 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)))))
% 108.69/108.73 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power2__diff,axiom,
% 108.69/108.73 ! [V_y,V_x,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_power__minus1__even,axiom,
% 108.69/108.73 ! [V_n,T_a] :
% 108.69/108.73 ( class_Rings_Oring__1(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zero__le__even__power_H,axiom,
% 108.69/108.73 ! [V_n,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.73 => 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)))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_zmult__int,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_int__mult,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_of__nat__mult,axiom,
% 108.69/108.73 ! [V_n,V_m,T_a] :
% 108.69/108.73 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_mult__number__of__left,axiom,
% 108.69/108.73 ! [V_z,V_w,V_v,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_arith__simps_I32_J,axiom,
% 108.69/108.73 ! [V_w,V_v,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_number__of__mult,axiom,
% 108.69/108.73 ! [V_w,V_v,T_a] :
% 108.69/108.73 ( class_Int_Onumber__ring(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 108.69/108.73 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 108.69/108.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 108.69/108.73 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 108.69/108.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 108.69/108.73 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 108.69/108.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.73 => 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))) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 108.69/108.73 ! [V_rx,V_ly,V_lx,T_a] :
% 108.69/108.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 108.69/108.73 ! [V_rx,V_ly,V_lx,T_a] :
% 108.69/108.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 108.69/108.73 ! [V_ry,V_rx,V_lx,T_a] :
% 108.69/108.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 108.69/108.73 ! [V_ry,V_rx,V_lx,T_a] :
% 108.69/108.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 108.69/108.73 ! [V_b,V_a,T_a] :
% 108.69/108.73 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__mult__assoc,axiom,
% 108.69/108.73 ! [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)) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_nat__mult__commute,axiom,
% 108.69/108.73 ! [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) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 108.69/108.73 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.73 ( class_Groups_Oab__semigroup__mult(T_a)
% 108.69/108.73 => 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)) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_mult__left__idem,axiom,
% 108.69/108.73 ! [V_b,V_a,T_a] :
% 108.69/108.73 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 108.69/108.73 => 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) ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_mult__idem,axiom,
% 108.69/108.73 ! [V_x,T_a] :
% 108.69/108.73 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 108.69/108.73 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 108.69/108.73
% 108.69/108.73 fof(fact_times_Oidem,axiom,
% 108.69/108.73 ! [V_a,T_a] :
% 108.69/108.74 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 108.69/108.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__zero__left,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Rings_Omult__zero(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__zero__right,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Rings_Omult__zero(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__eq__0__iff,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Oring__no__zero__divisors(T_b)
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.74 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.74 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_no__zero__divisors,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ono__zero__divisors(T_a)
% 108.69/108.74 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.74 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_divisors__zero,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ono__zero__divisors(T_a)
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.74 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.74 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_combine__common__factor,axiom,
% 108.69/108.74 ! [V_c,V_b,V_e,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Osemiring(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__class_Odistrib,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 108.69/108.74 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_crossproduct__noteq,axiom,
% 108.69/108.74 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 108.69/108.74 => ( ( V_a_2 != V_b_2
% 108.69/108.74 & V_c_2 != V_d_2 )
% 108.69/108.74 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 108.69/108.74 ! [V_b,V_m,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_crossproduct__eq,axiom,
% 108.69/108.74 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 108.69/108.74 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_z_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_y_2))
% 108.69/108.74 <=> ( V_w_2 = V_x_2
% 108.69/108.74 | V_y_2 = V_z_2 ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult_Ocomm__neutral,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Groups_Ocomm__monoid__mult(T_a)
% 108.69/108.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__1__right,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__1,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Groups_Ocomm__monoid__mult(T_a)
% 108.69/108.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__1__left,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__cancel2,axiom,
% 108.69/108.74 ! [V_n_2,V_k_2,V_m_2] :
% 108.69/108.74 ( 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)
% 108.69/108.74 <=> ( V_m_2 = V_n_2
% 108.69/108.74 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__cancel1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( 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)
% 108.69/108.74 <=> ( V_m_2 = V_n_2
% 108.69/108.74 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__is__0,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2] :
% 108.69/108.74 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.74 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.74 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__0__right,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__0,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_minus__mult__right,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oring(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_minus__mult__left,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oring(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_minus__mult__commute,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oring(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_minus__mult__minus,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oring(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_square__eq__iff,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Oidom(T_b)
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_a_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_b_2)
% 108.69/108.74 <=> ( V_a_2 = V_b_2
% 108.69/108.74 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_Suc__mult__cancel1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( 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)
% 108.69/108.74 <=> V_m_2 = V_n_2 ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_add__mult__distrib2,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_add__mult__distrib,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__mult__distrib,axiom,
% 108.69/108.74 ! [V_n,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Groups_Ocomm__monoid__mult(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__commutes,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 108.69/108.74 ! [V_q,V_y,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_le__square,axiom,
% 108.69/108.74 ! [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))) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_le__cube,axiom,
% 108.69/108.74 ! [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)))) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__le__mono1,axiom,
% 108.69/108.74 ! [V_k,V_j,V_i] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 108.69/108.74 => 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__le__mono2,axiom,
% 108.69/108.74 ! [V_k,V_j,V_i] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 108.69/108.74 => 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__le__mono,axiom,
% 108.69/108.74 ! [V_l,V_k,V_j,V_i] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__Pls,axiom,
% 108.69/108.74 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zadd__zmult__distrib,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zadd__zmult__distrib2,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__mult,axiom,
% 108.69/108.74 ! [V_n,V_m,V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 108.69/108.74 ! [V_q,V_p,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_times__numeral__code_I5_J,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__Bit0,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_diff__mult__distrib,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_diff__mult__distrib2,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmult__1__right,axiom,
% 108.69/108.74 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmult__1,axiom,
% 108.69/108.74 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiff__zmult__distrib2,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiff__zmult__distrib,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmult__zminus,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__mult__eq__1__iff,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2] :
% 108.69/108.74 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 108.69/108.74 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 108.69/108.74 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__mult__1__right,axiom,
% 108.69/108.74 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__1__eq__mult__iff,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2] :
% 108.69/108.74 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 108.69/108.74 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 108.69/108.74 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__mult__1,axiom,
% 108.69/108.74 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zpower__zpower,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_sgn__times,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_fun__left__comm,axiom,
% 108.69/108.74 ! [T_b] :
% 108.69/108.74 ( class_Groups_Oab__semigroup__mult(T_b)
% 108.69/108.74 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__nat__number__of,axiom,
% 108.69/108.74 ! [V_v_H,V_v] :
% 108.69/108.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.74 => 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) )
% 108.69/108.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.74 => 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)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__number__of__mult__left,axiom,
% 108.69/108.74 ! [V_k,V_v_H,V_v] :
% 108.69/108.74 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.74 => 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) )
% 108.69/108.74 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 108.69/108.74 => 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) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_split__mult__neg__le,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__cancel__semiring(T_a)
% 108.69/108.74 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 108.69/108.74 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_split__mult__pos__le,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__ring(T_a)
% 108.69/108.74 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 108.69/108.74 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__mono,axiom,
% 108.69/108.74 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__semiring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__mono_H,axiom,
% 108.69/108.74 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__semiring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__left__mono__neg,axiom,
% 108.69/108.74 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__ring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__right__mono__neg,axiom,
% 108.69/108.74 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__ring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__mult__left__mono,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__comm__semiring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__left__mono,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__semiring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__right__mono,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__semiring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__nonpos__nonpos,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__ring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__nonpos__nonneg,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__cancel__semiring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__nonneg__nonpos2,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__cancel__semiring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__nonneg__nonpos,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__cancel__semiring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__nonneg__nonneg,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oordered__cancel__semiring(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__le__0__iff,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.74 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 108.69/108.74 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zero__le__mult__iff,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)))
% 108.69/108.74 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 108.69/108.74 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zero__le__square,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__ring(T_a)
% 108.69/108.74 => 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_not__square__less__zero,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__ring(T_a)
% 108.69/108.74 => ~ 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__cancel__right__disj,axiom,
% 108.69/108.74 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 108.69/108.74 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 108.69/108.74 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__cancel__left__disj,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 108.69/108.74 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 108.69/108.74 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__cancel__left__pos,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__pos__pos,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__pos__neg,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__pos__neg2,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zero__less__mult__pos,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zero__less__mult__pos2,axiom,
% 108.69/108.74 ! [V_a,V_b,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__cancel__left__neg,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__neg__pos,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__neg__neg,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__strict__right__mono,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__strict__left__mono,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__mult__strict__left__mono,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__strict__right__mono__neg,axiom,
% 108.69/108.74 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__strict__left__mono__neg,axiom,
% 108.69/108.74 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_sum__squares__eq__zero__iff,axiom,
% 108.69/108.74 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2)) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.74 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.74 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_add__scale__eq__noteq,axiom,
% 108.69/108.74 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 108.69/108.74 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 108.69/108.74 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.74 => ( ( V_a = V_b
% 108.69/108.74 & V_c != V_d )
% 108.69/108.74 => 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)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_less__1__mult,axiom,
% 108.69/108.74 ! [V_n,V_m,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_eq__add__iff1,axiom,
% 108.69/108.74 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Oring(T_b)
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 108.69/108.74 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_eq__add__iff2,axiom,
% 108.69/108.74 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Oring(T_b)
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)
% 108.69/108.74 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_left__distrib__number__of,axiom,
% 108.69/108.74 ! [V_v,V_b,V_a,T_b] :
% 108.69/108.74 ( ( class_Int_Onumber(T_b)
% 108.69/108.74 & class_Rings_Osemiring(T_b) )
% 108.69/108.74 => 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_right__distrib__number__of,axiom,
% 108.69/108.74 ! [V_c,V_b,V_v,T_b] :
% 108.69/108.74 ( ( class_Int_Onumber(T_b)
% 108.69/108.74 & class_Rings_Osemiring(T_b) )
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 108.69/108.74 ! [V_m,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 108.69/108.74 ! [V_a,V_m,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 108.69/108.74 ! [V_m,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_right__diff__distrib__number__of,axiom,
% 108.69/108.74 ! [V_c,V_b,V_v,T_b] :
% 108.69/108.74 ( ( class_Int_Onumber(T_b)
% 108.69/108.74 & class_Rings_Oring(T_b) )
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_left__diff__distrib__number__of,axiom,
% 108.69/108.74 ! [V_v,V_b,V_a,T_b] :
% 108.69/108.74 ( ( class_Int_Onumber(T_b)
% 108.69/108.74 & class_Rings_Oring(T_b) )
% 108.69/108.74 => 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 108.69/108.74 ! [V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__ring__1(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_square__eq__1__iff,axiom,
% 108.69/108.74 ! [V_x_2,T_b] :
% 108.69/108.74 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 108.69/108.74 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 108.69/108.74 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__eq__1__iff,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2] :
% 108.69/108.74 ( 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))
% 108.69/108.74 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 108.69/108.74 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__0__less__mult__iff,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__cancel1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__cancel2,axiom,
% 108.69/108.74 ! [V_n_2,V_k_2,V_m_2] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 108.69/108.74 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__mono1,axiom,
% 108.69/108.74 ! [V_k,V_j,V_i] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__mono2,axiom,
% 108.69/108.74 ! [V_k,V_j,V_i] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_Suc__mult__less__cancel1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__Suc2,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__Suc,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Power_Opower(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 108.69/108.74 ! [V_q,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 108.69/108.74 ! [V_q,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 108.69/108.74 ! [V_q,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 108.69/108.74 ! [V_y,V_x] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__Suc__right,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__Suc,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmult__zless__mono2,axiom,
% 108.69/108.74 ! [V_k,V_j,V_i] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__add,axiom,
% 108.69/108.74 ! [V_n,V_m,V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 108.69/108.74 ! [V_q,V_p,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_Suc__mult__le__cancel1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__eq__self__implies__10,axiom,
% 108.69/108.74 ! [V_n,V_m] :
% 108.69/108.74 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 108.69/108.74 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 108.69/108.74 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_Ints__mult,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Oring__1(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Int_Oring__1__class_OInts(T_b))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zpower__zadd__distrib,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_Nats__mult,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Osemiring__1(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 108.69/108.74 ! [V_n,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__left__le__imp__le,axiom,
% 108.69/108.74 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__right__le__imp__le,axiom,
% 108.69/108.74 ! [V_b,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__imp__less__left,axiom,
% 108.69/108.74 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__left__less__imp__less,axiom,
% 108.69/108.74 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring(T_a)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__imp__less__right,axiom,
% 108.69/108.74 ! [V_b,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__right__less__imp__less,axiom,
% 108.69/108.74 ! [V_b,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring(T_a)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__le__less__imp__less,axiom,
% 108.69/108.74 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__less__le__imp__less,axiom,
% 108.69/108.74 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__strict__mono_H,axiom,
% 108.69/108.74 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__strict__mono,axiom,
% 108.69/108.74 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.74 => 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))) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__le__cancel__left__neg,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__le__cancel__left__pos,axiom,
% 108.69/108.74 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_sum__squares__le__zero__iff,axiom,
% 108.69/108.74 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.74 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.74 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_sum__squares__ge__zero,axiom,
% 108.69/108.74 ! [V_y,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__ring(T_a)
% 108.69/108.74 => 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)))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_sum__squares__gt__zero__iff,axiom,
% 108.69/108.74 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.74 ( class_Rings_Olinordered__ring__strict(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_y_2),V_y_2))))
% 108.69/108.74 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.74 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_not__sum__squares__lt__zero,axiom,
% 108.69/108.74 ! [V_y,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__ring(T_a)
% 108.69/108.74 => ~ 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__left__le__one__le,axiom,
% 108.69/108.74 ! [V_y,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 108.69/108.74 => 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)) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__right__le__one__le,axiom,
% 108.69/108.74 ! [V_y,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 108.69/108.74 => 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)) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 108.69/108.74 ! [V_n,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__odd__eq,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => 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))))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_le__add__iff1,axiom,
% 108.69/108.74 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Oordered__ring(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_le__add__iff2,axiom,
% 108.69/108.74 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Oordered__ring(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_less__add__iff1,axiom,
% 108.69/108.74 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Oordered__ring(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_less__add__iff2,axiom,
% 108.69/108.74 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 108.69/108.74 ( class_Rings_Oordered__ring(T_b)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__gt1__lemma,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 108.69/108.74 => 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)))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__less__power__Suc,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 108.69/108.74 => 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)))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_n__less__m__mult__n,axiom,
% 108.69/108.74 ! [V_m,V_n] :
% 108.69/108.74 ( 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))
% 108.69/108.74 => ( 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))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_n__less__n__mult__m,axiom,
% 108.69/108.74 ! [V_m,V_n] :
% 108.69/108.74 ( 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))
% 108.69/108.74 => ( 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))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_one__less__mult,axiom,
% 108.69/108.74 ! [V_m,V_n] :
% 108.69/108.74 ( 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))
% 108.69/108.74 => ( 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))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__minus,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__numeral__1__right,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Int_Onumber__ring(T_a)
% 108.69/108.74 => 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 ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__numeral__1,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Int_Onumber__ring(T_a)
% 108.69/108.74 => 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 ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_one__le__mult__iff,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 <=> ( 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))
% 108.69/108.74 & 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)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__le__cancel2,axiom,
% 108.69/108.74 ! [V_n_2,V_k_2,V_m_2] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__le__cancel1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_minus__number__of__mult,axiom,
% 108.69/108.74 ! [V_z,V_w,T_a] :
% 108.69/108.74 ( class_Int_Onumber__ring(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_pos__zmult__eq__1__iff,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 108.69/108.74 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 108.69/108.74 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__Bit1,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_convex__bound__le,axiom,
% 108.69/108.74 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__1(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 108.69/108.74 => 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)) ) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__Suc__less,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semidom(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 108.69/108.74 => 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))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_double__number__of__Bit0,axiom,
% 108.69/108.74 ! [V_w,T_a] :
% 108.69/108.74 ( class_Int_Onumber__ring(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmult__zless__mono2__lemma,axiom,
% 108.69/108.74 ! [V_k,V_j,V_i] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power3__eq__cube,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__eq__if,axiom,
% 108.69/108.74 ! [V_n,V_m] :
% 108.69/108.74 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.74 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 108.69/108.74 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.74 => 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)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__eq__if,axiom,
% 108.69/108.74 ! [V_p,V_m] :
% 108.69/108.74 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.74 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 108.69/108.74 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.74 => 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)))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_convex__bound__lt,axiom,
% 108.69/108.74 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 108.69/108.74 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 108.69/108.74 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 108.69/108.74 => 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)) ) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__2__right,axiom,
% 108.69/108.74 ! [V_z,T_a] :
% 108.69/108.74 ( class_Int_Onumber__ring(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mult__2,axiom,
% 108.69/108.74 ! [V_z,T_a] :
% 108.69/108.74 ( class_Int_Onumber__ring(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 108.69/108.74 ! [V_x,T_a] :
% 108.69/108.74 ( class_Rings_Ocomm__semiring__1(T_a)
% 108.69/108.74 => 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)))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power2__eq__square,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__mult__2__right,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__mult__2,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__even__eq,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Groups_Omonoid__mult(T_a)
% 108.69/108.74 => 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)))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power2__eq__square__number__of,axiom,
% 108.69/108.74 ! [V_w,T_b] :
% 108.69/108.74 ( ( class_Groups_Omonoid__mult(T_b)
% 108.69/108.74 & class_Int_Onumber(T_b) )
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power__minus__even,axiom,
% 108.69/108.74 ! [V_n,V_a,T_a] :
% 108.69/108.74 ( class_Rings_Oring__1(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_power2__sum,axiom,
% 108.69/108.74 ! [V_y,V_x,T_a] :
% 108.69/108.74 ( class_Int_Onumber__ring(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__less__add__iff1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 108.69/108.74 => ( 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)))
% 108.69/108.74 <=> 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)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__less__add__iff2,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 108.69/108.74 => ( 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)))
% 108.69/108.74 <=> 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_self__quotient__aux1,axiom,
% 108.69/108.74 ! [V_q,V_r,V_a] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.74 => ( 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))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_self__quotient__aux2,axiom,
% 108.69/108.74 ! [V_q,V_r,V_a] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.74 => ( 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))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__le__add__iff1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 108.69/108.74 => ( 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)))
% 108.69/108.74 <=> 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)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__diff__add__eq1,axiom,
% 108.69/108.74 ! [V_n,V_m,V_u,V_i,V_j] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmult__assoc,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmult__commute,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( 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)
% 108.69/108.74 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.74 | V_m_2 = V_n_2 ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_left__add__mult__distrib,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__mult__less__cancel1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 108.69/108.74 => ( 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)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__mult__eq__cancel1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 108.69/108.74 => ( 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)
% 108.69/108.74 <=> V_m_2 = V_n_2 ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__mult__le__cancel1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_k_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 108.69/108.74 => ( 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)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 108.69/108.74 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 108.69/108.74 ( 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)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_unique__quotient__lemma__neg,axiom,
% 108.69/108.74 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__mono2__lemma,axiom,
% 108.69/108.74 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 108.69/108.74 ( 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)
% 108.69/108.74 => ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_unique__quotient__lemma,axiom,
% 108.69/108.74 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_q__neg__lemma,axiom,
% 108.69/108.74 ! [V_r_H,V_q_H,V_b_H] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_q__pos__lemma,axiom,
% 108.69/108.74 ! [V_r_H,V_q_H,V_b_H] :
% 108.69/108.74 ( 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)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 108.69/108.74 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__eq__add__iff2,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 108.69/108.74 => ( 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)
% 108.69/108.74 <=> 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) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__diff__add__eq2,axiom,
% 108.69/108.74 ! [V_n,V_m,V_u,V_j,V_i] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__le__add__iff2,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 108.69/108.74 => ( 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)))
% 108.69/108.74 <=> 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__eq__add__iff1,axiom,
% 108.69/108.74 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 108.69/108.74 => ( 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)
% 108.69/108.74 <=> 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 ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_nat__of__aux__code,axiom,
% 108.69/108.74 ! [V_n,V_i] :
% 108.69/108.74 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 108.69/108.74 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 108.69/108.74 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 108.69/108.74 => 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)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__number__of__Bit1,axiom,
% 108.69/108.74 ! [V_v,V_w] :
% 108.69/108.74 ( ( 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)))
% 108.69/108.74 => 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)) )
% 108.69/108.74 & ( ~ 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)))
% 108.69/108.74 => 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)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_neg__zmod__mult__2,axiom,
% 108.69/108.74 ! [V_b,V_a] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_pos__zmod__mult__2,axiom,
% 108.69/108.74 ! [V_b,V_a] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.74 => 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_neg__zdiv__mult__2,axiom,
% 108.69/108.74 ! [V_b,V_a] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__zmod__equality2,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__mod__equality,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__zmod__equality,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__mod__equality2,axiom,
% 108.69/108.74 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__div__equality,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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 ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__div__equality2,axiom,
% 108.69/108.74 ! [V_a,V_b,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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 ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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 ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__zmult1__eq,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zdiv__equality,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__diff__cong,axiom,
% 108.69/108.74 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Oring__div(T_a)
% 108.69/108.74 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 108.69/108.74 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 108.69/108.74 => 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) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__diff__eq,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Oring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__diff__left__eq,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Oring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__diff__right__eq,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Oring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zdiv__equality_H,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmult__div__cancel,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__right__eq,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__left__eq,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__eq,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__mult1,axiom,
% 108.69/108.74 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__mult2,axiom,
% 108.69/108.74 ! [V_b,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__simps_I4_J,axiom,
% 108.69/108.74 ! [V_b,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__cong,axiom,
% 108.69/108.74 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 108.69/108.74 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 108.69/108.74 => 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) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__0,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__by__0,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__self,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zdiv__trivial,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__div__trivial,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_DIVISION__BY__ZERO,axiom,
% 108.69/108.74 ! [V_a] :
% 108.69/108.74 ( 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)
% 108.69/108.74 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__zero,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mod__trivial,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__minus__cong,axiom,
% 108.69/108.74 ! [V_a_H,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Oring__div(T_a)
% 108.69/108.74 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 108.69/108.74 => 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) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__minus__eq,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Oring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__add__self2,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__add__self1,axiom,
% 108.69/108.74 ! [V_a,V_b,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__add__right__eq,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__add__left__eq,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__add__eq,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__zadd1__eq,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__simps_I2_J,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__simps_I1_J,axiom,
% 108.69/108.74 ! [V_b,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__add__cong,axiom,
% 108.69/108.74 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 108.69/108.74 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 108.69/108.74 => 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) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zero,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__self,axiom,
% 108.69/108.74 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__zminus__zminus,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__zminus2,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__simps_I3_J,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zmult1__eq,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiff__zmod__left,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiff__zmod__right,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zminus__zmod,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zminus__zminus,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zminus2,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__by__0,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__0,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__by__1,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zpower__zmod,axiom,
% 108.69/108.74 ! [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) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__self1__is__0,axiom,
% 108.69/108.74 ! [V_a,V_b,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__self2__is__0,axiom,
% 108.69/108.74 ! [V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zmult2__eq,axiom,
% 108.69/108.74 ! [V_b,V_a,V_c] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__self1,axiom,
% 108.69/108.74 ! [V_b,V_c,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__mult__self2,axiom,
% 108.69/108.74 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => 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) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_mod__by__1,axiom,
% 108.69/108.74 ! [V_a,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__zminus1__eq__if,axiom,
% 108.69/108.74 ! [V_a,V_b] :
% 108.69/108.74 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.74 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.74 => 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)) )
% 108.69/108.74 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.74 => 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)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__zminus2__eq__if,axiom,
% 108.69/108.74 ! [V_a,V_b] :
% 108.69/108.74 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.74 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.74 => 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)) )
% 108.69/108.74 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.74 => 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)) ) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 108.69/108.74 ! [V_y,V_x] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__neg__pos__less0,axiom,
% 108.69/108.74 ! [V_b,V_a] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 108.69/108.74 ! [V_a_2,V_b_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.74 => ( 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)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 108.69/108.74 ! [V_a_2,V_b_2] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 108.69/108.74 => ( 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)))
% 108.69/108.74 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__self,axiom,
% 108.69/108.74 ! [V_a] :
% 108.69/108.74 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.74 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 108.69/108.74 ! [V_y,V_x] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.74 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.74 => 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))) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__le__nonneg__dividend,axiom,
% 108.69/108.74 ! [V_k,V_m] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_neg__mod__bound,axiom,
% 108.69/108.74 ! [V_a,V_b] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.74 => 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))) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_pos__mod__bound,axiom,
% 108.69/108.74 ! [V_a,V_b] :
% 108.69/108.74 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 108.69/108.74 => 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)) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zdiv__number__of__Bit0,axiom,
% 108.69/108.74 ! [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)) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__eq__0__iff,axiom,
% 108.69/108.74 ! [V_d_2,V_m_2] :
% 108.69/108.74 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.74 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zminus1__not__zero,axiom,
% 108.69/108.74 ! [V_l,V_k] :
% 108.69/108.74 ( 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)
% 108.69/108.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_zmod__zminus2__not__zero,axiom,
% 108.69/108.74 ! [V_l,V_k] :
% 108.69/108.74 ( 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)
% 108.69/108.74 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__mult__mult1,axiom,
% 108.69/108.74 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.74 => 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) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__mult__mult2,axiom,
% 108.69/108.74 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.74 => 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) ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__mult__self1__is__id,axiom,
% 108.69/108.74 ! [V_a,V_b,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.74 => 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 ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__mult__self2__is__id,axiom,
% 108.69/108.74 ! [V_a,V_b,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.74 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.74 => 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 ) ) ).
% 108.69/108.74
% 108.69/108.74 fof(fact_div__mult__mult1__if,axiom,
% 108.69/108.74 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.74 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.75 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.75 => 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) )
% 108.69/108.75 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.75 => 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) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__self,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.75 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.75 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_split__neg__lemma,axiom,
% 108.69/108.75 ! [V_n_2,V_P_2,V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> ! [B_i,B_j] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 & 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) )
% 108.69/108.75 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_split__pos__lemma,axiom,
% 108.69/108.75 ! [V_n_2,V_P_2,V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> ! [B_i,B_j] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 108.69/108.75 & 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) )
% 108.69/108.75 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zdiv__eq__0__iff,axiom,
% 108.69/108.75 ! [V_k_2,V_i_2] :
% 108.69/108.75 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 108.69/108.75 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 108.69/108.75 ! [V_a_2,V_b_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 108.69/108.75 ! [V_i_2,V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 108.69/108.75 ! [V_b_2,V_a_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zdiv__mono2,axiom,
% 108.69/108.75 ! [V_b,V_b_H,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 108.69/108.75 => 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__nonneg__neg__le0,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__pos__pos__trivial,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 108.69/108.75 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 108.69/108.75 ! [V_a_2,V_b_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__nonpos__pos__le0,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zdiv__mono2__neg,axiom,
% 108.69/108.75 ! [V_b,V_b_H,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 108.69/108.75 => 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__neg__neg__trivial,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 108.69/108.75 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zdiv__mono1,axiom,
% 108.69/108.75 ! [V_b,V_a_H,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zdiv__mono1__neg,axiom,
% 108.69/108.75 ! [V_b,V_a_H,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_int__div__less__self,axiom,
% 108.69/108.75 ! [V_k,V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zdiv__zmult2__eq,axiom,
% 108.69/108.75 ! [V_b,V_a,V_c] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_pos__mod__sign,axiom,
% 108.69/108.75 ! [V_a,V_b] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 108.69/108.75 => 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_pos__mod__conj,axiom,
% 108.69/108.75 ! [V_a,V_b] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 & 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__pos__pos__trivial,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 108.69/108.75 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_neg__mod__sign,axiom,
% 108.69/108.75 ! [V_a,V_b] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_neg__mod__conj,axiom,
% 108.69/108.75 ! [V_a,V_b] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 & 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__neg__neg__trivial,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 108.69/108.75 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmod__zminus2__eq__if,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 => 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) )
% 108.69/108.75 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 => 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) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmod__zminus1__eq__if,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 => 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) )
% 108.69/108.75 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__mult__self1,axiom,
% 108.69/108.75 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.75 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.75 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__mult__self2,axiom,
% 108.69/108.75 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.75 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.75 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__add__self1,axiom,
% 108.69/108.75 ! [V_a,V_b,T_a] :
% 108.69/108.75 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.75 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__add__self2,axiom,
% 108.69/108.75 ! [V_a,V_b,T_a] :
% 108.69/108.75 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.75 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__pos__neg__trivial,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 => 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) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_split__zdiv,axiom,
% 108.69/108.75 ! [V_k_2,V_n_2,V_P_2] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 108.69/108.75 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 108.69/108.75 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 108.69/108.75 => ! [B_i] :
% 108.69/108.75 ( ? [B_j] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 108.69/108.75 & 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) )
% 108.69/108.75 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 108.69/108.75 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ! [B_i] :
% 108.69/108.75 ( ? [B_j] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 & 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) )
% 108.69/108.75 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_divmod__int__rel__div__eq,axiom,
% 108.69/108.75 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 108.69/108.75 ( 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)
% 108.69/108.75 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 108.69/108.75 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_split__zmod,axiom,
% 108.69/108.75 ! [V_k_2,V_n_2,V_P_2] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 108.69/108.75 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 108.69/108.75 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 108.69/108.75 => ! [B_i,B_j] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 108.69/108.75 & 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) )
% 108.69/108.75 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 108.69/108.75 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ! [B_i,B_j] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 & 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) )
% 108.69/108.75 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmult2__lemma__aux3,axiom,
% 108.69/108.75 ! [V_q,V_b,V_r,V_c] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 108.69/108.75 => 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmult2__lemma__aux4,axiom,
% 108.69/108.75 ! [V_q,V_b,V_r,V_c] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 108.69/108.75 => 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmult2__lemma__aux1,axiom,
% 108.69/108.75 ! [V_q,V_r,V_b,V_c] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmult2__lemma__aux2,axiom,
% 108.69/108.75 ! [V_q,V_r,V_b,V_c] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_divmod__int__rel__mod__eq,axiom,
% 108.69/108.75 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 108.69/108.75 ( 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)
% 108.69/108.75 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 108.69/108.75 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmod__number__of__Bit0,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zdiv__number__of__Bit1,axiom,
% 108.69/108.75 ! [V_v,V_w] :
% 108.69/108.75 ( ( 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)))
% 108.69/108.75 => 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)) )
% 108.69/108.75 & ( ~ 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)))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_int__power__div__base,axiom,
% 108.69/108.75 ! [V_k,V_m] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 108.69/108.75 => 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)))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_pos__zdiv__mult__2,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_z3div__def,axiom,
% 108.69/108.75 ! [V_k,V_l] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 108.69/108.75 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_z3mod__def,axiom,
% 108.69/108.75 ! [V_k,V_l] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 108.69/108.75 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__nat__double,axiom,
% 108.69/108.75 ! [V_x,T_a] :
% 108.69/108.75 ( class_Rings_Osemiring__1(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_power__power__power,axiom,
% 108.69/108.75 ! [T_b] :
% 108.69/108.75 ( class_Power_Opower(T_b)
% 108.69/108.75 => c_Power_Opower__class_Opower(T_b) = c_Power_Opower_Opower(T_b,c_Groups_Oone__class_Oone(T_b),c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_power__m1__odd,axiom,
% 108.69/108.75 ! [V_n,T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__mult1__eq,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__mult2__eq,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Divides_Omod__div__equality_H,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mult__div__cancel,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__mod__equality_H,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__add1__eq,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__le__mono,axiom,
% 108.69/108.75 ! [V_k,V_n,V_m] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__le__dividend,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__mult2__eq,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__less,axiom,
% 108.69/108.75 ! [V_n,V_m] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__less__eq__dividend,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__mult__distrib2,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__mult__distrib,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__int,axiom,
% 108.69/108.75 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I24_J,axiom,
% 108.69/108.75 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I7_J,axiom,
% 108.69/108.75 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I40_J,axiom,
% 108.69/108.75 c_Int_OMin != c_Int_OPls ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I37_J,axiom,
% 108.69/108.75 c_Int_OPls != c_Int_OMin ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Bit1__Min,axiom,
% 108.69/108.75 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I43_J,axiom,
% 108.69/108.75 ! [V_l_2] :
% 108.69/108.75 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 108.69/108.75 <=> c_Int_OMin = V_l_2 ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I47_J,axiom,
% 108.69/108.75 ! [V_k_2] :
% 108.69/108.75 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 108.69/108.75 <=> V_k_2 = c_Int_OMin ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I42_J,axiom,
% 108.69/108.75 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I45_J,axiom,
% 108.69/108.75 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__div__distrib,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__mod__distrib,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__1,axiom,
% 108.69/108.75 ! [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 ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__less,axiom,
% 108.69/108.75 ! [V_n,V_m] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__mult__div__cancel__disj,axiom,
% 108.69/108.75 ! [V_n,V_m,V_k] :
% 108.69/108.75 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.75 => 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) )
% 108.69/108.75 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.75 => 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) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 108.69/108.75 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__0,axiom,
% 108.69/108.75 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__1,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__Suc,axiom,
% 108.69/108.75 ! [V_n,V_m] :
% 108.69/108.75 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 108.69/108.75 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 108.69/108.75 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__less__divisor,axiom,
% 108.69/108.75 ! [V_m,V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_ex__nat,axiom,
% 108.69/108.75 ! [V_P_2] :
% 108.69/108.75 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 108.69/108.75 <=> ? [B_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 108.69/108.75 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_all__nat,axiom,
% 108.69/108.75 ! [V_P_2] :
% 108.69/108.75 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 108.69/108.75 <=> ! [B_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 108.69/108.75 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 108.69/108.75 ! [V_y_2,V_x_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 108.69/108.75 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 108.69/108.75 <=> V_x_2 = V_y_2 ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_eq__nat__nat__iff,axiom,
% 108.69/108.75 ! [V_z_H_2,V_z_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 108.69/108.75 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 108.69/108.75 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__eq__0__iff,axiom,
% 108.69/108.75 ! [V_d_2,V_m_2] :
% 108.69/108.75 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.75 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__geq,axiom,
% 108.69/108.75 ! [V_n,V_m] :
% 108.69/108.75 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__if,axiom,
% 108.69/108.75 ! [V_n,V_m] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => 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) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__mult__self3,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_le__mod__geq,axiom,
% 108.69/108.75 ! [V_m,V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zdiv__int,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__number__of,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__number__of__def,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_bin__less__0__simps_I2_J,axiom,
% 108.69/108.75 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I20_J,axiom,
% 108.69/108.75 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I23_J,axiom,
% 108.69/108.75 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I30_J,axiom,
% 108.69/108.75 ! [V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I26_J,axiom,
% 108.69/108.75 ! [V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I3_J,axiom,
% 108.69/108.75 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I6_J,axiom,
% 108.69/108.75 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I13_J,axiom,
% 108.69/108.75 ! [V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I9_J,axiom,
% 108.69/108.75 ! [V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I28_J,axiom,
% 108.69/108.75 ! [V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 108.69/108.75 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I8_J,axiom,
% 108.69/108.75 ! [V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmod__int,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_eq__number__of__Pls__Min,axiom,
% 108.69/108.75 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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_neg__nat,axiom,
% 108.69/108.75 ! [V_z] :
% 108.69/108.75 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 108.69/108.75 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Int_OMin__def,axiom,
% 108.69/108.75 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mult__Min,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_not__neg__nat,axiom,
% 108.69/108.75 ! [V_z] :
% 108.69/108.75 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 108.69/108.75 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_neg__number__of__Min,axiom,
% 108.69/108.75 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 108.69/108.75 ! [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 ).
% 108.69/108.75
% 108.69/108.75 fof(fact_pred__Pls,axiom,
% 108.69/108.75 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 108.69/108.75
% 108.69/108.75 fof(fact_add__Min,axiom,
% 108.69/108.75 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_add__Min__right,axiom,
% 108.69/108.75 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_pred__Min,axiom,
% 108.69/108.75 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nonzero__number__of__Min,axiom,
% 108.69/108.75 ! [T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_succ__Min,axiom,
% 108.69/108.75 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__nat__number__of,axiom,
% 108.69/108.75 ! [V_v_H,V_v] :
% 108.69/108.75 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.75 => 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) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__nat__number__of,axiom,
% 108.69/108.75 ! [V_v_H,V_v] :
% 108.69/108.75 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.75 => 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) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.75 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 108.69/108.75 => 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) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 108.69/108.75 => 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))) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_diff__bin__simps_I2_J,axiom,
% 108.69/108.75 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_one__div__nat__number__of,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 108.69/108.75 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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__le__mono2,axiom,
% 108.69/108.75 ! [V_k,V_n,V_m] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__mult__div__cancel1,axiom,
% 108.69/108.75 ! [V_n,V_m,V_k] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__mult__self1__is__m,axiom,
% 108.69/108.75 ! [V_m,V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.75 => 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 ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__mult__self__is__m,axiom,
% 108.69/108.75 ! [V_m,V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.75 => 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 ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__less__dividend,axiom,
% 108.69/108.75 ! [V_m,V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__0__iff,axiom,
% 108.69/108.75 ! [V_i_2] :
% 108.69/108.75 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__le__0,axiom,
% 108.69/108.75 ! [V_z] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__mono__iff,axiom,
% 108.69/108.75 ! [V_w_2,V_z_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zless__nat__conj,axiom,
% 108.69/108.75 ! [V_z_2,V_w_2] :
% 108.69/108.75 ( 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)))
% 108.69/108.75 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__le__divisor,axiom,
% 108.69/108.75 ! [V_m,V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 108.69/108.75 ! [V_y_2,V_x_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__1,axiom,
% 108.69/108.75 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__mult__self4,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__0__le,axiom,
% 108.69/108.75 ! [V_z] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 108.69/108.75 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_int__eq__iff,axiom,
% 108.69/108.75 ! [V_z_2,V_m_2] :
% 108.69/108.75 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 108.69/108.75 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_int__nat__eq,axiom,
% 108.69/108.75 ! [V_z] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 108.69/108.75 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 108.69/108.75 => 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) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mult__minus1__right,axiom,
% 108.69/108.75 ! [V_z,T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mult__minus1,axiom,
% 108.69/108.75 ! [V_z,T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zless__nat__eq__int__zless,axiom,
% 108.69/108.75 ! [V_z_2,V_m_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 108.69/108.75 <=> 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_arith__simps_I31_J,axiom,
% 108.69/108.75 ! [T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_number__of__Min,axiom,
% 108.69/108.75 ! [T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__zminus__int,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I25_J,axiom,
% 108.69/108.75 ! [V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_rel__simps_I11_J,axiom,
% 108.69/108.75 ! [V_k_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmod__minus1__right,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_diff__bin__simps_I4_J,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_minus__Min,axiom,
% 108.69/108.75 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmult__eq__1__iff,axiom,
% 108.69/108.75 ! [V_n_2,V_m_2] :
% 108.69/108.75 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 108.69/108.75 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 108.69/108.75 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 108.69/108.75 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 108.69/108.75 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 108.69/108.75 ! [V_n,V_m] :
% 108.69/108.75 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 108.69/108.75 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 108.69/108.75 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_diff__bin__simps_I5_J,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_diff__bin__simps_I6_J,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_power_Opower_Opower__0,axiom,
% 108.69/108.75 ! [V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,V_one_2,V_times_2),V_a_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_one_2 ).
% 108.69/108.75
% 108.69/108.75 fof(fact_power_Opower_Opower__Suc,axiom,
% 108.69/108.75 ! [V_n_2,V_a_2,V_times_2,V_one_2,T_b] : hAPP(hAPP(c_Power_Opower_Opower(T_b,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_b,V_one_2,V_times_2),V_a_2),V_n_2)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zdiv__minus1__right,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_one__mod__nat__number__of,axiom,
% 108.69/108.75 ! [V_v_H] :
% 108.69/108.75 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 108.69/108.75 => 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)) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__if,axiom,
% 108.69/108.75 ! [V_m,V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.75 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => 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)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__geq,axiom,
% 108.69/108.75 ! [V_m,V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.75 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_card__atLeastLessThan__int,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_split__div,axiom,
% 108.69/108.75 ! [V_k_2,V_n_2,V_P_2] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 108.69/108.75 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.75 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 108.69/108.75 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.75 => ! [B_i,B_j] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 108.69/108.75 => ( 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)
% 108.69/108.75 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zero__less__nat__eq,axiom,
% 108.69/108.75 ! [V_z_2] :
% 108.69/108.75 ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 108.69/108.75 ! [V_y_2,V_x_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__less__eq__zless,axiom,
% 108.69/108.75 ! [V_z_2,V_w_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__eq__iff2,axiom,
% 108.69/108.75 ! [V_w_2,V_m_2] :
% 108.69/108.75 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 108.69/108.75 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 108.69/108.75 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 108.69/108.75 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__eq__iff,axiom,
% 108.69/108.75 ! [V_m_2,V_w_2] :
% 108.69/108.75 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 108.69/108.75 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 108.69/108.75 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 108.69/108.75 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__le__eq__zle,axiom,
% 108.69/108.75 ! [V_z_2,V_w_2] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 108.69/108.75 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 108.69/108.75 => ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_split__nat,axiom,
% 108.69/108.75 ! [V_i_2,V_P_2] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 108.69/108.75 <=> ( ! [B_n] :
% 108.69/108.75 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 108.69/108.75 => hBOOL(hAPP(V_P_2,B_n)) )
% 108.69/108.75 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__lemma,axiom,
% 108.69/108.75 ! [V_q,V_b,V_r,V_c] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_split__mod,axiom,
% 108.69/108.75 ! [V_k_2,V_n_2,V_P_2] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 108.69/108.75 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.75 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 108.69/108.75 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.75 => ! [B_i,B_j] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 108.69/108.75 => ( 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)
% 108.69/108.75 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__add__distrib,axiom,
% 108.69/108.75 ! [V_z_H,V_z] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_int__eq__iff__number__of,axiom,
% 108.69/108.75 ! [V_v_2,V_m_2] :
% 108.69/108.75 ( 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)
% 108.69/108.75 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 108.69/108.75 & 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__mult__distrib,axiom,
% 108.69/108.75 ! [V_z_H,V_z] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__diff__distrib,axiom,
% 108.69/108.75 ! [V_z,V_z_H] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Suc__times__mod__eq,axiom,
% 108.69/108.75 ! [V_m,V_k] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 108.69/108.75 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)))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_card__greaterThanAtMost__int,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__eq__minus1,axiom,
% 108.69/108.75 ! [V_b] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 108.69/108.75 ! [V_n,V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__power__eq,axiom,
% 108.69/108.75 ! [V_n,V_z] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_le__div__geq,axiom,
% 108.69/108.75 ! [V_m,V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_split__div_H,axiom,
% 108.69/108.75 ! [V_n_2,V_m_2,V_P_2] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 108.69/108.75 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.75 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 108.69/108.75 | ? [B_q] :
% 108.69/108.75 ( 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))
% 108.69/108.75 & 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))))
% 108.69/108.75 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_split__div__lemma,axiom,
% 108.69/108.75 ! [V_m_2,V_q_2,V_n_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 108.69/108.75 => ( ( 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))
% 108.69/108.75 & 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)))) )
% 108.69/108.75 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Suc__div__eq__add3__div,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__Suc__eq__div__add3,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div2__Suc__Suc,axiom,
% 108.69/108.75 ! [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))))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_add__self__div__2,axiom,
% 108.69/108.75 ! [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 ).
% 108.69/108.75
% 108.69/108.75 fof(fact_one__less__nat__eq,axiom,
% 108.69/108.75 ! [V_z_2] :
% 108.69/108.75 ( 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)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__less__iff,axiom,
% 108.69/108.75 ! [V_m_2,V_w_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 108.69/108.75 <=> 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 108.69/108.75 ! [V_z] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod2__Suc__Suc,axiom,
% 108.69/108.75 ! [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)))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 108.69/108.75 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)))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__mult__distrib__neg,axiom,
% 108.69/108.75 ! [V_z_H,V_z] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_card__atLeastAtMost__int,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__2,axiom,
% 108.69/108.75 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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_card__greaterThanLessThan__int,axiom,
% 108.69/108.75 ! [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)))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__pos__neg__trivial,axiom,
% 108.69/108.75 ! [V_b,V_a] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 108.69/108.75 => ( 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)))
% 108.69/108.75 => 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) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zmod__minus1,axiom,
% 108.69/108.75 ! [V_b] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_power__nat__number__of__number__of,axiom,
% 108.69/108.75 ! [V_w,V_v] :
% 108.69/108.75 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.75 => 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)) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_power__nat__number__of,axiom,
% 108.69/108.75 ! [V_n,V_v] :
% 108.69/108.75 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.75 => 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) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 108.69/108.75 ! [V_u_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 108.69/108.75 => 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_div__2__gt__zero,axiom,
% 108.69/108.75 ! [V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 108.69/108.75 => 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)))))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mod2__gr__0,axiom,
% 108.69/108.75 ! [V_m_2] :
% 108.69/108.75 ( 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))))))
% 108.69/108.75 <=> 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 108.69/108.75 ! [V_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 108.69/108.75 => 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)))))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_power__m1__even,axiom,
% 108.69/108.75 ! [V_n,T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_int__of__code,axiom,
% 108.69/108.75 ! [V_k] :
% 108.69/108.75 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 108.69/108.75 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 108.69/108.75 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 108.69/108.75 => ( ( 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)
% 108.69/108.75 => 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)))))) )
% 108.69/108.75 & ( 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)
% 108.69/108.75 => 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)) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__aux__def,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__morphism__nat__int,axiom,
% 108.69/108.75 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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_periodic__finite__ex,axiom,
% 108.69/108.75 ! [V_P_2,V_d_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 108.69/108.75 => ( ! [B_x,B_k] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,B_x))
% 108.69/108.75 <=> 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)))) )
% 108.69/108.75 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 108.69/108.75 <=> ? [B_x] :
% 108.69/108.75 ( 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)))
% 108.69/108.75 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_code__numeral_Osize_I1_J,axiom,
% 108.69/108.75 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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 108.69/108.75 ! [V_B_2,V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 108.69/108.75 ! [V_B_2,V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_code__numeral_Osize_I2_J,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 108.69/108.75 ! [V_B_2,V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.75 <=> 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 108.69/108.75 ! [V_B_2,V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.75 <=> 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_code__numeral_Oinject,axiom,
% 108.69/108.75 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 108.69/108.75 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 108.69/108.75 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 108.69/108.75 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 108.69/108.75 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 108.69/108.75 ! [V_B_2,V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 108.69/108.75 ! [V_B_2,V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__set__def,axiom,
% 108.69/108.75 ! [V_S_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_S_2)
% 108.69/108.75 <=> ! [B_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 108.69/108.75 ! [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)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 108.69/108.75 ! [V_B_2,V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 108.69/108.75 => ( V_A_2 = V_B_2
% 108.69/108.75 <=> 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) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 108.69/108.75 ! [V_y_2,V_x_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 108.69/108.75 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 108.69/108.75 ! [V_x_2,V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Suc__code__numeral__minus__one,axiom,
% 108.69/108.75 ! [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 ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 108.69/108.75 ! [V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => 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 ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 108.69/108.75 ! [V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 108.69/108.75 <=> 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 108.69/108.75 ! [V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_code__numeral_Osize_I4_J,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 108.69/108.75 ! [V_A_2,V_x_2] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 108.69/108.75 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 108.69/108.75 <=> 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_setsum__bounded,axiom,
% 108.69/108.75 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 108.69/108.75 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 108.69/108.75 & class_Rings_Osemiring__1(T_c) )
% 108.69/108.75 => ( ! [B_i] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 108.69/108.75 ! [V_n_2,V_m_2] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 108.69/108.75 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 108.69/108.75 => 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))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__of__nat,axiom,
% 108.69/108.75 ! [V_k,T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => 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)))) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => 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)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__eq__iff,axiom,
% 108.69/108.75 ! [V_z_2,V_w_2,T_b] :
% 108.69/108.75 ( class_Int_Oring__char__0(T_b)
% 108.69/108.75 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 108.69/108.75 <=> V_w_2 = V_z_2 ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_number__of__eq,axiom,
% 108.69/108.75 ! [V_k,T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_int__number__of__def,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__int__eq,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 108.69/108.75 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_x)
% 108.69/108.75 => ( c_Nat__Transfer_Ois__nat(V_y)
% 108.69/108.75 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 108.69/108.75 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 108.69/108.75 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_x)
% 108.69/108.75 => ( c_Nat__Transfer_Ois__nat(V_y)
% 108.69/108.75 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_x)
% 108.69/108.75 => ( c_Nat__Transfer_Ois__nat(V_y)
% 108.69/108.75 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_x)
% 108.69/108.75 => ( c_Nat__Transfer_Ois__nat(V_y)
% 108.69/108.75 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 108.69/108.75 ! [V_n,V_x] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_x)
% 108.69/108.75 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 108.69/108.75 ! [V_y,V_x] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_x)
% 108.69/108.75 => ( c_Nat__Transfer_Ois__nat(V_y)
% 108.69/108.75 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__eq__0__iff,axiom,
% 108.69/108.75 ! [V_z_2,T_b] :
% 108.69/108.75 ( class_Int_Oring__char__0(T_b)
% 108.69/108.75 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.75 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__0__eq__iff,axiom,
% 108.69/108.75 ! [V_z_2,T_b] :
% 108.69/108.75 ( class_Int_Oring__char__0(T_b)
% 108.69/108.75 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 108.69/108.75 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__0,axiom,
% 108.69/108.75 ! [T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__le__iff,axiom,
% 108.69/108.75 ! [V_z_2,V_w_2,T_b] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__less__iff,axiom,
% 108.69/108.75 ! [V_z_2,V_w_2,T_b] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_w_2)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__add,axiom,
% 108.69/108.75 ! [V_z,V_w,T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__number__of__eq,axiom,
% 108.69/108.75 ! [V_v,T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__mult,axiom,
% 108.69/108.75 ! [V_z,V_w,T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__1,axiom,
% 108.69/108.75 ! [T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__diff,axiom,
% 108.69/108.75 ! [V_z,V_w,T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__of__nat__eq,axiom,
% 108.69/108.75 ! [V_n,T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__minus,axiom,
% 108.69/108.75 ! [V_z,T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Ints__of__int,axiom,
% 108.69/108.75 ! [V_z_2,T_b] :
% 108.69/108.75 ( class_Rings_Oring__1(T_b)
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__power,axiom,
% 108.69/108.75 ! [V_n,V_z,T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_is__nat__def,axiom,
% 108.69/108.75 ! [V_x_2] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 108.69/108.75 ! [V_y_2,V_x_2] :
% 108.69/108.75 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 108.69/108.75 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 108.69/108.75 ! [V_x_2,V_A_2] :
% 108.69/108.75 ( c_Nat__Transfer_Onat__set(V_A_2)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 108.69/108.75 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__m1,axiom,
% 108.69/108.75 ! [T_a] :
% 108.69/108.75 ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 108.69/108.75 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__le__0__iff,axiom,
% 108.69/108.75 ! [V_z_2,T_b] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__0__le__iff,axiom,
% 108.69/108.75 ! [V_z_2,T_b] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__0__less__iff,axiom,
% 108.69/108.75 ! [V_z_2,T_b] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__int__less__0__iff,axiom,
% 108.69/108.75 ! [V_z_2,T_b] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.75 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_of__nat__nat,axiom,
% 108.69/108.75 ! [V_z,T_a] :
% 108.69/108.75 ( class_Rings_Oring__1(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 108.69/108.75 => 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) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 108.69/108.75 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_code__numeral_Osize_I3_J,axiom,
% 108.69/108.75 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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__Un__disjoint,axiom,
% 108.69/108.75 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.75 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.75 => ( 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))
% 108.69/108.75 => hAPP(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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_A_2)),hAPP(hAPP(hAPP(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)) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_decr__mult__lemma,axiom,
% 108.69/108.75 ! [V_k_2,V_P_2,V_d_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 108.69/108.75 => ( ! [B_x] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,B_x))
% 108.69/108.75 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 108.69/108.75 => ! [B_x] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,B_x))
% 108.69/108.75 => 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)))) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_negD,axiom,
% 108.69/108.75 ! [V_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => ? [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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_incr__mult__lemma,axiom,
% 108.69/108.75 ! [V_k_2,V_P_2,V_d_2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 108.69/108.75 => ( ! [B_x] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,B_x))
% 108.69/108.75 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 108.69/108.75 => ! [B_x] :
% 108.69/108.75 ( hBOOL(hAPP(V_P_2,B_x))
% 108.69/108.75 => 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)))) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_card__partition,axiom,
% 108.69/108.75 ! [V_k_2,V_C_2,T_b] :
% 108.69/108.75 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 108.69/108.75 => ( ! [B_c] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 108.69/108.75 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 108.69/108.75 => ( ! [B_c1] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 108.69/108.75 => ! [B_c2] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 108.69/108.75 => ( B_c1 != B_c2
% 108.69/108.75 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_c1),B_c2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 108.69/108.75 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),V_C_2)) = hAPP(c_Finite__Set_Ocard(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__image__empty,axiom,
% 108.69/108.75 ! [V_z_2,V_g_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ).
% 108.69/108.75
% 108.69/108.75 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 108.69/108.75 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.75 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.75 => hAPP(V_F_2,V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__image__insert,axiom,
% 108.69/108.75 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 108.69/108.75 ( class_Groups_Oab__semigroup__mult(T_c)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.75 => 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(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),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),V_A_2)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_setsum_Oeq__fold,axiom,
% 108.69/108.75 ! [V_g_2,V_A_2,T_b,T_c] :
% 108.69/108.75 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_setsum_OF__eq,axiom,
% 108.69/108.75 ! [V_g_2,V_A_2,T_b,T_c] :
% 108.69/108.75 ( class_Groups_Ocomm__monoid__add(T_c)
% 108.69/108.75 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__image__Un__Int,axiom,
% 108.69/108.75 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.75 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.75 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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_A_2)),hAPP(hAPP(hAPP(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)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(hAPP(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)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_comm__monoid__big_OF__eq,axiom,
% 108.69/108.75 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.75 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 108.69/108.75 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.75 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.75 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__image__Un__one,axiom,
% 108.69/108.75 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 108.69/108.75 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 108.69/108.75 => ( ! [B_x] :
% 108.69/108.75 ( 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_S_2),V_T_2)))
% 108.69/108.75 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 108.69/108.75 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_T_2)) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zero__less__imp__eq__int,axiom,
% 108.69/108.75 ! [V_k] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 108.69/108.75 => ? [B_n] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 108.69/108.75 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 108.69/108.75 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(V_f2_2,V_code__numeral_2) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 108.69/108.75 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.75 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 108.69/108.75 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 108.69/108.75 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 108.69/108.75 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__graph__permute__diff,axiom,
% 108.69/108.75 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 108.69/108.75 ( class_Groups_Oab__semigroup__mult(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_x_2))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 108.69/108.75 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_a_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_x_2)) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_incr__lemma,axiom,
% 108.69/108.75 ! [V_x,V_z,V_d] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 108.69/108.75 => 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)))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_decr__lemma,axiom,
% 108.69/108.75 ! [V_z,V_x,V_d] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold1__eq__fold,axiom,
% 108.69/108.75 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.75 ( class_Groups_Oab__semigroup__mult(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.75 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__idempotent,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__of__nat,axiom,
% 108.69/108.75 ! [V_n,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_power__abs,axiom,
% 108.69/108.75 ! [V_n,V_a,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__minus__cancel,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__one,axiom,
% 108.69/108.75 ! [T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__minus__commute,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__mult__self,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__mult,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__add__abs,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__eq__0,axiom,
% 108.69/108.75 ! [V_a_2,T_b] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 108.69/108.75 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.75 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__zero,axiom,
% 108.69/108.75 ! [T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__le__D1,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__ge__self,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__int__eq,axiom,
% 108.69/108.75 ! [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) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_empty__fold__graphE,axiom,
% 108.69/108.75 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.75 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2))
% 108.69/108.75 => V_x_2 = V_z_2 ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__graph_OemptyI,axiom,
% 108.69/108.75 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 108.69/108.75 ! [V_z_2,V_f_2,T_c,T_b] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_z_2)) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__graph__imp__finite,axiom,
% 108.69/108.75 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.75 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 108.69/108.75 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 108.69/108.75 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.75 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 108.69/108.75 => V_y_2 = V_x_2 ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__ge__zero,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__le__zero__iff,axiom,
% 108.69/108.75 ! [V_a_2,T_b] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.75 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__of__nonneg,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__not__less__zero,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => ~ 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zero__less__abs__iff,axiom,
% 108.69/108.75 ! [V_a_2,T_b] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
% 108.69/108.75 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__of__pos,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__triangle__ineq,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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)))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__mult__less,axiom,
% 108.69/108.75 ! [V_d,V_b,V_c,V_a,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 108.69/108.75 => 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))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__triangle__ineq2__sym,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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)))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__triangle__ineq2,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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)))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__triangle__ineq3,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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)))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__ge__minus__self,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__le__iff,axiom,
% 108.69/108.75 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 108.69/108.75 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__leI,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__le__D2,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__less__iff,axiom,
% 108.69/108.75 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 108.69/108.75 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 108.69/108.75 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__power__minus,axiom,
% 108.69/108.75 ! [V_n,V_a,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__zmult__eq__1,axiom,
% 108.69/108.75 ! [V_n,V_m] :
% 108.69/108.75 ( 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)
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__sgn,axiom,
% 108.69/108.75 ! [V_k,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => 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)) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_mult__sgn__abs,axiom,
% 108.69/108.75 ! [V_x,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => 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 ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold1__singleton,axiom,
% 108.69/108.75 ! [V_a_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(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)))) = V_a_2 ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold1__singleton__def,axiom,
% 108.69/108.75 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 108.69/108.75 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 108.69/108.75 => hAPP(V_g_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_a_2 ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__graph_OinsertI,axiom,
% 108.69/108.75 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 108.69/108.75 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 108.69/108.75 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__eq__mult,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Rings_Oordered__ring__abs(T_a)
% 108.69/108.75 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 108.69/108.75 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 108.69/108.75 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 108.69/108.75 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__mult__pos,axiom,
% 108.69/108.75 ! [V_y,V_x,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.75 => 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)) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__diff__triangle__ineq,axiom,
% 108.69/108.75 ! [V_d,V_c,V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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))))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__triangle__ineq4,axiom,
% 108.69/108.75 ! [V_b,V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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)))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__minus__le__zero,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__of__nonpos,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__of__neg,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__if,axiom,
% 108.69/108.75 ! [V_a,T_a] :
% 108.69/108.75 ( class_Groups_Oabs__if(T_a)
% 108.69/108.75 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zero__le__power__abs,axiom,
% 108.69/108.75 ! [V_n,V_a,T_a] :
% 108.69/108.75 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.75 => 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))) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_folding__one_Oeq__fold,axiom,
% 108.69/108.75 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.75 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__minus__one,axiom,
% 108.69/108.75 ! [T_a] :
% 108.69/108.75 ( ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 & class_Rings_Olinordered__idom(T_a) )
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zabs__less__one__iff,axiom,
% 108.69/108.75 ! [V_z_2] :
% 108.69/108.75 ( 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)))
% 108.69/108.75 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 108.69/108.75 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.75 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 108.69/108.75 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zabs__def,axiom,
% 108.69/108.75 ! [V_i] :
% 108.69/108.75 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 108.69/108.75 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 108.69/108.75 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_nat__abs__mult__distrib,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zero__le__zpower__abs,axiom,
% 108.69/108.75 ! [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))) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold__graph__insert__swap,axiom,
% 108.69/108.75 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 108.69/108.75 ( class_Groups_Oab__semigroup__mult(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_b_2,V_A_2),V_y_2))
% 108.69/108.75 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 108.69/108.75 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2),V_y_2))) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Sup__fin_OF__eq,axiom,
% 108.69/108.75 ! [V_A_2,T_b] :
% 108.69/108.75 ( class_Lattices_Olattice(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_Inf__fin_OF__eq,axiom,
% 108.69/108.75 ! [V_A_2,T_b] :
% 108.69/108.75 ( class_Lattices_Olattice(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__number__of,axiom,
% 108.69/108.75 ! [V_x,T_a] :
% 108.69/108.75 ( ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 & class_Rings_Olinordered__idom(T_a) )
% 108.69/108.75 => ( ( 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)))
% 108.69/108.75 => 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)) )
% 108.69/108.75 & ( ~ 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)))
% 108.69/108.75 => 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) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_abs__power__minus__one,axiom,
% 108.69/108.75 ! [V_n,T_a] :
% 108.69/108.75 ( ( class_Int_Onumber__ring(T_a)
% 108.69/108.75 & class_Rings_Olinordered__idom(T_a) )
% 108.69/108.75 => 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) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_zero__less__zpower__abs__iff,axiom,
% 108.69/108.75 ! [V_n_2,V_x_2] :
% 108.69/108.75 ( 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)))
% 108.69/108.75 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 108.69/108.75 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 108.69/108.75 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.75 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold1__belowI,axiom,
% 108.69/108.75 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.75 ( class_Lattices_Osemilattice__inf(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_below__fold1__iff,axiom,
% 108.69/108.75 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.75 ( class_Lattices_Osemilattice__inf(T_b)
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.75 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
% 108.69/108.75 <=> ! [B_x] :
% 108.69/108.75 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.75 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold1__insert__idem,axiom,
% 108.69/108.75 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.75 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 108.69/108.75 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.75 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.75 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ).
% 108.69/108.75
% 108.69/108.75 fof(fact_fold1__Un2,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1__eq__fold__idem,axiom,
% 108.69/108.76 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)),V_a_2),V_A_2) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_abs__power2,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.76 => 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)))) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_power2__abs,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( class_Rings_Olinordered__idom(T_a)
% 108.69/108.76 => 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)))) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Diff1__fold__graph,axiom,
% 108.69/108.76 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_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))))),V_y_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(V_f_2,V_x_2),V_y_2))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1__insert,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Groups_Oab__semigroup__mult(T_b)
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1__Un,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Groups_Oab__semigroup__mult(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( 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))
% 108.69/108.76 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_semilattice__big_OF__eq,axiom,
% 108.69/108.76 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 108.69/108.76 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1Set_Ointros,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 108.69/108.76 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.76 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.76 => ? [B_y_H] :
% 108.69/108.76 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 108.69/108.76 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1__in,axiom,
% 108.69/108.76 ! [V_A_2,T_b] :
% 108.69/108.76 ( class_Groups_Oab__semigroup__mult(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),V_A_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_empty__fold1SetE,axiom,
% 108.69/108.76 ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1Set__nonempty,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 108.69/108.76 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1Set__sing,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(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)))),V_b_2))
% 108.69/108.76 <=> V_a_2 = V_b_2 ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_hom__fold1__commute,axiom,
% 108.69/108.76 ! [V_N_2,V_h_2,T_b] :
% 108.69/108.76 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 108.69/108.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_x),B_y)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => hAPP(V_h_2,hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_N_2)) = hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_insert__fold1SetE,axiom,
% 108.69/108.76 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
% 108.69/108.76 => ~ ! [B_a,B_A] :
% 108.69/108.76 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1Set_Oequations,axiom,
% 108.69/108.76 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
% 108.69/108.76 <=> ? [B_a,B_A] :
% 108.69/108.76 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 108.69/108.76 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 108.69/108.76 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_half__gt__zero__iff,axiom,
% 108.69/108.76 ! [V_r_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber__ring(T_b) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_r_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
% 108.69/108.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_minus__divide__left,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__1,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_diff__divide__distrib,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_times__divide__eq__right,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_add__divide__distrib,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__zero,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__zero__left,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_power__divide,axiom,
% 108.69/108.76 ! [V_n,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_eq__divide__imp,axiom,
% 108.69/108.76 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 108.69/108.76 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__eq__imp,axiom,
% 108.69/108.76 ! [V_a,V_b,V_c,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 108.69/108.76 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nonzero__divide__eq__eq,axiom,
% 108.69/108.76 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_b)
% 108.69/108.76 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 108.69/108.76 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nonzero__eq__divide__eq,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_b)
% 108.69/108.76 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 108.69/108.76 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__self__if,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 108.69/108.76 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 108.69/108.76 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__self,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_right__inverse__eq,axiom,
% 108.69/108.76 ! [V_a_2,V_b_2,T_b] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_b)
% 108.69/108.76 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 108.69/108.76 <=> V_a_2 = V_b_2 ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nonzero__minus__divide__divide,axiom,
% 108.69/108.76 ! [V_a,V_b,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nonzero__minus__divide__right,axiom,
% 108.69/108.76 ! [V_a,V_b,T_a] :
% 108.69/108.76 ( class_Rings_Odivision__ring(T_a)
% 108.69/108.76 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nonzero__power__divide,axiom,
% 108.69/108.76 ! [V_n,V_a,V_b,T_a] :
% 108.69/108.76 ( class_Fields_Ofield(T_a)
% 108.69/108.76 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_power__one__over,axiom,
% 108.69/108.76 ! [V_n,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__eq__eq__number__of1,axiom,
% 108.69/108.76 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_a_2
% 108.69/108.76 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) )
% 108.69/108.76 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__eq__eq__number__of,axiom,
% 108.69/108.76 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)
% 108.69/108.76 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) )
% 108.69/108.76 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_eq__divide__eq__number__of,axiom,
% 108.69/108.76 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 108.69/108.76 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2) = V_b_2 )
% 108.69/108.76 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_eq__divide__eq__number__of1,axiom,
% 108.69/108.76 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))
% 108.69/108.76 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) = V_b_2 )
% 108.69/108.76 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__Numeral0,axiom,
% 108.69/108.76 ! [V_x,T_a] :
% 108.69/108.76 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 & class_Int_Onumber__ring(T_a) )
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__Numeral1,axiom,
% 108.69/108.76 ! [V_x,T_a] :
% 108.69/108.76 ( ( class_Fields_Ofield(T_a)
% 108.69/108.76 & class_Int_Onumber__ring(T_a) )
% 108.69/108.76 => 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 ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__numeral__1,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( ( class_Fields_Ofield(T_a)
% 108.69/108.76 & class_Int_Onumber__ring(T_a) )
% 108.69/108.76 => 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 ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__minus1,axiom,
% 108.69/108.76 ! [V_x,T_a] :
% 108.69/108.76 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 & class_Int_Onumber__ring(T_a) )
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_less__divide__eq__number__of1,axiom,
% 108.69/108.76 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_less__divide__eq__number__of,axiom,
% 108.69/108.76 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__less__eq__number__of,axiom,
% 108.69/108.76 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__less__eq__number__of1,axiom,
% 108.69/108.76 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_power__diff,axiom,
% 108.69/108.76 ! [V_m,V_n,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Ofield(T_a)
% 108.69/108.76 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 108.69/108.76 => 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)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_minus1__divide,axiom,
% 108.69/108.76 ! [V_x,T_a] :
% 108.69/108.76 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 & class_Int_Onumber__ring(T_a) )
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__le__eq__number__of1,axiom,
% 108.69/108.76 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_a_2))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__le__eq__number__of,axiom,
% 108.69/108.76 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_le__divide__eq__number__of,axiom,
% 108.69/108.76 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2)),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),V_c_2))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_le__divide__eq__number__of1,axiom,
% 108.69/108.76 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 & class_Int_Onumber(T_b) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2))),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_half__gt__zero,axiom,
% 108.69/108.76 ! [V_r,T_a] :
% 108.69/108.76 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 108.69/108.76 & class_Int_Onumber__ring(T_a) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 108.69/108.76 => 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)))))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_le__divide__eq,axiom,
% 108.69/108.76 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__le__eq,axiom,
% 108.69/108.76 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_pos__le__divide__eq,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 108.69/108.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_pos__divide__le__eq,axiom,
% 108.69/108.76 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 108.69/108.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_times__divide__times__eq,axiom,
% 108.69/108.76 ! [V_w,V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_minus__divide__right,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_minus__divide__divide,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_abs__divide,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_zero__le__divide__iff,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 108.69/108.76 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__le__0__iff,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 108.69/108.76 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__right__mono,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__right__mono__neg,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__strict__right__mono__neg,axiom,
% 108.69/108.76 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__strict__right__mono,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__neg__neg,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__neg__pos,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__pos__neg,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__pos__pos,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__less__0__iff,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 108.69/108.76 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_zero__less__divide__iff,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 108.69/108.76 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_eq__divide__eq,axiom,
% 108.69/108.76 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_b)
% 108.69/108.76 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 108.69/108.76 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 108.69/108.76 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__eq__eq,axiom,
% 108.69/108.76 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_b)
% 108.69/108.76 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 108.69/108.76 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 108.69/108.76 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_mult__divide__mult__cancel__right,axiom,
% 108.69/108.76 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_mult__divide__mult__cancel__left,axiom,
% 108.69/108.76 ! [V_b,V_a,V_c,T_a] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_frac__eq__eq,axiom,
% 108.69/108.76 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 108.69/108.76 ( class_Fields_Ofield(T_b)
% 108.69/108.76 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 108.69/108.76 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
% 108.69/108.76 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nonzero__abs__divide,axiom,
% 108.69/108.76 ! [V_a,V_b,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__nonpos__neg,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__nonpos__pos,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_frac__le,axiom,
% 108.69/108.76 ! [V_z,V_w,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 108.69/108.76 => 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))) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_frac__less,axiom,
% 108.69/108.76 ! [V_z,V_w,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 108.69/108.76 => 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))) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_frac__less2,axiom,
% 108.69/108.76 ! [V_z,V_w,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 108.69/108.76 => 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))) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__nonneg__neg,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__nonneg__pos,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__strict__left__mono__neg,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => ( 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)))
% 108.69/108.76 => 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))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__strict__left__mono,axiom,
% 108.69/108.76 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.76 => ( 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)))
% 108.69/108.76 => 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))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_neg__divide__less__eq,axiom,
% 108.69/108.76 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 108.69/108.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_neg__less__divide__eq,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 108.69/108.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_mult__imp__less__div__pos,axiom,
% 108.69/108.76 ! [V_x,V_z,V_y,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.76 => ( 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))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_mult__imp__div__pos__less,axiom,
% 108.69/108.76 ! [V_z,V_x,V_y,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.76 => ( 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)))
% 108.69/108.76 => 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)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_pos__divide__less__eq,axiom,
% 108.69/108.76 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 108.69/108.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_pos__less__divide__eq,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 108.69/108.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__less__eq,axiom,
% 108.69/108.76 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_less__divide__eq,axiom,
% 108.69/108.76 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 108.69/108.76 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_add__num__frac,axiom,
% 108.69/108.76 ! [V_x,V_z,V_y,T_a] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_add__divide__eq__iff,axiom,
% 108.69/108.76 ! [V_y,V_x,V_z,T_a] :
% 108.69/108.76 ( class_Fields_Ofield(T_a)
% 108.69/108.76 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_add__frac__num,axiom,
% 108.69/108.76 ! [V_z,V_x,V_y,T_a] :
% 108.69/108.76 ( class_Fields_Ofield__inverse__zero(T_a)
% 108.69/108.76 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__add__eq__iff,axiom,
% 108.69/108.76 ! [V_y,V_x,V_z,T_a] :
% 108.69/108.76 ( class_Fields_Ofield(T_a)
% 108.69/108.76 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_add__frac__eq,axiom,
% 108.69/108.76 ! [V_w,V_x,V_z,V_y,T_a] :
% 108.69/108.76 ( class_Fields_Ofield(T_a)
% 108.69/108.76 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_diff__divide__eq__iff,axiom,
% 108.69/108.76 ! [V_y,V_x,V_z,T_a] :
% 108.69/108.76 ( class_Fields_Ofield(T_a)
% 108.69/108.76 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__diff__eq__iff,axiom,
% 108.69/108.76 ! [V_y,V_x,V_z,T_a] :
% 108.69/108.76 ( class_Fields_Ofield(T_a)
% 108.69/108.76 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_diff__frac__eq,axiom,
% 108.69/108.76 ! [V_w,V_x,V_z,V_y,T_a] :
% 108.69/108.76 ( class_Fields_Ofield(T_a)
% 108.69/108.76 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 108.69/108.76 => 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)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_less__half__sum,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.76 => 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))))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_gt__half__sum,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_abs__div__pos,axiom,
% 108.69/108.76 ! [V_x,V_y,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__left__mono__neg,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 108.69/108.76 => ( 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)))
% 108.69/108.76 => 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))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_divide__left__mono,axiom,
% 108.69/108.76 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 108.69/108.76 => ( 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)))
% 108.69/108.76 => 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))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_neg__divide__le__eq,axiom,
% 108.69/108.76 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)),V_a_2))
% 108.69/108.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),V_b_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_neg__le__divide__eq,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)))
% 108.69/108.76 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_mult__imp__le__div__pos,axiom,
% 108.69/108.76 ! [V_x,V_z,V_y,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.76 => ( 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))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_mult__imp__div__pos__le,axiom,
% 108.69/108.76 ! [V_z,V_x,V_y,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 108.69/108.76 => ( 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)))
% 108.69/108.76 => 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)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__diff1,axiom,
% 108.69/108.76 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Fields_Ofield(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 108.69/108.76 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(V_f_2,V_a_2)) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_field__le__mult__one__interval,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 108.69/108.76 => ( ! [B_z] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 108.69/108.76 => 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)) ) )
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nat0__intermed__int__val,axiom,
% 108.69/108.76 ! [V_k_2,V_f_2,V_n_2] :
% 108.69/108.76 ( ! [B_i] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 108.69/108.76 => 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))) )
% 108.69/108.76 => ( 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))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 108.69/108.76 => ? [B_i] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 108.69/108.76 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_int__val__lemma,axiom,
% 108.69/108.76 ! [V_k_2,V_f_2,V_n_2] :
% 108.69/108.76 ( ! [B_i] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 108.69/108.76 => 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))) )
% 108.69/108.76 => ( 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))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 108.69/108.76 => ? [B_i] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 108.69/108.76 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__zero__iff,axiom,
% 108.69/108.76 ! [V_f_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 108.69/108.76 & class_Rings_Ono__zero__divisors(T_c) )
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c)
% 108.69/108.76 <=> ? [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__zero,axiom,
% 108.69/108.76 ! [V_f_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Rings_Ocomm__semiring__1(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ? [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__empty,axiom,
% 108.69/108.76 ! [V_f_2,T_c,T_b] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_b)
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_Oempty,axiom,
% 108.69/108.76 ! [V_g_2,T_c,T_b] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_b)
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(T_b) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_Oinfinite,axiom,
% 108.69/108.76 ! [V_g_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__infinite,axiom,
% 108.69/108.76 ! [V_f_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__eq__1__iff,axiom,
% 108.69/108.76 ! [V_f_2,V_F_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.76 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_F_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 108.69/108.76 <=> ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 108.69/108.76 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__pos__nat__iff,axiom,
% 108.69/108.76 ! [V_f_2,V_S_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 108.69/108.76 => ( 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_b,tc_Nat_Onat),V_f_2),V_S_2)))
% 108.69/108.76 <=> ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__insert,axiom,
% 108.69/108.76 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_Oinsert,axiom,
% 108.69/108.76 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_Ounion__inter,axiom,
% 108.69/108.76 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__Un__Int,axiom,
% 108.69/108.76 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_OF__eq,axiom,
% 108.69/108.76 ! [V_g_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(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_A_2) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_Oeq__fold,axiom,
% 108.69/108.76 ! [V_g_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(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_A_2) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_Oinsert__remove,axiom,
% 108.69/108.76 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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)))))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_Ounion__disjoint,axiom,
% 108.69/108.76 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( 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))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__Un__disjoint,axiom,
% 108.69/108.76 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( 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))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_Oremove,axiom,
% 108.69/108.76 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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)))))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__Un,axiom,
% 108.69/108.76 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Fields_Ofield(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( 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)))
% 108.69/108.76 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),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_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 108.69/108.76 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( 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)))
% 108.69/108.76 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_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_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_B_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__Un__one,axiom,
% 108.69/108.76 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( 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_S_2),V_T_2)))
% 108.69/108.76 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__mono__one__left,axiom,
% 108.69/108.76 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 108.69/108.76 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__mono__one__right,axiom,
% 108.69/108.76 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_T_2),V_S_2)))
% 108.69/108.76 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 108.69/108.76 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_S_2) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__pos__nat,axiom,
% 108.69/108.76 ! [V_f_2,V_S_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 108.69/108.76 => 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))) )
% 108.69/108.76 => 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_b,tc_Nat_Onat),V_f_2),V_S_2))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 108.69/108.76 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 108.69/108.76 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_v_2))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => ~ ! [B_y] :
% 108.69/108.76 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 108.69/108.76 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 108.69/108.76 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.76 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 108.69/108.76 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 108.69/108.76 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fun__left__comm__idem__insert,axiom,
% 108.69/108.76 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fun__left__comm__idem,axiom,
% 108.69/108.76 ! [T_b] :
% 108.69/108.76 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 108.69/108.76 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fun__left__comm__idem__sup,axiom,
% 108.69/108.76 ! [T_b] :
% 108.69/108.76 ( class_Lattices_Osemilattice__sup(T_b)
% 108.69/108.76 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fun__left__comm__idem__inf,axiom,
% 108.69/108.76 ! [T_b] :
% 108.69/108.76 ( class_Lattices_Osemilattice__inf(T_b)
% 108.69/108.76 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 108.69/108.76 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 108.69/108.76 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nat__mod__eq__lemma,axiom,
% 108.69/108.76 ! [V_y,V_n,V_x] :
% 108.69/108.76 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 108.69/108.76 => ? [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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold__image__1,axiom,
% 108.69/108.76 ! [V_f_2,V_S_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Ocomm__monoid__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 108.69/108.76 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 108.69/108.76 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_f_2),c_Groups_Oone__class_Oone(T_c)),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_mod__induct__0,axiom,
% 108.69/108.76 ! [V_i_2,V_P_2,V_p_2] :
% 108.69/108.76 ( ! [B_i] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 108.69/108.76 => ( hBOOL(hAPP(V_P_2,B_i))
% 108.69/108.76 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 108.69/108.76 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 108.69/108.76 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold__image__cong,axiom,
% 108.69/108.76 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Groups_Oab__semigroup__mult(T_c)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 108.69/108.76 => 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),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),V_z_2),V_A_2) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_inf__le__fold__inf,axiom,
% 108.69/108.76 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Lattices_Osemilattice__inf(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold__sup__le__sup,axiom,
% 108.69/108.76 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Lattices_Osemilattice__sup(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_b_2),V_c_2))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nat__intermed__int__val,axiom,
% 108.69/108.76 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 108.69/108.76 ( ! [B_i] :
% 108.69/108.76 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 108.69/108.76 => 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))) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 108.69/108.76 => ? [B_i] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 108.69/108.76 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_log_Osimps,axiom,
% 108.69/108.76 ! [V_i,V_b] :
% 108.69/108.76 ( ( ( 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)))
% 108.69/108.76 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 108.69/108.76 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 108.69/108.76 & ( ~ ( 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)))
% 108.69/108.76 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 108.69/108.76 => 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))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_minus__shift__def,axiom,
% 108.69/108.76 ! [V_r,V_l,V_k] :
% 108.69/108.76 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 108.69/108.76 => 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) )
% 108.69/108.76 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 108.69/108.76 => 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) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_inc__shift__def,axiom,
% 108.69/108.76 ! [V_k,V_v] :
% 108.69/108.76 ( ( V_v = V_k
% 108.69/108.76 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 108.69/108.76 & ( V_v != V_k
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_mod__div__decomp,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Divides_Osemiring__div(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__pos,axiom,
% 108.69/108.76 ! [V_f_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Rings_Olinordered__semidom(T_c)
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_setprod__nonneg,axiom,
% 108.69/108.76 ! [V_f_2,V_A_2,T_b,T_c] :
% 108.69/108.76 ( class_Rings_Olinordered__semidom(T_c)
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_finite__induct,axiom,
% 108.69/108.76 ! [V_P_2,V_F_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 108.69/108.76 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 108.69/108.76 => ( ! [B_x,B_F] :
% 108.69/108.76 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 108.69/108.76 => ( hBOOL(hAPP(V_P_2,B_F))
% 108.69/108.76 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 108.69/108.76 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 108.69/108.76 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_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)))),V_y_2)
% 108.69/108.76 => c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,V_A_2,hAPP(hAPP(V_f_2,V_x_2),V_y_2)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1__antimono,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_B_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 108.69/108.76 ! [T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_inf__min,axiom,
% 108.69/108.76 ! [T_b] :
% 108.69/108.76 ( ( class_Lattices_Osemilattice__inf(T_b)
% 108.69/108.76 & class_Orderings_Olinorder(T_b) )
% 108.69/108.76 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__of__mono,axiom,
% 108.69/108.76 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 108.69/108.76 ( ( class_Orderings_Olinorder(T_c)
% 108.69/108.76 & class_Orderings_Olinorder(T_b) )
% 108.69/108.76 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_m_2),V_n_2)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__0R,axiom,
% 108.69/108.76 ! [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) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__0L,axiom,
% 108.69/108.76 ! [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) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf_Oidem,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf_Ocommute,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__commute,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__left__idem,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 108.69/108.76 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__left__commute,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf_Oassoc,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__assoc,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Oidem,axiom,
% 108.69/108.76 ! [V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 108.69/108.76 ! [V_a2_2,V_a1_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_a1_2,V_a2_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_a2_2) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 108.69/108.76 ! [V_z_2,V_f_2,T_c,T_b] : c_Nitpick_Ofold__graph_H(T_b,T_c,V_f_2,V_z_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_z_2) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__diff__distrib__left,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Groups_Oordered__ab__group__add(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__diff,axiom,
% 108.69/108.76 ! [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) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__Suc__Suc,axiom,
% 108.69/108.76 ! [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)) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__le__iff__disj,axiom,
% 108.69/108.76 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 108.69/108.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 108.69/108.76 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__le1,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__le2,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__iff__inf,axiom,
% 108.69/108.76 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.76 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__inf__iff,axiom,
% 108.69/108.76 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_y_2),V_z_2)))
% 108.69/108.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__infI1,axiom,
% 108.69/108.76 ! [V_b,V_x,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__infI2,axiom,
% 108.69/108.76 ! [V_a,V_x,V_b,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__absorb1,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__absorb2,axiom,
% 108.69/108.76 ! [V_x,V_y,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__infI,axiom,
% 108.69/108.76 ! [V_b,V_a,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__greatest,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__mono,axiom,
% 108.69/108.76 ! [V_d,V_b,V_c,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__infE,axiom,
% 108.69/108.76 ! [V_b,V_a,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( 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)))
% 108.69/108.76 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 108.69/108.76 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oless__infI1,axiom,
% 108.69/108.76 ! [V_b,V_x,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oless__infI2,axiom,
% 108.69/108.76 ! [V_a,V_x,V_b,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__less__iff__conj,axiom,
% 108.69/108.76 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)))
% 108.69/108.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__less__iff__disj,axiom,
% 108.69/108.76 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2)),V_z_2))
% 108.69/108.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 108.69/108.76 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__add__distrib__left,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__number__of,axiom,
% 108.69/108.76 ! [V_v,V_u,T_b] :
% 108.69/108.76 ( ( class_Int_Onumber(T_b)
% 108.69/108.76 & class_Orderings_Oord(T_b) )
% 108.69/108.76 => ( ( 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)))
% 108.69/108.76 => 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) )
% 108.69/108.76 & ( ~ 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)))
% 108.69/108.76 => 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) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ofold__inf__insert,axiom,
% 108.69/108.76 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Omono__inf,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 108.69/108.76 ( ( class_Lattices_Osemilattice__inf(T_c)
% 108.69/108.76 & class_Orderings_Olinorder(T_b) )
% 108.69/108.76 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Int__atLeastAtMostL1,axiom,
% 108.69/108.76 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Int__atLeastAtMostR1,axiom,
% 108.69/108.76 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 108.69/108.76 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_b_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),V_b_2))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ofold1__belowI,axiom,
% 108.69/108.76 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 108.69/108.76 <=> ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1__below__iff,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 108.69/108.76 <=> ? [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold1__strict__below__iff,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
% 108.69/108.76 <=> ? [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_strict__below__fold1__iff,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
% 108.69/108.76 <=> ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__ord__min,axiom,
% 108.69/108.76 ! [T_b] :
% 108.69/108.76 ( class_Orderings_Oord(T_b)
% 108.69/108.76 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Oremove,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 108.69/108.76 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,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)))))) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 108.69/108.76 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 108.69/108.76 ( c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,V_a2_2,hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2))
% 108.69/108.76 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 108.69/108.76 | ? [B_x,B_y] :
% 108.69/108.76 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 108.69/108.76 & c_Nitpick_Ofold__graph_H(T_b,T_c,V_a3_2,V_a4_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_a2_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),B_y) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 108.69/108.76 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),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)))))) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_inf__nat__def,axiom,
% 108.69/108.76 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Osingleton,axiom,
% 108.69/108.76 ! [V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min__le,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_x_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 108.69/108.76 ! [V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min__in,axiom,
% 108.69/108.76 ! [V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Oin__idem,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 108.69/108.76 ! [V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_OF__eq,axiom,
% 108.69/108.76 ! [V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min__antimono,axiom,
% 108.69/108.76 ! [V_N_2,V_M_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 108.69/108.76 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_M_2))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 108.69/108.76 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min__insert,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Osubset__idem,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min__Un,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 108.69/108.76 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_a_2),V_A_2) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 108.69/108.76 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),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)))))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( 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))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( 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))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Oinsert,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Oinsert__remove,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 108.69/108.76 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMin(T_b,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)))))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Ounion__disjoint,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( 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))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Ounion__inter,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.76 => ( 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))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMin(T_b,V_B_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Oeq__fold_H,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_x_2),V_A_2) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 108.69/108.76 ! [V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Oclosed,axiom,
% 108.69/108.76 ! [V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 108.69/108.76 ! [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)))) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 108.69/108.76 ! [V_N_2,V_h_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => hAPP(V_h_2,c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_N_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 108.69/108.76 ! [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)) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Min_Ohom__commute,axiom,
% 108.69/108.76 ! [V_N_2,V_h_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.76 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_minus__Min__eq__Max,axiom,
% 108.69/108.76 ! [V_S_2,T_b] :
% 108.69/108.76 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 108.69/108.76 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_minus__Max__eq__Min,axiom,
% 108.69/108.76 ! [V_S_2,T_b] :
% 108.69/108.76 ( class_Groups_Olinordered__ab__group__add(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 108.69/108.76 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_S_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_Oimage(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b)),V_S_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Max_Osingleton,axiom,
% 108.69/108.76 ! [V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Max__ge,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Max__in,axiom,
% 108.69/108.76 ! [V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Max__mono,axiom,
% 108.69/108.76 ! [V_N_2,V_M_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 108.69/108.76 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_M_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2))) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nat__gcd_Osimps,axiom,
% 108.69/108.76 ! [V_x,V_y] :
% 108.69/108.76 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.76 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 108.69/108.76 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 108.69/108.76 => 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)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 108.69/108.76 ! [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)))) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Max_Oremove,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 108.69/108.76 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,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)))))) ) ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 108.69/108.76 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ! [B_x] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)),V_c_2),V_A_2))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Max__eqI,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( ! [B_y] :
% 108.69/108.76 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__inf__absorb,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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 ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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 ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 108.69/108.76 ! [V_x,V_z,V_y,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 108.69/108.76 ! [V_x,V_z,V_y,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 108.69/108.76 ! [T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_sup__max,axiom,
% 108.69/108.76 ! [T_b] :
% 108.69/108.76 ( ( class_Lattices_Osemilattice__sup(T_b)
% 108.69/108.76 & class_Orderings_Olinorder(T_b) )
% 108.69/108.76 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_max__of__mono,axiom,
% 108.69/108.76 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 108.69/108.76 ( ( class_Orderings_Olinorder(T_c)
% 108.69/108.76 & class_Orderings_Olinorder(T_b) )
% 108.69/108.76 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_c),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_m_2),V_n_2)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_max__0R,axiom,
% 108.69/108.76 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 108.69/108.76
% 108.69/108.76 fof(fact_max__0L,axiom,
% 108.69/108.76 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup_Oidem,axiom,
% 108.69/108.76 ! [V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup_Ocommute,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__commute,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 108.69/108.76 ! [V_b,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__left__idem,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 108.69/108.76 ! [V_c,V_a,V_b,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__left__commute,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup_Oassoc,axiom,
% 108.69/108.76 ! [V_c,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__assoc,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Max_Oidem,axiom,
% 108.69/108.76 ! [V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_max__diff__distrib__left,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Groups_Oordered__ab__group__add(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_max__Suc__Suc,axiom,
% 108.69/108.76 ! [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)) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_le__max__iff__disj,axiom,
% 108.69/108.76 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 108.69/108.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 108.69/108.76 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_le__maxI1,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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))) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_le__maxI2,axiom,
% 108.69/108.76 ! [V_x,V_y,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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))) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__iff__sup,axiom,
% 108.69/108.76 ! [V_y_2,V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 108.69/108.76 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__sup__iff,axiom,
% 108.69/108.76 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 108.69/108.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__supI1,axiom,
% 108.69/108.76 ! [V_b,V_a,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 108.69/108.76 => 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))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__supI2,axiom,
% 108.69/108.76 ! [V_a,V_b,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 108.69/108.76 => 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))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__absorb2,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__absorb1,axiom,
% 108.69/108.76 ! [V_x,V_y,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__supI,axiom,
% 108.69/108.76 ! [V_b,V_x,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 108.69/108.76 => 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)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__least,axiom,
% 108.69/108.76 ! [V_z,V_x,V_y,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 108.69/108.76 => 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)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Osup__mono,axiom,
% 108.69/108.76 ! [V_d,V_b,V_c,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 108.69/108.76 => 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))) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ole__supE,axiom,
% 108.69/108.76 ! [V_x,V_b,V_a,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( 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))
% 108.69/108.76 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 108.69/108.76 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oless__supI1,axiom,
% 108.69/108.76 ! [V_b,V_a,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 108.69/108.76 => 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))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Oless__supI2,axiom,
% 108.69/108.76 ! [V_a,V_b,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 108.69/108.76 => 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))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_less__max__iff__disj,axiom,
% 108.69/108.76 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)))
% 108.69/108.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 108.69/108.76 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_max__less__iff__conj,axiom,
% 108.69/108.76 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
% 108.69/108.76 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 108.69/108.76 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_max__add__distrib__left,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_max__number__of,axiom,
% 108.69/108.76 ! [V_v,V_u,T_b] :
% 108.69/108.76 ( ( class_Int_Onumber(T_b)
% 108.69/108.76 & class_Orderings_Oord(T_b) )
% 108.69/108.76 => ( ( 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)))
% 108.69/108.76 => 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) )
% 108.69/108.76 & ( ~ 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)))
% 108.69/108.76 => 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) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Odistrib__inf__le,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)))) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Odistrib__sup__le,axiom,
% 108.69/108.76 ! [V_z,V_y,V_x,T_a] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_a)
% 108.69/108.76 => 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)))) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_minus__max__eq__min,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Groups_Olinordered__ab__group__add(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_minus__min__eq__max,axiom,
% 108.69/108.76 ! [V_y,V_x,T_a] :
% 108.69/108.76 ( class_Groups_Olinordered__ab__group__add(T_a)
% 108.69/108.76 => 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)) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_nat__minus__add__max,axiom,
% 108.69/108.76 ! [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) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Ofold__sup__insert,axiom,
% 108.69/108.76 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2)) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Max_Oin__idem,axiom,
% 108.69/108.76 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.76 ( class_Orderings_Olinorder(T_b)
% 108.69/108.76 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.76 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.76 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_min__max_Omono__sup,axiom,
% 108.69/108.76 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 108.69/108.76 ( ( class_Lattices_Osemilattice__sup(T_c)
% 108.69/108.76 & class_Orderings_Olinorder(T_b) )
% 108.69/108.76 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 108.69/108.76 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_A_2),V_B_2)))) ) ) ).
% 108.69/108.76
% 108.69/108.76 fof(fact_Int__atLeastAtMost,axiom,
% 108.69/108.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Int__atLeastLessThan,axiom,
% 108.69/108.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Int__greaterThanAtMost,axiom,
% 108.69/108.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Int__greaterThanLessThan,axiom,
% 108.69/108.77 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Int__atLeastAtMostL2,axiom,
% 108.69/108.77 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Int__atLeastAtMostR2,axiom,
% 108.69/108.77 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_OF__eq,axiom,
% 108.69/108.77 ! [V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 108.69/108.77 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_b_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_b_2),V_A_2))) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max__insert,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_Osubset__idem,axiom,
% 108.69/108.77 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.77 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 108.69/108.77 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.77 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max__Un,axiom,
% 108.69/108.77 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 108.69/108.77 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_Oinsert,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_Oinsert__remove,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 108.69/108.77 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olinorder__class_OMax(T_b,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)))))) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_Ounion__inter,axiom,
% 108.69/108.77 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.77 => ( 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))
% 108.69/108.77 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_Ounion__disjoint,axiom,
% 108.69/108.77 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( 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))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),c_Big__Operators_Olinorder__class_OMax(T_b,V_B_2)) ) ) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_Oeq__fold_H,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_max__ord__max,axiom,
% 108.69/108.77 ! [T_b] :
% 108.69/108.77 ( class_Orderings_Oord(T_b)
% 108.69/108.77 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_Oclosed,axiom,
% 108.69/108.77 ! [V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OInf__le__Sup,axiom,
% 108.69/108.77 ! [V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.77 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 108.69/108.77 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),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)))))) ) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_sup__nat__def,axiom,
% 108.69/108.77 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.77 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 108.69/108.77 ! [V_x_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 108.69/108.77 ! [V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 108.69/108.77 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 108.69/108.77 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 108.69/108.77 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.77 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 108.69/108.77 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 108.69/108.77 ! [V_a_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_a_2),V_A_2) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( ( 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)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 108.69/108.77 & ( 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)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),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)))))) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 108.69/108.77 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.77 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( 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))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 108.69/108.77 ! [V_B_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 108.69/108.77 => ( 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))
% 108.69/108.77 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.77 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_x_2),V_A_2) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 108.69/108.77 ! [V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => ( ! [B_x,B_y] : hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),hAPP(hAPP(c_Set_Oinsert(T_b),B_y),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),V_A_2)) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 108.69/108.77 ! [V_N_2,V_h_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.77 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => hAPP(V_h_2,c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_N_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Max_Ohom__commute,axiom,
% 108.69/108.77 ! [V_N_2,V_h_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( ! [B_x,B_y] : hAPP(V_h_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),B_x),B_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_h_2,B_x)),hAPP(V_h_2,B_y))
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 108.69/108.77 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 108.69/108.77 => hAPP(V_h_2,c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_N_2)) ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 108.69/108.77 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( ! [B_x] :
% 108.69/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_b_2),V_c_2))) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_Min__eqI,axiom,
% 108.69/108.77 ! [V_x_2,V_A_2,T_b] :
% 108.69/108.77 ( class_Orderings_Olinorder(T_b)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( ! [B_y] :
% 108.69/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 108.69/108.77 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_field__le__epsilon,axiom,
% 108.69/108.77 ! [V_y,V_x,T_a] :
% 108.69/108.77 ( class_Fields_Olinordered__field(T_a)
% 108.69/108.77 => ( ! [B_e] :
% 108.69/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) )
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_minus__code__numeral__code,axiom,
% 108.69/108.77 ! [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) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_subtract__code__numeral__def,axiom,
% 108.69/108.77 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_pair__box_Osize_I1_J,axiom,
% 108.69/108.77 ! [V_b_2,V_a_2,V_fb_2,V_fa_2,T_c,T_b] : c_Nitpick_Opair__box_Opair__box__size(T_b,T_c,V_fa_2,V_fb_2,c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_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(V_fb_2,V_b_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_arith__series__int,axiom,
% 108.69/108.77 ! [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)))) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 108.69/108.77 ! [V_w] :
% 108.69/108.77 ( 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)))
% 108.69/108.77 => ( ( 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))))
% 108.69/108.77 => 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))) )
% 108.69/108.77 & ( ~ 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))))
% 108.69/108.77 => 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)))) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_fold__image__reindex,axiom,
% 108.69/108.77 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 108.69/108.77 ( class_Groups_Oab__semigroup__mult(T_d)
% 108.69/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 108.69/108.77 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 108.69/108.77 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_INF1__D,axiom,
% 108.69/108.77 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 108.69/108.77 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.77 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_INF1__E,axiom,
% 108.69/108.77 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 108.69/108.77 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 108.69/108.77 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 108.69/108.77 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_INF2__D,axiom,
% 108.69/108.77 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 108.69/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 108.69/108.77 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_INF2__E,axiom,
% 108.69/108.77 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 108.69/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 108.69/108.77 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 108.69/108.77 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 108.69/108.77
% 108.69/108.77 fof(fact_INT__D,axiom,
% 108.69/108.77 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 108.69/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_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)))
% 108.69/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 108.69/108.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__E,axiom,
% 109.04/108.77 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_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)))
% 109.04/108.77 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 109.04/108.77 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUP2__I,axiom,
% 109.04/108.77 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_finite__INT,axiom,
% 109.04/108.77 ! [V_A_2,T_c,V_I_2,T_b] :
% 109.04/108.77 ( ? [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 109.04/108.77 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 109.04/108.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUP1__I,axiom,
% 109.04/108.77 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 109.04/108.77 => hBOOL(hAPP(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_b_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__I,axiom,
% 109.04/108.77 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__abs,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__abs__ge__zero,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 109.04/108.77 => 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__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_max__Suc2,axiom,
% 109.04/108.77 ! [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) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_max__Suc1,axiom,
% 109.04/108.77 ! [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) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Union__image__eq,axiom,
% 109.04/108.77 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_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) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UNION__eq__Union__image,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Int__Inter__image,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,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_c),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)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_min__Suc1,axiom,
% 109.04/108.77 ! [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) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_min__Suc2,axiom,
% 109.04/108.77 ! [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) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 109.04/108.77 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),V_n_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 109.04/108.77 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_card__eq__setsum,axiom,
% 109.04/108.77 ! [V_A_2,T_b] : hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_A_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__UN__finite__eq,axiom,
% 109.04/108.77 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),tc_fun(T_b,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_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 109.04/108.77 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Nat_Onat),V_f_2),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_b] :
% 109.04/108.77 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 & class_Groups_Ocomm__monoid__mult(T_b) )
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 109.04/108.77 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 109.04/108.77 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 109.04/108.77 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 109.04/108.77 => c_Finite__Set_Ofun__left__comm__idem(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 109.04/108.77 ! [V_x_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 109.04/108.77 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_of__nat__setsum,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Rings_Osemiring__1(T_b)
% 109.04/108.77 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_abs__setprod,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Fields_Olinordered__field(T_b)
% 109.04/108.77 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod__1,axiom,
% 109.04/108.77 ! [V_A_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_int__setprod,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod__timesf,axiom,
% 109.04/108.77 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_g_2),V_A_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod_Odistrib,axiom,
% 109.04/108.77 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_of__int__setprod,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 109.04/108.77 & class_Rings_Oring__1(T_b) )
% 109.04/108.77 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod__dividef,axiom,
% 109.04/108.77 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Fields_Ofield__inverse__zero(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Rings_Oinverse__class_Odivide(T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),V_A_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_abs__setsum__abs,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 109.04/108.77 => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inj__singleton,axiom,
% 109.04/108.77 ! [T_b] : c_Fun_Oinj__on(T_b,tc_fun(T_b,tc_HOL_Obool),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))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__constant__conv,axiom,
% 109.04/108.77 ! [V_c_2,T_c,T_b,V_A_2] :
% 109.04/108.77 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__insert__distrib,axiom,
% 109.04/108.77 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUP__UN__eq,axiom,
% 109.04/108.77 ! [V_x_2,V_r_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_finite__range__imageI,axiom,
% 109.04/108.77 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
% 109.04/108.77 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I1_J,axiom,
% 109.04/108.77 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__singleton,axiom,
% 109.04/108.77 ! [V_A_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_b,tc_HOL_Obool)),V_A_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)))) = V_A_2 ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I1_J,axiom,
% 109.04/108.77 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I3_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I3_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,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_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_diff__Suc,axiom,
% 109.04/108.77 ! [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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I4_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__compose,axiom,
% 109.04/108.77 ! [V_r_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_b,T_c,V_f_2),V_g_2)),V_r_2) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),V_r_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__ident,axiom,
% 109.04/108.77 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__image,axiom,
% 109.04/108.77 ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I10_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I10_J,axiom,
% 109.04/108.77 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : 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(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I10_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_c,V_f_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),V_B_2),V_f_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__UN,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Oimage(T_c,T_b,V_f_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I10_J,axiom,
% 109.04/108.77 ! [V_f_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_B_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__Union,axiom,
% 109.04/108.77 ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_range__composition,axiom,
% 109.04/108.77 ! [V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBB(T_d,T_b,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = hAPP(c_Set_Oimage(T_d,T_b,V_f_2),hAPP(c_Set_Oimage(T_c,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Inter__image__eq,axiom,
% 109.04/108.77 ! [V_A_2,V_B_2,T_c,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_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) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INTER__eq__Inter__image,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_A_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Powp__def,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 109.04/108.77 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__atLeast__UNIV,axiom,
% 109.04/108.77 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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INF__INT__eq2,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUP__UN__eq2,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),T_b),hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d))))),V_r_2)),V_x_2),V_y_2))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INF__INT__eq,axiom,
% 109.04/108.77 ! [V_x_2,V_r_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__subtractf,axiom,
% 109.04/108.77 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Oab__group__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fun__diff__def,axiom,
% 109.04/108.77 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Ominus(T_b)
% 109.04/108.77 => hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,T_b)),V_A_2),V_B_2),V_x_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(V_A_2,V_x_2)),hAPP(V_B_2,V_x_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inj__fun,axiom,
% 109.04/108.77 ! [T_d,V_f_2,T_c,T_b] :
% 109.04/108.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.04/108.77 => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I6_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I6_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I7_J,axiom,
% 109.04/108.77 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : 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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I7_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__constant,axiom,
% 109.04/108.77 ! [V_c_2,T_c,T_b,V_A_2] :
% 109.04/108.77 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__empty,axiom,
% 109.04/108.77 ! [V_B_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_B_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__0,axiom,
% 109.04/108.77 ! [V_A_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Compl__INT,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),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_OSUPR(T_c,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_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Compl__UN,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,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)) = 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_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_vimage__UN,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I8_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I8_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_comp__cong,axiom,
% 109.04/108.77 ! [T_f,T_e,T_d,T_b,T_c,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] :
% 109.04/108.77 ( 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))
% 109.04/108.77 => hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_e,T_b,T_f,V_f_H_2),V_g_H_2),V_x_H_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Pow__INT__eq,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),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(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Inter__def,axiom,
% 109.04/108.77 ! [V_S_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_S_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_o__def,axiom,
% 109.04/108.77 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_o__assoc,axiom,
% 109.04/108.77 ! [V_h_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),hAPP(c_Fun_Ocomp(T_e,T_d,T_b,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_h_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_o__apply,axiom,
% 109.04/108.77 ! [V_x_2,V_g_2,V_f_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2),V_x_2) = hAPP(V_f_2,hAPP(V_g_2,V_x_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_o__eq__dest,axiom,
% 109.04/108.77 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 109.04/108.77 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 109.04/108.77 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_o__eq__elim,axiom,
% 109.04/108.77 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 109.04/108.77 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_e,T_c,T_b,V_c_2),V_d_2)
% 109.04/108.77 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INFI__apply,axiom,
% 109.04/108.77 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.77 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INF__commute,axiom,
% 109.04/108.77 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I8_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I8_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)),V_B_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_vimage__INT,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_Ovimage(T_b,T_c,V_f_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_vimage__ident,axiom,
% 109.04/108.77 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 109.04/108.77
% 109.04/108.77 fof(fact_K__record__comp,axiom,
% 109.04/108.77 ! [V_x_2,V_f_2,V_c_2,T_d,T_b,T_c] : hAPP(hAPP(c_Fun_Ocomp(T_c,T_b,T_d,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_f_2),V_x_2) = V_c_2 ).
% 109.04/108.77
% 109.04/108.77 fof(fact_o__eq__dest__lhs,axiom,
% 109.04/108.77 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 109.04/108.77 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 109.04/108.77 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fun__upd__def,axiom,
% 109.04/108.77 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 109.04/108.77 ( ( V_x_2 = V_a_2
% 109.04/108.77 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 109.04/108.77 & ( V_x_2 != V_a_2
% 109.04/108.77 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = hAPP(V_f_2,V_x_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__commute,axiom,
% 109.04/108.77 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Union__def,axiom,
% 109.04/108.77 ! [V_S_2,T_b] : 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_b,tc_HOL_Obool)),V_S_2),c_COMBI(tc_fun(T_b,tc_HOL_Obool))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUP1__iff,axiom,
% 109.04/108.77 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(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_b_2))
% 109.04/108.77 <=> ? [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.77 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__UN__flatten,axiom,
% 109.04/108.77 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I9_J,axiom,
% 109.04/108.77 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I9_J,axiom,
% 109.04/108.77 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I9_J,axiom,
% 109.04/108.77 ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I9_J,axiom,
% 109.04/108.77 ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUP__commute,axiom,
% 109.04/108.77 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),T_b,T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2)),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,T_b),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),T_b,T_d),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I5_J,axiom,
% 109.04/108.77 ! [V_B_2,V_C_2,T_c,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),hAPP(c_Set_Oinsert(T_b),V_a_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I5_J,axiom,
% 109.04/108.77 ! [V_B_2,V_a_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 109.04/108.77 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 109.04/108.77 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 109.04/108.77 => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_bot__fun__def,axiom,
% 109.04/108.77 ! [V_x_2,T_c,T_b] :
% 109.04/108.77 ( class_Orderings_Obot(T_b)
% 109.04/108.77 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fun__Compl__def,axiom,
% 109.04/108.77 ! [V_x_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Ouminus(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,T_b)),V_A_2),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(V_A_2,V_x_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUPR__apply,axiom,
% 109.04/108.77 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.77 => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INF__const,axiom,
% 109.04/108.77 ! [V_M_2,T_b,V_A_2,T_c] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 109.04/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__negf,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Oab__group__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UNION__empty__conv_I2_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__constant,axiom,
% 109.04/108.77 ! [V_c_2,T_c,T_b,V_A_2] :
% 109.04/108.77 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_c_2)) = V_c_2 ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__empty2,axiom,
% 109.04/108.77 ! [V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UNION__empty__conv_I1_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,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)
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUP__const,axiom,
% 109.04/108.77 ! [V_M_2,T_b,V_A_2,T_c] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 109.04/108.77 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),hAPP(c_COMBK(T_c,T_b),V_M_2)) = V_M_2 ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inj__on__id2,axiom,
% 109.04/108.77 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__insert__distrib,axiom,
% 109.04/108.77 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_Oinsert(T_c),V_a_2)),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__iff,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_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)))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_pred__equals__eq2,axiom,
% 109.04/108.77 ! [V_S_2,V_R_2,T_c,T_b] :
% 109.04/108.77 ( 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_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)
% 109.04/108.77 <=> V_R_2 = V_S_2 ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_pred__equals__eq,axiom,
% 109.04/108.77 ! [V_S_2,V_R_2,T_b] :
% 109.04/108.77 ( hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2) = hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)
% 109.04/108.77 <=> V_R_2 = V_S_2 ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_bot__empty__eq,axiom,
% 109.04/108.77 ! [V_x_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_bot__empty__eq2,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2))
% 109.04/108.77 <=> 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)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__iff,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_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)))
% 109.04/108.77 <=> ? [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__lessThan__UNIV,axiom,
% 109.04/108.77 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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inj__on__imageI2,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 109.04/108.77 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_H_2),V_f_2),V_A_2)
% 109.04/108.77 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_vimage__Union,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Set_Ovimage(T_b,T_c,V_f_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_int__setsum,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),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,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__product,axiom,
% 109.04/108.77 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Rings_Osemiring__0(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__left__distrib,axiom,
% 109.04/108.77 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Rings_Osemiring__0(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__right__distrib,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 109.04/108.77 ( class_Rings_Osemiring__0(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_vimage__compose,axiom,
% 109.04/108.77 ! [V_x_2,V_f_2,V_g_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2)),V_x_2) = hAPP(c_Set_Ovimage(T_b,T_d,V_f_2),hAPP(c_Set_Ovimage(T_d,T_c,V_g_2),V_x_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fun__upd__comp,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),c_Fun_Ofun__upd(T_b,T_d,V_g_2,V_x_2,V_y_2)) = c_Fun_Ofun__upd(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2),V_x_2,hAPP(V_f_2,V_y_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__atMost__UNIV,axiom,
% 109.04/108.77 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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 109.04/108.77 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fold__image__def,axiom,
% 109.04/108.77 ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_of__int__setsum,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Rings_Oring__1(T_b)
% 109.04/108.77 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Int_Oint),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,T_c),c_Int_Oring__1__class_Oof__int(T_b)),V_f_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__divide__distrib,axiom,
% 109.04/108.77 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Fields_Ofield(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Rings_Oinverse__class_Odivide(T_b)),V_f_2)),V_r_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inj__on__add__nat,axiom,
% 109.04/108.77 ! [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) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUP__le__iff,axiom,
% 109.04/108.77 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_M_2)),V_u_2))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_pred__subset__eq2,axiom,
% 109.04/108.77 ! [V_S_2,V_R_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),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_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)))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__subset__iff,axiom,
% 109.04/108.77 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_pred__subset__eq,axiom,
% 109.04/108.77 ! [V_S_2,V_R_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__lower,axiom,
% 109.04/108.77 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_le__INF__iff,axiom,
% 109.04/108.77 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_M_2)))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 109.04/108.77 ! [V_n_2,V_m_2] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 109.04/108.77 <=> 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)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__subset__iff,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),V_B_2))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_A_2,B_x)),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__addf,axiom,
% 109.04/108.77 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),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_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_less__SUP__iff,axiom,
% 109.04/108.77 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 109.04/108.77 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.77 & class_Orderings_Olinorder(T_b) )
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),V_f_2)))
% 109.04/108.77 <=> ? [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INF__less__iff,axiom,
% 109.04/108.77 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.77 & class_Orderings_Olinorder(T_b) )
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),V_A_2),V_f_2)),V_a_2))
% 109.04/108.77 <=> ? [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.77 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_le__SUPI,axiom,
% 109.04/108.77 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_M_2,V_i_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_M_2))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_less__eq__Suc__le__raw,axiom,
% 109.04/108.77 ! [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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__upper,axiom,
% 109.04/108.77 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum_Odistrib,axiom,
% 109.04/108.77 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Oplus__class_Oplus(T_c)),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_h_2),V_A_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INF__leI,axiom,
% 109.04/108.77 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_M_2)),hAPP(V_M_2,V_i_2))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_nat__number__of__Bit0,axiom,
% 109.04/108.77 ! [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))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_pair__box_Oinject,axiom,
% 109.04/108.77 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 109.04/108.77 ( c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_2,V_b_2) = c_Nitpick_Opair__box_OPairBox(T_b,T_c,V_a_H_2,V_b_H_2)
% 109.04/108.77 <=> ( V_a_2 = V_a_H_2
% 109.04/108.77 & V_b_2 = V_b_H_2 ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Int__Union,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Int__Union2,axiom,
% 109.04/108.77 ! [V_A_2,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2)),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I2_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I1_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,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_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__Int__distrib,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),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_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I5_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I4_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I5_J,axiom,
% 109.04/108.77 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : 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_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Int__UN__distrib,axiom,
% 109.04/108.77 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I4_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Int__UN__distrib2,axiom,
% 109.04/108.77 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),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_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inf__fun__def,axiom,
% 109.04/108.77 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Lattices_Olattice(T_b)
% 109.04/108.77 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__insert,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inf__Int__eq2,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),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_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))
% 109.04/108.77 <=> 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_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__absorb,axiom,
% 109.04/108.77 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inf__Int__eq,axiom,
% 109.04/108.77 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I1_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I2_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__Pow__subset,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2))),hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__le__add__shift,axiom,
% 109.04/108.77 ! [V_k_2,V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,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_b,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) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__Un,axiom,
% 109.04/108.77 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Un__Inter,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Un__INT__distrib2,axiom,
% 109.04/108.77 ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I6_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Un__INT__distrib,axiom,
% 109.04/108.77 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__extend__simps_I7_J,axiom,
% 109.04/108.77 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : 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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I6_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,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_c),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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I7_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,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_c),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_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__Un,axiom,
% 109.04/108.77 ! [V_M_2,V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_M_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_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_M_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_M_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__Un__distrib,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_I_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBS(T_c,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_c),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_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_B_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_sup__fun__def,axiom,
% 109.04/108.77 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( class_Lattices_Olattice(T_b)
% 109.04/108.77 => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_sup__Un__eq2,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),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_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))
% 109.04/108.77 <=> 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_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_sup__Un__eq,axiom,
% 109.04/108.77 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_R_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2)),V_x_2))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__insert,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I3_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__simps_I2_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I3_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__extend__simps_I2_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,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_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__absorb,axiom,
% 109.04/108.77 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,V_k_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_of__nat__setprod,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 109.04/108.77 & class_Rings_Osemiring__1(T_b) )
% 109.04/108.77 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__add__atLeastLessThan,axiom,
% 109.04/108.77 ! [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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__add__atLeastAtMost,axiom,
% 109.04/108.77 ! [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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__delta_H,axiom,
% 109.04/108.77 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__delta,axiom,
% 109.04/108.77 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Ozero__class_Ozero(T_c))),V_S_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__constant,axiom,
% 109.04/108.77 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.04/108.77 => hAPP(c_Set_Oimage(T_b,T_c,hAPP(c_COMBK(T_c,T_b),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_c),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__greaterThan__UNIV,axiom,
% 109.04/108.77 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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod__delta_H,axiom,
% 109.04/108.77 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(c_fequal,V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod__delta,axiom,
% 109.04/108.77 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = hAPP(V_b_2,V_a_2) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),c_Groups_Oone__class_Oone(T_c))),V_S_2) = c_Groups_Oone__class_Oone(T_c) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__eq__UN,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,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_c),c_Set_Oinsert(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INT__simps_I4_J,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 109.04/108.77 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_vimage__const,axiom,
% 109.04/108.77 ! [T_c,V_A_2,V_c_2,T_b] :
% 109.04/108.77 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 109.04/108.77 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 109.04/108.77 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(c_COMBK(T_b,T_c),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__constant,axiom,
% 109.04/108.77 ! [V_A_2,V_y_2,T_c,T_b] :
% 109.04/108.77 ( class_Rings_Osemiring__1(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_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_c),V_A_2))),V_y_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_power__number__of__even,axiom,
% 109.04/108.77 ! [V_w_2,V_z_2,T_b] :
% 109.04/108.77 ( class_Int_Onumber__ring(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fold__image__distrib,axiom,
% 109.04/108.77 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(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_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_dual__max,axiom,
% 109.04/108.77 ! [T_b] :
% 109.04/108.77 ( class_Orderings_Olinorder(T_b)
% 109.04/108.77 => c_Orderings_Oord_Omax(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_dual__min,axiom,
% 109.04/108.77 ! [T_b] :
% 109.04/108.77 ( class_Orderings_Olinorder(T_b)
% 109.04/108.77 => c_Orderings_Oord_Omin(T_b,hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b))) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod__constant,axiom,
% 109.04/108.77 ! [V_y_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_COMBK(T_c,T_b),V_y_2)),V_A_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_y_2),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_sup__SUPR__fold__sup,axiom,
% 109.04/108.77 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_vimage__eq__UN,axiom,
% 109.04/108.77 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_Ovimage(T_b,T_c,V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inf__INFI__fold__inf,axiom,
% 109.04/108.77 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_c),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),V_B_2),V_A_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_zpower__number__of__even,axiom,
% 109.04/108.77 ! [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))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_comp__surj,axiom,
% 109.04/108.77 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 109.04/108.77 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.77 => ( hAPP(c_Set_Oimage(T_b,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 109.04/108.77 => hAPP(c_Set_Oimage(T_c,T_d,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__lessThan__Suc,axiom,
% 109.04/108.77 ! [V_n_2,V_f_2,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__o,axiom,
% 109.04/108.77 ! [V_f_2,V_g_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Fun_Ocomp(T_d,tc_fun(T_b,tc_HOL_Obool),T_c,V_g_2),V_f_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_d,V_f_2),V_A_2)),V_g_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inj__comp,axiom,
% 109.04/108.77 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 109.04/108.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.04/108.77 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 109.04/108.77 => c_Fun_Oinj__on(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inj__on__imageI,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 109.04/108.77 ( c_Fun_Oinj__on(T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_g_2),V_f_2),V_A_2)
% 109.04/108.77 => c_Fun_Oinj__on(T_d,T_c,V_g_2,hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_A_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_comp__inj__on,axiom,
% 109.04/108.77 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.04/108.77 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 109.04/108.77 => c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_comp__inj__on__iff,axiom,
% 109.04/108.77 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.04/108.77 => ( c_Fun_Oinj__on(T_c,T_d,V_f_H_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))
% 109.04/108.77 <=> c_Fun_Oinj__on(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__atMost__Suc,axiom,
% 109.04/108.77 ! [V_n_2,V_f_2,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 109.04/108.77 ! [V_A_2,V_f_2,T_b] :
% 109.04/108.77 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 & class_Groups_Ocomm__monoid__mult(T_b) )
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Un__Union__image,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_c,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_c),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)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(T_c,tc_fun(T_b,tc_HOL_Obool),V_B_2),V_C_2))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__add__int__atLeastLessThan,axiom,
% 109.04/108.77 ! [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) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 109.04/108.77 ! [V_f_2,V_A_2,T_b] :
% 109.04/108.77 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 & class_Groups_Ocomm__monoid__mult(T_b) )
% 109.04/108.77 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,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)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Powp__Pow__eq,axiom,
% 109.04/108.77 ! [V_x_2,V_A_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 109.04/108.77 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__restrict__set,axiom,
% 109.04/108.77 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),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_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__eq__fold__image,axiom,
% 109.04/108.77 ! [V_f_2,T_c,V_A_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(T_c,tc_HOL_Obool),T_b,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Set_Oinsert(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_power__number__of__even__number__of,axiom,
% 109.04/108.77 ! [V_w_2,V_v_2,T_b] :
% 109.04/108.77 ( class_Int_Onumber__ring(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUPR__fold__sup,axiom,
% 109.04/108.77 ! [V_f_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__sup__class_Osup(T_c)),V_f_2)),c_Orderings_Obot__class_Obot(T_c)),V_A_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_card__def,axiom,
% 109.04/108.77 ! [V_A_2,T_b] :
% 109.04/108.77 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_card_Oeq__fold__g,axiom,
% 109.04/108.77 ! [V_A_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,T_b,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,T_b),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_fun__left__comm__idem__remove,axiom,
% 109.04/108.77 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,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_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),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))))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INFI__fold__inf,axiom,
% 109.04/108.77 ! [V_f_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_c),V_A_2),V_f_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Lattices_Osemilattice__inf__class_Oinf(T_c)),V_f_2)),c_Orderings_Otop__class_Otop(T_c)),V_A_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_vimage__if,axiom,
% 109.04/108.77 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 109.04/108.77 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 109.04/108.77 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 109.04/108.77 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 109.04/108.77 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_B_2) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 109.04/108.77 => hAPP(c_Set_Ovimage(T_c,T_b,hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBC(T_c,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_c),c_If(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_diff__nat__eq__if,axiom,
% 109.04/108.77 ! [V_z_2,V_z_H_2] :
% 109.04/108.77 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 109.04/108.77 => 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) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 109.04/108.77 => 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)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_negDivAlg__div__mod,axiom,
% 109.04/108.77 ! [V_l,V_k] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 109.04/108.77 => 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)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_negDivAlg__minus1,axiom,
% 109.04/108.77 ! [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))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_UN__le__eq__Un0,axiom,
% 109.04/108.77 ! [V_M_2,V_n_2,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 109.04/108.77 ! [V_f_2,V_A_2,T_b] :
% 109.04/108.77 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 & class_Groups_Ocomm__monoid__mult(T_b) )
% 109.04/108.77 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,T_b,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)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 109.04/108.77 ! [V_n_2,T_b] :
% 109.04/108.77 ( class_Rings_Osemiring__1(T_b)
% 109.04/108.77 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_adjust__eq,axiom,
% 109.04/108.77 ! [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))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__head,axiom,
% 109.04/108.77 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(V_P_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_P_2),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_m_2,V_n_2))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_minus__fold__remove,axiom,
% 109.04/108.77 ! [V_B_2,V_A_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,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_b),hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)))),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))))),V_B_2),V_A_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__reindex,axiom,
% 109.04/108.77 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_d)
% 109.04/108.77 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_eq__number__of__Suc,axiom,
% 109.04/108.77 ! [V_n_2,V_v_2] :
% 109.04/108.77 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 109.04/108.77 <=> 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))))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Suc__eq__number__of,axiom,
% 109.04/108.77 ! [V_v_2,V_n_2] :
% 109.04/108.77 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 109.04/108.77 <=> 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))))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod__reindex,axiom,
% 109.04/108.77 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_d)
% 109.04/108.77 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_B_2) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod__reindex__cong,axiom,
% 109.04/108.77 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_d)
% 109.04/108.77 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.04/108.77 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 109.04/108.77 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_nat__case__number__of,axiom,
% 109.04/108.77 ! [V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),c_Int_Onat))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_nat__number__of__Bit1,axiom,
% 109.04/108.77 ! [V_w_2] :
% 109.04/108.77 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 109.04/108.77 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 109.04/108.77 => 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)))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_geometric__sum,axiom,
% 109.04/108.77 ! [V_n_2,V_x_2,T_b] :
% 109.04/108.77 ( class_Fields_Ofield(T_b)
% 109.04/108.77 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_Power_Opower__class_Opower(T_b),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_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),V_n_2)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_x_2),c_Groups_Oone__class_Oone(T_b))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_gauss__sum,axiom,
% 109.04/108.77 ! [V_n_2,T_b] :
% 109.04/108.77 ( class_Rings_Ocomm__semiring__1(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),c_Nat_Osemiring__1__class_Oof__nat(T_b)),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_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),c_Groups_Oone__class_Oone(T_b))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum__natinterval__difff,axiom,
% 109.04/108.77 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 109.04/108.77 ( class_Groups_Oab__group__add(T_b)
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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_b),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)))) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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_b) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_less__Suc__number__of,axiom,
% 109.04/108.77 ! [V_v_2,V_n_2] :
% 109.04/108.77 ( 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)))
% 109.04/108.77 <=> 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))))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_less__number__of__Suc,axiom,
% 109.04/108.77 ! [V_n_2,V_v_2] :
% 109.04/108.77 ( 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)))
% 109.04/108.77 <=> 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)))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_le__Suc__number__of,axiom,
% 109.04/108.77 ! [V_v_2,V_n_2] :
% 109.04/108.77 ( 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)))
% 109.04/108.77 <=> 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))))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_le__number__of__Suc,axiom,
% 109.04/108.77 ! [V_n_2,V_v_2] :
% 109.04/108.77 ( 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)))
% 109.04/108.77 <=> 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)))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_max__number__of__Suc,axiom,
% 109.04/108.77 ! [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)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_max__Suc__number__of,axiom,
% 109.04/108.77 ! [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)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_nat__case__add__eq__if,axiom,
% 109.04/108.77 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,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)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_power__number__of__odd,axiom,
% 109.04/108.77 ! [V_z_2,V_w_2,T_b] :
% 109.04/108.77 ( class_Int_Onumber__ring(T_b)
% 109.04/108.77 => ( ( 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)))
% 109.04/108.77 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_z_2))),c_COMBI(T_b))) )
% 109.04/108.77 & ( ~ 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)))
% 109.04/108.77 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),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_b) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod__gen__delta,axiom,
% 109.04/108.77 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,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_c),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_c),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,T_b,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_c),V_c_2),hAPP(c_Finite__Set_Ocard(T_b),V_S_2)) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 109.04/108.77 ! [V_x_2,V_y_2,V_c_2] :
% 109.04/108.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 109.04/108.77 => 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)) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 109.04/108.77 => 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))) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 109.04/108.77 => 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)) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setsum_Oreindex,axiom,
% 109.04/108.77 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_zpower__number__of__odd,axiom,
% 109.04/108.77 ! [V_z_2,V_w_2] :
% 109.04/108.77 ( ( 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)))
% 109.04/108.77 => 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))) )
% 109.04/108.77 & ( ~ 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)))
% 109.04/108.77 => 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) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_setprod_Oreindex,axiom,
% 109.04/108.77 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 109.04/108.77 ( class_Groups_Ocomm__monoid__mult(T_c)
% 109.04/108.77 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.77 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 109.04/108.77 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_arith__series__general,axiom,
% 109.04/108.77 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 109.04/108.77 ( class_Rings_Ocomm__semiring__1(T_b)
% 109.04/108.77 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),c_Groups_Oone__class_Oone(T_b)),c_Groups_Oone__class_Oone(T_b))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(T_b)),c_Nat_Osemiring__1__class_Oof__nat(T_b))),V_d_2))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),V_d_2)))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_negDivAlg_Osimps,axiom,
% 109.04/108.77 ! [V_b,V_a] :
% 109.04/108.77 ( ( ( 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)))
% 109.04/108.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.77 => 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)) )
% 109.04/108.77 & ( ~ ( 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)))
% 109.04/108.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.77 => 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))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_min__Suc__number__of,axiom,
% 109.04/108.77 ! [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)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_min__number__of__Suc,axiom,
% 109.04/108.77 ! [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)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_arith__series__nat,axiom,
% 109.04/108.77 ! [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)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_the__inv__into__comp,axiom,
% 109.04/108.77 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 109.04/108.77 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
% 109.04/108.77 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
% 109.04/108.77 => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_power__number__of__odd__number__of,axiom,
% 109.04/108.77 ! [V_v_2,V_w_2,T_b] :
% 109.04/108.77 ( class_Int_Onumber__ring(T_b)
% 109.04/108.77 => ( ( 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)))
% 109.04/108.77 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),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_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)))),c_COMBI(T_b))) )
% 109.04/108.77 & ( ~ 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)))
% 109.04/108.77 => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),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_b) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_negDivAlg__eqn__number__of,axiom,
% 109.04/108.77 ! [V_w,V_v] :
% 109.04/108.77 ( 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)))
% 109.04/108.77 => ( ( 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))))
% 109.04/108.77 => 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))) )
% 109.04/108.77 & ( ~ 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))))
% 109.04/108.77 => 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)))) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_negDivAlg__eqn,axiom,
% 109.04/108.77 ! [V_a,V_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.77 => ( ( 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)))
% 109.04/108.77 => 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)) )
% 109.04/108.77 & ( ~ 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)))
% 109.04/108.77 => 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))) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_diff__nat__number__of,axiom,
% 109.04/108.77 ! [V_v_2,V_v_H_2] :
% 109.04/108.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 109.04/108.77 => 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) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 109.04/108.77 => 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)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_norm__frac_Osimps,axiom,
% 109.04/108.77 ! [V_a_2,V_b_2] :
% 109.04/108.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.77 => 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)) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.77 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 109.04/108.77 => 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)) )
% 109.04/108.77 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 109.04/108.77 => 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))) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 109.04/108.77 ! [V_w] :
% 109.04/108.77 ( 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)))
% 109.04/108.77 => ( ( 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)))
% 109.04/108.77 => 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)) )
% 109.04/108.77 & ( ~ 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)))
% 109.04/108.77 => 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)))) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_posDivAlg_Osimps,axiom,
% 109.04/108.77 ! [V_b,V_a] :
% 109.04/108.77 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 109.04/108.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.77 => 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) )
% 109.04/108.77 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 109.04/108.77 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.77 => 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))) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_adjust__def,axiom,
% 109.04/108.77 ! [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))))))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_sup2E,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 109.04/108.77 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_sup2CI,axiom,
% 109.04/108.77 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 109.04/108.77 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 109.04/108.77 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inf2E,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 109.04/108.77 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 109.04/108.77 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inf2I,axiom,
% 109.04/108.77 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_bot2E,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,T_c,T_b] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_x_2),V_y_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INF1__iff,axiom,
% 109.04/108.77 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2),V_b_2))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_INF2__iff,axiom,
% 109.04/108.77 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 109.04/108.77 <=> ! [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_SUP2__iff,axiom,
% 109.04/108.77 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 109.04/108.77 <=> ? [B_x] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.77 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_sup2I1,axiom,
% 109.04/108.77 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_sup2I2,axiom,
% 109.04/108.77 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inf2D2,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_inf2D1,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_x_2),V_y_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_less__by__empty,axiom,
% 109.04/108.77 ! [V_B_2,T_b,V_A_2] :
% 109.04/108.77 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_rev__predicate2D,axiom,
% 109.04/108.77 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_predicate2D,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_P_2),V_Q_2))
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_posDivAlg__0,axiom,
% 109.04/108.77 ! [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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_posDivAlg__div__mod,axiom,
% 109.04/108.77 ! [V_l,V_k] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 109.04/108.77 => 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)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_posDivAlg__eqn,axiom,
% 109.04/108.77 ! [V_a,V_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 109.04/108.77 => 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) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 109.04/108.77 => 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))) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_posDivAlg__eqn__number__of,axiom,
% 109.04/108.77 ! [V_w,V_v] :
% 109.04/108.77 ( 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)))
% 109.04/108.77 => ( ( 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)))
% 109.04/108.77 => 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)) )
% 109.04/108.77 & ( ~ 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)))
% 109.04/108.77 => 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)))) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_pair__imageI,axiom,
% 109.04/108.77 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_A_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_member(T_d),hAPP(hAPP(V_f_2,V_a_2),V_b_2)),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),V_A_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_of__int__num,axiom,
% 109.04/108.77 ! [V_k_2,T_b] :
% 109.04/108.77 ( class_Rings_Oring__1(T_b)
% 109.04/108.77 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 109.04/108.77 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.77 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_Int_Oring__1__class_Oof__int(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k_2))) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.77 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),T_b),tc_fun(tc_fun(tc_Int_Oint,tc_fun(T_b,T_b)),tc_fun(tc_Int_Oint,T_b)),tc_Int_Oint),c_COMBB(tc_fun(T_b,T_b),T_b,tc_Int_Oint)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_fun(T_b,T_b),T_b),tc_Int_Oint),c_HOL_OLet(T_b,T_b)),c_Int_Oring__1__class_Oof__int(T_b)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,T_b)),tc_Int_Oint),c_COMBS(T_b,T_b,T_b)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_fun(T_b,T_b))),tc_Int_Oint),c_COMBB(T_b,tc_fun(T_b,T_b),T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),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_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(T_b,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_b),c_Groups_Oplus__class_Oplus(T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_COMBI(T_b)))),c_Groups_Oone__class_Oone(T_b))))),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))))) ) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_in__rel__def,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 109.04/108.77 <=> 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)),V_R_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_prod__caseI,axiom,
% 109.04/108.77 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_splitI,axiom,
% 109.04/108.77 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_mem__splitI,axiom,
% 109.04/108.77 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 109.04/108.77 => hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_splitD_H,axiom,
% 109.04/108.77 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2))
% 109.04/108.77 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_splitD,axiom,
% 109.04/108.77 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 109.04/108.77 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Pair__inject,axiom,
% 109.04/108.77 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 109.04/108.77 ( 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)
% 109.04/108.77 => ~ ( V_a = V_a_H
% 109.04/108.77 => V_b != V_b_H ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Pair__eq,axiom,
% 109.04/108.77 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 109.04/108.77 ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2)
% 109.04/108.77 <=> ( V_a_2 = V_a_H_2
% 109.04/108.77 & V_b_2 = V_b_H_2 ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_split__paired__All,axiom,
% 109.04/108.77 ! [T_c,T_b,V_P_2] :
% 109.04/108.77 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 109.04/108.77 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_split__weak__cong,axiom,
% 109.04/108.77 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 109.04/108.77 ( V_p_2 = V_q_2
% 109.04/108.77 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_divmod__int__mod__div,axiom,
% 109.04/108.77 ! [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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_split__conv,axiom,
% 109.04/108.77 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f_2,V_a_2),V_b_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_prod_Osimps_I2_J,axiom,
% 109.04/108.77 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f1_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_split__eta,axiom,
% 109.04/108.77 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2 ).
% 109.04/108.77
% 109.04/108.77 fof(fact_swap__inj__on,axiom,
% 109.04/108.77 ! [V_A_2,T_c,T_b] : c_Fun_Oinj__on(tc_prod(T_b,T_c),tc_prod(T_c,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,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_A_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_split__twice,axiom,
% 109.04/108.77 ! [V_p_2,V_g_2,T_f,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,tc_prod(T_c,T_d)),V_g_2),V_p_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_f,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_f,tc_prod(T_c,T_d)),tc_fun(T_f,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_f),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2))),V_g_2)),V_p_2) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Nitpick_OFrac__def,axiom,
% 109.04/108.77 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)))) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_div__mod__code__numeral__def,axiom,
% 109.04/108.77 ! [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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_divmod__int__def,axiom,
% 109.04/108.77 ! [V_b,V_a] :
% 109.04/108.77 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.77 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.77 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 => 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)) )
% 109.04/108.77 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 => 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))) ) ) ) ) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 109.04/108.77 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.77 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 109.04/108.77 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.77 => 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))) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_negateSnd__eq,axiom,
% 109.04/108.77 ! [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)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_Nitpick_Orefl_H__def,axiom,
% 109.04/108.77 ! [V_r_2,T_b] :
% 109.04/108.77 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 109.04/108.77 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_divmod__nat__step,axiom,
% 109.04/108.77 ! [V_m,V_n] :
% 109.04/108.77 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 109.04/108.77 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 109.04/108.77 => 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)) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_divmod__int__pdivmod,axiom,
% 109.04/108.77 ! [V_l_2,V_k_2] :
% 109.04/108.77 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 => 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)) )
% 109.04/108.77 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 => 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) )
% 109.04/108.77 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.77 => 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)))) ) ) ) ) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_apsnd__conv,axiom,
% 109.04/108.77 ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)) ).
% 109.04/108.77
% 109.04/108.77 fof(fact_apsnd__compose,axiom,
% 109.04/108.78 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__zero,axiom,
% 109.04/108.78 ! [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) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_negateSnd__def,axiom,
% 109.04/108.78 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__base,axiom,
% 109.04/108.78 ! [V_n,V_m] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 109.04/108.78 => 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) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__div__mod,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__if,axiom,
% 109.04/108.78 ! [V_m_2,V_n_2] :
% 109.04/108.78 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.04/108.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 109.04/108.78 => 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) )
% 109.04/108.78 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.04/108.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 109.04/108.78 => 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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pdivmod__def,axiom,
% 109.04/108.78 ! [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))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pdivmod__posDivAlg,axiom,
% 109.04/108.78 ! [V_k,V_l] :
% 109.04/108.78 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => 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)) )
% 109.04/108.78 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => 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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__int__code,axiom,
% 109.04/108.78 ! [V_l_2,V_k_2] :
% 109.04/108.78 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => 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)) )
% 109.04/108.78 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => 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) )
% 109.04/108.78 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => 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)))) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat__rec__add__eq__if,axiom,
% 109.04/108.78 ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2),V_n_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),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_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,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))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 109.04/108.78 ! [V_a,V_r,V_q,V_c,V_b] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 109.04/108.78 => 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)))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 109.04/108.78 ! [V_c,V_r,V_q,V_b,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 109.04/108.78 => 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)))) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__rel__unique,axiom,
% 109.04/108.78 ! [V_qr_H,V_qr,V_n,V_m] :
% 109.04/108.78 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 109.04/108.78 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 109.04/108.78 => V_qr = V_qr_H ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat__rec__0,axiom,
% 109.04/108.78 ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2 ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat__rec__Suc,axiom,
% 109.04/108.78 ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,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_b,V_f1_2,V_f2_2),V_nat_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__eq,axiom,
% 109.04/108.78 ! [V_qr,V_n,V_m] :
% 109.04/108.78 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 109.04/108.78 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 109.04/108.78 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mod__eq,axiom,
% 109.04/108.78 ! [V_r,V_q,V_n,V_m] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_div__eq,axiom,
% 109.04/108.78 ! [V_r,V_q,V_n,V_m] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__rel,axiom,
% 109.04/108.78 ! [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)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 109.04/108.78 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( 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)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 109.04/108.78 => 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)))) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat__rec__number__of,axiom,
% 109.04/108.78 ! [V_v_2,V_f_2,V_a_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,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_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,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)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),V_a_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,T_b),tc_Int_Oint),V_f_2),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),c_Nat_Onat_Onat__rec(T_b,V_a_2,V_f_2)),c_Int_Onat)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pair__box_Osize_I2_J,axiom,
% 109.04/108.78 ! [V_b,V_a,T_b,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(T_a,T_b)),c_Nitpick_Opair__box_OPairBox(T_a,T_b,V_a,V_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pair__box_Osimps_I2_J,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__case(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pair__box_Orecs,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Nitpick_Opair__box_Opair__box__rec(T_c,T_d,T_b,V_f1_2,c_Nitpick_Opair__box_OPairBox(T_c,T_d,V_a_2,V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_negDivAlg_Opsimps,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ( ( 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)))
% 109.04/108.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.78 => 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)) )
% 109.04/108.78 & ( ~ ( 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)))
% 109.04/108.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.78 => 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))) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_zmult2__lemma,axiom,
% 109.04/108.78 ! [V_c,V_r,V_q,V_b,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 109.04/108.78 => 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)))) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_coinduct3__mono__lemma,axiom,
% 109.04/108.78 ! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( class_Orderings_Oorder(T_b)
% 109.04/108.78 => ( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 109.04/108.78 => c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_f_2)),V_X_2))),V_B_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_unique__remainder,axiom,
% 109.04/108.78 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( 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)))
% 109.04/108.78 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => V_r = V_r_H ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_unique__quotient,axiom,
% 109.04/108.78 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( 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)))
% 109.04/108.78 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => V_q = V_q_H ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_self__remainder,axiom,
% 109.04/108.78 ! [V_r,V_q,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__int__rel__0,axiom,
% 109.04/108.78 ! [V_b] :
% 109.04/108.78 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => 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)))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__int__rel__neg,axiom,
% 109.04/108.78 ! [V_qr,V_b,V_a] :
% 109.04/108.78 ( 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))
% 109.04/108.78 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__int__correct,axiom,
% 109.04/108.78 ! [V_a,V_b] :
% 109.04/108.78 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_self__quotient,axiom,
% 109.04/108.78 ! [V_r,V_q,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__int__rel__mod,axiom,
% 109.04/108.78 ! [V_r,V_q,V_b,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__int__rel__div,axiom,
% 109.04/108.78 ! [V_r,V_q,V_b,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_negDivAlg__correct,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.78 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__int__rel__div__mod,axiom,
% 109.04/108.78 ! [V_a,V_b] :
% 109.04/108.78 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => 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)))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_posDivAlg__correct,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.78 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_zadd1__lemma,axiom,
% 109.04/108.78 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( 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)))
% 109.04/108.78 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => 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)))) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_zminus1__lemma,axiom,
% 109.04/108.78 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => 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))))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__int__relI,axiom,
% 109.04/108.78 ! [V_r,V_q,V_b,V_a] :
% 109.04/108.78 ( 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)
% 109.04/108.78 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 109.04/108.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 109.04/108.78 => 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))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_zmult1__lemma,axiom,
% 109.04/108.78 ! [V_a,V_r,V_q,V_c,V_b] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 => 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)))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__int__rel__def,axiom,
% 109.04/108.78 ! [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))))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_posDivAlg_Opsimps,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 109.04/108.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.78 => 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) )
% 109.04/108.78 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 109.04/108.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.78 => 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))) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_norm__frac_Opsimps,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => 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)) )
% 109.04/108.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 109.04/108.78 => 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)) )
% 109.04/108.78 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 109.04/108.78 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 109.04/108.78 => 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))) ) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_negDivAlg_Opinduct,axiom,
% 109.04/108.78 ! [V_P_2,V_a1_2,V_a0_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ! [B_a,B_b] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ( ~ ( 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)))
% 109.04/108.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.78 => 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))) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_posDivAlg_Opinduct,axiom,
% 109.04/108.78 ! [V_P_2,V_a1_2,V_a0_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ! [B_a,B_b] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 109.04/108.78 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 109.04/108.78 => 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))) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_accp__subset,axiom,
% 109.04/108.78 ! [V_R2_2,V_R1_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_R1_2),V_R2_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oaccp(T_b,V_R2_2)),c_Wellfounded_Oaccp(T_b,V_R1_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 109.04/108.78 ! [V_f_2,V_A_2,T_b] :
% 109.04/108.78 ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,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_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_accp_Osimps,axiom,
% 109.04/108.78 ! [V_a_2,V_r_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 109.04/108.78 <=> ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 109.04/108.78 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_accp_Oequations,axiom,
% 109.04/108.78 ! [V_a_2,V_r_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 109.04/108.78 <=> ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 109.04/108.78 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_accp__downward,axiom,
% 109.04/108.78 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 109.04/108.78 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat__gcd_Opsimps,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.04/108.78 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 109.04/108.78 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.04/108.78 => 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)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat_Osize_I2_J,axiom,
% 109.04/108.78 ! [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))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mod__pos__neg__1__number__of,axiom,
% 109.04/108.78 ! [V_w] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => 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))))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_snd__apsnd,axiom,
% 109.04/108.78 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapsnd(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_apsnd__eq__conv,axiom,
% 109.04/108.78 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 109.04/108.78 ( hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_g_2),V_x_2)
% 109.04/108.78 <=> hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_d),V_x_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_snd__def,axiom,
% 109.04/108.78 ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_snd__conv,axiom,
% 109.04/108.78 ! [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 ).
% 109.04/108.78
% 109.04/108.78 fof(fact_snd__eqD,axiom,
% 109.04/108.78 ! [V_a,V_y,V_x,T_a,T_b] :
% 109.04/108.78 ( 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
% 109.04/108.78 => V_y = V_a ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mod__int__def,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat_Osize_I1_J,axiom,
% 109.04/108.78 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mod__neg__pos,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.78 => 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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mod__pos__pos,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.78 => 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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mod__pos__pos__1__number__of,axiom,
% 109.04/108.78 ! [V_w] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => 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))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mod__pos__neg,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => 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)))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mod__neg__neg,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => 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)))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_in__measure,axiom,
% 109.04/108.78 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)))
% 109.04/108.78 <=> 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))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 109.04/108.78 ! [V_f_2,V_A_2,T_b] :
% 109.04/108.78 ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,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_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,T_b),c_Int_Onat),V_f_2)),V_A_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Oremove,axiom,
% 109.04/108.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.04/108.78 => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,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)))))),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Ocommute__left__comp,axiom,
% 109.04/108.78 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_y_2)),V_g_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Ocommute__comp,axiom,
% 109.04/108.78 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 109.04/108.78 ! [V_h_2,V_g_2,T_g,V_f_2,T_d,T_e,T_f,V_F_2,V_fa_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_f,T_e,T_d,V_f_2),hAPP(c_Fun_Ocomp(T_g,T_f,T_d,V_g_2),V_h_2)) = hAPP(c_Fun_Ocomp(T_g,T_e,T_d,hAPP(c_Fun_Ocomp(T_f,T_e,T_g,V_f_2),V_g_2)),V_h_2) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mod__nat__def,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Ocommute__comp_H,axiom,
% 109.04/108.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 109.04/108.78 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 109.04/108.78 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Oeq__fold,axiom,
% 109.04/108.78 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => hAPP(hAPP(V_F_2,V_A_2),V_s_2) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_s_2),V_A_2) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Oinsert,axiom,
% 109.04/108.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.04/108.78 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Ounion__inter,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,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(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Oinsert__remove,axiom,
% 109.04/108.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,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)))))),hAPP(V_f_2,V_x_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding_Ounion,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.04/108.78 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_norm__frac_Opinduct,axiom,
% 109.04/108.78 ! [V_P_2,V_a1_2,V_a0_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ! [B_a,B_b] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => 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))) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_div__pos__neg__1__number__of,axiom,
% 109.04/108.78 ! [V_w] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => 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))))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat__def,axiom,
% 109.04/108.78 ! [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)))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Pair__fst__snd__eq,axiom,
% 109.04/108.78 ! [T_c,T_b,V_t_2,V_s_2] :
% 109.04/108.78 ( V_s_2 = V_t_2
% 109.04/108.78 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 109.04/108.78 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_prod__eqI,axiom,
% 109.04/108.78 ! [V_q,V_p,T_b,T_a] :
% 109.04/108.78 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 109.04/108.78 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 109.04/108.78 => V_p = V_q ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fst__apsnd,axiom,
% 109.04/108.78 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fst__def,axiom,
% 109.04/108.78 ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Rep__Integ__inject,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2] :
% 109.04/108.78 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 109.04/108.78 <=> V_x_2 = V_y_2 ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fst__conv,axiom,
% 109.04/108.78 ! [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 ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fst__eqD,axiom,
% 109.04/108.78 ! [V_a,V_y,V_x,T_b,T_a] :
% 109.04/108.78 ( 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
% 109.04/108.78 => V_x = V_a ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_surjective__pairing,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pair__collapse,axiom,
% 109.04/108.78 ! [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 ).
% 109.04/108.78
% 109.04/108.78 fof(fact_prod__case__beta,axiom,
% 109.04/108.78 ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_div__int__def,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_split__comp__eq,axiom,
% 109.04/108.78 ! [V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),tc_prod(T_b,T_c)),V_f_2),hAPP(hAPP(c_COMBB(T_b,T_e,tc_prod(T_b,T_c)),V_g_2),c_Product__Type_Ofst(T_b,T_c)))),c_Product__Type_Osnd(T_b,T_c)) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(T_e,tc_fun(T_c,T_d),T_b),V_f_2),V_g_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_split__beta,axiom,
% 109.04/108.78 ! [V_z_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_P_2),V_z_2) = hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_z_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_z_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_split__def,axiom,
% 109.04/108.78 ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_split__comp,axiom,
% 109.04/108.78 ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_div__neg__pos,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.78 => 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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_div__pos__pos,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 109.04/108.78 => 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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_div__pos__pos__1__number__of,axiom,
% 109.04/108.78 ! [V_w] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => 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))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_div__pos__neg,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => 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)))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_div__neg__neg,axiom,
% 109.04/108.78 ! [V_b,V_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 109.04/108.78 => 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)))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_prod__size__simp,axiom,
% 109.04/108.78 ! [V_p_2,V_g_2,V_f_2,T_c,T_b] : c_Product__Type_Oprod_Oprod__size(T_b,T_c,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_b,T_c),V_p_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_exI__realizer,axiom,
% 109.04/108.78 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2))),hAPP(c_Product__Type_Ofst(T_c,T_b),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_conjI__realizer,axiom,
% 109.04/108.78 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 109.04/108.78 ( hBOOL(hAPP(V_P_2,V_p_2))
% 109.04/108.78 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 109.04/108.78 => ( hBOOL(hAPP(V_P_2,hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2))))
% 109.04/108.78 & hBOOL(hAPP(V_Q_2,hAPP(c_Product__Type_Osnd(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_p_2),V_q_2)))) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_div__nat__def,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__rel__def,axiom,
% 109.04/108.78 ! [V_qr_2,V_n_2,V_m_2] :
% 109.04/108.78 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 109.04/108.78 <=> ( 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))
% 109.04/108.78 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.04/108.78 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 109.04/108.78 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.04/108.78 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 109.04/108.78 => ( 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)))
% 109.04/108.78 & 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)) ) )
% 109.04/108.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 109.04/108.78 => ( 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)))
% 109.04/108.78 & 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))) ) ) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_inj__vimage__singleton,axiom,
% 109.04/108.78 ! [V_a_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(T_b),c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_a_2))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UN__finite2__subset,axiom,
% 109.04/108.78 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 109.04/108.78 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,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)))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat__gcd_Opinduct,axiom,
% 109.04/108.78 ! [V_P_2,V_a1_2,V_a0_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ! [B_x,B_y] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_The__split__eq,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_split__paired__The,axiom,
% 109.04/108.78 ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_P_2) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_the__inv__into__def,axiom,
% 109.04/108.78 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_HOL_OThe(T_b,hAPP(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_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fold__def,axiom,
% 109.04/108.78 ! [V_A_2,V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold__graph(T_c,T_b,V_f_2,V_z_2,V_A_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_divmod__nat__def,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fold1__def,axiom,
% 109.04/108.78 ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_The__split,axiom,
% 109.04/108.78 ! [V_P_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_HOL_OThe(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_the__elem__def,axiom,
% 109.04/108.78 ! [V_X_2,T_b] : c_Set_Othe__elem(T_b,V_X_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),hAPP(c_fequal,V_X_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))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_range,axiom,
% 109.04/108.78 ! [V_s,V_k] :
% 109.04/108.78 ( 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))
% 109.04/108.78 => 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)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_flat__lub__def,axiom,
% 109.04/108.78 ! [V_b_2,V_A_2,T_b] :
% 109.04/108.78 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 109.04/108.78 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 109.04/108.78 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))
% 109.04/108.78 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),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_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mlex__leq,axiom,
% 109.04/108.78 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mlex__less,axiom,
% 109.04/108.78 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 109.04/108.78 ( 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)))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Least__mono,axiom,
% 109.04/108.78 ! [V_S_2,V_f_2,T_b,T_c] :
% 109.04/108.78 ( ( class_Orderings_Oorder(T_c)
% 109.04/108.78 & class_Orderings_Oorder(T_b) )
% 109.04/108.78 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 109.04/108.78 => ( ? [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 109.04/108.78 & ! [B_xa] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
% 109.04/108.78 => c_Orderings_Oord__class_OLeast(T_c,hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2))) = hAPP(V_f_2,c_Orderings_Oord__class_OLeast(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_S_2))) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding__image_Oreindex,axiom,
% 109.04/108.78 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 109.04/108.78 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 109.04/108.78 => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat_Osize_I4_J,axiom,
% 109.04/108.78 ! [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))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_LeastI,axiom,
% 109.04/108.78 ! [V_k_2,V_P_2,T_b] :
% 109.04/108.78 ( class_Orderings_Owellorder(T_b)
% 109.04/108.78 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 109.04/108.78 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat__size,axiom,
% 109.04/108.78 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 109.04/108.78
% 109.04/108.78 fof(fact_LeastI__ex,axiom,
% 109.04/108.78 ! [V_P_2,T_b] :
% 109.04/108.78 ( class_Orderings_Owellorder(T_b)
% 109.04/108.78 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 109.04/108.78 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Least__le,axiom,
% 109.04/108.78 ! [V_k_2,V_P_2,T_b] :
% 109.04/108.78 ( class_Orderings_Owellorder(T_b)
% 109.04/108.78 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_not__less__Least,axiom,
% 109.04/108.78 ! [V_P_2,V_k_2,T_b] :
% 109.04/108.78 ( class_Orderings_Owellorder(T_b)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
% 109.04/108.78 => ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding__image_Odistrib,axiom,
% 109.04/108.78 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 109.04/108.78 => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat_Osize_I3_J,axiom,
% 109.04/108.78 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) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Least__Suc,axiom,
% 109.04/108.78 ! [V_n_2,V_P_2] :
% 109.04/108.78 ( hBOOL(hAPP(V_P_2,V_n_2))
% 109.04/108.78 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 109.04/108.78 => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding__image_Oeq__fold,axiom,
% 109.04/108.78 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 109.04/108.78 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_prod_Orecs,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2,V_f1_2,T_b,T_d,T_c] : c_Product__Type_Oprod_Oprod__rec(T_c,T_d,T_b,V_f1_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_f1_2,V_a_2),V_b_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_setsum__reindex__nonzero,axiom,
% 109.04/108.78 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 109.04/108.78 ( class_Groups_Ocomm__monoid__add(T_d)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 109.04/108.78 => ! [B_y] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 109.04/108.78 => ( B_x != B_y
% 109.04/108.78 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 109.04/108.78 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UN__finite2__eq,axiom,
% 109.04/108.78 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 109.04/108.78 ( ! [B_n] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,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)
% 109.04/108.78 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_B_2) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UN__finite__subset,axiom,
% 109.04/108.78 ! [V_C_2,V_A_2,T_b] :
% 109.04/108.78 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,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))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),V_A_2)),V_C_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_image__INT,axiom,
% 109.04/108.78 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,B_x)),V_C_2)) )
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 109.04/108.78 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_in__lex__prod,axiom,
% 109.04/108.78 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_H_2),V_b_H_2))),c_Wellfounded_Olex__prod(T_b,T_c,V_r_2,V_s_2)))
% 109.04/108.78 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_H_2)),V_r_2))
% 109.04/108.78 | ( V_a_2 = V_a_H_2
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_b_2),V_b_H_2)),V_s_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_same__fstI,axiom,
% 109.04/108.78 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 109.04/108.78 ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y_H_2),V_y_2)),hAPP(V_R_2,V_x_2)))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_H_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2))),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_in__finite__psubset,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_b)))
% 109.04/108.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 109.04/108.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding__idem_Ounion__idem,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.04/108.78 => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 109.04/108.78 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding__idem_Oidem__comp,axiom,
% 109.04/108.78 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_f_2,V_x_2) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 109.04/108.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding__idem_Oinsert__idem,axiom,
% 109.04/108.78 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 109.04/108.78 => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_setsum__nonneg__leq__bound,axiom,
% 109.04/108.78 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 109.04/108.78 ( class_Groups_Oordered__ab__group__add(T_c)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 109.04/108.78 => ( ! [B_i] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 109.04/108.78 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_setsum__nonneg__0,axiom,
% 109.04/108.78 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 109.04/108.78 ( class_Groups_Oordered__ab__group__add(T_c)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 109.04/108.78 => ( ! [B_i] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 109.04/108.78 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = c_Groups_Ozero__class_Ozero(T_c)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 109.04/108.78 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_sum__diff__distrib,axiom,
% 109.04/108.78 ! [V_n_2,V_P_2,V_Q_2] :
% 109.04/108.78 ( ! [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)))
% 109.04/108.78 => 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)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_apsnd__apfst,axiom,
% 109.04/108.78 ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_e,T_d),V_x_2))),hAPP(V_f_2,hAPP(c_Product__Type_Osnd(T_e,T_d),V_x_2))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_apfst__apsnd,axiom,
% 109.04/108.78 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_d,V_g_2),V_x_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2))),hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pair__lessI2,axiom,
% 109.04/108.78 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 109.04/108.78 => 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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_apfst__compose,axiom,
% 109.04/108.78 ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_snd__apfst,axiom,
% 109.04/108.78 ! [V_x_2,V_f_2,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Oapfst(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Osnd(T_d,T_b),V_x_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_apfst__eq__conv,axiom,
% 109.04/108.78 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 109.04/108.78 ( hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2) = hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_g_2),V_x_2)
% 109.04/108.78 <=> hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fst__apfst,axiom,
% 109.04/108.78 ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_c),V_x_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_apfst__conv,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_x_2)),V_y_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_apsnd__apfst__commute,axiom,
% 109.04/108.78 ! [V_p_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_b,T_d,V_g_2),V_p_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,V_g_2),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_e,V_f_2),V_p_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pair__lessI1,axiom,
% 109.04/108.78 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 109.04/108.78 => 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)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pair__leqI2,axiom,
% 109.04/108.78 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 109.04/108.78 => 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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_smin__insertI,axiom,
% 109.04/108.78 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 109.04/108.78 => ( 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))
% 109.04/108.78 => ( 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))
% 109.04/108.78 => 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)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_smax__insertI,axiom,
% 109.04/108.78 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 109.04/108.78 => ( 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))
% 109.04/108.78 => ( 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))
% 109.04/108.78 => 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)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_smax__emptyI,axiom,
% 109.04/108.78 ! [V_Y_2] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 109.04/108.78 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 109.04/108.78 => 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)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_smin__emptyI,axiom,
% 109.04/108.78 ! [V_X_2] :
% 109.04/108.78 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 109.04/108.78 => 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)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pair__leqI1,axiom,
% 109.04/108.78 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 109.04/108.78 => 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)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_wmax__insertI,axiom,
% 109.04/108.78 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 109.04/108.78 => ( 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))
% 109.04/108.78 => ( 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))
% 109.04/108.78 => 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)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_wmin__insertI,axiom,
% 109.04/108.78 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 109.04/108.78 => ( 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))
% 109.04/108.78 => ( 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))
% 109.04/108.78 => 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)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_wmax__emptyI,axiom,
% 109.04/108.78 ! [V_X_2] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 109.04/108.78 => 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)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_wmin__emptyI,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_min__weak__def,axiom,
% 109.04/108.78 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)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_max__weak__def,axiom,
% 109.04/108.78 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)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_max__rpair__set,axiom,
% 109.04/108.78 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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_max__strict__def,axiom,
% 109.04/108.78 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_max__ext__additive,axiom,
% 109.04/108.78 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_min__strict__def,axiom,
% 109.04/108.78 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_min__rpair__set,axiom,
% 109.04/108.78 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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_max__extp__max__ext__eq,axiom,
% 109.04/108.78 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 109.04/108.78 ( c_Wellfounded_Omax__extp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_R_2),V_x_2,V_xa_2)
% 109.04/108.78 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_less__than__iff,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2] :
% 109.04/108.78 ( 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))
% 109.04/108.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_intrel__iff,axiom,
% 109.04/108.78 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 109.04/108.78 ( 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))
% 109.04/108.78 <=> 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) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_pair__less__def,axiom,
% 109.04/108.78 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mlex__prod__def,axiom,
% 109.04/108.78 ! [V_R_2,V_f_2,T_b] : c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,T_b),T_b),c_Wellfounded_Olex__prod(tc_Nat_Onat,T_b,c_Wellfounded_Oless__than,V_R_2)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(tc_Nat_Onat,T_b)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(T_b,tc_prod(tc_Nat_Onat,T_b)),T_b),c_Product__Type_OPair(tc_Nat_Onat,T_b)),V_f_2)),c_COMBI(T_b))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_rp__inv__image__rp,axiom,
% 109.04/108.78 ! [V_f_2,T_c,V_P_2,T_b] :
% 109.04/108.78 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 109.04/108.78 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_strong__setprod__reindex__cong,axiom,
% 109.04/108.78 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 109.04/108.78 ( class_Groups_Ocomm__monoid__mult(T_d)
% 109.04/108.78 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.04/108.78 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_rp__inv__image__def,axiom,
% 109.04/108.78 ! [T_c,T_b] : c_FunDef_Orp__inv__image(T_b,T_c) = hAPP(c_Product__Type_Oprod_Oprod__case(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(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(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_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_COMBS(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_c,T_b),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool))),tc_fun(T_c,T_b)),c_Product__Type_OPair(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)))),c_Relation_Oinv__image(T_b,T_c))))),c_Relation_Oinv__image(T_b,T_c))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_in__inv__image,axiom,
% 109.04/108.78 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2)))
% 109.04/108.78 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))),V_r_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equiv__intrel__iff,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2] :
% 109.04/108.78 ( 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))))
% 109.04/108.78 <=> 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)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 109.04/108.78 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 109.04/108.78 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.78 & class_Groups_Ocomm__monoid__mult(T_b) )
% 109.04/108.78 => ( V_A_2 = V_B_2
% 109.04/108.78 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 109.04/108.78 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__empty,axiom,
% 109.04/108.78 ! [V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__Un,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,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(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Un__Image,axiom,
% 109.04/108.78 ! [V_A_2,V_S_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_R_2),V_S_2)),V_A_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_S_2),V_A_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__mono,axiom,
% 109.04/108.78 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_H_2),V_A_H_2)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__Int__subset,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__INT__subset,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__UN,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_d,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_rev__ImageI,axiom,
% 109.04/108.78 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__iff,axiom,
% 109.04/108.78 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 109.04/108.78 <=> ? [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__eq__UN,axiom,
% 109.04/108.78 ! [V_B_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Relation_OImage(T_c,T_b,V_r_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),c_Set_Oinsert(T_c)),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__singleton__iff,axiom,
% 109.04/108.78 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))))))
% 109.04/108.78 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_measure__def,axiom,
% 109.04/108.78 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_of__int,axiom,
% 109.04/108.78 ! [V_j_2,V_i_2,T_b] :
% 109.04/108.78 ( class_Rings_Oring__1(T_b)
% 109.04/108.78 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),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_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_i_2)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_j_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_One__int__def,axiom,
% 109.04/108.78 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))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mult,axiom,
% 109.04/108.78 ! [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))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Rep__Integ__inverse,axiom,
% 109.04/108.78 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 109.04/108.78
% 109.04/108.78 fof(fact_minus,axiom,
% 109.04/108.78 ! [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))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Zero__int__def,axiom,
% 109.04/108.78 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))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_int__def,axiom,
% 109.04/108.78 ! [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))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_add,axiom,
% 109.04/108.78 ! [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))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_nat,axiom,
% 109.04/108.78 ! [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) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_minus__int__def,axiom,
% 109.04/108.78 ! [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))))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_less,axiom,
% 109.04/108.78 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 109.04/108.78 ( 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)))))))
% 109.04/108.78 <=> 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))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_le,axiom,
% 109.04/108.78 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 109.04/108.78 ( 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)))))))
% 109.04/108.78 <=> 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))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_irrefl__def,axiom,
% 109.04/108.78 ! [V_r_2,T_b] :
% 109.04/108.78 ( c_Relation_Oirrefl(T_b,V_r_2)
% 109.04/108.78 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_eq__Abs__Integ,axiom,
% 109.04/108.78 ! [V_z_2] :
% 109.04/108.78 ~ ! [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))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Field__insert,axiom,
% 109.04/108.78 ! [V_r_2,V_b_2,V_a_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OField(T_b),V_r_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Field__Union,axiom,
% 109.04/108.78 ! [V_R_2,T_b] : hAPP(c_Relation_OField(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),V_R_2)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),c_Relation_OField(T_b)),V_R_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Field__empty,axiom,
% 109.04/108.78 ! [T_b] : hAPP(c_Relation_OField(T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mono__Field,axiom,
% 109.04/108.78 ! [V_s_2,V_r_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Field__Un,axiom,
% 109.04/108.78 ! [V_s_2,V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_Relation_OField(T_b),V_s_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__Field,axiom,
% 109.04/108.78 ! [V_r_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Id__on__def,axiom,
% 109.04/108.78 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,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_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotient__def,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),c_Relation_OImage(T_b,T_b,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)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_ImageE,axiom,
% 109.04/108.78 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 109.04/108.78 => ~ ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2))
% 109.04/108.78 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotient__empty,axiom,
% 109.04/108.78 ! [V_r_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotient__is__empty2,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)
% 109.04/108.78 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotient__is__empty,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 109.04/108.78 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Id__on__def_H,axiom,
% 109.04/108.78 ! [V_A_2,T_b] : c_Relation_OId__on(T_b,V_A_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),c_fequal))),V_A_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Id__on__empty,axiom,
% 109.04/108.78 ! [T_b] : c_Relation_OId__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__Id__on,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotient__diff1,axiom,
% 109.04/108.78 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 109.04/108.78 ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),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))))),V_r_2),V_A_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 => hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),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_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_r_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotientI,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Id__on__eqI,axiom,
% 109.04/108.78 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 109.04/108.78 ( V_a_2 = V_b_2
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Id__on__iff,axiom,
% 109.04/108.78 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
% 109.04/108.78 <=> ( V_x_2 = V_y_2
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_singleton__quotient,axiom,
% 109.04/108.78 ! [V_r_2,V_x_2,T_b] : hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Set_Oinsert(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_card__quotient__disjoint,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( c_Fun_Oinj__on(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),T_b),c_Equiv__Relations_Oquotient(T_b)),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))))),V_r_2),V_A_2)
% 109.04/108.78 => hAPP(c_Finite__Set_Ocard(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equiv__class__nondisjoint,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_subset__equiv__class,axiom,
% 109.04/108.78 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,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))))))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotientE,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ~ ! [B_x] :
% 109.04/108.78 ( V_X_2 = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 109.04/108.78 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equiv__intrel,axiom,
% 109.04/108.78 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) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Union__quotient,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)) = V_A_2 ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equiv__class__self,axiom,
% 109.04/108.78 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_OImage(T_b,T_b,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)))))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotient__disj,axiom,
% 109.04/108.78 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ( V_X_2 = V_Y_2
% 109.04/108.78 | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equiv__class__eq,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.04/108.78 => hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotient__eqI,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 109.04/108.78 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_quotient__eq__iff,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 109.04/108.78 => ( V_X_2 = V_Y_2
% 109.04/108.78 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_eq__equiv__class__iff,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 109.04/108.78 => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 109.04/108.78 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_eq__equiv__class,axiom,
% 109.04/108.78 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 109.04/108.78 ( hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 109.04/108.78 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equiv__class__eq__iff,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 109.04/108.78 <=> ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equiv__class__subset,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,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_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_eq__equiv__class__iff2,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 109.04/108.78 => ( hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2) = hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),V_r_2)
% 109.04/108.78 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UN__equiv__class2,axiom,
% 109.04/108.78 ! [V_a2_2,V_a1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 109.04/108.78 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 109.04/108.78 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 109.04/108.78 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r1_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a2_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) = hAPP(hAPP(V_f_2,V_a1_2),V_a2_2) ) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UN__equiv__class,axiom,
% 109.04/108.78 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 => hAPP(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_r_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) = hAPP(V_f_2,V_a_2) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equivp__equiv,axiom,
% 109.04/108.78 ! [V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 109.04/108.78 <=> c_Equiv__Relations_Oequivp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_A_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_identity__equivp,axiom,
% 109.04/108.78 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equivp__def,axiom,
% 109.04/108.78 ! [V_R_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.04/108.78 <=> ! [B_x,B_y] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 109.04/108.78 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equivp__reflp,axiom,
% 109.04/108.78 ! [V_x_2,V_R_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equivp__symp,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equivp__transp,axiom,
% 109.04/108.78 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_congruent2__implies__congruent,axiom,
% 109.04/108.78 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 109.04/108.78 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_congruent__def,axiom,
% 109.04/108.78 ! [V_f_2,V_r_2,T_c,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 109.04/108.78 <=> ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),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_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_congruent2D,axiom,
% 109.04/108.78 ! [V_z2_2,V_y2_2,V_z1_2,V_y1_2,V_f_2,V_r2_2,V_r1_2,T_d,T_c,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y1_2),V_z1_2)),V_r1_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),V_y2_2),V_z2_2)),V_r2_2))
% 109.04/108.78 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_congruentD,axiom,
% 109.04/108.78 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_r_2))
% 109.04/108.78 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_congruent2__implies__congruent__UN,axiom,
% 109.04/108.78 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 109.04/108.78 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 109.04/108.78 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 109.04/108.78 => c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_d,tc_HOL_Obool),V_r1_2,hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_c,V_r2_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))))),V_f_2)) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UN__equiv__class__inject,axiom,
% 109.04/108.78 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 109.04/108.78 => ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_Y_2),V_f_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_Y_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => ! [B_y] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 109.04/108.78 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2)) ) ) )
% 109.04/108.78 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UN__equiv__class__type2,axiom,
% 109.04/108.78 ! [V_B_2,V_X2_2,V_X1_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 109.04/108.78 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 109.04/108.78 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A1_2),V_r1_2)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),V_X2_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_c),V_A2_2),V_r2_2)))
% 109.04/108.78 => ( ! [B_x1] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 109.04/108.78 => ! [B_x2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_d,tc_HOL_Obool)),V_X1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_X2_2)),V_f_2))),V_B_2)) ) ) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UN__equiv__class__type,axiom,
% 109.04/108.78 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_X_2),V_f_2)),V_B_2)) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Integ__def,axiom,
% 109.04/108.78 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) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__on__def_H,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.04/108.78 <=> ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))),B_x)) )
% 109.04/108.78 & ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Id__onE,axiom,
% 109.04/108.78 ! [V_A_2,V_c_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 109.04/108.78 => ~ ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__on__Id__on,axiom,
% 109.04/108.78 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__on__empty,axiom,
% 109.04/108.78 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__on__Un,axiom,
% 109.04/108.78 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 109.04/108.78 => c_Relation_Orefl__on(T_b,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(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__on__Int,axiom,
% 109.04/108.78 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 109.04/108.78 => c_Relation_Orefl__on(T_b,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(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Rep__Integ,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__onD,axiom,
% 109.04/108.78 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__onD1,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__onD2,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_type__definition__Integ,axiom,
% 109.04/108.78 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) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 109.04/108.78 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 109.04/108.78 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.78 & class_Groups_Ocomm__monoid__mult(T_b) )
% 109.04/108.78 => ( V_A_2 = V_B_2
% 109.04/108.78 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 109.04/108.78 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_g_2),V_B_2) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_accp__acc__eq,axiom,
% 109.04/108.78 ! [V_x_2,V_r_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),V_x_2))
% 109.04/108.78 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_acc__subset,axiom,
% 109.04/108.78 ! [V_R2_2,V_R1_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R1_2),V_R2_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Oacc(T_b,V_R2_2)),c_Wellfounded_Oacc(T_b,V_R1_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_acc_Osimps,axiom,
% 109.04/108.78 ! [V_r_2,V_a_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 109.04/108.78 <=> ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_acc__downward,axiom,
% 109.04/108.78 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_type__definition_ORep__range,axiom,
% 109.04/108.78 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 109.04/108.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 109.04/108.78 => hAPP(c_Set_Oimage(T_b,T_c,V_Rep_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = V_A_2 ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_type__definition_OAbs__image,axiom,
% 109.04/108.78 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 109.04/108.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 109.04/108.78 => hAPP(c_Set_Oimage(T_c,T_b,V_Abs_2),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_type__definition_OAbs__inject,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 109.04/108.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 109.04/108.78 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 109.04/108.78 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_type__definition_ORep__inject,axiom,
% 109.04/108.78 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 109.04/108.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 109.04/108.78 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 109.04/108.78 <=> V_x_2 = V_y_2 ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_type__definition_ORep__inverse,axiom,
% 109.04/108.78 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 109.04/108.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 109.04/108.78 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_type__definition_ORep,axiom,
% 109.04/108.78 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 109.04/108.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_type__definition_OAbs__inverse,axiom,
% 109.04/108.78 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 109.04/108.78 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 109.04/108.78 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_max__extp_Oequations,axiom,
% 109.04/108.78 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 109.04/108.78 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 109.04/108.78 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 109.04/108.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 109.04/108.78 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 & ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 109.04/108.78 => ? [B_xa] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 109.04/108.78 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_max__ext_Ointros,axiom,
% 109.04/108.78 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 109.04/108.78 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 109.04/108.78 => ? [B_xa] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) )
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_Y_2)),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 109.04/108.78 ! [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))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Nitpick_Oone__frac__def,axiom,
% 109.04/108.78 ! [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))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 109.04/108.78 ! [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))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Nitpick_Ofrac__def,axiom,
% 109.04/108.78 ! [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)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_image__split__eq__Sigma,axiom,
% 109.04/108.78 ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,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_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,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)))))),V_A_2))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Rep__Integ__induct,axiom,
% 109.04/108.78 ! [V_P_2,V_y_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 109.04/108.78 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 109.04/108.78 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Rep__Integ__cases,axiom,
% 109.04/108.78 ! [V_y_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 109.04/108.78 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_SigmaI,axiom,
% 109.04/108.78 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__Union,axiom,
% 109.04/108.78 ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__empty1,axiom,
% 109.04/108.78 ! [V_B_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__Diff__distrib1,axiom,
% 109.04/108.78 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Times__Diff__distrib1,axiom,
% 109.04/108.78 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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_C_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))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__Diff__distrib2,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,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_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Times__eq__cancel2,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 109.04/108.78 => ( hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))
% 109.04/108.78 <=> V_A_2 = V_B_2 ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_card__cartesian__product,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),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_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_setsum__cartesian__product,axiom,
% 109.04/108.78 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 109.04/108.78 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),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))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__empty2,axiom,
% 109.04/108.78 ! [V_A_2,T_c,T_b] : 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),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Times__empty,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.78 ( 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)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
% 109.04/108.78 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Compl__Times__UNIV2,axiom,
% 109.04/108.78 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Compl__Times__UNIV1,axiom,
% 109.04/108.78 ! [V_A_2,T_c,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),V_A_2))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_setprod__cartesian__product,axiom,
% 109.04/108.78 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 109.04/108.78 ( class_Groups_Ocomm__monoid__mult(T_b)
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(T_c,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2)),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))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__Un__distrib1,axiom,
% 109.04/108.78 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,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_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Times__Un__distrib1,axiom,
% 109.04/108.78 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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_C_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))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__Un__distrib2,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,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_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_swap__product,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_prod(T_b,T_c)),hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_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_A_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__cartesian__product,axiom,
% 109.04/108.78 ! [V_B_2,T_c,V_A_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),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)))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_equiv__type,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__Int__distrib2,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,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_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Times__Int__distrib1,axiom,
% 109.04/108.78 ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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_C_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))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__Int__distrib1,axiom,
% 109.04/108.78 ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,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_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Id__on__subset__Times,axiom,
% 109.04/108.78 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UNIV__Times__UNIV,axiom,
% 109.04/108.78 ! [T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_SigmaE2,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 109.04/108.78 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_SigmaD2,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_SigmaD1,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_mem__Sigma__iff,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 109.04/108.78 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_card__cartesian__product__singleton,axiom,
% 109.04/108.78 ! [V_A_2,V_x_2,T_c,T_b] : hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_A_2))) = hAPP(c_Finite__Set_Ocard(T_c),V_A_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Times__subset__cancel2,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_B_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_C_2))))
% 109.04/108.78 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Image__subset,axiom,
% 109.04/108.78 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_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))))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_C_2)),V_B_2)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__cartesian__productD1,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),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))))
% 109.04/108.78 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__cartesian__productD2,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),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))))
% 109.04/108.78 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fst__image__times,axiom,
% 109.04/108.78 ! [V_A_2,T_c,T_b,V_B_2] :
% 109.04/108.78 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.78 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 => hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_c,c_Product__Type_Ofst(T_c,T_b)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_c),V_B_2))) = V_A_2 ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_snd__image__times,axiom,
% 109.04/108.78 ! [V_B_2,T_c,T_b,V_A_2] :
% 109.04/108.78 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),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))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 109.04/108.78 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 => hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_c,c_Product__Type_Osnd(T_b,T_c)),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))) = V_B_2 ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__on__def,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.04/108.78 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 109.04/108.78 & ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_insert__times__insert,axiom,
% 109.04/108.78 ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),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),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__equiv__class,axiom,
% 109.04/108.78 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_vimage__Times,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),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(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UN__Times__distrib,axiom,
% 109.04/108.78 ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Sigma__def,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,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_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),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_fun(tc_prod(T_b,T_c),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_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__quotient,axiom,
% 109.04/108.78 ! [V_r_2,V_A_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 109.04/108.78 ! [V_A_2,V_I_2,T_c,T_b] :
% 109.04/108.78 ? [B_f] :
% 109.04/108.78 ( c_Fun_Oinj__on(T_b,tc_prod(T_c,T_b),B_f,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))
% 109.04/108.78 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,tc_prod(T_c,T_b),B_f),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2))),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_b),V_I_2),V_A_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_refl__onI,axiom,
% 109.04/108.78 ! [V_A_2,V_r_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
% 109.04/108.78 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fold__image__Sigma,axiom,
% 109.04/108.78 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 109.04/108.78 ( class_Groups_Ocomm__monoid__mult(T_d)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 109.04/108.78 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBC(T_b,T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(T_d,tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d)),T_b),c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d))),V_g_2)),c_Groups_Oone__class_Oone(T_d))),V_B_2)),c_Groups_Oone__class_Oone(T_d)),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,tc_prod(T_b,T_c),c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_g_2)),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_setprod__Sigma,axiom,
% 109.04/108.78 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 109.04/108.78 ( class_Groups_Ocomm__monoid__mult(T_d)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d)),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_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_setsum__Sigma,axiom,
% 109.04/108.78 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 109.04/108.78 ( class_Groups_Ocomm__monoid__add(T_d)
% 109.04/108.78 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 109.04/108.78 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),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_d),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_card__SigmaI,axiom,
% 109.04/108.78 ! [V_B_2,T_c,V_A_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 109.04/108.78 => hAPP(c_Finite__Set_Ocard(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),V_B_2)),V_A_2) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__SigmaI,axiom,
% 109.04/108.78 ! [V_B_2,T_c,V_A_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.78 => ( ! [B_a] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_SigmaE,axiom,
% 109.04/108.78 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)))
% 109.04/108.78 => ~ ! [B_x] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.04/108.78 => ! [B_y] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 109.04/108.78 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair__surj,axiom,
% 109.04/108.78 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 109.04/108.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_e,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool))
% 109.04/108.78 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_c,T_e),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair__imageI,axiom,
% 109.04/108.78 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_R_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2))),hAPP(c_Set_Oimage(tc_prod(T_b,T_c),tc_prod(T_d,T_e),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)),V_R_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair__simp,axiom,
% 109.04/108.78 ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fst__map__pair,axiom,
% 109.04/108.78 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),V_x_2)) = hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_d,T_e),V_x_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair__ident,axiom,
% 109.04/108.78 ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2 ).
% 109.04/108.78
% 109.04/108.78 fof(fact_snd__prod__fun,axiom,
% 109.04/108.78 ! [V_x_2,V_g_2,V_f_2,T_e,T_d,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),hAPP(c_Product__Type_Omap__pair(T_d,T_c,T_e,T_b,V_f_2,V_g_2),V_x_2)) = hAPP(V_g_2,hAPP(c_Product__Type_Osnd(T_d,T_e),V_x_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair_Ocomp,axiom,
% 109.04/108.78 ! [V_i_2,V_h_2,V_g_2,V_f_2,T_c,T_b,T_e,T_d,T_g,T_f] : hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f_2,V_g_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_h_2,V_i_2)) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g_2),V_i_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair__compose,axiom,
% 109.04/108.78 ! [V_g2_2,V_g1_2,T_g,V_f2_2,V_f1_2,T_f,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,hAPP(c_Fun_Ocomp(T_f,T_d,T_b,V_f1_2),V_f2_2),hAPP(c_Fun_Ocomp(T_g,T_e,T_c,V_g1_2),V_g2_2)) = hAPP(c_Fun_Ocomp(tc_prod(T_f,T_g),tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_f1_2,V_g1_2)),c_Product__Type_Omap__pair(T_b,T_f,T_c,T_g,V_f2_2,V_g2_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair_Ocompositionality,axiom,
% 109.04/108.78 ! [V_prod_2,V_i_2,V_h_2,T_g,T_f,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(c_Product__Type_Omap__pair(T_f,T_d,T_g,T_e,V_h_2,V_i_2),V_prod_2)) = hAPP(c_Product__Type_Omap__pair(T_f,T_b,T_g,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_f,V_f_2),V_h_2),hAPP(c_Fun_Ocomp(T_e,T_c,T_g,V_g_2),V_i_2)),V_prod_2) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_snd__comp__map__pair,axiom,
% 109.04/108.78 ! [V_g_2,V_f_2,T_c,T_b,T_d,T_e] : hAPP(c_Fun_Ocomp(tc_prod(T_e,T_d),T_d,tc_prod(T_b,T_c),c_Product__Type_Osnd(T_e,T_d)),c_Product__Type_Omap__pair(T_b,T_e,T_c,T_d,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_d,tc_prod(T_b,T_c),V_g_2),c_Product__Type_Osnd(T_b,T_c)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_fst__comp__map__pair,axiom,
% 109.04/108.78 ! [V_g_2,V_f_2,T_c,T_b,T_e,T_d] : hAPP(c_Fun_Ocomp(tc_prod(T_d,T_e),T_d,tc_prod(T_b,T_c),c_Product__Type_Ofst(T_d,T_e)),c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,tc_prod(T_b,T_c),V_f_2),c_Product__Type_Ofst(T_b,T_c)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair__def,axiom,
% 109.04/108.78 ! [V_g_2,V_f_2,T_e,T_c,T_d,T_b] : c_Product__Type_Omap__pair(T_b,T_d,T_c,T_e,V_f_2,V_g_2) = hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_d,T_e)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_c,T_e),tc_fun(T_c,tc_prod(T_d,T_e))),T_b),c_COMBB(T_e,tc_prod(T_d,T_e),T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_e,tc_prod(T_d,T_e)),T_b),c_Product__Type_OPair(T_d,T_e)),V_f_2))),V_g_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair__surj__on,axiom,
% 109.04/108.78 ! [V_B_H_2,V_B_2,V_g_2,T_d,T_e,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 109.04/108.78 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 109.04/108.78 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 109.04/108.78 => hAPP(c_Set_Oimage(tc_prod(T_c,T_e),tc_prod(T_b,T_d),c_Product__Type_Omap__pair(T_c,T_b,T_e,T_d,V_f_2,V_g_2)),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_d),V_A_H_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_b),V_B_H_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_map__pair__inj__on,axiom,
% 109.04/108.78 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 109.04/108.78 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.04/108.78 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 109.04/108.78 => c_Fun_Oinj__on(tc_prod(T_b,T_d),tc_prod(T_c,T_e),c_Product__Type_Omap__pair(T_b,T_c,T_d,T_e,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))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_prod__fun__imageE,axiom,
% 109.04/108.78 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
% 109.04/108.78 => ~ ! [B_x,B_y] :
% 109.04/108.78 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
% 109.04/108.78 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_inj__on__INTER,axiom,
% 109.04/108.78 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 109.04/108.78 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 => ( ! [B_i] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 109.04/108.78 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 109.04/108.78 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_card__less__Suc,axiom,
% 109.04/108.78 ! [V_i_2,V_M_2] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 109.04/108.78 => 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))))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_CollectI,axiom,
% 109.04/108.78 ! [T_b,V_a_2,V_P_2] :
% 109.04/108.78 ( hBOOL(hAPP(V_P_2,V_a_2))
% 109.04/108.78 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__Collect__conjI,axiom,
% 109.04/108.78 ! [V_Q_2,V_P_2,T_b] :
% 109.04/108.78 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 109.04/108.78 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 109.04/108.78 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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),V_P_2)),V_Q_2)))) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__Collect__less__nat,axiom,
% 109.04/108.78 ! [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)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__Collect__le__nat,axiom,
% 109.04/108.78 ! [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)))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_SetCompr__Sigma__eq,axiom,
% 109.04/108.78 ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),V_Q_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Collect__split,axiom,
% 109.04/108.78 ! [V_Q_2,V_P_2,T_c,T_b] : hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),V_P_2))),V_Q_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Q_2))) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_vimage__Collect__eq,axiom,
% 109.04/108.78 ! [V_P_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_c),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_P_2),V_f_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Collect__neg__eq,axiom,
% 109.04/108.78 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_UNIV__def,axiom,
% 109.04/108.78 ! [T_b] : c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fTrue)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Collect__empty__eq,axiom,
% 109.04/108.78 ! [V_P_2,T_b] :
% 109.04/108.78 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.04/108.78 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_empty__Collect__eq,axiom,
% 109.04/108.78 ! [V_P_2,T_b] :
% 109.04/108.78 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 109.04/108.78 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_empty__def,axiom,
% 109.04/108.78 ! [T_b] : c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Collect__disj__eq,axiom,
% 109.04/108.78 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Collect__def,axiom,
% 109.04/108.78 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 109.04/108.78
% 109.04/108.78 fof(fact_Collect__conj__eq,axiom,
% 109.04/108.78 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(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),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2)),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_finite__Collect__disjI,axiom,
% 109.04/108.78 ! [V_Q_2,V_P_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),V_P_2)),V_Q_2))))
% 109.04/108.78 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 109.04/108.78 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_insert__Collect,axiom,
% 109.04/108.78 ! [V_P_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_b),hAPP(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_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)))),V_P_2)) ).
% 109.04/108.78
% 109.04/108.78 fof(fact_CollectE,axiom,
% 109.04/108.78 ! [V_P_2,V_a_2,T_b] :
% 109.04/108.78 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 109.04/108.79 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_CollectD,axiom,
% 109.04/108.79 ! [V_P_2,V_a_2,T_b] :
% 109.04/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 109.04/108.79 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_mem__Collect__eq,axiom,
% 109.04/108.79 ! [V_P_2,V_a_2,T_b] :
% 109.04/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 109.04/108.79 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Collect__mem__eq,axiom,
% 109.04/108.79 ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2 ).
% 109.04/108.79
% 109.04/108.79 fof(fact_insert__compr__raw,axiom,
% 109.04/108.79 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),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))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_insert__compr,axiom,
% 109.04/108.79 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),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))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Un__def,axiom,
% 109.04/108.79 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_fdisj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Int__Collect,axiom,
% 109.04/108.79 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 109.04/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))))
% 109.04/108.79 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.04/108.79 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Int__def,axiom,
% 109.04/108.79 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_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))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Collect__conv__if,axiom,
% 109.04/108.79 ! [T_b,V_a_2,V_P_2] :
% 109.04/108.79 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 109.04/108.79 => hAPP(c_Set_OCollect(T_b),hAPP(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,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 109.04/108.79 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 109.04/108.79 => hAPP(c_Set_OCollect(T_b),hAPP(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,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Collect__conv__if2,axiom,
% 109.04/108.79 ! [T_b,V_a_2,V_P_2] :
% 109.04/108.79 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 109.04/108.79 => hAPP(c_Set_OCollect(T_b),hAPP(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(c_fequal,V_a_2))),V_P_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) )
% 109.04/108.79 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 109.04/108.79 => hAPP(c_Set_OCollect(T_b),hAPP(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(c_fequal,V_a_2))),V_P_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_singleton__conv,axiom,
% 109.04/108.79 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_singleton__conv2,axiom,
% 109.04/108.79 ! [V_a_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(c_fequal,V_a_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_set__diff__eq,axiom,
% 109.04/108.79 ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(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_A_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2)))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_finite__Collect__not,axiom,
% 109.04/108.79 ! [V_P_2,T_b] :
% 109.04/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 109.04/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))))
% 109.04/108.79 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_insert__def,axiom,
% 109.04/108.79 ! [V_B_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2))),V_B_2) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Compl__eq,axiom,
% 109.04/108.79 ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_vimage__def,axiom,
% 109.04/108.79 ! [V_B_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(T_c)),V_f_2)),V_B_2)) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Collect__ball__eq,axiom,
% 109.04/108.79 ! [V_P_2,V_A_2,T_c,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),V_P_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_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_P_2))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Collect__imp__eq,axiom,
% 109.04/108.79 ! [V_Q_2,V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(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),V_P_2)),V_Q_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(c_Set_OCollect(T_b),V_Q_2)) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Inter__eq,axiom,
% 109.04/108.79 ! [V_A_2,T_b] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,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_b,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_finite__M__bounded__by__nat,axiom,
% 109.04/108.79 ! [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))))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_setsum__setsum__restrict,axiom,
% 109.04/108.79 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 109.04/108.79 ( class_Groups_Ocomm__monoid__add(T_d)
% 109.04/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 109.04/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 109.04/108.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_d),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_d),T_b),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d)),V_f_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_T_2)))),V_R_2)))),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),hAPP(hAPP(c_COMBS(T_c,tc_fun(T_b,tc_HOL_Obool),T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_d),tc_fun(tc_fun(T_b,tc_HOL_Obool),T_d),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d)),hAPP(c_COMBC(T_b,T_c,T_d),V_f_2))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),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_S_2)))),hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2))))),V_T_2) ) ) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_INTER__def,axiom,
% 109.04/108.79 ! [V_B_2,V_A_2,T_b,T_c] : 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(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fimplies),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_member(T_b))),V_B_2)))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_if__image__distrib,axiom,
% 109.04/108.79 ! [V_S_2,V_g_2,V_f_2,V_P_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBS(T_c,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_c),c_If(T_b)),V_P_2)),V_f_2)),V_g_2)),V_S_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),V_P_2)))),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_S_2),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c),c_fNot),V_P_2))))) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_nat__seg__image__imp__finite,axiom,
% 109.04/108.79 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 109.04/108.79 ( V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,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)))
% 109.04/108.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_setsum__restrict__set_H,axiom,
% 109.04/108.79 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 109.04/108.79 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.04/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_Set_OCollect(T_b),hAPP(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_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)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBC(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_f_2)),c_Groups_Ozero__class_Ozero(T_c))),V_A_2) ) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_setsum__image__gen,axiom,
% 109.04/108.79 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 109.04/108.79 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.04/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 109.04/108.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),T_c,T_d),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Set_OCollect(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),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_S_2)))),hAPP(c_COMBC(T_b,T_d,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,tc_HOL_Obool),T_b),c_fequal),V_f_2)))))),hAPP(c_Set_Oimage(T_b,T_d,V_f_2),V_S_2)) ) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Sup__Inf,axiom,
% 109.04/108.79 ! [V_A_2,T_b] :
% 109.04/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.79 => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),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(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Inf__Sup,axiom,
% 109.04/108.79 ! [V_A_2,T_b] :
% 109.04/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.04/108.79 => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),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)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_Image__singleton,axiom,
% 109.04/108.79 ! [V_a_2,V_r_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_b),c_member(tc_prod(T_c,T_b))),hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2))),V_r_2)) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_setsum__cases,axiom,
% 109.04/108.79 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 109.04/108.79 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.04/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.04/108.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBS(T_b,T_c,tc_fun(T_c,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_c,tc_fun(T_c,T_c)),T_b),c_If(T_c)),V_P_2)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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_Set_OCollect(T_b),V_P_2))))) ) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_card__less__Suc2,axiom,
% 109.04/108.79 ! [V_i_2,V_M_2] :
% 109.04/108.79 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 109.04/108.79 => 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))))) ) ).
% 109.04/108.79
% 109.04/108.79 fof(fact_card__less,axiom,
% 109.10/108.79 ! [V_i_2,V_M_2] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 109.10/108.79 => 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) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_setsum__multicount,axiom,
% 109.10/108.79 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 109.10/108.79 => ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 109.10/108.79 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_S_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = V_k_2 )
% 109.10/108.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),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_c),V_T_2)) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 109.10/108.79 ! [V_x_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Orderings_Olinorder(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 109.10/108.79 ! [V_x_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Orderings_Olinorder(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__Collect__subsets,axiom,
% 109.10/108.79 ! [V_A_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Pow__Compl,axiom,
% 109.10/108.79 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),c_Set_OPow(T_b))))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Pow__def,axiom,
% 109.10/108.79 ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__image__set,axiom,
% 109.10/108.79 ! [V_f_2,T_c,V_P_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 109.10/108.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_c),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_c),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_b,T_c),tc_fun(T_b,tc_HOL_Obool)),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)),V_f_2)))),V_P_2))))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__Collect__bounded__ex,axiom,
% 109.10/108.79 ! [V_Q_2,T_c,V_P_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),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),V_P_2))),V_Q_2)))))
% 109.10/108.79 <=> ! [B_y] :
% 109.10/108.79 ( hBOOL(hAPP(V_P_2,B_y))
% 109.10/108.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_y)))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_inj__graph,axiom,
% 109.10/108.79 ! [T_c,T_b] : c_Fun_Oinj__on(tc_fun(T_b,T_c),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Set_OCollect(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,T_c)),c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool)),hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,T_c,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 109.10/108.79 ! [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))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__psubset__def,axiom,
% 109.10/108.79 ! [T_b] : c_Wellfounded_Ofinite__psubset(T_b) = hAPP(c_Set_OCollect(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBS(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool))))),c_Finite__Set_Ofinite(T_b)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_inv__image__def,axiom,
% 109.10/108.79 ! [V_f_2,V_r_2,T_b,T_c] : hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_r_2),V_f_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),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_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_c,T_c)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_c,T_c),tc_fun(tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_c,T_c)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_c,T_c)),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_prod(T_c,T_c))),T_b),c_COMBB(T_c,tc_prod(T_c,T_c),T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_prod(T_c,T_c)),T_b),c_Product__Type_OPair(T_c,T_c)),V_f_2))),V_f_2)))),V_r_2))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 109.10/108.79 ! [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)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 109.10/108.79 ! [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)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_add__Max__commute,axiom,
% 109.10/108.79 ! [V_k_2,V_N_2,T_b] :
% 109.10/108.79 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 109.10/108.79 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMax(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_add__Min__commute,axiom,
% 109.10/108.79 ! [V_k_2,V_N_2,T_b] :
% 109.10/108.79 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 109.10/108.79 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2),c_Big__Operators_Olinorder__class_OMin(T_b,V_N_2)) = c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(T_b),V_k_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_N_2))))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_sup__Inf2__distrib,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Lattices_Odistrib__lattice(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.10/108.79 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_sup__Inf1__distrib,axiom,
% 109.10/108.79 ! [V_x_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Lattices_Odistrib__lattice(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_inf__Sup1__distrib,axiom,
% 109.10/108.79 ! [V_x_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Lattices_Odistrib__lattice(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_inf__Sup2__distrib,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Lattices_Odistrib__lattice(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.10/108.79 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_B_2)) = c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Orderings_Olinorder(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.10/108.79 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omin(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Orderings_Olinorder(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.10/108.79 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBS(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),T_b),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_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,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_b),c_fconj))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_b,T_b)),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal))),c_Orderings_Oord__class_Omax(T_b)))))),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))))))) ) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Oprod__def,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_c,T_b] : c_Nitpick_Oprod(T_b,T_c,V_A_2,V_B_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),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_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_int__ge__less__than__def,axiom,
% 109.10/108.79 ! [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)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_int__ge__less__than2__def,axiom,
% 109.10/108.79 ! [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)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_reflp__def,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Predicate_Oreflp(T_b,V_r_2)
% 109.10/108.79 <=> c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 109.10/108.79 ( class_Rings_Osemiring__0(T_d)
% 109.10/108.79 => ( c_Fun_Oinj__on(tc_prod(T_b,T_c),T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_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)))
% 109.10/108.79 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_d),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_d),c_Fun_Oid(T_d)),hAPP(c_Set_OCollect(T_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_d),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_d),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_d,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(T_b,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_d),c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool))),T_d),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_b),c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_fun(T_c,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),T_d),hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,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_c),c_fconj))),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(T_c,T_d)),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,tc_HOL_Obool)),T_d),c_COMBB(T_d,tc_HOL_Obool,T_c)),c_fequal))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,T_d),tc_fun(T_c,T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_d),tc_fun(tc_fun(T_c,T_d),tc_fun(T_c,T_d)),T_b),c_COMBB(T_d,T_d,T_c)),hAPP(hAPP(c_COMBB(T_d,tc_fun(T_d,T_d),T_b),c_Groups_Otimes__class_Otimes(T_d)),V_f_2))),V_g_2)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),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_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_B_2))))))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_setsum__multicount__gen,axiom,
% 109.10/108.79 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 109.10/108.79 => ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 109.10/108.79 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_s_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),V_R_2),B_x)))) = hAPP(V_k_2,B_x) )
% 109.10/108.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_Nat_Onat,T_b),c_Finite__Set_Ocard(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_OCollect(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_t_2)))),V_R_2)))),V_s_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_k_2),V_t_2) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_inj__on__id,axiom,
% 109.10/108.79 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_o__eq__id__dest,axiom,
% 109.10/108.79 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 109.10/108.79 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_c_2)
% 109.10/108.79 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_o__id,axiom,
% 109.10/108.79 ! [V_f_2,T_c,T_b] : hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_f_2),c_Fun_Oid(T_b)) = V_f_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_id__o,axiom,
% 109.10/108.79 ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_apfst__id,axiom,
% 109.10/108.79 ! [T_c,T_b] : c_Product__Type_Oapfst(T_b,T_b,T_c,c_Fun_Oid(T_b)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_id__def,axiom,
% 109.10/108.79 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_apsnd__id,axiom,
% 109.10/108.79 ! [T_b,T_c] : c_Product__Type_Oapsnd(T_c,T_c,T_b,c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_reflpE,axiom,
% 109.10/108.79 ! [V_x_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Predicate_Oreflp(T_b,V_r_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_id__apply,axiom,
% 109.10/108.79 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 109.10/108.79
% 109.10/108.79 fof(fact_vimage__id,axiom,
% 109.10/108.79 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_map__pair_Oid,axiom,
% 109.10/108.79 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_Fun_Oid(T_b),c_Fun_Oid(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_map__pair_Oidentity,axiom,
% 109.10/108.79 ! [T_c,T_b] : c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_of__int__eq__id,axiom,
% 109.10/108.79 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_image__id,axiom,
% 109.10/108.79 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_surj__id,axiom,
% 109.10/108.79 ! [T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_folding_Oempty,axiom,
% 109.10/108.79 ! [V_F_2,V_f_2,T_c,T_b] :
% 109.10/108.79 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 109.10/108.79 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_apfst__def,axiom,
% 109.10/108.79 ! [V_f_2,T_c,T_d,T_b] : c_Product__Type_Oapfst(T_b,T_d,T_c,V_f_2) = c_Product__Type_Omap__pair(T_b,T_d,T_c,T_c,V_f_2,c_Fun_Oid(T_c)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_apsnd__def,axiom,
% 109.10/108.79 ! [V_f_2,T_b,T_d,T_c] : c_Product__Type_Oapsnd(T_c,T_d,T_b,V_f_2) = c_Product__Type_Omap__pair(T_b,T_b,T_c,T_d,c_Fun_Oid(T_b),V_f_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_split__Pair,axiom,
% 109.10/108.79 ! [T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)) = c_Fun_Oid(tc_prod(T_b,T_c)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_setsum__reindex__id,axiom,
% 109.10/108.79 ! [V_B_2,V_f_2,T_b,T_c] :
% 109.10/108.79 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.10/108.79 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 109.10/108.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_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_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_setprod__reindex__id,axiom,
% 109.10/108.79 ! [V_B_2,V_f_2,T_b,T_c] :
% 109.10/108.79 ( class_Groups_Ocomm__monoid__mult(T_c)
% 109.10/108.79 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 109.10/108.79 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_c),c_Fun_Oid(T_c)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__conv__nat__seg__image,axiom,
% 109.10/108.79 ! [V_A_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 <=> ? [B_n,B_f] : V_A_2 = hAPP(c_Set_Oimage(tc_Nat_Onat,T_b,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))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__comp__def,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_d))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),tc_fun(tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool)),tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),T_b),c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBS(T_d,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,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_d),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBC(T_d,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_b,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_d),tc_fun(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_b,T_d)))),c_Product__Type_OPair(T_b,T_d)))),V_r_2))))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_d,T_c)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_d,T_c),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_d,T_c)))),hAPP(c_COMBC(T_d,T_c,tc_prod(T_d,T_c)),c_Product__Type_OPair(T_d,T_c))))),V_s_2))))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__Collect__split,axiom,
% 109.10/108.79 ! [V_P_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__compI,axiom,
% 109.10/108.79 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_b_2),V_c_2)),V_s_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_RangeI,axiom,
% 109.10/108.79 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__comp__UNION__distrib2,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,V_I_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),V_I_2),V_r_2)),V_s_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBC(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_e),c_Relation_Orel__comp(T_b,T_d,T_c)),V_r_2)),V_s_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__comp__UNION__distrib,axiom,
% 109.10/108.79 ! [V_r_2,V_I_2,T_e,V_s_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_I_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e),hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_s_2)),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__Id__on,axiom,
% 109.10/108.79 ! [V_A_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__comp__mono,axiom,
% 109.10/108.79 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_H_2),V_r_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_H_2),V_s_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_H_2),V_s_H_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_O__assoc,axiom,
% 109.10/108.79 ! [V_T_2,V_S_2,V_R_2,T_e,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_d),V_R_2),V_S_2)),V_T_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_e,T_c),V_R_2),hAPP(hAPP(c_Relation_Orel__comp(T_e,T_d,T_c),V_S_2),V_T_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__comp__distrib,axiom,
% 109.10/108.79 ! [V_T_2,V_S_2,V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_S_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),V_T_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__comp__distrib2,axiom,
% 109.10/108.79 ! [V_R_2,V_T_2,V_S_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_d),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_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_S_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_T_2),V_R_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__comp__empty1,axiom,
% 109.10/108.79 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool))),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__comp__empty2,axiom,
% 109.10/108.79 ! [V_R_2,T_c,T_d,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_R_2),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_d,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_union__comp__emptyR,axiom,
% 109.10/108.79 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 109.10/108.79 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 109.10/108.79 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_B_2),V_C_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_union__comp__emptyL,axiom,
% 109.10/108.79 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 109.10/108.79 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_A_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 109.10/108.79 => ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_B_2),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 109.10/108.79 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__Union,axiom,
% 109.10/108.79 ! [V_S_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ORange(T_c,T_b)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__empty,axiom,
% 109.10/108.79 ! [T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__empty__iff,axiom,
% 109.10/108.79 ! [V_r_2,T_b,T_c] :
% 109.10/108.79 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__comp__subset__Sigma,axiom,
% 109.10/108.79 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_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))))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool)),V_s_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_B_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_C_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_d),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_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_C_2)))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__Un__eq,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,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(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__Range,axiom,
% 109.10/108.79 ! [V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_snd__eq__Range,axiom,
% 109.10/108.79 ! [V_R_2,T_b,T_c] : hAPP(c_Set_Oimage(tc_prod(T_c,T_b),T_b,c_Product__Type_Osnd(T_c,T_b)),V_R_2) = hAPP(c_Relation_ORange(T_c,T_b),V_R_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__iff,axiom,
% 109.10/108.79 ! [V_r_2,T_c,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 109.10/108.79 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_y),V_a_2)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__insert,axiom,
% 109.10/108.79 ! [V_r_2,V_b_2,V_a_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__Int__subset,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,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(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__Diff__subset,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ORange(T_c,T_b),V_A_2)),hAPP(c_Relation_ORange(T_c,T_b),V_B_2))),hAPP(c_Relation_ORange(T_c,T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_max__ext__compat,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(T_b,V_R_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_min__ext__compat,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_R_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(T_b,V_S_2)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(T_b,V_R_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_RangeP__Range__eq,axiom,
% 109.10/108.79 ! [V_x_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,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_r_2)),V_x_2))
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_RangeE,axiom,
% 109.10/108.79 ! [V_r_2,T_c,V_b_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 109.10/108.79 => ~ ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),V_b_2)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_pred__comp__rel__comp__eq,axiom,
% 109.10/108.79 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,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_r_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_c),c_COMBC(T_d,tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool)),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),tc_fun(tc_fun(tc_prod(T_c,T_d),tc_HOL_Obool),tc_HOL_Obool),T_d),c_member(tc_prod(T_c,T_d)))),c_Product__Type_OPair(T_c,T_d)))),V_s_2)),V_x_2),V_y_2))
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_pred__comp_Ointros,axiom,
% 109.10/108.79 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a_2),V_c_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_RangeP_Ointros,axiom,
% 109.10/108.79 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 109.10/108.79 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_pred__comp_Oequations,axiom,
% 109.10/108.79 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_b,T_c,T_d,V_r_2,V_s_2),V_a1_2),V_a3_2))
% 109.10/108.79 <=> ? [B_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 109.10/108.79 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_RangeP_Oequations,axiom,
% 109.10/108.79 ! [V_a2_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 109.10/108.79 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_reduction__pairI,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_R_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 109.10/108.79 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(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)),V_R_2),V_S_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__Collect__split,axiom,
% 109.10/108.79 ! [V_P_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),V_P_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_the__eq__trivial,axiom,
% 109.10/108.79 ! [V_a_2,T_b] : c_HOL_OThe(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_a_2)) = V_a_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__less__than,axiom,
% 109.10/108.79 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__empty,axiom,
% 109.10/108.79 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__inv__image,axiom,
% 109.10/108.79 ! [V_f_2,T_c,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__lex__prod,axiom,
% 109.10/108.79 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 109.10/108.79 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 109.10/108.79 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__measure,axiom,
% 109.10/108.79 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_DomainI,axiom,
% 109.10/108.79 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__comp__self,axiom,
% 109.10/108.79 ! [V_R_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_R_2)
% 109.10/108.79 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__subset,axiom,
% 109.10/108.79 ! [V_p_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_p_2),V_r_2))
% 109.10/108.79 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_min__ext__wf,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__irrefl,axiom,
% 109.10/108.79 ! [V_a_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__asym,axiom,
% 109.10/108.79 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__not__sym,axiom,
% 109.10/108.79 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_x_2)),V_r_2))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_a_2)),V_r_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__not__refl,axiom,
% 109.10/108.79 ! [V_a_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__Id__on,axiom,
% 109.10/108.79 ! [V_A_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = V_A_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__Int1,axiom,
% 109.10/108.79 ! [V_r_H_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__Int2,axiom,
% 109.10/108.79 ! [V_r_H_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_H_2),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__mlex,axiom,
% 109.10/108.79 ! [V_f_2,V_R_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_R_2)
% 109.10/108.79 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__finite__psubset,axiom,
% 109.10/108.79 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__pair__less,axiom,
% 109.10/108.79 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_max__ext__wf,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__less,axiom,
% 109.10/108.79 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)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__int__ge__less__than2,axiom,
% 109.10/108.79 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__int__ge__less__than,axiom,
% 109.10/108.79 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__Un,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 109.10/108.79 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_s_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__acc__iff,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_acc__wfD,axiom,
% 109.10/108.79 ! [V_x_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__no__loop,axiom,
% 109.10/108.79 ! [V_R_2,T_b] :
% 109.10/108.79 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 109.10/108.79 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__union__merge,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 109.10/108.79 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_S_2),V_R_2))),V_S_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__empty,axiom,
% 109.10/108.79 ! [T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__empty__iff,axiom,
% 109.10/108.79 ! [V_r_2,T_c,T_b] :
% 109.10/108.79 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__mono,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_s_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__Un__eq,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),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(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__Domain,axiom,
% 109.10/108.79 ! [V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_fst__eq__Domain,axiom,
% 109.10/108.79 ! [V_R_2,T_c,T_b] : hAPP(c_Set_Oimage(tc_prod(T_b,T_c),T_b,c_Product__Type_Ofst(T_b,T_c)),V_R_2) = hAPP(c_Relation_ODomain(T_b,T_c),V_R_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 <=> ~ ? [B_f] :
% 109.10/108.79 ! [B_i] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(B_f,hAPP(c_Nat_OSuc,B_i))),hAPP(B_f,B_i))),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wfE__pf,axiom,
% 109.10/108.79 ! [V_A_2,V_R_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_R_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),V_A_2)))
% 109.10/108.79 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__union__compatible,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_R_2)
% 109.10/108.79 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_S_2)),V_R_2))
% 109.10/108.79 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__iff,axiom,
% 109.10/108.79 ! [V_r_2,T_c,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 109.10/108.79 <=> ? [B_y] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf,axiom,
% 109.10/108.79 ! [T_b] :
% 109.10/108.79 ( class_Orderings_Owellorder(T_b)
% 109.10/108.79 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless(T_b)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__insert,axiom,
% 109.10/108.79 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_reduction__pair__def,axiom,
% 109.10/108.79 ! [V_P_2,T_b] :
% 109.10/108.79 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 109.10/108.79 <=> ( c_Wellfounded_Owf(T_b,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_reduction__pair__lemma,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 109.10/108.79 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2)))
% 109.10/108.79 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 109.10/108.79 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__Int__subset,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),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_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__Diff__subset,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_c),V_A_2)),hAPP(c_Relation_ODomain(T_b,T_c),V_B_2))),hAPP(c_Relation_ODomain(T_b,T_c),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),V_B_2)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Field__def,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_ODomain(T_b,T_b),V_r_2)),hAPP(c_Relation_ORange(T_b,T_b),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__map__pair__image,axiom,
% 109.10/108.79 ! [V_f_2,T_c,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.79 => c_Wellfounded_Owf(T_c,hAPP(c_Set_Oimage(tc_prod(T_b,T_b),tc_prod(T_c,T_c),c_Product__Type_Omap__pair(T_b,T_c,T_b,T_c,V_f_2,V_f_2)),V_r_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__Union,axiom,
% 109.10/108.79 ! [V_S_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Relation_ODomain(T_b,T_c)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_the__sym__eq__trivial,axiom,
% 109.10/108.79 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_DomainP__Domain__eq,axiom,
% 109.10/108.79 ! [V_x_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,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_r_2)),V_x_2))
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__lenlex,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_DomainE,axiom,
% 109.10/108.79 ! [V_r_2,T_c,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 109.10/108.79 => ~ ! [B_y] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),B_y)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_DomainP_Ointros,axiom,
% 109.10/108.79 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 109.10/108.79 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_DomainP_Oequations,axiom,
% 109.10/108.79 ! [V_a1_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 109.10/108.79 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_pred__nat__def,axiom,
% 109.10/108.79 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))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__lex,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__lexn,axiom,
% 109.10/108.79 ! [V_n_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lex__def,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_List_Olex(T_b,V_r_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(T_b,V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lexn_Osimps_I1_J,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__pred__nat,axiom,
% 109.10/108.79 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__same__fst,axiom,
% 109.10/108.79 ! [T_b,V_R_2,T_c,V_P_2] :
% 109.10/108.79 ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(V_P_2,B_x))
% 109.10/108.79 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 109.10/108.79 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__if__measure,axiom,
% 109.10/108.79 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 109.10/108.79 ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(V_P_2,B_x))
% 109.10/108.79 => 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))) )
% 109.10/108.79 => c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),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),V_P_2))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),V_g_2))))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wfP__def,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 109.10/108.79 <=> c_Wellfounded_Owf(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wfP__empty,axiom,
% 109.10/108.79 ! [T_b] : c_Wellfounded_OwfP(T_b,hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBK(tc_HOL_Obool,T_b),c_fFalse))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_accp__wfPD,axiom,
% 109.10/108.79 ! [V_x_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 109.10/108.79 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wfP__accp__iff,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 109.10/108.79 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wfP__subset,axiom,
% 109.10/108.79 ! [V_p_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),V_p_2),V_r_2))
% 109.10/108.79 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__in__rel,axiom,
% 109.10/108.79 ! [V_R_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_R_2)
% 109.10/108.79 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wfP__wf__eq,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_OwfP(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2))
% 109.10/108.79 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wfP__acyclicP,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_pigeonhole__infinite,axiom,
% 109.10/108.79 ! [V_f_2,T_c,V_A_2,T_b] :
% 109.10/108.79 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 109.10/108.79 => ? [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.10/108.79 & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),hAPP(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_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),hAPP(V_f_2,B_x)))))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Abs__Integ__cases,axiom,
% 109.10/108.79 ! [V_x_2] :
% 109.10/108.79 ~ ! [B_y] :
% 109.10/108.79 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__acyclic,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_acyclic__subset,axiom,
% 109.10/108.79 ! [V_r_2,V_s_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.10/108.79 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 109.10/108.79 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__acyclic__wf,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 109.10/108.79 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Owf_H__def,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 109.10/108.79 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 109.10/108.79 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 109.10/108.79 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Abs__Integ__induct,axiom,
% 109.10/108.79 ! [V_x_2,V_P_2] :
% 109.10/108.79 ( ! [B_y] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 109.10/108.79 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 109.10/108.79 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__UN__I,axiom,
% 109.10/108.79 ! [V_B_2,T_c,V_A_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.79 => ( ! [B_a] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 109.10/108.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 109.10/108.79 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_inj__on__diff__nat,axiom,
% 109.10/108.79 ! [V_k_2,V_N_2] :
% 109.10/108.79 ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 109.10/108.79 => 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) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wfP__SUP,axiom,
% 109.10/108.79 ! [T_b,V_r_2,T_c] :
% 109.10/108.79 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 109.10/108.79 => ( ! [B_i,B_j] :
% 109.10/108.79 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 109.10/108.79 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),c_Predicate_ODomainP(T_c,T_c,hAPP(V_r_2,B_i))),c_Predicate_ORangeP(T_c,T_c,hAPP(V_r_2,B_j))) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) )
% 109.10/108.79 => c_Wellfounded_OwfP(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_c,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_mem__splitE,axiom,
% 109.10/108.79 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,tc_fun(T_b,tc_HOL_Obool)),V_c_2),V_p_2)))
% 109.10/108.79 => ~ ! [B_x,B_y] :
% 109.10/108.79 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_mem__splitI2,axiom,
% 109.10/108.79 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 109.10/108.79 ( ! [B_a,B_b] :
% 109.10/108.79 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_c_2),V_p_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Eps__split,axiom,
% 109.10/108.79 ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2)) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(tc_prod(T_b,T_c),T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),tc_prod(T_b,T_c)),V_P_2),c_Product__Type_Ofst(T_b,T_c))),c_Product__Type_Osnd(T_b,T_c))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wfI__pf,axiom,
% 109.10/108.79 ! [V_R_2,T_b] :
% 109.10/108.79 ( ! [B_A] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_A),hAPP(c_Relation_OImage(T_b,T_b,V_R_2),B_A)))
% 109.10/108.79 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 109.10/108.79 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_exE__some,axiom,
% 109.10/108.79 ! [T_b,V_c_2,V_P_2] :
% 109.10/108.79 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 109.10/108.79 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 109.10/108.79 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_some__sym__eq__trivial,axiom,
% 109.10/108.79 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_some__eq__trivial,axiom,
% 109.10/108.79 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)) = V_x_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_some__eq__ex,axiom,
% 109.10/108.79 ! [T_b,V_P_2] :
% 109.10/108.79 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 109.10/108.79 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_someI__ex,axiom,
% 109.10/108.79 ! [T_b,V_P_2] :
% 109.10/108.79 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 109.10/108.79 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_tfl__some,axiom,
% 109.10/108.79 ! [T_b,B_P] :
% 109.10/108.79 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 109.10/108.79 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_someI,axiom,
% 109.10/108.79 ! [T_b,V_x_2,V_P_2] :
% 109.10/108.79 ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.79 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_split__paired__Eps,axiom,
% 109.10/108.79 ! [V_P_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_P_2) = c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Eps__split__eq,axiom,
% 109.10/108.79 ! [V_y_2,V_x_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(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_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_c)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(c_fequal,V_x_2)))),hAPP(c_fequal,V_y_2)))) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Sigma__mono,axiom,
% 109.10/108.79 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 109.10/108.79 => ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_B_2,B_x)),hAPP(V_D_2,B_x))) )
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_C_2),V_D_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_not__acc__down,axiom,
% 109.10/108.79 ! [V_R_2,V_x_2,T_b] :
% 109.10/108.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 109.10/108.79 => ~ ! [B_z] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_x_2)),V_R_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_acc_OaccI,axiom,
% 109.10/108.79 ! [V_r_2,V_x_2,T_b] :
% 109.10/108.79 ( ! [B_y] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_x_2)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_max__ext_Osimps,axiom,
% 109.10/108.79 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_a1_2),V_a2_2)),c_Wellfounded_Omax__ext(T_b,V_R_2)))
% 109.10/108.79 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 109.10/108.79 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 109.10/108.79 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.79 & ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 109.10/108.79 => ? [B_xa] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_R_2)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_coinduct__set,axiom,
% 109.10/108.79 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 109.10/108.79 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_def__coinduct__set,axiom,
% 109.10/108.79 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 109.10/108.79 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_def__gfp__unfold,axiom,
% 109.10/108.79 ! [V_f_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => V_A_2 = hAPP(V_f_2,V_A_2) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_gfp__unfold,axiom,
% 109.10/108.79 ! [V_f_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_gfp__upperbound,axiom,
% 109.10/108.79 ! [V_f_2,V_X_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_weak__coinduct,axiom,
% 109.10/108.79 ! [V_f_2,V_X_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,V_X_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_gfp__lemma2,axiom,
% 109.10/108.79 ! [V_f_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_gfp__lemma3,axiom,
% 109.10/108.79 ! [V_f_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_weak__coinduct__image,axiom,
% 109.10/108.79 ! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2)),hAPP(V_f_2,hAPP(c_Set_Oimage(T_b,T_c,V_g_2),V_X_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_g_2,V_a_2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_c,tc_HOL_Obool),V_f_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_gfp__fun__UnI2,axiom,
% 109.10/108.79 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 109.10/108.79 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_coinduct,axiom,
% 109.10/108.79 ! [V_X_2,V_f_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_coinduct__lemma,axiom,
% 109.10/108.79 ! [V_f_2,V_X_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)))))
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2))))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_def__coinduct,axiom,
% 109.10/108.79 ! [V_X_2,V_f_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_X_2),V_A_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_def__coinduct3,axiom,
% 109.10/108.79 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 109.10/108.79 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),V_A_2)))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_coinduct3,axiom,
% 109.10/108.79 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 109.10/108.79 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_def__Collect__coinduct,axiom,
% 109.10/108.79 ! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
% 109.10/108.79 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(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(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_OCollect(T_b)),V_P_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 109.10/108.79 => ( ! [B_z] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_A_2)),B_z)) )
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lfp__lowerbound,axiom,
% 109.10/108.79 ! [V_A_2,V_f_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_A_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lfp__const,axiom,
% 109.10/108.79 ! [V_t_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2 ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lfp__unfold,axiom,
% 109.10/108.79 ! [V_f_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_def__lfp__unfold,axiom,
% 109.10/108.79 ! [V_f_2,V_h_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => V_h_2 = hAPP(V_f_2,V_h_2) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lfp__lemma2,axiom,
% 109.10/108.79 ! [V_f_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lfp__lemma3,axiom,
% 109.10/108.79 ! [V_f_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_def__lfp__induct,axiom,
% 109.10/108.79 ! [V_P_2,V_f_2,V_A_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_A_2),V_P_2))),V_P_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lfp__induct,axiom,
% 109.10/108.79 ! [V_P_2,V_f_2,T_b] :
% 109.10/108.79 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2))),V_P_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)),V_P_2)) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_coinduct3__lemma,axiom,
% 109.10/108.79 ! [V_f_2,V_X_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))))))
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),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)),tc_fun(T_b,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_def__lfp__induct__set,axiom,
% 109.10/108.79 ! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
% 109.10/108.79 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.10/108.79 => ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2)))))
% 109.10/108.79 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.79 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lfp__induct__set,axiom,
% 109.10/108.79 ! [V_P_2,V_f_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)))
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(T_b),V_P_2)))))
% 109.10/108.79 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.79 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lfp__induct2,axiom,
% 109.10/108.79 ! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)))
% 109.10/108.79 => ( c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)
% 109.10/108.79 => ( ! [B_a,B_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2))))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
% 109.10/108.79 => hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__no__infinite__down__chainE,axiom,
% 109.10/108.79 ! [V_f_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => ~ ! [B_k] : 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,hAPP(c_Nat_OSuc,B_k))),hAPP(V_f_2,B_k))),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_iterate_Osimps,axiom,
% 109.10/108.79 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 109.10/108.79 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 109.10/108.79 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2) )
% 109.10/108.79 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 109.10/108.79 => hAPP(c_Random_Oiterate(T_c,T_b,V_k_2,V_f_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_b,tc_prod(T_c,T_b)),hAPP(V_f_2,V_x_2)),c_Random_Oiterate(T_c,T_b,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)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_scomp__unfold,axiom,
% 109.10/108.79 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_d,T_e),hAPP(V_f_2,V_x_2))),hAPP(c_Product__Type_Osnd(T_d,T_e),hAPP(V_f_2,V_x_2))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Pair__scomp,axiom,
% 109.10/108.79 ! [V_f_2,V_x_2,T_c,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_b,T_c),hAPP(c_Product__Type_OPair(T_d,T_b),V_x_2)),V_f_2) = hAPP(V_f_2,V_x_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_scomp__Pair,axiom,
% 109.10/108.79 ! [V_x_2,T_d,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_c,T_d,tc_prod(T_c,T_d)),V_x_2),c_Product__Type_OPair(T_c,T_d)) = V_x_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_scomp__scomp,axiom,
% 109.10/108.79 ! [V_h_2,V_g_2,V_f_2,T_g,T_f,T_c,T_e,T_d,T_b] : hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_d,T_e,T_c),hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,tc_prod(T_d,T_e)),V_f_2),V_g_2)),V_h_2) = hAPP(hAPP(c_Product__Type_Oscomp(T_b,T_f,T_g,T_c),V_f_2),hAPP(hAPP(c_COMBC(T_f,tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_g,tc_prod(T_d,T_e)),tc_fun(tc_fun(T_d,tc_fun(T_e,T_c)),tc_fun(T_g,T_c)),T_f),c_Product__Type_Oscomp(T_g,T_d,T_e,T_c)),V_g_2)),V_h_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_scomp__apply,axiom,
% 109.10/108.79 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_scomp__def,axiom,
% 109.10/108.79 ! [V_x_2,V_g_2,V_f_2,T_b,T_e,T_d,T_c] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(T_c,T_d,T_e,T_b),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,T_b),V_g_2),hAPP(V_f_2,V_x_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_less__eq,axiom,
% 109.10/108.79 ! [V_n_2,V_m_2] :
% 109.10/108.79 ( 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)))
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__eq__minimal,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 <=> ! [B_Q] :
% 109.10/108.79 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 109.10/108.79 => ? [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 109.10/108.79 & ! [B_y] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__trancl,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_less__than__def,axiom,
% 109.10/108.79 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_acyclic__def,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 109.10/108.79 <=> ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl_Or__into__trancl,axiom,
% 109.10/108.79 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__subset__Field2,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),hAPP(c_Relation_OField(T_b),V_r_2)),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_Relation_OField(T_b),V_r_2))))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_r__into__trancl_H,axiom,
% 109.10/108.79 ! [V_r_2,V_p_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__empty,axiom,
% 109.10/108.79 ! [T_b] : c_Transitive__Closure_Otrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__domain,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__range,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) = hAPP(c_Relation_ORange(T_b,T_b),V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__trancl,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__trans,axiom,
% 109.10/108.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 109.10/108.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 => ( 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_c_2)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__into__trancl2,axiom,
% 109.10/108.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.10/108.79 => ( 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_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_r__r__into__trancl,axiom,
% 109.10/108.79 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
% 109.10/108.79 => ( 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_c_2)),V_R_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__mono,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__unfold,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__subset__Sigma,axiom,
% 109.10/108.79 ! [V_A_2,V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__Int__subset,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__insert,axiom,
% 109.10/108.79 ! [V_r_2,V_x_2,V_y_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,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_b),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_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_b),c_member(tc_prod(T_b,T_b))),hAPP(hAPP(c_COMBC(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),V_y_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),hAPP(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_b),c_member(tc_prod(T_b,T_b))),hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_reflcl__set__eq,axiom,
% 109.10/108.79 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),c_fequal),V_x_2),V_y_2))
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_r__into__rtrancl,axiom,
% 109.10/108.79 ! [V_r_2,V_p_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 109.10/108.79 ! [V_r_2,V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_IdI,axiom,
% 109.10/108.79 ! [V_a_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),c_Relation_OId(T_b))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__into__rtrancl,axiom,
% 109.10/108.79 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__unfold__left,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__unfold__right,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,V_r_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__reflcl,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_reflcl__trancl,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__trancl__absorb,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : c_Transitive__Closure_Otrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__rtrancl__absorb,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Otrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__rtrancl,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__rtrancl,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__trans,axiom,
% 109.10/108.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 109.10/108.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => ( 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_c_2)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 109.10/108.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.10/108.79 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__idemp,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_refl__rtrancl,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__r__diff__Id,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Image__closed__trancl,axiom,
% 109.10/108.79 ! [V_X_2,V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),V_X_2)),V_X_2))
% 109.10/108.79 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__reflcl__absorb,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__Un__rtrancl,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) = c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__reflcl,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__Un__subset,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_S_2))),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__mono,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__subset,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_S_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 109.10/108.79 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__subset__rtrancl,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_s_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_s_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_in__rtrancl__UnI,axiom,
% 109.10/108.79 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 109.10/108.79 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 109.10/108.79 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2),V_S_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__Int__subset,axiom,
% 109.10/108.79 ! [V_r_2,V_s_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),V_s_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)),V_r_2)),V_s_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_s_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__idemp__self__comp,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_R_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_r__comp__rtrancl__eq,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__unfold,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__empty,axiom,
% 109.10/108.79 ! [T_b] : c_Transitive__Closure_Ortrancl(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) = c_Relation_OId(T_b) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_R__O__Id,axiom,
% 109.10/108.79 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_c),V_R_2),c_Relation_OId(T_c)) = V_R_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Id__O__R,axiom,
% 109.10/108.79 ! [V_R_2,T_c,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_c),c_Relation_OId(T_b)),V_R_2) = V_R_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Image__Id,axiom,
% 109.10/108.79 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_pair__in__Id__conv,axiom,
% 109.10/108.79 ! [V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId(T_b)))
% 109.10/108.79 <=> V_a_2 = V_b_2 ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__trancl__trancl,axiom,
% 109.10/108.79 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__rtrancl__trancl,axiom,
% 109.10/108.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__into__trancl1,axiom,
% 109.10/108.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => ( 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_c_2)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtranclD,axiom,
% 109.10/108.79 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 109.10/108.79 => ( V_a_2 = V_b_2
% 109.10/108.79 | ( V_a_2 != V_b_2
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__into__trancl2,axiom,
% 109.10/108.79 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.10/108.79 => ( 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_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__eq__or__trancl,axiom,
% 109.10/108.79 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 109.10/108.79 <=> ( V_x_2 = V_y_2
% 109.10/108.79 | ( V_x_2 != V_y_2
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__Id,axiom,
% 109.10/108.79 ! [T_b] : hAPP(c_Relation_ODomain(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__Id,axiom,
% 109.10/108.79 ! [T_b] : hAPP(c_Relation_ORange(T_b,T_b),c_Relation_OId(T_b)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_refl__Id,axiom,
% 109.10/108.79 ! [T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Relation_OId(T_b)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_pair__leq__def,axiom,
% 109.10/108.79 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))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Not__Domain__rtrancl,axiom,
% 109.10/108.79 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 109.10/108.79 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 109.10/108.79 <=> V_x_2 = V_y_2 ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_acc__downwards,axiom,
% 109.10/108.79 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 109.10/108.79 => ( 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_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_acc__downwards__aux,axiom,
% 109.10/108.79 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 109.10/108.79 ( 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_a_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__insert,axiom,
% 109.10/108.79 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 109.10/108.79 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 109.10/108.79 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_acyclic__insert,axiom,
% 109.10/108.79 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Oacyclic(T_b,hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),V_r_2))
% 109.10/108.79 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 109.10/108.79 & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_refl__reflcl,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Id__def,axiom,
% 109.10/108.79 ! [T_b] : c_Relation_OId(T_b) = hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_b),tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_HOL_Obool)),tc_prod(T_b,T_b)),c_COMBB(tc_prod(T_b,T_b),tc_HOL_Obool,T_b)),c_fequal)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_irrefl__diff__Id,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Relation_Oirrefl(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_pred__nat__trancl__eq__le,axiom,
% 109.10/108.79 ! [V_n_2,V_m_2] :
% 109.10/108.79 ( 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)))
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__subset__Sigma__aux,axiom,
% 109.10/108.79 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 109.10/108.79 => ( V_a_2 = V_b_2
% 109.10/108.79 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_irrefl__tranclI,axiom,
% 109.10/108.79 ! [V_x_2,V_r_2,T_b] :
% 109.10/108.79 ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_sequence__trans,axiom,
% 109.10/108.79 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 109.10/108.79 ( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => 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,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_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__Id,axiom,
% 109.10/108.79 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_acyclic__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 109.10/108.79 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Field__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hAPP(c_Relation_OField(T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_OField(T_b),V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__Int,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 109.10/108.79 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__inv__image,axiom,
% 109.10/108.79 ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__Id__on,axiom,
% 109.10/108.79 ! [V_A_2,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId__on(T_b,V_A_2)) = c_Relation_OId__on(T_b,V_A_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_refl__on__converse,axiom,
% 109.10/108.79 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.79 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 109.10/108.79 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__INTER,axiom,
% 109.10/108.79 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__iff,axiom,
% 109.10/108.79 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converseI,axiom,
% 109.10/108.79 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converseD,axiom,
% 109.10/108.79 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__Un,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_s_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__rel__comp,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Relation_Orel__comp(T_c,T_d,T_b),V_r_2),V_s_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),hAPP(c_Relation_Oconverse(T_d,T_b),V_s_2)),hAPP(c_Relation_Oconverse(T_c,T_d),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__UNION,axiom,
% 109.10/108.79 ! [V_r_2,V_S_2,T_d,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)),V_S_2),V_r_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_S_2),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_d),c_Relation_Oconverse(T_c,T_b)),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__converse__trancl,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 109.10/108.79 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_equiv__comp__eq,axiom,
% 109.10/108.79 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.79 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.10/108.79 => hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2 ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__def,axiom,
% 109.10/108.79 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Domain__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_c,T_b] : hAPP(c_Relation_ODomain(T_b,T_c),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)) = hAPP(c_Relation_ORange(T_c,T_b),V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Range__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_ORange(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__converseI,axiom,
% 109.10/108.79 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__converseD,axiom,
% 109.10/108.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__converseI,axiom,
% 109.10/108.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__converseD,axiom,
% 109.10/108.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Image__subset__eq,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)),V_B_2))
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2))))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_refl__on__comp__subset,axiom,
% 109.10/108.79 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.79 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_comp__equivI,axiom,
% 109.10/108.79 ! [V_A_2,V_r_2,T_b] :
% 109.10/108.79 ( hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2) = V_r_2
% 109.10/108.79 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 109.10/108.79 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__acyclic__wf__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 109.10/108.79 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 109.10/108.79 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converse__def,axiom,
% 109.10/108.79 ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),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_r_2))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Image__INT__eq,axiom,
% 109.10/108.79 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 109.10/108.79 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 109.10/108.79 => hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_total__on__diff__Id,axiom,
% 109.10/108.79 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.79 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
% 109.10/108.79 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_single__valued__Id,axiom,
% 109.10/108.79 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_single__valued__subset,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.10/108.79 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 109.10/108.79 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_single__valued__rel__comp,axiom,
% 109.10/108.79 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 109.10/108.79 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 109.10/108.79 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 109.10/108.79 => c_Relation_Osingle__valued(T_b,T_d,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_c,T_d),V_r_2),V_s_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_single__valued__Id__on,axiom,
% 109.10/108.79 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_total__on__empty,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_Relation_Ototal__on(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_r_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_total__on__converse,axiom,
% 109.10/108.79 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.79 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 109.10/108.79 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_single__valuedD,axiom,
% 109.10/108.79 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 109.10/108.79 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 109.10/108.79 => ( 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)),V_r_2))
% 109.10/108.79 => ( 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_z_2)),V_r_2))
% 109.10/108.79 => V_y_2 = V_z_2 ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_single__valued__def,axiom,
% 109.10/108.79 ! [V_r_2,T_c,T_b] :
% 109.10/108.79 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 109.10/108.79 <=> ! [B_x,B_y] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y)),V_r_2))
% 109.10/108.79 => ! [B_z] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)),V_r_2))
% 109.10/108.79 => B_y = B_z ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_total__on__def,axiom,
% 109.10/108.79 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.79 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 109.10/108.79 <=> ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.10/108.79 => ! [B_xa] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 109.10/108.79 => ( B_x != B_xa
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_xa)),V_r_2))
% 109.10/108.79 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_xa),B_x)),V_r_2)) ) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_single__valued__confluent,axiom,
% 109.10/108.79 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 109.10/108.79 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_z_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Image__Int__eq,axiom,
% 109.10/108.79 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 109.10/108.79 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 109.10/108.79 => hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,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_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 109.10/108.79 ! [V_R_2,V_p_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),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_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_acyclicI,axiom,
% 109.10/108.79 ! [V_r_2,T_b] :
% 109.10/108.79 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 109.10/108.79 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_single__valued__rel__pow,axiom,
% 109.10/108.79 ! [V_n_2,V_R_2,T_b] :
% 109.10/108.79 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 109.10/108.79 => c_Relation_Osingle__valued(T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_comp__funpow,axiom,
% 109.10/108.79 ! [V_f_2,V_n_2,T_c,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(T_b,T_c),tc_fun(T_b,T_c)),V_n_2),c_Fun_Ocomp(T_c,T_c,T_b,V_f_2)) = c_Fun_Ocomp(T_c,T_c,T_b,hAPP(hAPP(c_Nat_Ocompow(T_c,T_c),V_n_2),V_f_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_funpow__swap1,axiom,
% 109.10/108.79 ! [V_x_2,V_n_2,T_b,V_f_2] : hAPP(V_f_2,hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),V_x_2)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2),hAPP(V_f_2,V_x_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_funpow__mult,axiom,
% 109.10/108.79 ! [V_f_2,V_m_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)) = hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_wf__exp,axiom,
% 109.10/108.79 ! [V_R_2,V_n_2,T_b] :
% 109.10/108.79 ( c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))
% 109.10/108.79 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__commute,axiom,
% 109.10/108.79 ! [V_n_2,V_R_2,T_b] : hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__1,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_R_2) = V_R_2 ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__power,axiom,
% 109.10/108.79 ! [V_R_2,V_p_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 109.10/108.79 <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__imp__rtrancl,axiom,
% 109.10/108.79 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_relpow_Osimps_I2_J,axiom,
% 109.10/108.79 ! [V_R_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2) = hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)),V_R_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__add,axiom,
% 109.10/108.79 ! [V_R_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),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_b,T_b,T_b),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_m_2),V_R_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_relpow_Osimps_I1_J,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2) = c_Relation_OId(T_b) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__0__E,axiom,
% 109.10/108.79 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2)))
% 109.10/108.79 => V_x_2 = V_y_2 ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__0__I,axiom,
% 109.10/108.79 ! [V_R_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_x_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_R_2))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__Suc__I2,axiom,
% 109.10/108.79 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__Suc__I,axiom,
% 109.10/108.79 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_funpow_Osimps_I2_J,axiom,
% 109.10/108.79 ! [V_f_2,V_n_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(c_Nat_OSuc,V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,V_f_2),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_funpow__add,axiom,
% 109.10/108.79 ! [V_f_2,V_n_2,V_m_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)),V_f_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_b,hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_m_2),V_f_2)),hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),V_n_2),V_f_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_funpow_Osimps_I1_J,axiom,
% 109.10/108.79 ! [V_f_2,T_b] : hAPP(hAPP(c_Nat_Ocompow(T_b,T_b),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_f_2) = c_Fun_Oid(T_b) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_trancl__power,axiom,
% 109.10/108.79 ! [V_R_2,V_p_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 109.10/108.79 <=> ? [B_n] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 109.10/108.79 ! [V_R_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_R_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(T_b,T_b),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_b,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool)),V_R_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_funpow__code__def,axiom,
% 109.10/108.79 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__E,axiom,
% 109.10/108.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 109.10/108.79 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.79 => V_x_2 != V_z_2 )
% 109.10/108.79 => ~ ! [B_y,B_m] :
% 109.10/108.79 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2)))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__E2,axiom,
% 109.10/108.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 109.10/108.79 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.79 => V_x_2 != V_z_2 )
% 109.10/108.79 => ~ ! [B_y,B_m] :
% 109.10/108.79 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_m),V_R_2))) ) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 109.10/108.79 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 109.10/108.79 => ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
% 109.10/108.79 => ! [B_y] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_Q_2))
% 109.10/108.79 => B_y = B_x ) )
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__Un__separatorE,axiom,
% 109.10/108.79 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_P_2),V_Q_2))))
% 109.10/108.79 => ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),B_x)),c_Transitive__Closure_Ortrancl(T_b,V_P_2)))
% 109.10/108.79 => ! [B_y] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_Q_2))
% 109.10/108.79 => B_x = B_y ) )
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_P_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__Suc__E,axiom,
% 109.10/108.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 109.10/108.79 => ~ ! [B_y] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__Suc__D2,axiom,
% 109.10/108.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 109.10/108.79 => ? [B_y] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__pow__Suc__E2,axiom,
% 109.10/108.79 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
% 109.10/108.79 => ~ ! [B_y] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_tranclD2,axiom,
% 109.10/108.79 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 109.10/108.79 => ? [B_z] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_tranclD,axiom,
% 109.10/108.79 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 109.10/108.79 => ? [B_z] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2))
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_IdE,axiom,
% 109.10/108.79 ! [V_p_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 109.10/108.79 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_transfer__nat__int__set__cong,axiom,
% 109.10/108.79 ! [V_P_H_2,V_P_2] :
% 109.10/108.79 ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 109.10/108.79 => ( hBOOL(hAPP(V_P_2,B_x))
% 109.10/108.79 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 109.10/108.79 => 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)) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Int__Collect__mono,axiom,
% 109.10/108.79 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 109.10/108.79 => ( ! [B_x] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.10/108.79 => ( hBOOL(hAPP(V_P_2,B_x))
% 109.10/108.79 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OCollect(T_b),V_P_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_OCollect(T_b),V_Q_2)))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_converseE,axiom,
% 109.10/108.79 ! [V_r_2,V_yx_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_yx_2),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 109.10/108.79 => ~ ! [B_x,B_y] :
% 109.10/108.79 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),B_x),B_y)),V_r_2)) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rel__compE,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_xz_2),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_d,T_c),V_r_2),V_s_2)))
% 109.10/108.79 => ~ ! [B_x,B_y,B_z] :
% 109.10/108.79 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_d)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),B_x),B_y)),V_r_2))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_c),B_y),B_z)),V_s_2)) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 109.10/108.79 ! [V_r_2,V_q_2,T_b] : c_Nitpick_Oplus__frac(T_b,V_q_2,V_r_2) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(T_b),V_q_2),hAPP(c_Nitpick_Odenom(T_b),V_r_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,T_b),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,T_b),tc_Int_Oint),c_Nitpick_Ofrac(T_b)),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_b),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_b),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_b),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_b),V_r_2)))))),c_COMBI(tc_Int_Oint))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 109.10/108.79 ! [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))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Oof__frac__def,axiom,
% 109.10/108.79 ! [V_q,T_a,T_b] :
% 109.10/108.79 ( ( class_Rings_Oinverse(T_b)
% 109.10/108.79 & class_Rings_Oring__1(T_b) )
% 109.10/108.79 => 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))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 109.10/108.79 ! [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)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 109.10/108.79 ! [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))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Oless__frac__def,axiom,
% 109.10/108.79 ! [V_r_2,V_q_2,T_b] :
% 109.10/108.79 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 109.10/108.79 ! [V_r_2,V_q_2,T_b] :
% 109.10/108.79 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Odenom__def,axiom,
% 109.10/108.79 ! [T_b] : c_Nitpick_Odenom(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Nitpick_Onum__def,axiom,
% 109.10/108.79 ! [T_b] : c_Nitpick_Onum(T_b) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,T_b,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(T_b)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_internal__split__def,axiom,
% 109.10/108.79 ! [T_d,T_c,T_b] : c_Product__Type_Ointernal__split(T_b,T_c,T_d) = c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_bool_Osize_I1_J,axiom,
% 109.10/108.79 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_internal__split__conv,axiom,
% 109.10/108.79 ! [V_b_2,V_a_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_c,T_d,T_b),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_bool_Osize_I2_J,axiom,
% 109.10/108.79 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_finite__less__ub,axiom,
% 109.10/108.79 ! [V_u_2,V_f_2] :
% 109.10/108.79 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 109.10/108.79 => 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)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lenlex__def,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lexn__length,axiom,
% 109.10/108.79 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
% 109.10/108.79 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 109.10/108.79 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_neq__if__length__neq,axiom,
% 109.10/108.79 ! [V_ys,V_xs,T_a] :
% 109.10/108.79 ( 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)
% 109.10/108.79 => V_xs != V_ys ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lenlex__conv,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_length__sublist,axiom,
% 109.10/108.79 ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,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_b)),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)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lexn_Osimps_I2_J,axiom,
% 109.10/108.79 ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,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_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_impossible__Cons,axiom,
% 109.10/108.79 ! [V_x,V_ys,V_xs,T_a] :
% 109.10/108.79 ( 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)))
% 109.10/108.79 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_list_Oinject,axiom,
% 109.10/108.79 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 109.10/108.79 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
% 109.10/108.79 <=> ( V_a_2 = V_a_H_2
% 109.10/108.79 & V_list_2 = V_list_H_2 ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_not__Cons__self2,axiom,
% 109.10/108.79 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 109.10/108.79
% 109.10/108.79 fof(fact_not__Cons__self,axiom,
% 109.10/108.79 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_list_Osize_I4_J,axiom,
% 109.10/108.79 ! [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))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Cons__in__lex,axiom,
% 109.10/108.79 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
% 109.10/108.79 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 109.10/108.79 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) )
% 109.10/108.79 | ( V_x_2 = V_y_2
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_set__Cons__def,axiom,
% 109.10/108.79 ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),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_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_pick_Osimps,axiom,
% 109.10/108.79 ! [V_xs,V_x,T_a,V_i] :
% 109.10/108.79 ( ( 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)))
% 109.10/108.79 => 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) )
% 109.10/108.79 & ( ~ 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)))
% 109.10/108.79 => 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))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_select__weight__cons__zero,axiom,
% 109.10/108.79 ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lexord__cons__cons,axiom,
% 109.10/108.79 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
% 109.10/108.79 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.10/108.79 | ( V_a_2 = V_b_2
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lexord__lex,axiom,
% 109.10/108.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olex(T_b,V_r_2)))
% 109.10/108.79 <=> ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 109.10/108.79 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 109.10/108.79 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_list_Osize_I2_J,axiom,
% 109.10/108.79 ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),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_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Cons__acc__listrel1I,axiom,
% 109.10/108.79 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel1__mono,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel1__converse,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 109.10/108.79 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel1I2,axiom,
% 109.10/108.79 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 109.10/108.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 109.10/108.79 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel1__eq__len,axiom,
% 109.10/108.79 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 109.10/108.79 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_in__listrel1__converse,axiom,
% 109.10/108.79 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
% 109.10/108.79 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel1I1,axiom,
% 109.10/108.79 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_Cons__listrel1__Cons,axiom,
% 109.10/108.79 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
% 109.10/108.79 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 109.10/108.79 & V_xs_2 = V_ys_2 )
% 109.10/108.79 | ( V_x_2 = V_y_2
% 109.10/108.79 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel__Cons,axiom,
% 109.10/108.79 ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_lexord__irreflexive,axiom,
% 109.10/108.79 ! [V_y_2,V_r_2,T_b] :
% 109.10/108.79 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
% 109.10/108.79 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel__rtrancl__refl,axiom,
% 109.10/108.79 ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel__mono,axiom,
% 109.10/108.79 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel__eq__len,axiom,
% 109.10/108.79 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 109.10/108.79 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel__rtrancl__trans,axiom,
% 109.10/108.79 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 109.10/108.79 ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 109.10/108.79 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel1__subset__listrel,axiom,
% 109.10/108.79 ! [V_r_H_2,V_r_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
% 109.10/108.79 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 109.10/108.79 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 109.10/108.79 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 109.10/108.79
% 109.10/108.79 fof(fact_listrel_OCons,axiom,
% 109.10/108.79 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.79 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 109.10/108.79 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrelp__listrel__eq,axiom,
% 109.10/108.80 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 109.10/108.80 ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
% 109.10/108.80 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel__Cons2,axiom,
% 109.10/108.80 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
% 109.10/108.80 => ~ ! [B_x,B_xs] :
% 109.10/108.80 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
% 109.10/108.80 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrelp_Oequations_I2_J,axiom,
% 109.10/108.80 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 109.10/108.80 ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
% 109.10/108.80 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 109.10/108.80 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrelp_OCons,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 109.10/108.80 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 109.10/108.80 => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel__Cons1,axiom,
% 109.10/108.80 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 109.10/108.80 => ~ ! [B_y,B_ys] :
% 109.10/108.80 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
% 109.10/108.80 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel__subset,axiom,
% 109.10/108.80 ! [V_A_2,V_r_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_List_Olist(T_b)),c_List_Olists(T_b,V_A_2))))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists__UNIV,axiom,
% 109.10/108.80 ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists__mono,axiom,
% 109.10/108.80 ! [V_B_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_equiv__listrel,axiom,
% 109.10/108.80 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.80 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.10/108.80 => c_Equiv__Relations_Oequiv(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel__refl__on,axiom,
% 109.10/108.80 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.80 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.10/108.80 => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Cons__in__lists__iff,axiom,
% 109.10/108.80 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
% 109.10/108.80 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.10/108.80 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists__accI,axiom,
% 109.10/108.80 ! [V_r_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists__accD,axiom,
% 109.10/108.80 ! [V_r_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel__iff__nth,axiom,
% 109.10/108.80 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 109.10/108.80 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 109.10/108.80 & ! [B_n] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_n))),V_r_2)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lexord__linear,axiom,
% 109.10/108.80 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 109.10/108.80 ( ! [B_a,B_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2))
% 109.10/108.80 | B_a = B_b
% 109.10/108.80 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2)) )
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 109.10/108.80 | V_x_2 = V_y_2
% 109.10/108.80 | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_infinite__UNIV__listI,axiom,
% 109.10/108.80 ! [T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__eq__iff__nth__eq,axiom,
% 109.10/108.80 ! [T_b,V_ys_2,V_xs_2] :
% 109.10/108.80 ( V_xs_2 = V_ys_2
% 109.10/108.80 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 109.10/108.80 & ! [B_i] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__Cons__0,axiom,
% 109.10/108.80 ! [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 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__Cons__Suc,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth_Osimps,axiom,
% 109.10/108.80 ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__Cons_H,axiom,
% 109.10/108.80 ! [V_xs,V_x,T_a,V_n] :
% 109.10/108.80 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 109.10/108.80 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__Cons__number__of,axiom,
% 109.10/108.80 ! [V_xs,V_x,T_a,V_v] :
% 109.10/108.80 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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 )
% 109.10/108.80 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lexord__take__index__conv,axiom,
% 109.10/108.80 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 109.10/108.80 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2)))
% 109.10/108.80 & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2)),V_y_2) = V_x_2 )
% 109.10/108.80 | ? [B_i] :
% 109.10/108.80 ( 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_b)),V_x_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2))))
% 109.10/108.80 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 109.10/108.80 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_x_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_y_2),B_i))),V_r_2)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__sublist,axiom,
% 109.10/108.80 ! [V_I_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),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_b)),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))))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_finite__set,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__subset__Cons,axiom,
% 109.10/108.80 ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__all,axiom,
% 109.10/108.80 ! [V_n,V_xs,T_a] :
% 109.10/108.80 ( 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))
% 109.10/108.80 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__take__subset__set__take,axiom,
% 109.10/108.80 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__take__subset,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__sublist__subset,axiom,
% 109.10/108.80 ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__take,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_n,V_i] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__Suc__Cons,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__ConsD,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
% 109.10/108.80 => ( V_y_2 = V_x_2
% 109.10/108.80 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__set__sublistD,axiom,
% 109.10/108.80 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__set__takeD,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_notin__set__sublistI,axiom,
% 109.10/108.80 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__take,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__take,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sublist__upt__eq__take,axiom,
% 109.10/108.80 ! [V_n_2,V_l_2,T_b] : c_List_Osublist(T_b,V_l_2,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2)) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_l_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_card__length,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_all__set__conv__all__nth,axiom,
% 109.10/108.80 ! [V_P_2,V_xs_2,T_b] :
% 109.10/108.80 ( ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.80 <=> ! [B_i] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__size__estimation,axiom,
% 109.10/108.80 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__size__estimation_H,axiom,
% 109.10/108.80 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__lists__conv__set,axiom,
% 109.10/108.80 ! [V_A_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 109.10/108.80 <=> ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__pos__if__in__set,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => 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_b)),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__mem,axiom,
% 109.10/108.80 ! [V_xs_2,T_b,V_n_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__set__conv__nth,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 <=> ? [B_i] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists__eq__set,axiom,
% 109.10/108.80 ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__conv__nth,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(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)),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)),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(T_b,tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(T_b),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_b)),V_xs_2))))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_finite__lists__length__eq,axiom,
% 109.10/108.80 ! [V_n_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.80 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_finite__lists__length__le,axiom,
% 109.10/108.80 ! [V_n_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.80 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel__iff__zip,axiom,
% 109.10/108.80 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
% 109.10/108.80 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 109.10/108.80 & ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,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_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_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),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_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__zip,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),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_b,T_c)),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_b,T_c)),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_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),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_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__zip,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__zip,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__Cons__Cons,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__eq__iff__zip__eq,axiom,
% 109.10/108.80 ! [T_b,V_ys_2,V_xs_2] :
% 109.10/108.80 ( V_xs_2 = V_ys_2
% 109.10/108.80 <=> ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
% 109.10/108.80 & ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__same,axiom,
% 109.10/108.80 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
% 109.10/108.80 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 & V_a_2 = V_b_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__zip__leftD,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 109.10/108.80 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__zip__rightD,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 109.10/108.80 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__set__zipE,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 109.10/108.80 ( 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(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 109.10/108.80 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__zip,axiom,
% 109.10/108.80 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => ( 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)))
% 109.10/108.80 => 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)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_greaterThanLessThan__upto,axiom,
% 109.10/108.80 ! [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)))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__setsum__nth,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),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_b)),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__upto,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_atLeastAtMost__upto,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 109.10/108.80 ! [V_ns_2] :
% 109.10/108.80 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 <=> ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 109.10/108.80 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_elem__le__listsum__nat,axiom,
% 109.10/108.80 ! [V_ns,V_k] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__simps_I2_J,axiom,
% 109.10/108.80 ! [V_xs,V_x,T_a] :
% 109.10/108.80 ( class_Groups_Omonoid__add(T_a)
% 109.10/108.80 => 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)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_atLeastLessThan__upto,axiom,
% 109.10/108.80 ! [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)))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_greaterThanAtMost__upto,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nat__list__def,axiom,
% 109.10/108.80 ! [V_l_2] :
% 109.10/108.80 ( c_List_Onat__list(V_l_2)
% 109.10/108.80 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__size__pointwise,axiom,
% 109.10/108.80 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 109.10/108.80 ( ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__update__nat,axiom,
% 109.10/108.80 ! [V_n,V_ns,V_k] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_butlast__take,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_n] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__beyond,axiom,
% 109.10/108.80 ! [V_x,V_i,V_xs,T_a] :
% 109.10/108.80 ( 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))
% 109.10/108.80 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__id,axiom,
% 109.10/108.80 ! [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 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__list__update__neq,axiom,
% 109.10/108.80 ! [V_x,V_xs,T_a,V_j,V_i] :
% 109.10/108.80 ( V_i != V_j
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__list__update,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_butlast__list__update,axiom,
% 109.10/108.80 ! [V_x,V_xs,T_a,V_k] :
% 109.10/108.80 ( ( 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))
% 109.10/108.80 => 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) )
% 109.10/108.80 & ( 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))
% 109.10/108.80 => 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) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__update,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_update__zip,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__swap,axiom,
% 109.10/108.80 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 109.10/108.80 ( V_i != V_i_H
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__overwrite,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__code_I2_J,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__code_I3_J,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__set__butlastD,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__update__subsetI,axiom,
% 109.10/108.80 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__update__subset__insert,axiom,
% 109.10/108.80 ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__list__update__eq,axiom,
% 109.10/108.80 ! [V_x,V_xs,T_a,V_i] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__same__conv,axiom,
% 109.10/108.80 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 109.10/108.80 ( 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_xs_2)))
% 109.10/108.80 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 109.10/108.80 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__list__update,axiom,
% 109.10/108.80 ! [V_x,V_j,V_xs,T_a,V_i] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => ( ( V_i = V_j
% 109.10/108.80 => 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 )
% 109.10/108.80 & ( V_i != V_j
% 109.10/108.80 => 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) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__butlast,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_n] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__butlast,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__update__memI,axiom,
% 109.10/108.80 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_butlast__conv__take,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel1__iff__update,axiom,
% 109.10/108.80 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 109.10/108.80 <=> ? [B_y,B_n] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2))
% 109.10/108.80 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__list__update,axiom,
% 109.10/108.80 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__upto,axiom,
% 109.10/108.80 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__take,axiom,
% 109.10/108.80 ! [V_i,V_xs,T_a] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__sublistI,axiom,
% 109.10/108.80 ! [V_I_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__zipI2,axiom,
% 109.10/108.80 ! [V_xs,T_b,V_ys,T_a] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__zipI1,axiom,
% 109.10/108.80 ! [V_ys,T_b,V_xs,T_a] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 109.10/108.80 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_card__distinct,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__card,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__eq__iff__index__eq,axiom,
% 109.10/108.80 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 => ( 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_xs_2)))
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => ( hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
% 109.10/108.80 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__conv__nth,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 <=> ! [B_i] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => ! [B_j] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => ( B_i != B_j
% 109.10/108.80 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.10/108.80 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Nitpick_Ocard_H__def,axiom,
% 109.10/108.80 ! [V_A_2,T_b] :
% 109.10/108.80 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.80 => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) )
% 109.10/108.80 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.80 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__take__lemma,axiom,
% 109.10/108.80 ! [V_ys,V_xs,T_a,V_k] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => ( 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)))
% 109.10/108.80 => ( ! [B_i] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 109.10/108.80 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 109.10/108.80 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__remove1__eq,axiom,
% 109.10/108.80 ! [V_x_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 => hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__Cons__number__of,axiom,
% 109.10/108.80 ! [V_xs,V_x,T_a,V_v] :
% 109.10/108.80 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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) )
% 109.10/108.80 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists_ONil,axiom,
% 109.10/108.80 ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel__Nil1,axiom,
% 109.10/108.80 ! [V_r_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
% 109.10/108.80 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel__Nil2,axiom,
% 109.10/108.80 ! [V_r_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
% 109.10/108.80 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__butlast,axiom,
% 109.10/108.80 ! [T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct_Osimps_I1_J,axiom,
% 109.10/108.80 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__remove1,axiom,
% 109.10/108.80 ! [V_x,V_xs,T_a] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_butlast_Osimps_I1_J,axiom,
% 109.10/108.80 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_butlast_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_x,T_a,V_xs] :
% 109.10/108.80 ( ( V_xs = c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 109.10/108.80 & ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_remove1_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_y,V_x] :
% 109.10/108.80 ( ( V_x = V_y
% 109.10/108.80 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 109.10/108.80 & ( V_x != V_y
% 109.10/108.80 => 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)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list_Osimps_I3_J,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list_Osimps_I2_J,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_upto__empty,axiom,
% 109.10/108.80 ! [V_i,V_j] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 109.10/108.80 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__eq__Nil,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 109.10/108.80 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__0,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__Nil,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list_Osize_I1_J,axiom,
% 109.10/108.80 ! [V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,c_List_Olist_ONil(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sublist__nil,axiom,
% 109.10/108.80 ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_remove1_Osimps_I1_J,axiom,
% 109.10/108.80 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_remove1__commute,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrelp_ONil,axiom,
% 109.10/108.80 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrelp_Oequations_I1_J,axiom,
% 109.10/108.80 ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip_Osimps_I1_J,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__Nil,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__simps_I1_J,axiom,
% 109.10/108.80 ! [T_a] :
% 109.10/108.80 ( class_Groups_Omonoid__add(T_a)
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__0__conv,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list_Osize_I3_J,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__empty,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__empty2,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 109.10/108.80 ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__nonempty,axiom,
% 109.10/108.80 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update_Osimps_I1_J,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__code_I1_J,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__set__remove1,axiom,
% 109.10/108.80 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 109.10/108.80 ( V_a_2 != V_b_2
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
% 109.10/108.80 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_notin__set__remove1,axiom,
% 109.10/108.80 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_remove1__idem,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sublist__empty,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__remove1__subset,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__greater__0__conv,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( 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_b)),V_xs_2)))
% 109.10/108.80 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__1__Cons,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_not__Nil__listrel1,axiom,
% 109.10/108.80 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_not__listrel1__Nil,axiom,
% 109.10/108.80 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel_ONil,axiom,
% 109.10/108.80 ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lexord__Nil__right,axiom,
% 109.10/108.80 ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Nil__notin__lex,axiom,
% 109.10/108.80 ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Nil2__notin__lex,axiom,
% 109.10/108.80 ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__Cons,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_upto_Osimps,axiom,
% 109.10/108.80 ! [V_j,V_i] :
% 109.10/108.80 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 109.10/108.80 => 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)) )
% 109.10/108.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 109.10/108.80 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sublist__singleton,axiom,
% 109.10/108.80 ! [V_x_2,T_b,V_A_2] :
% 109.10/108.80 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 109.10/108.80 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) )
% 109.10/108.80 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 109.10/108.80 => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists__empty,axiom,
% 109.10/108.80 ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__Cons_H,axiom,
% 109.10/108.80 ! [V_xs,V_x,T_a,V_n] :
% 109.10/108.80 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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) )
% 109.10/108.80 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_upto__rec__number__of,axiom,
% 109.10/108.80 ! [V_n,V_m] :
% 109.10/108.80 ( ( 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)))
% 109.10/108.80 => 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))) )
% 109.10/108.80 & ( ~ 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)))
% 109.10/108.80 => 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) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel__Nil,axiom,
% 109.10/108.80 ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__Cons__sing__Nil,axiom,
% 109.10/108.80 ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__remove1,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,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_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
% 109.10/108.80 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_upto_Opsimps,axiom,
% 109.10/108.80 ! [V_j_2,V_i_2] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 109.10/108.80 => 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)) )
% 109.10/108.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 109.10/108.80 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_select,axiom,
% 109.10/108.80 ! [V_s_2,T_b,V_xs_2] :
% 109.10/108.80 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listset_Osimps_I1_J,axiom,
% 109.10/108.80 ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__Cons1,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_ys_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_c,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c)))),T_c),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_c))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_c),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)))),hAPP(c_List_Ozip(T_b,T_c),V_xs_2))),V_ys_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list_Osimps_I5_J,axiom,
% 109.10/108.80 ! [V_list_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_a_2),V_list_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_list_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list_Osimps_I4_J,axiom,
% 109.10/108.80 ! [V_f2_2,V_f1_2,T_c,T_b] : hAPP(c_List_Olist_Olist__case(T_b,T_c,V_f1_2,V_f2_2),c_List_Olist_ONil(T_c)) = V_f1_2 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listset_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_As_2,V_A_2,T_b] : c_List_Olistset(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_As_2)) = c_List_Oset__Cons(T_b,V_A_2,c_List_Olistset(T_b,V_As_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__Cons,axiom,
% 109.10/108.80 ! [V_ys_2,V_y_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(T_b,T_c)),T_b,c_List_Olist_ONil(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c))),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_prod(T_b,T_c)))),T_b),c_COMBB(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_List_Olist(tc_prod(T_b,T_c)),tc_List_Olist(tc_prod(T_b,T_c))),T_b),c_List_Olist_OCons(tc_prod(T_b,T_c))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_prod(T_b,T_c)),c_Product__Type_OPair(T_b,T_c)),V_y_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_c),tc_List_Olist(tc_prod(T_b,T_c))),c_List_Ozip(T_b,T_c)),V_ys_2))),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sorted__list__of__set__remove,axiom,
% 109.10/108.80 ! [V_x_2,V_A_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.80 => c_List_Olinorder__class_Osorted__list__of__set(T_b,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))))) = c_List_Oremove1(T_b,V_x_2,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_upto_Opinduct,axiom,
% 109.10/108.80 ! [V_P_2,V_a1_2,V_a0_2] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => ( ! [B_i,B_j] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 109.10/108.80 => 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)) )
% 109.10/108.80 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 109.10/108.80 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sorted__list__of__set__empty,axiom,
% 109.10/108.80 ! [T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => c_List_Olinorder__class_Osorted__list__of__set(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_anamorph_Osimps,axiom,
% 109.10/108.80 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 109.10/108.80 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 109.10/108.80 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) )
% 109.10/108.80 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 109.10/108.80 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2),V_k_2),V_x_2) = c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,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)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sublist__Cons,axiom,
% 109.10/108.80 ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),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_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,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)))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append1__eq__conv,axiom,
% 109.10/108.80 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
% 109.10/108.80 <=> ( V_xs_2 = V_ys_2
% 109.10/108.80 & V_x_2 = V_y_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Cons__eq__append__conv,axiom,
% 109.10/108.80 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
% 109.10/108.80 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 109.10/108.80 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 109.10/108.80 | ? [B_ys_H] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 109.10/108.80 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__eq__Cons__conv,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 109.10/108.80 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 109.10/108.80 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 109.10/108.80 | ? [B_ys_H] :
% 109.10/108.80 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 109.10/108.80 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Cons__eq__appendI,axiom,
% 109.10/108.80 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 109.10/108.80 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 109.10/108.80 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__Cons,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__in__lists__conv,axiom,
% 109.10/108.80 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
% 109.10/108.80 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 109.10/108.80 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__assoc,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__eq__append__conv2,axiom,
% 109.10/108.80 ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_tsa_2)
% 109.10/108.80 <=> ? [B_us] :
% 109.10/108.80 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 109.10/108.80 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2 )
% 109.10/108.80 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 109.10/108.80 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_same__append__eq,axiom,
% 109.10/108.80 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2)
% 109.10/108.80 <=> V_ys_2 = V_zs_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__same__eq,axiom,
% 109.10/108.80 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),V_xs_2)
% 109.10/108.80 <=> V_ys_2 = V_zs_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__eq__appendI,axiom,
% 109.10/108.80 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 109.10/108.80 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 109.10/108.80 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__append,axiom,
% 109.10/108.80 ! [V_ys,V_xs,T_a] :
% 109.10/108.80 ( class_Groups_Omonoid__add(T_a)
% 109.10/108.80 => 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)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__append,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__append,axiom,
% 109.10/108.80 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 109.10/108.80 ( 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)
% 109.10/108.80 => ( 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)
% 109.10/108.80 => 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)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__append,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_eq__Nil__appendI,axiom,
% 109.10/108.80 ! [T_a,V_ys,V_xs] :
% 109.10/108.80 ( V_xs = V_ys
% 109.10/108.80 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__self__conv2,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__self__conv,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 109.10/108.80 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__is__Nil__conv,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 109.10/108.80 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 109.10/108.80 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_self__append__conv2,axiom,
% 109.10/108.80 ! [V_xs_2,T_b,V_ys_2] :
% 109.10/108.80 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_self__append__conv,axiom,
% 109.10/108.80 ! [V_ys_2,T_b,V_xs_2] :
% 109.10/108.80 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 109.10/108.80 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__Nil2,axiom,
% 109.10/108.80 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Nil__is__append__conv,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 109.10/108.80 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 109.10/108.80 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__Nil,axiom,
% 109.10/108.80 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 109.10/108.80
% 109.10/108.80 fof(fact_butlast__append,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_ys] :
% 109.10/108.80 ( ( V_ys = c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 109.10/108.80 & ( V_ys != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__append__length,axiom,
% 109.10/108.80 ! [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 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__append__length__plus,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__append,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__append1,axiom,
% 109.10/108.80 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__length,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_remove1__append,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) )
% 109.10/108.80 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__set__butlast__appendI,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 109.10/108.80 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_butlast__snoc,axiom,
% 109.10/108.80 ! [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 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__listrel1I,axiom,
% 109.10/108.80 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 109.10/108.80 & V_us_2 = V_vs_2 )
% 109.10/108.80 | ( V_xs_2 = V_ys_2
% 109.10/108.80 & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lexord__append__leftI,axiom,
% 109.10/108.80 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__append,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 109.10/108.80 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 109.10/108.80 & hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(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)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__append,axiom,
% 109.10/108.80 ! [V_ys,V_xs,T_a,V_n] :
% 109.10/108.80 ( ( 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)))
% 109.10/108.80 => 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) )
% 109.10/108.80 & ( ~ 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)))
% 109.10/108.80 => 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))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__update__append,axiom,
% 109.10/108.80 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 109.10/108.80 ( ( 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)))
% 109.10/108.80 => 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) )
% 109.10/108.80 & ( ~ 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)))
% 109.10/108.80 => 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)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sublist__append,axiom,
% 109.10/108.80 ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,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_b)),V_l_2)))),V_A_2)))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel1I,axiom,
% 109.10/108.80 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
% 109.10/108.80 => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
% 109.10/108.80 => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lexord__append__left__rightI,axiom,
% 109.10/108.80 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__Suc__conv__app__nth,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_i] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 109.10/108.80 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
% 109.10/108.80 <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 109.10/108.80 & V_x_2 = V_y_2 )
% 109.10/108.80 | ( V_xs_2 = V_ys_2
% 109.10/108.80 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listrel1E,axiom,
% 109.10/108.80 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
% 109.10/108.80 => ~ ! [B_x,B_y] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 109.10/108.80 => ! [B_us,B_vs] :
% 109.10/108.80 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 109.10/108.80 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lexord__append__leftD,axiom,
% 109.10/108.80 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
% 109.10/108.80 => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate1__def,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_upd__conv__take__nth__drop,axiom,
% 109.10/108.80 ! [V_a,V_xs,T_a,V_i] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__take__drop__id,axiom,
% 109.10/108.80 ! [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 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__1__Cons,axiom,
% 109.10/108.80 ! [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 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__Suc__Cons,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__via__drop,axiom,
% 109.10/108.80 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 109.10/108.80 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct1__rotate,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 109.10/108.80 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__drop,axiom,
% 109.10/108.80 ! [V_i,V_xs,T_a] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__butlast,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_butlast__drop,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__drop,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__take,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__0,axiom,
% 109.10/108.80 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__drop,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__zip,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__drop,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__rotate1,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__rotate1,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__set__dropD,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__drop__subset,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate1__is__Nil__conv,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__Nil,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__drop__subset__set__drop,axiom,
% 109.10/108.80 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__all,axiom,
% 109.10/108.80 ! [V_n,V_xs,T_a] :
% 109.10/108.80 ( 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))
% 109.10/108.80 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__eq__Nil,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 109.10/108.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__append,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__eq__conv__conj,axiom,
% 109.10/108.80 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 109.10/108.80 <=> ( V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
% 109.10/108.80 & V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__Cons,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__Cons_H,axiom,
% 109.10/108.80 ! [V_xs,V_x,T_a,V_n] :
% 109.10/108.80 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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) )
% 109.10/108.80 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__drop,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_i,V_n] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__eq__append__conv__if,axiom,
% 109.10/108.80 ! [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_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
% 109.10/108.80 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 109.10/108.80 => ( V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)
% 109.10/108.80 & V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2) ) )
% 109.10/108.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
% 109.10/108.80 => ( hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2
% 109.10/108.80 & hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),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 ) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__drop_H,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_i] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__simps,axiom,
% 109.10/108.80 ! [V_xs,V_x,T_b,T_a] :
% 109.10/108.80 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 109.10/108.80 & 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__Cons__number__of,axiom,
% 109.10/108.80 ! [V_xs,V_x,T_a,V_v] :
% 109.10/108.80 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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) )
% 109.10/108.80 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__add,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_j,V_i] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate1__length01,axiom,
% 109.10/108.80 ! [V_xs,T_a] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__append2,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__append1,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_id__take__nth__drop,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_i] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__hd__drop,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_n] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_hd__drop__conv__nth,axiom,
% 109.10/108.80 ! [V_n,T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => ( 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)))
% 109.10/108.80 => 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) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_hd_Osimps,axiom,
% 109.10/108.80 ! [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 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_hd__append,axiom,
% 109.10/108.80 ! [V_ys,T_a,V_xs] :
% 109.10/108.80 ( ( V_xs = c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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) )
% 109.10/108.80 & ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_hd__append2,axiom,
% 109.10/108.80 ! [V_ys,T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_hd__in__set,axiom,
% 109.10/108.80 ! [T_b,V_xs_2] :
% 109.10/108.80 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_hd__conv__nth,axiom,
% 109.10/108.80 ! [T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate1__hd__tl,axiom,
% 109.10/108.80 ! [T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_hd__rotate__conv__nth,axiom,
% 109.10/108.80 ! [V_n,T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_tl__drop,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__tl,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_tl_Osimps_I2_J,axiom,
% 109.10/108.80 ! [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 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__rotate,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 109.10/108.80 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__tl,axiom,
% 109.10/108.80 ! [V_xs,T_a] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate0,axiom,
% 109.10/108.80 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__rotate,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__add,axiom,
% 109.10/108.80 ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__rotate,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__rotate,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__is__Nil__conv,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,T_b] :
% 109.10/108.80 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_tl_Osimps_I1_J,axiom,
% 109.10/108.80 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate1__rotate__swap,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__def,axiom,
% 109.10/108.80 ! [V_n_2,T_b] : c_List_Orotate(T_b,V_n_2) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_n_2),c_List_Orotate1(T_b)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_tl__append2,axiom,
% 109.10/108.80 ! [V_ys,T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__tl,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__conv__mod,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__Suc,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__Suc,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_tl__append,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__id,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_n] :
% 109.10/108.80 ( 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)
% 109.10/108.80 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__length01,axiom,
% 109.10/108.80 ! [V_n,V_xs,T_a] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__tl,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_tl__take,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__Suc,axiom,
% 109.10/108.80 ! [V_n,T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__drop__take,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_fold1__set,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 109.10/108.80 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 109.10/108.80 => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lexord__append__rightI,axiom,
% 109.10/108.80 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 109.10/108.80 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_foldl__Nil,axiom,
% 109.10/108.80 ! [V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),c_List_Olist_ONil(T_c)) = V_a_2 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_start__le__sum,axiom,
% 109.10/108.80 ! [V_ns_2,V_n_2,V_m_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_foldl__assoc,axiom,
% 109.10/108.80 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Groups_Osemigroup__add(T_b)
% 109.10/108.80 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2)),V_zs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_y_2),V_zs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_foldl__absorb0,axiom,
% 109.10/108.80 ! [V_zs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Groups_Omonoid__add(T_b)
% 109.10/108.80 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_zs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_zs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_foldl__Cons,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_foldl__append,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__foldl,axiom,
% 109.10/108.80 ! [T_b] :
% 109.10/108.80 ( class_Groups_Omonoid__add(T_b)
% 109.10/108.80 => c_List_Omonoid__add__class_Olistsum(T_b) = c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sum__eq__0__conv,axiom,
% 109.10/108.80 ! [V_ns_2,V_m_2] :
% 109.10/108.80 ( 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)
% 109.10/108.80 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 & ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 109.10/108.80 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 109.10/108.80 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 109.10/108.80 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Sup__set__fold,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.80 => c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Inf__set__fold,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.80 => c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Sup__fin__set__fold,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Lattices_Olattice(T_b)
% 109.10/108.80 => c_Big__Operators_Olattice__class_OSup__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Inf__fin__set__fold,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Lattices_Olattice(T_b)
% 109.10/108.80 => c_Big__Operators_Olattice__class_OInf__fin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Min__fin__set__fold,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Max__fin__set__fold,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omin(T_b),V_x_2),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))) = hAPP(c_List_Ofoldl(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_x_2),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_SUPR__set__fold,axiom,
% 109.10/108.80 ! [V_f_2,V_xs_2,T_c,T_b] :
% 109.10/108.80 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.80 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_f_2)),c_Orderings_Obot__class_Obot(T_b)),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_INFI__set__fold,axiom,
% 109.10/108.80 ! [V_f_2,V_xs_2,T_c,T_b] :
% 109.10/108.80 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.80 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,T_b),hAPP(c_List_Oset(T_c),V_xs_2)),V_f_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_f_2)),c_Orderings_Otop__class_Otop(T_b)),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_elem__le__sum,axiom,
% 109.10/108.80 ! [V_ns_2,V_n_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sorted__list__of__set__insert,axiom,
% 109.10/108.80 ! [V_x_2,V_A_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.80 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),c_List_Olinorder__class_Osorted__list__of__set(T_b,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)))))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lexord__Nil__left,axiom,
% 109.10/108.80 ! [V_r_2,V_y_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 109.10/108.80 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_insort__key_Osimps_I1_J,axiom,
% 109.10/108.80 ! [V_x_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_c)
% 109.10/108.80 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_insort__key_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 109.10/108.80 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) )
% 109.10/108.80 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 109.10/108.80 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_insort__left__comm,axiom,
% 109.10/108.80 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_fun__left__comm__insort,axiom,
% 109.10/108.80 ! [T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => c_Finite__Set_Ofun__left__comm(T_b,tc_List_Olist(T_b),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_insort__key__left__comm,axiom,
% 109.10/108.80 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 109.10/108.80 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_y_2),V_xs_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__insort,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_c)
% 109.10/108.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__insort,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_c)
% 109.10/108.80 => hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_remove1__insort,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_insort__not__Nil,axiom,
% 109.10/108.80 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_c)
% 109.10/108.80 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__insort,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_c)
% 109.10/108.80 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
% 109.10/108.80 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_insort__insert__insort__key,axiom,
% 109.10/108.80 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 109.10/108.80 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_insort__insert__insort,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__insort__insert,axiom,
% 109.10/108.80 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_c)
% 109.10/108.80 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_insort__insert__triv,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__insort__insert,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_insort__insert__key__triv,axiom,
% 109.10/108.80 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 109.10/108.80 ( class_Orderings_Olinorder(T_b)
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
% 109.10/108.80 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__list__update,axiom,
% 109.10/108.80 ! [V_x,V_k,T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => ( ( 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))
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 109.10/108.80 & ( 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))
% 109.10/108.80 => 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) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__conv__nth,axiom,
% 109.10/108.80 ! [T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__ConsL,axiom,
% 109.10/108.80 ! [V_x,T_a,V_xs] :
% 109.10/108.80 ( V_xs = c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__ConsR,axiom,
% 109.10/108.80 ! [V_x,T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last_Osimps,axiom,
% 109.10/108.80 ! [V_x,T_a,V_xs] :
% 109.10/108.80 ( ( V_xs = c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 109.10/108.80 & ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__appendL,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_ys] :
% 109.10/108.80 ( V_ys = c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__appendR,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_ys] :
% 109.10/108.80 ( V_ys != c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__append,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_ys] :
% 109.10/108.80 ( ( V_ys = c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 109.10/108.80 & ( V_ys != c_List_Olist_ONil(T_a)
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__in__set,axiom,
% 109.10/108.80 ! [T_b,V_as_2] :
% 109.10/108.80 ( V_as_2 != c_List_Olist_ONil(T_b)
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__snoc,axiom,
% 109.10/108.80 ! [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 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__drop,axiom,
% 109.10/108.80 ! [V_xs,T_a,V_n] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_snoc__eq__iff__butlast,axiom,
% 109.10/108.80 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
% 109.10/108.80 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 109.10/108.80 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 109.10/108.80 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__butlast__last__id,axiom,
% 109.10/108.80 ! [T_a,V_xs] :
% 109.10/108.80 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.80 => 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 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists_Osimps,axiom,
% 109.10/108.80 ! [V_A_2,V_a_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 109.10/108.80 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 109.10/108.80 | ? [B_a,B_l] :
% 109.10/108.80 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 109.10/108.80 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 109.10/108.80 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_select__weigth__select,axiom,
% 109.10/108.80 ! [T_b,V_xs_2] :
% 109.10/108.80 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 109.10/108.80 => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_inj__mapI,axiom,
% 109.10/108.80 ! [V_f_2,T_c,T_b] :
% 109.10/108.80 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.80 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_last__map,axiom,
% 109.10/108.80 ! [V_f_2,T_c,T_b,V_xs_2] :
% 109.10/108.80 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 109.10/108.80 => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_foldl__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_d,V_a_2,V_g_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_g_2,V_a_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,T_b)),T_b),c_COMBB(T_c,T_b,T_d)),V_g_2)),V_f_2),V_a_2),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__tl,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_rotate__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__same__conv__map,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,tc_prod(T_b,T_b)),hAPP(hAPP(c_COMBS(T_b,T_b,tc_prod(T_b,T_b)),c_Product__Type_OPair(T_b,T_b)),c_COMBI(T_b))),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__map__map,axiom,
% 109.10/108.80 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_e),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,T_c),tc_fun(T_e,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_e,T_c),tc_fun(T_e,tc_prod(T_b,T_c))),T_d),c_COMBB(T_c,tc_prod(T_b,T_c),T_e)),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_f_2))),V_g_2))),hAPP(hAPP(c_List_Ozip(T_d,T_e),V_xs_2),V_ys_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__map1,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_f_2,T_d,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_xs_2)),V_ys_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_d,T_c),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,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_d),c_Product__Type_OPair(T_b,T_c)),V_f_2))),hAPP(hAPP(c_List_Ozip(T_d,T_c),V_xs_2),V_ys_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__zip__map,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_g_2,T_e,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),hAPP(hAPP(c_List_Omap(T_e,T_c),V_g_2),V_xs_2)),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_e,T_d),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_e,T_d,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_prod(T_c,T_d)),tc_fun(T_d,T_b),T_e),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_d),V_f_2)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,tc_prod(T_c,T_d)),T_e),c_Product__Type_OPair(T_c,T_d)),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_e,T_d),V_xs_2),V_ys_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__zip__map2,axiom,
% 109.10/108.80 ! [V_ys_2,V_g_2,T_e,V_xs_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_d),T_b),V_f_2),hAPP(hAPP(c_List_Ozip(T_c,T_d),V_xs_2),hAPP(hAPP(c_List_Omap(T_e,T_d),V_g_2),V_ys_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_c,T_e),T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_e,T_b),hAPP(hAPP(c_COMBB(tc_fun(T_e,tc_prod(T_c,T_d)),tc_fun(T_e,T_b),T_c),hAPP(c_COMBB(tc_prod(T_c,T_d),T_b,T_e),V_f_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_e,T_d),tc_fun(T_e,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_e,T_d),tc_fun(T_e,tc_prod(T_c,T_d))),T_c),c_COMBB(T_d,tc_prod(T_c,T_d),T_e)),c_Product__Type_OPair(T_c,T_d))),V_g_2)))),hAPP(hAPP(c_List_Ozip(T_c,T_e),V_xs_2),V_ys_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__map2,axiom,
% 109.10/108.80 ! [V_ys_2,V_f_2,T_d,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_ys_2)) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_d),tc_prod(T_b,T_c)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_d,tc_prod(T_b,T_c)),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_f_2))),hAPP(hAPP(c_List_Ozip(T_b,T_d),V_xs_2),V_ys_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Nil__is__map__conv,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map_Osimps_I1_J,axiom,
% 109.10/108.80 ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__is__Nil__conv,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__update,axiom,
% 109.10/108.80 ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__eq__conv,axiom,
% 109.10/108.80 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)
% 109.10/108.80 <=> ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 109.10/108.80 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__eq__imp__length__eq,axiom,
% 109.10/108.80 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
% 109.10/108.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__subtractf,axiom,
% 109.10/108.80 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( class_Groups_Oab__group__add(T_b)
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Ominus__class_Ominus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__addf,axiom,
% 109.10/108.80 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__mult__const,axiom,
% 109.10/108.80 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( class_Rings_Osemiring__0(T_b)
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__const__mult,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 109.10/108.80 ( class_Rings_Osemiring__0(T_b)
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__0,axiom,
% 109.10/108.80 ! [V_xs_2,T_c,T_b] :
% 109.10/108.80 ( class_Groups_Omonoid__add(T_b)
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_inj__map__eq__map,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.80 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 109.10/108.80 <=> V_xs_2 = V_ys_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__injective,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 109.10/108.80 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 109.10/108.80 => V_xs_2 = V_ys_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__ident,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_take__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__butlast,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__append,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_hd__map,axiom,
% 109.10/108.80 ! [V_f_2,T_c,T_b,V_xs_2] :
% 109.10/108.80 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 109.10/108.80 => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_drop__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_List_Omap_Oidentity,axiom,
% 109.10/108.80 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_List_Omap_Oid,axiom,
% 109.10/108.80 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_List_Omap_Ocompositionality,axiom,
% 109.10/108.80 ! [V_list_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Omap(T_d,T_c),V_g_2),V_list_2)) = hAPP(hAPP(c_List_Omap(T_d,T_b),hAPP(c_Fun_Ocomp(T_c,T_b,T_d,V_f_2),V_g_2)),V_list_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__comp__map,axiom,
% 109.10/108.80 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_List_Omap_Ocomp,axiom,
% 109.10/108.80 ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_List_Olist(T_d),tc_List_Olist(T_c),tc_List_Olist(T_b),hAPP(c_List_Omap(T_d,T_c),V_f_2)),hAPP(c_List_Omap(T_b,T_d),V_g_2)) = hAPP(c_List_Omap(T_b,T_c),hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_f_2),V_g_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__size__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_g_2,T_c,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,V_f_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2)) = c_List_Olist_Olist__size(T_c,hAPP(c_Fun_Ocomp(T_b,tc_Nat_Onat,T_c,V_f_2),V_g_2),V_xs_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__inj__on,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 109.10/108.80 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)
% 109.10/108.80 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_List_Oset(T_c),V_xs_2)),hAPP(c_List_Oset(T_c),V_ys_2)))
% 109.10/108.80 => V_xs_2 = V_ys_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_inj__on__map__eq__map,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( c_Fun_Oinj__on(T_b,T_c,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)))
% 109.10/108.80 => ( hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)
% 109.10/108.80 <=> V_xs_2 = V_ys_2 ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nth__map,axiom,
% 109.10/108.80 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__fun__upd,axiom,
% 109.10/108.80 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 109.10/108.80 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => hAPP(hAPP(c_List_Omap(T_b,T_c),c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_y_2,V_v_2)),V_xs_2) = hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 109.10/108.80 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 109.10/108.80 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__abs,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_uminus__listsum__map,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( class_Groups_Oab__group__add(T_b)
% 109.10/108.80 => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_inj__on__mapI,axiom,
% 109.10/108.80 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.80 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),V_A_2)))
% 109.10/108.80 => c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),V_A_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_inj__mapD,axiom,
% 109.10/108.80 ! [V_f_2,T_c,T_b] :
% 109.10/108.80 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 109.10/108.80 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_inj__map,axiom,
% 109.10/108.80 ! [V_f_2,T_c,T_b] :
% 109.10/108.80 ( c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_c),hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))
% 109.10/108.80 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 109.10/108.80 ! [V_f_2,V_xs_2,T_b,T_c] :
% 109.10/108.80 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.10/108.80 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__triv,axiom,
% 109.10/108.80 ! [V_xs_2,V_r_2,T_c,T_b] :
% 109.10/108.80 ( class_Rings_Osemiring__1(T_b)
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__map__remove1,axiom,
% 109.10/108.80 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 109.10/108.80 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 109.10/108.80 ! [V_f_2,V_A_2,T_b,T_c] :
% 109.10/108.80 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.10/108.80 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.80 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) )
% 109.10/108.80 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.80 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_pick__same,axiom,
% 109.10/108.80 ! [V_xs_2,T_b,V_l_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_l_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => hAPP(c_Random_Opick(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),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_b),V_xs_2),V_l_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zero__code__numeral__def,axiom,
% 109.10/108.80 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_times__code__numeral__code,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 109.10/108.80 ! [V_m_2,V_n_2] :
% 109.10/108.80 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 109.10/108.80 <=> V_n_2 = V_m_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 109.10/108.80 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_one__code__numeral__def,axiom,
% 109.10/108.80 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_less__code__numeral__code,axiom,
% 109.10/108.80 ! [V_m_2,V_n_2] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 109.10/108.80 ! [V_y_2,V_x_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 109.10/108.80 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 109.10/108.80 <=> V_x_2 = V_y_2 ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__fst__zip,axiom,
% 109.10/108.80 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 109.10/108.80 ( 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)
% 109.10/108.80 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_map__snd__zip,axiom,
% 109.10/108.80 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 109.10/108.80 ( 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)
% 109.10/108.80 => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_number__of__code__numeral__def,axiom,
% 109.10/108.80 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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__map__fst__snd,axiom,
% 109.10/108.80 ! [V_zs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2)),hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2)) = V_zs_2 ).
% 109.10/108.80
% 109.10/108.80 fof(fact_plus__code__numeral__code,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_less__eq__code__numeral__code,axiom,
% 109.10/108.80 ! [V_m_2,V_n_2] :
% 109.10/108.80 ( 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)))
% 109.10/108.80 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_subtract__code__numeral__code,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_pick__member,axiom,
% 109.10/108.80 ! [V_xs_2,T_b,V_i_2] :
% 109.10/108.80 ( 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_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_zip__eq__conv,axiom,
% 109.10/108.80 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 109.10/108.80 ( 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)
% 109.10/108.80 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 109.10/108.80 <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2
% 109.10/108.80 & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2 ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__size__conv__listsum,axiom,
% 109.10/108.80 ! [V_xs_2,V_f_2,T_b] : c_List_Olist_Olist__size(T_b,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_b,tc_Nat_Onat),V_f_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_code__numeral__not__eq__zero,axiom,
% 109.10/108.80 ! [V_i_2] :
% 109.10/108.80 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 109.10/108.80 <=> 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)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 109.10/108.80 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 109.10/108.80 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.10/108.80 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),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_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 109.10/108.80 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 109.10/108.80 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.10/108.80 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),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_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_select__weight__member,axiom,
% 109.10/108.80 ! [V_s_2,V_xs_2,T_b] :
% 109.10/108.80 ( 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_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_select__weight__def,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,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_b,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_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_select__def,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : c_Random_Oselect(T_b,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_b,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_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(T_b),V_xs_2)),c_Code__Numeral_Onat__of))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsum__mono,axiom,
% 109.10/108.80 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 109.10/108.80 ( ( class_Groups_Omonoid__add(T_c)
% 109.10/108.80 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 109.10/108.80 => ( ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nat__of__of__nat,axiom,
% 109.10/108.80 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 109.10/108.80
% 109.10/108.80 fof(fact_of__nat__nat__of,axiom,
% 109.10/108.80 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nat__of__inverse,axiom,
% 109.10/108.80 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 109.10/108.80
% 109.10/108.80 fof(fact_times__code__numeral__def,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_code__numeral_Onat__of__inject,axiom,
% 109.10/108.80 ! [V_y_2,V_x_2] :
% 109.10/108.80 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 109.10/108.80 <=> V_x_2 = V_y_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 109.10/108.80 ! [V_l_2,V_k_2] :
% 109.10/108.80 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 109.10/108.80 <=> V_k_2 = V_l_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_type__definition__code__numeral,axiom,
% 109.10/108.80 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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_less__code__numeral__def,axiom,
% 109.10/108.80 ! [V_m_2,V_n_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 109.10/108.80 <=> 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nat__of,axiom,
% 109.10/108.80 ! [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)))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nat__of__number,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_int__of__def,axiom,
% 109.10/108.80 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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_less__eq__code__numeral__def,axiom,
% 109.10/108.80 ! [V_m_2,V_n_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 109.10/108.80 <=> 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nat__of__code,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_nat__of__aux__def,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_Suc__code__numeral__def,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_minus__code__numeral__def,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_of__nat__inverse,axiom,
% 109.10/108.80 ! [V_y_2] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 109.10/108.80 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_plus__code__numeral__def,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_div__code__numeral__def,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_mod__code__numeral__def,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_code__numeral__decr,axiom,
% 109.10/108.80 ! [V_k] :
% 109.10/108.80 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 109.10/108.80 => 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))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_partition__set,axiom,
% 109.10/108.80 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 109.10/108.80 ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 109.10/108.80 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_yes_2)),hAPP(c_List_Oset(T_b),V_no_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_partition__P,axiom,
% 109.10/108.80 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 109.10/108.80 ( c_List_Opartition(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_yes_2),V_no_2)
% 109.10/108.80 => ( ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 109.10/108.80 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.80 & ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 109.10/108.80 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_partition_Osimps_I1_J,axiom,
% 109.10/108.80 ! [V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_partition_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,V_P_2,T_b] : c_List_Opartition(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),hAPP(c_If(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(V_P_2,V_x_2)))),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_List_Olist_OCons(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)))),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_List_Olist(T_b))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)))),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_List_Opartition(T_b,V_P_2,V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists__Int__eq,axiom,
% 109.10/108.80 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),c_List_Olists(T_b,V_B_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_lists__IntI,axiom,
% 109.10/108.80 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 109.10/108.80 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_l_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsp_ONil,axiom,
% 109.10/108.80 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsp_Oequations_I1_J,axiom,
% 109.10/108.80 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_in__listsp__conv__set,axiom,
% 109.10/108.80 ! [V_xs_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 109.10/108.80 <=> ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsp__conj__eq,axiom,
% 109.10/108.80 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(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),V_A_2)),V_B_2)),V_x_2))
% 109.10/108.80 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 109.10/108.80 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsp__inf__eq,axiom,
% 109.10/108.80 ! [V_B_2,V_A_2,T_b] : c_List_Olistsp(T_b,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(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsp__infI,axiom,
% 109.10/108.80 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 109.10/108.80 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 109.10/108.80 => hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_l_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsp_Oequations_I2_J,axiom,
% 109.10/108.80 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 109.10/108.80 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 109.10/108.80 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_append__in__listsp__conv,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 109.10/108.80 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 109.10/108.80 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsp__mono,axiom,
% 109.10/108.80 ! [V_B_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olistsp(T_b,V_A_2)),c_List_Olistsp(T_b,V_B_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_listsp__lists__eq,axiom,
% 109.10/108.80 ! [V_x_2,V_A_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Olistsp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)),V_x_2))
% 109.10/108.80 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_product_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_x_2,T_c,T_b] : c_Enum_Oproduct(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),V_ys_2) = hAPP(hAPP(c_List_Oappend(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Omap(T_c,tc_prod(T_b,T_c)),hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2)),V_ys_2)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__def,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 109.10/108.80 <=> ( 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)
% 109.10/108.80 & ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__map1,axiom,
% 109.10/108.80 ! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Omap(T_d,T_b),V_f_2),V_as_2),V_bs_2)
% 109.10/108.80 <=> c_List_Olist__all2(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_HOL_Obool),T_d),V_P_2),V_f_2),V_as_2,V_bs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__map2,axiom,
% 109.10/108.80 ! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_bs_2))
% 109.10/108.80 <=> c_List_Olist__all2(T_b,T_d,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_fun(T_d,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_d)),V_P_2)),V_f_2),V_as_2,V_bs_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__dropI,axiom,
% 109.10/108.80 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
% 109.10/108.80 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_as_2),hAPP(hAPP(c_List_Odrop(T_c),V_n_2),V_bs_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__appendI,axiom,
% 109.10/108.80 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
% 109.10/108.80 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
% 109.10/108.80 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_c),V_b_2),V_d_2)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__append,axiom,
% 109.10/108.80 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 109.10/108.80 ( 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)
% 109.10/108.80 => ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2),hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_vs_2))
% 109.10/108.80 <=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 109.10/108.80 & c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__Cons,axiom,
% 109.10/108.80 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2))
% 109.10/108.80 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 109.10/108.80 & c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__takeI,axiom,
% 109.10/108.80 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 109.10/108.80 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2),hAPP(hAPP(c_List_Otake(T_c),V_n_2),V_ys_2)) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__eq,axiom,
% 109.10/108.80 ! [T_b,V_ys_2,V_xs_2] :
% 109.10/108.80 ( V_xs_2 = V_ys_2
% 109.10/108.80 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__lengthD,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 109.10/108.80 => 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) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__Nil2,axiom,
% 109.10/108.80 ! [V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
% 109.10/108.80 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__Nil,axiom,
% 109.10/108.80 ! [V_ys_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
% 109.10/108.80 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_product_Osimps_I1_J,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__nthD2,axiom,
% 109.10/108.80 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_p_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__nthD,axiom,
% 109.10/108.80 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 109.10/108.80 => ( 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_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_p_2)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),V_p_2))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__conv__all__nth,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 109.10/108.80 <=> ( 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)
% 109.10/108.80 & ! [B_i] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.80 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),B_i))) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__update__cong2,axiom,
% 109.10/108.80 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.80 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
% 109.10/108.80 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2__update__cong,axiom,
% 109.10/108.80 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
% 109.10/108.80 ( 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_xs_2)))
% 109.10/108.80 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 109.10/108.80 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 109.10/108.80 => c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2),hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) ) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__product,axiom,
% 109.10/108.80 ! [V_ys,T_b,V_xs,T_a] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.80 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_product__list__set,axiom,
% 109.10/108.80 ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),c_Enum_Oproduct(T_b,T_c,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_List_Oset(T_c),V_ys_2))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sublists__powset,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__sublists,axiom,
% 109.10/108.80 ! [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)) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sublists_Osimps_I1_J,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_sublists_Osimps_I2_J,axiom,
% 109.10/108.80 ! [V_xs_2,V_x_2,T_b] : c_Enum_Osublists(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_HOL_OLet(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_Enum_Osublists(T_b,V_xs_2)),hAPP(hAPP(c_COMBS(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_List_Olist(tc_List_Olist(T_b)),tc_fun(tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(tc_List_Olist(T_b))),c_List_Oappend(tc_List_Olist(T_b))),hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Olist_OCons(T_b),V_x_2)))),c_COMBI(tc_List_Olist(tc_List_Olist(T_b))))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__set__sublists,axiom,
% 109.10/108.80 ! [V_xs_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_set__n__lists,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),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_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),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_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),hAPP(c_List_Oset(T_b),V_xs_2)))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_enum__the__def,axiom,
% 109.10/108.80 ! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_distinct__n__lists,axiom,
% 109.10/108.80 ! [V_n,V_xs,T_a] :
% 109.10/108.80 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.80 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_n__lists_Osimps_I1_J,axiom,
% 109.10/108.80 ! [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))) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_n__lists__Nil,axiom,
% 109.10/108.80 ! [T_a,V_n] :
% 109.10/108.80 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => 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))) )
% 109.10/108.80 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.80 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__n__lists,axiom,
% 109.10/108.80 ! [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) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_length__n__lists__elem,axiom,
% 109.10/108.80 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))))
% 109.10/108.80 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 109.10/108.80
% 109.10/108.80 fof(fact_list__all2I,axiom,
% 109.10/108.80 ! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
% 109.10/108.80 ( ! [B_x] :
% 109.10/108.80 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_a_2),V_b_2))))
% 109.10/108.80 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
% 109.10/108.81 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
% 109.10/108.81 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_all__nth__imp__all__set,axiom,
% 109.10/108.81 ! [V_x_2,V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( ! [B_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 109.10/108.81 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 109.10/108.81 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_map__removeAll__inj__on,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__remdups,axiom,
% 109.10/108.81 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__remdups__leq,axiom,
% 109.10/108.81 ! [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))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remdups__id__iff__distinct,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 109.10/108.81 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__removeAll,axiom,
% 109.10/108.81 ! [V_x,V_xs,T_a] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.81 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__remdups__id,axiom,
% 109.10/108.81 ! [V_xs,T_a] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.81 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__remdups,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__remdups__eq,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
% 109.10/108.81 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remdups__remdups,axiom,
% 109.10/108.81 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remdups_Osimps_I1_J,axiom,
% 109.10/108.81 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remdups__eq__nil__right__iff,axiom,
% 109.10/108.81 ! [V_x_2,T_b] :
% 109.10/108.81 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 109.10/108.81 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_removeAll_Osimps_I1_J,axiom,
% 109.10/108.81 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remdups__eq__nil__iff,axiom,
% 109.10/108.81 ! [V_x_2,T_b] :
% 109.10/108.81 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 109.10/108.81 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_removeAll_Osimps_I2_J,axiom,
% 109.10/108.81 ! [V_xs,T_a,V_y,V_x] :
% 109.10/108.81 ( ( V_x = V_y
% 109.10/108.81 => 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) )
% 109.10/108.81 & ( V_x != V_y
% 109.10/108.81 => 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)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_removeAll__append,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remdups__map__remdups,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remove1__remdups,axiom,
% 109.10/108.81 ! [V_x,V_xs,T_a] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.81 => 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)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_removeAll__id,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__remove1__removeAll,axiom,
% 109.10/108.81 ! [V_x,V_xs,T_a] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.81 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remdups_Osimps_I2_J,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__remdups__card__conv,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_map__removeAll__inj,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.81 => hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(c_List_OremoveAll(T_c,hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__removeAll,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__remdups__concat,axiom,
% 109.10/108.81 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => c_List_Olinorder__class_Osorted__list__of__set(T_b,hAPP(c_List_Oset(T_b),V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),c_List_Oremdups(T_b,V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sort__key__simps_I1_J,axiom,
% 109.10/108.81 ! [V_f_2,T_b,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldl__conv__concat,axiom,
% 109.10/108.81 ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat__conv__foldl,axiom,
% 109.10/108.81 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__sort,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_b,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__sort,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_b,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__sort,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_b,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 109.10/108.81 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat_Osimps_I1_J,axiom,
% 109.10/108.81 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat_Osimps_I2_J,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Nil__eq__concat__conv,axiom,
% 109.10/108.81 ! [V_xss_2,T_b] :
% 109.10/108.81 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 109.10/108.81 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat__eq__Nil__conv,axiom,
% 109.10/108.81 ! [V_xss_2,T_b] :
% 109.10/108.81 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 109.10/108.81 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_map__concat,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__concat,axiom,
% 109.10/108.81 ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__concat,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sort__key__simps_I2_J,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat__append,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sort__foldl__insort,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b))),c_List_Olist_ONil(T_b)),V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat__eq__concat__iff,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.81 ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 109.10/108.81 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 109.10/108.81 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 109.10/108.81 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat__injective,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.81 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 109.10/108.81 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_ys_2)
% 109.10/108.81 => ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),B_x),hAPP(c_List_Oset(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2))))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),B_x)) )
% 109.10/108.81 => V_xs_2 = V_ys_2 ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat__map__singleton,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(T_c,tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_c),c_List_Olist_OCons(T_b)),V_f_2)),c_List_Olist_ONil(T_b))),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_n__lists_Osimps_I2_J,axiom,
% 109.10/108.81 ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),V_xs_2) = c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose_Osimps_I3_J,axiom,
% 109.10/108.81 ! [V_xss_2,V_xs_2,V_x_2,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__aux__filter__head,axiom,
% 109.10/108.81 ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__concat,axiom,
% 109.10/108.81 ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__sort,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)) = c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__filter,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.81 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__is__subset,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__id__conv,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__filter__le,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sum__length__filter__compl,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2)),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__filter,axiom,
% 109.10/108.81 ! [V_xs_2,V_Q_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(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),V_Q_2)),V_P_2)),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remove1__filter__not,axiom,
% 109.10/108.81 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 109.10/108.81 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__remove1,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_Q_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Q_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Q_2),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__insort__triv,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_partition__filter1,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_partition__filter2,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_P_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_P_2)),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_partition__filter__conv,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__map,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose_Osimps_I1_J,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter_Osimps_I1_J,axiom,
% 109.10/108.81 ! [V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter_Osimps_I2_J,axiom,
% 109.10/108.81 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 109.10/108.81 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__append,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,V_P_2,T_b] : hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__empty__conv,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__filter__map,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(c_List_Ofilter(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2)),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_removeAll__filter__not,axiom,
% 109.10/108.81 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 109.10/108.81 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => hAPP(c_List_OremoveAll(T_b,V_x_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_remdups__filter,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oremdups(T_b,V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_removeAll__filter__not__eq,axiom,
% 109.10/108.81 ! [V_x_2,T_b] : c_List_OremoveAll(T_b,V_x_2) = c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(c_fequal,V_x_2))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose_Osimps_I2_J,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_nth__transpose,axiom,
% 109.10/108.81 ! [V_xs_2,T_b,V_i_2] :
% 109.10/108.81 ( 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_b))),c_List_Otranspose(T_b,V_xs_2))))
% 109.10/108.81 => hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__map__map,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Otranspose(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),c_List_Otranspose(T_c,V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__filter,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_Set_OCollect(T_b),hAPP(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)),hAPP(c_List_Oset(T_b),V_xs_2)))),V_P_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__filter__less,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__minus__filter__out,axiom,
% 109.10/108.81 ! [V_y_2,V_xs_2,T_b] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_List_Oset(T_b),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,T_b,tc_HOL_Obool),c_fequal),V_y_2))),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__in__sublist,axiom,
% 109.10/108.81 ! [V_s_2,V_xs_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.81 => hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_s_2)))),V_xs_2) = c_List_Osublist(T_b,V_xs_2,V_s_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__empty,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__filter__conv__card,axiom,
% 109.10/108.81 ! [V_xs_2,V_p_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,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_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,tc_Nat_Onat),V_p_2),hAPP(c_List_Onth(T_b),V_xs_2))))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__aux__filter__tail,axiom,
% 109.10/108.81 ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose_Opsimps_I3_J,axiom,
% 109.10/108.81 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)))
% 109.10/108.81 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_xss_2)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)))),c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),V_xs_2),c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2))))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose_Opsimps_I2_J,axiom,
% 109.10/108.81 ! [V_xss_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
% 109.10/108.81 => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sublist__shift__lemma__Suc,axiom,
% 109.10/108.81 ! [V_is_2,V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(T_b,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(T_b,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),V_is_2))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(T_b,tc_Nat_Onat)),V_P_2),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),V_is_2)))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_select__weigth__drop__zero,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),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_b,V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_pick__drop__zero,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : c_Random_Opick(T_b,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,T_b)),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_b,V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose_Opsimps_I1_J,axiom,
% 109.10/108.81 ! [T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
% 109.10/108.81 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__max__length,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : 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))),c_List_Otranspose(T_b,V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),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_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__aux__max,axiom,
% 109.10/108.81 ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),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_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),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_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldr_Osimps_I1_J,axiom,
% 109.10/108.81 ! [V_a_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c),V_a_2) = V_a_2 ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldr_Osimps_I2_J,axiom,
% 109.10/108.81 ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldr__append,axiom,
% 109.10/108.81 ! [V_a_2,V_ys_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2),V_a_2) = c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,c_List_Ofoldr(T_c,T_b,V_f_2,V_ys_2,V_a_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldr__conv__foldl,axiom,
% 109.10/108.81 ! [V_a_2,V_xs_2,T_b] :
% 109.10/108.81 ( class_Groups_Oab__semigroup__add(T_b)
% 109.10/108.81 => c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldr__map,axiom,
% 109.10/108.81 ! [V_a_2,V_xs_2,V_f_2,T_d,V_g_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_g_2,hAPP(hAPP(c_List_Omap(T_d,T_c),V_f_2),V_xs_2),V_a_2) = c_List_Ofoldr(T_d,T_b,hAPP(c_Fun_Ocomp(T_c,tc_fun(T_b,T_b),T_d,V_g_2),V_f_2),V_xs_2,V_a_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldl__foldr1__lemma,axiom,
% 109.10/108.81 ! [V_xs_2,V_a_2,T_b] :
% 109.10/108.81 ( class_Groups_Omonoid__add(T_b)
% 109.10/108.81 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_xs_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldl__foldr1,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( class_Groups_Omonoid__add(T_b)
% 109.10/108.81 => hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_xs_2) = c_List_Ofoldr(T_b,T_b,c_Groups_Oplus__class_Oplus(T_b),V_xs_2,c_Groups_Ozero__class_Ozero(T_b)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__transpose,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,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_xs_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sublist__def,axiom,
% 109.10/108.81 ! [V_A_2,V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,V_A_2) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,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_b)),V_xs_2))))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sublist__shift__lemma,axiom,
% 109.10/108.81 ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,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_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,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_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,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_b)),V_xs_2))))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__upt,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_atLeastLessThan__upt,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__Suc,axiom,
% 109.10/108.81 ! [V_j,V_i] :
% 109.10/108.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => 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))) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__Suc__append,axiom,
% 109.10/108.81 ! [V_j,V_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => 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))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__add__eq__append,axiom,
% 109.10/108.81 ! [V_k,V_j,V_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => 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))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__rec,axiom,
% 109.10/108.81 ! [V_j,V_i] :
% 109.10/108.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => 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)) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__conv__Cons,axiom,
% 109.10/108.81 ! [V_j,V_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => 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)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__conv__Nil,axiom,
% 109.10/108.81 ! [V_i,V_j] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 109.10/108.81 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__eq__Nil__conv,axiom,
% 109.10/108.81 ! [V_j_2,V_i_2] :
% 109.10/108.81 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 109.10/108.81 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.81 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__0,axiom,
% 109.10/108.81 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_take__upt,axiom,
% 109.10/108.81 ! [V_n,V_m,V_i] :
% 109.10/108.81 ( 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))
% 109.10/108.81 => 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)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__list__of__set__range,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_hd__upt,axiom,
% 109.10/108.81 ! [V_j,V_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_drop__upt,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__upt,axiom,
% 109.10/108.81 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__upt,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__rec__number__of,axiom,
% 109.10/108.81 ! [V_n,V_m] :
% 109.10/108.81 ( ( 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)))
% 109.10/108.81 => 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))) )
% 109.10/108.81 & ( ~ 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)))
% 109.10/108.81 => 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) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_upt__eq__Cons__conv,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 109.10/108.81 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 109.10/108.81 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 109.10/108.81 & V_i_2 = V_x_2
% 109.10/108.81 & 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 ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_last__upt,axiom,
% 109.10/108.81 ! [V_j,V_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => 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)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_map__Suc__upt,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_atLeastAtMost__upt,axiom,
% 109.10/108.81 ! [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))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_atLeast__upt,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_nth__upt,axiom,
% 109.10/108.81 ! [V_j,V_k,V_i] :
% 109.10/108.81 ( 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))
% 109.10/108.81 => 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) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_greaterThanAtMost__upt,axiom,
% 109.10/108.81 ! [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))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_greaterThanLessThan__upt,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_atMost__upto,axiom,
% 109.10/108.81 ! [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))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_map__nth,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2 ).
% 109.10/108.81
% 109.10/108.81 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 109.10/108.81 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 109.10/108.81 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.10/108.81 => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),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_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 109.10/108.81 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 109.10/108.81 ( class_Groups_Ocomm__monoid__add(T_b)
% 109.10/108.81 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),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_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_nth__map__upt,axiom,
% 109.10/108.81 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 109.10/108.81 ( 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)))
% 109.10/108.81 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),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)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__rectangle,axiom,
% 109.10/108.81 ! [V_n_2,T_b,V_xs_2] :
% 109.10/108.81 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 109.10/108.81 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 109.10/108.81 => ( ! [B_i] :
% 109.10/108.81 ( 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_b))),V_xs_2)))
% 109.10/108.81 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
% 109.10/108.81 => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),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_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_insort__key__remove1,axiom,
% 109.10/108.81 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 109.10/108.81 => ( hAPP(c_List_Ohd(T_b),hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),hAPP(c_fequal,hAPP(V_f_2,V_a_2))),V_f_2)),V_xs_2)) = V_a_2
% 109.10/108.81 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted_ONil,axiom,
% 109.10/108.81 ! [T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__single,axiom,
% 109.10/108.81 ! [V_x,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__upt,axiom,
% 109.10/108.81 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__sort,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__insort__insert,axiom,
% 109.10/108.81 ! [V_x_2,V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__drop,axiom,
% 109.10/108.81 ! [V_n,V_xs,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__upto,axiom,
% 109.10/108.81 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__take,axiom,
% 109.10/108.81 ! [V_n,V_xs,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__remove1,axiom,
% 109.10/108.81 ! [V_a,V_xs,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__tl,axiom,
% 109.10/108.81 ! [V_xs,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__insort,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2))
% 109.10/108.81 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__butlast,axiom,
% 109.10/108.81 ! [V_xs,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted_Oequations_I1_J,axiom,
% 109.10/108.81 ! [T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__many,axiom,
% 109.10/108.81 ! [V_zs,V_y,V_x,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 109.10/108.81 => 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))) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__many__eq,axiom,
% 109.10/108.81 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
% 109.10/108.81 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 109.10/108.81 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__remdups,axiom,
% 109.10/108.81 ! [V_l,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__distinct__set__unique,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 109.10/108.81 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 109.10/108.81 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 109.10/108.81 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 109.10/108.81 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__sort__key,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Osort__key(T_c,T_b,V_f_2,V_xs_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__insort__insert__key,axiom,
% 109.10/108.81 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__map__remove1,axiom,
% 109.10/108.81 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__insort__key,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
% 109.10/108.81 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__filter,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__map__same,axiom,
% 109.10/108.81 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,tc_HOL_Obool),T_c),c_fequal),V_f_2)),hAPP(V_g_2,V_xs_2))),V_xs_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__same,axiom,
% 109.10/108.81 ! [V_xs_2,V_g_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Ofilter(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),hAPP(V_g_2,V_xs_2))),V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__Cons,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 109.10/108.81 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 109.10/108.81 & ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__append,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 109.10/108.81 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 109.10/108.81 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 109.10/108.81 & ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => ! [B_xa] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__insort,axiom,
% 109.10/108.81 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 109.10/108.81 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => hAPP(c_List_Ofilter(T_c,V_P_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(c_List_Ofilter(T_c,V_P_2),V_xs_2)) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted_Oequations_I2_J,axiom,
% 109.10/108.81 ! [V_a1_2,V_a2_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 109.10/108.81 <=> ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 109.10/108.81 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__list__of__set,axiom,
% 109.10/108.81 ! [V_A_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.81 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 109.10/108.81 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 109.10/108.81 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_insort__remove1,axiom,
% 109.10/108.81 ! [V_xs_2,V_a_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 109.10/108.81 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__nth__mono,axiom,
% 109.10/108.81 ! [V_j,V_i,V_xs,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => ( 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)))
% 109.10/108.81 => 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))) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__equals__nth__mono,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 109.10/108.81 <=> ! [B_j] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => ! [B_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_map__sorted__distinct__set__unique,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => ( c_Fun_Oinj__on(T_b,T_c,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)))
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 109.10/108.81 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 109.10/108.81 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 109.10/108.81 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 109.10/108.81 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__column,axiom,
% 109.10/108.81 ! [V_i_2,V_xs_2,T_b] :
% 109.10/108.81 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 109.10/108.81 => ( 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_b))),V_xs_2)))
% 109.10/108.81 => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_nth__nth__transpose__sorted,axiom,
% 109.10/108.81 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 109.10/108.81 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 109.10/108.81 => ( 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_b))),c_List_Otranspose(T_b,V_xs_2))))
% 109.10/108.81 => ( 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_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
% 109.10/108.81 => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_inj__on__rev,axiom,
% 109.10/108.81 ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__rev,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 109.10/108.81 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev_Osimps_I1_J,axiom,
% 109.10/108.81 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Nil__is__rev__conv,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 109.10/108.81 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__is__Nil__conv,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 109.10/108.81 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__singleton__conv,axiom,
% 109.10/108.81 ! [V_x_2,V_xs_2,T_b] :
% 109.10/108.81 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))
% 109.10/108.81 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_singleton__rev__conv,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(c_List_Orev(T_b),V_xs_2)
% 109.10/108.81 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__append,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__concat,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__map,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__filter,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_P_2),hAPP(c_List_Orev(T_b),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_zip__rev,axiom,
% 109.10/108.81 ! [V_ys,T_b,V_xs,T_a] :
% 109.10/108.81 ( 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)
% 109.10/108.81 => 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)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__rev,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all2__rev1,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.81 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 109.10/108.81 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all2__rev,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 109.10/108.81 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),hAPP(c_List_Orev(T_c),V_ys_2))
% 109.10/108.81 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__is__rev__conv,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.81 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 109.10/108.81 <=> V_xs_2 = V_ys_2 ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__swap,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,T_b] :
% 109.10/108.81 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 109.10/108.81 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__rev__ident,axiom,
% 109.10/108.81 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 109.10/108.81
% 109.10/108.81 fof(fact_listsum__rev,axiom,
% 109.10/108.81 ! [V_xs,T_a] :
% 109.10/108.81 ( class_Groups_Ocomm__monoid__add(T_a)
% 109.10/108.81 => 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) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__rev,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldr__foldl,axiom,
% 109.10/108.81 ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldl__foldr,axiom,
% 109.10/108.81 ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev_Osimps_I2_J,axiom,
% 109.10/108.81 ! [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))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__eq__Cons__iff,axiom,
% 109.10/108.81 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 109.10/108.81 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 109.10/108.81 <=> V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(c_List_Orev(T_b),V_ys_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_last__rev,axiom,
% 109.10/108.81 ! [T_a,V_xs] :
% 109.10/108.81 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.81 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_hd__rev,axiom,
% 109.10/108.81 ! [T_a,V_xs] :
% 109.10/108.81 ( V_xs != c_List_Olist_ONil(T_a)
% 109.10/108.81 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__transpose,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__foldl__cons,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__drop,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__take,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rotate__rev,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__nth,axiom,
% 109.10/108.81 ! [V_xs,T_a,V_n] :
% 109.10/108.81 ( 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)))
% 109.10/108.81 => 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))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__update,axiom,
% 109.10/108.81 ! [V_y,V_xs,T_a,V_k] :
% 109.10/108.81 ( 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)))
% 109.10/108.81 => 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) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__rev__nth__mono,axiom,
% 109.10/108.81 ! [V_j,V_i,V_xs,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 109.10/108.81 => ( 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)))
% 109.10/108.81 => 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))) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldr__max__sorted,axiom,
% 109.10/108.81 ! [V_y_2,V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 109.10/108.81 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 109.10/108.81 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 109.10/108.81 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 109.10/108.81 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_y_2) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__transpose__sorted,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 109.10/108.81 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 109.10/108.81 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 109.10/108.81 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 109.10/108.81 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__column__length,axiom,
% 109.10/108.81 ! [V_i_2,V_xs_2,T_b] :
% 109.10/108.81 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 109.10/108.81 => ( 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_b))),V_xs_2)))
% 109.10/108.81 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpose__transpose,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
% 109.10/108.81 => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(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_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 109.10/108.81 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__takeWhile,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__takeWhile__le,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__eq__all__conv,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__takeWhileD,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_zip__takeWhile__snd,axiom,
% 109.10/108.81 ! [V_ys_2,V_P_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_P_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_zip__takeWhile__fst,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_P_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__map,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__tail,axiom,
% 109.10/108.81 ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
% 109.10/108.81 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 109.10/108.81 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 109.10/108.81 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 109.10/108.81 ! [V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__eq__take,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__takeWhile,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.81 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_return__list__def,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__append1,axiom,
% 109.10/108.81 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_P_2,V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_nth__length__takeWhile,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__nth,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))))
% 109.10/108.81 => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__not__last,axiom,
% 109.10/108.81 ! [T_b,V_xs_2] :
% 109.10/108.81 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 109.10/108.81 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.81 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 109.10/108.81 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 109.10/108.81 => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 109.10/108.81 ! [V_l] :
% 109.10/108.81 ( c_List_Onat__list(V_l)
% 109.10/108.81 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 109.10/108.81 ! [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))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_embed__list__def,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__neq__rev,axiom,
% 109.10/108.81 ! [V_x_2,V_xs_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile__neq__rev,axiom,
% 109.10/108.81 ! [V_x_2,V_xs_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__dropWhile__id,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),c_List_OdropWhile(T_b,V_P_2,V_xs_2)) = V_xs_2 ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__dropWhile,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__dropWhile__le,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 109.10/108.81 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 109.10/108.81 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_P_2,V_xs_2) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 109.10/108.81 ! [V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__dropWhile,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 109.10/108.81 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_hd__dropWhile,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 109.10/108.81 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile__map,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_P_2),V_f_2),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile__append1,axiom,
% 109.10/108.81 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_ys_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 109.10/108.81 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 109.10/108.81 <=> ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))
% 109.10/108.81 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile__eq__drop,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] : c_List_OdropWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile__nth,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
% 109.10/108.81 => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),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_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_listsum__map__filter,axiom,
% 109.10/108.81 ! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
% 109.10/108.81 ( class_Groups_Omonoid__add(T_c)
% 109.10/108.81 => ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 109.10/108.81 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 109.10/108.81 => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted__nth__monoI,axiom,
% 109.10/108.81 ! [V_xs,T_a] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_a)
% 109.10/108.81 => ( ! [B_i,B_j] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 109.10/108.81 => ( 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)))
% 109.10/108.81 => 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))) ) )
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__eq__filter,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))))
% 109.10/108.81 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 109.10/108.81 ( ! [B_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 109.10/108.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 109.10/108.81 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__takeWhile__less__P__nth,axiom,
% 109.10/108.81 ! [V_xs_2,T_b,V_P_2,V_j_2] :
% 109.10/108.81 ( ! [B_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 109.10/108.81 => ( 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_b)),V_xs_2)))
% 109.10/108.81 => 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_b)),c_List_OtakeWhile(T_b,V_P_2,V_xs_2)))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted_Osimps,axiom,
% 109.10/108.81 ! [V_a_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 109.10/108.81 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 109.10/108.81 | ? [B_xs,B_x] :
% 109.10/108.81 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 109.10/108.81 & ! [B_xa] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 109.10/108.81 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_not__in__set__insert,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_List_Oinsert__def,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 109.10/108.81 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_insert__remdups,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__insert,axiom,
% 109.10/108.81 ! [V_x,V_xs,T_a] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 109.10/108.81 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_in__set__insert,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_List_Oset__insert,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oinsert(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_insert__Nil,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat__map__maps,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) = c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_maps__def,axiom,
% 109.10/108.81 ! [V_xs_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,V_xs_2) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(T_c,tc_List_Olist(T_b)),V_f_2),V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_maps__simps_I2_J,axiom,
% 109.10/108.81 ! [V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_maps__simps_I1_J,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Omaps(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(V_f_2,V_x_2)),c_List_Omaps(T_c,T_b,V_f_2,V_xs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_distinct__concat,axiom,
% 109.10/108.81 ! [V_xs_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 109.10/108.81 => ( ! [B_ys] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 109.10/108.81 => ( ! [B_ys] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => ! [B_zs] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => ( B_ys != B_zs
% 109.10/108.81 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),B_ys)),hAPP(c_List_Oset(T_b),B_zs)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) )
% 109.10/108.81 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_measures__lesseq,axiom,
% 109.10/108.81 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 109.10/108.81 ( 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)))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2)))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_wf__measures,axiom,
% 109.10/108.81 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_in__measures_I1_J,axiom,
% 109.10/108.81 ! [V_y_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_Nat_Onat))))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_measures__def,axiom,
% 109.10/108.81 ! [V_fs_2,T_b] : c_List_Omeasures(T_b,V_fs_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_List_Olist(tc_Nat_Onat),T_b),c_List_Olex(tc_Nat_Onat,c_Wellfounded_Oless__than)),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat),tc_fun(tc_List_Olist(tc_fun(T_b,tc_Nat_Onat)),tc_List_Olist(tc_Nat_Onat)),T_b),c_List_Omap(tc_fun(T_b,tc_Nat_Onat),tc_Nat_Onat)),hAPP(c_COMBC(tc_fun(T_b,tc_Nat_Onat),T_b,tc_Nat_Onat),c_COMBI(tc_fun(T_b,tc_Nat_Onat))))),V_fs_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_measures__less,axiom,
% 109.10/108.81 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 109.10/108.81 ( 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)))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2)))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_in__measures_I2_J,axiom,
% 109.10/108.81 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_fun(T_b,tc_Nat_Onat)),V_f_2),V_fs_2))))
% 109.10/108.81 <=> ( 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)))
% 109.10/108.81 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 109.10/108.81 & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_List_Omeasures(T_b,V_fs_2))) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_foldl__apply,axiom,
% 109.10/108.81 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 109.10/108.81 ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hAPP(c_Fun_Ocomp(T_d,T_d,T_c,hAPP(V_f_2,B_x)),V_h_2) = hAPP(c_Fun_Ocomp(T_c,T_d,T_c,V_h_2),hAPP(V_g_2,B_x)) )
% 109.10/108.81 => hAPP(c_List_Ofoldl(T_d,T_b,hAPP(c_COMBC(T_b,T_d,T_d),V_f_2),hAPP(V_h_2,V_s_2)),V_xs_2) = hAPP(V_h_2,hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_g_2),V_s_2),V_xs_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_order__fun_I2_J,axiom,
% 109.10/108.81 ! [V_g_2,V_f_2,T_b,T_c] :
% 109.10/108.81 ( ( class_Orderings_Oorder(T_c)
% 109.10/108.81 & class_Enum_Oenum(T_b) )
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 109.10/108.81 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 109.10/108.81 & hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_g_2)))) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_enum__ex__prod__def,axiom,
% 109.10/108.81 ! [V_P_2,T_b,T_c] :
% 109.10/108.81 ( ( class_Enum_Oenum(T_c)
% 109.10/108.81 & class_Enum_Oenum(T_b) )
% 109.10/108.81 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
% 109.10/108.81 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__ex(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_exists__code,axiom,
% 109.10/108.81 ! [V_P_2,T_b] :
% 109.10/108.81 ( class_Enum_Oenum(T_b)
% 109.10/108.81 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 109.10/108.81 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_enum__ex,axiom,
% 109.10/108.81 ! [V_P_2,T_b] :
% 109.10/108.81 ( class_Enum_Oenum(T_b)
% 109.10/108.81 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
% 109.10/108.81 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_zip__obtain__same__length,axiom,
% 109.10/108.81 ! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 109.10/108.81 ( ( 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_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),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_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2))),V_xs_2)),hAPP(hAPP(c_List_Otake(T_c),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),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))),V_ys_2)))) )
% 109.10/108.81 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_pos__not__random__dseq__def,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_dropWhile__append2,axiom,
% 109.10/108.81 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 => c_List_OdropWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OdropWhile(T_b,V_P_2,V_ys_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all2__all__nthI,axiom,
% 109.10/108.81 ! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
% 109.10/108.81 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_b_2)
% 109.10/108.81 => ( ! [B_n] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_a_2)))
% 109.10/108.81 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_a_2),B_n)),hAPP(hAPP(c_List_Onth(T_c),V_b_2),B_n))) )
% 109.10/108.81 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_finite__sorted__distinct__unique,axiom,
% 109.10/108.81 ! [V_A_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.81 => ? [B_x] :
% 109.10/108.81 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 109.10/108.81 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 109.10/108.81 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 109.10/108.81 & ! [B_y] :
% 109.10/108.81 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 109.10/108.81 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 109.10/108.81 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 109.10/108.81 => B_y = B_x ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_takeWhile__append2,axiom,
% 109.10/108.81 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 => c_List_OtakeWhile(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_OtakeWhile(T_b,V_P_2,V_ys_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_insort__is__Cons,axiom,
% 109.10/108.81 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_c)
% 109.10/108.81 => ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 109.10/108.81 => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__eq__Cons__iff,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
% 109.10/108.81 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
% 109.10/108.81 <=> ? [B_us,B_vs] :
% 109.10/108.81 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs))
% 109.10/108.81 & ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 109.10/108.81 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 & hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Cons__eq__filter__iff,axiom,
% 109.10/108.81 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_ys_2)
% 109.10/108.81 <=> ? [B_us,B_vs] :
% 109.10/108.81 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_vs))
% 109.10/108.81 & ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 109.10/108.81 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 & hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_order__fun_I1_J,axiom,
% 109.10/108.81 ! [V_g_2,V_f_2,T_b,T_c] :
% 109.10/108.81 ( ( class_Orderings_Oorder(T_c)
% 109.10/108.81 & class_Enum_Oenum(T_b) )
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 109.10/108.81 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBS(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Oord__class_Oless__eq(T_c)),V_f_2)),V_g_2))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_enum__all,axiom,
% 109.10/108.81 ! [V_P_2,T_b] :
% 109.10/108.81 ( class_Enum_Oenum(T_b)
% 109.10/108.81 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
% 109.10/108.81 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_all__code,axiom,
% 109.10/108.81 ! [V_P_2,T_b] :
% 109.10/108.81 ( class_Enum_Oenum(T_b)
% 109.10/108.81 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 109.10/108.81 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_enum__all__prod__def,axiom,
% 109.10/108.81 ! [V_P_2,T_b,T_c] :
% 109.10/108.81 ( ( class_Enum_Oenum(T_c)
% 109.10/108.81 & class_Enum_Oenum(T_b) )
% 109.10/108.81 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
% 109.10/108.81 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_Enum_Oenum__class_Oenum__all(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,T_c),V_P_2)),c_Product__Type_OPair(T_b,T_c))))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ball__nth,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sorted_OCons,axiom,
% 109.10/108.81 ! [V_x_2,V_xs_2,T_b] :
% 109.10/108.81 ( class_Orderings_Olinorder(T_b)
% 109.10/108.81 => ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 109.10/108.81 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 109.10/108.81 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex__length,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 109.10/108.81 <=> ? [B_n] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_in__set__conv__decomp__first,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 <=> ? [B_ys] :
% 109.10/108.81 ( ? [B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))
% 109.10/108.81 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex__simps_I2_J,axiom,
% 109.10/108.81 ! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex__append,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 109.10/108.81 <=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 109.10/108.81 | c_List_Olist__ex(T_b,V_P_2,V_ys_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex__iff,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 109.10/108.81 <=> ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex__rev,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 109.10/108.81 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex__simps_I1_J,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 109.10/108.81 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 | c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 109.10/108.81 ! [V_j_2,V_i_2,V_P_2] :
% 109.10/108.81 ( c_List_Olist__ex(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 109.10/108.81 <=> ~ c_List_Oall__interval__nat(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat,c_fNot),V_P_2),V_i_2,V_j_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_in__set__conv__decomp,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 <=> ? [B_ys,B_zs] : V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_in__set__conv__decomp__last,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 <=> ? [B_ys,B_zs] :
% 109.10/108.81 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_zs))
% 109.10/108.81 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all__length,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 109.10/108.81 <=> ! [B_n] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_measure__function__int,axiom,
% 109.10/108.81 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))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all__simps_I2_J,axiom,
% 109.10/108.81 ! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all__append,axiom,
% 109.10/108.81 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 109.10/108.81 <=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 109.10/108.81 & c_List_Olist__all(T_b,V_P_2,V_ys_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_measure__size,axiom,
% 109.10/108.81 ! [T_b] :
% 109.10/108.81 ( class_Nat_Osize(T_b)
% 109.10/108.81 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_is__measure_Ointros,axiom,
% 109.10/108.81 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_is__measure_Oequations,axiom,
% 109.10/108.81 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_is__measure_Osimps,axiom,
% 109.10/108.81 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all__iff,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_measure__fst,axiom,
% 109.10/108.81 ! [T_c,V_f_2,T_b] :
% 109.10/108.81 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 109.10/108.81 => c_FunDef_Ois__measure(tc_prod(T_b,T_c),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_b,T_c)),V_f_2),c_Product__Type_Ofst(T_b,T_c))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_measure__snd,axiom,
% 109.10/108.81 ! [T_c,V_f_2,T_b] :
% 109.10/108.81 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 109.10/108.81 => c_FunDef_Ois__measure(tc_prod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,tc_Nat_Onat,tc_prod(T_c,T_b)),V_f_2),c_Product__Type_Osnd(T_c,T_b))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all__rev,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 109.10/108.81 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all__simps_I1_J,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 109.10/108.81 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 & c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Ball__set__list__all,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all__iff__raw,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all__iff__all__interval__nat,axiom,
% 109.10/108.81 ! [V_j_2,V_i_2,V_P_2] :
% 109.10/108.81 ( c_List_Olist__all(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 109.10/108.81 <=> c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex1__simps_I2_J,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 109.10/108.81 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_Olist__all(T_b,hAPP(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_fdisj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_P_2))),hAPP(c_fequal,V_x_2)),V_xs_2) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => c_List_Olist__ex1(T_b,V_P_2,V_xs_2) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transfer__morphism__int__nat,axiom,
% 109.10/108.81 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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex1__simps_I1_J,axiom,
% 109.10/108.81 ! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_bool_Osize_I3_J,axiom,
% 109.10/108.81 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_bool_Osize_I4_J,axiom,
% 109.10/108.81 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex1__iff,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 109.10/108.81 <=> ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_x))
% 109.10/108.81 & ! [B_y] :
% 109.10/108.81 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_y)) )
% 109.10/108.81 => B_y = B_x ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 109.10/108.81 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 109.10/108.81 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 109.10/108.81 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) )
% 109.10/108.81 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 109.10/108.81 => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,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_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 109.10/108.81 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 109.10/108.81 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 109.10/108.81 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) )
% 109.10/108.81 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 109.10/108.81 => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,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_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 109.10/108.81 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),hAPP(hAPP(c_COMBC(T_c,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_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 109.10/108.81 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b))),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 109.10/108.81 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 109.10/108.81 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_pos__empty__def,axiom,
% 109.10/108.81 ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_neg__bind__def,axiom,
% 109.10/108.81 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),hAPP(hAPP(c_COMBC(T_c,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_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 109.10/108.81 ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_neg__map__def,axiom,
% 109.10/108.81 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,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_b)))))),T_c,c_New__Random__Sequence_Oneg__single(T_b)),V_f_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_neg__single__def,axiom,
% 109.10/108.81 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_b,V_x_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_pos__bind__def,axiom,
% 109.10/108.81 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,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_b))),hAPP(hAPP(c_COMBC(T_c,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_b)))),hAPP(hAPP(c_COMBC(T_c,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_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_pos__map__def,axiom,
% 109.10/108.81 ! [V_P_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,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_b))))),T_c,c_New__Random__Sequence_Opos__single(T_b)),V_f_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_pos__single__def,axiom,
% 109.10/108.81 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_b),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_b,V_x_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__splice,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_splice_Osimps_I3_J,axiom,
% 109.10/108.81 ! [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))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_splice__Nil2,axiom,
% 109.10/108.81 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 109.10/108.81
% 109.10/108.81 fof(fact_splice_Osimps_I1_J,axiom,
% 109.10/108.81 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 109.10/108.81
% 109.10/108.81 fof(fact_splice_Osimps_I2_J,axiom,
% 109.10/108.81 ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__DSequence_Opos__single__def,axiom,
% 109.10/108.81 ! [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) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_acyclicP__converse,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_Predicate_Oconversep(T_b,T_b,V_r_2))))
% 109.10/108.81 <=> c_Wellfounded_Oacyclic(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_converse__meet,axiom,
% 109.10/108.81 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_conversep__noteq,axiom,
% 109.10/108.81 ! [V_y_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
% 109.10/108.81 <=> V_x_2 != V_y_2 ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_conversep__eq,axiom,
% 109.10/108.81 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 109.10/108.81
% 109.10/108.81 fof(fact_conversep__conversep,axiom,
% 109.10/108.81 ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2 ).
% 109.10/108.81
% 109.10/108.81 fof(fact_conversep__iff,axiom,
% 109.10/108.81 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 109.10/108.81 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_conversep_Oequations,axiom,
% 109.10/108.81 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 109.10/108.81 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_conversep_Ointros,axiom,
% 109.10/108.81 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_conversepD,axiom,
% 109.10/108.81 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_converse__pred__comp,axiom,
% 109.10/108.81 ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_converse__join,axiom,
% 109.10/108.81 ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_conversep__converse__eq,axiom,
% 109.10/108.81 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,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_r_2)),V_x_2),V_y_2))
% 109.10/108.81 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_,axiom,
% 109.10/108.81 ! [V_s2_2,V_s1_2,T_c,T_b] : c_Lazy__Sequence_Oproduct(T_b,T_c,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_b,tc_prod(T_b,T_c),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_b),c_Lazy__Sequence_Obind(T_c,tc_prod(T_b,T_c),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_b,T_c)),T_c),c_Lazy__Sequence_Osingle(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_tl__replicate,axiom,
% 109.10/108.81 ! [V_x,T_a,V_n] :
% 109.10/108.81 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.81 => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_replicate__length__filter,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] : c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_b,hAPP(c_fequal,V_x_2)),V_xs_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_length__replicate,axiom,
% 109.10/108.81 ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n ).
% 109.10/108.81
% 109.10/108.81 fof(fact_map__replicate__const,axiom,
% 109.10/108.81 ! [V_lst_2,V_k_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_k_2)),V_lst_2) = c_List_Oreplicate(T_b,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_lst_2),V_k_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_replicate__app__Cons__same,axiom,
% 109.10/108.81 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_replicate__Suc,axiom,
% 109.10/108.81 ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_rev__replicate,axiom,
% 109.10/108.81 ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_take__replicate,axiom,
% 109.10/108.81 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_drop__replicate,axiom,
% 109.10/108.81 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_hd__replicate,axiom,
% 109.10/108.81 ! [V_x,T_a,V_n] :
% 109.10/108.81 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.81 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_last__replicate,axiom,
% 109.10/108.81 ! [V_x,T_a,V_n] :
% 109.10/108.81 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.81 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_zip__replicate,axiom,
% 109.10/108.81 ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Bex__set__replicate,axiom,
% 109.10/108.81 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 109.10/108.81 ( ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 109.10/108.81 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Ball__set__replicate,axiom,
% 109.10/108.81 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 109.10/108.81 ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_a_2))))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 109.10/108.81 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_replicate__eq__replicate,axiom,
% 109.10/108.81 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 109.10/108.81 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 109.10/108.81 <=> ( V_m_2 = V_n_2
% 109.10/108.81 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.81 => V_x_2 = V_y_2 ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_nth__replicate,axiom,
% 109.10/108.81 ! [V_x,T_a,V_n,V_i] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 109.10/108.81 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_append__replicate__commute,axiom,
% 109.10/108.81 ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_replicate__add,axiom,
% 109.10/108.81 ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_filter__replicate,axiom,
% 109.10/108.81 ! [V_n_2,T_b,V_x_2,V_P_2] :
% 109.10/108.81 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,V_x_2) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 109.10/108.81 => hAPP(c_List_Ofilter(T_b,V_P_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Olist_ONil(T_b) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_concat__replicate__trivial,axiom,
% 109.10/108.81 ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_replicate__0,axiom,
% 109.10/108.81 ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_empty__replicate,axiom,
% 109.10/108.81 ! [V_x_2,V_n_2,T_b] :
% 109.10/108.81 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 109.10/108.81 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_replicate__empty,axiom,
% 109.10/108.81 ! [V_x_2,V_n_2,T_b] :
% 109.10/108.81 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 109.10/108.81 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_map__replicate,axiom,
% 109.10/108.81 ! [V_x_2,V_n_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oreplicate(T_c,V_n_2,V_x_2)) = c_List_Oreplicate(T_b,V_n_2,hAPP(V_f_2,V_x_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_in__set__replicate,axiom,
% 109.10/108.81 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_y_2))))
% 109.10/108.81 <=> ( V_x_2 = V_y_2
% 109.10/108.81 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_replicate__append__same,axiom,
% 109.10/108.81 ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_map__replicate__trivial,axiom,
% 109.10/108.81 ! [V_i_2,V_x_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_COMBK(T_b,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_b,V_i_2,V_x_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__replicate__conv__if,axiom,
% 109.10/108.81 ! [V_x_2,T_b,V_n_2] :
% 109.10/108.81 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.81 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 109.10/108.81 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.81 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__replicate,axiom,
% 109.10/108.81 ! [V_x_2,T_b,V_n_2] :
% 109.10/108.81 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.10/108.81 => hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_set__replicate__Suc,axiom,
% 109.10/108.81 ! [V_x_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oreplicate(T_b,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_small__lazy__list_Osimps,axiom,
% 109.10/108.81 ! [V_d_2,T_b] :
% 109.10/108.81 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 109.10/108.81 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_b),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_b),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),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_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),c_Lazy__Sequence_Oproduct(T_b,tc_List_Olist(T_b),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,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_b),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_b,tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_b)))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_b)))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_eq__comp__r,axiom,
% 109.10/108.81 ! [V_R_2,T_b] : c_Predicate_Opred__comp(T_b,T_b,T_b,c_fequal,c_Predicate_Opred__comp(T_b,T_b,T_b,V_R_2,c_fequal)) = V_R_2 ).
% 109.10/108.81
% 109.10/108.81 fof(fact_small__lazy__prod__def,axiom,
% 109.10/108.81 ! [V_d,T_b,T_a] :
% 109.10/108.81 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 109.10/108.81 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 109.10/108.81 => 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)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_New__DSequence_Opos__union__def,axiom,
% 109.10/108.81 ! [V_i_2,V_yq_2,V_xq_2,T_b] : hAPP(c_New__DSequence_Opos__union(T_b,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_b,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 109.10/108.81 ! [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))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact__01,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence_Oinject,axiom,
% 109.10/108.81 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 109.10/108.81 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_H_2,V_lazy__sequence_H_2)
% 109.10/108.81 <=> ( V_a_2 = V_a_H_2
% 109.10/108.81 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_pos__union__def,axiom,
% 109.10/108.81 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_b] : c_New__Random__Sequence_Opos__union(T_b,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_b,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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 109.10/108.81 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,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_b,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_small__lazy_H_Osimps,axiom,
% 109.10/108.81 ! [V_i,V_d] :
% 109.10/108.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 109.10/108.81 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 109.10/108.81 => 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)))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_small__lazy_H_Opsimps,axiom,
% 109.10/108.81 ! [V_i_2,V_d_2] :
% 109.10/108.81 ( 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)))
% 109.10/108.81 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 109.10/108.81 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 109.10/108.81 => 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)))) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_small__lazy__int__def,axiom,
% 109.10/108.81 ! [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)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_small__lazy_H_Opinduct,axiom,
% 109.10/108.81 ! [V_P_2,V_a1_2,V_a0_2] :
% 109.10/108.81 ( 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)))
% 109.10/108.81 => ( ! [B_d,B_i] :
% 109.10/108.81 ( 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)))
% 109.10/108.81 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 109.10/108.81 => 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)))) )
% 109.10/108.81 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
% 109.10/108.81 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_size__code,axiom,
% 109.10/108.81 ! [V_xq_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),T_b),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),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_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_b)))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence__size__code,axiom,
% 109.10/108.81 ! [V_xq_2,V_s_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2),V_xq_2) = c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_b,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_b),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_b)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),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_b),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_b),tc_Nat_Onat)),T_b),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_b),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_seq__case,axiom,
% 109.10/108.81 ! [V_xq_2,V_g_2,V_f_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f_2,V_g_2,V_xq_2) = c_Option_Ooption_Ooption__case(T_b,tc_prod(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_c,tc_Lazy__Sequence_Olazy__sequence(T_c),T_b),V_g_2),hAPP(c_Lazy__Sequence_Oyield(T_c),V_xq_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_yieldn__def,axiom,
% 109.10/108.81 ! [T_b] : c_Lazy__Sequence_Oyieldn(T_b) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_b),T_b,c_Lazy__Sequence_Oyield(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 109.10/108.81 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_refl__on__INTER,axiom,
% 109.10/108.81 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 109.10/108.81 ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 109.10/108.81 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 109.10/108.81 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_List_Omember__def,axiom,
% 109.10/108.81 ! [V_x_2,V_xs_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 109.10/108.81 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_member__rec_I2_J,axiom,
% 109.10/108.81 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_member__set,axiom,
% 109.10/108.81 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_member__rec_I1_J,axiom,
% 109.10/108.81 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_y_2))
% 109.10/108.81 <=> ( V_x_2 = V_y_2
% 109.10/108.81 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_in__set__member,axiom,
% 109.10/108.81 ! [V_xs_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex1__iff__raw,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 109.10/108.81 <=> ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_x))
% 109.10/108.81 & ! [B_y] :
% 109.10/108.81 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_y)) )
% 109.10/108.81 => B_y = B_x ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_setsum__UNION__zero,axiom,
% 109.10/108.81 ! [V_f_2,V_S_2,T_b,T_c] :
% 109.10/108.81 ( class_Groups_Ocomm__monoid__add(T_c)
% 109.10/108.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 109.10/108.81 => ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 109.10/108.81 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 109.10/108.81 => ( ! [B_T1] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 109.10/108.81 => ! [B_T2] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 109.10/108.81 => ( B_T1 != B_T2
% 109.10/108.81 => ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 109.10/108.81 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 109.10/108.81 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2)),V_S_2) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_THE__default__def,axiom,
% 109.10/108.81 ! [V_d_2,T_b,V_P_2] :
% 109.10/108.81 ( ( ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(V_P_2,B_x))
% 109.10/108.81 & ! [B_y] :
% 109.10/108.81 ( hBOOL(hAPP(V_P_2,B_y))
% 109.10/108.81 => B_y = B_x ) )
% 109.10/108.81 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2) )
% 109.10/108.81 & ( ~ ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(V_P_2,B_x))
% 109.10/108.81 & ! [B_y] :
% 109.10/108.81 ( hBOOL(hAPP(V_P_2,B_y))
% 109.10/108.81 => B_y = B_x ) )
% 109.10/108.81 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2 ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_SUP2__E,axiom,
% 109.10/108.81 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2))
% 109.10/108.81 => ~ ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.10/108.81 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_INF2__I,axiom,
% 109.10/108.81 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
% 109.10/108.81 ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
% 109.10/108.81 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_finite__maxlen,axiom,
% 109.10/108.81 ! [V_M_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 109.10/108.81 => ? [B_n] :
% 109.10/108.81 ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),B_x)),B_n)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 109.10/108.81 ! [T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 109.10/108.81 ! [V_fa_2,T_b] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_b,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 109.10/108.81
% 109.10/108.81 fof(fact__02,axiom,
% 109.10/108.81 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 109.10/108.81 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) != c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 109.10/108.81 ! [V_lazy__sequence_H,V_a_H,T_a] : c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) != c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H,V_lazy__sequence_H) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 109.10/108.81 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__all__iff__all__interval__int,axiom,
% 109.10/108.81 ! [V_j_2,V_i_2,V_P_2] :
% 109.10/108.81 ( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 109.10/108.81 <=> c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 109.10/108.81 ! [V_j_2,V_i_2,V_P_2] :
% 109.10/108.81 ( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 109.10/108.81 <=> ~ c_List_Oall__interval__int(hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint,c_fNot),V_P_2),V_i_2,V_j_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_all__interval__int__def,axiom,
% 109.10/108.81 ! [V_j_2,V_i_2,V_P_2] :
% 109.10/108.81 ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 109.10/108.81 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 109.10/108.81 ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Random_Osimps,axiom,
% 109.10/108.81 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 109.10/108.81 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 109.10/108.81 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) )
% 109.10/108.81 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
% 109.10/108.81 => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 109.10/108.81 ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2 ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Random__Sequence_Oempty__def,axiom,
% 109.10/108.81 ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Random__Sequence_Osingle__def,axiom,
% 109.10/108.81 ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Random__Sequence_Omap__def,axiom,
% 109.10/108.81 ! [V_P_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_P_2) = c_Random__Sequence_Obind(T_c,T_b,V_P_2,hAPP(c_Fun_Ocomp(T_b,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_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_exE__realizer,axiom,
% 109.10/108.81 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(V_P_2,hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2)),hAPP(c_Product__Type_Ofst(T_c,T_b),V_p_2)))
% 109.10/108.81 => ( ! [B_x,B_y] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
% 109.10/108.81 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 109.10/108.81 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_d),V_f_2),V_p_2))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Image__Collect__split,axiom,
% 109.10/108.81 ! [V_A_2,V_P_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,hAPP(c_Set_OCollect(tc_prod(T_c,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,tc_HOL_Obool),V_P_2))),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_P_2)))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lexord__trans,axiom,
% 109.10/108.81 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_z_2)),c_List_Olexord(T_b,V_r_2)))
% 109.10/108.81 => ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_z_2)),c_List_Olexord(T_b,V_r_2))) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__less__than,axiom,
% 109.10/108.81 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__lex__prod,axiom,
% 109.10/108.81 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_R1_2)
% 109.10/108.81 => ( c_Relation_Otrans(T_c,V_R2_2)
% 109.10/108.81 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transD,axiom,
% 109.10/108.81 ! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.10/108.81 => ( 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_c_2)),V_r_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),V_r_2)) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__def,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 <=> ! [B_x,B_y] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 109.10/108.81 => ! [B_z] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_z)),V_r_2)) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__reflclI,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__rtrancl,axiom,
% 109.10/108.81 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__Id,axiom,
% 109.10/108.81 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__trancl,axiom,
% 109.10/108.81 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trancl__id,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__Id__on,axiom,
% 109.10/108.81 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__finite__psubset,axiom,
% 109.10/108.81 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_lexord__transI,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_listrel__trans,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_bex__empty,axiom,
% 109.10/108.81 ! [V_P_2,T_b] :
% 109.10/108.81 ~ ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_x)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__converse,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 109.10/108.81 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_finite__Collect__bex,axiom,
% 109.10/108.81 ! [V_Q_2,T_c,V_A_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),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_A_2)))),V_Q_2)))))
% 109.10/108.81 <=> ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.10/108.81 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBC(T_c,T_b,tc_HOL_Obool),V_Q_2),B_x)))) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_bex__UNIV,axiom,
% 109.10/108.81 ! [V_P_2,T_b] :
% 109.10/108.81 ( ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__Int,axiom,
% 109.10/108.81 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => ( c_Relation_Otrans(T_b,V_s_2)
% 109.10/108.81 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_SUPR__bool__eq,axiom,
% 109.10/108.81 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__O__subset,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_r_2),V_r_2)),V_r_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__inv__image,axiom,
% 109.10/108.81 ! [V_f_2,T_c,V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Union__eq,axiom,
% 109.10/108.81 ! [V_A_2,T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_b,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_b,tc_HOL_Obool)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_b,tc_HOL_Obool))),V_A_2)))),c_member(T_b)))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_list__ex__iff__raw,axiom,
% 109.10/108.81 ! [V_xs_2,V_P_2,T_b] :
% 109.10/108.81 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 109.10/108.81 <=> ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Bex__set__list__ex,axiom,
% 109.10/108.81 ! [V_P_2,V_xs_2,T_b] :
% 109.10/108.81 ( ? [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 109.10/108.81 & hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.81 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_UN__eq,axiom,
% 109.10/108.81 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_INT__eq,axiom,
% 109.10/108.81 ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_c)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_COMBS(T_c,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_c),c_fconj),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_c,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_c)),c_fequal)),V_B_2))))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Sup__fun__def,axiom,
% 109.10/108.81 ! [V_x_2,V_A_2,T_c,T_b] :
% 109.10/108.81 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.81 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Sup__apply,axiom,
% 109.10/108.81 ! [V_x_2,V_A_2,T_c,T_b] :
% 109.10/108.81 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.81 => hAPP(c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Inf__apply,axiom,
% 109.10/108.81 ! [V_x_2,V_A_2,T_c,T_b] :
% 109.10/108.81 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.81 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_Inf__fun__def,axiom,
% 109.10/108.81 ! [V_x_2,V_A_2,T_c,T_b] :
% 109.10/108.81 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 109.10/108.81 => hAPP(c_Complete__Lattice_OInf__class_OInf(tc_fun(T_c,T_b),V_A_2),V_x_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_fun(T_c,T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),T_b),hAPP(c_COMBS(tc_fun(T_c,T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_c,T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_c,T_b))),V_A_2)))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_c,T_b),T_b),tc_fun(tc_fun(T_c,T_b),tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,tc_fun(T_c,T_b))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_c,T_b),T_c,T_b),c_COMBI(tc_fun(T_c,T_b))),V_x_2)))))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_max__extp_Ointros,axiom,
% 109.10/108.81 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 109.10/108.81 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 109.10/108.81 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.81 => ( ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 109.10/108.81 => ? [B_xa] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 109.10/108.81 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 109.10/108.81 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transp__def,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Predicate_Otransp(T_b,V_r_2)
% 109.10/108.81 <=> c_Relation_Otrans(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_transpE,axiom,
% 109.10/108.81 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 109.10/108.81 ( c_Predicate_Otransp(T_b,V_r_2)
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_equivp__reflp__symp__transp,axiom,
% 109.10/108.81 ! [V_R_2,T_b] :
% 109.10/108.81 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.10/108.81 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 109.10/108.81 & c_Predicate_Osymp(T_b,V_R_2)
% 109.10/108.81 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_equivpI,axiom,
% 109.10/108.81 ! [V_R_2,T_b] :
% 109.10/108.81 ( c_Predicate_Oreflp(T_b,V_R_2)
% 109.10/108.81 => ( c_Predicate_Osymp(T_b,V_R_2)
% 109.10/108.81 => ( c_Predicate_Otransp(T_b,V_R_2)
% 109.10/108.81 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sympE,axiom,
% 109.10/108.81 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 109.10/108.81 ( c_Predicate_Osymp(T_b,V_r_2)
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_equivpE,axiom,
% 109.10/108.81 ! [V_R_2,T_b] :
% 109.10/108.81 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.10/108.81 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 109.10/108.81 => ( c_Predicate_Osymp(T_b,V_R_2)
% 109.10/108.81 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_max__extp_Osimps,axiom,
% 109.10/108.81 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 109.10/108.81 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 109.10/108.81 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 109.10/108.81 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 109.10/108.81 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.81 & ! [B_x] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 109.10/108.81 => ? [B_xa] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 109.10/108.81 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_trans__diff__Id,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => ( c_Relation_Oantisym(T_b,V_r_2)
% 109.10/108.81 => c_Relation_Otrans(T_b,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_antisym__Id__on,axiom,
% 109.10/108.81 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_antisym__converse,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 109.10/108.81 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_antisym__empty,axiom,
% 109.10/108.81 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_antisym__Id,axiom,
% 109.10/108.81 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_antisym__subset,axiom,
% 109.10/108.81 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
% 109.10/108.81 => ( c_Relation_Oantisym(T_b,V_s_2)
% 109.10/108.81 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_antisym__def,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Oantisym(T_b,V_r_2)
% 109.10/108.81 <=> ! [B_x,B_y] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2))
% 109.10/108.81 => B_x = B_y ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_antisymD,axiom,
% 109.10/108.81 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Oantisym(T_b,V_r_2)
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.10/108.81 => ( 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_a_2)),V_r_2))
% 109.10/108.81 => V_a_2 = V_b_2 ) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_antisym__reflcl,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Oantisym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b)))
% 109.10/108.81 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 109.10/108.81 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_fun__lub__def,axiom,
% 109.10/108.81 ! [V_x_2,V_A_2,V_L_2,T_d,T_b,T_c] : c_Partial__Function_Ofun__lub(T_c,T_b,T_d,V_L_2,V_A_2,V_x_2) = hAPP(V_L_2,hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool,T_c),c_HOL_OEx(tc_fun(T_d,T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),T_c),hAPP(c_COMBS(tc_fun(T_d,T_c),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(T_d,T_c)),c_fconj),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(T_d,T_c))),V_A_2)))),hAPP(hAPP(c_COMBC(T_c,tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(T_d,T_c),T_c),tc_fun(tc_fun(T_d,T_c),tc_HOL_Obool)),T_c),c_COMBB(T_c,tc_HOL_Obool,tc_fun(T_d,T_c))),c_fequal)),hAPP(hAPP(c_COMBC(tc_fun(T_d,T_c),T_d,T_c),c_COMBI(tc_fun(T_d,T_c))),V_x_2)))))) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sym__trans__comp__subset,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.81 => ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)),V_r_2)),V_r_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_symD,axiom,
% 109.10/108.81 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.81 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
% 109.10/108.81 => 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_a_2)),V_r_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sym__def,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.81 <=> ! [B_x,B_y] :
% 109.10/108.81 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
% 109.10/108.81 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_x)),V_r_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sym__rtrancl,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.81 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sym__Id,axiom,
% 109.10/108.81 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sym__Un,axiom,
% 109.10/108.81 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.81 => ( c_Relation_Osym(T_b,V_s_2)
% 109.10/108.81 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sym__trancl,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.81 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sym__Id__on,axiom,
% 109.10/108.81 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_listrel__sym,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.81 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.81 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 109.10/108.81
% 109.10/108.81 fof(fact_sym__converse,axiom,
% 109.10/108.81 ! [V_r_2,T_b] :
% 109.10/108.82 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 109.10/108.82 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_sym__conv__converse__eq,axiom,
% 109.10/108.82 ! [V_r_2,T_b] :
% 109.10/108.82 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.82 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_sym__Int,axiom,
% 109.10/108.82 ! [V_s_2,V_r_2,T_b] :
% 109.10/108.82 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.82 => ( c_Relation_Osym(T_b,V_s_2)
% 109.10/108.82 => c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_sym__Un__converse,axiom,
% 109.10/108.82 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_sym__inv__image,axiom,
% 109.10/108.82 ! [V_f_2,T_c,V_r_2,T_b] :
% 109.10/108.82 ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.82 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_sym__Int__converse,axiom,
% 109.10/108.82 ! [V_r_2,T_b] : c_Relation_Osym(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_equivE,axiom,
% 109.10/108.82 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.10/108.82 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.10/108.82 => ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.82 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_equivI,axiom,
% 109.10/108.82 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.82 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.10/108.82 => ( c_Relation_Osym(T_b,V_r_2)
% 109.10/108.82 => ( c_Relation_Otrans(T_b,V_r_2)
% 109.10/108.82 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_equiv__def,axiom,
% 109.10/108.82 ! [V_r_2,V_A_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 109.10/108.82 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 109.10/108.82 & c_Relation_Osym(T_b,V_r_2)
% 109.10/108.82 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_symp__def,axiom,
% 109.10/108.82 ! [V_r_2,T_b] :
% 109.10/108.82 ( c_Predicate_Osymp(T_b,V_r_2)
% 109.10/108.82 <=> c_Relation_Osym(T_b,hAPP(c_Set_OCollect(tc_prod(T_b,T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),V_r_2))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_part__equivp__refl__symp__transp,axiom,
% 109.10/108.82 ! [V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 109.10/108.82 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 109.10/108.82 & c_Predicate_Osymp(T_b,V_R_2)
% 109.10/108.82 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_part__equivpI,axiom,
% 109.10/108.82 ! [T_b,V_R_2] :
% 109.10/108.82 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 109.10/108.82 => ( c_Predicate_Osymp(T_b,V_R_2)
% 109.10/108.82 => ( c_Predicate_Otransp(T_b,V_R_2)
% 109.10/108.82 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_equivp__implies__part__equivp,axiom,
% 109.10/108.82 ! [V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.10/108.82 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_part__equivp__def,axiom,
% 109.10/108.82 ! [V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 109.10/108.82 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 109.10/108.82 & ! [B_x,B_y] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 109.10/108.82 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 109.10/108.82 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 109.10/108.82 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_part__equivp__symp,axiom,
% 109.10/108.82 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 109.10/108.82 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_part__equivp__transp,axiom,
% 109.10/108.82 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 109.10/108.82 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_part__equivpE,axiom,
% 109.10/108.82 ! [V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 109.10/108.82 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 109.10/108.82 => ( c_Predicate_Osymp(T_b,V_R_2)
% 109.10/108.82 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_part__equivp__typedef,axiom,
% 109.10/108.82 ! [V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 109.10/108.82 => ? [B_d] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_d),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_fun(T_b,tc_HOL_Obool)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),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_COMBS(T_b,T_b,tc_HOL_Obool),V_R_2),c_COMBI(T_b))))),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b)),c_fequal)),V_R_2))))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inj__iff,axiom,
% 109.10/108.82 ! [V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__o__cancel,axiom,
% 109.10/108.82 ! [V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => hAPP(c_Fun_Ocomp(T_c,T_b,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_f_2) = c_Fun_Oid(T_b) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__id,axiom,
% 109.10/108.82 ! [T_b] : c_Hilbert__Choice_Oinv__into(T_b,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Fun_Oid(T_b)) = c_Fun_Oid(T_b) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__f__eq,axiom,
% 109.10/108.82 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 109.10/108.82 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = V_x_2 ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__f__f,axiom,
% 109.10/108.82 ! [V_x_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__into__f__f,axiom,
% 109.10/108.82 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.10/108.82 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__into__f__eq,axiom,
% 109.10/108.82 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 109.10/108.82 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 109.10/108.82 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_f__inv__into__f,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 109.10/108.82 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_y_2)) = V_y_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__into__into,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 109.10/108.82 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_x_2)),V_A_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__into__injective,axiom,
% 109.10/108.82 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 109.10/108.82 ( hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 109.10/108.82 => V_x_2 = V_y_2 ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_surj__iff__all,axiom,
% 109.10/108.82 ! [V_f_2,T_b,T_c] :
% 109.10/108.82 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.82 <=> ! [B_x] : hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),B_x)) = B_x ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_surj__f__inv__f,axiom,
% 109.10/108.82 ! [V_y_2,V_f_2,T_b,T_c] :
% 109.10/108.82 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.82 => hAPP(V_f_2,hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),V_y_2)) = V_y_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_image__surj__f__inv__f,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_b,T_c] :
% 109.10/108.82 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)),V_A_2)) = V_A_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_image__inv__into__cancel,axiom,
% 109.10/108.82 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 109.10/108.82 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2)),V_B_H_2)) = V_B_H_2 ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__into__def,axiom,
% 109.10/108.82 ! [V_x_2,V_f_2,V_A_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_x_2) = c_Hilbert__Choice_OEps(T_b,hAPP(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_A_2))),hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_x_2))) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__def,axiom,
% 109.10/108.82 ! [V_y_2,V_f_2,T_c,T_b] : hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),V_y_2) = c_Hilbert__Choice_OEps(T_b,hAPP(hAPP(c_COMBC(T_b,T_c,tc_HOL_Obool),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2)),V_y_2)) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_o__inv__o__cancel,axiom,
% 109.10/108.82 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => hAPP(c_Fun_Ocomp(T_c,T_d,T_b,hAPP(c_Fun_Ocomp(T_b,T_d,T_c,V_g_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))),V_f_2) = V_g_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_surj__imp__inj__inv,axiom,
% 109.10/108.82 ! [V_f_2,T_b,T_c] :
% 109.10/108.82 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.82 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__image__comp,axiom,
% 109.10/108.82 ! [V_X_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_X_2)) = V_X_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_image__inv__f__f,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = V_A_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inj__imp__surj__inv,axiom,
% 109.10/108.82 ! [V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inj__on__inv__into,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 109.10/108.82 => c_Fun_Oinj__on(T_b,T_c,c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_2,V_f_2),V_B_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__into__image__cancel,axiom,
% 109.10/108.82 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = V_S_2 ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__into__comp,axiom,
% 109.10/108.82 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
% 109.10/108.82 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
% 109.10/108.82 => hAPP(c_Hilbert__Choice_Oinv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,V_A_2,V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_surj__iff,axiom,
% 109.10/108.82 ! [V_f_2,T_b,T_c] :
% 109.10/108.82 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))
% 109.10/108.82 <=> hAPP(c_Fun_Ocomp(T_c,T_b,T_b,V_f_2),c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),V_f_2)) = c_Fun_Oid(T_b) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inj__transfer,axiom,
% 109.10/108.82 ! [V_x_2,V_P_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => ( ! [B_y] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))))
% 109.10/108.82 => hBOOL(hAPP(V_P_2,hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),B_y))) )
% 109.10/108.82 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_fold__image__UN__disjoint,axiom,
% 109.10/108.82 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 109.10/108.82 ( class_Groups_Ocomm__monoid__mult(T_d)
% 109.10/108.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 109.10/108.82 => ( ! [B_x] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 109.10/108.82 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 109.10/108.82 => ( ! [B_x] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 109.10/108.82 => ! [B_xa] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 109.10/108.82 => ( B_x != B_xa
% 109.10/108.82 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_A_2,B_x)),hAPP(V_A_2,B_xa)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) )
% 109.10/108.82 => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),T_d,T_b),hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),c_Groups_Oone__class_Oone(T_d))),V_A_2)),c_Groups_Oone__class_Oone(T_d)),V_I_2) ) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_nat__of__cases,axiom,
% 109.10/108.82 ! [V_y_2] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 109.10/108.82 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_nat__of__induct,axiom,
% 109.10/108.82 ! [V_P_2,V_y_2] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 109.10/108.82 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 109.10/108.82 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_of__nat__cases,axiom,
% 109.10/108.82 ! [V_x_2] :
% 109.10/108.82 ~ ! [B_y] :
% 109.10/108.82 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 109.10/108.82 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_of__nat__induct,axiom,
% 109.10/108.82 ! [V_x_2,V_P_2] :
% 109.10/108.82 ( ! [B_y] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 109.10/108.82 => hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 109.10/108.82 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 109.10/108.82 ! [V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = V_f1_2 ).
% 109.10/108.82
% 109.10/108.82 fof(fact_Least__Suc2,axiom,
% 109.10/108.82 ! [V_m_2,V_Q_2,V_n_2,V_P_2] :
% 109.10/108.82 ( hBOOL(hAPP(V_P_2,V_n_2))
% 109.10/108.82 => ( hBOOL(hAPP(V_Q_2,V_m_2))
% 109.10/108.82 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 109.10/108.82 => ( ! [B_k] :
% 109.10/108.82 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k)))
% 109.10/108.82 <=> hBOOL(hAPP(V_Q_2,B_k)) )
% 109.10/108.82 => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_Q_2)) ) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 109.10/108.82 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_c,T_b] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__rec(T_b,T_c,V_f1_2,V_f2_2,V_lazy__sequence_2)) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_beyond__def,axiom,
% 109.10/108.82 ! [V_l,V_k] :
% 109.10/108.82 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 109.10/108.82 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 109.10/108.82 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 109.10/108.82 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__image__Collect__eq,axiom,
% 109.10/108.82 ! [V_P_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_OCollect(T_b),V_P_2)) = hAPP(c_Set_OCollect(T_c),hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),V_P_2),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__id,axiom,
% 109.10/108.82 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__inv__into,axiom,
% 109.10/108.82 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 109.10/108.82 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__into__inv__into__eq,axiom,
% 109.10/108.82 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 109.10/108.82 => hAPP(c_Hilbert__Choice_Oinv__into(T_c,T_b,V_A_H_2,c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2)),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__imp__bij__inv,axiom,
% 109.10/108.82 ! [V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => c_Fun_Obij__betw(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inv__inv__eq,axiom,
% 109.10/108.82 ! [V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => c_Hilbert__Choice_Oinv__into(T_c,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) = V_f_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_o__inv__distrib,axiom,
% 109.10/108.82 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => ( c_Fun_Obij__betw(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => c_Hilbert__Choice_Oinv__into(T_d,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)) = hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Hilbert__Choice_Oinv__into(T_d,T_b,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)),V_g_2)),c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__comp,axiom,
% 109.10/108.82 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 109.10/108.82 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,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_d,tc_HOL_Obool))) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__trans,axiom,
% 109.10/108.82 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 109.10/108.82 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 109.10/108.82 => c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_f_2),V_A_2,V_C_2) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__comp__iff,axiom,
% 109.10/108.82 ! [V_A_H_H_2,V_f_H_2,T_d,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 109.10/108.82 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 109.10/108.82 <=> c_Fun_Obij__betw(T_b,T_d,hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__comp__iff2,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_d,V_A_H_H_2,V_A_H_2,V_f_H_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),V_A_H_2))
% 109.10/108.82 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 109.10/108.82 <=> c_Fun_Obij__betw(T_d,T_c,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_H_2),V_f_2),V_A_2,V_A_H_H_2) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_finite__vimage__iff,axiom,
% 109.10/108.82 ! [V_F_2,V_h_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_h_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)))
% 109.10/108.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 109.10/108.82 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__image__Compl__eq,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_b,T_c,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_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__def,axiom,
% 109.10/108.82 ! [V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 & hAPP(c_Set_Oimage(T_b,T_c,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)) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bijI,axiom,
% 109.10/108.82 ! [V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 109.10/108.82 => ( hAPP(c_Set_Oimage(T_b,T_c,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))
% 109.10/108.82 => c_Fun_Obij__betw(T_b,T_c,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))) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__subset,axiom,
% 109.10/108.82 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 109.10/108.82 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 109.10/108.82 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__imp__surj,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_b,T_c,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)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__is__surj,axiom,
% 109.10/108.82 ! [V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_b,T_c,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)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_inj__on__imp__bij__betw,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.10/108.82 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__def,axiom,
% 109.10/108.82 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 109.10/108.82 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.10/108.82 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__imp__inj__on,axiom,
% 109.10/108.82 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 109.10/108.82 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__is__inj,axiom,
% 109.10/108.82 ! [V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__same__card,axiom,
% 109.10/108.82 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 109.10/108.82 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__the__inv__into,axiom,
% 109.10/108.82 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 109.10/108.82 => c_Fun_Obij__betw(T_c,T_b,c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_B_2,V_A_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_beyond__zero,axiom,
% 109.10/108.82 ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__empty2,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))
% 109.10/108.82 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__empty1,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 109.10/108.82 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__finite,axiom,
% 109.10/108.82 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 109.10/108.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.82 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_BIJ,axiom,
% 109.10/108.82 ! [V_B_2,T_c,V_A_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.10/108.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 109.10/108.82 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 109.10/108.82 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__id__iff,axiom,
% 109.10/108.82 ! [V_B_2,V_A_2,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 109.10/108.82 <=> V_A_2 = V_B_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__id,axiom,
% 109.10/108.82 ! [T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__Disj__Un,axiom,
% 109.10/108.82 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 109.10/108.82 ( 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))
% 109.10/108.82 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 109.10/108.82 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 109.10/108.82 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 109.10/108.82 => c_Fun_Obij__betw(T_b,T_c,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_c,tc_HOL_Obool)),V_A_H_2),V_B_H_2)) ) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__betw__combine,axiom,
% 109.10/108.82 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 109.10/108.82 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 109.10/108.82 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 109.10/108.82 => c_Fun_Obij__betw(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_D_2)) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__image__INT,axiom,
% 109.10/108.82 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_d),c_Set_Oimage(T_b,T_c,V_f_2)),V_B_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_vimage__subset__eq,axiom,
% 109.10/108.82 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),V_A_2))
% 109.10/108.82 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bij__vimage__eq__inv__image,axiom,
% 109.10/108.82 ! [V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Obij__betw(T_b,T_c,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)))
% 109.10/108.82 => hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_c,T_b,c_Hilbert__Choice_Oinv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2)),V_A_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 109.10/108.82 ! [V_M_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 109.10/108.82 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_Cantor__Bernstein,axiom,
% 109.10/108.82 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),V_B_2))
% 109.10/108.82 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),V_B_2)),V_A_2))
% 109.10/108.82 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_ex__bij__betw__nat__finite,axiom,
% 109.10/108.82 ! [V_M_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 109.10/108.82 => ? [B_h] : c_Fun_Obij__betw(tc_Nat_Onat,T_b,B_h,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2)),V_M_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_ex__bij__betw__finite__nat,axiom,
% 109.10/108.82 ! [V_M_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 109.10/108.82 => ? [B_h] : c_Fun_Obij__betw(T_b,tc_Nat_Onat,B_h,V_M_2,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(T_b),V_M_2))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_curry__def,axiom,
% 109.10/108.82 ! [V_y_2,V_x_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_c_2),V_x_2),V_y_2) = hAPP(V_c_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_x_2),V_y_2)) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_refl__on__UNION,axiom,
% 109.10/108.82 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 109.10/108.82 ( ! [B_x] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 109.10/108.82 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 109.10/108.82 => c_Relation_Orefl__on(T_c,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_S_2),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_c,T_c),tc_HOL_Obool)),V_S_2),V_r_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_curryI,axiom,
% 109.10/108.82 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 109.10/108.82 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 109.10/108.82 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_split__curry,axiom,
% 109.10/108.82 ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),c_Product__Type_Ocurry(T_b,T_c,T_d,V_f_2)) = V_f_2 ).
% 109.10/108.82
% 109.10/108.82 fof(fact_curry__split,axiom,
% 109.10/108.82 ! [V_f_2,T_d,T_c,T_b] : c_Product__Type_Ocurry(T_b,T_c,T_d,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_f_2)) = V_f_2 ).
% 109.10/108.82
% 109.10/108.82 fof(fact_curryD,axiom,
% 109.10/108.82 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 109.10/108.82 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_curryE,axiom,
% 109.10/108.82 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 109.10/108.82 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_curry__conv,axiom,
% 109.10/108.82 ! [V_b_2,V_a_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Ocurry(T_c,T_d,T_b,V_f_2),V_a_2),V_b_2) = hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),V_a_2),V_b_2)) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bex__reg__eqv,axiom,
% 109.10/108.82 ! [V_P_2,V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.10/108.82 => ( ? [B_x] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 109.10/108.82 & hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.82 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_wf__weak__decr__stable,axiom,
% 109.10/108.82 ! [V_r_2,V_f_2,T_b] :
% 109.10/108.82 ( ! [B_i] : 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,hAPP(c_Nat_OSuc,B_i))),hAPP(V_f_2,B_i))),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
% 109.10/108.82 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 109.10/108.82 => ? [B_i] :
% 109.10/108.82 ! [B_k] : hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),B_k)) = hAPP(V_f_2,B_i) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_Respects__def,axiom,
% 109.10/108.82 ! [V_x_2,V_R_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 109.10/108.82 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_in__respects,axiom,
% 109.10/108.82 ! [V_R_2,V_x_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 109.10/108.82 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_bex__reg__right,axiom,
% 109.10/108.82 ! [V_P_2,V_Q_2,V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.10/108.82 => ( ! [B_x] :
% 109.10/108.82 ( hBOOL(hAPP(V_Q_2,B_x))
% 109.10/108.82 => hBOOL(hAPP(V_P_2,B_x)) )
% 109.10/108.82 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1))
% 109.10/108.82 => ? [B_x] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 109.10/108.82 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_babs__reg__eqv,axiom,
% 109.10/108.82 ! [V_P_2,T_c,V_R_2,T_b] :
% 109.10/108.82 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 109.10/108.82 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_P_2) = V_P_2 ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_Babs__def,axiom,
% 109.10/108.82 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 109.10/108.82 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_INT__anti__mono,axiom,
% 109.10/108.82 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 109.10/108.82 => ( ! [B_x] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.10/108.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 109.10/108.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_f_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_g_2))) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_INT__greatest,axiom,
% 109.10/108.82 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 109.10/108.82 ( ! [B_x] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 109.10/108.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(V_B_2,B_x))) )
% 109.10/108.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_converse__rtranclE2,axiom,
% 109.10/108.82 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 109.10/108.82 => ( hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2) != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2)
% 109.10/108.82 => ~ ! [B_a,B_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_xa_2),V_xb_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),V_r_2))
% 109.10/108.82 => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_za_2),V_zb_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2))) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_converse__rtrancl__induct2,axiom,
% 109.10/108.82 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))
% 109.10/108.82 => ( ! [B_a,B_b,B_aa,B_ba] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))
% 109.10/108.82 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) )
% 109.10/108.82 => hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_rtrancl__induct2,axiom,
% 109.10/108.82 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_bx_2),V_by_2))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))
% 109.10/108.82 => ( ! [B_a,B_b] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_ax_2),V_ay_2)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))),c_Transitive__Closure_Ortrancl(tc_prod(T_b,T_c),V_r_2)))
% 109.10/108.82 => ! [B_aa,B_ba] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(T_b,T_c),tc_prod(T_b,T_c))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(T_b,T_c),tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_aa),B_ba))),V_r_2))
% 109.10/108.82 => ( hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
% 109.10/108.82 => hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba)) ) ) )
% 109.10/108.82 => hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_congruentI,axiom,
% 109.10/108.82 ! [T_c,V_f_2,V_r_2,T_b] :
% 109.10/108.82 ( ! [B_y,B_z] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),B_z)),V_r_2))
% 109.10/108.82 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 109.10/108.82 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_congruent2I_H,axiom,
% 109.10/108.82 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 109.10/108.82 ( ! [B_y1,B_z1] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y1),B_z1)),V_r1_2))
% 109.10/108.82 => ! [B_y2,B_z2] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_c),B_y2),B_z2)),V_r2_2))
% 109.10/108.82 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 109.10/108.82 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact__03,axiom,
% 109.10/108.82 ! [V_xqq,V_xq,T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(tc_Lazy__Sequence_Olazy__sequence(T_a),V_xq,V_xqq)) = c_Lazy__Sequence_Oappend(T_a,V_xq,c_Lazy__Sequence_Oflat(T_a,V_xqq)) ).
% 109.10/108.82
% 109.10/108.82 fof(fact__04,axiom,
% 109.10/108.82 ! [T_a] : c_Lazy__Sequence_Oflat(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(tc_Lazy__Sequence_Olazy__sequence(T_a))) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a) ).
% 109.10/108.82
% 109.10/108.82 fof(fact__05,axiom,
% 109.10/108.82 ! [V_f_2,V_xq_2,T_b,T_c] : hAPP(c_Lazy__Sequence_Obind(T_c,T_b,V_xq_2),V_f_2) = c_Lazy__Sequence_Oflat(T_b,c_Lazy__Sequence_Omap(T_c,tc_Lazy__Sequence_Olazy__sequence(T_b),V_f_2,V_xq_2)) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_folding__image_Ocong,axiom,
% 109.10/108.82 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 109.10/108.82 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 109.10/108.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 109.10/108.82 => ( ! [B_x] :
% 109.10/108.82 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 109.10/108.82 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 109.10/108.82 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 109.10/108.82
% 109.10/108.82 fof(fact__06,axiom,
% 109.10/108.82 ! [V_xq_2,V_x_2,V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_c,V_x_2,V_xq_2)) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,hAPP(V_f_2,V_x_2),c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,V_xq_2)) ).
% 109.10/108.82
% 109.10/108.82 fof(fact__07,axiom,
% 109.10/108.82 ! [V_f_2,T_b,T_c] : c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_c)) = c_Lazy__Sequence_Olazy__sequence_OEmpty(T_b) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_New__DSequence_Opos__map__def,axiom,
% 109.10/108.82 ! [V_i_2,V_xq_2,V_f_2,T_b,T_c] : c_New__DSequence_Opos__map(T_c,T_b,V_f_2,V_xq_2,V_i_2) = c_Lazy__Sequence_Omap(T_c,T_b,V_f_2,hAPP(V_xq_2,V_i_2)) ).
% 109.10/108.82
% 109.10/108.82 fof(fact_power__dvd__imp__le,axiom,
% 109.13/108.82 ! [V_n,V_m,V_i] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_Oorder__refl,axiom,
% 109.13/108.82 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__0__right,axiom,
% 109.13/108.82 ! [V_a,T_a] :
% 109.13/108.82 ( class_Rings_Ocomm__semiring__1(T_a)
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__1__left,axiom,
% 109.13/108.82 ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mult__cancel,axiom,
% 109.13/108.82 ! [V_n,V_m,V_k] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_nat__mult__dvd__cancel1,axiom,
% 109.13/108.82 ! [V_n_2,V_m_2,V_k_2] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 109.13/108.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_setprod__dvd__setprod__subset,axiom,
% 109.13/108.82 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 109.13/108.82 ( ( class_Groups_Ocomm__monoid__mult(T_c)
% 109.13/108.82 & class_Rings_Odvd(T_c) )
% 109.13/108.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_B_2))) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_inf__period_I4_J,axiom,
% 109.13/108.82 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 109.13/108.82 ( ( class_Rings_Ocomm__ring(T_b)
% 109.13/108.82 & class_Rings_Odvd(T_b) )
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 109.13/108.82 => ! [B_x,B_k] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 109.13/108.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_inf__period_I3_J,axiom,
% 109.13/108.82 ! [V_t_2,V_D_2,V_d_2,T_b] :
% 109.13/108.82 ( ( class_Rings_Ocomm__ring(T_b)
% 109.13/108.82 & class_Rings_Odvd(T_b) )
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
% 109.13/108.82 => ! [B_x,B_k] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
% 109.13/108.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__div__div__eq__mult,axiom,
% 109.13/108.82 ! [V_d_2,V_b_2,V_c_2,V_a_2,T_b] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_b)
% 109.13/108.82 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 109.13/108.82 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_c_2),V_d_2))
% 109.13/108.82 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_d_2),V_c_2)
% 109.13/108.82 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_d_2) ) ) ) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__div__eq__mult,axiom,
% 109.13/108.82 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_b)
% 109.13/108.82 => ( V_a_2 != c_Groups_Ozero__class_Ozero(T_b)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 109.13/108.82 => ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2) = V_c_2
% 109.13/108.82 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2) ) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__triv__left,axiom,
% 109.13/108.82 ! [V_b,V_a,T_a] :
% 109.13/108.82 ( class_Rings_Ocomm__semiring__1(T_a)
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b))) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__triv__right,axiom,
% 109.13/108.82 ! [V_b,V_a,T_a] :
% 109.13/108.82 ( class_Rings_Ocomm__semiring__1(T_a)
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a))) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mult2,axiom,
% 109.13/108.82 ! [V_c,V_b,V_a,T_a] :
% 109.13/108.82 ( class_Rings_Ocomm__semiring__1(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mult,axiom,
% 109.13/108.82 ! [V_b,V_c,V_a,T_a] :
% 109.13/108.82 ( class_Rings_Ocomm__semiring__1(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c))) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_mult__dvd__mono,axiom,
% 109.13/108.82 ! [V_d,V_c,V_b,V_a,T_a] :
% 109.13/108.82 ( class_Rings_Ocomm__semiring__1(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_d))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvdI,axiom,
% 109.13/108.82 ! [V_k,V_b,V_a,T_a] :
% 109.13/108.82 ( class_Rings_Odvd(T_a)
% 109.13/108.82 => ( V_a = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_k)
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_a)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mult__left,axiom,
% 109.13/108.82 ! [V_c,V_b,V_a,T_a] :
% 109.13/108.82 ( class_Rings_Ocomm__semiring__1(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mult__right,axiom,
% 109.13/108.82 ! [V_c,V_b,V_a,T_a] :
% 109.13/108.82 ( class_Rings_Ocomm__semiring__1(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mult__cancel__left,axiom,
% 109.13/108.82 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 109.13/108.82 ( class_Rings_Oidom(T_b)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),V_b_2)))
% 109.13/108.82 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 109.13/108.82 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mult__cancel__right,axiom,
% 109.13/108.82 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 109.13/108.82 ( class_Rings_Oidom(T_b)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_c_2)))
% 109.13/108.82 <=> ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 109.13/108.82 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2)) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_div__mult__div__if__dvd,axiom,
% 109.13/108.82 ! [V_w,V_z,V_x,V_y,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_w))
% 109.13/108.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_w),V_z)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_w)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__div__mult,axiom,
% 109.13/108.82 ! [V_c,V_b,V_a,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 109.13/108.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_c) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)),V_a) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__div__mult__self,axiom,
% 109.13/108.82 ! [V_b,V_a,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 109.13/108.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)),V_a) = V_b ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_div__mult__swap,axiom,
% 109.13/108.82 ! [V_a,V_b,V_c,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 109.13/108.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_c)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b)),V_c) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mult__div__cancel,axiom,
% 109.13/108.82 ! [V_b,V_a,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 109.13/108.82 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_b),V_a)) = V_b ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_nat__mult__dvd__cancel__disj,axiom,
% 109.13/108.82 ! [V_n_2,V_m_2,V_k_2] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 109.13/108.82 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 109.13/108.82 | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_unity__coeff__ex,axiom,
% 109.13/108.82 ! [V_l_2,V_P_2,T_b] :
% 109.13/108.82 ( ( class_Rings_Odvd(T_b)
% 109.13/108.82 & class_Rings_Osemiring__0(T_b) )
% 109.13/108.82 => ( ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
% 109.13/108.82 <=> ? [B_x] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b))))
% 109.13/108.82 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__setprod,axiom,
% 109.13/108.82 ! [V_f_2,V_i_2,V_A_2,T_b,T_c] :
% 109.13/108.82 ( class_Rings_Ocomm__semiring__1(T_c)
% 109.13/108.82 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_c),hAPP(V_f_2,V_i_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2))) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OatLeastAtMost__singleton_H,axiom,
% 109.13/108.82 ! [V_b_2,V_a_2] :
% 109.13/108.82 ( V_a_2 = V_b_2
% 109.13/108.82 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OatLeastAtMost__singleton,axiom,
% 109.13/108.82 ! [V_a_2] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_a_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OatLeastAtMost__singleton__iff,axiom,
% 109.13/108.82 ! [V_c_2,V_b_2,V_a_2] :
% 109.13/108.82 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
% 109.13/108.82 <=> ( V_a_2 = V_b_2
% 109.13/108.82 & V_b_2 = V_c_2 ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OatLeastatMost__empty,axiom,
% 109.13/108.82 ! [V_a_2,V_b_2] :
% 109.13/108.82 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 109.13/108.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) )
% 109.13/108.82 => c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OatLeastatMost__empty__iff,axiom,
% 109.13/108.82 ! [V_b_2,V_a_2] :
% 109.13/108.82 ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 109.13/108.82 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OatLeastatMost__empty__iff2,axiom,
% 109.13/108.82 ! [V_b_2,V_a_2] :
% 109.13/108.82 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2,V_b_2)
% 109.13/108.82 <=> ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OatLeastLessThan__empty__iff2,axiom,
% 109.13/108.82 ! [V_b_2,V_a_2] :
% 109.13/108.82 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
% 109.13/108.82 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 109.13/108.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
% 109.13/108.82 ! [V_l_2,V_k_2] :
% 109.13/108.82 ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
% 109.13/108.82 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 109.13/108.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
% 109.13/108.82 ! [V_b_2,V_a_2] :
% 109.13/108.82 ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 109.13/108.82 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 109.13/108.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
% 109.13/108.82 ! [V_l_2,V_k_2] :
% 109.13/108.82 ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
% 109.13/108.82 <=> ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2))
% 109.13/108.82 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OgreaterThanLessThan__empty,axiom,
% 109.13/108.82 ! [V_k_2,V_l_2] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 109.13/108.82 => c_SetInterval_Oord_OgreaterThanLessThan(tc_Nat_Onat,hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OatLeastLessThan__empty,axiom,
% 109.13/108.82 ! [V_a_2,V_b_2] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
% 109.13/108.82 => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
% 109.13/108.82 ! [V_k_2,V_l_2] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
% 109.13/108.82 => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(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_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_Nat_Onat),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_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_div__add,axiom,
% 109.13/108.82 ! [V_y,V_x,V_z,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_x))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_z),V_y))
% 109.13/108.82 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_z)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_y),V_z)) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__imp__mod__0,axiom,
% 109.13/108.82 ! [V_b,V_a,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 109.13/108.82 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__eq__mod__eq__0,axiom,
% 109.13/108.82 ! [V_b_2,V_a_2,T_b] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_b)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 109.13/108.82 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__abs__iff,axiom,
% 109.13/108.82 ! [V_k_2,V_m_2,T_b] :
% 109.13/108.82 ( class_Rings_Olinordered__idom(T_b)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_k_2)))
% 109.13/108.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_abs__dvd__iff,axiom,
% 109.13/108.82 ! [V_k_2,V_m_2,T_b] :
% 109.13/108.82 ( class_Rings_Olinordered__idom(T_b)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_m_2)),V_k_2))
% 109.13/108.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_m_2),V_k_2)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__if__abs__eq,axiom,
% 109.13/108.82 ! [V_k,V_l,T_a] :
% 109.13/108.82 ( class_Rings_Olinordered__idom(T_a)
% 109.13/108.82 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_l) = hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k)
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_l),V_k)) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mod__imp__dvd,axiom,
% 109.13/108.82 ! [V_n,V_m,V_k,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_div__dvd__div,axiom,
% 109.13/108.82 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_b)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_b_2),V_a_2)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_b),V_c_2),V_a_2)))
% 109.13/108.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mod,axiom,
% 109.13/108.82 ! [V_n,V_m,V_k,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 109.13/108.82 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_mod__mod__cancel,axiom,
% 109.13/108.82 ! [V_a,V_b,V_c,T_a] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_a)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 109.13/108.82 => c_Divides_Odiv__class_Omod(T_a,c_Divides_Odiv__class_Omod(T_a,V_a,V_b),V_c) = c_Divides_Odiv__class_Omod(T_a,V_a,V_c) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_dvd__mod__iff,axiom,
% 109.13/108.82 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 109.13/108.82 ( class_Divides_Osemiring__div(T_b)
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 109.13/108.82 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),c_Divides_Odiv__class_Omod(T_b,V_m_2,V_n_2)))
% 109.13/108.82 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 109.13/108.82
% 109.13/108.82 fof(fact_nat__dvd__1__iff__1,axiom,
% 109.13/108.82 ! [V_m_2] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
% 109.13/108.82 <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ).
% 109.13/108.82
% 109.13/108.82 %----Arity declarations (220)
% 109.13/108.82 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 109.13/108.82 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Lattices_Obounded__lattice(T_1)
% 109.13/108.82 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 109.13/108.82 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Lattices_Obounded__lattice(T_1)
% 109.13/108.82 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Lattices_Obounded__lattice(T_1)
% 109.13/108.82 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Lattices_Olattice(T_1)
% 109.13/108.82 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Lattices_Olattice(T_1)
% 109.13/108.82 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Lattices_Odistrib__lattice(T_1)
% 109.13/108.82 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Lattices_Oboolean__algebra(T_1)
% 109.13/108.82 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Orderings_Opreorder,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Orderings_Opreorder(T_1)
% 109.13/108.82 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 109.13/108.82 ! [T_1,T_2] :
% 109.13/108.82 ( ( class_Finite__Set_Ofinite(T_2)
% 109.13/108.82 & class_Finite__Set_Ofinite(T_1) )
% 109.13/108.82 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Lattices_Olattice,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Lattices_Olattice(T_1)
% 109.13/108.82 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Orderings_Oorder,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Orderings_Oorder(T_1)
% 109.13/108.82 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Orderings_Otop,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Orderings_Otop(T_1)
% 109.13/108.82 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Orderings_Oord,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Orderings_Oord(T_1)
% 109.13/108.82 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Orderings_Obot,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Orderings_Obot(T_1)
% 109.13/108.82 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Groups_Ouminus,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Groups_Ouminus(T_1)
% 109.13/108.82 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Groups_Ominus,axiom,
% 109.13/108.82 ! [T_2,T_1] :
% 109.13/108.82 ( class_Groups_Ominus(T_1)
% 109.13/108.82 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_fun__Enum_Oenum,axiom,
% 109.13/108.82 ! [T_1,T_2] :
% 109.13/108.82 ( ( class_Enum_Oenum(T_2)
% 109.13/108.82 & class_Enum_Oenum(T_1) )
% 109.13/108.82 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 109.13/108.82 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 109.13/108.82 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 109.13/108.82 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 109.13/108.82 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 109.13/108.82 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 109.13/108.82 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 109.13/108.82 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 109.13/108.82 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 109.13/108.82 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 109.13/108.82 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 109.13/108.82 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 109.13/108.82 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 109.13/108.82 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 109.13/108.82 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 109.13/108.82 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 109.13/108.82 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 109.13/108.82 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 109.13/108.82 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 109.13/108.82 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 109.13/108.82 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 109.13/108.82 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 109.13/108.82 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 109.13/108.82 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 109.13/108.82 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 109.13/108.82 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 109.13/108.82 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 109.13/108.82 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 109.13/108.82 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 109.13/108.82 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 109.13/108.82 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 109.13/108.82 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 109.13/108.82 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 109.13/108.82 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 109.13/108.82 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 109.13/108.82 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 109.13/108.82 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 109.13/108.82 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 109.13/108.82 class_Orderings_Opreorder(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 109.13/108.82 class_Orderings_Olinorder(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 109.13/108.82 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 109.13/108.82 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 109.13/108.82 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 109.13/108.82 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 109.13/108.82 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 109.13/108.82 class_Lattices_Olattice(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 109.13/108.82 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 109.13/108.82 class_Divides_Oring__div(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 109.13/108.82 class_Rings_Omult__zero(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Ocomm__ring,axiom,
% 109.13/108.82 class_Rings_Ocomm__ring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 109.13/108.82 class_Orderings_Oorder(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 109.13/108.82 class_Int_Oring__char__0(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 109.13/108.82 class_Int_Onumber__ring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 109.13/108.82 class_Rings_Osemiring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 109.13/108.82 class_Orderings_Oord(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 109.13/108.82 class_Groups_Ouminus(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 109.13/108.82 class_Groups_Osgn__if(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 109.13/108.82 class_Groups_Oabs__if(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 109.13/108.82 class_Rings_Oring__1(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 109.13/108.82 class_Groups_Ominus(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Power_Opower,axiom,
% 109.13/108.82 class_Power_Opower(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 109.13/108.82 class_Groups_Ozero(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oring,axiom,
% 109.13/108.82 class_Rings_Oring(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 109.13/108.82 class_Rings_Oidom(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Int_Onumber,axiom,
% 109.13/108.82 class_Int_Onumber(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Groups_Oone,axiom,
% 109.13/108.82 class_Groups_Oone(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Int__Oint__Rings_Odvd,axiom,
% 109.13/108.82 class_Rings_Odvd(tc_Int_Oint) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 109.13/108.82 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 109.13/108.82 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 109.13/108.82 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 109.13/108.82 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 109.13/108.82 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 109.13/108.82 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 109.13/108.82 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 109.13/108.82 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 109.13/108.82 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 109.13/108.82 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 109.13/108.82 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 109.13/108.82 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 109.13/108.82 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 109.13/108.82 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 109.13/108.82 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 109.13/108.82 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 109.13/108.82 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 109.13/108.82 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 109.13/108.82 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 109.13/108.82 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 109.13/108.82 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 109.13/108.82 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 109.13/108.82 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 109.13/108.82 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 109.13/108.82 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 109.13/108.82 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 109.13/108.82 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 109.13/108.82 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 109.13/108.82 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 109.13/108.82 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 109.13/108.82 class_Lattices_Olattice(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 109.13/108.82 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 109.13/108.82 class_Orderings_Oorder(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 109.13/108.82 class_Rings_Osemiring(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 109.13/108.82 class_Orderings_Oord(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 109.13/108.82 class_Orderings_Obot(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 109.13/108.82 class_Groups_Ominus(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Power_Opower,axiom,
% 109.13/108.82 class_Power_Opower(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 109.13/108.82 class_Groups_Ozero(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 109.13/108.82 class_Int_Onumber(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 109.13/108.82 class_Groups_Oone(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Rings_Odvd,axiom,
% 109.13/108.82 class_Rings_Odvd(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 109.13/108.82 class_Nat_Osize(tc_Nat_Onat) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 109.13/108.82 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 109.13/108.82 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 109.13/108.82 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 109.13/108.82 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 109.13/108.82 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 109.13/108.82 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 109.13/108.82 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 109.13/108.82 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 109.13/108.82 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 109.13/108.82 class_Lattices_Olattice(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 109.13/108.82 class_Orderings_Oorder(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 109.13/108.82 class_Orderings_Otop(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 109.13/108.82 class_Orderings_Oord(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 109.13/108.82 class_Orderings_Obot(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 109.13/108.82 class_Groups_Ouminus(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 109.13/108.82 class_Groups_Ominus(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 109.13/108.82 class_Enum_Oenum(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 109.13/108.82 class_Nat_Osize(tc_HOL_Obool) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 109.13/108.82 ! [T_1] :
% 109.13/108.82 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 109.13/108.82 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_List__Olist__Nat_Osize,axiom,
% 109.13/108.82 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 109.13/108.82 ! [T_1,T_2] :
% 109.13/108.82 ( ( class_Finite__Set_Ofinite(T_2)
% 109.13/108.82 & class_Finite__Set_Ofinite(T_1) )
% 109.13/108.82 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_sum__Enum_Oenum,axiom,
% 109.13/108.82 ! [T_1,T_2] :
% 109.13/108.82 ( ( class_Enum_Oenum(T_2)
% 109.13/108.82 & class_Enum_Oenum(T_1) )
% 109.13/108.82 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_sum__Nat_Osize,axiom,
% 109.13/108.82 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 109.13/108.82 ! [T_1] :
% 109.13/108.82 ( class_Finite__Set_Ofinite(T_1)
% 109.13/108.82 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 109.13/108.82 ! [T_1] :
% 109.13/108.82 ( class_Enum_Oenum(T_1)
% 109.13/108.82 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 109.13/108.82 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 109.13/108.82 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 109.13/108.82 ! [T_1,T_2] :
% 109.13/108.82 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 109.13/108.82 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 109.13/108.82 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 109.13/108.82 ! [T_1,T_2] :
% 109.13/108.82 ( ( class_Finite__Set_Ofinite(T_2)
% 109.13/108.82 & class_Finite__Set_Ofinite(T_1) )
% 109.13/108.82 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_prod__Enum_Oenum,axiom,
% 109.13/108.82 ! [T_1,T_2] :
% 109.13/108.82 ( ( class_Enum_Oenum(T_2)
% 109.13/108.82 & class_Enum_Oenum(T_1) )
% 109.13/108.82 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_prod__Nat_Osize,axiom,
% 109.13/108.82 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 109.13/108.82 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 109.13/108.82 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 109.13/108.82 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 109.13/108.82 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 109.13/108.82 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 109.13/108.82 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 109.13/108.82 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 109.13/108.82 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 109.13/108.82 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 109.13/108.82 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 109.13/108.82 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 109.13/108.82 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 109.13/108.82 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 109.13/108.82 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 109.13/108.82 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 109.13/108.82 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 109.13/108.82 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 109.13/108.82 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 109.13/108.82 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 109.13/108.82 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 109.13/108.82 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 109.13/108.82 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 109.13/108.82 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 109.13/108.82 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 109.13/108.82 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 109.13/108.82 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 109.13/108.82 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 109.13/108.82 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 109.13/108.82 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 109.13/108.82 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 109.13/108.82 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 109.13/108.82 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 109.13/108.82 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 109.13/108.82 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 109.13/108.82 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 109.13/108.82 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 109.13/108.82 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 109.13/108.82 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 109.13/108.82 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 109.13/108.82 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 109.13/108.82 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Rings_Odvd,axiom,
% 109.13/108.82 class_Rings_Odvd(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 109.13/108.82 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 109.13/108.82
% 109.13/108.82 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 109.13/108.82 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 109.13/108.82
% 109.13/108.82 %----Helper facts (20)
% 109.13/108.82 fof(help_c__COMBI__1,axiom,
% 109.13/108.82 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__COMBK__1,axiom,
% 109.13/108.82 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__COMBB__1,axiom,
% 109.13/108.82 ! [V_R_2,V_Q_2,V_P_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_P_2),V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__COMBC__1,axiom,
% 109.13/108.82 ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),V_Q_2) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__COMBS__1,axiom,
% 109.13/108.82 ! [V_R_2,V_Q_2,V_P_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_P_2),V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fequal__1,axiom,
% 109.13/108.82 ! [V_y_2,V_x_2] :
% 109.13/108.82 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 109.13/108.82 | V_x_2 = V_y_2 ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fequal__2,axiom,
% 109.13/108.82 ! [V_y_2,V_x_2] :
% 109.13/108.82 ( V_x_2 != V_y_2
% 109.13/108.82 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fFalse__1,axiom,
% 109.13/108.82 ~ hBOOL(c_fFalse) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fTrue__1,axiom,
% 109.13/108.82 hBOOL(c_fTrue) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fNot__1,axiom,
% 109.13/108.82 ! [V_P_2] :
% 109.13/108.82 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 109.13/108.82 | ~ hBOOL(V_P_2) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fNot__2,axiom,
% 109.13/108.82 ! [V_P_2] :
% 109.13/108.82 ( ~ ~ hBOOL(V_P_2)
% 109.13/108.82 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fconj__1,axiom,
% 109.13/108.82 ! [V_Q_2,V_P_2] :
% 109.13/108.82 ( ~ hBOOL(V_P_2)
% 109.13/108.82 | ~ hBOOL(V_Q_2)
% 109.13/108.82 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fconj__2,axiom,
% 109.13/108.82 ! [V_Q_2,V_P_2] :
% 109.13/108.82 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 109.13/108.82 | hBOOL(V_P_2) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fconj__3,axiom,
% 109.13/108.82 ! [V_Q_2,V_P_2] :
% 109.13/108.82 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 109.13/108.82 | hBOOL(V_Q_2) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fdisj__1,axiom,
% 109.13/108.82 ! [V_Q_2,V_P_2] :
% 109.13/108.82 ( ~ hBOOL(V_P_2)
% 109.13/108.82 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fdisj__2,axiom,
% 109.13/108.82 ! [V_P_2,V_Q_2] :
% 109.13/108.82 ( ~ hBOOL(V_Q_2)
% 109.13/108.82 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fdisj__3,axiom,
% 109.13/108.82 ! [V_Q_2,V_P_2] :
% 109.13/108.82 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 109.13/108.82 | hBOOL(V_P_2)
% 109.13/108.82 | hBOOL(V_Q_2) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fimplies__1,axiom,
% 109.13/108.82 ! [V_Q_2,V_P_2] :
% 109.13/108.82 ( hBOOL(V_P_2)
% 109.13/108.82 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fimplies__2,axiom,
% 109.13/108.82 ! [V_P_2,V_Q_2] :
% 109.13/108.82 ( ~ hBOOL(V_Q_2)
% 109.13/108.82 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 109.13/108.82
% 109.13/108.82 fof(help_c__fimplies__3,axiom,
% 109.13/108.82 ! [V_Q_2,V_P_2] :
% 109.13/108.82 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 109.13/108.82 | ~ hBOOL(V_P_2)
% 109.13/108.82 | hBOOL(V_Q_2) ) ).
% 109.13/108.82
% 109.13/108.82 %----Conjectures (2)
% 109.13/108.82 fof(conj_0,hypothesis,
% 109.13/108.82 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_ts),v_G)) ).
% 109.13/108.82
% 109.13/108.82 fof(conj_1,conjecture,
% 109.13/108.82 ! [B_n] :
% 109.13/108.82 ( ! [B_x] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G))
% 109.13/108.82 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) )
% 109.13/108.82 => ! [B_x] :
% 109.13/108.82 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_ts))
% 109.13/108.82 => c_Hoare__Mirabelle_Otriple__valid(t_a,B_n,B_x) ) ) ).
% 109.13/108.82
% 109.13/108.82 %------------------------------------------------------------------------------
% 109.13/108.82 %-------------------------------------------
% 109.13/108.82 % Proof found
% 109.13/108.82 % SZS status Theorem for theBenchmark
% 109.13/108.82 % SZS output start Proof
% 109.13/108.83 %ClaNum:10448(EqnAxiom:3096)
% 109.13/108.83 %VarNum:80925(SingletonVarNum:23661)
% 109.13/108.83 %MaxLitNum:8
% 109.13/108.83 %MaxfuncDepth:15
% 109.13/108.83 %SharedTerms:1005
% 109.13/108.83 %goalClause: 3535 4646 5722
% 109.13/108.83 %singleGoalClaCount:2
% 109.13/108.83 [3100]P1(a178)
% 109.13/108.83 [3101]P2(a909)
% 109.13/108.83 [3102]P2(a911)
% 109.13/108.83 [3103]P2(a1)
% 109.13/108.83 [3104]P2(a90)
% 109.13/108.83 [3105]P3(a909)
% 109.13/108.83 [3106]P3(a911)
% 109.13/108.83 [3107]P3(a1)
% 109.13/108.83 [3108]P3(a90)
% 109.13/108.83 [3109]P4(a911)
% 109.13/108.83 [3110]P4(a1)
% 109.13/108.83 [3111]P4(a90)
% 109.13/108.83 [3112]P113(a909)
% 109.13/108.83 [3113]P113(a911)
% 109.13/108.83 [3114]P113(a1)
% 109.13/108.83 [3115]P113(a90)
% 109.13/108.83 [3116]P5(a909)
% 109.13/108.83 [3117]P114(a911)
% 109.13/108.83 [3118]P114(a1)
% 109.13/108.83 [3119]P114(a90)
% 109.13/108.83 [3120]P64(a909)
% 109.13/108.83 [3121]P64(a1)
% 109.13/108.83 [3122]P65(a1)
% 109.13/108.83 [3123]P96(a909)
% 109.13/108.83 [3124]P66(a1)
% 109.13/108.83 [3125]P102(a909)
% 109.13/108.83 [3126]P102(a911)
% 109.14/108.83 [3127]P102(a1)
% 109.14/108.83 [3128]P103(a909)
% 109.14/108.83 [3129]P103(a911)
% 109.14/108.83 [3130]P103(a1)
% 109.14/108.83 [3131]P104(a909)
% 109.14/108.83 [3132]P108(a909)
% 109.14/108.83 [3133]P108(a911)
% 109.14/108.83 [3134]P108(a1)
% 109.14/108.83 [3135]P115(a909)
% 109.14/108.83 [3136]P107(a909)
% 109.14/108.83 [3137]P107(a911)
% 109.14/108.83 [3138]P107(a1)
% 109.14/108.83 [3139]P109(a909)
% 109.14/108.83 [3140]P109(a911)
% 109.14/108.83 [3141]P97(a911)
% 109.14/108.83 [3142]P97(a1)
% 109.14/108.83 [3143]P97(a90)
% 109.14/108.83 [3144]P83(a1)
% 109.14/108.83 [3145]P105(a909)
% 109.14/108.83 [3146]P84(a909)
% 109.14/108.83 [3147]P84(a911)
% 109.14/108.83 [3148]P84(a1)
% 109.14/108.83 [3149]P84(a90)
% 109.14/108.83 [3150]P67(a1)
% 109.14/108.83 [3151]P116(a1)
% 109.14/108.83 [3152]P76(a911)
% 109.14/108.83 [3153]P76(a1)
% 109.14/108.83 [3154]P76(a90)
% 109.14/108.83 [3155]P129(a1)
% 109.14/108.83 [3156]P77(a911)
% 109.14/108.83 [3157]P77(a1)
% 109.14/108.83 [3158]P77(a90)
% 109.14/108.83 [3159]P78(a911)
% 109.14/108.83 [3160]P78(a1)
% 109.14/108.83 [3161]P78(a90)
% 109.14/108.83 [3162]P79(a911)
% 109.14/108.83 [3163]P79(a1)
% 109.14/108.83 [3164]P79(a90)
% 109.14/108.83 [3165]P89(a911)
% 109.14/108.83 [3166]P89(a1)
% 109.14/108.83 [3167]P89(a90)
% 109.14/108.83 [3168]P90(a911)
% 109.14/108.83 [3169]P90(a1)
% 109.14/108.83 [3170]P90(a90)
% 109.14/108.83 [3171]P86(a911)
% 109.14/108.83 [3172]P86(a1)
% 109.14/108.83 [3173]P86(a90)
% 109.14/108.83 [3174]P92(a911)
% 109.14/108.83 [3175]P92(a1)
% 109.14/108.83 [3176]P92(a90)
% 109.14/108.83 [3177]P93(a911)
% 109.14/108.83 [3178]P93(a1)
% 109.14/108.83 [3179]P93(a90)
% 109.14/108.83 [3180]P130(a911)
% 109.14/108.83 [3181]P130(a1)
% 109.14/108.83 [3182]P130(a90)
% 109.14/108.83 [3183]P68(a909)
% 109.14/108.83 [3184]P68(a914)
% 109.14/108.83 [3185]P117(a1)
% 109.14/108.83 [3186]P121(a911)
% 109.14/108.83 [3187]P121(a1)
% 109.14/108.83 [3188]P121(a90)
% 109.14/108.83 [3189]P149(a911)
% 109.14/108.83 [3190]P149(a1)
% 109.14/108.83 [3191]P87(a911)
% 109.14/108.83 [3192]P87(a1)
% 109.14/108.83 [3193]P87(a90)
% 109.14/108.83 [3194]P150(a911)
% 109.14/108.83 [3195]P150(a1)
% 109.14/108.83 [3196]P150(a90)
% 109.14/108.83 [3197]P144(a1)
% 109.14/108.83 [3198]P98(a1)
% 109.14/108.83 [3199]P94(a1)
% 109.14/108.83 [3200]P99(a1)
% 109.14/108.83 [3201]P100(a911)
% 109.14/108.83 [3202]P100(a1)
% 109.14/108.83 [3203]P100(a90)
% 109.14/108.83 [3204]P145(a1)
% 109.14/108.83 [3205]P88(a911)
% 109.14/108.83 [3206]P88(a1)
% 109.14/108.83 [3207]P88(a90)
% 109.14/108.83 [3208]P118(a911)
% 109.14/108.83 [3209]P118(a1)
% 109.14/108.83 [3210]P118(a90)
% 109.14/108.83 [3211]P133(a911)
% 109.14/108.83 [3212]P133(a1)
% 109.14/108.83 [3213]P133(a90)
% 109.14/108.83 [3214]P138(a911)
% 109.14/108.83 [3215]P138(a1)
% 109.14/108.83 [3216]P138(a90)
% 109.14/108.83 [3217]P146(a911)
% 109.14/108.83 [3218]P146(a1)
% 109.14/108.83 [3219]P146(a90)
% 109.14/108.83 [3220]P110(a911)
% 109.14/108.83 [3221]P110(a1)
% 109.14/108.83 [3222]P110(a90)
% 109.14/108.83 [3223]P80(a911)
% 109.14/108.83 [3224]P80(a1)
% 109.14/108.83 [3225]P80(a90)
% 109.14/108.83 [3226]P147(a1)
% 109.14/108.83 [3227]P148(a911)
% 109.14/108.83 [3228]P148(a1)
% 109.14/108.83 [3229]P148(a90)
% 109.14/108.83 [3230]P122(a911)
% 109.14/108.83 [3231]P122(a1)
% 109.14/108.83 [3232]P122(a90)
% 109.14/108.83 [3233]P82(a911)
% 109.14/108.83 [3234]P82(a1)
% 109.14/108.83 [3235]P82(a90)
% 109.14/108.83 [3236]P123(a1)
% 109.14/108.83 [3237]P139(a911)
% 109.14/108.83 [3238]P139(a1)
% 109.14/108.83 [3239]P139(a90)
% 109.14/108.83 [3240]P140(a1)
% 109.14/108.83 [3241]P142(a911)
% 109.14/108.83 [3242]P142(a1)
% 109.14/108.83 [3243]P142(a90)
% 109.14/108.83 [3244]P141(a911)
% 109.14/108.83 [3245]P141(a1)
% 109.14/108.83 [3246]P141(a90)
% 109.14/108.83 [3247]P131(a1)
% 109.14/108.83 [3248]P132(a1)
% 109.14/108.83 [3249]P134(a911)
% 109.14/108.83 [3250]P134(a1)
% 109.14/108.83 [3251]P134(a90)
% 109.14/108.83 [3252]P127(a911)
% 109.14/108.83 [3253]P127(a1)
% 109.14/108.83 [3254]P127(a90)
% 109.14/108.83 [3255]P135(a911)
% 109.14/108.83 [3256]P135(a1)
% 109.14/108.83 [3257]P135(a90)
% 109.14/108.83 [3258]P136(a1)
% 109.14/108.83 [3259]P137(a1)
% 109.14/108.83 [3260]P69(a911)
% 109.14/108.83 [3261]P69(a1)
% 109.14/108.83 [3262]P69(a90)
% 109.14/108.83 [3263]P70(a1)
% 109.14/108.83 [3264]P91(a1)
% 109.14/108.83 [3265]P143(a1)
% 109.14/108.83 [3266]P81(a1)
% 109.14/108.83 [3267]P119(a911)
% 109.14/108.83 [3268]P85(a911)
% 109.14/108.83 [3269]P85(a1)
% 109.14/108.83 [3270]P85(a90)
% 109.14/108.83 [3271]P95(a911)
% 109.14/108.83 [3272]P95(a1)
% 109.14/108.83 [3273]P95(a90)
% 109.14/108.83 [3274]P71(a909)
% 109.14/108.83 [3275]P71(a914)
% 109.14/108.83 [3276]P112(a909)
% 109.14/108.83 [3277]P112(a911)
% 109.14/108.83 [3278]P112(a914)
% 109.14/108.83 [3279]P112(a90)
% 109.14/108.83 [3280]P112(a314)
% 109.14/108.83 [3281]P111(a914)
% 109.14/108.83 [3282]P111(a1)
% 109.14/108.83 [3283]P124(a911)
% 109.14/108.83 [3284]P124(a1)
% 109.14/108.83 [3285]P124(a90)
% 109.14/108.83 [3286]P120(a1)
% 109.14/108.83 [3287]P106(a909)
% 109.14/108.83 [3302]P39(a911,a231)
% 109.14/108.83 [3303]P39(a911,a308)
% 109.14/108.83 [3304]P40(a911,a231)
% 109.14/108.83 [3383]P42(a911,a911,a103)
% 109.14/108.83 [4631]~E(a88,a76)
% 109.14/108.83 [4632]~E(a88,a76)
% 109.14/108.83 [4633]~P1(a230)
% 109.14/108.83 [4646]~P28(a908,a813,a812)
% 109.14/108.83 [3097]E(f2(a1),a76)
% 109.14/108.83 [3098]E(f3(a90),a4)
% 109.14/108.83 [3099]E(f91(a90),a5)
% 109.14/108.83 [3288]E(f179(a911),f2(a911))
% 109.14/108.83 [3289]E(f92(a911),f223(a911))
% 109.14/108.83 [3290]E(f101(a911),f224(a911))
% 109.14/108.83 [3291]E(f93(a1),f25(a1))
% 109.14/108.83 [3292]E(f77(a230),f2(a911))
% 109.14/108.83 [3293]E(f77(a178),f2(a911))
% 109.14/108.83 [3294]P6(f2(a1))
% 109.14/108.83 [3295]P6(f71(a1))
% 109.14/108.83 [3350]P39(f917(a911,a911),a26)
% 109.14/108.83 [3691]E(f311(a911,a911,a231,a231),a26)
% 109.14/108.83 [4634]~E(f71(a1),f2(a1))
% 109.14/108.83 [3296]E(f6(f2(a90)),f2(a911))
% 109.14/108.83 [3297]E(f102(f2(a911)),f2(a911))
% 109.14/108.83 [3306]E(f318(f72(a1),a76),a76)
% 109.14/108.83 [3309]E(f318(a95,f2(a1)),f2(a911))
% 109.14/108.83 [3310]E(f318(a5,f2(a911)),f2(a90))
% 109.14/108.83 [3311]E(f318(a103,f2(a911)),f71(a911))
% 109.14/108.83 [3312]E(f318(a95,f71(a1)),f71(a911))
% 109.14/108.83 [3313]E(f318(a5,f71(a911)),f71(a90))
% 109.14/108.83 [3314]E(f318(f94(a911),a76),f2(a911))
% 109.14/108.83 [3315]E(f318(f94(a1),a76),f2(a1))
% 109.14/108.83 [3316]E(f318(f94(a90),a76),f2(a90))
% 109.14/108.83 [3317]E(f318(a95,f2(a1)),f2(a911))
% 109.14/108.83 [3318]E(f318(f94(a911),a76),f2(a911))
% 109.14/108.83 [3319]E(f318(f180(a909),a230),f2(a911))
% 109.14/108.83 [3320]E(f318(f180(a909),a178),f2(a911))
% 109.14/108.83 [3326]E(f318(f72(a1),f71(a1)),a88)
% 109.14/108.83 [3331]E(f318(f91(a1),f2(a911)),f2(a1))
% 109.14/108.83 [3332]E(f318(f91(a1),f71(a911)),f71(a1))
% 109.14/108.83 [3333]E(f318(f72(a1),f2(a1)),f2(a1))
% 109.14/108.83 [3334]E(f318(f91(a1),f2(a911)),f2(a1))
% 109.14/108.83 [3335]E(f318(f91(a1),f71(a911)),f71(a1))
% 109.14/108.83 [3336]E(f318(f180(a911),f2(a911)),f2(a911))
% 109.14/108.83 [3337]E(f318(f180(a90),f2(a90)),f2(a911))
% 109.14/108.83 [3347]E(f318(a95,f71(a1)),f318(a103,f2(a911)))
% 109.14/108.83 [3348]E(f309(f917(a911,a911),a26),a27)
% 109.14/108.83 [3349]E(f310(f917(a911,a911),a26),a28)
% 109.14/108.83 [3375]E(f318(f273(a911),f2(a911)),f179(f918(a911,a909)))
% 109.14/108.83 [3376]E(f318(f274(a911),f2(a911)),f233(f918(a911,a909)))
% 109.14/108.83 [3385]P43(f179(f918(a1,a909)))
% 109.14/108.83 [3419]E(f318(f318(f3(a90),f2(a90)),f71(a90)),f2(a90))
% 109.14/108.83 [3463]E(f318(f318(f145(a1,a911),a95),f104(a1)),f104(a911))
% 109.14/108.83 [3494]P1(f318(f318(f226(a1),a88),f2(a1)))
% 109.14/108.83 [3518]P1(f318(f318(f225(a1),f2(a1)),f2(a1)))
% 109.14/108.83 [3519]P1(f318(f318(f225(a1),f2(a1)),f71(a1)))
% 109.14/108.83 [3520]P1(f318(f318(f226(a1),f2(a1)),f71(a1)))
% 109.14/108.83 [3721]E(f318(f318(f280(a911,a911,a911),a308),f298(a911,a308)),a231)
% 109.14/108.83 [3759]P44(a1,a911,a95,f318(f225(a1),f2(a1)))
% 109.14/108.83 [3763]E(f318(f318(f33(a911,f918(a911,a909)),f233(f918(a911,a909))),f273(a911)),f233(f918(a911,a909)))
% 109.14/108.83 [3764]E(f318(f318(f33(a911,f918(a911,a909)),f233(f918(a911,a909))),f274(a911)),f233(f918(a911,a909)))
% 109.14/108.83 [3765]E(f318(f318(f33(a911,f918(a911,a909)),f233(f918(a911,a909))),f292(a911)),f233(f918(a911,a909)))
% 109.14/108.83 [3766]E(f318(f318(f34(a911,f918(a911,a909)),f233(f918(a911,a909))),f295(a911)),f179(f918(a911,a909)))
% 109.14/108.83 [3782]P25(a911,a1,f91(a1),f233(f918(a911,a909)))
% 109.14/108.83 [3796]P44(a911,a1,f91(a1),f318(f18(a909,a911),a178))
% 109.14/108.83 [3925]E(f318(f66(a911,a90,a1,a5),a95),f94(a90))
% 109.14/108.83 [4145]P60(a90,a911,a22,a5,f233(f918(a911,a909)))
% 109.14/108.83 [4148]P60(a1,f918(f917(a911,a911),a909),a97,a82,a89)
% 109.14/108.83 [4398]E(f249(a1,a1,a1,a1,f25(a1),f72(a1)),a45)
% 109.14/108.83 [4643]~E(f318(f94(a1),a88),f318(f94(a1),a76))
% 109.14/108.83 [4644]~P1(f318(a184,f2(a1)))
% 109.14/108.83 [4645]~P1(f318(a184,f71(a1)))
% 109.14/108.83 [4669]~P1(f318(f318(f226(a1),a76),f2(a1)))
% 109.14/108.83 [3368]E(f318(f318(f3(a1),a88),a88),a76)
% 109.14/108.83 [3369]E(f318(f318(f73(a1),a76),a88),a88)
% 109.14/108.83 [3382]E(f318(f91(a1),f318(a103,f2(a911))),f71(a1))
% 109.14/108.83 [3448]E(f318(f29(a914),f233(f918(a914,a909))),f71(a911))
% 109.14/108.83 [3468]P1(f318(a184,f318(f94(a1),a88)))
% 109.14/108.83 [3469]P1(f318(f318(f225(a1),a76),a76))
% 109.14/108.83 [3470]P1(f318(f318(f225(a1),a88),a76))
% 109.14/108.83 [3471]P1(f318(f318(f225(a1),a88),a88))
% 109.14/108.83 [3472]P1(f318(f318(f226(a1),a88),a76))
% 109.14/108.83 [3528]E(f318(f318(f300(a911),f2(a911)),f179(f918(a911,a909))),f318(f292(a911),f2(a911)))
% 109.14/108.83 [3584]P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),a76)))
% 109.14/108.83 [3596]E(f318(f301(a911,a911,a103),f233(f918(a911,a909))),f318(f295(a911),f2(a911)))
% 109.14/108.83 [3602]E(f318(f301(a1,a911,a95),f179(f918(a1,a909))),f179(f918(a911,a909)))
% 109.14/108.83 [3610]E(f318(f301(a911,a1,f91(a1)),f179(f918(a911,a909))),f179(f918(a1,a909)))
% 109.14/108.83 [3631]P8(f917(a911,a911),f233(f918(f917(a911,a911),a909)),a99)
% 109.14/108.83 [3932]E(f318(f66(a911,a1,a90,f91(a1)),a22),a24)
% 109.14/108.83 [3995]P39(a911,f318(f253(f917(a911,a911)),f318(f248(a911,a911,a909),f226(a911))))
% 109.14/108.83 [4660]~P1(f318(a184,f318(f94(a1),a76)))
% 109.14/108.83 [4661]~P1(f318(f318(f225(a1),a76),a88))
% 109.14/108.83 [4662]~P1(f318(f318(f226(a1),a76),a76))
% 109.14/108.83 [4663]~P1(f318(f318(f226(a1),a76),a88))
% 109.14/108.83 [4664]~P1(f318(f318(f226(a1),a88),a88))
% 109.14/108.83 [4673]~P1(f318(f55(a911),f233(f918(a911,a909))))
% 109.14/108.83 [4674]~P1(f318(f55(a1),f233(f918(a1,a909))))
% 109.14/108.83 [3535]P1(f318(f318(f320(f910(a908)),a812),a920))
% 109.14/108.83 [4573]E(f318(f248(a1,a1,a909),f318(f318(f10(f918(a1,a909),f918(a1,a909),a1),f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f226(a1),f2(a1))))),f318(f318(f9(a1,a1,f918(a1,a909)),f318(f318(f10(f918(a1,f918(a1,a909)),f918(a1,f918(a1,a909)),a1),f9(a1,a1,a909)),f318(f318(f10(f918(a1,a1),f918(a1,f918(a1,a909)),a1),f318(f10(a1,f918(a1,a909),a1),a315)),a208))),f71(a1)))),a204)
% 109.14/108.83 [3693]E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a88)),a88),a88)
% 109.14/108.83 [3731]E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76),f318(f72(a1),a88))
% 109.14/108.83 [3768]E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76),f318(f318(f3(a1),a76),a88))
% 109.14/108.83 [3814]P1(f318(f318(f225(f918(f910(a908),a909)),a920),a921))
% 109.14/108.83 [3866]E(f318(f318(f54(f917(a911,a911)),f233(f918(f917(a911,a911),a909))),a99),a89)
% 109.14/108.83 [3933]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f71(a911))
% 109.14/108.83 [3934]E(f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f71(a1))
% 109.14/108.83 [3935]E(f318(f94(a90),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f71(a90))
% 109.14/108.83 [3936]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f71(a911))
% 109.14/108.83 [3943]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f318(a103,f2(a911)))
% 109.14/108.83 [4266]E(f318(f318(f101(f918(f917(f917(a911,a911),f917(a911,a911)),a909)),a26),f298(f917(a911,a911),f179(f918(f917(f917(a911,a911),f917(a911,a911)),a909)))),a64)
% 109.14/108.83 [4326]E(f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),f2(a911)),f2(a911))),f179(f918(f917(a911,a911),a909))))),f2(a1))
% 109.14/108.83 [4327]E(f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),f71(a911)),f2(a911))),f179(f918(f917(a911,a911),a909))))),f71(a1))
% 109.14/108.83 [4340]E(f318(f253(f917(a911,a911)),f318(f248(a911,a911,a909),f318(f318(f10(a911,f918(a911,a909),a911),f318(f9(a911,a911,a909),a315)),a103))),a308)
% 109.14/108.83 [4095]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),a88),a76)
% 109.14/108.83 [4107]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a88)),a88)),a88),f318(f318(f73(a1),a88),a88))
% 109.14/108.83 [4391]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(a103,f318(a103,f318(a103,f2(a911)))))
% 109.14/108.83 [4456]P27(f918(f917(a911,a911),a909),f318(f318(f243(f918(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),a909),f918(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),a909)),a27),a65))
% 109.14/108.83 [4457]P27(f918(f917(a911,a911),a909),f318(f318(f243(f918(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),a909),f918(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),a909)),a28),a63))
% 109.14/108.83 [4467]P6(f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))))
% 109.14/108.83 [4494]E(f318(f318(f101(f918(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),a909)),f310(f917(a911,a911),a64)),f318(f318(f300(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),f179(f918(f917(a911,a911),a909))),f179(f918(f917(a911,a911),a909)))),f179(f918(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),a909)))),a63)
% 109.14/108.83 [4495]E(f318(f318(f101(f918(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),a909)),f309(f917(a911,a911),a64)),f318(f318(f300(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),f179(f918(f917(a911,a911),a909))),f179(f918(f917(a911,a911),a909)))),f179(f918(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),a909)))),a65)
% 109.14/108.83 [4500]E(f318(a95,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))))
% 109.14/108.83 [4501]E(f318(f91(a1),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))))
% 109.14/108.83 [4514]P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))))
% 109.14/108.83 [4510]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)),f318(a103,f318(a103,f2(a911))))
% 109.14/108.83 [4511]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)),f318(a103,f318(a103,f2(a911))))
% 109.14/108.83 [4512]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)),f318(f318(f73(a911),f71(a911)),f71(a911)))
% 109.14/108.83 [4513]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)),f318(f29(a909),f233(f918(a909,a909))))
% 109.14/108.83 [4553]P6(f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))
% 109.14/108.83 [4554]E(f318(a95,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(a103,f318(a103,f2(a911))))
% 109.14/108.83 [4574]E(f318(a95,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))
% 109.14/108.83 [4575]E(f318(f91(a1),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))
% 109.14/108.83 [4588]P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.83 [3305]P7(x33051,a315)
% 109.14/108.83 [3692]P25(a911,a911,a103,x36921)
% 109.14/108.83 [3298]P112(f910(x32981))
% 109.14/108.83 [3299]P112(f915(x32991))
% 109.14/108.83 [3300]P112(f912(x33001))
% 109.14/108.83 [3301]P112(f913(x33011))
% 109.14/108.83 [3321]P39(a1,f96(x33211))
% 109.14/108.83 [3322]P39(a1,f98(x33221))
% 109.14/108.83 [3371]P39(f918(x33711,a909),f305(x33711))
% 109.14/108.83 [3372]P40(f918(x33721,a909),f305(x33721))
% 109.14/108.83 [3397]E(f234(x33971,x33971,a315),a315)
% 109.14/108.83 [3412]E(f39(a1,x34121,x34121),f2(a1))
% 109.14/108.83 [3465]P14(x34651,f918(x34651,a909),f300(x34651))
% 109.14/108.83 [4635]~E(f318(a103,x46351),x46351)
% 109.14/108.83 [4636]~E(f318(a103,x46361),x46361)
% 109.14/108.83 [4637]~E(f318(a103,x46371),f2(a911))
% 109.14/108.83 [4638]~E(f318(a103,x46381),f2(a911))
% 109.14/108.83 [4639]~E(f318(a103,x46391),f2(a911))
% 109.14/108.83 [4640]~E(f318(a103,x46401),f2(a911))
% 109.14/108.83 [4641]~E(f318(a103,x46411),f2(a911))
% 109.14/108.83 [4642]~E(f318(a103,x46421),f2(a911))
% 109.14/108.83 [3307]E(f318(f94(a1),x33071),x33071)
% 109.14/108.83 [3308]E(f318(f180(a911),x33081),x33081)
% 109.14/108.83 [3323]E(f318(a82,f319(x33231)),x33231)
% 109.14/108.83 [3324]E(f318(a5,f575(x33241)),x33241)
% 109.14/108.83 [3325]E(f232(x33251,f2(a90)),f2(a90))
% 109.14/108.83 [3338]E(f105(x33381,f104(x33381)),f104(x33381))
% 109.14/108.83 [3339]E(f143(x33391,f104(x33391)),f104(x33391))
% 109.14/108.83 [3344]E(f318(f158(x33441),f104(x33441)),f104(x33441))
% 109.14/108.83 [3345]E(f318(f162(x33451),f104(x33451)),f104(x33451))
% 109.14/108.83 [3346]E(f318(f159(x33461),f104(x33461)),f104(x33461))
% 109.14/108.83 [3351]E(f318(f94(a1),x33511),f318(f93(a1),x33511))
% 109.14/108.83 [3352]E(f318(a82,f318(a97,x33521)),x33521)
% 109.14/108.83 [3353]E(f318(a5,f318(a22,x33531)),x33531)
% 109.14/108.83 [3354]E(f318(a5,f318(a22,x33541)),x33541)
% 109.14/108.83 [3355]E(f318(a22,f318(a5,x33551)),x33551)
% 109.14/108.83 [3357]P6(f318(f91(a1),x33571))
% 109.14/108.83 [3366]E(f318(f180(f912(x33661)),f104(x33661)),f2(a911))
% 109.14/108.83 [3367]E(f318(f180(f913(x33671)),f110(x33671)),f2(a911))
% 109.14/108.83 [3388]E(f318(f318(f3(a911),x33881),f2(a911)),x33881)
% 109.14/108.83 [3389]E(f318(f318(f73(a911),x33891),f2(a911)),x33891)
% 109.14/108.83 [3390]E(f318(f318(f73(a1),x33901),f2(a1)),x33901)
% 109.14/108.83 [3391]E(f318(f318(f74(a911),x33911),f71(a911)),x33911)
% 109.14/108.83 [3392]E(f318(f318(f74(a1),x33921),f71(a1)),x33921)
% 109.14/108.83 [3393]E(f318(f318(f224(a911),x33931),f2(a911)),x33931)
% 109.14/108.83 [3394]E(f318(f318(f74(a911),x33941),f2(a911)),f2(a911))
% 109.14/108.83 [3395]E(f318(f318(f30(a1),x33951),f2(a1)),f2(a1))
% 109.14/108.83 [3396]E(f318(f318(f223(a911),x33961),f2(a911)),f2(a911))
% 109.14/108.83 [3403]E(f318(f163(x34031),f104(x34031)),f179(f918(x34031,a909)))
% 109.14/108.83 [3407]P1(f318(f128(x34071),f104(x34071)))
% 109.14/108.83 [3413]E(f318(f145(x34131,x34131),f7(x34131)),f25(f912(x34131)))
% 109.14/108.83 [3414]E(f318(f145(x34141,x34141),f25(x34141)),f25(f912(x34141)))
% 109.14/108.83 [3415]E(f39(a1,x34151,f2(a1)),x34151)
% 109.14/108.83 [3416]E(f318(f225(a911),f318(a103,x34161)),f318(f226(a911),x34161))
% 109.14/108.83 [3417]E(f318(f273(a911),f318(a103,x34171)),f318(f292(a911),x34171))
% 109.14/108.83 [3418]E(f318(f274(a911),f318(a103,x34181)),f318(f295(a911),x34181))
% 109.14/108.83 [3420]E(f39(a1,f2(a1),x34201),f2(a1))
% 109.14/108.83 [3433]E(f318(f318(f73(a911),x34331),f71(a911)),f318(a103,x34331))
% 109.14/108.83 [3442]E(f318(f293(a911,x34421),f2(a911)),f179(f918(a911,a909)))
% 109.14/108.83 [3454]E(f294(a911,f2(a911),x34541),f318(f292(a911),x34541))
% 109.14/108.83 [3497]E(f318(f318(f3(a911),f318(a103,x34971)),f71(a911)),x34971)
% 109.14/108.83 [3509]E(f41(f2(a1),x35091),f318(f318(f243(a1,a1),f2(a1)),f2(a1)))
% 109.14/108.83 [3513]E(f318(f318(f73(a911),f318(a22,x35131)),f2(a911)),f318(a22,x35131))
% 109.14/108.83 [3559]P1(f318(f318(f226(a911),x35591),f318(a103,x35591)))
% 109.14/108.83 [3571]P1(f318(f318(f226(a911),f2(a911)),f318(a103,x35711)))
% 109.14/108.83 [3582]E(f318(f318(f174(f912(x35821),f912(x35821)),f2(a911)),f158(x35821)),f25(f912(x35821)))
% 109.14/108.83 [3795]E(f84(x37951,x37951,f233(f918(x37951,a909)),f25(x37951)),f25(x37951))
% 109.14/108.83 [3853]E(f318(f318(f3(a90),f318(a5,f318(a103,f318(a22,x38531)))),f71(a90)),x38531)
% 109.14/108.83 [3916]P1(f318(f318(f225(a1),f318(f72(a1),f318(f91(a1),x39161))),f2(a1)))
% 109.14/108.83 [4058]P1(f318(f318(f226(a1),f318(f72(a1),f318(f91(a1),f318(a103,x40581)))),f2(a1)))
% 109.14/108.83 [4156]P26(x41561,x41561,f25(x41561),f233(f918(x41561,a909)),f233(f918(x41561,a909)))
% 109.14/108.83 [4649]~E(f233(f918(x46491,a909)),f179(f918(x46491,a909)))
% 109.14/108.83 [4670]~P1(f318(f318(f226(a911),x46701),f2(a911)))
% 109.14/108.83 [4671]~P1(f318(f318(f226(a911),x46711),f2(a911)))
% 109.14/108.83 [4672]~P1(f318(f318(f226(a911),x46721),f2(a911)))
% 109.14/108.83 [4681]~P1(f318(f318(f226(a1),f318(f91(a1),x46811)),f2(a1)))
% 109.14/108.83 [3356]E(f111(x33561,f110(f913(x33561))),f110(x33561))
% 109.14/108.83 [3370]E(f170(x33701,f104(f912(x33701))),f104(f912(x33701)))
% 109.14/108.83 [3373]E(f318(f318(f74(a1),a76),x33731),a76)
% 109.14/108.83 [3374]E(f318(f318(f73(a1),a76),x33741),x33741)
% 109.14/108.83 [3377]E(f318(a95,f318(f91(a1),x33771)),x33771)
% 109.14/108.83 [3378]E(f318(f318(f3(a1),x33781),a76),x33781)
% 109.14/108.83 [3379]E(f318(f318(f73(a1),x33791),a76),x33791)
% 109.14/108.83 [3381]E(f318(f318(f3(a911),x33811),x33811),f2(a911))
% 109.14/108.83 [3386]E(f318(f72(a1),f318(f72(a1),x33861)),x33861)
% 109.14/108.83 [3387]E(f318(f29(a911),f318(f273(a911),x33871)),x33871)
% 109.14/108.83 [3398]E(f318(f318(f73(a911),f2(a911)),x33981),x33981)
% 109.14/108.83 [3399]E(f318(f318(f73(a1),f2(a1)),x33991),x33991)
% 109.14/108.83 [3400]E(f318(f318(f74(a911),f71(a911)),x34001),x34001)
% 109.14/108.83 [3401]E(f318(f318(f74(a1),f71(a1)),x34011),x34011)
% 109.14/108.83 [3402]E(f318(f318(f224(a911),f2(a911)),x34021),x34021)
% 109.14/108.83 [3408]E(f318(f318(f3(a911),f2(a911)),x34081),f2(a911))
% 109.14/108.83 [3409]E(f318(f318(f74(a911),f2(a911)),x34091),f2(a911))
% 109.14/108.83 [3410]E(f318(f318(f30(a1),f2(a1)),x34101),f2(a1))
% 109.14/108.83 [3411]E(f318(f318(f223(a911),f2(a911)),x34111),f2(a911))
% 109.14/108.83 [3421]E(f119(x34211,f318(f72(a1),x34211)),f123(a1,x34211))
% 109.14/108.83 [3426]E(f318(f293(a911,f2(a911)),x34261),f318(f273(a911),x34261))
% 109.14/108.83 [3427]E(f318(f318(f74(a1),a88),x34271),f318(f72(a1),x34271))
% 109.14/108.83 [3434]E(f318(a95,f318(f94(a1),x34341)),f318(f94(a911),x34341))
% 109.14/108.83 [3435]E(f318(a95,f318(f94(a1),x34351)),f318(f94(a911),x34351))
% 109.14/108.83 [3436]E(f318(a22,f318(f94(a90),x34361)),f318(f94(a911),x34361))
% 109.14/108.83 [3437]E(f318(f29(a911),f318(f292(a911),x34371)),f318(a103,x34371))
% 109.14/108.83 [3446]E(f318(f318(f73(a911),f71(a911)),x34461),f318(a103,x34461))
% 109.14/108.83 [3450]E(f318(f93(a1),f318(f91(a1),x34501)),f318(f91(a1),x34501))
% 109.14/108.83 [3451]E(f318(f69(a1),f318(f91(a1),x34511)),f318(f91(a1),x34511))
% 109.14/108.83 [3455]E(f318(f29(x34551),f179(f918(x34551,a909))),f2(a911))
% 109.14/108.83 [3457]E(f318(f318(f30(a911),x34571),f318(a103,f2(a911))),x34571)
% 109.14/108.83 [3466]E(f39(a911,x34661,f318(a103,f2(a911))),f2(a911))
% 109.14/108.83 [3467]E(f39(a1,x34671,f318(f94(a1),a88)),f2(a1))
% 109.14/108.83 [3474]E(f318(f318(f73(a1),a88),x34741),f318(f318(f73(a1),x34741),a88))
% 109.14/108.83 [3481]E(f318(f318(f30(a1),x34811),f318(f94(a1),a88)),f318(f72(a1),x34811))
% 109.14/108.83 [3485]E(f130(a911,f318(f293(a911,x34851),f2(a911))),f104(a911))
% 109.14/108.83 [3486]E(f318(f318(f73(a1),x34861),f71(a1)),f318(f318(f3(a1),x34861),a88))
% 109.14/108.83 [3487]E(f318(f318(f3(a1),x34871),f71(a1)),f318(f318(f73(a1),x34871),a88))
% 109.14/108.83 [3491]P1(f318(f318(f225(a911),x34911),x34911))
% 109.14/108.83 [3492]P1(f318(f318(f225(a1),x34921),x34921))
% 109.14/108.83 [3493]P1(f318(f318(f278(a911),x34931),x34931))
% 109.14/108.83 [3498]E(f318(f72(a1),f318(f94(a1),x34981)),f318(f94(a1),f318(f72(a1),x34981)))
% 109.14/108.83 [3499]P1(f318(f55(a911),f318(f273(a911),x34991)))
% 109.14/108.83 [3500]P1(f318(f55(a911),f318(f292(a911),x35001)))
% 109.14/108.83 [3507]E(f152(x35071,f233(f918(x35071,a909))),f233(f918(f912(x35071),a909)))
% 109.14/108.83 [3511]P1(f318(f318(f225(a911),f2(a911)),x35111))
% 109.14/108.83 [3512]P1(f318(f318(f225(a911),f2(a911)),x35121))
% 109.14/108.83 [3522]E(f318(f318(f73(a911),f102(x35221)),f318(a103,f2(a911))),f102(f318(a103,x35221)))
% 109.14/108.83 [3523]E(f318(f253(x35231),f318(f18(a909,x35231),a178)),f233(f918(x35231,a909)))
% 109.14/108.83 [3524]E(f318(f253(x35241),f318(f18(a909,x35241),a230)),f179(f918(x35241,a909)))
% 109.14/108.83 [3527]E(f318(f318(f300(a911),x35271),f318(f273(a911),x35271)),f318(f273(a911),f318(a103,x35271)))
% 109.14/108.83 [3540]E(f318(f318(f73(a1),f71(a1)),f318(f91(a1),x35401)),f318(f91(a1),f318(a103,x35401)))
% 109.14/108.83 [3542]E(f318(f318(f142(f912(x35421)),f104(x35421)),f104(f912(x35421))),f48(x35421,f104(x35421)))
% 109.14/108.83 [3562]E(f179(f918(f917(x35621,x35621),a909)),f254(x35621,f179(f918(x35621,a909))))
% 109.14/108.83 [3563]E(f318(f299(x35631),f233(f918(x35631,a909))),f233(f918(f918(x35631,a909),a909)))
% 109.14/108.83 [3564]E(f318(f72(f918(x35641,a909)),f233(f918(x35641,a909))),f179(f918(x35641,a909)))
% 109.14/108.83 [3565]E(f318(f72(f918(x35651,a909)),f179(f918(x35651,a909))),f233(f918(x35651,a909)))
% 109.14/108.83 [3566]P1(f318(f55(x35661),f179(f918(x35661,a909))))
% 109.14/108.83 [3567]P1(f318(f55(x35671),f179(f918(x35671,a909))))
% 109.14/108.83 [3569]E(f318(f293(a911,x35691),f318(a103,x35691)),f318(f318(f300(a911),x35691),f179(f918(a911,a909))))
% 109.14/108.83 [3570]E(f78(f917(a911,a911),f42(x35701,f2(a911))),f318(f318(f243(a911,a911),f2(a911)),x35701))
% 109.14/108.83 [3583]E(f318(f318(f300(a911),f318(a103,x35831)),f318(f292(a911),x35831)),f318(f292(a911),f318(a103,x35831)))
% 109.14/108.83 [3587]P39(x35871,f179(f918(f917(x35871,x35871),a909)))
% 109.14/108.83 [3588]P41(x35881,f179(f918(f917(x35881,x35881),a909)))
% 109.14/108.83 [3590]P1(f318(f318(f225(a1),f2(a1)),f318(f91(a1),x35901)))
% 109.14/108.83 [3591]P1(f318(f318(f225(a1),f2(a1)),f318(f91(a1),x35911)))
% 109.14/108.83 [3598]E(f318(f318(f73(a911),f318(f180(a911),x35981)),f318(a103,f2(a911))),f318(f180(a911),f318(a103,x35981)))
% 109.14/108.83 [3643]P1(f318(f318(f320(a911),f575(x36431)),f233(f918(a911,a909))))
% 109.14/108.83 [3645]E(f318(f301(x36451,x36451,f25(x36451)),f233(f918(x36451,a909))),f233(f918(x36451,a909)))
% 109.14/108.83 [3700]P43(f318(f301(a911,a1,f91(a1)),x37001))
% 109.14/108.83 [3737]P56(x37371,f179(f918(x37371,a909)),f179(f918(f917(x37371,x37371),a909)))
% 109.14/108.83 [3755]E(f318(f318(f243(a1,a1),f318(f94(a1),a88)),f318(f318(f3(a1),x37551),f71(a1))),f44(f318(f94(a1),a88),x37551))
% 109.14/108.83 [3756]P1(f318(f318(f320(a911),f318(a22,x37561)),f233(f918(a911,a909))))
% 109.14/108.83 [3808]P63(x38081,f318(f18(f918(x38081,a909),x38081),f318(f18(a909,x38081),a230)))
% 109.14/108.83 [3821]E(f281(a911,f278(a911),x38211,x38211),f318(f318(f300(a911),x38211),f179(f918(a911,a909))))
% 109.14/108.83 [3989]E(f318(f133(f912(x39891),f912(x39891),f125(x39891),f104(x39891)),f104(f912(x39891))),f104(x39891))
% 109.14/108.83 [4007]P1(f318(f318(f320(f918(f917(a911,a911),a909)),f319(x40071)),a89))
% 109.14/108.83 [4030]P1(f318(f318(f320(f918(f917(a911,a911),a909)),f318(a97,x40301)),a89))
% 109.14/108.83 [4157]P25(x41571,f918(x41571,a909),f318(f318(f9(x41571,f918(x41571,a909),f918(x41571,a909)),f300(x41571)),f179(f918(x41571,a909))),f233(f918(x41571,a909)))
% 109.14/108.83 [4658]~E(f318(a5,f318(a103,f318(a22,x46581))),f2(a90))
% 109.14/108.83 [4659]~E(f318(a5,f318(a103,f318(a22,x46591))),f2(a90))
% 109.14/108.83 [4665]~P1(f318(a184,f318(f91(a1),x46651)))
% 109.14/108.83 [4667]~P1(f318(f318(f226(a911),x46671),x46671))
% 109.14/108.83 [4668]~P1(f318(f318(f226(a911),x46681),x46681))
% 109.14/108.83 [4676]~P1(f318(f318(f225(a911),f318(a103,x46761)),x46761))
% 109.14/108.83 [3514]E(f318(a95,f318(f72(a1),f318(f91(a1),x35141))),f2(a911))
% 109.14/108.83 [3517]E(f318(f318(f73(a1),f318(f72(a1),x35171)),x35171),f2(a1))
% 109.14/108.83 [3521]E(f318(f29(a1),f318(f293(a1,f2(a1)),x35211)),f318(a95,x35211))
% 109.14/108.83 [3532]E(f318(f318(f235(a911),f318(a103,f2(a911))),x35321),f318(a103,f2(a911)))
% 109.14/108.83 [3628]E(f318(f272(x36281),f179(f918(f917(x36281,x36281),a909))),f179(f918(x36281,a909)))
% 109.14/108.83 [3630]P1(f318(f55(a1),f318(f293(a1,f2(a1)),x36301)))
% 109.14/108.83 [3635]E(f32(f918(x36351,a909),f233(f918(f918(x36351,a909),a909))),f179(f918(x36351,a909)))
% 109.14/108.83 [3636]E(f32(f918(x36361,a909),f179(f918(f918(x36361,a909),a909))),f233(f918(x36361,a909)))
% 109.14/108.83 [3637]E(f31(f918(x36371,a909),f233(f918(f918(x36371,a909),a909))),f233(f918(x36371,a909)))
% 109.14/108.83 [3638]E(f31(f918(x36381,a909),f179(f918(f918(x36381,a909),a909))),f179(f918(x36381,a909)))
% 109.14/108.83 [3642]P1(f318(f318(f278(a911),f318(a103,f2(a911))),x36421))
% 109.14/108.83 [3682]E(f318(f318(f300(f912(x36821)),f104(x36821)),f179(f918(f912(x36821),a909))),f152(x36821,f179(f918(x36821,a909))))
% 109.14/108.83 [3683]E(f318(f318(f300(f912(x36831)),f104(x36831)),f179(f918(f912(x36831),a909))),f153(x36831,f104(f918(x36831,a909))))
% 109.14/108.83 [3720]E(f318(f318(f73(a911),f6(x37201)),f318(a103,f2(a911))),f6(f318(a5,f318(a103,f318(a22,x37201)))))
% 109.14/108.83 [3746]E(f318(f29(a1),f318(f301(a911,a1,f91(a1)),x37461)),f318(f29(a911),x37461))
% 109.14/108.83 [3749]P1(f318(f318(f225(a911),x37491),f318(f318(f74(a911),x37491),x37491)))
% 109.14/108.83 [3786]E(f318(f301(a1,a911,a95),f294(a1,f2(a1),f318(f91(a1),x37861))),f318(f292(a911),x37861))
% 109.14/108.83 [3803]E(f318(f318(f30(a911),f318(a103,f2(a911))),f318(f94(a911),x38031)),f318(a95,f318(f318(f30(a1),f71(a1)),f318(f94(a1),x38031))))
% 109.14/108.83 [3805]E(f318(f163(a911),f130(a911,f318(f293(a911,f2(a911)),f318(a103,x38051)))),f318(f292(a911),x38051))
% 109.14/108.83 [3806]E(f318(f318(f73(a911),f318(f180(a90),x38061)),f318(a103,f2(a911))),f318(f180(a90),f318(a5,f318(a103,f318(a22,x38061)))))
% 109.14/108.83 [3826]P40(x38261,f298(x38261,f179(f918(f917(x38261,x38261),a909))))
% 109.14/108.83 [3827]P41(x38271,f298(x38271,f179(f918(f917(x38271,x38271),a909))))
% 109.14/108.83 [3828]P55(x38281,f298(x38281,f179(f918(f917(x38281,x38281),a909))))
% 109.14/108.83 [3829]E(f318(f301(a1,a911,a95),f318(f301(a911,a1,f91(a1)),x38291)),x38291)
% 109.14/108.83 [3859]E(f318(f318(f300(a911),f2(a911)),f318(f301(a911,a911,a103),f318(f273(a911),x38591))),f318(f273(a911),f318(a103,x38591)))
% 109.14/108.83 [3865]P58(x38651,x38651,f298(x38651,f179(f918(f917(x38651,x38651),a909))))
% 109.14/108.83 [3871]P1(f318(a184,f318(f72(a1),f318(f91(a1),f318(a103,x38711)))))
% 109.14/108.83 [3881]E(f318(f318(f3(f918(a911,a909)),f318(f274(a911),x38811)),f318(f318(f300(a911),x38811),f179(f918(a911,a909)))),f318(f274(a911),f318(a103,x38811)))
% 109.14/108.83 [3895]P56(x38951,f233(f918(x38951,a909)),f298(x38951,f179(f918(f917(x38951,x38951),a909))))
% 109.14/108.83 [3906]E(f318(f318(f300(f918(x39061,a909)),f179(f918(x39061,a909))),f179(f918(f918(x39061,a909),a909))),f318(f299(x39061),f179(f918(x39061,a909))))
% 109.14/108.83 [3937]E(f318(f318(f3(f918(a911,a909)),f318(f295(a911),x39371)),f318(f318(f300(a911),f318(a103,x39371)),f179(f918(a911,a909)))),f318(f295(a911),f318(a103,x39371)))
% 109.14/108.83 [4406]P14(x44061,f918(x44061,a909),f318(f318(f10(f918(x44061,a909),f918(f918(x44061,a909),f918(x44061,a909)),x44061),f318(f9(f918(x44061,a909),f918(x44061,a909),f918(x44061,a909)),f3(f918(x44061,a909)))),f318(f318(f9(x44061,f918(x44061,a909),f918(x44061,a909)),f300(x44061)),f179(f918(x44061,a909)))))
% 109.14/108.83 [4493]E(f318(f253(f917(a1,a1)),f318(f248(a1,a1,a909),f318(f318(f10(f918(a1,a909),f918(a1,a909),a1),f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),x44931)))),f226(a1)))),f98(x44931))
% 109.14/108.83 [4532]E(f318(f253(f917(a1,a1)),f318(f248(a1,a1,a909),f318(f318(f20(a1,f918(a1,a909),f918(a1,a909)),f318(f318(f10(f918(a909,a909),f918(f918(a1,a909),f918(a1,a909)),a1),f10(a909,a909,a1)),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),x45321)))),f226(a1)))),f96(x45321))
% 109.14/108.83 [4595]E(f318(f253(f917(f918(x45951,a909),f918(x45951,a909))),f318(f248(f918(x45951,a909),f918(x45951,a909),a909),f318(f318(f9(f918(x45951,a909),f918(f918(x45951,a909),a909),f918(f918(x45951,a909),a909)),f318(f318(f10(f918(f918(x45951,a909),f918(a909,a909)),f918(f918(f918(x45951,a909),a909),f918(f918(x45951,a909),a909)),f918(x45951,a909)),f20(f918(x45951,a909),a909,a909)),f318(f318(f10(f918(f918(x45951,a909),a909),f918(f918(x45951,a909),f918(a909,a909)),f918(x45951,a909)),f318(f10(a909,f918(a909,a909),f918(x45951,a909)),a316)),f226(f918(x45951,a909))))),f55(x45951)))),f305(x45951))
% 109.14/108.83 [4680]~P1(f318(f55(f912(x46801)),f233(f918(f912(x46801),a909))))
% 109.14/108.83 [4690]~P1(f318(f318(f225(a1),f2(a1)),f318(f72(a1),f318(f91(a1),f318(a103,x46901)))))
% 109.14/108.83 [3662]E(f318(f318(f3(a1),f318(f318(f73(a1),x36621),a88)),a88),x36621)
% 109.14/108.83 [3675]E(f318(f163(a911),f130(a911,f318(f293(a911,f2(a911)),x36751))),f318(f273(a911),x36751))
% 109.14/108.83 [3872]E(f318(f275(x38721,x38721),f298(x38721,f179(f918(f917(x38721,x38721),a909)))),f233(f918(x38721,a909)))
% 109.14/108.83 [3873]E(f318(f255(x38731,x38731),f298(x38731,f179(f918(f917(x38731,x38731),a909)))),f233(f918(x38731,a909)))
% 109.14/108.83 [3964]E(f318(f277(x39641,x39641),f298(x39641,f179(f918(f917(x39641,x39641),a909)))),f298(x39641,f179(f918(f917(x39641,x39641),a909))))
% 109.14/108.83 [4008]P1(f318(f318(f225(a911),x40081),f318(f318(f74(a911),x40081),f318(f318(f74(a911),x40081),x40081))))
% 109.14/108.83 [4093]E(f318(f318(f280(x40931,x40931,x40931),f179(f918(f917(x40931,x40931),a909))),f298(x40931,f179(f918(f917(x40931,x40931),a909)))),f179(f918(f917(x40931,x40931),a909)))
% 109.14/108.83 [4270]P1(f318(f55(a911),f318(f253(a911),f318(f318(f9(a911,a911,a909),f225(a911)),x42701))))
% 109.14/108.83 [4271]P1(f318(f55(a911),f318(f253(a911),f318(f318(f9(a911,a911,a909),f226(a911)),x42711))))
% 109.14/108.83 [4546]E(f318(f253(f917(x45461,x45461)),f318(f318(f10(f918(x45461,a909),a909,f917(x45461,x45461)),f79(x45461)),f318(f318(f9(f917(x45461,x45461),f918(x45461,f917(x45461,x45461)),f918(x45461,a909)),f318(f318(f10(f918(f917(x45461,x45461),a909),f918(f918(x45461,f917(x45461,x45461)),f918(x45461,a909)),f917(x45461,x45461)),f10(f917(x45461,x45461),a909,x45461)),a315)),f318(f318(f20(x45461,x45461,f917(x45461,x45461)),f243(x45461,x45461)),f7(x45461))))),f298(x45461,f179(f918(f917(x45461,x45461),a909))))
% 109.14/108.83 [4682]~E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x46821)),x46821),a76)
% 109.14/108.83 [4683]~E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x46831)),x46831),a76)
% 109.14/108.83 [4684]~E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x46841)),x46841),f2(a1))
% 109.14/108.83 [4137]E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f3(a1),a88),x41371))),f318(f318(f3(a1),a88),x41371)),f318(f318(f3(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x41371)),x41371)))
% 109.14/108.83 [4251]E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f72(a1),x42511)),a88))),f318(f318(f73(a1),f318(f72(a1),x42511)),a88)),f318(f72(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x42511)),x42511)))
% 109.14/108.83 [4321]E(f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x43211),f2(a911))),f179(f918(f917(a911,a911),a909))))),f318(f91(a1),x43211))
% 109.14/108.83 [4332]E(f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),f323(x43321)),f515(x43321))),f179(f918(f917(a911,a911),a909))))),x43321)
% 109.14/108.83 [4338]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f3(a1),a88),x43381))),f318(f318(f3(a1),a88),x43381))),a88),f318(f318(f3(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43381)),x43381)))
% 109.14/108.83 [4370]E(f318(f253(a1),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),x43701)),f318(f301(a911,a1,f91(a1)),f318(f253(a911),f318(f318(f10(a1,a909,a911),x43701),f91(a1)))))
% 109.14/108.83 [4414]P43(f318(f253(a1),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),x44141)))
% 109.14/108.83 [4435]P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),x44351),f179(f918(f917(a911,a911),a909)))),a65))
% 109.14/108.83 [4440]E(f318(f301(a1,a911,a95),f318(f253(a1),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),f318(f318(f10(a911,a909,a1),x44401),a95)))),f318(f253(a911),x44401))
% 109.14/108.83 [4609]E(f303(a911,f318(f318(f33(f917(a911,a911),f918(a911,a909)),f318(a97,x46091)),f318(f248(a911,a911,f918(a911,a909)),f318(f318(f9(a911,f918(a911,a909),f918(a911,f918(a911,a909))),f318(f318(f10(f918(a911,f918(f918(a911,a909),f918(a911,a909))),f918(f918(a911,a909),f918(a911,f918(a911,a909))),a911),f9(a911,f918(a911,a909),f918(a911,a909))),f318(f318(f10(f918(a911,a911),f918(a911,f918(f918(a911,a909),f918(a911,a909))),a911),f318(f10(a911,f918(f918(a911,a909),f918(a911,a909)),a911),f300(a911))),f3(a911)))),f179(f918(a911,a909)))))),f318(a95,x46091))
% 109.14/108.83 [4110]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x41101)),x41101)),a88),f318(f318(f73(a1),x41101),x41101))
% 109.14/108.83 [4355]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f3(a1),x43551),a88))),f318(f318(f3(a1),x43551),a88))),a88),f318(f318(f3(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43551)),x43551)),a88))
% 109.14/108.83 [4692]~E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x46921)),x46921)),a88),a88)
% 109.14/108.83 [4693]~E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x46931)),x46931)),a88),a88)
% 109.14/108.83 [4317]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43171)),x43171)),a88)),f318(f318(f81(a911,a911),f318(f94(a911),x43171)),f318(f318(f20(a911,a911,a911),f73(a911)),f7(a911))))
% 109.14/108.83 [4323]E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f3(a1),a88),x43231))),f318(f318(f3(a1),a88),x43231)),f318(f318(f3(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43231)),x43231)),a88)))
% 109.14/108.83 [4353]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f72(a1),x43531))),f318(f72(a1),x43531))),a88),f318(f72(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43531)),x43531)),a88)))
% 109.14/108.83 [4379]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f3(a1),a76),x43791))),f318(f318(f3(a1),a76),x43791))),a88),f318(f318(f3(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43791)),x43791)),a88)))
% 109.14/108.83 [4623]E(f318(a82,f318(f318(f33(f917(a911,a911),f918(f917(a911,a911),a909)),f318(a97,x46231)),f318(f248(a911,a911,f918(f917(a911,a911),a909)),f318(f318(f10(f918(a911,f918(f917(a911,a911),a909)),f918(a911,f918(f917(a911,a911),a909)),a911),f318(f10(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909),a911),f276(f917(a911,a911),f917(a911,a911),a99))),f318(f318(f9(a911,f918(f917(a911,a911),a909),f918(a911,f918(f917(a911,a911),a909))),f318(f318(f10(f918(a911,f918(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f918(f918(f917(a911,a911),a909),f918(a911,f918(f917(a911,a911),a909))),a911),f9(a911,f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f10(f918(a911,f917(a911,a911)),f918(a911,f918(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),a911),f318(f10(f917(a911,a911),f918(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),a911),f300(f917(a911,a911)))),f318(f9(a911,a911,f917(a911,a911)),f243(a911,a911))))),f179(f918(f917(a911,a911),a909))))))),f318(f72(a1),x46231))
% 109.14/108.83 [4371]E(f318(f318(f3(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43711)),x43711)),a88)),a88),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43711)),x43711))
% 109.14/108.83 [4382]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43821)),x43821)),a88)),a88),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),x43821),a88))),f318(f318(f73(a1),x43821),a88)))
% 109.14/108.83 [4515]E(f318(f318(f73(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),x45151),f318(a103,f318(a103,f318(a103,x45151))))
% 109.14/108.83 [4555]E(f318(f318(f73(a911),x45551),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(a103,f318(a103,x45551)))
% 109.14/108.83 [4556]E(f318(f318(f74(a911),x45561),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f318(f73(a911),x45561),x45561))
% 109.14/108.83 [4557]E(f318(f318(f30(a911),f318(f318(f73(a911),x45571),x45571)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x45571)
% 109.14/108.83 [4589]E(f39(a911,f318(a103,f318(a103,x45891)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f39(a911,x45891,f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.83 [4586]E(f318(f318(f73(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x45861),f318(a103,f318(a103,x45861)))
% 109.14/108.83 [4587]E(f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x45871),f318(f318(f73(a911),x45871),x45871))
% 109.14/108.83 [4599]E(f318(f318(f30(a911),f318(a103,f318(a103,x45991))),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(a103,f318(f318(f30(a911),x45991),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.83 [4630]E(f318(f248(a1,a1,f917(a1,a1)),f318(f318(f20(a1,f918(a1,f917(a1,a1)),f918(a1,f917(a1,a1))),f318(f318(f10(f918(a1,f918(f917(a1,a1),f917(a1,a1))),f918(f918(a1,f917(a1,a1)),f918(a1,f917(a1,a1))),a1),f20(a1,f917(a1,a1),f917(a1,a1))),f318(f318(f10(f918(a1,f917(a1,a1)),f918(a1,f918(f917(a1,a1),f917(a1,a1))),a1),f318(f20(a1,f917(a1,a1),f918(f917(a1,a1),f917(a1,a1))),f318(f318(f10(a909,f918(f917(a1,a1),f918(f917(a1,a1),f917(a1,a1))),a1),f85(f917(a1,a1))),f318(f318(f10(a1,a909,a1),f318(f225(a1),f2(a1))),f318(f318(f9(a1,a1,a1),f3(a1)),x46301))))),f318(f318(f9(a1,f918(a1,a1),f918(a1,f917(a1,a1))),f318(f318(f10(f918(a1,f917(a1,a1)),f918(f918(a1,a1),f918(a1,f917(a1,a1))),a1),f10(a1,f917(a1,a1),a1)),f318(f318(f10(a1,f918(a1,f917(a1,a1)),a1),f243(a1,a1)),f318(f318(f9(a1,a1,a1),f318(f318(f10(a1,f918(a1,a1),a1),f73(a1)),f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))),f71(a1))))),f318(f318(f9(a1,a1,a1),f3(a1)),x46301))))),f318(f318(f10(a1,f918(a1,f917(a1,a1)),a1),f243(a1,a1)),f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))),f37(x46301))
% 109.14/108.83 [3341]P112(f917(x33411,x33412))
% 109.14/108.83 [3342]P112(f919(x33421,x33422))
% 109.14/108.83 [3343]P112(f916(x33431,x33432))
% 109.14/108.83 [3360]P13(a1,f169(x33601,x33602))
% 109.14/108.83 [3361]P39(x33611,f144(x33611,x33612))
% 109.14/108.83 [3362]P40(x33621,f254(x33621,x33622))
% 109.14/108.83 [3363]P40(x33631,f298(x33631,x33632))
% 109.14/108.83 [3364]P41(x33641,f254(x33641,x33642))
% 109.14/108.83 [3365]P55(x33651,f254(x33651,x33652))
% 109.14/108.83 [3428]P33(x34281,x34282,f104(x34281))
% 109.14/108.83 [3461]P56(x34611,x34612,f254(x34611,x34612))
% 109.14/108.83 [3462]P58(x34621,x34621,f254(x34621,x34622))
% 109.14/108.83 [3723]P25(x37231,x37231,f7(x37231),x37232)
% 109.14/108.83 [3724]P25(x37241,x37241,f25(x37241),x37242)
% 109.14/108.83 [3732]P34(x37321,x37322,f104(x37321),f104(x37321))
% 109.14/108.83 [3733]P34(x37331,x37332,f104(x37331),f104(x37331))
% 109.14/108.83 [3740]P25(f912(x37401),f912(x37401),f159(x37401),x37402)
% 109.14/108.83 [4135]P26(x41351,x41351,f25(x41351),x41352,x41352)
% 109.14/108.83 [4654]~P35(x46541,x46542,f104(x46541))
% 109.14/108.83 [4655]~P37(x46551,x46552,f104(x46551))
% 109.14/108.83 [3327]E(f318(f7(x33271),x33272),x33272)
% 109.14/108.83 [3328]E(f318(f253(x33281),x33282),x33282)
% 109.14/108.83 [3329]E(f318(f25(x33291),x33292),x33292)
% 109.14/108.83 [3330]E(f318(f25(x33301),x33302),x33302)
% 109.14/108.83 [3340]E(f318(f182(x33401),x33402),f106(x33401))
% 109.14/108.83 [3358]E(f78(x33581,f318(a315,x33582)),x33582)
% 109.14/108.83 [3359]E(f83(x33591,f318(a315,x33592)),x33592)
% 109.14/108.83 [3380]E(f318(f116(x33801,x33802),f110(x33801)),f2(a911))
% 109.14/108.83 [3384]E(f318(f127(x33841,x33842),f104(x33841)),f104(x33841))
% 109.14/108.83 [3404]E(f298(x34041,f298(x34041,x34042)),f298(x34041,x34042))
% 109.14/108.83 [3405]E(f143(x34051,f143(x34051,x34052)),f143(x34051,x34052))
% 109.14/108.83 [3423]E(f318(f318(f125(x34231),x34232),f104(x34231)),x34232)
% 109.14/108.83 [3429]E(f164(x34291,x34292,f104(x34291)),x34292)
% 109.14/108.83 [3430]E(f164(x34301,f104(x34301),x34302),x34302)
% 109.14/108.83 [3431]E(f107(x34311,f110(x34311),x34312),x34312)
% 109.14/108.83 [3432]E(f160(x34321,f2(a911),x34322),f104(x34321))
% 109.14/108.83 [3438]E(f318(f318(f166(x34381),x34382),f104(x34381)),f104(x34381))
% 109.14/108.83 [3439]E(f318(f318(f129(x34391),x34392),f104(x34391)),f104(x34391))
% 109.14/108.83 [3441]E(f146(x34411,x34412,f104(x34411)),f2(a911))
% 109.14/108.83 [3443]E(f161(x34431,x34432,f104(x34431)),f104(x34431))
% 109.14/108.83 [3444]E(f168(x34441,x34442,f104(x34441)),f104(x34441))
% 109.14/108.83 [3445]E(f167(x34451,f104(x34451),x34452),f104(x34451))
% 109.14/108.83 [3449]E(f318(f163(x34491),f143(x34491,x34492)),f318(f163(x34491),x34492))
% 109.14/108.83 [3452]E(f318(f275(x34521,x34521),f254(x34521,x34522)),x34522)
% 109.14/108.83 [3453]E(f318(f255(x34531,x34531),f254(x34531,x34532)),x34532)
% 109.14/108.83 [3460]E(f318(f277(x34601,x34601),f254(x34601,x34602)),f254(x34601,x34602))
% 109.14/108.83 [3473]E(f298(f912(x34731),f148(x34731,x34732)),f149(x34731,f298(x34731,x34732)))
% 109.14/108.83 [3475]P1(f318(f128(a1),f169(x34751,x34752)))
% 109.14/108.83 [3483]E(f318(f275(x34831,x34831),f298(x34831,x34832)),f233(f918(x34831,a909)))
% 109.14/108.83 [3484]E(f318(f255(x34841,x34841),f298(x34841,x34842)),f233(f918(x34841,a909)))
% 109.14/108.83 [3488]P1(f318(f128(x34881),f143(x34881,x34882)))
% 109.14/108.83 [3489]P1(f318(f151(x34891,x34892),f104(x34891)))
% 109.14/108.83 [3490]P1(f318(f151(x34901,x34902),f104(x34901)))
% 109.14/108.83 [3495]E(f318(f163(a1),f169(x34951,x34952)),f294(a1,x34951,x34952))
% 109.14/108.83 [3496]E(f318(f163(a1),f169(x34961,x34962)),f294(a1,x34961,x34962))
% 109.14/108.83 [3510]P59(x35101,f179(f918(x35101,a909)),x35102)
% 109.14/108.83 [3515]E(f318(f247(a1,a1),f40(x35151,x35152)),f39(a1,x35151,x35152))
% 109.14/108.83 [3516]E(f318(f293(a911,x35161),f318(a103,x35162)),f294(a911,x35161,x35162))
% 109.14/108.83 [3531]E(f318(f318(f142(x35311),x35312),f104(x35311)),f131(x35311,x35312,f104(x35311)))
% 109.14/108.83 [3544]E(f294(a911,f318(a103,x35441),x35442),f296(a911,x35441,x35442))
% 109.14/108.83 [3547]P56(x35471,f233(f918(x35471,a909)),f298(x35471,x35472))
% 109.14/108.83 [3609]E(f318(f318(f3(a911),x36091),f318(a103,x36092)),f318(f29(a911),f297(a911,x36092,x36091)))
% 109.14/108.83 [3663]E(f157(x36631,x36632,f104(x36631)),f318(f318(f243(f912(x36631),f912(x36631)),f104(x36631)),f104(x36631)))
% 109.14/108.83 [3680]E(f318(f248(x36801,x36802,f917(x36801,x36802)),f243(x36801,x36802)),f25(f917(x36801,x36802)))
% 109.14/108.83 [3684]P1(f318(f318(f320(f912(x36841)),f104(x36841)),f152(x36841,x36842)))
% 109.14/108.83 [3685]E(f318(f180(f912(x36851)),f105(x36851,x36852)),f318(f318(f3(a911),f318(f180(f912(x36851)),x36852)),f71(a911)))
% 109.14/108.83 [3694]P1(f318(f55(a911),f294(a911,x36941,x36942)))
% 109.14/108.83 [3695]P1(f318(f55(a911),f296(a911,x36951,x36952)))
% 109.14/108.83 [3696]P1(f318(f55(a911),f297(a911,x36961,x36962)))
% 109.14/108.83 [3697]P1(f318(f55(a1),f294(a1,x36971,x36972)))
% 109.14/108.83 [3698]P1(f318(f55(a1),f296(a1,x36981,x36982)))
% 109.14/108.83 [3699]P1(f318(f55(a1),f297(a1,x36991,x36992)))
% 109.14/108.83 [3802]E(f318(f301(a911,a911,a103),f294(a911,x38021,x38022)),f294(a911,f318(a103,x38021),f318(a103,x38022)))
% 109.14/108.83 [3823]E(f318(f318(f280(x38231,x38231,x38231),f298(x38231,x38232)),f298(x38231,x38232)),f298(x38231,x38232))
% 109.14/108.83 [3857]E(f318(f318(f243(a1,a1),f318(f318(f30(a1),x38571),x38572)),f39(a1,x38571,x38572)),f40(x38571,x38572))
% 109.14/108.83 [3858]E(f318(f318(f243(a90,a90),f318(f318(f30(a90),x38581),x38582)),f39(a90,x38581,x38582)),f23(x38581,x38582))
% 109.14/108.83 [3885]E(f318(f318(f243(a911,a911),f318(f318(f30(a911),x38851),x38852)),f39(a911,x38851,x38852)),f78(f917(a911,a911),f42(x38851,x38852)))
% 109.14/108.83 [3929]P1(f318(f318(f226(a911),f318(f318(f3(a911),x39291),x39292)),f318(a103,x39291)))
% 109.14/108.83 [3981]P40(x39811,f318(f318(f280(x39811,x39811,x39811),x39812),f298(x39811,x39812)))
% 109.14/108.83 [4019]E(f318(f318(f129(x40191),f318(f180(f912(x40191)),f168(x40191,x40192,f104(x40191)))),f104(x40191)),f104(x40191))
% 109.14/108.83 [4029]E(f318(f318(f73(a1),f318(f318(f74(a1),x40291),f318(f318(f30(a1),x40292),x40291))),f39(a1,x40292,x40291)),x40292)
% 109.14/108.83 [4033]E(f318(f318(f33(a911,f918(f917(f912(x40331),f912(x40331)),a909)),f233(f918(a911,a909))),f134(x40331,x40332)),f136(x40331,x40332))
% 109.14/108.83 [4111]E(f318(f127(x41111,f318(f318(f10(a909,a909,x41111),a313),f318(a315,x41112))),f104(x41111)),f104(x41111))
% 109.14/108.83 [4247]P1(f318(f318(f320(f917(f912(x42471),f912(x42471))),f318(f318(f243(f912(x42471),f912(x42471)),f104(x42471)),f104(x42471))),f149(x42471,x42472)))
% 109.14/108.83 [4350]E(f244(x43501,x43501,x43501,a315,f244(x43501,x43501,x43501,x43502,a315)),x43502)
% 109.14/108.83 [4399]E(f249(x43991,x43991,x43992,x43992,f25(x43991),f25(x43992)),f25(f917(x43991,x43992)))
% 109.14/108.83 [4400]E(f249(x44001,x44001,x44002,x44002,f7(x44001),f7(x44002)),f25(f917(x44001,x44002)))
% 109.14/108.83 [4401]E(f249(x44011,x44011,x44012,x44012,f25(x44011),f25(x44012)),f25(f917(x44011,x44012)))
% 109.14/108.83 [4402]E(f249(x44021,x44021,x44022,x44022,f25(x44021),f25(x44022)),f25(f917(x44021,x44022)))
% 109.14/108.83 [3422]E(f318(f159(x34221),f318(f159(x34221),x34222)),x34222)
% 109.14/108.83 [3424]E(f318(f318(f129(x34241),f2(a911)),x34242),x34242)
% 109.14/108.83 [3440]E(f318(f318(f166(x34401),f2(a911)),x34402),f104(x34401))
% 109.14/108.83 [3447]E(f318(f318(f125(x34471),f104(x34471)),x34472),x34472)
% 109.14/108.83 [3456]E(f31(f918(x34561,a909),f318(f299(x34561),x34562)),x34562)
% 109.14/108.83 [3458]E(f318(f163(x34581),f318(f158(x34581),x34582)),f318(f163(x34581),x34582))
% 109.14/108.83 [3459]E(f318(f163(x34591),f318(f159(x34591),x34592)),f318(f163(x34591),x34592))
% 109.14/108.83 [3464]E(f318(f318(f3(a90),x34641),x34642),f318(f318(a4,x34641),x34642))
% 109.14/108.83 [3477]E(f318(f318(f73(a911),x34771),x34772),f318(f318(f73(a911),x34772),x34771))
% 109.14/108.83 [3478]E(f318(f318(f73(a1),x34781),x34782),f318(f318(f73(a1),x34782),x34781))
% 109.14/108.83 [3479]E(f318(f318(f74(a911),x34791),x34792),f318(f318(f74(a911),x34792),x34791))
% 109.14/108.83 [3480]E(f318(f318(f74(a1),x34801),x34802),f318(f318(f74(a1),x34802),x34801))
% 109.14/108.83 [3502]E(f318(f318(f174(x35021,x35021),f2(a911)),x35022),f25(x35021))
% 109.14/108.83 [3503]E(f318(f180(f912(x35031)),f318(f158(x35031),x35032)),f318(f180(f912(x35031)),x35032))
% 109.14/108.83 [3504]E(f318(f180(f912(x35041)),f318(f159(x35041),x35042)),f318(f180(f912(x35041)),x35042))
% 109.14/108.83 [3505]E(f167(x35051,x35052,f179(f918(a911,a909))),f104(x35051))
% 109.14/108.83 [3506]E(f318(f318(f145(x35061,x35061),f7(x35061)),x35062),x35062)
% 109.14/108.83 [3508]E(f318(f242(a1,a1),f40(x35081,x35082)),f318(f318(f30(a1),x35081),x35082))
% 109.14/108.83 [3525]E(f318(f180(f912(x35251)),f143(x35251,x35252)),f318(f29(x35251),f318(f163(x35251),x35252)))
% 109.14/108.83 [3526]E(f318(f272(x35261),f318(f277(x35261,x35261),x35262)),f318(f272(x35261),x35262))
% 109.14/108.83 [3530]P1(f318(f55(x35301),f318(f163(x35301),x35302)))
% 109.14/108.83 [3538]E(f318(f318(f73(a1),x35381),f318(f72(a1),x35382)),f318(f318(f3(a1),x35381),x35382))
% 109.14/108.83 [3539]E(f318(f318(f73(a1),x35391),f318(f72(a1),x35392)),f318(f318(f3(a1),x35391),x35392))
% 109.14/108.83 [3545]P24(x35451,x35452,f179(f918(f910(x35451),a909)))
% 109.14/108.83 [3546]P24(x35461,x35462,f179(f918(f910(x35461),a909)))
% 109.14/108.83 [3548]E(f318(f301(x35481,x35481,f7(x35481)),x35482),x35482)
% 109.14/108.83 [3549]E(f318(f301(x35491,x35491,f25(x35491)),x35492),x35492)
% 109.14/108.83 [3550]E(f318(f302(x35501,x35501,f7(x35501)),x35502),x35502)
% 109.14/108.83 [3551]E(f318(f302(x35511,x35511,f25(x35511)),x35512),x35512)
% 109.14/108.83 [3552]P1(f318(f233(f918(x35521,a909)),x35522))
% 109.14/108.83 [3554]E(f318(f29(a911),f318(f293(a911,x35541),x35542)),f318(f318(f3(a911),x35542),x35541))
% 109.14/108.83 [3555]E(f318(f293(a911,f318(a103,x35551)),x35552),f297(a911,x35551,x35552))
% 109.14/108.83 [3568]E(f318(f318(f300(x35681),x35682),f179(f918(x35681,a909))),f318(f253(x35681),f318(a315,x35682)))
% 109.14/108.83 [3573]E(f298(x35731,f318(f277(x35731,x35731),x35732)),f318(f277(x35731,x35731),f298(x35731,x35732)))
% 109.14/108.83 [3578]E(f318(f318(f73(a911),f318(a103,x35781)),x35782),f318(f318(f73(a911),x35781),f318(a103,x35782)))
% 109.14/108.83 [3579]E(f318(f318(f3(a911),f318(a103,x35791)),f318(a103,x35792)),f318(f318(f3(a911),x35791),x35792))
% 109.14/108.83 [3585]E(f49(x35851,f2(a911),x35852),f318(f318(f142(f912(x35851)),f104(x35851)),f104(f912(x35851))))
% 109.14/108.83 [3586]E(f318(f29(a911),f296(a911,x35861,x35862)),f318(f318(f3(a911),x35862),x35861))
% 109.14/108.83 [3595]P39(x35951,f318(f318(f279(a911,x35951),a231),x35952))
% 109.14/108.83 [3597]P13(a911,f130(a911,f318(f293(a911,x35971),x35972)))
% 109.14/108.83 [3599]P1(f318(f55(a911),f318(f293(a911,x35991),x35992)))
% 109.14/108.83 [3600]P1(f318(f55(a1),f318(f293(a1,x36001),x36002)))
% 109.14/108.83 [3603]E(f318(f277(f912(x36031),f912(x36031)),f148(x36031,x36032)),f148(x36031,f318(f277(x36031,x36031),x36032)))
% 109.14/108.83 [3605]E(f318(f293(a1,x36051),f318(f318(f73(a1),x36052),f71(a1))),f294(a1,x36051,x36052))
% 109.14/108.83 [3608]E(f318(f318(f30(a1),f318(f72(a1),x36081)),f318(f72(a1),x36082)),f318(f318(f30(a1),x36081),x36082))
% 109.14/108.83 [3616]E(f318(f318(f174(f917(x36161,x36161),a909),f71(a911)),x36162),x36162)
% 109.14/108.83 [3618]E(f318(f318(f101(f918(x36181,a909)),x36182),f179(f918(x36181,a909))),x36182)
% 109.14/108.83 [3619]E(f318(f318(f92(f918(x36191,a909)),x36192),f233(f918(x36191,a909))),x36192)
% 109.14/108.83 [3620]E(f318(f318(f3(f918(x36201,a909)),x36202),f179(f918(x36201,a909))),x36202)
% 109.14/108.83 [3621]E(f318(f242(a911,a911),f78(f917(a911,a911),f42(x36211,x36212))),f318(f318(f30(a911),x36211),x36212))
% 109.14/108.83 [3627]E(f294(a1,f318(f318(f73(a1),x36271),f71(a1)),x36272),f296(a1,x36271,x36272))
% 109.14/108.83 [3632]E(f318(f247(a911,a911),f78(f917(a911,a911),f42(x36321,x36322))),f39(a911,x36321,x36322))
% 109.14/108.83 [3640]P1(f318(f318(f320(x36401),x36402),f233(f918(x36401,a909))))
% 109.14/108.83 [3641]P1(f318(f318(f320(x36411),x36412),f233(f918(x36411,a909))))
% 109.14/108.83 [3646]E(f318(f318(f3(a911),f318(a103,x36461)),x36462),f318(f29(a911),f294(a911,x36462,x36461)))
% 109.14/108.83 [3671]E(f318(f318(f101(f918(x36711,a909)),x36712),f233(f918(x36711,a909))),f233(f918(x36711,a909)))
% 109.14/108.83 [3672]E(f318(f318(f92(f918(x36721,a909)),x36722),f179(f918(x36721,a909))),f179(f918(x36721,a909)))
% 109.14/108.83 [3673]E(f318(f318(f3(f918(x36731,a909)),x36732),f233(f918(x36731,a909))),f179(f918(x36731,a909)))
% 109.14/108.83 [3687]E(f39(a1,f318(f91(a1),x36871),f318(f91(a1),x36872)),f318(f91(a1),f39(a911,x36871,x36872)))
% 109.14/108.83 [3688]E(f39(a1,f318(f72(a1),x36881),f318(f72(a1),x36882)),f318(f72(a1),f39(a1,x36881,x36882)))
% 109.14/108.83 [3689]E(f39(a1,f318(f91(a1),x36891),f318(f91(a1),x36892)),f318(f91(a1),f39(a911,x36891,x36892)))
% 109.14/108.83 [3701]E(f318(f180(f912(x37011)),f318(f162(x37011),x37012)),f318(f318(f3(a911),f318(f180(f912(x37011)),x37012)),f71(a911)))
% 109.14/108.83 [3725]E(f318(f318(f30(a1),f39(a1,x37251,x37252)),x37252),f2(a1))
% 109.14/108.83 [3735]E(f318(a5,f39(a911,f318(a22,x37351),f318(a22,x37352))),f39(a90,x37351,x37352))
% 109.14/108.83 [3769]E(f318(a5,f318(f318(f3(a911),f318(a22,x37691)),f318(a22,x37692))),f318(f318(f3(a90),x37691),x37692))
% 109.14/108.83 [3770]E(f318(a5,f318(f318(f73(a911),f318(a22,x37701)),f318(a22,x37702))),f318(f318(f73(a90),x37701),x37702))
% 109.14/108.83 [3771]E(f318(a5,f318(f318(f74(a911),f318(a22,x37711)),f318(a22,x37712))),f318(f318(f74(a90),x37711),x37712))
% 109.14/108.83 [3772]E(f318(a5,f318(f318(f30(a911),f318(a22,x37721)),f318(a22,x37722))),f318(f318(f30(a90),x37721),x37722))
% 109.14/108.83 [3780]E(f318(f301(a911,a911,a103),f318(f293(a911,x37801),x37802)),f318(f293(a911,f318(a103,x37801)),f318(a103,x37802)))
% 109.14/108.83 [3807]P1(f318(f42(x38071,x38072),f78(f917(a911,a911),f42(x38071,x38072))))
% 109.14/108.83 [3832]E(f39(a911,f318(a103,f39(a911,x38321,x38322)),x38322),f39(a911,f318(a103,x38321),x38322))
% 109.14/108.83 [3844]E(f318(f318(f34(f918(x38441,a909),f918(x38441,a909)),x38442),f7(f918(x38441,a909))),f32(f918(x38441,a909),x38442))
% 109.14/108.83 [3845]E(f318(f318(f33(f918(x38451,a909),f918(x38451,a909)),x38452),f7(f918(x38451,a909))),f31(f918(x38451,a909),x38452))
% 109.14/108.83 [3846]E(f318(f301(f912(x38461),f918(x38461,a909),f163(x38461)),f318(f163(f912(x38461)),f48(x38461,x38462))),f318(f299(x38461),f318(f163(x38461),x38462)))
% 109.14/108.83 [3850]P1(f318(f318(f320(f918(x38501,a909)),x38502),f318(f299(x38501),x38502)))
% 109.14/108.83 [3856]E(f39(a1,f318(f72(a1),f39(a1,x38561,x38562)),x38562),f39(a1,f318(f72(a1),x38561),x38562))
% 109.14/108.83 [3867]P1(f318(f318(f225(f918(x38671,a909)),x38672),f233(f918(x38671,a909))))
% 109.14/108.83 [3869]E(f318(f318(f280(x38691,x38691,x38691),f298(x38691,x38692)),f298(x38691,f298(x38691,x38692))),f298(x38691,x38692))
% 109.14/108.83 [3870]E(f318(f318(f101(f918(x38701,a909)),f318(f255(x38701,x38701),x38702)),f318(f275(x38701,x38701),x38702)),f318(f272(x38701),x38702))
% 109.14/108.83 [3891]E(f304(x38911,x38912,f233(f918(x38911,a909)),f233(f918(x38912,a909))),f233(f918(f919(x38911,x38912),a909)))
% 109.14/108.83 [3938]P1(f318(f318(f225(a911),f39(a911,x39381,x39382)),x39381))
% 109.14/108.83 [3962]P1(f318(f318(f225(a1),f318(f72(a1),f318(f91(a1),x39621))),f318(f91(a1),x39622)))
% 109.14/108.83 [3986]P1(f318(f318(f320(f918(x39861,a909)),f179(f918(x39861,a909))),f318(f299(x39861),x39862)))
% 109.14/108.83 [3991]E(f298(x39911,f318(f318(f280(x39911,x39911,x39911),x39912),f298(x39911,x39912))),f298(x39911,x39912))
% 109.14/108.83 [3993]E(f318(f318(f280(x39931,x39931,x39931),f298(x39931,x39932)),x39932),f318(f318(f280(x39931,x39931,x39931),x39932),f298(x39931,x39932)))
% 109.14/108.83 [3994]E(f318(f318(f280(x39941,x39941,x39941),f298(x39941,x39942)),x39942),f318(f318(f280(x39941,x39941,x39941),x39942),f298(x39941,x39942)))
% 109.14/108.83 [3996]E(f318(a95,f318(f318(f73(a1),f318(f318(f3(a1),x39961),x39962)),f71(a1))),f318(f29(a1),f294(a1,x39962,x39961)))
% 109.14/108.83 [4009]E(f318(f275(x40091,x40091),f318(f318(f280(x40091,x40091,x40091),x40092),f298(x40091,x40092))),f318(f275(x40091,x40091),x40092))
% 109.14/108.83 [4010]E(f318(f255(x40101,x40101),f318(f318(f280(x40101,x40101,x40101),x40102),f298(x40101,x40102))),f318(f255(x40101,x40101),x40102))
% 109.14/108.83 [4028]E(f318(f133(f912(x40281),f912(x40281),f125(x40281),f104(x40281)),f160(f912(x40281),x40282,f104(x40281))),f104(x40281))
% 109.14/108.83 [4037]P25(a911,a911,f318(f318(f9(a911,a911,a911),f73(a911)),x40371),x40372)
% 109.14/108.83 [4039]P13(a911,f318(f159(a911),f318(f318(f145(f912(x40391),a911),f180(f912(x40391))),f170(x40391,x40392))))
% 109.14/108.83 [4066]P55(x40661,f318(f318(f101(f918(f917(x40661,x40661),a909)),x40662),f318(f277(x40661,x40661),x40662)))
% 109.14/108.83 [4067]P55(x40671,f318(f318(f92(f918(f917(x40671,x40671),a909)),x40672),f318(f277(x40671,x40671),x40672)))
% 109.14/108.83 [4078]P1(f318(f318(f226(a1),f318(f72(a1),f318(f91(a1),f318(a103,x40781)))),f318(f91(a1),x40782)))
% 109.14/108.83 [4124]E(f318(f133(f912(x41241),x41241,f318(f9(x41241,f912(x41241),f912(x41241)),f142(x41241)),f104(x41241)),x41242),f318(f159(x41241),x41242))
% 109.14/108.83 [4171]P1(f318(f318(f225(f918(f917(f912(x41711),f912(x41711)),a909)),f149(x41711,x41712)),f298(f912(x41711),f148(x41711,x41712))))
% 109.14/108.83 [4199]P1(f318(f42(x41991,x41992),f318(f318(f243(a911,a911),f318(f318(f30(a911),x41991),x41992)),f39(a911,x41991,x41992))))
% 109.14/108.83 [4211]P1(f318(f318(f225(f918(f917(f912(x42111),f912(x42111)),a909)),f148(x42111,f298(x42111,x42112))),f298(f912(x42111),f148(x42111,x42112))))
% 109.14/108.83 [4426]E(f318(f318(f250(f917(a90,a90),a90,f917(a90,a90),f917(x44261,f917(a90,a90))),f258(f318(f156(a90),f318(f318(f145(f917(a90,x44261),a90),f242(a90,x44261)),x44262)))),f318(f318(f10(x44261,f918(f917(a90,a90),f917(x44261,f917(a90,a90))),a90),f243(x44261,f917(a90,a90))),f259(x44261,x44262))),f257(x44261,x44262))
% 109.14/108.83 [4502]E(f214(a911,f917(x45021,f913(x45021)),f2(a911),f318(f248(x45021,f913(x45021),a911),f318(f18(f918(f913(x45021),a911),x45021),f318(f318(f9(f913(x45021),a911,a911),f318(f318(f10(a911,f918(a911,a911),f913(x45021)),f73(a911)),f180(f913(x45021)))),f71(a911)))),f318(f126(x45021),x45022)),f318(f180(f913(x45021)),x45022))
% 109.14/108.83 [4562]E(f39(a911,f318(f318(f73(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),x45621),f318(f94(a911),x45622)),f39(a911,f318(a103,f318(a103,f318(a103,x45621))),f318(f94(a911),x45622)))
% 109.14/108.83 [4591]E(f318(f318(f30(a911),f318(f318(f73(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),x45911)),f318(f94(a911),x45912)),f318(f318(f30(a911),f318(a103,f318(a103,f318(a103,x45911)))),f318(f94(a911),x45912)))
% 109.14/108.83 [4622]E(f318(f248(f918(f917(x46221,x46221),a909),f918(f917(x46221,x46221),a909),f918(f918(x46222,x46221),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909)))),f318(f318(f9(f918(f917(x46221,x46221),a909),f918(f918(f917(x46221,x46221),a909),f918(f918(x46222,x46221),f918(f917(x46222,x46222),a909))),f918(f918(f917(x46221,x46221),a909),f918(f918(x46222,x46221),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909))))),f318(f318(f10(f918(f918(f918(x46222,x46221),f918(f917(x46222,x46222),a909)),f918(f918(x46222,x46221),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909)))),f918(f918(f918(f917(x46221,x46221),a909),f918(f918(x46222,x46221),f918(f917(x46222,x46222),a909))),f918(f918(f917(x46221,x46221),a909),f918(f918(x46222,x46221),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909))))),f918(f917(x46221,x46221),a909)),f10(f918(f918(x46222,x46221),f918(f917(x46222,x46222),a909)),f918(f918(x46222,x46221),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909))),f918(f917(x46221,x46221),a909))),f318(f318(f10(f918(f918(x46222,x46221),f918(f918(f917(x46222,x46222),a909),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909)))),f918(f918(f918(x46222,x46221),f918(f917(x46222,x46222),a909)),f918(f918(x46222,x46221),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909)))),f918(f917(x46221,x46221),a909)),f20(f918(x46222,x46221),f918(f917(x46222,x46222),a909),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909)))),f318(f318(f10(f918(f918(x46222,x46221),f918(f917(x46222,x46222),a909)),f918(f918(x46222,x46221),f918(f918(f917(x46222,x46222),a909),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909)))),f918(f917(x46221,x46221),a909)),f318(f10(f918(f917(x46222,x46222),a909),f918(f918(f917(x46222,x46222),a909),f917(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909))),f918(x46222,x46221)),f243(f918(f917(x46222,x46222),a909),f918(f917(x46222,x46222),a909)))),f279(x46221,x46222))))),f279(x46221,x46222))),f67(x46221,x46222))
% 109.14/108.83 [4666]~E(f318(f299(x46661),x46662),f179(f918(f918(x46661,a909),a909)))
% 109.14/108.83 [4675]~P1(f318(f318(f163(x46751),f104(x46751)),x46752))
% 109.14/108.83 [4678]~P1(f318(f318(f320(x46781),x46782),f179(f918(x46781,a909))))
% 109.14/108.83 [4679]~P1(f318(f318(f320(x46791),x46792),f179(f918(x46791,a909))))
% 109.14/108.83 [4685]~P1(f318(f318(f226(f918(x46851,a909)),x46852),f179(f918(x46851,a909))))
% 109.14/108.83 [3557]E(f318(f318(f3(a911),x35571),f318(f318(f73(a911),x35571),x35572)),f2(a911))
% 109.14/108.83 [3560]E(f318(f318(f101(f918(x35601,a909)),x35602),x35602),x35602)
% 109.14/108.83 [3561]E(f318(f318(f92(f918(x35611,a909)),x35612),x35612),x35612)
% 109.14/108.83 [3589]E(f318(f318(f3(f918(x35891,a909)),x35892),x35892),f179(f918(x35891,a909)))
% 109.14/108.83 [3592]E(f318(f134(x35921,x35922),f2(a911)),f179(f918(f917(f912(x35921),f912(x35921)),a909)))
% 109.14/108.83 [3593]E(f318(f318(f73(a911),x35931),f318(a103,x35932)),f318(a103,f318(f318(f73(a911),x35931),x35932)))
% 109.14/108.83 [3604]E(f185(f318(f91(a1),x36041),f318(f91(a1),x36042)),f318(f91(a1),f318(f318(f3(a911),x36041),x36042)))
% 109.14/108.83 [3607]E(f318(f318(f30(a1),f318(f72(a1),x36071)),x36072),f318(f318(f30(a1),x36071),f318(f72(a1),x36072)))
% 109.14/108.83 [3611]E(f318(f29(a1),f318(f293(a1,x36111),x36112)),f318(a95,f318(f318(f3(a1),x36112),x36111)))
% 109.14/108.83 [3614]E(f318(f318(f73(a911),f318(a103,x36141)),x36142),f318(a103,f318(f318(f73(a911),x36141),x36142)))
% 109.14/108.83 [3617]E(f318(f72(f918(x36171,a909)),f318(f72(f918(x36171,a909)),x36172)),x36172)
% 109.14/108.83 [3629]E(f170(x36291,f318(f318(f142(f912(x36291)),f104(x36291)),x36292)),f170(x36291,x36292))
% 109.14/108.83 [3633]E(f318(f318(f73(a911),x36331),f318(f318(f74(a911),x36331),x36332)),f318(f318(f74(a911),x36331),f318(a103,x36332)))
% 109.14/108.83 [3639]E(f318(f318(a4,f318(a5,x36391)),f318(a5,x36392)),f318(a5,f318(f318(f3(a911),x36391),x36392)))
% 109.14/108.83 [3653]E(f318(f318(f235(a1),f318(f91(a1),x36531)),x36532),f318(f91(a1),f318(f318(f235(a911),x36531),x36532)))
% 109.14/108.83 [3654]E(f318(f318(f235(a1),f318(f91(a1),x36541)),x36542),f318(f91(a1),f318(f318(f235(a911),x36541),x36542)))
% 109.14/108.83 [3655]E(f318(f318(f235(a1),f318(f91(a1),x36551)),x36552),f318(f91(a1),f318(f318(f235(a911),x36551),x36552)))
% 109.14/108.83 [3656]E(f318(f318(f74(a1),f318(f72(a1),x36561)),x36562),f318(f72(a1),f318(f318(f74(a1),x36561),x36562)))
% 109.14/108.83 [3657]E(f318(f318(f73(a90),f318(a5,x36571)),f318(a5,x36572)),f318(a5,f318(f318(f73(a911),x36571),x36572)))
% 109.14/108.83 [3658]E(f318(f318(f74(a90),f318(a5,x36581)),f318(a5,x36582)),f318(a5,f318(f318(f74(a911),x36581),x36582)))
% 109.14/108.83 [3659]E(f318(f318(f223(a911),f318(a103,x36591)),f318(a103,x36592)),f318(a103,f318(f318(f223(a911),x36591),x36592)))
% 109.14/108.83 [3660]E(f318(f318(f224(a911),f318(a103,x36601)),f318(a103,x36602)),f318(a103,f318(f318(f224(a911),x36601),x36602)))
% 109.14/108.83 [3664]E(f318(f163(a911),f130(a911,f318(f293(a911,x36641),x36642))),f318(f293(a911,x36641),x36642))
% 109.14/108.83 [3665]E(f318(f163(a911),f130(a911,f318(f293(a911,x36651),x36652))),f318(f293(a911,x36651),x36652))
% 109.14/108.83 [3666]E(f303(x36661,f318(f318(f300(x36661),x36662),f179(f918(x36661,a909)))),x36662)
% 109.14/108.83 [3669]E(f318(f275(x36691,x36692),f179(f918(f917(x36691,x36692),a909))),f179(f918(x36692,a909)))
% 109.14/108.83 [3670]E(f318(f255(x36701,x36702),f179(f918(f917(x36701,x36702),a909))),f179(f918(x36701,a909)))
% 109.14/108.83 [3674]E(f318(a95,f318(f318(f3(a1),x36741),x36742)),f318(f29(a1),f296(a1,x36742,x36741)))
% 109.14/108.83 [3679]E(f318(f318(f73(a911),x36791),f318(f318(f74(a911),x36792),x36791)),f318(f318(f74(a911),f318(a103,x36792)),x36791))
% 109.14/108.83 [3681]E(f318(f318(f54(x36811),f179(f918(x36811,a909))),x36812),f179(f918(f918(x36811,a909),a909)))
% 109.14/108.83 [3690]E(f318(f180(f912(a911)),f130(a911,f318(f293(a911,x36901),x36902))),f318(f318(f3(a911),x36902),x36901))
% 109.14/108.83 [3705]E(f318(f318(f101(f918(x37051,a909)),f179(f918(x37051,a909))),x37052),x37052)
% 109.14/108.83 [3706]E(f318(f318(f92(f918(x37061,a909)),f233(f918(x37061,a909))),x37062),x37062)
% 109.14/108.83 [3707]E(f318(f318(f73(a1),f318(f72(a1),x37071)),f318(f72(a1),x37072)),f318(f72(a1),f318(f318(f73(a1),x37071),x37072)))
% 109.14/108.83 [3708]E(f318(f318(f74(a1),f318(f91(a1),x37081)),f318(f91(a1),x37082)),f318(f91(a1),f318(f318(f74(a911),x37081),x37082)))
% 109.14/108.83 [3709]E(f318(f318(f30(a1),f318(f91(a1),x37091)),f318(f91(a1),x37092)),f318(f91(a1),f318(f318(f30(a911),x37091),x37092)))
% 109.14/108.83 [3710]E(f318(f318(f73(a1),f318(f94(a1),x37101)),f318(f94(a1),x37102)),f318(f94(a1),f318(f318(f73(a1),x37101),x37102)))
% 109.14/108.83 [3711]E(f318(f318(f73(a1),f318(f91(a1),x37111)),f318(f91(a1),x37112)),f318(f91(a1),f318(f318(f73(a911),x37111),x37112)))
% 109.14/108.83 [3712]E(f318(f318(f73(a1),f318(f91(a1),x37121)),f318(f91(a1),x37122)),f318(f91(a1),f318(f318(f73(a911),x37121),x37122)))
% 109.14/108.83 [3713]E(f318(f318(f74(a1),f318(f94(a1),x37131)),f318(f94(a1),x37132)),f318(f94(a1),f318(f318(f74(a1),x37131),x37132)))
% 109.14/108.83 [3714]E(f318(f318(f74(a1),f318(f91(a1),x37141)),f318(f91(a1),x37142)),f318(f91(a1),f318(f318(f74(a911),x37141),x37142)))
% 109.14/108.83 [3715]E(f318(f318(f74(a1),f318(f91(a1),x37151)),f318(f91(a1),x37152)),f318(f91(a1),f318(f318(f74(a911),x37151),x37152)))
% 109.14/108.83 [3716]E(f318(f318(f30(a1),f318(f91(a1),x37161)),f318(f91(a1),x37162)),f318(f91(a1),f318(f318(f30(a911),x37161),x37162)))
% 109.14/108.83 [3736]E(f318(f318(f8(x37361,a911),f318(f18(a911,x37361),f71(a911))),x37362),f318(f29(x37361),x37362))
% 109.14/108.83 [3741]E(f318(f72(a1),f39(a1,f318(f72(a1),x37411),x37412)),f39(a1,x37411,f318(f72(a1),x37412)))
% 109.14/108.83 [3743]E(f318(f163(a1),f169(x37431,f318(f318(f3(a1),x37432),f71(a1)))),f318(f293(a1,x37431),x37432))
% 109.14/108.83 [3747]P1(f318(f318(f225(a911),x37471),f318(f318(f73(a911),x37472),x37471)))
% 109.14/108.83 [3748]P1(f318(f318(f225(a911),x37481),f318(f318(f73(a911),x37481),x37482)))
% 109.14/108.83 [3751]E(f318(f318(f101(f918(x37511,a909)),f233(f918(x37511,a909))),x37512),f233(f918(x37511,a909)))
% 109.14/108.83 [3752]E(f318(f318(f92(f918(x37521,a909)),f179(f918(x37521,a909))),x37522),f179(f918(x37521,a909)))
% 109.14/108.83 [3753]E(f318(f318(f3(f918(x37531,a909)),f179(f918(x37531,a909))),x37532),f179(f918(x37531,a909)))
% 109.14/108.83 [3760]E(f318(f318(f243(a1,a1),x37601),f318(f72(a1),x37602)),f318(a45,f318(f318(f243(a1,a1),x37601),x37602)))
% 109.14/108.83 [3761]E(f318(f293(a1,f318(f318(f73(a1),x37611),f71(a1))),x37612),f297(a1,x37611,x37612))
% 109.14/108.83 [3773]E(f318(f318(f74(a911),x37731),f318(f318(f30(a911),x37732),x37731)),f318(f318(f3(a911),x37732),f39(a911,x37732,x37731)))
% 109.14/108.83 [3774]E(f318(f318(f74(a1),x37741),f318(f318(f30(a1),x37742),x37741)),f318(f318(f3(a1),x37742),f39(a1,x37742,x37741)))
% 109.14/108.83 [3777]E(f318(f163(a1),f169(f318(f318(f73(a1),x37771),f71(a1)),x37772)),f296(a1,x37771,x37772))
% 109.14/108.83 [3781]P1(f318(f318(f225(f918(x37811,a909)),x37812),x37812))
% 109.14/108.83 [3784]E(f318(f318(f101(f918(x37841,a909)),x37842),f318(f72(f918(x37841,a909)),x37842)),f233(f918(x37841,a909)))
% 109.14/108.83 [3785]E(f318(f318(f92(f918(x37851,a909)),x37852),f318(f72(f918(x37851,a909)),x37852)),f179(f918(x37851,a909)))
% 109.14/108.83 [3793]E(f318(f318(f3(a911),f318(f318(f3(a911),x37931),f71(a911))),x37932),f318(f318(f3(a911),x37931),f318(a103,x37932)))
% 109.14/108.83 [3799]E(f318(f318(f3(f918(x37991,a909)),f233(f918(x37991,a909))),x37992),f318(f72(f918(x37991,a909)),x37992))
% 109.14/108.83 [3800]E(f318(f318(f3(a1),f318(f94(a1),x38001)),f318(f94(a1),x38002)),f318(f94(a1),f318(f318(f73(a1),x38001),f318(f72(a1),x38002))))
% 109.14/108.83 [3813]E(f318(f163(a911),f130(a911,f318(f293(a911,x38131),f318(a103,x38132)))),f294(a911,x38131,x38132))
% 109.14/108.83 [3830]E(f318(f180(f912(f912(x38301))),f48(x38301,x38302)),f318(f318(f235(a911),f318(a103,f318(a103,f2(a911)))),f318(f180(f912(x38301)),x38302)))
% 109.14/108.83 [3848]E(f318(f318(f174(f917(x38481,x38481),a909),f2(a911)),x38482),f298(x38481,f179(f918(f917(x38481,x38481),a909))))
% 109.14/108.83 [3852]P1(f318(f128(a911),f130(a911,f318(f293(a911,x38521),x38522))))
% 109.14/108.83 [3868]E(f318(f301(a1,a911,a95),f294(a1,f318(f91(a1),x38681),f318(f91(a1),x38682))),f294(a911,x38681,x38682))
% 109.14/108.83 [3877]E(f176(a911,f2(a911),f7(a911),f318(f318(f3(a911),x38771),x38772)),f318(f318(f3(a911),x38771),f318(a103,x38772)))
% 109.14/108.83 [3878]E(f318(a95,f318(f318(f3(a1),x38781),f318(f318(f73(a1),x38782),f71(a1)))),f318(f29(a1),f297(a1,x38782,x38781)))
% 109.14/108.83 [3907]E(f318(f318(f145(a911,a911),a103),f130(a911,f318(f293(a911,x39071),x39072))),f130(a911,f318(f293(a911,f318(a103,x39071)),f318(a103,x39072))))
% 109.14/108.83 [3914]E(f318(f163(a1),f169(f318(f318(f73(a1),x39141),f71(a1)),f318(f318(f3(a1),x39142),f71(a1)))),f297(a1,x39141,x39142))
% 109.14/108.83 [3926]P1(f318(f318(f225(f918(x39261,a909)),f179(f918(x39261,a909))),x39262))
% 109.14/108.83 [3930]E(f78(x39301,f318(f318(f9(x39301,x39301,a909),a315),x39302)),x39302)
% 109.14/108.83 [3931]E(f83(x39311,f318(f318(f9(x39311,x39311,a909),a315),x39312)),x39312)
% 109.14/108.83 [3939]E(f318(f163(a911),f130(a911,f318(f293(a911,f318(a103,x39391)),f318(a103,x39392)))),f296(a911,x39391,x39392))
% 109.14/108.83 [3965]E(f318(f318(f245(x39651,x39652),f233(f918(x39651,a909))),f318(f18(f918(x39652,a909),x39651),f233(f918(x39652,a909)))),f233(f918(f917(x39651,x39652),a909)))
% 109.14/108.83 [3998]E(f318(f253(x39981),f318(f318(f10(a909,a909,x39981),a313),x39982)),f318(f72(f918(x39981,a909)),f318(f253(x39981),x39982)))
% 109.14/108.83 [4001]E(f318(f253(x40011),f318(f318(f9(x40011,x40011,a909),a315),x40012)),f318(f318(f300(x40011),x40012),f179(f918(x40011,a909))))
% 109.14/108.83 [4023]P1(f318(f318(f225(a911),f318(f29(x40231),f318(f163(x40231),x40232))),f318(f180(f912(x40231)),x40232)))
% 109.14/108.83 [4024]P1(f318(f318(f225(a911),f318(f180(f912(x40241)),f143(x40241,x40242))),f318(f180(f912(x40241)),x40242)))
% 109.14/108.83 [4034]E(f318(f253(x40341),f318(f318(f9(x40341,f918(x40341,a909),a909),f320(x40341)),x40342)),x40342)
% 109.14/108.83 [4047]E(f318(f318(f166(x40471),f318(f318(f3(a911),f318(f180(f912(x40471)),x40472)),f71(a911))),x40472),f105(x40471,x40472))
% 109.14/108.83 [4065]E(f176(a911,f2(a911),f318(f318(f10(a911,a911,a911),a103),f318(f223(a911),x40651)),x40652),f318(f318(f223(a911),f318(a103,x40651)),x40652))
% 109.14/108.83 [4070]E(f31(f918(x40701,a909),f318(f301(f918(f917(x40701,x40701),a909),f918(x40701,a909),f272(x40701)),x40702)),f318(f272(x40701),f31(f918(f917(x40701,x40701),a909),x40702)))
% 109.14/108.83 [4071]E(f176(a911,f318(a103,x40711),f318(f318(f10(a911,a911,a911),a103),f318(f224(a911),x40711)),x40712),f318(f318(f224(a911),f318(a103,x40711)),x40712))
% 109.14/108.83 [4073]E(f318(f318(f243(a1,a1),f318(f318(f30(a1),f318(f69(a1),x40731)),f318(f69(a1),x40732))),f39(a1,f318(f69(a1),x40731),f318(f69(a1),x40732))),f47(x40731,x40732))
% 109.14/108.83 [4096]P1(f318(f318(f225(f918(f918(x40961,a909),a909)),x40962),f318(f299(x40961),f31(f918(x40961,a909),x40962))))
% 109.14/108.83 [4129]E(f318(f318(f33(x41291,f918(x41291,a909)),x41292),f318(f318(f9(x41291,f918(x41291,a909),f918(x41291,a909)),f300(x41291)),f179(f918(x41291,a909)))),x41292)
% 109.14/108.83 [4130]E(f318(f318(f280(x41301,x41301,x41301),f318(f277(x41301,x41301),x41302)),f298(x41301,f318(f277(x41301,x41301),x41302))),f318(f277(x41301,x41301),f318(f318(f280(x41301,x41301,x41301),x41302),f298(x41301,x41302))))
% 109.14/108.83 [4192]E(f318(f163(x41921),f318(f133(f912(x41921),f912(x41921),f125(x41921),f104(x41921)),x41922)),f318(f318(f33(f912(x41921),f918(x41921,a909)),f318(f163(f912(x41921)),x41922)),f163(x41921)))
% 109.14/108.83 [4222]E(f318(f318(f101(f918(f917(x42221,x42221),a909)),f298(x42221,f179(f918(f917(x42221,x42221),a909)))),f318(f318(f280(x42221,x42221,x42221),f298(x42221,x42222)),x42222)),f298(x42221,x42222))
% 109.14/108.83 [4257]E(f318(f318(f172(x42571,x42571),x42572),x42572),f318(f318(f145(x42571,f917(x42571,x42571)),f318(f318(f20(x42571,x42571,f917(x42571,x42571)),f243(x42571,x42571)),f7(x42571))),x42572))
% 109.14/108.83 [4365]E(f318(f133(a911,f912(x43651),f318(f9(f912(x43651),a911,a911),f318(f318(f10(a911,f918(a911,a911),f912(x43651)),f224(a911)),f180(f912(x43651)))),f2(a911)),f318(f159(f912(x43651)),x43652)),f318(f180(f912(f912(x43651))),f170(x43651,x43652)))
% 109.14/108.83 [4439]E(f318(f318(f279(f917(a911,f912(x44391)),f912(x44391)),f311(a911,f912(x44391),a231,f136(x44391,x44392))),f318(f318(f20(f912(x44391),f912(x44391),f917(a911,f912(x44391))),f318(f318(f10(a911,f918(f912(x44391),f917(a911,f912(x44391))),f912(x44391)),f243(a911,f912(x44391))),f180(f912(x44391)))),f7(f912(x44391)))),f137(x44391,x44392))
% 109.14/108.83 [4577]E(f318(f253(x45771),f318(f318(f10(f918(f918(x45771,a909),a909),a909,x45771),f80(f918(x45771,a909))),f318(f318(f10(f918(f918(x45771,a909),a909),f918(f918(x45771,a909),a909),x45771),f318(f20(f918(x45771,a909),a909,a909),f318(f318(f10(a909,f918(a909,a909),f918(x45771,a909)),a321),f318(f318(f9(f918(x45771,a909),f918(f918(x45771,a909),a909),a909),f320(f918(x45771,a909))),x45772)))),f320(x45771)))),f32(f918(x45771,a909),x45772))
% 109.14/108.83 [4578]E(f318(f253(x45781),f318(f318(f10(f918(f918(x45781,a909),a909),a909,x45781),f79(f918(x45781,a909))),f318(f318(f10(f918(f918(x45781,a909),a909),f918(f918(x45781,a909),a909),x45781),f318(f20(f918(x45781,a909),a909,a909),f318(f318(f10(a909,f918(a909,a909),f918(x45781,a909)),a316),f318(f318(f9(f918(x45781,a909),f918(f918(x45781,a909),a909),a909),f320(f918(x45781,a909))),x45782)))),f320(x45781)))),f31(f918(x45781,a909),x45782))
% 109.14/108.83 [4686]~P1(f318(f318(f226(a1),f318(f91(a1),x46861)),f318(f72(a1),f318(f91(a1),x46862))))
% 109.14/108.83 [3677]E(f318(f318(f3(a911),f318(f318(f73(a911),x36771),x36772)),x36772),x36771)
% 109.14/108.83 [3678]E(f318(f318(f3(a911),f318(f318(f73(a911),x36781),x36782)),x36781),x36782)
% 109.14/108.83 [3742]E(f318(f318(f73(a911),f318(f318(f3(a911),x37421),x37422)),x37422),f318(f318(f224(a911),x37421),x37422))
% 109.14/108.83 [3855]E(f318(f318(f74(a911),f318(f318(f30(a911),x38551),x38552)),x38552),f318(f318(f3(a911),x38551),f39(a911,x38551,x38552)))
% 109.14/108.83 [3882]E(f318(f163(a911),f130(a911,f318(f293(a911,f318(a103,x38821)),x38822))),f297(a911,x38821,x38822))
% 109.14/108.83 [3890]E(f318(f91(a1),f207(f318(a95,f318(f69(a1),x38901)),f318(a95,f318(f69(a1),x38902)))),f318(f318(a208,x38901),x38902))
% 109.14/108.83 [3892]E(f318(f318(f101(f918(x38921,a909)),f318(f72(f918(x38921,a909)),x38922)),x38922),f233(f918(x38921,a909)))
% 109.14/108.83 [3893]E(f318(f318(f92(f918(x38931,a909)),f318(f72(f918(x38931,a909)),x38932)),x38932),f179(f918(x38931,a909)))
% 109.14/108.83 [3903]P1(f318(f318(f225(a911),f318(f318(f3(a911),x39031),x39032)),x39031))
% 109.14/108.83 [3904]P1(f318(f318(f225(a911),f318(f318(f30(a911),x39041),x39042)),x39041))
% 109.14/108.83 [3927]P1(f318(f318(f226(a911),x39271),f318(a103,f318(f318(f73(a911),x39272),x39271))))
% 109.14/108.83 [3928]P1(f318(f318(f226(a911),x39281),f318(a103,f318(f318(f73(a911),x39281),x39282))))
% 109.14/108.83 [3950]E(f318(f318(f74(a911),f318(a95,f318(f69(a1),x39501))),f318(a95,f318(f69(a1),x39502))),f318(a95,f318(f69(a1),f318(f318(f74(a1),x39501),x39502))))
% 109.14/108.83 [3961]P1(f318(f318(f225(a1),f2(a1)),f318(f318(f235(a1),f318(f69(a1),x39611)),x39612)))
% 109.14/108.83 [4027]E(f318(f276(f912(x40271),f912(x40271),f149(x40271,x40272)),f318(f318(f300(f912(x40271)),f104(x40271)),f179(f918(f912(x40271),a909)))),f318(f318(f300(f912(x40271)),f104(x40271)),f179(f918(f912(x40271),a909))))
% 109.14/108.83 [4045]E(f318(f318(f101(f918(f917(x40451,x40451),a909)),f298(x40451,x40452)),f298(x40451,f179(f918(f917(x40451,x40451),a909)))),f298(x40451,x40452))
% 109.14/108.83 [4125]E(f318(f253(f918(x41251,a909)),f318(f318(f9(f918(x41251,a909),f918(x41251,a909),a909),f225(f918(x41251,a909))),x41252)),f318(f299(x41251),x41252))
% 109.14/108.83 [4142]E(f318(f318(f145(a1,a911),a95),f318(f318(f125(a1),f318(f318(f145(a911,a1),f91(a1)),x41421)),f318(f318(f145(a911,a1),f91(a1)),x41422))),f318(f318(f125(a911),x41421),x41422))
% 109.14/108.83 [4170]E(f318(f301(a1,a1,f318(f318(f9(a1,a1,a1),f73(a1)),x41701)),f318(f293(a1,f2(a1)),f318(f318(f3(a1),x41702),x41701))),f318(f293(a1,x41701),x41702))
% 109.14/108.83 [4172]P57(x41721,f318(f318(f3(f918(f917(x41721,x41721),a909)),x41722),f298(x41721,f179(f918(f917(x41721,x41721),a909)))))
% 109.14/108.83 [4190]E(f318(f180(f912(x41901)),f318(f133(f912(x41901),f912(x41901),f125(x41901),f104(x41901)),x41902)),f318(f156(a911),f318(f318(f145(f912(x41901),a911),f180(f912(x41901))),x41902)))
% 109.14/108.83 [4194]P56(x41941,f233(f918(x41941,a909)),f318(f318(f101(f918(f917(x41941,x41941),a909)),x41942),f298(x41941,f179(f918(f917(x41941,x41941),a909)))))
% 109.14/108.83 [4231]P1(f318(f318(f320(f917(x42311,x42311)),f318(f318(f243(x42311,x42311),x42312),x42312)),f298(x42311,f179(f918(f917(x42311,x42311),a909)))))
% 109.14/108.83 [4236]E(f176(a911,f2(a911),f318(f318(f10(a911,a911,a911),a103),f318(f318(f9(a911,a911,a911),f223(a911)),x42361)),x42362),f318(f318(f223(a911),x42362),f318(a103,x42361)))
% 109.14/108.83 [4239]E(f176(a911,f318(a103,x42391),f318(f318(f10(a911,a911,a911),a103),f318(f318(f9(a911,a911,a911),f224(a911)),x42391)),x42392),f318(f318(f224(a911),x42392),f318(a103,x42391)))
% 109.14/108.83 [4242]E(f318(f301(x42421,f912(x42421),f318(f318(f9(x42421,f912(x42421),f912(x42421)),f142(x42421)),f104(x42421))),x42422),f165(x42421,x42422,f318(f318(f300(f912(x42421)),f104(x42421)),f179(f918(f912(x42421),a909)))))
% 109.14/108.83 [4244]E(f318(f318(f101(f918(f917(x42441,x42441),a909)),f318(f318(f280(x42441,x42441,x42441),x42442),f298(x42441,x42442))),f298(x42441,f179(f918(f917(x42441,x42441),a909)))),f298(x42441,x42442))
% 109.14/108.83 [4252]P1(f318(f318(f225(f918(f917(x42521,x42521),a909)),f254(x42521,x42522)),f318(f318(f245(x42521,x42521),x42522),f318(f18(f918(x42521,a909),x42521),x42522))))
% 109.14/108.83 [4255]E(f318(f301(a1,a911,a95),f318(f318(f101(f918(a1,a909)),f318(f301(a911,a1,f91(a1)),x42551)),f318(f301(a911,a1,f91(a1)),x42552))),f318(f318(f101(f918(a911,a909)),x42551),x42552))
% 109.14/108.83 [4256]E(f318(f301(a1,a911,a95),f318(f318(f92(f918(a1,a909)),f318(f301(a911,a1,f91(a1)),x42561)),f318(f301(a911,a1,f91(a1)),x42562))),f318(f318(f92(f918(a911,a909)),x42561),x42562))
% 109.14/108.83 [4259]E(f318(f253(x42591),f318(f318(f10(a909,a909,x42591),a313),f318(f318(f9(x42591,f918(x42591,a909),a909),f320(x42591)),x42592))),f318(f72(f918(x42591,a909)),x42592))
% 109.14/108.83 [4285]E(f318(f133(f912(x42851),f912(x42851),f125(x42851),f104(x42851)),f318(f318(f145(f912(x42851),f912(x42851)),f159(x42851)),f318(f159(f912(x42851)),x42852))),f318(f159(x42851),f318(f133(f912(x42851),f912(x42851),f125(x42851),f104(x42851)),x42852)))
% 109.14/108.83 [4307]E(f318(f318(f33(a911,f918(f917(x43071,x43071),a909)),f233(f918(a911,a909))),f318(f318(f9(a911,f918(f917(x43071,x43071),a909),f918(f917(x43071,x43071),a909)),f174(f917(x43071,x43071),a909)),x43072)),f298(x43071,x43072))
% 109.14/108.83 [4322]E(f78(x43221,f318(f318(f10(f918(x43221,a909),a909,x43221),f318(a315,x43222)),f318(f318(f9(x43221,f918(x43221,a909),f918(x43221,a909)),f300(x43221)),f179(f918(x43221,a909))))),f303(x43221,x43222))
% 109.14/108.83 [4331]E(f318(f180(f912(x43311)),f143(x43311,f318(f133(f912(x43311),f912(x43311),f125(x43311),f104(x43311)),x43312))),f318(f29(x43311),f318(f318(f33(f912(x43311),f918(x43311,a909)),f318(f163(f912(x43311)),x43312)),f163(x43311))))
% 109.14/108.83 [4345]E(f318(f318(f101(f918(f917(x43451,x43451),a909)),x43452),f318(f318(f280(x43451,x43451,x43451),f318(f318(f280(x43451,x43451,x43451),x43452),f298(x43451,x43452))),x43452)),f318(f318(f280(x43451,x43451,x43451),x43452),f298(x43451,x43452)))
% 109.14/108.83 [4375]P1(f318(f318(f225(f918(f917(x43751,x43751),a909)),f318(f318(f280(x43751,x43751,x43751),x43752),f298(x43751,x43752))),f318(f318(f245(x43751,x43751),f318(f272(x43751),x43752)),f318(f18(f918(x43751,a909),x43751),f318(f272(x43751),x43752)))))
% 109.14/108.83 [4415]E(f318(f253(f912(x44151)),f318(f318(f9(f912(x44151),f918(x44151,a909),a909),f318(f318(f10(f918(x44151,a909),f918(f918(x44151,a909),a909),f912(x44151)),f225(f918(x44151,a909))),f163(x44151))),x44152)),f152(x44151,x44152))
% 109.14/108.83 [4428]E(f318(f147(f912(x44281),x44281,f104(x44281),f318(f318(f10(f912(x44281),f918(f912(x44281),f912(x44281)),x44281),f318(f9(f912(x44281),f912(x44281),f912(x44281)),f125(x44281))),f318(f318(f9(x44281,f912(x44281),f912(x44281)),f142(x44281)),f104(x44281)))),x44282),f318(f158(x44281),x44282))
% 109.14/108.83 [4465]P25(f918(x44651,x44652),f918(f917(x44651,x44652),a909),f318(f318(f10(f918(f917(x44651,x44652),a909),f918(f917(x44651,x44652),a909),f918(x44651,x44652)),f253(f917(x44651,x44652))),f318(f318(f10(f918(x44651,f918(x44652,a909)),f918(f917(x44651,x44652),a909),f918(x44651,x44652)),f248(x44651,x44652,a909)),f318(f10(x44652,f918(x44652,a909),x44651),f318(f9(x44652,x44652,a909),a315)))),f233(f918(f918(x44651,x44652),a909)))
% 109.14/108.83 [4521]E(f318(f318(f33(x45211,f918(f917(x45211,x45211),a909)),x45212),f318(f318(f9(x45211,f918(f917(x45211,x45211),a909),f918(f917(x45211,x45211),a909)),f318(f318(f10(f917(x45211,x45211),f918(f918(f917(x45211,x45211),a909),f918(f917(x45211,x45211),a909)),x45211),f300(f917(x45211,x45211))),f318(f318(f20(x45211,x45211,f917(x45211,x45211)),f243(x45211,x45211)),f7(x45211)))),f179(f918(f917(x45211,x45211),a909)))),f254(x45211,x45212))
% 109.14/108.83 [4529]E(f193(x45291,f318(f318(f243(a1,a1),f318(f72(a1),f318(f318(f66(f917(a1,a1),a1,x45291,f242(a1,a1)),f203(x45291)),x45292))),f318(f318(f66(f917(a1,a1),a1,x45291,f247(a1,a1)),f203(x45291)),x45292))),f218(x45291,x45292))
% 109.14/108.83 [4619]E(f318(f253(f918(x46191,a909)),f318(f318(f10(f918(f918(x46191,a909),a909),a909,f918(x46191,a909)),f79(f918(x46191,a909))),f318(f318(f9(f918(x46191,a909),f918(f918(x46191,a909),a909),f918(f918(x46191,a909),a909)),f318(f318(f10(f918(f918(x46191,a909),f918(a909,a909)),f918(f918(f918(x46191,a909),a909),f918(f918(x46191,a909),a909)),f918(x46191,a909)),f20(f918(x46191,a909),a909,a909)),f318(f318(f10(f918(f918(x46191,a909),a909),f918(f918(x46191,a909),f918(a909,a909)),f918(x46191,a909)),f318(f10(a909,f918(a909,a909),f918(x46191,a909)),a316)),f318(f318(f9(f918(x46191,a909),f918(f918(x46191,a909),f918(x46191,a909)),f918(f918(x46191,a909),a909)),f318(f318(f10(f918(f918(x46191,a909),a909),f918(f918(f918(x46191,a909),f918(x46191,a909)),f918(f918(x46191,a909),a909)),f918(x46191,a909)),f10(f918(x46191,a909),a909,f918(x46191,a909))),a315)),f72(f918(x46191,a909)))))),f318(f318(f10(f918(f918(x46191,a909),a909),a909,f918(x46191,a909)),f318(f320(f918(x46191,a909)),x46192)),f299(x46191))))),f318(f299(x46191),f318(f72(f918(x46191,a909)),x46192)))
% 109.14/108.83 [4688]~P1(f318(f318(f226(a911),f318(f318(f73(a911),x46881),x46882)),x46882))
% 109.14/108.83 [4689]~P1(f318(f318(f226(a911),f318(f318(f73(a911),x46891),x46892)),x46891))
% 109.14/108.83 [3966]E(f318(f318(f3(a911),x39661),f318(f318(f74(a911),f318(f318(f30(a911),x39661),x39662)),x39662)),f39(a911,x39661,x39662))
% 109.14/108.83 [3967]E(f318(f318(f3(a1),x39671),f318(f318(f74(a1),f318(f318(f30(a1),x39671),x39672)),x39672)),f39(a1,x39671,x39672))
% 109.14/108.83 [3999]E(f318(f318(f145(a911,x39991),f318(f155(x39991),x39992)),f130(a911,f318(f293(a911,f2(a911)),f318(f180(f912(x39991)),x39992)))),x39992)
% 109.14/108.83 [4052]E(f318(f276(x40521,x40521,f298(x40521,f179(f918(f917(x40521,x40521),a909)))),x40522),x40522)
% 109.14/108.83 [4175]E(f298(x41751,f318(f318(f101(f918(f917(x41751,x41751),a909)),x41752),f298(x41751,f179(f918(f917(x41751,x41751),a909))))),f298(x41751,x41752))
% 109.14/108.83 [4176]E(f298(x41761,f318(f318(f3(f918(f917(x41761,x41761),a909)),x41762),f298(x41761,f179(f918(f917(x41761,x41761),a909))))),f298(x41761,x41762))
% 109.14/108.83 [4342]E(f318(f91(a1),f318(f318(f30(a911),f318(f318(f74(a911),f318(a95,f318(f69(a1),x43421))),f318(a95,f318(f69(a1),x43422)))),f207(f318(a95,f318(f69(a1),x43421)),f318(a95,f318(f69(a1),x43422))))),f209(x43421,x43422))
% 109.14/108.83 [4367]E(f318(f318(f3(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43671)),x43671)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43672)),x43672)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f3(a1),x43671),x43672))),f318(f318(f3(a1),x43671),x43672))),a88))
% 109.14/108.83 [4390]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43901)),x43901)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43902)),x43902)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),x43901),x43902))),f318(f318(f73(a1),x43901),x43902)))
% 109.14/108.83 [4393]E(f318(f318(f250(f917(a90,a90),a90,f917(a90,a90),f917(x43931,f917(a90,a90))),f258(f318(a5,f318(f180(f912(x43931)),x43932)))),f318(f318(f10(x43931,f918(f917(a90,a90),f917(x43931,f917(a90,a90))),a90),f243(x43931,f917(a90,a90))),f318(f318(f10(a911,x43931,a90),f318(f155(x43931),x43932)),a22))),f266(x43931,x43932))
% 109.14/108.83 [4421]E(f318(f318(f3(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44211)),x44211)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44212)),x44212)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f3(a1),f318(f318(f73(a1),x44211),a88)),x44212))),f318(f318(f3(a1),f318(f318(f73(a1),x44211),a88)),x44212)))
% 109.14/108.83 [4470]E(f318(f133(a911,f912(x44701),f318(f9(f912(x44701),a911,a911),f318(f318(f10(a911,f918(a911,a911),f912(x44701)),f224(a911)),f180(f912(x44701)))),f2(a911)),f318(f159(f912(x44701)),f170(x44701,x44702))),f318(f180(f912(f912(x44701))),f318(f127(f912(x44701),f318(f318(f10(a909,a909,f912(x44701)),a313),f318(f318(f9(f912(x44701),f912(x44701),a909),a315),f104(x44701)))),x44702)))
% 109.14/108.83 [4476]E(f318(f318(f33(a911,f918(x44761,a909)),f233(f918(a911,a909))),f318(f318(f9(a911,f918(a911,f918(x44761,a909)),f918(x44761,a909)),f318(f318(f10(f918(a911,a909),f918(f918(a911,f918(x44761,a909)),f918(x44761,a909)),a911),f33(a911,f918(x44761,a909))),f293(a911,f2(a911)))),x44762)),f318(f318(f33(a911,f918(x44761,a909)),f233(f918(a911,a909))),x44762))
% 109.14/108.83 [4499]P1(f318(f55(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),x44991)),f318(f318(f9(a911,a911,a909),f226(a911)),x44992)))))
% 109.14/108.83 [4626]E(f318(f253(f917(f912(x46261),f912(x46261))),f318(f248(f912(x46261),f912(x46261),a909),f318(f318(f20(f912(x46261),f918(f912(x46261),a909),f918(f912(x46261),a909)),f318(f318(f10(f918(f912(x46261),f918(a909,a909)),f918(f918(f912(x46261),a909),f918(f912(x46261),a909)),f912(x46261)),f20(f912(x46261),a909,a909)),f318(f318(f10(f918(f912(x46261),a909),f918(f912(x46261),f918(a909,a909)),f912(x46261)),f318(f10(a909,f918(a909,a909),f912(x46261)),a317)),f318(f318(f9(f912(x46261),f918(f912(x46261),a911),f918(f912(x46261),a909)),f318(f318(f10(f918(a911,a909),f918(f918(f912(x46261),a911),f918(f912(x46261),a909)),f912(x46261)),f10(a911,a909,f912(x46261))),f318(f318(f10(a911,f918(a911,a909),f912(x46261)),f226(a911)),f180(f912(x46261))))),f180(f912(x46261)))))),f318(f318(f20(f912(x46261),f918(f912(x46261),a909),f918(f912(x46261),a909)),f318(f318(f10(f918(f912(x46261),f918(a909,a909)),f918(f918(f912(x46261),a909),f918(f912(x46261),a909)),f912(x46261)),f20(f912(x46261),a909,a909)),f318(f318(f10(f918(f912(x46261),a909),f918(f912(x46261),f918(a909,a909)),f912(x46261)),f318(f10(a909,f918(a909,a909),f912(x46261)),a316)),f318(f318(f9(f912(x46261),f918(f912(x46261),a911),f918(f912(x46261),a909)),f318(f318(f10(f918(a911,a909),f918(f918(f912(x46261),a911),f918(f912(x46261),a909)),f912(x46261)),f10(a911,a909,f912(x46261))),f318(f318(f10(a911,f918(a911,a909),f912(x46261)),a315),f180(f912(x46261))))),f180(f912(x46261)))))),f318(f318(f9(f912(x46261),f918(f917(f912(x46261),f912(x46261)),a909),f918(f912(x46261),a909)),f318(f318(f10(f918(f912(x46261),f918(f918(f917(f912(x46261),f912(x46261)),a909),a909)),f918(f918(f917(f912(x46261),f912(x46261)),a909),f918(f912(x46261),a909)),f912(x46261)),f9(f912(x46261),f918(f917(f912(x46261),f912(x46261)),a909),a909)),f318(f318(f10(f918(f912(x46261),f917(f912(x46261),f912(x46261))),f918(f912(x46261),f918(f918(f917(f912(x46261),f912(x46261)),a909),a909)),f912(x46261)),f318(f10(f917(f912(x46261),f912(x46261)),f918(f918(f917(f912(x46261),f912(x46261)),a909),a909),f912(x46261)),f320(f917(f912(x46261),f912(x46261))))),f243(f912(x46261),f912(x46261))))),f136(x46261,x46262)))))),f137(x46261,x46262))
% 109.14/108.83 [4392]E(f318(a95,f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x43921),x43922)),f179(f918(f917(a911,a911),a909)))))),f318(f318(f3(a911),x43921),x43922))
% 109.14/108.83 [4396]E(f318(f318(f280(x43961,x43961,x43961),f318(f318(f101(f918(f917(x43961,x43961),a909)),x43962),f298(x43961,f179(f918(f917(x43961,x43961),a909))))),f298(x43961,f318(f318(f101(f918(f917(x43961,x43961),a909)),x43962),f298(x43961,f179(f918(f917(x43961,x43961),a909)))))),f298(x43961,x43962))
% 109.14/108.83 [4432]E(f259(x44321,f318(f127(f917(a90,x44321),f318(f248(a90,x44321,a909),f318(f318(f10(a909,f918(x44321,a909),a90),f18(a909,x44321)),f318(f226(a90),f2(a90))))),x44322)),f259(x44321,x44322))
% 109.14/108.83 [4433]E(f257(x44331,f318(f127(f917(a90,x44331),f318(f248(a90,x44331,a909),f318(f318(f10(a909,f918(x44331,a909),a90),f18(a909,x44331)),f318(f226(a90),f2(a90))))),x44332)),f257(x44331,x44332))
% 109.14/108.83 [4434]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),x44341),f318(f318(f3(a1),x44342),a88)))),f318(f318(f73(a1),x44341),f318(f318(f3(a1),x44342),a88)))),a88),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44341)),x44341)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44342)),x44342)))
% 109.14/108.83 [4436]E(f318(f72(a1),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x44361),x44362)),f179(f918(f917(a911,a911),a909)))))),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x44362),x44361)),f179(f918(f917(a911,a911),a909))))))
% 109.14/108.83 [4491]E(f318(f318(f279(f912(a911),x44911),f136(a911,a231)),f318(f318(f9(x44911,f912(f918(x44911,a911)),f912(a911)),f318(f318(f10(f918(f918(x44911,a911),a911),f918(f912(f918(x44911,a911)),f912(a911)),x44911),f145(f918(x44911,a911),a911)),f318(f9(f918(x44911,a911),x44911,a911),f7(f918(x44911,a911))))),x44912)),f144(x44911,x44912))
% 109.14/108.83 [4518]E(f318(f318(f81(a1,a911),f318(f94(a1),f318(f318(f73(a1),x45181),a88))),f318(f318(f20(a1,a911,a911),f318(f318(f9(a1,a911,f918(a911,a911)),f318(f318(f10(a909,f918(a911,f918(a911,a911)),a1),f85(a911)),a184)),f2(a911))),f318(f318(f10(a911,a911,a1),a103),f318(f318(f10(a911,a911,a1),f318(f223(a911),x45182)),a95)))),f318(f318(f223(a911),f318(a103,x45182)),f318(f94(a911),x45181)))
% 109.14/108.83 [4519]E(f318(f318(f81(a1,a911),f318(f94(a1),f318(f318(f73(a1),x45191),a88))),f318(f318(f20(a1,a911,a911),f318(f318(f9(a1,a911,f918(a911,a911)),f318(f318(f10(a909,f918(a911,f918(a911,a911)),a1),f85(a911)),a184)),f318(a103,x45192))),f318(f318(f10(a911,a911,a1),a103),f318(f318(f10(a911,a911,a1),f318(f224(a911),x45192)),a95)))),f318(f318(f224(a911),f318(a103,x45192)),f318(f94(a911),x45191)))
% 109.14/108.83 [4539]E(f318(f133(f912(x45391),f912(x45391),f125(x45391),f104(x45391)),f318(f318(f145(f912(x45391),f912(x45391)),f147(f912(x45391),x45391,f104(x45391),f318(f318(f10(f912(x45391),f918(f912(x45391),f912(x45391)),x45391),f18(f912(x45391),f912(x45391))),f318(f318(f9(x45391,f912(x45391),f912(x45391)),f142(x45391)),f104(x45391))))),x45392)),f318(f318(f145(f912(x45391),x45391),f132(x45391)),f318(f127(f912(x45391),f318(f318(f10(a909,a909,f912(x45391)),a313),f318(f318(f9(f912(x45391),f912(x45391),a909),a315),f104(x45391)))),x45392)))
% 109.14/108.83 [4610]E(f318(f248(a1,a1,a909),f318(f318(f9(a1,f918(a1,a909),f918(a1,a909)),f318(f318(f10(f918(a1,f918(a909,a909)),f918(f918(a1,a909),f918(a1,a909)),a1),f20(a1,a909,a909)),f318(f318(f10(f918(a1,a909),f918(a1,f918(a909,a909)),a1),f318(f10(a909,f918(a909,a909),a1),a316)),f318(f318(f10(f918(a1,a1),f918(a1,a909),a1),f318(f10(a1,a909,a1),f318(a315,x46101))),f318(f318(f10(a1,f918(a1,a1),a1),f73(a1)),f318(f74(a1),x46102)))))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f318(f10(a909,a909,a1),f318(a321,f318(f318(f226(a1),f2(a1)),x46102))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),f318(f318(f9(a1,a1,a909),f226(a1)),x46102))))),f318(f318(f10(a909,a909,a1),f318(a321,f318(a313,f318(f318(f226(a1),f2(a1)),x46102)))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f226(a1),x46102))),f318(f318(f9(a1,a1,a909),f225(a1)),f2(a1))))))),f43(x46101,x46102))
% 109.14/108.83 [4613]E(f318(f253(x46131),f318(f318(f10(f918(a911,a909),a909,x46131),f79(a911)),f318(f318(f9(x46131,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),x46131),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),x46131),f318(f10(a909,f918(a909,a909),a911),a316)),f318(f318(f9(x46131,f918(a911,x46131),f918(a911,a909)),f318(f318(f10(f918(x46131,a909),f918(f918(a911,x46131),f918(a911,a909)),x46131),f10(x46131,a909,a911)),a315)),f318(f155(x46131),x46132))))),f318(f318(f9(a911,a911,a909),f226(a911)),f318(f180(f912(x46131)),x46132))))),f318(f163(x46131),x46132))
% 109.14/108.83 [4694]~E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x46941)),x46941)),a88),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x46942)),x46942))
% 109.14/108.83 [4695]~E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x46951)),x46951)),a88),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x46952)),x46952))
% 109.14/108.83 [4356]E(f318(f318(f3(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43561)),x43561)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43562)),x43562)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f3(a1),x43561),x43562))),f318(f318(f3(a1),x43561),x43562)))
% 109.14/108.83 [4357]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43571)),x43571)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43572)),x43572)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),x43571),x43572))),f318(f318(f73(a1),x43571),x43572)))
% 109.14/108.83 [4444]E(f318(f318(f3(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44441)),x44441)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44442)),x44442)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f3(a1),x44441),x44442))),f318(f318(f3(a1),x44441),x44442))),a88))
% 109.14/108.83 [4445]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44451)),x44451)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44452)),x44452)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),x44451),x44452))),f318(f318(f73(a1),x44451),x44452))),a88))
% 109.14/108.83 [4477]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f74(a1),x44771),x44772))),f318(f318(f74(a1),x44771),x44772))),a88)),x44772),f318(f318(f74(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44771)),x44771)),x44772))
% 109.14/108.83 [4534]E(f318(f133(f912(f912(x45341)),f912(f912(x45341)),f125(f912(x45341)),f104(f912(x45341))),f318(f318(f145(f912(x45341),f912(f912(x45341))),f147(f912(f912(x45341)),x45341,f104(f912(x45341)),f318(f18(f918(f912(x45341),f912(f912(x45341))),x45341),f318(f318(f9(f912(x45341),f912(f912(x45341)),f912(f912(x45341))),f142(f912(x45341))),f104(f912(x45341)))))),x45342)),f318(f318(f145(f912(x45341),f912(x45341)),f162(x45341)),f318(f127(f912(x45341),f318(f318(f10(a909,a909,f912(x45341)),a313),f318(f318(f9(f912(x45341),f912(x45341),a909),a315),f104(x45341)))),x45342)))
% 109.14/108.83 [4542]E(f318(f318(f81(a1,a911),f318(f94(a1),f318(f318(f73(a1),x45421),a88))),f318(f318(f20(a1,a911,a911),f318(f318(f9(a1,a911,f918(a911,a911)),f318(f318(f10(a909,f918(a911,f918(a911,a911)),a1),f85(a911)),a184)),f2(a911))),f318(f318(f10(a911,a911,a1),a103),f318(f318(f9(a1,a911,a911),f318(f318(f10(a911,f918(a911,a911),a1),f223(a911)),a95)),x45422)))),f318(f318(f223(a911),f318(f94(a911),x45421)),f318(a103,x45422)))
% 109.14/108.83 [4543]E(f318(f318(f81(a1,a911),f318(f94(a1),f318(f318(f73(a1),x45431),a88))),f318(f318(f20(a1,a911,a911),f318(f318(f9(a1,a911,f918(a911,a911)),f318(f318(f10(a909,f918(a911,f918(a911,a911)),a1),f85(a911)),a184)),f318(a103,x45432))),f318(f318(f10(a911,a911,a1),a103),f318(f318(f9(a1,a911,a911),f318(f318(f10(a911,f918(a911,a911),a1),f224(a911)),a95)),x45432)))),f318(f318(f224(a911),f318(f94(a911),x45431)),f318(a103,x45432)))
% 109.14/108.83 [4385]E(f318(f318(f235(a1),x43851),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x43852)),x43852)),a88))),f318(f318(f81(a1,a1),f318(f318(f235(a1),x43851),f318(f94(a911),x43852))),f318(f318(f20(a1,a1,a1),f74(a1)),f7(a1))))
% 109.14/108.83 [4420]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f74(a1),x44201),x44202))),f318(f318(f74(a1),x44201),x44202))),a88),f318(f318(f74(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44201)),x44201)),a88)),x44202))
% 109.14/108.83 [4479]E(f318(f318(f30(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44791)),x44791)),a88))),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x44792)),x44792)),a88))),f318(f318(f30(a1),f318(f94(a1),x44791)),f318(f94(a1),x44792)))
% 109.14/108.83 [4533]E(f318(f248(x45331,x45331,a909),f318(f318(f20(x45331,a909,f918(x45331,a909)),f318(f318(f10(f918(x45331,f918(a909,a909)),f918(a909,f918(x45331,a909)),x45331),f9(x45331,a909,a909)),f318(f318(f10(f918(x45331,a909),f918(x45331,f918(a909,a909)),x45331),f318(f10(a909,f918(a909,a909),x45331),a316)),a315))),x45332)),f254(x45331,x45332))
% 109.14/108.83 [4592]E(f39(a1,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x45921)),x45921)),a88)),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x45922)),x45922)),a88))),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f39(a1,f318(f94(a1),x45921),f318(f94(a1),x45922))))
% 109.14/108.83 [4558]E(f318(f318(f30(a911),x45581),f318(f318(f73(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),x45582)),f318(f318(f30(a911),x45581),f318(a103,f318(a103,f318(a103,x45582)))))
% 109.14/108.83 [4559]E(f39(a911,x45591,f318(f318(f73(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),x45592)),f39(a911,x45591,f318(a103,f318(a103,f318(a103,x45592)))))
% 109.14/108.83 [4560]E(f39(a911,f318(f318(f73(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),x45601),x45602),f39(a911,f318(a103,f318(a103,f318(a103,x45601))),x45602))
% 109.14/108.83 [4585]E(f114(f318(x45851,f318(f318(f74(a90),f318(f94(a90),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),x45852))),f318(f191(x45851),x45852))
% 109.14/108.83 [4590]E(f318(f318(f30(a911),f318(f318(f73(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),x45901)),x45902),f318(f318(f30(a911),f318(a103,f318(a103,f318(a103,x45901)))),x45902))
% 109.14/108.83 [4652]~E(f117(x46521,x46522,x46523),f110(x46521))
% 109.14/108.83 [4653]~E(f117(x46531,x46532,x46533),f110(x46531))
% 109.14/108.83 [3406]E(f318(f183(x34061,x34062),x34063),f112(x34061,x34062))
% 109.14/108.83 [3425]E(f318(f190(x34251,x34252),x34253),f318(f120(x34251),x34252))
% 109.14/108.83 [3501]E(f318(f318(f145(x35011,x35012),x35013),f104(x35011)),f104(x35012))
% 109.14/108.83 [3541]E(f318(f175(x35411,x35412,x35413),f2(a911)),x35412)
% 109.14/108.83 [3543]E(f318(f318(f172(x35431,x35432),x35433),f104(x35432)),f104(f917(x35431,x35432)))
% 109.14/108.83 [3558]E(f318(f180(f912(x35581)),f160(x35581,x35582,x35583)),x35582)
% 109.14/108.83 [3577]E(f78(x35771,f56(x35771,x35772,x35773)),f318(f57(x35771,x35772),x35773))
% 109.14/108.83 [3581]E(f234(x35811,x35812,f234(x35812,x35811,x35813)),x35813)
% 109.14/108.83 [3601]E(f318(f159(x36011),f160(x36011,x36012,x36013)),f160(x36011,x36012,x36013))
% 109.14/108.83 [3626]E(f131(x36261,x36262,f143(x36261,x36263)),f143(x36261,f131(x36261,x36262,x36263)))
% 109.14/108.83 [3644]E(f318(f242(f912(x36441),f912(x36441)),f157(x36441,x36442,x36443)),f318(f127(x36441,x36442),x36443))
% 109.14/108.83 [3686]E(f318(f318(f142(x36861),x36862),f160(x36861,x36863,x36862)),f160(x36861,f318(a103,x36863),x36862))
% 109.14/108.83 [3717]E(f176(x37171,x37172,x37173,f2(a911)),x37172)
% 109.14/108.83 [3718]E(f19(x37181,x37182,x37183,f2(a90)),x37182)
% 109.14/108.83 [3719]E(f21(x37191,x37192,x37193,f2(a90)),x37192)
% 109.14/108.83 [3726]E(f154(x37261,x37262,x37263,f104(x37261)),f104(x37262))
% 109.14/108.83 [3727]E(f121(x37271,x37272,x37273,f110(x37271)),f110(x37272))
% 109.14/108.83 [3734]E(f318(f318(f155(x37341),f318(f318(f142(x37341),x37342),x37343)),f2(a911)),x37342)
% 109.14/108.83 [3762]E(f53(x37621,x37622,f104(x37621),x37623),f104(f917(x37621,x37622)))
% 109.14/108.83 [3783]P25(x37831,x37832,x37833,f179(f918(x37831,a909)))
% 109.14/108.83 [3886]E(f256(x38861,x38862,x38863),f318(f243(f918(a90,f918(a909,f915(f913(x38861)))),f917(a90,a90)),f35(x38861)))
% 109.14/108.83 [3940]E(f318(f66(x39401,x39402,x39401,x39403),f25(x39401)),x39403)
% 109.14/108.83 [4112]P1(f318(f318(f320(f917(x41121,x41121)),f318(f318(f243(x41121,x41121),x41122),x41122)),f298(x41121,x41123)))
% 109.14/108.83 [4697]~P1(f318(f318(f320(f917(f912(x46971),f912(x46971))),f318(f318(f243(f912(x46971),f912(x46971)),x46972),f104(x46971))),f136(x46971,x46973)))
% 109.14/108.83 [4698]~P1(f318(f318(f320(f917(f912(x46981),f912(x46981))),f318(f318(f243(f912(x46981),f912(x46981)),x46982),f104(x46981))),f138(x46981,x46983)))
% 109.14/108.83 [4699]~P1(f318(f318(f320(f917(f912(x46991),f912(x46991))),f318(f318(f243(f912(x46991),f912(x46991)),x46992),f104(x46991))),f148(x46991,x46993)))
% 109.14/108.83 [4700]~P1(f318(f318(f320(f917(f912(x47001),f912(x47001))),f318(f318(f243(f912(x47001),f912(x47001)),f104(x47001)),x47002)),f136(x47001,x47003)))
% 109.14/108.83 [4701]~P1(f318(f318(f320(f917(f912(x47011),f912(x47011))),f318(f318(f243(f912(x47011),f912(x47011)),f104(x47011)),x47012)),f148(x47011,x47013)))
% 109.14/108.83 [3476]E(f318(f318(f192(x34761),x34762),x34763),f193(x34761,f206(x34762,x34763)))
% 109.14/108.83 [3529]E(f318(f277(x35291,x35292),f318(f277(x35292,x35291),x35293)),x35293)
% 109.14/108.83 [3553]E(f318(f318(f172(x35531,x35532),f104(x35531)),x35533),f104(f917(x35531,x35532)))
% 109.14/108.83 [3556]E(f167(x35561,x35562,f318(f273(a911),x35563)),f318(f318(f166(x35561),x35563),x35562))
% 109.14/108.83 [3572]E(f318(f255(x35721,x35722),f318(f277(x35722,x35721),x35723)),f318(f275(x35722,x35721),x35723))
% 109.14/108.83 [3574]E(f143(x35741,f318(f127(x35741,x35742),x35743)),f318(f127(x35741,x35742),f143(x35741,x35743)))
% 109.14/108.83 [3575]E(f318(f275(x35751,x35752),f318(f277(x35752,x35751),x35753)),f318(f255(x35752,x35751),x35753))
% 109.14/108.83 [3576]E(f318(f255(x35761,x35762),f318(f277(x35762,x35761),x35763)),f318(f275(x35762,x35761),x35763))
% 109.14/108.83 [3594]E(f318(f127(x35941,x35942),f318(f159(x35941),x35943)),f318(f159(x35941),f318(f127(x35941,x35942),x35943)))
% 109.14/108.83 [3606]E(f318(f318(f129(x36061),x36062),f318(f162(x36061),x36063)),f318(f318(f129(x36061),f318(a103,x36062)),x36063))
% 109.14/108.83 [3622]E(f318(f301(x36221,x36222,x36223),f179(f918(x36221,a909))),f179(f918(x36222,a909)))
% 109.14/108.83 [3623]E(f318(f302(x36231,x36232,x36233),f233(f918(x36232,a909))),f233(f918(x36231,a909)))
% 109.14/108.83 [3624]E(f318(f302(x36241,x36242,x36243),f179(f918(x36242,a909))),f179(f918(x36241,a909)))
% 109.14/108.83 [3625]E(f318(f276(x36251,x36252,x36253),f179(f918(x36251,a909))),f179(f918(x36252,a909)))
% 109.14/108.83 [3650]E(f111(x36501,f117(f913(x36501),x36502,x36503)),f107(x36501,x36502,f111(x36501,x36503)))
% 109.14/108.83 [3651]E(f164(x36511,f318(f318(f142(x36511),x36512),x36513),f104(x36511)),f318(f318(f142(x36511),x36512),x36513))
% 109.14/108.83 [3652]E(f318(f318(f300(x36521),x36522),f318(f163(x36521),x36523)),f318(f163(x36521),f131(x36521,x36522,x36523)))
% 109.14/108.83 [3738]E(f318(f301(f917(x37381,x37382),x37382,f247(x37381,x37382)),x37383),f318(f275(x37381,x37382),x37383))
% 109.14/108.83 [3739]E(f318(f301(f917(x37391,x37392),x37391,f242(x37391,x37392)),x37393),f318(f255(x37391,x37392),x37393))
% 109.14/108.83 [3754]E(f318(f163(x37541),f160(x37541,f318(a103,x37542),x37543)),f318(f318(f300(x37541),x37543),f179(f918(x37541,a909))))
% 109.14/108.83 [3811]E(f318(f318(f243(x38111,x38112),f318(f242(x38111,x38112),x38113)),f318(f247(x38111,x38112),x38113)),x38113)
% 109.14/108.83 [3812]E(f318(f318(f243(x38121,x38122),f318(f242(x38121,x38122),x38123)),f318(f247(x38121,x38122),x38123)),x38123)
% 109.14/108.83 [3820]E(f318(f180(f913(x38201)),f117(x38201,x38202,x38203)),f318(f318(f73(a911),f318(f180(f913(x38201)),x38203)),f318(a103,f2(a911))))
% 109.14/108.83 [3822]E(f318(f318(f248(x38221,x38222,x38221),f18(x38221,x38222)),x38223),f318(f242(x38221,x38222),x38223))
% 109.14/108.83 [3946]E(f318(f66(x39461,x39461,x39462,f25(x39461)),x39463),x39463)
% 109.14/108.83 [3953]E(f318(f318(f125(x39531),f160(x39531,x39532,x39533)),f318(f318(f142(x39531),x39533),f104(x39531))),f318(f318(f142(x39531),x39533),f160(x39531,x39532,x39533)))
% 109.14/108.83 [4120]P1(f318(f318(f225(f918(x41201,a909)),f318(f163(x41201),f318(f127(x41201,x41202),x41203))),f318(f163(x41201),x41203)))
% 109.14/108.83 [4162]P1(f318(f318(f225(f918(x41621,a909)),f318(f163(x41621),f318(f318(f166(x41621),x41622),x41623))),f318(f163(x41621),x41623)))
% 109.14/108.83 [4163]P1(f318(f318(f225(f918(x41631,a909)),f318(f163(x41631),f318(f318(f129(x41631),x41632),x41633))),f318(f163(x41631),x41633)))
% 109.14/108.83 [4166]P1(f318(f318(f225(f918(x41661,a909)),f318(f163(x41661),f167(x41661,x41662,x41663))),f318(f163(x41661),x41662)))
% 109.14/108.83 [4167]P1(f318(f318(f225(f918(x41671,a909)),f318(f163(x41671),f161(x41671,x41672,x41673))),f318(f163(x41671),x41673)))
% 109.14/108.83 [4188]P25(f917(x41881,x41882),f917(x41882,x41881),f318(f248(x41881,x41882,f917(x41882,x41881)),f318(f9(x41882,x41881,f917(x41882,x41881)),f243(x41882,x41881))),x41883)
% 109.14/108.83 [4198]E(f318(f318(f318(f174(f912(x41981),f912(x41981)),f39(a911,x41982,f318(f180(f912(x41981)),x41983))),f158(x41981)),x41983),f318(f318(f318(f174(f912(x41981),f912(x41981)),x41982),f158(x41981)),x41983))
% 109.14/108.83 [4237]E(f318(f66(f912(x42371),f912(x42371),f912(x42371),f318(f318(f174(f912(x42371),f912(x42371)),x42372),f158(x42371))),f318(f318(f174(f912(x42371),f912(x42371)),x42373),f158(x42371))),f318(f318(f174(f912(x42371),f912(x42371)),f318(f318(f73(a911),x42372),x42373)),f158(x42371)))
% 109.14/108.83 [4240]P1(f318(f318(f320(f917(f912(x42401),f912(x42401))),f318(f318(f243(f912(x42401),f912(x42401)),x42402),x42402)),f149(x42401,f298(x42401,x42403))))
% 109.14/108.83 [4380]E(f78(f917(x43801,x43802),f318(f318(f20(f917(x43801,x43802),x43802,a909),f318(f318(f10(x43801,f918(x43802,a909),f917(x43801,x43802)),x43803),f242(x43801,x43802))),f247(x43801,x43802))),f78(f917(x43801,x43802),f318(f248(x43801,x43802,a909),x43803)))
% 109.14/108.83 [4381]E(f83(f917(x43811,x43812),f318(f318(f20(f917(x43811,x43812),x43812,a909),f318(f318(f10(x43811,f918(x43812,a909),f917(x43811,x43812)),x43813),f242(x43811,x43812))),f247(x43811,x43812))),f83(f917(x43811,x43812),f318(f248(x43811,x43812,a909),x43813)))
% 109.14/108.83 [4412]E(f318(f318(f279(f917(a911,x44121),x44121),f311(a911,x44121,a231,x44122)),f318(f318(f20(x44121,x44121,f917(a911,x44121)),f318(f318(f10(a911,f918(x44121,f917(a911,x44121)),x44121),f243(a911,x44121)),x44123)),f7(x44121))),f312(x44121,x44123,x44122))
% 109.14/108.83 [4472]E(f318(f249(x44721,x44721,x44722,x44722,f7(x44721),f7(x44722)),x44723),x44723)
% 109.14/108.83 [4551]E(f318(f133(f912(f912(x45511)),f912(f912(x45511)),f125(f912(x45511)),f104(f912(x45511))),f318(f318(f145(f912(x45511),f912(f912(x45511))),f318(f318(f9(f912(x45511),f912(x45511),f912(f912(x45511))),f318(f318(f10(f918(x45511,f912(x45511)),f918(f912(x45511),f912(f912(x45511))),f912(x45511)),f145(x45511,f912(x45511))),f318(f9(x45511,f912(x45511),f912(x45511)),f142(x45511)))),x45512)),f49(x45511,x45513,x45512))),f49(x45511,f318(a103,x45513),x45512))
% 109.14/108.83 [4618]E(f214(a911,f917(x46181,f913(x46181)),f2(a911),f318(f248(x46181,f913(x46181),a911),f318(f318(f9(x46181,a911,f918(f913(x46181),a911)),f318(f318(f10(f918(f913(x46181),f918(a911,a911)),f918(a911,f918(f913(x46181),a911)),x46181),f9(f913(x46181),a911,a911)),f318(f318(f10(f918(f913(x46181),a911),f918(f913(x46181),f918(a911,a911)),x46181),f318(f10(a911,f918(a911,a911),f913(x46181)),f73(a911))),f318(f318(f9(x46181,f918(f913(x46181),a911),f918(f913(x46181),a911)),f318(f318(f10(f918(a911,a911),f918(f918(f913(x46181),a911),f918(f913(x46181),a911)),x46181),f10(a911,a911,f913(x46181))),f318(f318(f10(a911,f918(a911,a911),x46181),f73(a911)),x46182))),f116(x46181,x46182))))),f71(a911))),f318(f126(x46181),x46183)),f318(f116(x46181,x46182),x46183))
% 109.14/108.83 [4625]E(f318(f318(f81(a1,x46251),f209(f318(f318(f66(f917(a1,a1),a1,x46251,f247(a1,a1)),f203(x46251)),x46252),f318(f318(f66(f917(a1,a1),a1,x46251,f247(a1,a1)),f203(x46251)),x46253))),f318(f318(f20(a1,a1,x46251),f318(f318(f10(a1,f918(a1,x46251),a1),f192(x46251)),f318(f318(f20(a1,a1,a1),f318(f318(f10(a1,f918(a1,a1),a1),f73(a1)),f318(f318(f10(a1,a1,a1),f318(f74(a1),f318(f318(f66(f917(a1,a1),a1,x46251,f242(a1,a1)),f203(x46251)),x46252))),f318(f318(f9(a1,a1,a1),f30(a1)),f318(f318(f66(f917(a1,a1),a1,x46251,f247(a1,a1)),f203(x46251)),x46252))))),f318(f318(f10(a1,a1,a1),f318(f74(a1),f318(f318(f66(f917(a1,a1),a1,x46251,f242(a1,a1)),f203(x46251)),x46253))),f318(f318(f9(a1,a1,a1),f30(a1)),f318(f318(f66(f917(a1,a1),a1,x46251,f247(a1,a1)),f203(x46251)),x46253)))))),f7(a1))),f221(x46251,x46252,x46253))
% 109.14/108.83 [4647]~E(f318(f318(f142(x46471),x46472),x46473),x46473)
% 109.14/108.83 [4648]~E(f318(f318(f142(x46481),x46482),x46483),x46483)
% 109.14/108.83 [4650]~E(f318(f318(f142(x46501),x46502),x46503),f104(x46501))
% 109.14/108.83 [4651]~E(f318(f318(f142(x46511),x46512),x46513),f104(x46511))
% 109.14/108.83 [4656]~E(f318(f318(f300(x46561),x46562),x46563),f179(f918(x46561,a909)))
% 109.14/108.83 [4657]~E(f318(f318(f300(x46571),x46572),x46573),f179(f918(x46571,a909)))
% 109.14/108.83 [4677]~E(f318(f301(x46771,f918(x46771,a909),x46772),x46773),f318(f299(x46771),x46773))
% 109.14/108.83 [3533]E(f318(f318(f150(x35331,f104(x35331)),x35332),x35333),f104(x35331))
% 109.14/108.83 [3534]E(f318(f318(f150(x35341,f104(x35341)),x35342),x35343),f104(x35341))
% 109.14/108.83 [3536]E(f318(f132(x35361),f318(f318(f142(x35361),x35362),x35363)),x35362)
% 109.14/108.83 [3537]E(f318(f162(x35371),f318(f318(f142(x35371),x35372),x35373)),x35373)
% 109.14/108.83 [3580]E(f318(f318(f129(x35801),f71(a911)),f318(f318(f142(x35801),x35802),x35803)),x35803)
% 109.14/108.83 [3612]E(f105(x36121,f318(f318(f129(x36121),x36122),x36123)),f318(f318(f129(x36121),x36122),f105(x36121,x36123)))
% 109.14/108.83 [3613]E(f105(x36131,f318(f318(f129(x36131),x36132),x36133)),f318(f318(f129(x36131),x36132),f105(x36131,x36133)))
% 109.14/108.83 [3615]E(f318(f318(f150(x36151,x36152),x36153),f318(f318(f155(x36151),x36152),x36153)),x36152)
% 109.14/108.83 [3634]E(f318(f318(f300(x36341),x36342),f318(f318(f300(x36341),x36342),x36343)),f318(f318(f300(x36341),x36342),x36343))
% 109.14/108.83 [3647]E(f318(f318(f300(x36471),x36472),f318(f163(x36471),x36473)),f318(f163(x36471),f318(f318(f142(x36471),x36472),x36473)))
% 109.14/108.83 [3648]E(f318(f318(f129(x36481),x36482),f318(f162(x36481),x36483)),f318(f162(x36481),f318(f318(f129(x36481),x36482),x36483)))
% 109.14/108.83 [3649]E(f318(f318(f129(x36491),x36492),f318(f162(x36491),x36493)),f318(f162(x36491),f318(f318(f129(x36491),x36492),x36493)))
% 109.14/108.83 [3661]E(f318(f318(f166(x36611),f71(a911)),f318(f318(f142(x36611),x36612),x36613)),f318(f318(f142(x36611),x36612),f104(x36611)))
% 109.14/108.83 [3704]E(f318(f57(x37041,x37042),f318(f318(f300(x37041),x37043),f179(f918(x37041,a909)))),x37043)
% 109.14/108.83 [3744]E(f318(f318(f73(a911),x37441),f318(f318(f73(a911),x37442),x37443)),f318(f318(f73(a911),x37442),f318(f318(f73(a911),x37441),x37443)))
% 109.14/108.83 [3745]E(f318(f318(f73(a1),x37451),f318(f318(f73(a1),x37452),x37453)),f318(f318(f73(a1),x37452),f318(f318(f73(a1),x37451),x37453)))
% 109.14/108.83 [3750]E(f318(f318(f245(x37501,x37502),f179(f918(x37501,a909))),x37503),f179(f918(f917(x37501,x37502),a909)))
% 109.14/108.83 [3775]E(f318(f318(f101(f918(x37751,a909)),x37752),x37753),f318(f318(f101(f918(x37751,a909)),x37753),x37752))
% 109.14/108.83 [3776]E(f318(f318(f92(f918(x37761,a909)),x37762),x37763),f318(f318(f92(f918(x37761,a909)),x37763),x37762))
% 109.14/108.83 [3778]E(f318(f318(f125(x37781),x37782),f318(f318(f142(x37781),x37783),f104(x37781))),f318(f158(x37781),f318(f318(f142(x37781),x37783),x37782)))
% 109.14/108.83 [3779]E(f318(f318(f125(x37791),f318(f159(x37791),x37792)),f318(f159(x37791),x37793)),f318(f159(x37791),f318(f318(f125(x37791),x37793),x37792)))
% 109.14/108.83 [3789]E(f318(f162(x37891),f318(f318(f166(x37891),f318(a103,x37892)),x37893)),f318(f318(f166(x37891),x37892),f318(f162(x37891),x37893)))
% 109.14/108.83 [3797]P1(f318(f318(f320(x37971),x37972),f318(f318(f300(x37971),x37972),x37973)))
% 109.14/108.83 [3801]E(f318(f318(f34(x38011,f918(x38012,a909)),f179(f918(x38011,a909))),x38013),f233(f918(x38012,a909)))
% 109.14/108.83 [3804]E(f318(f276(x38041,x38041,f254(x38041,x38042)),x38043),f318(f318(f92(f918(x38041,a909)),x38042),x38043))
% 109.14/108.83 [3819]E(f318(f180(f912(x38191)),f318(f318(f142(x38191),x38192),x38193)),f318(f318(f73(a911),f318(f180(f912(x38191)),x38193)),f318(a103,f2(a911))))
% 109.14/108.83 [3824]E(f105(x38241,f318(f318(f125(x38241),x38242),f318(f318(f142(x38241),x38243),f104(x38241)))),x38242)
% 109.14/108.83 [3825]E(f135(x38251,f318(f318(f125(x38251),x38252),f318(f318(f142(x38251),x38253),f104(x38251)))),x38253)
% 109.14/108.83 [3833]E(f318(f318(f125(x38331),f318(f318(f166(x38331),x38332),x38333)),f318(f318(f129(x38331),x38332),x38333)),x38333)
% 109.14/108.83 [3842]E(f318(f318(f3(a911),f318(f318(f73(a911),x38421),x38422)),f318(f318(f73(a911),x38423),x38422)),f318(f318(f3(a911),x38421),x38423))
% 109.14/108.83 [3843]E(f318(f318(f3(a911),f318(f318(f73(a911),x38431),x38432)),f318(f318(f73(a911),x38431),x38433)),f318(f318(f3(a911),x38432),x38433))
% 109.14/108.83 [3849]E(f318(f318(f125(x38491),f318(f159(x38491),x38492)),f318(f318(f142(x38491),x38493),f104(x38491))),f318(f159(x38491),f318(f318(f142(x38491),x38493),x38492)))
% 109.14/108.83 [3851]E(f318(f318(f73(a911),f318(f180(f912(x38511)),x38512)),f318(f180(f912(x38511)),x38513)),f318(f180(f912(x38511)),f318(f318(f125(x38511),x38512),x38513)))
% 109.14/108.83 [3854]E(f318(f318(f73(a911),f318(f180(f912(x38541)),x38542)),f318(f180(f912(x38541)),x38543)),f318(f180(f912(x38541)),f164(x38541,x38542,x38543)))
% 109.14/108.83 [3861]E(f318(f318(f101(f918(x38611,a909)),f318(f163(x38611),x38612)),f318(f163(x38611),x38613)),f318(f163(x38611),f318(f318(f125(x38611),x38612),x38613)))
% 109.14/108.83 [3862]E(f39(a911,f318(f318(f74(a911),x38621),x38622),f318(f318(f74(a911),x38621),x38623)),f318(f318(f74(a911),x38621),f39(a911,x38622,x38623)))
% 109.14/108.83 [3874]E(f318(f318(f166(x38741),f318(f318(f3(a911),x38742),f71(a911))),f318(f162(x38741),x38743)),f318(f162(x38741),f318(f318(f166(x38741),x38742),x38743)))
% 109.14/108.83 [3879]E(f318(f318(f92(f918(x38791,a909)),x38792),f318(f72(f918(x38791,a909)),x38793)),f318(f318(f3(f918(x38791,a909)),x38792),x38793))
% 109.14/108.83 [3880]E(f318(f318(f3(f918(x38801,a909)),x38802),f318(f72(f918(x38801,a909)),x38803)),f318(f318(f92(f918(x38801,a909)),x38802),x38803))
% 109.14/108.83 [3896]E(f318(f318(f245(x38961,x38962),x38963),f318(f18(f918(x38962,a909),x38961),f179(f918(x38962,a909)))),f179(f918(f917(x38961,x38962),a909)))
% 109.14/108.83 [3898]E(f318(f318(f74(a1),f318(f318(f235(a1),x38981),x38982)),f318(f318(f235(a1),x38981),x38983)),f318(f318(f235(a1),x38981),f318(f318(f73(a911),x38982),x38983)))
% 109.14/108.83 [3899]E(f318(f318(f3(a911),f318(f318(f74(a911),x38991),x38992)),f318(f318(f74(a911),x38991),x38993)),f318(f318(f74(a911),x38991),f318(f318(f3(a911),x38992),x38993)))
% 109.14/108.83 [3900]E(f318(f318(f73(a911),f318(f318(f74(a911),x39001),x39002)),f318(f318(f74(a911),x39001),x39003)),f318(f318(f74(a911),x39001),f318(f318(f73(a911),x39002),x39003)))
% 109.14/108.83 [3901]E(f318(f318(f3(a1),f318(f318(f74(a1),x39011),x39012)),f318(f318(f74(a1),x39011),x39013)),f318(f318(f74(a1),x39011),f318(f318(f3(a1),x39012),x39013)))
% 109.14/108.83 [3902]E(f318(f318(f73(a1),f318(f318(f74(a1),x39021),x39022)),f318(f318(f74(a1),x39021),x39023)),f318(f318(f74(a1),x39021),f318(f318(f73(a1),x39022),x39023)))
% 109.14/108.83 [3915]E(f318(f318(f33(x39151,f918(x39152,a909)),x39153),f318(f18(f918(x39152,a909),x39151),f179(f918(x39152,a909)))),f179(f918(x39152,a909)))
% 109.14/108.83 [3917]E(f39(a911,f318(f318(f74(a911),x39171),x39172),f318(f318(f74(a911),x39173),x39172)),f318(f318(f74(a911),f39(a911,x39171,x39173)),x39172))
% 109.14/108.83 [3921]E(f39(a1,f318(f318(f74(a1),x39211),f39(a1,x39212,x39213)),x39213),f39(a1,f318(f318(f74(a1),x39211),x39212),x39213))
% 109.14/108.83 [3922]E(f39(a1,f318(f318(f3(a1),x39221),f39(a1,x39222,x39223)),x39223),f39(a1,f318(f318(f3(a1),x39221),x39222),x39223))
% 109.14/108.83 [3923]E(f39(a1,f318(f318(f74(a1),x39231),f39(a1,x39232,x39233)),x39233),f39(a1,f318(f318(f74(a1),x39231),x39232),x39233))
% 109.14/108.83 [3924]P1(f318(f318(f225(f918(x39241,a909)),x39242),f318(f318(f300(x39241),x39243),x39242)))
% 109.14/108.83 [4003]E(f318(f318(f34(f918(x40031,a909),f918(x40031,a909)),x40032),f318(f101(f918(x40031,a909)),x40033)),f318(f318(f101(f918(x40031,a909)),x40033),f32(f918(x40031,a909),x40032)))
% 109.14/108.83 [4004]E(f318(f318(f33(f918(x40041,a909),f918(x40041,a909)),x40042),f318(f92(f918(x40041,a909)),x40043)),f318(f318(f92(f918(x40041,a909)),x40043),f31(f918(x40041,a909),x40042)))
% 109.14/108.83 [4014]E(f318(f163(x40141),f318(f318(f318(f174(f912(x40141),f912(x40141)),x40142),f158(x40141)),x40143)),f318(f163(x40141),x40143))
% 109.14/108.83 [4018]E(f318(f318(f166(x40181),f318(f180(f912(x40181)),f168(x40181,x40182,x40183))),x40183),f168(x40181,x40182,x40183))
% 109.14/108.83 [4022]E(f318(f180(f912(x40221)),f318(f318(f318(f174(f912(x40221),f912(x40221)),x40222),f158(x40221)),x40223)),f318(f180(f912(x40221)),x40223))
% 109.14/108.83 [4025]E(f318(f318(f248(x40251,x40252,x40252),f318(f18(f918(x40252,x40252),x40251),f7(x40252))),x40253),f318(f247(x40251,x40252),x40253))
% 109.14/108.83 [4031]E(f39(a1,f318(f318(f3(a1),f39(a1,x40311,x40312)),x40313),x40312),f39(a1,f318(f318(f3(a1),x40311),x40313),x40312))
% 109.14/108.83 [4032]E(f39(a1,f318(f318(f235(a1),f39(a1,x40321,x40322)),x40323),x40322),f39(a1,f318(f318(f235(a1),x40321),x40323),x40322))
% 109.14/108.83 [4035]E(f318(f318(f33(f918(f917(x40351,x40352),a909),f918(x40352,a909)),x40353),f275(x40351,x40352)),f318(f275(x40351,x40352),f31(f918(f917(x40351,x40352),a909),x40353)))
% 109.14/108.83 [4036]E(f318(f318(f33(f918(f917(x40361,x40362),a909),f918(x40361,a909)),x40363),f255(x40361,x40362)),f318(f255(x40361,x40362),f31(f918(f917(x40361,x40362),a909),x40363)))
% 109.14/108.83 [4056]E(f318(f66(x40561,x40561,x40561,x40562),f318(f318(f174(x40561,x40561),x40563),x40562)),f318(f318(f174(x40561,x40561),f318(a103,x40563)),x40562))
% 109.14/108.83 [4074]E(f318(f318(f129(x40741),f318(f318(f3(a911),f318(f180(f912(x40741)),x40742)),x40743)),f318(f159(x40741),x40742)),f318(f159(x40741),f318(f318(f166(x40741),x40743),x40742)))
% 109.14/108.83 [4075]E(f318(f318(f166(x40751),f318(f318(f3(a911),f318(f180(f912(x40751)),x40752)),x40753)),f318(f159(x40751),x40752)),f318(f159(x40751),f318(f318(f129(x40751),x40753),x40752)))
% 109.14/108.83 [4077]E(f318(f318(f73(a911),f318(f156(a911),f318(f318(f145(x40771,a911),x40772),x40773))),f318(f180(f912(x40771)),x40773)),f146(x40771,x40772,x40773))
% 109.14/108.83 [4090]E(f318(f318(f318(f174(f912(x40901),f912(x40901)),x40902),f158(x40901)),f318(f158(x40901),x40903)),f318(f158(x40901),f318(f318(f318(f174(f912(x40901),f912(x40901)),x40902),f158(x40901)),x40903)))
% 109.14/108.83 [4097]E(f318(f158(x40971),f318(f318(f318(f174(f912(x40971),f912(x40971)),x40972),f158(x40971)),x40973)),f318(f318(f318(f174(f912(x40971),f912(x40971)),f318(a103,x40972)),f158(x40971)),x40973))
% 109.14/108.83 [4113]P1(f318(f318(f225(a911),f318(f180(f912(x41131)),f318(f127(x41131,x41132),x41133))),f318(f180(f912(x41131)),x41133)))
% 109.14/108.83 [4128]E(f318(f318(f101(f918(f918(x41281,a909),a909)),f318(f299(x41281),x41282)),f318(f301(f918(x41281,a909),f918(x41281,a909),f318(f300(x41281),x41283)),f318(f299(x41281),x41282))),f318(f299(x41281),f318(f318(f300(x41281),x41283),x41282)))
% 109.14/108.83 [4159]P1(f318(f318(f225(a911),f318(f180(f912(x41591)),f168(x41591,x41592,x41593))),f318(f180(f912(x41591)),x41593)))
% 109.14/108.83 [4165]E(f318(f255(x41651,x41652),f318(f253(f917(x41651,x41652)),f318(f248(x41651,x41652,a909),x41653))),f318(f253(x41651),f318(f318(f10(f918(x41652,a909),a909,x41651),f79(x41652)),x41653)))
% 109.14/108.83 [4177]E(f318(f301(a911,a911,f318(f318(f9(a911,a911,a911),f73(a911)),x41771)),f294(a911,x41772,x41773)),f294(a911,f318(f318(f73(a911),x41772),x41771),f318(f318(f73(a911),x41773),x41771)))
% 109.14/108.83 [4191]E(f318(f301(a911,a911,f318(f318(f9(a911,a911,a911),f73(a911)),x41911)),f318(f293(a911,x41912),x41913)),f318(f293(a911,f318(f318(f73(a911),x41912),x41911)),f318(f318(f73(a911),x41913),x41911)))
% 109.14/108.83 [4208]E(f318(f318(f172(x42081,x42082),f318(f318(f145(f917(x42081,x42082),x42081),f242(x42081,x42082)),x42083)),f318(f318(f145(f917(x42081,x42082),x42082),f247(x42081,x42082)),x42083)),x42083)
% 109.14/108.83 [4213]E(f318(f318(f73(a911),f318(f318(f74(a911),x42131),f39(a911,f318(f318(f30(a911),x42132),x42131),x42133))),f39(a911,x42132,x42131)),f39(a911,x42132,f318(f318(f74(a911),x42131),x42133)))
% 109.14/108.83 [4225]E(f318(f318(f125(x42251),x42252),f318(f133(f912(x42251),f912(x42251),f125(x42251),f104(x42251)),x42253)),f318(f133(f912(x42251),f912(x42251),f125(x42251),x42252),x42253))
% 109.14/108.83 [4245]P1(f318(f318(f320(f917(x42451,x42451)),f318(f318(f243(x42451,x42451),x42452),x42452)),f318(f318(f174(f917(x42451,x42451),a909),f2(a911)),x42453)))
% 109.14/108.83 [4250]E(f318(f253(x42501),f318(f318(f10(f918(x42502,a909),a909,x42501),f79(x42502)),f318(f9(x42502,x42501,a909),x42503))),f318(f275(x42502,x42501),f318(f253(f917(x42502,x42501)),f318(f248(x42502,x42501,a909),x42503))))
% 109.14/108.83 [4267]E(f318(f318(f101(f918(x42671,a909)),f318(f318(f33(a911,f918(x42671,a909)),f294(a911,f71(a911),x42672)),x42673)),f318(x42673,f2(a911))),f318(f318(f33(a911,f918(x42671,a909)),f318(f292(a911),x42672)),x42673))
% 109.14/108.83 [4282]E(f318(f133(f912(x42821),f912(x42821),f125(x42821),f104(x42821)),f318(f318(f145(f912(x42821),f912(x42821)),f127(x42821,x42822)),x42823)),f318(f127(x42821,x42822),f318(f133(f912(x42821),f912(x42821),f125(x42821),f104(x42821)),x42823)))
% 109.14/108.83 [4286]E(f318(f247(f912(x42861),f912(x42861)),f157(x42861,x42862,x42863)),f318(f127(x42861,f318(f66(a909,a909,x42861,a313),x42862)),x42863))
% 109.14/108.83 [4325]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f74(a1),x43251),f318(f318(f30(a1),x43252),x43251))),f39(a1,x43252,x43251))),x43253),f318(f318(f73(a1),x43252),x43253))
% 109.14/108.83 [4366]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f74(a1),f318(f318(f30(a1),x43661),x43662)),x43662)),f39(a1,x43661,x43662))),x43663),f318(f318(f73(a1),x43661),x43663))
% 109.14/108.83 [4394]E(f78(f917(x43941,x43942),f318(f248(x43941,x43942,a909),f318(f318(f10(f918(x43942,f917(x43941,x43942)),f918(x43942,a909),x43941),f318(f10(f917(x43941,x43942),a909,x43942),x43943)),f243(x43941,x43942)))),f78(f917(x43941,x43942),x43943))
% 109.14/108.83 [4395]E(f83(f917(x43951,x43952),f318(f248(x43951,x43952,a909),f318(f318(f10(f918(x43952,f917(x43951,x43952)),f918(x43952,a909),x43951),f318(f10(f917(x43951,x43952),a909,x43952),x43953)),f243(x43951,x43952)))),f83(f917(x43951,x43952),x43953))
% 109.14/108.83 [4423]P1(f318(f318(f225(f918(x44231,a909)),f31(f918(x44231,a909),f318(f318(f92(f918(f918(x44231,a909),a909)),x44232),x44233))),f318(f318(f92(f918(x44231,a909)),f31(f918(x44231,a909),x44232)),f31(f918(x44231,a909),x44233))))
% 109.14/108.83 [4424]E(f318(f159(x44241),f318(f318(f318(f174(f912(x44241),f912(x44241)),f318(f318(f3(a911),f318(f180(f912(x44241)),x44242)),f39(a911,x44243,f318(f180(f912(x44241)),x44242)))),f158(x44241)),x44242)),f318(f318(f318(f174(f912(x44241),f912(x44241)),x44243),f158(x44241)),f318(f159(x44241),x44242)))
% 109.14/108.83 [4462]P1(f318(f318(f225(a911),f318(f180(f912(x44621)),f318(f318(f129(x44621),f318(f180(f912(x44621)),f168(x44621,x44622,x44623))),x44623))),f318(f180(f912(x44621)),x44623)))
% 109.14/108.83 [4687]~P1(f318(f56(x46871,x46872,f179(f918(x46871,a909))),x46873))
% 109.14/108.83 [4696]~P1(f318(f318(f320(f917(x46961,x46961)),f318(f318(f243(x46961,x46961),x46962),x46963)),f144(x46961,f104(f918(x46961,a911)))))
% 109.14/108.83 [3790]E(f318(f180(f912(x37901)),f318(f318(f166(x37901),x37902),x37903)),f318(f318(f223(a911),f318(f180(f912(x37901)),x37903)),x37902))
% 109.14/108.83 [3791]E(f318(f180(f912(x37911)),f318(f318(f129(x37911),x37912),x37913)),f318(f318(f3(a911),f318(f180(f912(x37911)),x37913)),x37912))
% 109.14/108.83 [3818]E(f318(f180(f912(f912(x38181))),f49(x38181,x38182,x38183)),f318(f318(f235(a911),f318(f180(f912(x38181)),x38183)),x38182))
% 109.14/108.83 [3835]E(f318(f318(f30(a911),f318(f318(f30(a911),x38351),x38352)),x38353),f318(f318(f30(a911),x38351),f318(f318(f74(a911),x38352),x38353)))
% 109.14/108.83 [3836]E(f318(f318(f3(a911),f318(f318(f3(a911),x38361),x38362)),x38363),f318(f318(f3(a911),x38361),f318(f318(f73(a911),x38362),x38363)))
% 109.14/108.83 [3837]E(f318(f318(f73(a911),f318(f318(f73(a911),x38371),x38372)),x38373),f318(f318(f73(a911),x38371),f318(f318(f73(a911),x38372),x38373)))
% 109.14/108.83 [3838]E(f318(f318(f73(a1),f318(f318(f73(a1),x38381),x38382)),x38383),f318(f318(f73(a1),x38381),f318(f318(f73(a1),x38382),x38383)))
% 109.14/108.83 [3839]E(f318(f318(f235(a1),f318(f318(f235(a1),x38391),x38392)),x38393),f318(f318(f235(a1),x38391),f318(f318(f74(a911),x38392),x38393)))
% 109.14/108.83 [3840]E(f318(f318(f74(a911),f318(f318(f74(a911),x38401),x38402)),x38403),f318(f318(f74(a911),x38401),f318(f318(f74(a911),x38402),x38403)))
% 109.14/108.83 [3841]E(f318(f318(f74(a1),f318(f318(f74(a1),x38411),x38412)),x38413),f318(f318(f74(a1),x38411),f318(f318(f74(a1),x38412),x38413)))
% 109.14/108.83 [3860]E(f153(x38601,f318(f318(f142(f918(x38601,a909)),x38602),x38603)),f165(x38601,x38602,f153(x38601,x38603)))
% 109.14/108.83 [3897]E(f318(f318(f3(a911),f318(f318(f3(a911),x38971),x38972)),x38973),f318(f318(f3(a911),f318(f318(f3(a911),x38971),x38973)),x38972))
% 109.14/108.83 [3905]E(f318(f318(f92(f918(x39051,a909)),x39052),f318(f318(f3(f918(x39051,a909)),x39053),x39052)),f179(f918(x39051,a909)))
% 109.14/108.83 [3909]E(f318(f318(f145(a911,x39091),f318(f18(x39091,a911),x39092)),f130(a911,f318(f293(a911,f2(a911)),x39093))),f160(x39091,x39093,x39092))
% 109.14/108.83 [3951]E(f32(f918(x39511,a909),f318(f318(f300(f918(x39511,a909)),x39512),x39513)),f318(f318(f92(f918(x39511,a909)),x39512),f32(f918(x39511,a909),x39513)))
% 109.14/108.83 [3952]E(f31(f918(x39521,a909),f318(f318(f300(f918(x39521,a909)),x39522),x39523)),f318(f318(f101(f918(x39521,a909)),x39522),f31(f918(x39521,a909),x39523)))
% 109.14/108.83 [3954]E(f160(x39541,f318(f180(f912(x39541)),f318(f127(x39541,f318(a315,x39542)),x39543)),x39542),f318(f127(x39541,f318(a315,x39542)),x39543))
% 109.14/108.83 [3956]E(f318(f318(f3(a911),f318(f318(f74(a911),x39561),x39562)),f318(f318(f74(a911),x39563),x39562)),f318(f318(f74(a911),f318(f318(f3(a911),x39561),x39563)),x39562))
% 109.14/108.83 [3957]E(f318(f318(f73(a911),f318(f318(f74(a911),x39571),x39572)),f318(f318(f74(a911),x39573),x39572)),f318(f318(f74(a911),f318(f318(f73(a911),x39571),x39573)),x39572))
% 109.14/108.83 [3958]E(f318(f318(f3(a1),f318(f318(f74(a1),x39581),x39582)),f318(f318(f74(a1),x39583),x39582)),f318(f318(f74(a1),f318(f318(f3(a1),x39581),x39583)),x39582))
% 109.14/108.83 [3959]E(f318(f318(f73(a1),f318(f318(f74(a1),x39591),x39592)),f318(f318(f74(a1),x39593),x39592)),f318(f318(f74(a1),f318(f318(f73(a1),x39591),x39593)),x39592))
% 109.14/108.83 [3960]E(f318(f318(f223(a911),f318(f318(f3(a911),x39601),x39602)),f318(f318(f3(a911),x39603),x39602)),f318(f318(f3(a911),f318(f318(f223(a911),x39601),x39603)),x39602))
% 109.14/108.83 [3980]E(f318(f318(f92(f918(f912(x39801),a909)),f151(x39801,x39802)),f151(x39801,x39803)),f151(x39801,f318(f318(f92(f918(x39801,a909)),x39802),x39803)))
% 109.14/108.83 [3983]E(f318(f318(f101(f918(x39831,a909)),x39832),f318(f318(f101(f918(x39831,a909)),x39832),x39833)),f318(f318(f101(f918(x39831,a909)),x39832),x39833))
% 109.14/108.83 [3984]E(f318(f318(f101(f918(x39841,a909)),x39842),f318(f318(f3(f918(x39841,a909)),x39843),x39842)),f318(f318(f101(f918(x39841,a909)),x39842),x39843))
% 109.14/108.83 [3985]E(f318(f318(f92(f918(x39851,a909)),x39852),f318(f318(f92(f918(x39851,a909)),x39852),x39853)),f318(f318(f92(f918(x39851,a909)),x39852),x39853))
% 109.14/108.83 [3997]E(f318(f318(f280(x39971,x39972,x39972),x39973),f298(x39972,f179(f918(f917(x39972,x39972),a909)))),x39973)
% 109.14/108.83 [4000]E(f318(f318(f101(f918(x40001,a909)),f318(f318(f300(x40001),x40002),f179(f918(x40001,a909)))),x40003),f318(f318(f300(x40001),x40002),x40003))
% 109.14/108.83 [4017]E(f318(f318(f3(a911),f318(f318(f3(a911),f318(a103,x40171)),x40172)),f318(a103,x40173)),f318(f318(f3(a911),f318(f318(f3(a911),x40171),x40172)),x40173))
% 109.14/108.83 [4043]E(f318(f318(f92(f918(f918(x40431,a909),a909)),f318(f299(x40431),x40432)),f318(f299(x40431),x40433)),f318(f299(x40431),f318(f318(f92(f918(x40431,a909)),x40432),x40433)))
% 109.14/108.83 [4046]E(f318(f318(f101(f918(x40461,a909)),f318(f72(f918(x40461,a909)),x40462)),x40463),f318(f72(f918(x40461,a909)),f318(f318(f3(f918(x40461,a909)),x40462),x40463)))
% 109.14/108.83 [4054]E(f318(f318(f300(x40541),x40542),f318(f318(f3(f918(x40541,a909)),x40543),f318(f318(f300(x40541),x40542),f179(f918(x40541,a909))))),f318(f318(f300(x40541),x40542),x40543))
% 109.14/108.83 [4063]P1(f318(f318(f225(f918(x40631,a909)),x40632),f318(f318(f101(f918(x40631,a909)),x40633),x40632)))
% 109.14/108.83 [4064]P1(f318(f318(f225(f918(x40641,a909)),x40642),f318(f318(f101(f918(x40641,a909)),x40642),x40643)))
% 109.14/108.83 [4068]E(f318(f318(f92(f918(x40681,a909)),f318(f72(f918(x40681,a909)),x40682)),f318(f72(f918(x40681,a909)),x40683)),f318(f72(f918(x40681,a909)),f318(f318(f101(f918(x40681,a909)),x40682),x40683)))
% 109.14/108.83 [4069]E(f318(f318(f101(f918(x40691,a909)),f318(f72(f918(x40691,a909)),x40692)),f318(f72(f918(x40691,a909)),x40693)),f318(f72(f918(x40691,a909)),f318(f318(f92(f918(x40691,a909)),x40692),x40693)))
% 109.14/108.83 [4083]P1(f318(f318(f225(f918(x40831,a909)),f318(f163(x40831),x40832)),f318(f163(x40831),f318(f318(f142(x40831),x40833),x40832))))
% 109.14/108.83 [4094]E(f318(f318(f101(f918(x40941,a909)),f318(f318(f3(f918(x40941,a909)),x40942),x40943)),f318(f318(f92(f918(x40941,a909)),x40942),x40943)),x40942)
% 109.14/108.83 [4146]E(f318(f318(f8(x41461,a1),f318(f318(f10(a911,a1,x41461),f91(a1)),x41462)),x41463),f318(f91(a1),f318(f318(f8(x41461,a911),x41462),x41463)))
% 109.14/108.83 [4147]E(f318(f318(f11(x41471,a1),f318(f318(f10(a911,a1,x41471),f91(a1)),x41472)),x41473),f318(f91(a1),f318(f318(f11(x41471,a911),x41472),x41473)))
% 109.14/108.83 [4193]E(f318(f318(f125(x41931),f168(x41931,x41932,x41933)),f318(f318(f129(x41931),f318(f180(f912(x41931)),f168(x41931,x41932,x41933))),x41933)),x41933)
% 109.14/108.83 [4196]E(f318(f72(f918(f917(x41961,x41962),a909)),f318(f318(f245(x41961,x41962),x41963),f318(f18(f918(x41962,a909),x41961),f233(f918(x41962,a909))))),f318(f318(f245(x41961,x41962),f318(f72(f918(x41961,a909)),x41963)),f318(f18(f918(x41962,a909),x41961),f233(f918(x41962,a909)))))
% 109.14/108.83 [4197]E(f318(f72(f918(f917(x41971,x41972),a909)),f318(f318(f245(x41971,x41972),f233(f918(x41971,a909))),f318(f18(f918(x41972,a909),x41971),x41973))),f318(f318(f245(x41971,x41972),f233(f918(x41971,a909))),f318(f18(f918(x41972,a909),x41971),f318(f72(f918(x41972,a909)),x41973))))
% 109.14/108.83 [4246]E(f318(f318(f33(f918(x42461,a909),f918(x42461,a909)),x42462),f318(f318(f9(f918(x42461,a909),f918(x42461,a909),f918(x42461,a909)),f92(f918(x42461,a909))),x42463)),f318(f318(f92(f918(x42461,a909)),f31(f918(x42461,a909),x42462)),x42463))
% 109.14/108.83 [4253]E(f318(f133(f912(x42531),f912(x42531),f125(x42531),f104(x42531)),f318(f318(f142(f912(x42531)),x42532),x42533)),f318(f318(f125(x42531),x42532),f318(f133(f912(x42531),f912(x42531),f125(x42531),f104(x42531)),x42533)))
% 109.14/108.83 [4273]E(f318(f318(f300(f918(x42731,a909)),f318(f276(x42731,x42731,x42732),f318(f318(f300(x42731),x42733),f179(f918(x42731,a909))))),f179(f918(f918(x42731,a909),a909))),f318(f318(f54(x42731),f318(f318(f300(x42731),x42733),f179(f918(x42731,a909)))),x42732))
% 109.14/108.83 [4283]E(f318(f318(f73(a911),f318(f318(f74(a911),x42831),f318(f318(f30(a911),x42832),x42833))),f318(f318(f30(a911),f318(f318(f74(a911),x42831),f39(a911,x42832,x42833))),x42833)),f318(f318(f30(a911),f318(f318(f74(a911),x42831),x42832)),x42833))
% 109.14/108.83 [4284]E(f318(f318(f73(a1),f318(f318(f74(a1),x42841),f318(f318(f30(a1),x42842),x42843))),f318(f318(f30(a1),f318(f318(f74(a1),x42841),f39(a1,x42842,x42843))),x42843)),f318(f318(f30(a1),f318(f318(f74(a1),x42841),x42842)),x42843))
% 109.14/108.83 [4312]E(f318(f318(f3(f918(x43121,a909)),f318(f163(x43121),x43122)),f318(f318(f300(x43121),x43123),f179(f918(x43121,a909)))),f318(f163(x43121),f318(f127(x43121,f318(f318(f10(a909,a909,x43121),a313),f318(a315,x43123))),x43122)))
% 109.14/108.83 [4364]E(f318(f318(f125(x43641),f318(f133(f912(x43641),f912(x43641),f125(x43641),f104(x43641)),x43642)),f318(f133(f912(x43641),f912(x43641),f125(x43641),f104(x43641)),x43643)),f318(f133(f912(x43641),f912(x43641),f125(x43641),f104(x43641)),f318(f318(f125(f912(x43641)),x43642),x43643)))
% 109.14/108.83 [4368]E(f318(f318(f243(f912(x43681),f912(x43681)),f318(f127(x43681,x43682),x43683)),f318(f127(x43681,f318(f66(a909,a909,x43681,a313),x43682)),x43683)),f157(x43681,x43682,x43683))
% 109.14/108.83 [4372]E(f318(f318(f73(a911),f318(f318(f73(a911),f318(f318(f30(a911),x43721),x43722)),f318(f318(f30(a911),x43723),x43722))),f318(f318(f30(a911),f318(f318(f73(a911),f39(a911,x43721,x43722)),f39(a911,x43723,x43722))),x43722)),f318(f318(f30(a911),f318(f318(f73(a911),x43721),x43723)),x43722))
% 109.14/108.83 [4373]E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f30(a1),x43731),x43732)),f318(f318(f30(a1),x43733),x43732))),f318(f318(f30(a1),f318(f318(f73(a1),f39(a1,x43731,x43732)),f39(a1,x43733,x43732))),x43732)),f318(f318(f30(a1),f318(f318(f73(a1),x43731),x43733)),x43732))
% 109.14/108.83 [4427]E(f318(f318(f92(f918(f912(x44271),a909)),f318(f318(f9(f912(x44271),f918(f912(x44271),a909),a909),f320(f912(x44271))),f152(x44271,x44272))),f318(f318(f9(f912(x44271),f918(f912(x44271),a909),a909),f320(f912(x44271))),f152(x44271,x44273))),f151(x44271,f318(f318(f92(f918(x44271,a909)),f318(f318(f9(x44271,f918(x44271,a909),a909),f320(x44271)),x44272)),f318(f318(f9(x44271,f918(x44271,a909),a909),f320(x44271)),x44273))))
% 109.14/108.83 [4437]E(f318(f253(x44371),f318(f318(f20(x44371,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44371),a317),f318(f318(f9(x44371,x44371,a909),a315),x44372))),f318(f318(f9(x44371,f918(x44371,a909),a909),f320(x44371)),x44373))),f318(f318(f300(x44371),x44372),x44373))
% 109.14/108.83 [4438]E(f318(f253(x44381),f318(f318(f20(x44381,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44381),a317),f318(f318(f9(x44381,x44381,a909),a315),x44382))),f318(f318(f9(x44381,f918(x44381,a909),a909),f320(x44381)),x44383))),f318(f318(f300(x44381),x44382),x44383))
% 109.14/108.83 [4460]E(f318(f318(f81(f912(f912(x44601)),f912(f912(x44601))),f48(x44601,x44602)),f318(f318(f20(f912(f912(x44601)),f912(f912(x44601)),f912(f912(x44601))),f318(f318(f10(f912(f912(x44601)),f918(f912(f912(x44601)),f912(f912(x44601))),f912(f912(x44601))),f125(f912(x44601))),f318(f145(f912(x44601),f912(x44601)),f318(f142(x44601),x44603)))),f7(f912(f912(x44601))))),f48(x44601,f318(f318(f142(x44601),x44603),x44602)))
% 109.14/108.83 [4463]E(f318(f253(x44631),f318(f318(f20(x44631,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44631),a317),f318(f318(f9(x44631,f918(x44631,a909),a909),f320(x44631)),x44632))),f318(f318(f9(x44631,f918(x44631,a909),a909),f320(x44631)),x44633))),f318(f318(f101(f918(x44631,a909)),x44632),x44633))
% 109.14/108.83 [4464]E(f318(f253(x44641),f318(f318(f20(x44641,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44641),a316),f318(f318(f9(x44641,f918(x44641,a909),a909),f320(x44641)),x44642))),f318(f318(f9(x44641,f918(x44641,a909),a909),f320(x44641)),x44643))),f318(f318(f92(f918(x44641,a909)),x44642),x44643))
% 109.14/108.83 [4552]E(f318(f318(f33(x45521,f918(f918(x45521,a909),a909)),x45522),f318(f318(f9(x45521,f918(f918(x45521,a909),a909),f918(f918(x45521,a909),a909)),f318(f318(f10(f918(x45521,a909),f918(f918(f918(x45521,a909),a909),f918(f918(x45521,a909),a909)),x45521),f300(f918(x45521,a909))),f318(f318(f10(f918(x45521,a909),f918(x45521,a909),x45521),f276(x45521,x45521,x45523)),f318(f318(f9(x45521,f918(x45521,a909),f918(x45521,a909)),f300(x45521)),f179(f918(x45521,a909)))))),f179(f918(f918(x45521,a909),a909)))),f318(f318(f54(x45521),x45522),x45523))
% 109.14/108.83 [4561]E(f318(f318(f192(x45611),f318(f318(f74(a1),f318(f318(f66(f917(a1,a1),a1,x45611,f242(a1,a1)),f203(x45611)),x45612)),f318(f318(f66(f917(a1,a1),a1,x45611,f242(a1,a1)),f203(x45611)),x45613))),f318(f318(f74(a1),f318(f318(f66(f917(a1,a1),a1,x45611,f247(a1,a1)),f203(x45611)),x45612)),f318(f318(f66(f917(a1,a1),a1,x45611,f247(a1,a1)),f203(x45611)),x45613))),f219(x45611,x45612,x45613))
% 109.14/108.83 [4565]E(f318(f253(f912(x45651)),f318(f318(f20(f912(x45651),a909,a909),f318(f318(f10(a909,f918(a909,a909),f912(x45651)),a316),f318(f318(f9(f912(x45651),a911,a909),f318(f318(f10(a911,f918(a911,a909),f912(x45651)),a315),f180(f912(x45651)))),x45652))),f318(f318(f9(f912(x45651),f918(x45651,a909),a909),f318(f318(f10(f918(x45651,a909),f918(f918(x45651,a909),a909),f912(x45651)),f225(f918(x45651,a909))),f163(x45651))),f318(f163(x45651),x45653)))),f318(f163(f912(x45651)),f49(x45651,x45652,x45653)))
% 109.14/108.83 [3973]E(f39(a911,f318(f318(f73(a911),f318(f318(f74(a911),x39731),x39732)),x39733),x39732),f39(a911,x39733,x39732))
% 109.14/108.83 [4016]E(f130(a911,f318(f293(a911,f318(f318(f73(a911),x40161),x40162)),x40163)),f318(f318(f129(a911),x40162),f130(a911,f318(f293(a911,x40161),x40163))))
% 109.14/108.83 [4053]E(f318(f318(f73(a1),f318(f91(a1),x40531)),f318(f318(f73(a1),f318(f91(a1),x40532)),x40533)),f318(f318(f73(a1),f318(f91(a1),f318(f318(f73(a911),x40531),x40532))),x40533))
% 109.14/108.83 [4059]E(f318(f318(f101(f918(x40591,a909)),f318(f318(f3(f918(x40591,a909)),x40592),x40593)),x40593),f318(f318(f101(f918(x40591,a909)),x40592),x40593))
% 109.14/108.83 [4060]E(f318(f318(f3(f918(x40601,a909)),f318(f318(f3(f918(x40601,a909)),x40602),x40603)),x40603),f318(f318(f3(f918(x40601,a909)),x40602),x40603))
% 109.14/108.83 [4084]E(f318(f318(f280(x40841,x40841,x40842),f298(x40841,f179(f918(f917(x40841,x40841),a909)))),x40843),x40843)
% 109.14/108.83 [4092]E(f318(f318(f101(f918(x40921,a909)),f318(f272(x40921),x40922)),f318(f272(x40921),x40923)),f318(f272(x40921),f318(f318(f101(f918(f917(x40921,x40921),a909)),x40922),x40923)))
% 109.14/108.83 [4102]E(f257(x41021,f318(f318(f142(f917(a90,x41021)),f318(f318(f243(a90,x41021),f2(a90)),x41022)),x41023)),f257(x41021,x41023))
% 109.14/108.83 [4104]E(f318(f318(f92(f918(x41041,a909)),f32(f918(x41041,a909),x41042)),f32(f918(x41041,a909),x41043)),f32(f918(x41041,a909),f318(f318(f101(f918(f918(x41041,a909),a909)),x41042),x41043)))
% 109.14/108.83 [4105]E(f318(f318(f101(f918(x41051,a909)),f31(f918(x41051,a909),x41052)),f31(f918(x41051,a909),x41053)),f31(f918(x41051,a909),f318(f318(f101(f918(f918(x41051,a909),a909)),x41052),x41053)))
% 109.14/108.83 [4144]E(f318(f318(f280(x41441,x41441,x41441),f318(f318(f174(f917(x41441,x41441),a909),x41442),x41443)),x41443),f318(f318(f174(f917(x41441,x41441),a909),f318(a103,x41442)),x41443))
% 109.14/108.83 [4185]P1(f318(f318(f225(f918(x41851,a909)),f318(f318(f92(f918(x41851,a909)),x41852),x41853)),x41853))
% 109.14/108.83 [4186]P1(f318(f318(f225(f918(x41861,a909)),f318(f318(f92(f918(x41861,a909)),x41862),x41863)),x41862))
% 109.14/108.83 [4187]P1(f318(f318(f225(f918(x41871,a909)),f318(f318(f3(f918(x41871,a909)),x41872),x41873)),x41872))
% 109.14/108.83 [4210]E(f298(x42101,f318(f318(f101(f918(f917(x42101,x42101),a909)),f298(x42101,x42102)),f298(x42101,x42103))),f298(x42101,f318(f318(f101(f918(f917(x42101,x42101),a909)),x42102),x42103)))
% 109.14/108.83 [4214]E(f31(f918(x42141,a909),f318(f318(f300(f918(x42141,a909)),x42142),f318(f318(f300(f918(x42141,a909)),x42143),f179(f918(f918(x42141,a909),a909))))),f318(f318(f101(f918(x42141,a909)),x42142),x42143))
% 109.14/108.83 [4215]E(f32(f918(x42151,a909),f318(f318(f300(f918(x42151,a909)),x42152),f318(f318(f300(f918(x42151,a909)),x42153),f179(f918(f918(x42151,a909),a909))))),f318(f318(f92(f918(x42151,a909)),x42152),x42153))
% 109.14/108.83 [4220]E(f318(f318(f280(x42201,x42201,x42201),f318(f318(f174(f917(x42201,x42201),a909),x42202),x42203)),x42203),f318(f318(f280(x42201,x42201,x42201),x42203),f318(f318(f174(f917(x42201,x42201),a909),x42202),x42203)))
% 109.14/108.83 [4287]E(f318(f318(f101(f918(x42871,a909)),f318(f253(x42871),f318(f318(f9(x42871,x42871,a909),a315),x42872))),x42873),f318(f318(f300(x42871),x42872),x42873))
% 109.14/108.83 [4288]E(f318(a95,f318(f318(f8(x42881,a1),f318(f318(f10(a911,a1,x42881),f91(a1)),x42882)),x42883)),f318(f318(f8(x42881,a911),x42882),x42883))
% 109.14/108.83 [4289]E(f318(a95,f318(f318(f11(x42891,a1),f318(f318(f10(a911,a1,x42891),f91(a1)),x42892)),x42893)),f318(f318(f11(x42891,a911),x42892),x42893))
% 109.14/108.83 [4361]E(f318(f147(f912(x43611),x43611,f318(f162(x43611),x43612),f318(f18(f918(f912(x43611),f912(x43611)),x43611),f318(f318(f9(f912(x43611),f912(x43611),f912(x43611)),f125(x43611)),x43612))),x43613),f318(f162(x43611),f318(f318(f125(x43611),x43613),x43612)))
% 109.14/108.83 [4389]P1(f318(f318(f225(f918(f918(x43891,a909),a909)),f318(f318(f101(f918(f918(x43891,a909),a909)),f318(f299(x43891),x43892)),f318(f299(x43891),x43893))),f318(f299(x43891),f318(f318(f101(f918(x43891,a909)),x43892),x43893))))
% 109.14/108.83 [4478]E(f318(f253(x44781),f318(f318(f20(x44781,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44781),a316),f318(f318(f9(x44781,f918(x44781,a909),a909),f320(x44781)),x44782))),f318(f318(f10(a909,a909,x44781),a313),f318(f318(f9(x44781,f918(x44781,a909),a909),f320(x44781)),x44783)))),f318(f318(f3(f918(x44781,a909)),x44782),x44783))
% 109.14/108.83 [4504]E(f318(f29(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),f318(f318(f9(a911,a911,a909),f226(a911)),f318(f180(f912(x45041)),x45042)))),f318(f318(f10(x45041,a909,a911),x45043),f318(f155(x45041),x45042))))),f318(f180(f912(x45041)),f318(f127(x45041,x45043),x45042)))
% 109.14/108.83 [4506]E(f318(f180(f912(x45061)),f167(x45061,x45062,x45063)),f318(f29(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),f318(f318(f9(a911,a911,a909),f226(a911)),f318(f180(f912(x45061)),x45062)))),f318(f318(f9(a911,f918(a911,a909),a909),f320(a911)),x45063)))))
% 109.14/108.83 [4616]E(f318(f318(f92(f918(f917(f912(x46161),f912(x46161)),a909)),f318(f301(f917(f917(x46161,f912(x46161)),f917(x46161,f912(x46161))),f917(f912(x46161),f912(x46161)),f249(f917(x46161,f912(x46161)),f912(x46161),f917(x46161,f912(x46161)),f912(x46161),f318(f248(x46161,f912(x46161),f912(x46161)),f142(x46161)),f318(f248(x46161,f912(x46161),f912(x46161)),f142(x46161)))),f311(x46161,f912(x46161),x46162,f318(f134(x46161,x46162),x46163)))),f318(f253(f917(f912(x46161),f912(x46161))),f318(f248(f912(x46161),f912(x46161),a909),f318(f318(f9(f912(x46161),f918(f912(x46161),a909),f918(f912(x46161),a909)),f318(f318(f10(f918(a909,a909),f918(f918(f912(x46161),a909),f918(f912(x46161),a909)),f912(x46161)),f10(a909,a909,f912(x46161))),f318(f318(f10(a909,f918(a909,a909),f912(x46161)),a316),f318(f318(f9(f912(x46161),a911,a909),f318(f318(f10(a911,f918(a911,a909),f912(x46161)),a315),f180(f912(x46161)))),f318(a103,x46163))))),f318(f318(f9(f912(x46161),a911,a909),f318(f318(f10(a911,f918(a911,a909),f912(x46161)),a315),f180(f912(x46161)))),f318(a103,x46163)))))),f318(f134(x46161,x46162),f318(a103,x46163)))
% 109.14/108.83 [4106]E(f39(a911,f318(a103,f318(f318(f73(a911),f318(f318(f74(a911),x41061),x41062)),x41063)),x41062),f39(a911,f318(a103,x41063),x41062))
% 109.14/108.83 [4343]E(f318(f253(x43431),f318(f318(f20(x43431,a909,a909),f318(f318(f10(a909,f918(a909,a909),x43431),a316),x43432)),x43433)),f318(f318(f92(f918(x43431,a909)),f318(f253(x43431),x43432)),f318(f253(x43431),x43433)))
% 109.14/108.83 [4344]E(f318(f253(x43441),f318(f318(f20(x43441,a909,a909),f318(f318(f10(a909,f918(a909,a909),x43441),a317),x43442)),x43443)),f318(f318(f101(f918(x43441,a909)),f318(f253(x43441),x43442)),f318(f253(x43441),x43443)))
% 109.14/108.83 [4346]E(f318(f318(f125(x43461),f318(f318(f129(x43461),f39(a911,x43462,f318(f180(f912(x43461)),x43463))),x43463)),f318(f318(f166(x43461),f39(a911,x43462,f318(f180(f912(x43461)),x43463))),x43463)),f318(f318(f318(f174(f912(x43461),f912(x43461)),x43462),f158(x43461)),x43463))
% 109.14/108.83 [4352]E(f318(f253(x43521),f318(f318(f20(x43521,a909,a909),f318(f318(f10(a909,f918(a909,a909),x43521),a321),x43522)),x43523)),f318(f318(f101(f918(x43521,a909)),f318(f72(f918(x43521,a909)),f318(f253(x43521),x43522))),f318(f253(x43521),x43523)))
% 109.14/108.83 [4374]E(f318(f318(f73(a911),f318(f180(f912(x43741)),f318(f127(x43741,x43742),x43743))),f318(f180(f912(x43741)),f318(f127(x43741,f318(f318(f10(a909,a909,x43741),a313),x43742)),x43743))),f318(f180(f912(x43741)),x43743))
% 109.14/108.83 [4397]P1(f318(f318(f225(f918(x43971,a909)),f318(f318(f101(f918(x43971,a909)),f32(f918(x43971,a909),x43972)),f32(f918(x43971,a909),x43973))),f32(f918(x43971,a909),f318(f318(f92(f918(f918(x43971,a909),a909)),x43972),x43973))))
% 109.14/108.83 [4410]E(f318(f163(x44101),f318(f127(x44101,f318(f318(f10(a909,a909,x44101),a313),f318(f318(f9(x44101,x44101,a909),a315),x44102))),x44103)),f318(f318(f3(f918(x44101,a909)),f318(f163(x44101),x44103)),f318(f318(f300(x44101),x44102),f179(f918(x44101,a909)))))
% 109.14/108.83 [4419]P1(f318(f318(f225(f918(f917(x44191,x44191),a909)),f318(f318(f101(f918(f917(x44191,x44191),a909)),f298(x44191,x44192)),f298(x44191,x44193))),f298(x44191,f318(f318(f101(f918(f917(x44191,x44191),a909)),x44192),x44193))))
% 109.14/108.83 [4443]E(f318(f318(f74(a911),f318(a103,f318(a103,f2(a911)))),f318(f318(f8(a911,a911),f318(f318(f10(a911,a911,a911),f318(f73(a911),x44431)),f318(f318(f9(a911,a911,a911),f74(a911)),x44432))),f318(f273(a911),x44433))),f318(f318(f74(a911),x44433),f318(f318(f73(a911),x44431),f318(f318(f73(a911),x44431),f318(f318(f74(a911),f318(f318(f3(a911),x44433),f71(a911))),x44432)))))
% 109.14/108.83 [4455]E(f318(f253(x44551),f318(f318(f20(x44551,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44551),a316),f318(f318(f9(x44551,f918(x44551,a909),a909),f320(x44551)),f318(f163(x44551),x44552)))),x44553)),f318(f163(x44551),f318(f127(x44551,x44553),x44552)))
% 109.14/108.83 [4615]E(f318(f253(x46151),f318(f318(f10(f918(a911,a909),a909,x46151),f79(a911)),f318(f318(f9(x46151,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),x46151),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),x46151),f318(f10(a909,f918(a909,a909),a911),a316)),f318(f318(f9(x46151,f918(a911,x46151),f918(a911,a909)),f318(f318(f10(f918(x46151,a909),f918(f918(a911,x46151),f918(a911,a909)),x46151),f10(x46151,a909,a911)),a315)),f318(f155(x46151),x46152))))),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),f318(f318(f9(a911,a911,a909),f226(a911)),f318(f180(f912(x46151)),x46152)))),f318(f318(f9(a911,f918(a911,a909),a909),f320(a911)),x46153))))),f318(f163(x46151),f167(x46151,x46152,x46153)))
% 109.14/108.83 [4492]E(f318(f253(x44921),f318(f318(f20(x44921,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44921),a321),f318(f318(f10(a909,a909,x44921),a313),f318(f318(f9(x44921,x44921,a909),a315),x44922)))),x44923)),f318(f318(f300(x44921),x44922),f318(f253(x44921),x44923)))
% 109.14/108.83 [4530]E(f318(f318(f145(f917(x45301,a911),x45301),f242(x45301,a911)),f318(f127(f917(x45301,a911),f318(f318(f9(f917(x45301,a911),f918(a911,a909),a909),f318(f318(f10(a911,f918(f918(a911,a909),a909),f917(x45301,a911)),f320(a911)),f247(x45301,a911))),x45302)),f318(f318(f172(x45301,a911),x45303),f130(a911,f318(f293(a911,f2(a911)),f318(f180(f912(x45301)),x45303)))))),f167(x45301,x45303,x45302))
% 109.14/108.83 [4598]E(f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f318(f8(a911,a1),f318(f318(f10(a1,a1,a911),f318(f73(a1),x45981)),f318(f318(f9(a911,a1,a1),f318(f318(f10(a1,f918(a1,a1),a911),f74(a1)),f91(a1))),x45982))),f318(f273(a911),x45983))),f318(f318(f74(a1),f318(f91(a1),x45983)),f318(f318(f73(a1),x45981),f318(f318(f73(a1),x45981),f318(f318(f74(a1),f318(f91(a1),f318(f318(f3(a911),x45983),f71(a911)))),x45982)))))
% 109.14/108.83 [4608]E(f318(f253(f917(x46081,x46082)),f318(f248(x46081,x46082,a909),f318(f318(f9(x46081,f918(f917(x46082,x46081),a909),f918(x46082,a909)),f318(f318(f10(f918(x46082,f918(f918(f917(x46082,x46081),a909),a909)),f918(f918(f917(x46082,x46081),a909),f918(x46082,a909)),x46081),f9(x46082,f918(f917(x46082,x46081),a909),a909)),f318(f318(f10(f918(x46082,f917(x46082,x46081)),f918(x46082,f918(f918(f917(x46082,x46081),a909),a909)),x46081),f318(f10(f917(x46082,x46081),f918(f918(f917(x46082,x46081),a909),a909),x46082),f320(f917(x46082,x46081)))),f318(f9(x46082,x46081,f917(x46082,x46081)),f243(x46082,x46081))))),x46083))),f318(f277(x46082,x46081),x46083))
% 109.14/108.83 [4627]E(f318(f253(f912(x46271)),f318(f318(f10(f918(x46271,a909),a909,f912(x46271)),f79(x46271)),f318(f318(f10(f918(x46271,f918(f912(x46271),a909)),f918(x46271,a909),f912(x46271)),f318(f10(f918(f912(x46271),a909),a909,x46271),f79(f912(x46271)))),f318(f318(f9(f912(x46271),f918(x46271,f918(f912(x46271),a909)),f918(x46271,f918(f912(x46271),a909))),f318(f318(f10(f918(x46271,f918(f918(f912(x46271),a909),f918(f912(x46271),a909))),f918(f918(x46271,f918(f912(x46271),a909)),f918(x46271,f918(f912(x46271),a909))),f912(x46271)),f20(x46271,f918(f912(x46271),a909),f918(f912(x46271),a909))),f318(f318(f10(f918(x46271,f918(f912(x46271),f918(a909,a909))),f918(x46271,f918(f918(f912(x46271),a909),f918(f912(x46271),a909))),f912(x46271)),f318(f10(f918(f912(x46271),f918(a909,a909)),f918(f918(f912(x46271),a909),f918(f912(x46271),a909)),x46271),f20(f912(x46271),a909,a909))),f318(f318(f10(f918(x46271,f918(f912(x46271),a909)),f918(x46271,f918(f912(x46271),f918(a909,a909))),f912(x46271)),f318(f10(f918(f912(x46271),a909),f918(f912(x46271),f918(a909,a909)),x46271),f318(f10(a909,f918(a909,a909),f912(x46271)),a316))),f318(f318(f9(f912(x46271),f918(x46271,f918(f912(x46271),f912(x46271))),f918(x46271,f918(f912(x46271),a909))),f318(f318(f10(f918(f918(f912(x46271),f912(x46271)),f918(f912(x46271),a909)),f918(f918(x46271,f918(f912(x46271),f912(x46271))),f918(x46271,f918(f912(x46271),a909))),f912(x46271)),f10(f918(f912(x46271),f912(x46271)),f918(f912(x46271),a909),x46271)),f318(f318(f10(f918(f912(x46271),a909),f918(f918(f912(x46271),f912(x46271)),f918(f912(x46271),a909)),f912(x46271)),f10(f912(x46271),a909,f912(x46271))),a315))),f142(x46271)))))),f318(f318(f9(x46271,f918(f912(x46271),a909),f918(f912(x46271),a909)),f318(f318(f10(f918(a909,a909),f918(f918(f912(x46271),a909),f918(f912(x46271),a909)),x46271),f10(a909,a909,f912(x46271))),f318(f318(f10(a909,f918(a909,a909),x46271),a316),f318(f318(f9(x46271,f918(x46271,a909),a909),f320(x46271)),x46272)))),f318(f318(f9(f912(x46271),f918(f912(x46271),a909),a909),f320(f912(x46271))),x46273)))))),f165(x46271,x46272,x46273))
% 109.14/108.83 [4628]E(f318(f318(f81(a1,f917(a1,a1)),f318(f318(f3(a1),x46281),x46282)),f318(f318(f9(a1,f917(a1,a1),f917(a1,a1)),f318(f318(f20(a1,f917(a1,a1),f918(f917(a1,a1),f917(a1,a1))),f318(f318(f10(a909,f918(f917(a1,a1),f918(f917(a1,a1),f917(a1,a1))),a1),f85(f917(a1,a1))),f318(f225(a1),f2(a1)))),f318(f243(a1,a1),f318(f318(f73(a1),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x46283)),f71(a1))))),f318(f318(f243(a1,a1),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x46283)),x46281))),f318(f37(x46282),f318(f318(f243(a1,a1),x46283),x46281)))
% 109.14/108.83 [3676]E(f107(x36761,f318(x36762,x36763),f318(x36764,x36763)),f318(f194(x36761,x36762,x36764),x36763))
% 109.14/108.83 [3728]E(f318(f318(f236(x37281,x37282,x37283),x37284),f2(a911)),x37282)
% 109.14/108.83 [3767]E(f176(x37671,x37672,x37673,f318(a103,x37674)),f318(x37673,x37674))
% 109.14/108.83 [3809]E(f161(x38091,x38092,f161(x38091,x38093,x38094)),f161(x38091,x38093,f161(x38091,x38092,x38094)))
% 109.14/108.83 [3810]E(f117(x38101,x38102,f107(x38101,x38103,x38104)),f107(x38101,f117(x38101,x38102,x38103),x38104))
% 109.14/108.83 [3941]E(f318(f147(x39411,x39412,x39413,x39414),f104(x39412)),x39413)
% 109.14/108.83 [3942]E(f318(f133(x39421,x39422,x39423,x39424),f104(x39422)),x39424)
% 109.14/108.83 [3979]E(f318(f180(f916(x39791,x39792)),f211(x39791,x39792,x39793,x39794)),f2(a911))
% 109.14/108.83 [4002]E(f318(f248(x40021,x40022,x40023),f246(x40021,x40022,x40023,x40024)),x40024)
% 109.14/108.83 [4042]E(f318(f318(f125(x40421),f160(x40421,x40422,x40423)),f160(x40421,x40424,x40423)),f318(f318(f125(x40421),f160(x40421,x40424,x40423)),f160(x40421,x40422,x40423)))
% 109.14/108.83 [4126]E(f318(f318(f250(x41261,x41262,x41263,f917(x41262,x41263)),x41264),f243(x41262,x41263)),x41264)
% 109.14/108.83 [4136]E(f118(x41361,x41362,x41363,x41364,f110(x41362)),x41363)
% 109.14/108.83 [4143]E(f68(x41431,x41432,x41433,x41434,f318(x41433,x41434)),x41433)
% 109.14/108.83 [4403]P45(x44031,x44032,x44033,x44034,f179(f918(x44031,a909)),x44034)
% 109.14/108.83 [4404]P45(x44041,x44042,x44043,x44044,f179(f918(x44041,a909)),x44044)
% 109.14/108.83 [3482]E(f318(f318(f18(x34821,x34822),x34823),x34824),x34823)
% 109.14/108.83 [3757]E(f161(x37571,x37572,f318(f127(x37571,x37573),x37574)),f318(f127(x37571,x37573),f161(x37571,x37572,x37574)))
% 109.14/108.83 [3792]E(f318(f318(f58(x37921,x37922,x37923),x37924),f179(f918(x37921,a909))),x37924)
% 109.14/108.83 [3817]E(f318(f318(f155(x38171),f318(f318(f142(x38171),x38172),x38173)),f318(a103,x38174)),f318(f318(f155(x38171),x38173),x38174))
% 109.14/108.83 [3884]E(f318(f318(x38841,x38842),f318(f175(x38843,x38844,x38841),x38842)),f318(f175(x38843,x38844,x38841),f318(a103,x38842)))
% 109.14/108.83 [3918]E(f246(x39181,x39182,x39183,f318(f248(x39181,x39182,x39183),x39184)),x39184)
% 109.14/108.83 [3977]E(f318(f318(f150(x39771,f318(f318(f142(x39771),x39772),x39773)),f2(a911)),x39774),f318(f318(f142(x39771),x39774),x39773))
% 109.14/108.83 [3987]E(f318(f318(f33(f918(x39871,a909),f918(x39872,a909)),x39873),f301(x39871,x39872,x39874)),f318(f301(x39871,x39872,x39874),f31(f918(x39871,a909),x39873)))
% 109.14/108.83 [3988]E(f318(f318(f33(f918(x39881,a909),f918(x39882,a909)),x39883),f302(x39882,x39881,x39884)),f318(f302(x39882,x39881,x39884),f31(f918(x39881,a909),x39883)))
% 109.14/108.83 [4011]E(f111(x40111,f121(x40112,f913(x40111),x40113,x40114)),f318(f109(x40112,x40111,x40114),x40113))
% 109.14/108.83 [4080]E(f318(f116(x40801,x40802),f117(x40801,x40803,x40804)),f318(f318(f73(a911),f318(f318(f73(a911),f318(x40802,x40803)),f318(f116(x40801,x40802),x40804))),f318(a103,f2(a911))))
% 109.14/108.83 [4101]E(f318(f133(x41011,x41012,f318(f9(x41012,x41011,x41011),x41013),x41014),f318(f159(x41012),f104(x41012))),x41014)
% 109.14/108.83 [4204]E(f214(x42041,f917(x42042,f913(x42042)),x42043,f318(f248(x42042,f913(x42042),x42041),x42044),f318(f126(x42042),f110(x42042))),x42043)
% 109.14/108.83 [4328]E(f318(f248(x43281,x43282,x43283),f318(f318(f10(f918(x43282,f917(x43281,x43282)),f918(x43282,x43283),x43281),f318(f10(f917(x43281,x43282),x43283,x43282),x43284)),f243(x43281,x43282))),x43284)
% 109.14/108.83 [3667]E(f318(f247(x36671,x36672),f318(f318(f243(x36671,x36672),x36673),x36674)),x36674)
% 109.14/108.83 [3668]E(f318(f242(x36681,x36682),f318(f318(f243(x36681,x36682),x36683),x36684)),x36683)
% 109.14/108.83 [3702]E(f318(f180(f912(x37021)),f318(f318(f150(x37021,x37022),x37023),x37024)),f318(f180(f912(x37021)),x37022))
% 109.14/108.83 [3703]E(f318(f180(f912(x37031)),f318(f318(f145(x37032,x37031),x37033),x37034)),f318(f180(f912(x37032)),x37034))
% 109.14/108.83 [3722]E(f318(f318(f129(x37221),f318(a103,x37222)),f318(f318(f142(x37221),x37223),x37224)),f318(f318(f129(x37221),x37222),x37224))
% 109.14/108.83 [3787]E(f318(f318(f166(x37871),x37872),f160(x37871,x37873,x37874)),f160(x37871,f318(f318(f223(a911),x37872),x37873),x37874))
% 109.14/108.83 [3788]E(f318(f318(f129(x37881),x37882),f160(x37881,x37883,x37884)),f160(x37881,f318(f318(f3(a911),x37883),x37882),x37884))
% 109.14/108.83 [3794]E(f318(f318(f300(x37941),x37942),f318(f318(f300(x37941),x37943),x37944)),f318(f318(f300(x37941),x37943),f318(f318(f300(x37941),x37942),x37944)))
% 109.14/108.83 [3798]E(f318(f318(f145(x37981,x37982),x37983),f105(x37981,x37984)),f105(x37982,f318(f318(f145(x37981,x37982),x37983),x37984)))
% 109.14/108.83 [3815]E(f318(f159(x38151),f318(f318(f145(x38152,x38151),x38153),x38154)),f318(f318(f145(x38152,x38151),x38153),f318(f159(x38152),x38154)))
% 109.14/108.83 [3816]E(f318(f318(f145(x38161,x38162),x38163),f318(f162(x38161),x38164)),f318(f162(x38162),f318(f318(f145(x38161,x38162),x38163),x38164)))
% 109.14/108.83 [3831]E(f318(f318(f166(x38311),f318(a103,x38312)),f318(f318(f142(x38311),x38313),x38314)),f318(f318(f142(x38311),x38313),f318(f318(f166(x38311),x38312),x38314)))
% 109.14/108.83 [3834]E(f318(f163(x38341),f318(f318(f145(x38342,x38341),x38343),x38344)),f318(f301(x38342,x38341,x38343),f318(f163(x38342),x38344)))
% 109.14/108.83 [3847]E(f318(f318(f145(x38471,x38472),f318(f18(x38472,x38471),x38473)),x38474),f160(x38472,f318(f180(f912(x38471)),x38474),x38473))
% 109.14/108.83 [3883]E(f19(x38831,x38832,x38833,f318(a5,f318(a103,f318(a22,x38834)))),f318(x38833,x38834))
% 109.14/108.83 [3887]E(f318(f318(f125(x38871),f318(f127(x38871,x38872),x38873)),f318(f127(x38871,x38872),x38874)),f318(f127(x38871,x38872),f318(f318(f125(x38871),x38873),x38874)))
% 109.14/108.83 [3894]E(f143(x38941,f318(f318(f145(x38942,x38941),x38943),f143(x38942,x38944))),f143(x38941,f318(f318(f145(x38942,x38941),x38943),x38944)))
% 109.14/108.83 [3908]E(f318(f277(x39081,x39081),f318(f318(f279(x39082,x39081),x39083),x39084)),f318(f318(f279(x39082,x39081),f318(f277(x39082,x39082),x39083)),x39084))
% 109.14/108.83 [3919]E(f318(f318(f280(x39191,x39192,x39193),x39194),f179(f918(f917(x39192,x39193),a909))),f179(f918(f917(x39191,x39193),a909)))
% 109.14/108.83 [3920]E(f318(f318(f166(x39201),f318(f318(f3(a911),x39202),x39203)),f318(f318(f129(x39201),x39203),x39204)),f318(f318(f129(x39201),x39203),f318(f318(f166(x39201),x39202),x39204)))
% 109.14/108.83 [3944]E(f318(f318(f125(x39441),f160(x39441,x39442,x39443)),f160(x39441,x39444,x39443)),f160(x39441,f318(f318(f73(a911),x39442),x39444),x39443))
% 109.14/108.83 [3945]E(f318(f318(f318(f269(x39451),x39452),x39453),x39454),f318(f243(f918(a90,f918(a909,f915(f913(x39451)))),f917(a90,a90)),f318(f36(x39451),x39452)))
% 109.14/108.83 [3968]E(f31(f918(x39681,a909),f318(f301(x39682,f918(x39681,a909),x39683),x39684)),f318(f318(f33(x39682,f918(x39681,a909)),x39684),x39683))
% 109.14/108.83 [3969]E(f32(f918(x39691,a909),f318(f301(x39692,f918(x39691,a909),x39693),x39694)),f318(f318(f34(x39692,f918(x39691,a909)),x39694),x39693))
% 109.14/108.83 [3970]E(f32(f918(x39701,a909),f318(f301(x39702,f918(x39701,a909),x39703),x39704)),f318(f318(f34(x39702,f918(x39701,a909)),x39704),x39703))
% 109.14/108.83 [3971]E(f31(f918(x39711,a909),f318(f301(x39712,f918(x39711,a909),x39713),x39714)),f318(f318(f33(x39712,f918(x39711,a909)),x39714),x39713))
% 109.14/108.83 [3972]E(f318(f180(f912(f917(x39721,x39722))),f318(f318(f172(x39721,x39722),x39723),x39724)),f318(f318(f223(a911),f318(f180(f912(x39721)),x39723)),f318(f180(f912(x39722)),x39724)))
% 109.14/108.83 [3974]E(f318(f302(x39741,x39742,x39743),f318(f72(f918(x39742,a909)),x39744)),f318(f72(f918(x39741,a909)),f318(f302(x39741,x39742,x39743),x39744)))
% 109.14/108.83 [4021]E(f318(f302(x40211,x40212,x40213),f318(f253(x40212),x40214)),f318(f253(x40211),f318(f318(f10(x40212,a909,x40211),x40214),x40213)))
% 109.14/108.83 [4038]E(f318(f318(f155(x40381),f318(f318(f125(x40381),x40382),f318(f318(f142(x40381),x40383),x40384))),f318(f180(f912(x40381)),x40382)),x40383)
% 109.14/108.83 [4057]E(f318(f301(x40571,x40572,x40573),f318(f302(x40571,x40572,x40573),x40574)),f318(f318(f92(f918(x40572,a909)),x40574),f318(f301(x40571,x40572,x40573),f233(f918(x40571,a909)))))
% 109.14/108.83 [4076]P1(f318(f318(f320(x40761),f318(x40762,x40763)),f318(f301(x40764,x40761,x40762),f233(f918(x40764,a909)))))
% 109.14/108.83 [4085]E(f21(x40851,x40852,x40853,f318(a5,f318(a103,f318(a22,x40854)))),f318(f318(x40853,x40854),f21(x40851,x40852,x40853,x40854)))
% 109.14/108.83 [4089]E(f318(f318(f125(x40891),f160(x40891,x40892,x40893)),f318(f318(f142(x40891),x40893),x40894)),f318(f318(f142(x40891),x40893),f318(f318(f125(x40891),f160(x40891,x40892,x40893)),x40894)))
% 109.14/108.83 [4091]E(f318(f318(f245(x40911,x40912),f318(f163(x40911),x40913)),f318(f18(f918(x40912,a909),x40911),f318(f163(x40912),x40914))),f318(f163(f917(x40911,x40912)),f53(x40911,x40912,x40913,x40914)))
% 109.14/108.83 [4103]E(f146(x41031,x41032,f318(f318(f142(x41031),x41033),x41034)),f318(f318(f73(a911),f318(f318(f73(a911),f318(x41032,x41033)),f146(x41031,x41032,x41034))),f318(a103,f2(a911))))
% 109.14/108.83 [4118]E(f176(f912(x41181),f318(f318(f142(x41181),x41182),x41183),f318(f318(f9(a911,f912(x41181),f912(x41181)),f129(x41181)),x41183),x41184),f318(f318(f129(x41181),x41184),f318(f318(f142(x41181),x41182),x41183)))
% 109.14/108.83 [4119]P25(x41191,f917(x41192,x41191),f322(x41193,x41194,x41192,x41191),f318(f318(f33(x41192,f918(x41191,a909)),x41194),x41193))
% 109.14/108.83 [4127]E(f318(f318(f3(f918(x41271,a909)),f318(f318(f3(f918(x41271,a909)),x41272),x41273)),f318(f318(f300(x41271),x41274),f179(f918(x41271,a909)))),f318(f318(f3(f918(x41271,a909)),x41272),f318(f318(f300(x41271),x41274),x41273)))
% 109.14/108.83 [4141]E(f318(f318(f174(f918(x41411,x41412),f918(x41411,x41412)),x41413),f66(x41412,x41412,x41411,x41414)),f66(x41412,x41412,x41411,f318(f318(f174(x41412,x41412),x41413),x41414)))
% 109.14/108.83 [4209]E(f318(f318(f318(f174(f912(x42091),f912(x42091)),x42092),f158(x42091)),f318(f318(f318(f174(f912(x42091),f912(x42091)),x42093),f158(x42091)),x42094)),f318(f318(f318(f174(f912(x42091),f912(x42091)),f318(f318(f73(a911),x42092),x42093)),f158(x42091)),x42094))
% 109.14/108.83 [4290]P1(f318(f318(f225(f918(x42901,a909)),f318(f163(x42901),f318(f318(f150(x42901,x42902),x42903),x42904))),f318(f318(f300(x42901),x42904),f318(f163(x42901),x42902))))
% 109.14/108.83 [4316]E(f318(f318(f33(f918(x43161,a909),f918(f917(x43161,x43162),a909)),x43163),f318(f318(f9(f918(x43161,a909),f918(x43161,f918(x43162,a909)),f918(f917(x43161,x43162),a909)),f245(x43161,x43162)),x43164)),f318(f318(f245(x43161,x43162),f31(f918(x43161,a909),x43163)),x43164))
% 109.14/108.83 [4360]E(f200(x43601,x43602,x43603,f318(f66(x43602,f918(a90,f918(a90,f918(f917(a90,a90),f918(a90,f913(x43602))))),x43601,f199(x43602)),x43604)),f201(x43601,x43602,x43604,x43603))
% 109.14/108.83 [4377]E(f196(x43771,x43772,x43773,f318(f66(x43772,f918(a90,f918(a90,f918(f917(a90,a90),f918(a90,f913(f915(x43772)))))),x43771,f195(x43772)),x43774)),f197(x43771,x43772,x43774,x43773))
% 109.14/108.83 [4383]P1(f318(f60(x43831,x43832,x43833,x43834,f179(f918(x43831,a909))),x43834))
% 109.14/108.83 [4384]P1(f318(f60(x43841,x43842,x43843,x43844,f179(f918(x43841,a909))),x43844))
% 109.14/108.83 [4422]E(f318(f318(f33(x44221,f918(x44222,a909)),x44223),f318(f318(f9(x44221,f918(x44222,a909),f918(x44222,a909)),f318(f318(f10(x44222,f918(f918(x44222,a909),f918(x44222,a909)),x44221),f300(x44222)),x44224)),f179(f918(x44222,a909)))),f318(f301(x44221,x44222,x44224),x44223))
% 109.14/108.83 [4429]P1(f318(f318(f225(f918(x44291,a909)),f318(f275(x44292,x44291),f318(f318(f92(f918(f917(x44292,x44291),a909)),x44293),x44294))),f318(f318(f92(f918(x44291,a909)),f318(f275(x44292,x44291),x44293)),f318(f275(x44292,x44291),x44294))))
% 109.14/108.83 [4430]P1(f318(f318(f225(f918(x44301,a909)),f318(f255(x44301,x44302),f318(f318(f92(f918(f917(x44301,x44302),a909)),x44303),x44304))),f318(f318(f92(f918(x44301,a909)),f318(f255(x44301,x44302),x44303)),f318(f255(x44301,x44302),x44304))))
% 109.14/108.83 [4488]P1(f318(f318(f225(f918(f917(x44881,x44882),a909)),f318(f301(x44882,f917(x44881,x44882),f322(x44883,x44884,x44881,x44882)),f318(f318(f33(x44881,f918(x44882,a909)),x44884),x44883))),f318(f318(f245(x44881,x44882),x44884),x44883)))
% 109.14/108.83 [4489]E(f318(f109(x44891,f917(x44891,x44892),x44893),f318(f318(f10(f918(x44892,f913(f917(x44891,x44892))),f913(f917(x44891,x44892)),x44891),f109(x44892,f917(x44891,x44892),x44894)),f318(f318(f10(f918(x44892,f917(x44891,x44892)),f918(x44892,f913(f917(x44891,x44892))),x44891),f318(f10(f917(x44891,x44892),f913(f917(x44891,x44892)),x44892),f120(f917(x44891,x44892)))),f243(x44891,x44892)))),f122(x44891,x44892,x44893,x44894))
% 109.14/108.83 [4490]E(f267(x44901,x44902,x44903,f318(f66(x44902,f918(a90,f918(a90,f918(f917(a90,a90),f917(f918(a90,f918(a909,f915(f913(x44902)))),f917(a90,a90))))),x44901,f269(x44902)),x44904)),f270(x44901,x44902,x44904,x44903))
% 109.14/108.83 [4536]E(f78(f917(x45361,x45362),f318(f248(x45361,x45362,a909),f318(f318(f9(x45361,f918(x45362,a909),f918(x45362,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x45362,a909),f918(x45362,a909)),x45361),f10(a909,a909,x45362)),f318(f318(f10(a909,f918(a909,a909),x45361),a316),f318(a315,x45363)))),f318(a315,x45364)))),f318(f318(f243(x45361,x45362),x45363),x45364))
% 109.14/108.83 [4537]E(f83(f917(x45371,x45372),f318(f248(x45371,x45372,a909),f318(f318(f9(x45371,f918(x45372,a909),f918(x45372,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x45372,a909),f918(x45372,a909)),x45371),f10(a909,a909,x45372)),f318(f318(f10(a909,f918(a909,a909),x45371),a316),f318(a315,x45373)))),f318(a315,x45374)))),f318(f318(f243(x45371,x45372),x45373),x45374))
% 109.14/108.83 [4617]E(f318(f318(f248(f912(x46171),f912(x46171),f917(f912(x46171),f912(x46171))),f318(f318(f20(f912(x46171),f918(f912(x46171),f917(f912(x46171),f912(x46171))),f918(f912(x46171),f917(f912(x46171),f912(x46171)))),f318(f318(f10(f918(f912(x46171),f918(f917(f912(x46171),f912(x46171)),f917(f912(x46171),f912(x46171)))),f918(f918(f912(x46171),f917(f912(x46171),f912(x46171))),f918(f912(x46171),f917(f912(x46171),f912(x46171)))),f912(x46171)),f20(f912(x46171),f917(f912(x46171),f912(x46171)),f917(f912(x46171),f912(x46171)))),f318(f318(f10(f918(f912(x46171),f917(f912(x46171),f912(x46171))),f918(f912(x46171),f918(f917(f912(x46171),f912(x46171)),f917(f912(x46171),f912(x46171)))),f912(x46171)),f318(f10(f917(f912(x46171),f912(x46171)),f918(f917(f912(x46171),f912(x46171)),f917(f912(x46171),f912(x46171))),f912(x46171)),f318(f85(f917(f912(x46171),f912(x46171))),f318(x46172,x46173)))),f318(f318(f10(f912(x46171),f918(f912(x46171),f917(f912(x46171),f912(x46171))),f912(x46171)),f243(f912(x46171),f912(x46171))),f318(f142(x46171),x46173))))),f318(f318(f9(f912(x46171),f918(f912(x46171),f912(x46171)),f918(f912(x46171),f917(f912(x46171),f912(x46171)))),f318(f318(f10(f918(f912(x46171),f917(f912(x46171),f912(x46171))),f918(f918(f912(x46171),f912(x46171)),f918(f912(x46171),f917(f912(x46171),f912(x46171)))),f912(x46171)),f10(f912(x46171),f917(f912(x46171),f912(x46171)),f912(x46171))),f243(f912(x46171),f912(x46171)))),f318(f142(x46171),x46173)))),f157(x46171,x46172,x46174)),f157(x46171,x46172,f318(f318(f142(x46171),x46173),x46174)))
% 109.14/108.83 [3863]E(f318(f318(f166(x38631),x38632),f318(f318(f166(x38631),x38633),x38634)),f318(f318(f166(x38631),f318(f318(f223(a911),x38632),x38633)),x38634))
% 109.14/108.83 [3864]E(f318(f318(f129(x38641),x38642),f318(f318(f129(x38641),x38643),x38644)),f318(f318(f129(x38641),f318(f318(f73(a911),x38642),x38643)),x38644))
% 109.14/108.83 [3875]E(f318(f318(f125(x38751),f318(f318(f142(x38751),x38752),x38753)),x38754),f318(f318(f142(x38751),x38752),f318(f318(f125(x38751),x38753),x38754)))
% 109.14/108.83 [3876]E(f318(f318(f125(x38761),f318(f318(f125(x38761),x38762),x38763)),x38764),f318(f318(f125(x38761),x38762),f318(f318(f125(x38761),x38763),x38764)))
% 109.14/108.83 [3955]E(f318(f318(f155(x39551),f318(f318(f142(x39551),x39552),x39553)),x39554),f176(x39551,x39552,f318(f155(x39551),x39553),x39554))
% 109.14/108.83 [3963]E(f318(f318(f174(x39631,x39631),x39632),f318(f318(f174(x39631,x39631),x39633),x39634)),f318(f318(f174(x39631,x39631),f318(f318(f74(a911),x39633),x39632)),x39634))
% 109.14/108.83 [3990]E(f318(f318(f101(f918(x39901,a909)),x39902),f318(f318(f300(x39901),x39903),x39904)),f318(f318(f300(x39901),x39903),f318(f318(f101(f918(x39901,a909)),x39902),x39904)))
% 109.14/108.83 [4005]E(f318(f318(f318(f174(x40051,x40051),x40052),x40053),f318(x40053,x40054)),f318(x40053,f318(f318(f318(f174(x40051,x40051),x40052),x40053),x40054)))
% 109.14/108.83 [4012]E(f318(f318(f280(x40121,x40122,x40123),f179(f918(f917(x40121,x40122),a909))),x40124),f179(f918(f917(x40121,x40123),a909)))
% 109.14/108.83 [4026]E(f318(f318(f101(f918(x40261,a909)),f318(f318(f300(x40261),x40262),x40263)),x40264),f318(f318(f300(x40261),x40262),f318(f318(f101(f918(x40261,a909)),x40263),x40264)))
% 109.14/108.83 [4044]E(f318(f29(f917(x40441,x40442)),f318(f318(f245(x40441,x40442),x40443),f318(f18(f918(x40442,a909),x40441),x40444))),f318(f318(f74(a911),f318(f29(x40441),x40443)),f318(f29(x40442),x40444)))
% 109.14/108.83 [4050]E(f318(f318(f92(f918(x40501,a909)),f318(f318(f300(x40501),x40502),x40503)),f318(f318(f300(x40501),x40502),x40504)),f318(f318(f300(x40501),x40502),f318(f318(f92(f918(x40501,a909)),x40503),x40504)))
% 109.14/108.83 [4061]E(f318(f318(f101(f918(x40611,a909)),x40612),f318(f318(f101(f918(x40611,a909)),x40613),x40614)),f318(f318(f101(f918(x40611,a909)),x40613),f318(f318(f101(f918(x40611,a909)),x40612),x40614)))
% 109.14/108.83 [4062]E(f318(f318(f92(f918(x40621,a909)),x40622),f318(f318(f92(f918(x40621,a909)),x40623),x40624)),f318(f318(f92(f918(x40621,a909)),x40623),f318(f318(f92(f918(x40621,a909)),x40622),x40624)))
% 109.14/108.83 [4072]E(f58(x40721,x40722,f318(f318(f10(x40722,f918(x40722,x40722),x40721),x40723),x40724)),f318(f59(x40722,x40721,x40723),x40724))
% 109.14/108.83 [4081]E(f170(x40811,f318(f318(f145(f912(x40812),f912(x40811)),f318(f145(x40812,x40811),x40813)),x40814)),f318(f318(f145(f912(x40812),f912(x40811)),f318(f145(x40812,x40811),x40813)),f170(x40812,x40814)))
% 109.14/108.83 [4099]E(f318(f133(f912(x40991),f912(x40991),f125(x40991),f104(x40991)),f318(f318(f145(x40992,f912(x40991)),x40993),x40994)),f154(x40992,x40991,x40993,x40994))
% 109.14/108.83 [4100]E(f318(f133(f912(x41001),f912(x41001),f125(x41001),f104(x41001)),f318(f318(f145(x41002,f912(x41001)),x41003),x41004)),f154(x41002,x41001,x41003,x41004))
% 109.14/108.83 [4158]E(f318(f66(x41581,x41581,x41581,f318(f318(f174(x41581,x41581),x41582),x41583)),f318(f318(f174(x41581,x41581),x41584),x41583)),f318(f318(f174(x41581,x41581),f318(f318(f73(a911),x41582),x41584)),x41583))
% 109.14/108.83 [4180]E(f318(f318(f92(f918(x41801,a909)),f318(f318(f101(f918(x41801,a909)),x41802),x41803)),f318(f318(f101(f918(x41801,a909)),x41802),x41804)),f318(f318(f101(f918(x41801,a909)),x41802),f318(f318(f92(f918(x41801,a909)),x41803),x41804)))
% 109.14/108.83 [4181]E(f318(f318(f101(f918(x41811,a909)),f318(f318(f92(f918(x41811,a909)),x41812),x41813)),f318(f318(f92(f918(x41811,a909)),x41812),x41814)),f318(f318(f92(f918(x41811,a909)),x41812),f318(f318(f101(f918(x41811,a909)),x41813),x41814)))
% 109.14/108.83 [4182]E(f318(f318(f3(f918(x41821,a909)),f318(f318(f92(f918(x41821,a909)),x41822),x41823)),f318(f318(f92(f918(x41821,a909)),x41822),x41824)),f318(f318(f92(f918(x41821,a909)),x41822),f318(f318(f3(f918(x41821,a909)),x41823),x41824)))
% 109.14/108.83 [4183]E(f318(f318(f92(f918(x41831,a909)),f318(f318(f3(f918(x41831,a909)),x41832),x41833)),f318(f318(f3(f918(x41831,a909)),x41832),x41834)),f318(f318(f3(f918(x41831,a909)),x41832),f318(f318(f101(f918(x41831,a909)),x41833),x41834)))
% 109.14/108.83 [4184]E(f318(f318(f101(f918(x41841,a909)),f318(f318(f3(f918(x41841,a909)),x41842),x41843)),f318(f318(f3(f918(x41841,a909)),x41842),x41844)),f318(f318(f3(f918(x41841,a909)),x41842),f318(f318(f92(f918(x41841,a909)),x41843),x41844)))
% 109.14/108.83 [4189]E(f318(f29(f917(x41891,x41892)),f318(f318(f245(x41891,x41892),f318(f318(f300(x41891),x41893),f179(f918(x41891,a909)))),f318(f18(f918(x41892,a909),x41891),x41894))),f318(f29(x41892),x41894))
% 109.14/108.83 [4223]E(f318(f318(f34(x42231,f918(x42232,a909)),x42233),f318(f318(f10(f918(x42232,a909),f918(x42232,a909),x42231),f72(f918(x42232,a909))),x42234)),f318(f72(f918(x42232,a909)),f318(f318(f33(x42231,f918(x42232,a909)),x42233),x42234)))
% 109.14/108.83 [4224]E(f318(f318(f33(x42241,f918(x42242,a909)),x42243),f318(f318(f10(f918(x42242,a909),f918(x42242,a909),x42241),f72(f918(x42242,a909))),x42244)),f318(f72(f918(x42242,a909)),f318(f318(f34(x42241,f918(x42242,a909)),x42243),x42244)))
% 109.14/108.83 [4238]E(f318(f318(f280(x42381,x42381,x42381),f318(f318(f174(f917(x42381,x42381),a909),x42382),x42383)),f318(f318(f174(f917(x42381,x42381),a909),x42384),x42383)),f318(f318(f174(f917(x42381,x42381),a909),f318(f318(f73(a911),x42382),x42384)),x42383))
% 109.14/108.83 [4268]E(f318(f318(f34(x42681,f918(f918(x42682,a909),a909)),x42683),f318(f318(f10(f918(x42682,a909),f918(f918(x42682,a909),a909),x42681),f299(x42682)),x42684)),f318(f299(x42682),f318(f318(f34(x42681,f918(x42682,a909)),x42683),x42684)))
% 109.14/108.83 [4293]E(f318(f318(f33(f918(x42931,a909),f918(x42932,a909)),x42933),f318(f318(f9(f918(x42931,a909),f918(x42931,f918(x42932,a909)),f918(x42932,a909)),f33(x42931,f918(x42932,a909))),x42934)),f318(f318(f33(x42931,f918(x42932,a909)),f31(f918(x42931,a909),x42933)),x42934))
% 109.14/108.83 [4294]E(f318(f318(f34(f918(x42941,a909),f918(x42942,a909)),x42943),f318(f318(f9(f918(x42941,a909),f918(x42941,f918(x42942,a909)),f918(x42942,a909)),f34(x42941,f918(x42942,a909))),x42944)),f318(f318(f34(x42941,f918(x42942,a909)),f31(f918(x42941,a909),x42943)),x42944))
% 109.14/108.83 [4295]E(f318(f318(f33(f918(x42951,a909),f918(x42952,a909)),x42953),f318(f318(f9(f918(x42951,a909),f918(x42951,f918(x42952,a909)),f918(x42952,a909)),f33(x42951,f918(x42952,a909))),x42954)),f318(f318(f33(x42951,f918(x42952,a909)),f31(f918(x42951,a909),x42953)),x42954))
% 109.14/108.83 [4296]E(f318(f318(f34(f918(x42961,a909),f918(x42962,a909)),x42963),f318(f318(f9(f918(x42961,a909),f918(x42961,f918(x42962,a909)),f918(x42962,a909)),f34(x42961,f918(x42962,a909))),x42964)),f318(f318(f34(x42961,f918(x42962,a909)),f31(f918(x42961,a909),x42963)),x42964))
% 109.14/108.83 [4299]E(f318(f318(f145(x42991,x42992),x42993),f318(f133(f912(x42991),f912(x42991),f125(x42991),f104(x42991)),x42994)),f318(f133(f912(x42992),f912(x42992),f125(x42992),f104(x42992)),f318(f318(f145(f912(x42991),f912(x42992)),f318(f145(x42991,x42992),x42993)),x42994)))
% 109.14/108.83 [4301]E(f176(f912(x43011),f104(x43011),f318(f318(f10(f912(x43011),f912(x43011),a911),f318(f142(x43011),x43012)),f318(f318(f9(a911,f912(x43011),f912(x43011)),f166(x43011)),x43013)),x43014),f318(f318(f166(x43011),x43014),f318(f318(f142(x43011),x43012),x43013)))
% 109.14/108.83 [4337]P1(f318(f318(f225(f918(x43371,a909)),f318(f301(x43372,x43371,x43373),f318(f302(x43372,x43371,x43373),x43374))),x43374))
% 109.14/108.83 [4339]E(f318(f301(f917(x43391,x43392),f917(x43392,x43391),f318(f248(x43391,x43392,f917(x43392,x43391)),f318(f9(x43392,x43391,f917(x43392,x43391)),f243(x43392,x43391)))),f318(f318(f245(x43391,x43392),x43393),f318(f18(f918(x43392,a909),x43391),x43394))),f318(f318(f245(x43392,x43391),x43394),f318(f18(f918(x43391,a909),x43392),x43393)))
% 109.14/108.83 [4348]E(f318(f318(f33(x43481,f918(x43482,a909)),x43483),f318(f318(f10(f918(x43481,a909),f918(x43482,a909),x43481),f302(x43482,x43481,x43484)),f318(f318(f9(x43481,f918(x43481,a909),f918(x43481,a909)),f300(x43481)),f179(f918(x43481,a909))))),f318(f302(x43482,x43481,x43484),x43483))
% 109.14/108.83 [4349]E(f318(f318(f33(x43491,f918(x43492,a909)),x43493),f318(f318(f10(f918(x43491,a909),f918(x43492,a909),x43491),f276(x43491,x43492,x43494)),f318(f318(f9(x43491,f918(x43491,a909),f918(x43491,a909)),f300(x43491)),f179(f918(x43491,a909))))),f318(f276(x43491,x43492,x43494),x43493))
% 109.14/108.83 [4431]E(f318(f318(f125(x44311),f318(f127(x44311,f318(f318(f10(a909,a909,x44311),a313),f318(a315,x44312))),x44313)),f318(f127(x44311,f318(f318(f10(a909,a909,x44311),a313),f318(a315,x44312))),x44314)),f318(f127(x44311,f318(f318(f10(a909,a909,x44311),a313),f318(a315,x44312))),f318(f318(f125(x44311),x44313),x44314)))
% 109.14/108.83 [4442]E(f318(f318(f101(f918(x44421,a909)),f318(f318(f101(f918(x44421,a909)),f318(f318(f92(f918(x44421,a909)),x44422),x44423)),f318(f318(f92(f918(x44421,a909)),x44423),x44424))),f318(f318(f92(f918(x44421,a909)),x44424),x44422)),f318(f318(f92(f918(x44421,a909)),f318(f318(f92(f918(x44421,a909)),f318(f318(f101(f918(x44421,a909)),x44422),x44423)),f318(f318(f101(f918(x44421,a909)),x44423),x44424))),f318(f318(f101(f918(x44421,a909)),x44424),x44422)))
% 109.14/108.83 [4505]E(f318(f133(f912(x45051),f912(x45051),f125(x45051),f104(x45051)),f318(f318(f145(x45052,f912(x45051)),f318(f318(f9(x45052,f912(x45051),f912(x45051)),f318(f318(f10(x45051,f918(f912(x45051),f912(x45051)),x45052),f142(x45051)),x45053)),f104(x45051))),x45054)),f318(f318(f145(x45052,x45051),x45053),x45054))
% 109.14/108.83 [4520]E(f318(f318(f81(a1,x45201),f318(f94(a1),f318(f318(f73(a1),x45202),a88))),f318(f318(f20(a1,x45201,x45201),f318(f318(f9(a1,x45201,f918(x45201,x45201)),f318(f318(f10(a909,f918(x45201,f918(x45201,x45201)),a1),f85(x45201)),a184)),x45203)),f318(f318(f10(a911,x45201,a1),x45204),a95))),f176(x45201,x45203,x45204,f318(f94(a911),x45202)))
% 109.14/108.83 [4549]E(f318(f253(x45491),f318(f318(f10(f918(x45492,a909),a909,x45491),f79(x45492)),f318(f318(f10(f918(x45492,a909),f918(x45492,a909),x45491),f318(f20(x45492,a909,a909),f318(f318(f10(a909,f918(a909,a909),x45492),a316),f318(f318(f9(x45492,f918(x45492,a909),a909),f320(x45492)),x45493)))),f318(f9(x45492,x45491,a909),x45494)))),f318(f276(x45492,x45491,f318(f253(f917(x45492,x45491)),f318(f248(x45492,x45491,a909),x45494))),x45493))
% 109.14/108.83 [4691]~P1(f318(f318(f179(f918(x46911,f918(x46912,a909))),x46913),x46914))
% 109.14/108.83 [4015]E(f318(f318(f155(x40151),f318(f318(f125(x40151),x40152),x40153)),f318(f318(f73(a911),f318(f180(f912(x40151)),x40152)),x40154)),f318(f318(f155(x40151),x40153),x40154))
% 109.14/108.83 [4020]E(f318(f318(f129(x40201),x40202),f318(f318(f166(x40201),f318(f318(f73(a911),x40203),x40202)),x40204)),f318(f318(f166(x40201),x40203),f318(f318(f129(x40201),x40202),x40204)))
% 109.14/108.83 [4116]E(f318(f318(f101(f918(x41161,a909)),f318(f275(x41162,x41161),x41163)),f318(f275(x41162,x41161),x41164)),f318(f275(x41162,x41161),f318(f318(f101(f918(f917(x41162,x41161),a909)),x41163),x41164)))
% 109.14/108.83 [4117]E(f318(f318(f101(f918(x41171,a909)),f318(f255(x41171,x41172),x41173)),f318(f255(x41171,x41172),x41174)),f318(f255(x41171,x41172),f318(f318(f101(f918(f917(x41171,x41172),a909)),x41173),x41174)))
% 109.14/108.83 [4121]E(f318(f318(f101(f918(x41211,a909)),f318(f318(f101(f918(x41211,a909)),x41212),x41213)),x41214),f318(f318(f101(f918(x41211,a909)),x41212),f318(f318(f101(f918(x41211,a909)),x41213),x41214)))
% 109.14/108.83 [4122]E(f318(f318(f92(f918(x41221,a909)),f318(f318(f92(f918(x41221,a909)),x41222),x41223)),x41224),f318(f318(f92(f918(x41221,a909)),x41222),f318(f318(f92(f918(x41221,a909)),x41223),x41224)))
% 109.14/108.83 [4123]E(f318(f318(f3(f918(x41231,a909)),f318(f318(f92(f918(x41231,a909)),x41232),x41233)),x41234),f318(f318(f92(f918(x41231,a909)),x41232),f318(f318(f3(f918(x41231,a909)),x41233),x41234)))
% 109.14/108.83 [4160]E(f318(f318(f101(f918(f917(x41601,x41602),a909)),f318(f277(x41602,x41601),x41603)),f318(f277(x41602,x41601),x41604)),f318(f277(x41602,x41601),f318(f318(f101(f918(f917(x41602,x41601),a909)),x41603),x41604)))
% 109.14/108.83 [4161]E(f318(f318(f92(f918(f917(x41611,x41612),a909)),f318(f277(x41612,x41611),x41613)),f318(f277(x41612,x41611),x41614)),f318(f277(x41612,x41611),f318(f318(f92(f918(f917(x41612,x41611),a909)),x41613),x41614)))
% 109.14/108.84 [4173]E(f318(f318(f101(f918(x41731,f918(x41732,a909))),f234(x41732,x41731,x41733)),f234(x41732,x41731,x41734)),f234(x41732,x41731,f318(f318(f101(f918(x41732,f918(x41731,a909))),x41733),x41734)))
% 109.14/108.84 [4174]E(f318(f318(f92(f918(x41741,f918(x41742,a909))),f234(x41742,x41741,x41743)),f234(x41742,x41741,x41744)),f234(x41742,x41741,f318(f318(f92(f918(x41742,f918(x41741,a909))),x41743),x41744)))
% 109.14/108.84 [4226]E(f318(f318(f92(f918(x42261,a909)),f318(f318(f101(f918(x42261,a909)),x42262),x42263)),f318(f318(f101(f918(x42261,a909)),x42264),x42263)),f318(f318(f101(f918(x42261,a909)),f318(f318(f92(f918(x42261,a909)),x42262),x42264)),x42263))
% 109.14/108.84 [4227]E(f318(f318(f101(f918(x42271,a909)),f318(f318(f92(f918(x42271,a909)),x42272),x42273)),f318(f318(f92(f918(x42271,a909)),x42274),x42273)),f318(f318(f92(f918(x42271,a909)),f318(f318(f101(f918(x42271,a909)),x42272),x42274)),x42273))
% 109.14/108.84 [4228]E(f318(f318(f3(f918(x42281,a909)),f318(f318(f92(f918(x42281,a909)),x42282),x42283)),f318(f318(f92(f918(x42281,a909)),x42284),x42283)),f318(f318(f92(f918(x42281,a909)),f318(f318(f3(f918(x42281,a909)),x42282),x42284)),x42283))
% 109.14/108.84 [4229]E(f318(f318(f101(f918(x42291,a909)),f318(f318(f3(f918(x42291,a909)),x42292),x42293)),f318(f318(f3(f918(x42291,a909)),x42294),x42293)),f318(f318(f3(f918(x42291,a909)),f318(f318(f101(f918(x42291,a909)),x42292),x42294)),x42293))
% 109.14/108.84 [4230]E(f318(f318(f3(f918(x42301,a909)),f318(f318(f92(f918(x42301,a909)),x42302),x42303)),f318(f318(f92(f918(x42301,a909)),x42304),x42303)),f318(f318(f3(f918(x42301,a909)),f318(f318(f92(f918(x42301,a909)),x42302),x42303)),x42304))
% 109.14/108.84 [4241]E(f318(f318(f3(f918(x42411,a909)),f318(f318(f3(f918(x42411,a909)),x42412),f318(f318(f300(x42411),x42413),f179(f918(x42411,a909))))),x42414),f318(f318(f3(f918(x42411,a909)),x42412),f318(f318(f300(x42411),x42413),x42414)))
% 109.14/108.84 [4292]E(f318(f318(f101(f918(x42921,a909)),f318(f318(f300(x42921),x42922),f318(f318(f300(x42921),x42923),f179(f918(x42921,a909))))),f318(f272(x42921),x42924)),f318(f272(x42921),f318(f318(f300(f917(x42921,x42921)),f318(f318(f243(x42921,x42921),x42922),x42923)),x42924)))
% 109.14/108.84 [4313]E(f318(f318(f33(a911,f918(x43131,a909)),f318(f292(a911),x43132)),f318(f318(f10(a911,f918(x43131,a909),a911),x43133),f318(f318(f9(a911,a911,a911),f73(a911)),x43134))),f318(f318(f33(a911,f918(x43131,a909)),f294(a911,x43134,f318(f318(f73(a911),x43132),x43134))),x43133))
% 109.14/108.84 [4314]E(f165(x43141,f318(f276(x43141,x43141,x43142),f318(f318(f300(x43141),x43143),f179(f918(x43141,a909)))),f318(f276(f912(x43141),f912(x43141),f149(x43141,x43142)),f318(f318(f300(f912(x43141)),x43144),f179(f918(f912(x43141),a909))))),f318(f276(f912(x43141),f912(x43141),f149(x43141,x43142)),f318(f318(f300(f912(x43141)),f318(f318(f142(x43141),x43143),x43144)),f179(f918(f912(x43141),a909)))))
% 109.14/108.84 [4387]E(f318(f253(x43871),f318(f318(f9(x43871,f918(x43872,a909),a909),f318(f318(f10(x43872,f918(f918(x43872,a909),a909),x43871),f320(x43872)),x43873)),x43874)),f318(f302(x43871,x43872,x43873),x43874))
% 109.14/108.84 [4471]E(f318(f253(x44711),f318(f318(f9(x44711,f918(f917(x44712,x44711),a909),a909),f318(f318(f10(f917(x44712,x44711),f918(f918(f917(x44712,x44711),a909),a909),x44711),f320(f917(x44712,x44711))),f318(f243(x44712,x44711),x44713))),x44714)),f318(f276(x44712,x44711,x44714),f318(f318(f300(x44712),x44713),f179(f918(x44712,a909)))))
% 109.14/108.84 [4487]E(f318(f318(f145(f917(x44871,a911),x44871),f242(x44871,a911)),f318(f127(f917(x44871,a911),f318(f318(f10(a911,a909,f917(x44871,a911)),x44872),f318(f318(f10(a911,a911,f917(x44871,a911)),a103),f247(x44871,a911)))),f318(f318(f172(x44871,a911),x44873),x44874))),f318(f318(f145(f917(x44871,a911),x44871),f242(x44871,a911)),f318(f127(f917(x44871,a911),f318(f318(f10(a911,a909,f917(x44871,a911)),x44872),f247(x44871,a911))),f318(f318(f172(x44871,a911),x44873),f318(f318(f145(a911,a911),a103),x44874)))))
% 109.14/108.84 [4496]P1(f318(f318(f225(f918(f918(x44961,a909),a909)),f318(f318(f33(x44962,f918(f918(x44961,a909),a909)),x44963),f318(f318(f10(f918(x44961,a909),f918(f918(x44961,a909),a909),x44962),f299(x44961)),x44964))),f318(f299(x44961),f318(f318(f33(x44962,f918(x44961,a909)),x44963),x44964))))
% 109.14/108.84 [4541]E(f318(f318(f81(a1,x45411),f318(f94(a1),f318(f318(f73(a1),x45412),a88))),f318(f318(f20(a1,x45411,x45411),f318(f318(f9(a1,x45411,f918(x45411,x45411)),f318(f318(f10(a909,f918(x45411,f918(x45411,x45411)),a1),f85(x45411)),a184)),x45413)),f318(f318(f20(a1,x45411,x45411),f318(f318(f10(a911,f918(x45411,x45411),a1),x45414),a95)),f318(f318(f10(a911,x45411,a1),f175(x45411,x45413,x45414)),a95)))),f318(f175(x45411,x45413,x45414),f318(f94(a911),x45412)))
% 109.14/108.84 [4571]E(f318(f253(f917(x45711,x45712)),f318(f248(x45711,x45712,a909),f318(f318(f9(x45711,f918(x45712,a909),f918(x45712,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x45712,a909),f918(x45712,a909)),x45711),f10(a909,a909,x45712)),f318(f318(f10(a909,f918(a909,a909),x45711),a316),f318(f318(f9(x45711,f918(x45711,a909),a909),f320(x45711)),x45713)))),f318(f318(f9(x45712,f918(x45712,a909),a909),f320(x45712)),x45714)))),f220(x45711,x45712,x45713,x45714))
% 109.14/108.84 [4612]E(f318(f318(f33(x46121,f918(f917(x46121,x46122),a909)),x46123),f318(f318(f20(x46121,f918(x46122,f918(f917(x46121,x46122),a909)),f918(f917(x46121,x46122),a909)),f318(f318(f10(f918(x46122,a909),f918(f918(x46122,f918(f917(x46121,x46122),a909)),f918(f917(x46121,x46122),a909)),x46121),f33(x46122,f918(f917(x46121,x46122),a909))),x46124)),f318(f318(f9(x46121,f918(f917(x46121,x46122),a909),f918(x46122,f918(f917(x46121,x46122),a909))),f318(f318(f10(f918(x46122,f918(f918(f917(x46121,x46122),a909),f918(f917(x46121,x46122),a909))),f918(f918(f917(x46121,x46122),a909),f918(x46122,f918(f917(x46121,x46122),a909))),x46121),f9(x46122,f918(f917(x46121,x46122),a909),f918(f917(x46121,x46122),a909))),f318(f318(f10(f918(x46122,f917(x46121,x46122)),f918(x46122,f918(f918(f917(x46121,x46122),a909),f918(f917(x46121,x46122),a909))),x46121),f318(f10(f917(x46121,x46122),f918(f918(f917(x46121,x46122),a909),f918(f917(x46121,x46122),a909)),x46122),f300(f917(x46121,x46122)))),f243(x46121,x46122)))),f179(f918(f917(x46121,x46122),a909))))),f318(f318(f245(x46121,x46122),x46123),x46124))
% 109.14/108.84 [4168]E(f318(f318(f125(x41681),f318(f318(f166(x41681),x41682),x41683)),f318(f318(f166(x41681),f318(f318(f3(a911),x41682),f318(f180(f912(x41681)),x41683))),x41684)),f318(f318(f166(x41681),x41682),f318(f318(f125(x41681),x41683),x41684)))
% 109.14/108.84 [4169]E(f318(f318(f125(x41691),f318(f318(f129(x41691),x41692),x41693)),f318(f318(f129(x41691),f318(f318(f3(a911),x41692),f318(f180(f912(x41691)),x41693))),x41694)),f318(f318(f129(x41691),x41692),f318(f318(f125(x41691),x41693),x41694)))
% 109.14/108.84 [4217]E(f318(f318(f73(a911),f318(f318(f74(a911),x42171),x42172)),f318(f318(f73(a911),f318(f318(f74(a911),x42173),x42172)),x42174)),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f73(a911),x42171),x42173)),x42172)),x42174))
% 109.14/108.84 [4358]E(f83(x43581,f318(f318(f9(x43581,x43582,a909),f318(f318(f10(x43582,f918(x43582,a909),x43581),a315),x43583)),x43584)),f318(f84(x43581,x43582,f233(f918(x43581,a909)),x43583),x43584))
% 109.14/108.84 [4407]P1(f318(f318(f225(f918(x44071,a909)),f318(f318(f3(f918(x44071,a909)),f318(f275(x44072,x44071),x44073)),f318(f275(x44072,x44071),x44074))),f318(f275(x44072,x44071),f318(f318(f3(f918(f917(x44072,x44071),a909)),x44073),x44074))))
% 109.14/108.84 [4408]P1(f318(f318(f225(f918(x44081,a909)),f318(f318(f3(f918(x44081,a909)),f318(f255(x44081,x44082),x44083)),f318(f255(x44081,x44082),x44084))),f318(f255(x44081,x44082),f318(f318(f3(f918(f917(x44081,x44082),a909)),x44083),x44084))))
% 109.14/108.84 [4522]E(f318(f318(f73(a1),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x45221),x45222)),f179(f918(f917(a911,a911),a909)))))),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x45223),x45224)),f179(f918(f917(a911,a911),a909)))))),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),f318(f318(f73(a911),x45221),x45223)),f318(f318(f73(a911),x45222),x45224))),f179(f918(f917(a911,a911),a909))))))
% 109.14/108.84 [4566]E(f318(f318(f74(a1),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x45661),x45662)),f179(f918(f917(a911,a911),a909)))))),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x45663),x45664)),f179(f918(f917(a911,a911),a909)))))),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),f318(f318(f73(a911),f318(f318(f74(a911),x45661),x45663)),f318(f318(f74(a911),x45662),x45664))),f318(f318(f73(a911),f318(f318(f74(a911),x45661),x45664)),f318(f318(f74(a911),x45662),x45663)))),f179(f918(f917(a911,a911),a909))))))
% 109.14/108.84 [4593]E(f318(f253(x45931),f318(f318(f10(f918(x45932,a909),a909,x45931),f80(x45932)),f318(f318(f10(f918(x45932,a909),f918(x45932,a909),x45931),f318(f20(x45932,a909,a909),f318(f318(f10(a909,f918(a909,a909),x45932),a321),f318(f318(f9(x45932,f918(x45932,a909),a909),f320(x45932)),x45933)))),f318(f318(f9(x45931,f918(x45932,f918(x45931,a909)),f918(x45932,a909)),f318(f318(f10(f918(f918(x45931,a909),a909),f918(f918(x45932,f918(x45931,a909)),f918(x45932,a909)),x45931),f10(f918(x45931,a909),a909,x45932)),f320(x45931))),x45934)))),f318(f318(f34(x45932,f918(x45931,a909)),x45933),x45934))
% 109.14/108.84 [4624]E(f318(f318(f280(x46241,x46241,x46241),f318(f318(f300(f917(x46241,x46241)),f318(f318(f243(x46241,x46241),x46242),x46243)),x46244)),f298(x46241,f318(f318(f300(f917(x46241,x46241)),f318(f318(f243(x46241,x46241),x46242),x46243)),x46244))),f318(f318(f101(f918(f917(x46241,x46241),a909)),f318(f318(f280(x46241,x46241,x46241),x46244),f298(x46241,x46244))),f318(f253(f917(x46241,x46241)),f318(f248(x46241,x46241,a909),f318(f318(f9(x46241,f918(x46241,a909),f918(x46241,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x46241,a909),f918(x46241,a909)),x46241),f10(a909,a909,x46241)),f318(f318(f10(a909,f918(a909,a909),x46241),a316),f318(f318(f9(x46241,f918(f917(x46241,x46241),a909),a909),f318(f318(f10(f917(x46241,x46241),f918(f918(f917(x46241,x46241),a909),a909),x46241),f320(f917(x46241,x46241))),f318(f318(f9(x46241,x46241,f917(x46241,x46241)),f243(x46241,x46241)),x46242))),f298(x46241,x46244))))),f318(f318(f9(x46241,f918(f917(x46241,x46241),a909),a909),f318(f318(f10(f917(x46241,x46241),f918(f918(f917(x46241,x46241),a909),a909),x46241),f320(f917(x46241,x46241))),f318(f243(x46241,x46241),x46243))),f298(x46241,x46244)))))))
% 109.14/108.84 [4409]E(f318(f127(x44091,f318(f318(f20(x44091,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44091),a316),x44092)),x44093)),x44094),f318(f127(x44091,x44093),f318(f127(x44091,x44092),x44094)))
% 109.14/108.84 [4516]E(f318(f318(f125(x45161),f318(f318(f318(f85(f912(x45161)),f318(f318(f320(a911),f2(a911)),x45162)),f318(f318(f142(x45161),x45163),f104(x45161))),f104(x45161))),f167(x45161,x45164,f318(f253(a911),f318(f318(f9(a911,f918(a911,a909),a909),f318(f318(f10(a911,f918(f918(a911,a909),a909),a911),f320(a911)),a103)),x45162)))),f167(x45161,f318(f318(f142(x45161),x45163),x45164),x45162))
% 109.14/108.84 [4620]E(f318(f253(f917(x46201,x46202)),f318(f318(f10(f918(a911,a909),a909,f917(x46201,x46202)),f79(a911)),f318(f318(f9(f917(x46201,x46202),f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),f917(x46201,x46202)),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),f917(x46201,x46202)),f318(f10(a909,f918(a909,a909),a911),a316)),f318(f318(f9(f917(x46201,x46202),f918(a911,f917(x46201,x46202)),f918(a911,a909)),f318(f318(f10(f918(f917(x46201,x46202),a909),f918(f918(a911,f917(x46201,x46202)),f918(a911,a909)),f917(x46201,x46202)),f10(f917(x46201,x46202),a909,a911)),a315)),f318(f318(f20(a911,x46202,f917(x46201,x46202)),f318(f318(f10(x46201,f918(x46202,f917(x46201,x46202)),a911),f243(x46201,x46202)),f318(f155(x46201),x46203))),f318(f155(x46202),x46204)))))),f318(f318(f9(a911,a911,a909),f226(a911)),f318(f318(f223(a911),f318(f180(f912(x46201)),x46203)),f318(f180(f912(x46202)),x46204)))))),f318(f163(f917(x46201,x46202)),f318(f318(f172(x46201,x46202),x46203),x46204)))
% 109.14/108.84 [4535]E(f318(f253(f917(x45351,x45352)),f318(f248(x45351,x45352,a909),f318(f318(f9(x45351,f918(x45352,a909),f918(x45352,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x45352,a909),f918(x45352,a909)),x45351),f10(a909,a909,x45352)),f318(f318(f10(a909,f918(a909,a909),x45351),a316),x45353))),x45354))),f318(f318(f245(x45351,x45352),f318(f253(x45351),x45353)),f318(f18(f918(x45352,a909),x45351),f318(f253(x45352),x45354))))
% 109.14/108.84 [4538]E(f318(f253(f917(x45381,x45382)),f318(f248(x45381,x45382,a909),f318(f318(f20(x45381,f918(x45382,a909),f918(x45382,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x45382,a909),f918(x45382,a909)),x45381),f10(a909,a909,x45382)),f318(f318(f10(a909,f918(a909,a909),x45381),a316),x45383))),x45384))),f318(f318(f245(x45381,x45382),f318(f253(x45381),x45383)),f318(f318(f10(f918(x45382,a909),f918(x45382,a909),x45381),f253(x45382)),x45384)))
% 109.14/108.84 [4548]E(f318(f253(x45481),f318(f318(f10(f918(x45482,a909),a909,x45481),f80(x45482)),f318(f318(f10(f918(x45482,a909),f918(x45482,a909),x45481),f318(f20(x45482,a909,a909),f318(f318(f10(a909,f918(a909,a909),x45482),a321),f318(f318(f9(x45482,f918(x45482,a909),a909),f320(x45482)),x45483)))),x45484))),f318(f318(f34(x45482,f918(x45481,a909)),x45483),f318(f318(f10(f918(x45481,a909),f918(x45481,a909),x45482),f253(x45481)),f318(f9(x45481,x45482,a909),x45484))))
% 109.14/108.84 [4604]E(f318(f318(f145(f917(x46041,a911),x46041),f242(x46041,a911)),f318(f127(f917(x46041,a911),f318(f318(f9(f917(x46041,a911),f918(a911,a909),a909),f318(f318(f10(a911,f918(f918(a911,a909),a909),f917(x46041,a911)),f320(a911)),f247(x46041,a911))),x46042)),f318(f318(f172(x46041,a911),x46043),f130(a911,f318(f293(a911,x46044),f318(f318(f73(a911),x46044),f318(f180(f912(x46041)),x46043))))))),f318(f318(f145(f917(x46041,a911),x46041),f242(x46041,a911)),f318(f127(f917(x46041,a911),f318(f318(f9(f917(x46041,a911),f918(a911,a909),a909),f318(f318(f10(a911,f918(f918(a911,a909),a909),f917(x46041,a911)),f320(a911)),f318(f318(f9(f917(x46041,a911),a911,a911),f318(f318(f10(a911,f918(a911,a911),f917(x46041,a911)),f73(a911)),f247(x46041,a911))),x46044))),x46042)),f318(f318(f172(x46041,a911),x46043),f130(a911,f318(f293(a911,f2(a911)),f318(f180(f912(x46041)),x46043)))))))
% 109.14/108.84 [4605]E(f318(a103,f318(f318(f224(a911),f318(f180(f912(x46051)),x46052)),f318(f133(a911,f912(x46053),f318(f9(f912(x46053),a911,a911),f318(f318(f10(a911,f918(a911,a911),f912(x46053)),f224(a911)),f318(f318(f9(f912(x46053),a911,a911),f318(f318(f10(a911,f918(a911,a911),f912(x46053)),f3(a911)),f180(f912(x46053)))),f318(a103,f2(a911))))),f2(a911)),f318(f159(f912(x46053)),f318(f127(f912(x46053),f318(f318(f10(a909,a909,f912(x46053)),a313),f318(f318(f9(f912(x46053),f912(x46053),a909),a315),f104(x46053)))),x46054))))),f318(f318(f224(a911),f318(a103,f318(f180(f912(x46051)),x46052))),f318(f133(a911,f912(x46053),f318(f9(f912(x46053),a911,a911),f318(f318(f10(a911,f918(a911,a911),f912(x46053)),f224(a911)),f180(f912(x46053)))),f2(a911)),f318(f159(f912(x46053)),x46054))))
% 109.14/108.84 [4547]E(f318(f318(f125(x45471),f167(x45471,x45472,x45473)),f167(x45471,x45474,f318(f253(a911),f318(f318(f9(a911,f918(a911,a909),a909),f318(f318(f10(a911,f918(f918(a911,a909),a909),a911),f320(a911)),f318(f318(f9(a911,a911,a911),f73(a911)),f318(f180(f912(x45471)),x45472)))),x45473)))),f167(x45471,f318(f318(f125(x45471),x45472),x45474),x45473))
% 109.14/108.84 [4606]E(f31(f918(x46061,a909),f318(f253(f918(x46061,a909)),f318(f318(f10(f918(x46062,a909),a909,f918(x46061,a909)),f79(x46062)),f318(f318(f10(f918(x46062,a909),f918(x46062,a909),f918(x46061,a909)),f318(f20(x46062,a909,a909),f318(f318(f10(a909,f918(a909,a909),x46062),a316),f318(f318(f9(x46062,f918(x46062,a909),a909),f320(x46062)),x46063)))),f318(f318(f9(f918(x46061,a909),f918(x46062,f918(x46061,a909)),f918(x46062,a909)),f318(f318(f10(f918(f918(x46061,a909),a909),f918(f918(x46062,f918(x46061,a909)),f918(x46062,a909)),f918(x46061,a909)),f10(f918(x46061,a909),a909,x46062)),a315)),x46064))))),f318(f318(f33(x46062,f918(x46061,a909)),x46063),x46064))
% 109.14/108.84 [4607]E(f32(f918(x46071,a909),f318(f253(f918(x46071,a909)),f318(f318(f10(f918(x46072,a909),a909,f918(x46071,a909)),f79(x46072)),f318(f318(f10(f918(x46072,a909),f918(x46072,a909),f918(x46071,a909)),f318(f20(x46072,a909,a909),f318(f318(f10(a909,f918(a909,a909),x46072),a316),f318(f318(f9(x46072,f918(x46072,a909),a909),f320(x46072)),x46073)))),f318(f318(f9(f918(x46071,a909),f918(x46072,f918(x46071,a909)),f918(x46072,a909)),f318(f318(f10(f918(f918(x46071,a909),a909),f918(f918(x46072,f918(x46071,a909)),f918(x46072,a909)),f918(x46071,a909)),f10(f918(x46071,a909),a909,x46072)),a315)),x46074))))),f318(f318(f34(x46072,f918(x46071,a909)),x46073),x46074))
% 109.14/108.84 [4614]E(f318(f318(f142(f912(x46141)),f318(f318(f142(x46141),x46142),f318(f133(f912(x46141),f912(x46141),f125(x46141),f104(x46141)),f318(f318(f145(f912(x46141),f912(x46141)),f147(f912(x46141),x46141,f104(x46141),f318(f318(f10(f912(x46141),f918(f912(x46141),f912(x46141)),x46141),f18(f912(x46141),f912(x46141))),f318(f318(f9(x46141,f912(x46141),f912(x46141)),f142(x46141)),f104(x46141))))),x46143)))),f170(x46141,f318(f318(f142(f912(x46141)),x46144),f318(f133(f912(f912(x46141)),f912(f912(x46141)),f125(f912(x46141)),f104(f912(x46141))),f318(f318(f145(f912(x46141),f912(f912(x46141))),f147(f912(f912(x46141)),x46141,f104(f912(x46141)),f318(f18(f918(f912(x46141),f912(f912(x46141))),x46141),f318(f318(f9(f912(x46141),f912(f912(x46141)),f912(f912(x46141))),f142(f912(x46141))),f104(f912(x46141)))))),x46143))))),f170(x46141,f318(f318(f142(f912(x46141)),f318(f318(f142(x46141),x46142),x46144)),x46143)))
% 109.14/108.84 [4621]E(f318(f253(f917(x46211,x46211)),f318(f248(x46211,x46211,a909),f318(f318(f9(x46211,f918(f917(x46212,x46212),a909),f918(x46211,a909)),f318(f318(f10(f918(x46211,f918(f918(f917(x46212,x46212),a909),a909)),f918(f918(f917(x46212,x46212),a909),f918(x46211,a909)),x46211),f9(x46211,f918(f917(x46212,x46212),a909),a909)),f318(f318(f10(f918(x46211,f917(x46212,x46212)),f918(x46211,f918(f918(f917(x46212,x46212),a909),a909)),x46211),f318(f10(f917(x46212,x46212),f918(f918(f917(x46212,x46212),a909),a909),x46211),f320(f917(x46212,x46212)))),f318(f318(f9(x46211,f918(x46211,x46212),f918(x46211,f917(x46212,x46212))),f318(f318(f10(f918(x46212,f917(x46212,x46212)),f918(f918(x46211,x46212),f918(x46211,f917(x46212,x46212))),x46211),f10(x46212,f917(x46212,x46212),x46211)),f318(f318(f10(x46212,f918(x46212,f917(x46212,x46212)),x46211),f243(x46212,x46212)),x46213))),x46213)))),x46214))),f318(f318(f279(x46212,x46211),x46214),x46213))
% 109.14/108.84 [3758]E(f318(f318(f145(x37581,x37582),x37583),f160(x37581,x37584,x37585)),f160(x37582,x37584,f318(x37583,x37585)))
% 109.14/108.84 [4082]E(f121(x40821,x40822,x40823,f117(x40821,x40824,x40825)),f117(x40822,f318(x40823,x40824),f121(x40821,x40822,x40823,x40825)))
% 109.14/108.84 [4305]E(f318(f68(x43051,x43052,x43053,x43054,x43055),x43054),x43055)
% 109.14/108.84 [4359]E(f244(x43591,x43592,x43593,f234(x43592,x43591,x43594),f234(x43593,x43592,x43595)),f234(x43593,x43591,f244(x43593,x43592,x43591,x43595,x43594)))
% 109.14/108.84 [3947]E(f318(f318(f248(x39471,x39472,x39473),x39474),x39475),f318(f318(x39474,f318(f242(x39471,x39472),x39475)),f318(f247(x39471,x39472),x39475)))
% 109.14/108.84 [3948]E(f318(f318(f248(x39481,x39482,x39483),x39484),x39485),f318(f318(x39484,f318(f242(x39481,x39482),x39485)),f318(f247(x39481,x39482),x39485)))
% 109.14/108.84 [3949]E(f318(f318(f248(x39491,x39492,x39493),x39494),x39495),f318(f318(x39494,f318(f242(x39491,x39492),x39495)),f318(f247(x39491,x39492),x39495)))
% 109.14/108.84 [3982]E(f318(f318(f318(f59(x39821,x39822,x39823),x39824),x39825),f179(f918(x39822,a909))),x39825)
% 109.14/108.84 [4248]E(f318(f66(f912(x42481),f912(x42482),f912(x42483),f318(f145(x42481,x42482),x42484)),f318(f145(x42483,x42481),x42485)),f318(f145(x42483,x42482),f318(f66(x42481,x42482,x42483,x42484),x42485)))
% 109.14/108.84 [4249]E(f318(f66(f912(x42491),f912(x42492),f912(x42493),f318(f145(x42491,x42492),x42494)),f318(f145(x42493,x42491),x42495)),f318(f145(x42493,x42492),f318(f66(x42491,x42492,x42493,x42494),x42495)))
% 109.14/108.84 [4315]E(f78(x43151,f60(x43152,x43151,x43153,x43154,x43155)),f318(f318(f58(x43152,x43151,x43153),x43154),x43155))
% 109.14/108.84 [4351]E(f318(f318(f73(a911),f318(f318(f73(a911),f318(x43511,f318(f242(x43512,x43513),x43514))),f318(x43515,f318(f247(x43512,x43513),x43514)))),f318(a103,f2(a911))),f252(x43512,x43513,x43511,x43515,x43514))
% 109.14/108.84 [3888]E(f318(f318(f166(x38881),x38882),f318(f318(f145(x38883,x38881),x38884),x38885)),f318(f318(f145(x38883,x38881),x38884),f318(f318(f166(x38883),x38882),x38885)))
% 109.14/108.84 [3889]E(f318(f318(f129(x38891),x38892),f318(f318(f145(x38893,x38891),x38894),x38895)),f318(f318(f145(x38893,x38891),x38894),f318(f318(f129(x38893),x38892),x38895)))
% 109.14/108.84 [3913]E(f318(f318(f145(x39131,x39132),x39133),f318(f318(f142(x39131),x39134),x39135)),f318(f318(f142(x39132),f318(x39133,x39134)),f318(f318(f145(x39131,x39132),x39133),x39135)))
% 109.14/108.84 [3978]E(f318(f301(x39781,x39782,x39783),f318(f318(f300(x39781),x39784),x39785)),f318(f318(f300(x39782),f318(x39783,x39784)),f318(f301(x39781,x39782,x39783),x39785)))
% 109.14/108.84 [4006]E(f164(x40061,f318(f318(f142(x40061),x40062),x40063),f318(f318(f142(x40061),x40064),x40065)),f318(f318(f142(x40061),x40062),f318(f318(f142(x40061),x40064),f164(x40061,x40063,x40065))))
% 109.14/108.84 [4040]E(f318(f318(f172(x40401,x40402),f318(f318(f166(x40401),x40403),x40404)),f318(f318(f166(x40402),x40403),x40405)),f318(f318(f166(f917(x40401,x40402)),x40403),f318(f318(f172(x40401,x40402),x40404),x40405)))
% 109.14/108.84 [4041]E(f318(f318(f172(x40411,x40412),f318(f318(f129(x40411),x40413),x40414)),f318(f318(f129(x40412),x40413),x40415)),f318(f318(f129(f917(x40411,x40412)),x40413),f318(f318(f172(x40411,x40412),x40414),x40415)))
% 109.14/108.84 [4049]E(f318(f318(f150(x40491,f318(f318(f142(x40491),x40492),x40493)),f318(a103,x40494)),x40495),f318(f318(f142(x40491),x40492),f318(f318(f150(x40491,x40493),x40494),x40495)))
% 109.14/108.84 [4051]E(f318(f318(f125(x40511),f318(f318(f145(x40512,x40511),x40513),x40514)),f318(f318(f145(x40512,x40511),x40513),x40515)),f318(f318(f145(x40512,x40511),x40513),f318(f318(f125(x40512),x40514),x40515)))
% 109.14/108.84 [4055]E(f318(f318(x40551,x40552),f318(f318(f236(x40553,x40554,x40551),x40552),x40555)),f318(f318(f236(x40553,x40554,x40551),x40552),f318(a103,x40555)))
% 109.14/108.84 [4086]E(f154(x40861,x40862,x40863,f318(f318(f142(x40861),x40864),x40865)),f318(f318(f125(x40862),f318(x40863,x40864)),f154(x40861,x40862,x40863,x40865)))
% 109.14/108.84 [4098]E(f318(f318(f280(x40981,x40982,x40983),f318(f277(x40982,x40981),x40984)),f318(f277(x40983,x40982),x40985)),f318(f277(x40983,x40981),f318(f318(f280(x40983,x40982,x40981),x40985),x40984)))
% 109.14/108.84 [4131]E(f318(f318(f318(f174(f912(x41311),f912(x41311)),x41312),f158(x41311)),f318(f318(f145(x41313,x41311),x41314),x41315)),f318(f318(f145(x41313,x41311),x41314),f318(f318(f318(f174(f912(x41313),f912(x41313)),x41312),f158(x41313)),x41315)))
% 109.14/108.84 [4132]E(f318(f318(f250(x41321,x41322,x41321,x41323),f318(f243(x41322,x41321),x41324)),x41325),f318(x41325,x41324))
% 109.14/108.84 [4155]E(f146(x41551,x41552,f318(f318(f145(x41553,x41551),x41554),x41555)),f146(x41553,f318(f66(x41551,a911,x41553,x41552),x41554),x41555))
% 109.14/108.84 [4216]E(f168(f917(x42161,x42162),f318(f66(x42162,a909,f917(x42161,x42162),x42163),f247(x42161,x42162)),f318(f318(f172(x42161,x42162),x42164),x42165)),f318(f318(f172(x42161,x42162),x42164),f168(x42162,x42163,x42165)))
% 109.14/108.84 [4221]E(f318(f301(x42211,x42212,f318(f318(f10(x42213,x42212,x42211),x42214),x42215)),f233(f918(x42211,a909))),f318(f301(x42213,x42212,x42214),f318(f301(x42211,x42213,x42215),f233(f918(x42211,a909)))))
% 109.14/108.84 [4232]E(f168(f917(x42321,x42322),f318(f66(x42321,a909,f917(x42321,x42322),x42323),f242(x42321,x42322)),f318(f318(f172(x42321,x42322),x42324),x42325)),f318(f318(f172(x42321,x42322),f168(x42321,x42323,x42324)),x42325))
% 109.14/108.84 [4254]E(f318(f318(f101(f918(x42541,a909)),f318(f302(x42541,x42542,x42543),f318(f318(f300(x42542),x42544),f179(f918(x42542,a909))))),f318(f302(x42541,x42542,x42543),x42545)),f318(f302(x42541,x42542,x42543),f318(f318(f300(x42542),x42544),x42545)))
% 109.14/108.84 [4304]E(f318(f318(f125(f917(x43041,x43042)),f318(f318(f145(x43042,f917(x43041,x43042)),f318(f243(x43041,x43042),x43043)),x43044)),f53(x43041,x43042,x43045,x43044)),f53(x43041,x43042,f318(f318(f142(x43041),x43043),x43045),x43044))
% 109.14/108.84 [4306]E(f318(f318(f145(x43061,x43062),x43063),f168(x43061,f318(f66(x43062,a909,x43061,x43064),x43063),x43065)),f168(x43062,x43064,f318(f318(f145(x43061,x43062),x43063),x43065)))
% 109.14/108.84 [4311]E(f318(f133(x43111,x43112,f318(f9(x43112,x43111,x43111),f318(f9(x43111,x43112,x43111),x43113)),x43114),f318(f159(x43112),f318(f159(x43112),x43115))),f318(f133(x43111,x43112,x43113,x43114),x43115))
% 109.14/108.84 [4417]P1(f318(f318(f225(f918(x44171,a909)),f318(f301(x44172,x44171,x44173),f318(f318(f92(f918(x44172,a909)),x44174),x44175))),f318(f318(f92(f918(x44171,a909)),f318(f301(x44172,x44171,x44173),x44174)),f318(f301(x44172,x44171,x44173),x44175))))
% 109.14/108.84 [4418]P1(f318(f318(f225(f918(x44181,a909)),f318(f276(x44182,x44181,x44183),f318(f318(f92(f918(x44182,a909)),x44184),x44185))),f318(f318(f92(f918(x44181,a909)),f318(f276(x44182,x44181,x44183),x44184)),f318(f276(x44182,x44181,x44183),x44185))))
% 109.14/108.84 [4523]E(f318(f247(x45231,x45232),f318(f249(x45233,x45231,x45232,x45232,x45234,f25(x45232)),x45235)),f318(f247(x45233,x45232),x45235))
% 109.14/108.84 [4524]E(f318(f242(x45241,x45242),f318(f249(x45241,x45241,x45243,x45242,f25(x45241),x45244),x45245)),f318(f242(x45241,x45243),x45245))
% 109.14/108.84 [4527]E(f318(f242(x45271,x45272),f318(f249(x45273,x45271,x45272,x45272,x45274,f25(x45272)),x45275)),f318(x45274,f318(f242(x45273,x45272),x45275)))
% 109.14/108.84 [4528]E(f318(f247(x45281,x45282),f318(f249(x45281,x45281,x45283,x45282,f25(x45281),x45284),x45285)),f318(x45284,f318(f247(x45281,x45283),x45285)))
% 109.14/108.84 [3729]E(f318(f318(f318(f318(f195(x37291),x37292),x37293),x37294),x37295),f183(x37291,x37292))
% 109.14/108.84 [3730]E(f318(f318(f318(f318(f199(x37301),x37302),x37303),x37304),x37305),f190(x37301,x37302))
% 109.14/108.84 [4087]E(f318(f318(f33(x40871,f918(x40872,a909)),f318(f318(f300(x40871),x40873),x40874)),x40875),f318(f318(f101(f918(x40872,a909)),f318(x40875,x40873)),f318(f318(f33(x40871,f918(x40872,a909)),x40874),x40875)))
% 109.14/108.84 [4088]E(f318(f318(f34(x40881,f918(x40882,a909)),f318(f318(f300(x40881),x40883),x40884)),x40885),f318(f318(f92(f918(x40882,a909)),f318(x40885,x40883)),f318(f318(f34(x40881,f918(x40882,a909)),x40884),x40885)))
% 109.14/108.84 [4140]E(f318(f109(x41401,x41402,f318(x41403,x41404)),f318(f318(f9(x41401,a90,f913(x41402)),x41405),x41404)),f318(f188(x41401,x41402,x41403,x41405),x41404))
% 109.14/108.84 [4149]E(f318(f318(f101(f918(x41491,a909)),f318(f301(x41492,x41491,x41493),x41494)),f318(f301(x41492,x41491,x41493),x41495)),f318(f301(x41492,x41491,x41493),f318(f318(f101(f918(x41492,a909)),x41494),x41495)))
% 109.14/108.84 [4150]E(f318(f318(f101(f918(x41501,a909)),f318(f302(x41501,x41502,x41503),x41504)),f318(f302(x41501,x41502,x41503),x41505)),f318(f302(x41501,x41502,x41503),f318(f318(f101(f918(x41502,a909)),x41504),x41505)))
% 109.14/108.84 [4151]E(f318(f318(f92(f918(x41511,a909)),f318(f302(x41511,x41512,x41513),x41514)),f318(f302(x41511,x41512,x41513),x41515)),f318(f302(x41511,x41512,x41513),f318(f318(f92(f918(x41512,a909)),x41514),x41515)))
% 109.14/108.84 [4152]E(f318(f318(f3(f918(x41521,a909)),f318(f302(x41521,x41522,x41523),x41524)),f318(f302(x41521,x41522,x41523),x41525)),f318(f302(x41521,x41522,x41523),f318(f318(f3(f918(x41522,a909)),x41524),x41525)))
% 109.14/108.84 [4153]E(f318(f318(f101(f918(x41531,a909)),f318(f276(x41532,x41531,x41533),x41534)),f318(f276(x41532,x41531,x41533),x41535)),f318(f276(x41532,x41531,x41533),f318(f318(f101(f918(x41532,a909)),x41534),x41535)))
% 109.14/108.84 [4212]E(f318(f318(f150(x42121,f318(f318(f125(x42121),x42122),f318(f318(f142(x42121),x42123),x42124))),f318(f180(f912(x42121)),x42122)),x42125),f318(f318(f125(x42121),x42122),f318(f318(f142(x42121),x42125),x42124)))
% 109.14/108.84 [4218]E(f318(f318(f34(x42181,f918(x42182,a909)),x42183),f318(f318(f10(f918(x42182,a909),f918(x42182,a909),x42181),f318(f300(x42182),x42184)),x42185)),f318(f318(f300(x42182),x42184),f318(f318(f34(x42181,f918(x42182,a909)),x42183),x42185)))
% 109.14/108.84 [4219]E(f318(f318(f34(x42191,f918(x42192,a909)),x42193),f318(f318(f10(f918(x42192,a909),f918(x42192,a909),x42191),f318(f300(x42192),x42194)),x42195)),f318(f318(f300(x42192),x42194),f318(f318(f34(x42191,f918(x42192,a909)),x42193),x42195)))
% 109.14/108.84 [4318]E(f318(f318(f101(f918(f917(x43181,x43182),a909)),f318(f318(f245(x43181,x43182),x43183),f318(f18(f918(x43182,a909),x43181),x43184))),f318(f318(f245(x43181,x43182),x43185),f318(f18(f918(x43182,a909),x43181),x43184))),f318(f318(f245(x43181,x43182),f318(f318(f101(f918(x43181,a909)),x43183),x43185)),f318(f18(f918(x43182,a909),x43181),x43184)))
% 109.14/108.84 [4319]E(f318(f318(f92(f918(f917(x43191,x43192),a909)),f318(f318(f245(x43191,x43192),x43193),f318(f18(f918(x43192,a909),x43191),x43194))),f318(f318(f245(x43191,x43192),x43195),f318(f18(f918(x43192,a909),x43191),x43194))),f318(f318(f245(x43191,x43192),f318(f318(f92(f918(x43191,a909)),x43193),x43195)),f318(f18(f918(x43192,a909),x43191),x43194)))
% 109.14/108.84 [4320]E(f318(f318(f3(f918(f917(x43201,x43202),a909)),f318(f318(f245(x43201,x43202),x43203),f318(f18(f918(x43202,a909),x43201),x43204))),f318(f318(f245(x43201,x43202),x43205),f318(f18(f918(x43202,a909),x43201),x43204))),f318(f318(f245(x43201,x43202),f318(f318(f3(f918(x43201,a909)),x43203),x43205)),f318(f18(f918(x43202,a909),x43201),x43204)))
% 109.14/108.84 [4369]E(f318(f318(f145(x43691,x43692),x43693),f318(f127(x43691,f318(f66(x43692,a909,x43691,x43694),x43693)),x43695)),f318(f127(x43692,x43694),f318(f318(f145(x43691,x43692),x43693),x43695)))
% 109.14/108.84 [4376]E(f318(f180(f912(x43761)),f318(f127(x43761,x43762),f318(f318(f145(x43763,x43761),x43764),x43765))),f318(f180(f912(x43763)),f318(f127(x43763,f318(f66(x43761,a909,x43763,x43762),x43764)),x43765)))
% 109.14/108.84 [4600]E(f318(f147(f912(f917(x46001,x46002)),x46002,f104(f917(x46001,x46002)),f318(f318(f9(x46002,f918(f912(x46002),f912(f917(x46001,x46002))),f918(f912(x46002),f912(f917(x46001,x46002)))),f318(f318(f10(f918(f912(f917(x46001,x46002)),f912(f917(x46001,x46002))),f918(f918(f912(x46002),f912(f917(x46001,x46002))),f918(f912(x46002),f912(f917(x46001,x46002)))),x46002),f10(f912(f917(x46001,x46002)),f912(f917(x46001,x46002)),f912(x46002))),f318(f318(f10(f917(x46001,x46002),f918(f912(f917(x46001,x46002)),f912(f917(x46001,x46002))),x46002),f142(f917(x46001,x46002))),f318(f243(x46001,x46002),x46003)))),f318(f172(x46001,x46002),x46004))),x46005),f318(f318(f172(x46001,x46002),f318(f318(f142(x46001),x46003),x46004)),x46005))
% 109.14/108.84 [4079]E(f318(f318(f150(x40791,f318(f318(f150(x40791,x40792),x40793),x40794)),x40793),x40795),f318(f318(f150(x40791,x40792),x40793),x40795))
% 109.14/108.84 [4133]E(f318(f275(x41331,x41332),f318(f318(f300(f917(x41331,x41332)),f318(f318(f243(x41331,x41332),x41333),x41334)),x41335)),f318(f318(f300(x41332),x41334),f318(f275(x41331,x41332),x41335)))
% 109.14/108.84 [4134]E(f318(f255(x41341,x41342),f318(f318(f300(f917(x41341,x41342)),f318(f318(f243(x41341,x41342),x41343),x41344)),x41345)),f318(f318(f300(x41341),x41343),f318(f255(x41341,x41342),x41345)))
% 109.14/108.84 [4178]E(f113(x41781,x41782,f318(x41783,x41784),f318(f318(f9(x41781,a90,f913(f915(x41782))),x41785),x41784)),f318(f186(x41781,x41782,x41783,x41785),x41784))
% 109.14/108.84 [4205]E(f318(f318(f101(f918(f917(x42051,x42052),a909)),f318(f318(f245(x42051,x42052),x42053),x42054)),f318(f318(f245(x42051,x42052),x42055),x42054)),f318(f318(f245(x42051,x42052),f318(f318(f101(f918(x42051,a909)),x42053),x42055)),x42054))
% 109.14/108.84 [4206]E(f318(f318(f92(f918(f917(x42061,x42062),a909)),f318(f318(f245(x42061,x42062),x42063),x42064)),f318(f318(f245(x42061,x42062),x42065),x42064)),f318(f318(f245(x42061,x42062),f318(f318(f92(f918(x42061,a909)),x42063),x42065)),x42064))
% 109.14/108.84 [4207]E(f318(f318(f3(f918(f917(x42071,x42072),a909)),f318(f318(f245(x42071,x42072),x42073),x42074)),f318(f318(f245(x42071,x42072),x42075),x42074)),f318(f318(f245(x42071,x42072),f318(f318(f3(f918(x42071,a909)),x42073),x42075)),x42074))
% 109.14/108.84 [4264]E(f318(f318(f101(f918(x42641,a909)),f318(f318(f33(x42642,f918(x42641,a909)),x42643),x42644)),f318(f318(f33(x42642,f918(x42641,a909)),x42645),x42644)),f318(f318(f33(x42642,f918(x42641,a909)),f318(f318(f101(f918(x42642,a909)),x42643),x42645)),x42644))
% 109.14/108.84 [4265]E(f318(f318(f92(f918(x42651,a909)),f318(f318(f34(x42652,f918(x42651,a909)),x42653),x42654)),f318(f318(f34(x42652,f918(x42651,a909)),x42655),x42654)),f318(f318(f34(x42652,f918(x42651,a909)),f318(f318(f101(f918(x42652,a909)),x42653),x42655)),x42654))
% 109.14/108.84 [4274]E(f318(f318(f34(x42741,f918(x42742,a909)),x42743),f318(f318(f10(f918(x42742,a909),f918(x42742,a909),x42741),f318(f101(f918(x42742,a909)),x42744)),x42745)),f318(f318(f101(f918(x42742,a909)),x42744),f318(f318(f34(x42741,f918(x42742,a909)),x42743),x42745)))
% 109.14/108.84 [4275]E(f318(f318(f34(x42751,f918(x42752,a909)),x42753),f318(f318(f10(f918(x42752,a909),f918(x42752,a909),x42751),f318(f101(f918(x42752,a909)),x42754)),x42755)),f318(f318(f101(f918(x42752,a909)),x42754),f318(f318(f34(x42751,f918(x42752,a909)),x42753),x42755)))
% 109.14/108.84 [4276]E(f318(f318(f33(x42761,f918(x42762,a909)),x42763),f318(f318(f10(f918(x42762,a909),f918(x42762,a909),x42761),f318(f92(f918(x42762,a909)),x42764)),x42765)),f318(f318(f92(f918(x42762,a909)),x42764),f318(f318(f33(x42761,f918(x42762,a909)),x42763),x42765)))
% 109.14/108.84 [4277]E(f318(f318(f33(x42771,f918(x42772,a909)),x42773),f318(f318(f10(f918(x42772,a909),f918(x42772,a909),x42771),f318(f92(f918(x42772,a909)),x42774)),x42775)),f318(f318(f92(f918(x42772,a909)),x42774),f318(f318(f33(x42771,f918(x42772,a909)),x42773),x42775)))
% 109.14/108.84 [4278]E(f318(f318(f33(x42781,f918(x42782,a909)),x42783),f318(f318(f10(f918(x42782,a909),f918(x42782,a909),x42781),f318(f3(f918(x42782,a909)),x42784)),x42785)),f318(f318(f3(f918(x42782,a909)),x42784),f318(f318(f34(x42781,f918(x42782,a909)),x42783),x42785)))
% 109.14/108.84 [4279]E(f318(f318(f33(x42791,f918(x42792,a909)),x42793),f318(f318(f10(f918(x42792,a909),f918(x42792,a909),x42791),f318(f92(f918(x42792,a909)),x42794)),x42795)),f318(f318(f92(f918(x42792,a909)),x42794),f318(f318(f33(x42791,f918(x42792,a909)),x42793),x42795)))
% 109.14/108.84 [4280]E(f318(f318(f33(x42801,f918(x42802,a909)),x42803),f318(f318(f10(f918(x42802,a909),f918(x42802,a909),x42801),f318(f3(f918(x42802,a909)),x42804)),x42805)),f318(f318(f3(f918(x42802,a909)),x42804),f318(f318(f34(x42801,f918(x42802,a909)),x42803),x42805)))
% 109.14/108.84 [4281]E(f318(f318(f34(x42811,f918(x42812,a909)),x42813),f318(f318(f10(f918(x42812,a909),f918(x42812,a909),x42811),f318(f101(f918(x42812,a909)),x42814)),x42815)),f318(f318(f101(f918(x42812,a909)),x42814),f318(f318(f34(x42811,f918(x42812,a909)),x42813),x42815)))
% 109.14/108.84 [4329]E(f176(f912(x43291),f318(f318(f142(x43291),x43292),x43293),f318(f318(f10(f912(x43291),f912(x43291),a911),f318(f142(x43291),x43294)),f318(f318(f9(a911,x43291,f912(x43291)),f150(x43291,x43293)),x43292)),x43295),f318(f318(f150(x43291,f318(f318(f142(x43291),x43294),x43293)),x43295),x43292))
% 109.14/108.84 [4333]E(f318(f318(f33(x43331,f918(f917(x43332,x43333),a909)),x43334),f318(f318(f10(f918(f917(x43333,x43332),a909),f918(f917(x43332,x43333),a909),x43331),f277(x43333,x43332)),x43335)),f318(f277(x43333,x43332),f318(f318(f33(x43331,f918(f917(x43333,x43332),a909)),x43334),x43335)))
% 109.14/108.84 [4334]E(f318(f318(f34(x43341,f918(f917(x43342,x43343),a909)),x43344),f318(f318(f10(f918(f917(x43343,x43342),a909),f918(f917(x43342,x43343),a909),x43341),f277(x43343,x43342)),x43345)),f318(f277(x43343,x43342),f318(f318(f34(x43341,f918(f917(x43343,x43342),a909)),x43344),x43345)))
% 109.14/108.84 [4441]P1(f318(f318(f225(f918(x44411,a909)),f318(f318(f3(f918(x44411,a909)),f318(f301(x44412,x44411,x44413),x44414)),f318(f301(x44412,x44411,x44413),x44415))),f318(f301(x44412,x44411,x44413),f318(f318(f3(f918(x44412,a909)),x44414),x44415))))
% 109.14/108.84 [4603]E(f318(f147(f912(f917(x46031,x46032)),x46031,f104(f917(x46031,x46032)),f318(f318(f9(x46031,f918(f912(x46031),f912(f917(x46031,x46032))),f918(f912(x46031),f912(f917(x46031,x46032)))),f318(f318(f10(f918(f912(f917(x46031,x46032)),f912(f917(x46031,x46032))),f918(f918(f912(x46031),f912(f917(x46031,x46032))),f918(f912(x46031),f912(f917(x46031,x46032)))),x46031),f10(f912(f917(x46031,x46032)),f912(f917(x46031,x46032)),f912(x46031))),f318(f318(f10(f917(x46031,x46032),f918(f912(f917(x46031,x46032)),f912(f917(x46031,x46032))),x46031),f142(f917(x46031,x46032))),f318(f318(f9(x46031,x46032,f917(x46031,x46032)),f243(x46031,x46032)),x46033)))),f318(f318(f9(f912(x46031),f912(x46032),f912(f917(x46031,x46032))),f172(x46031,x46032)),x46034))),x46035),f318(f318(f172(x46031,x46032),x46035),f318(f318(f142(x46032),x46033),x46034)))
% 109.14/108.84 [4300]E(f318(f318(f101(f918(x43001,a909)),f318(f276(x43002,x43001,x43003),x43004)),f318(f276(x43002,x43001,x43005),x43004)),f318(f276(x43002,x43001,f318(f318(f101(f918(f917(x43002,x43001),a909)),x43003),x43005)),x43004))
% 109.14/108.84 [4335]E(f318(f318(f125(f917(x43351,x43352)),f318(f318(f172(x43351,x43352),x43353),f318(f318(f166(x43352),f318(f180(f912(x43351)),x43353)),x43354))),f318(f318(f172(x43351,x43352),x43355),f318(f318(f129(x43352),f318(f180(f912(x43351)),x43353)),x43354))),f318(f318(f172(x43351,x43352),f318(f318(f125(x43351),x43353),x43355)),x43354))
% 109.14/108.84 [4446]E(f318(f318(f245(x44461,x44462),x44463),f318(f318(f20(x44461,f918(x44462,a909),f918(x44462,a909)),f318(f318(f10(f918(x44462,a909),f918(f918(x44462,a909),f918(x44462,a909)),x44461),f101(f918(x44462,a909))),x44464)),x44465)),f318(f318(f101(f918(f917(x44461,x44462),a909)),f318(f318(f245(x44461,x44462),x44463),x44464)),f318(f318(f245(x44461,x44462),x44463),x44465)))
% 109.14/108.84 [4447]E(f318(f318(f245(x44471,x44472),x44473),f318(f318(f20(x44471,f918(x44472,a909),f918(x44472,a909)),f318(f318(f10(f918(x44472,a909),f918(f918(x44472,a909),f918(x44472,a909)),x44471),f92(f918(x44472,a909))),x44474)),x44475)),f318(f318(f92(f918(f917(x44471,x44472),a909)),f318(f318(f245(x44471,x44472),x44473),x44474)),f318(f318(f245(x44471,x44472),x44473),x44475)))
% 109.14/108.84 [4448]E(f318(f318(f245(x44481,x44482),x44483),f318(f318(f20(x44481,f918(x44482,a909),f918(x44482,a909)),f318(f318(f10(f918(x44482,a909),f918(f918(x44482,a909),f918(x44482,a909)),x44481),f3(f918(x44482,a909))),x44484)),x44485)),f318(f318(f3(f918(f917(x44481,x44482),a909)),f318(f318(f245(x44481,x44482),x44483),x44484)),f318(f318(f245(x44481,x44482),x44483),x44485)))
% 109.14/108.84 [4449]E(f318(f318(f34(x44491,f918(x44492,a909)),x44493),f318(f318(f9(x44491,f918(x44492,a909),f918(x44492,a909)),f318(f318(f10(f918(x44492,a909),f918(f918(x44492,a909),f918(x44492,a909)),x44491),f101(f918(x44492,a909))),x44494)),x44495)),f318(f318(f101(f918(x44492,a909)),f318(f318(f34(x44491,f918(x44492,a909)),x44493),x44494)),x44495))
% 109.14/108.84 [4450]E(f318(f318(f33(x44501,f918(x44502,a909)),x44503),f318(f318(f9(x44501,f918(x44502,a909),f918(x44502,a909)),f318(f318(f10(f918(x44502,a909),f918(f918(x44502,a909),f918(x44502,a909)),x44501),f92(f918(x44502,a909))),x44504)),x44505)),f318(f318(f92(f918(x44502,a909)),f318(f318(f33(x44501,f918(x44502,a909)),x44503),x44504)),x44505))
% 109.14/108.84 [4451]E(f318(f318(f33(x44511,f918(x44512,a909)),x44513),f318(f318(f9(x44511,f918(x44512,a909),f918(x44512,a909)),f318(f318(f10(f918(x44512,a909),f918(f918(x44512,a909),f918(x44512,a909)),x44511),f3(f918(x44512,a909))),x44514)),x44515)),f318(f318(f3(f918(x44512,a909)),f318(f318(f33(x44511,f918(x44512,a909)),x44513),x44514)),x44515))
% 109.14/108.84 [4452]E(f318(f318(f33(x44521,f918(x44522,a909)),x44523),f318(f318(f9(x44521,f918(x44522,a909),f918(x44522,a909)),f318(f318(f10(f918(x44522,a909),f918(f918(x44522,a909),f918(x44522,a909)),x44521),f92(f918(x44522,a909))),x44524)),x44525)),f318(f318(f92(f918(x44522,a909)),f318(f318(f33(x44521,f918(x44522,a909)),x44523),x44524)),x44525))
% 109.14/108.84 [4453]E(f318(f318(f33(x44531,f918(x44532,a909)),x44533),f318(f318(f9(x44531,f918(x44532,a909),f918(x44532,a909)),f318(f318(f10(f918(x44532,a909),f918(f918(x44532,a909),f918(x44532,a909)),x44531),f3(f918(x44532,a909))),x44534)),x44535)),f318(f318(f3(f918(x44532,a909)),f318(f318(f33(x44531,f918(x44532,a909)),x44533),x44534)),x44535))
% 109.14/108.84 [4454]E(f318(f318(f34(x44541,f918(x44542,a909)),x44543),f318(f318(f9(x44541,f918(x44542,a909),f918(x44542,a909)),f318(f318(f10(f918(x44542,a909),f918(f918(x44542,a909),f918(x44542,a909)),x44541),f101(f918(x44542,a909))),x44544)),x44545)),f318(f318(f101(f918(x44542,a909)),f318(f318(f34(x44541,f918(x44542,a909)),x44543),x44544)),x44545))
% 109.14/108.84 [4458]E(f318(f318(f33(x44581,f918(x44582,a909)),x44583),f318(f318(f20(x44581,f918(x44582,a909),f918(x44582,a909)),f318(f318(f10(f918(x44582,a909),f918(f918(x44582,a909),f918(x44582,a909)),x44581),f101(f918(x44582,a909))),x44584)),x44585)),f318(f318(f101(f918(x44582,a909)),f318(f318(f33(x44581,f918(x44582,a909)),x44583),x44584)),f318(f318(f33(x44581,f918(x44582,a909)),x44583),x44585)))
% 109.14/108.84 [4459]E(f318(f318(f34(x44591,f918(x44592,a909)),x44593),f318(f318(f20(x44591,f918(x44592,a909),f918(x44592,a909)),f318(f318(f10(f918(x44592,a909),f918(f918(x44592,a909),f918(x44592,a909)),x44591),f92(f918(x44592,a909))),x44594)),x44595)),f318(f318(f92(f918(x44592,a909)),f318(f318(f34(x44591,f918(x44592,a909)),x44593),x44594)),f318(f318(f34(x44591,f918(x44592,a909)),x44593),x44595)))
% 109.14/108.84 [4468]E(f318(f318(f33(x44681,f918(x44682,a909)),x44683),f318(f318(f20(x44681,f918(x44682,a909),f918(x44682,a909)),f318(f318(f10(f918(x44682,a909),f918(f918(x44682,a909),f918(x44682,a909)),x44681),f101(f918(x44682,a909))),x44684)),x44685)),f318(f318(f101(f918(x44682,a909)),f31(f918(x44682,a909),f318(f301(x44681,f918(x44682,a909),x44684),x44683))),f31(f918(x44682,a909),f318(f301(x44681,f918(x44682,a909),x44685),x44683))))
% 109.14/108.84 [4469]E(f318(f318(f34(x44691,f918(x44692,a909)),x44693),f318(f318(f20(x44691,f918(x44692,a909),f918(x44692,a909)),f318(f318(f10(f918(x44692,a909),f918(f918(x44692,a909),f918(x44692,a909)),x44691),f92(f918(x44692,a909))),x44694)),x44695)),f318(f318(f92(f918(x44692,a909)),f32(f918(x44692,a909),f318(f301(x44691,f918(x44692,a909),x44694),x44693))),f32(f918(x44692,a909),f318(f301(x44691,f918(x44692,a909),x44695),x44693))))
% 109.14/108.84 [4507]E(f318(f318(f129(x45071),f318(f180(f912(x45071)),f168(x45071,x45072,f318(f318(f145(x45073,x45071),x45074),x45075)))),f318(f318(f145(x45073,x45071),x45074),x45075)),f318(f318(f145(x45073,x45071),x45074),f318(f318(f129(x45073),f318(f180(f912(x45073)),f168(x45073,f318(f66(x45071,a909,x45073,x45072),x45074),x45075))),x45075)))
% 109.14/108.84 [4386]E(f318(f318(f125(f917(x43861,x43862)),f318(f318(f172(x43861,x43862),f318(f318(f166(x43861),f318(f180(f912(x43862)),x43863)),x43864)),x43863)),f318(f318(f172(x43861,x43862),f318(f318(f129(x43861),f318(f180(f912(x43862)),x43863)),x43864)),x43865)),f318(f318(f172(x43861,x43862),x43864),f318(f318(f125(x43862),x43863),x43865)))
% 109.14/108.84 [4497]E(f78(x44971,f318(f318(f20(x44971,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44971),a316),f318(f318(f9(x44971,f918(x44971,a909),a909),f320(x44971)),x44972))),f318(f318(f9(x44971,x44973,a909),f318(f318(f10(x44973,f918(x44973,a909),x44971),a315),x44974)),x44975))),f318(f70(x44971,x44973,x44972,x44974),x44975))
% 109.14/108.84 [4498]E(f83(x44981,f318(f318(f20(x44981,a909,a909),f318(f318(f10(a909,f918(a909,a909),x44981),a316),f318(f318(f9(x44981,f918(x44981,a909),a909),f320(x44981)),x44982))),f318(f318(f9(x44981,x44983,a909),f318(f318(f10(x44983,f918(x44983,a909),x44981),a315),x44984)),x44985))),f318(f84(x44981,x44983,x44982,x44984),x44985))
% 109.14/108.84 [4550]E(f318(f318(f81(a1,x45501),f318(f94(a1),f318(f318(f73(a1),x45502),a88))),f318(f318(f20(a1,x45501,x45501),f318(f318(f9(a1,x45501,f918(x45501,x45501)),f318(f318(f10(a909,f918(x45501,f918(x45501,x45501)),a1),f85(x45501)),a184)),f176(x45501,x45503,x45504,x45505))),f318(f318(f10(a911,x45501,a1),x45504),f318(f318(f9(a1,a911,a911),f318(f318(f10(a911,f918(a911,a911),a1),f73(a911)),a95)),x45505)))),f176(x45501,x45503,x45504,f318(f318(f73(a911),f318(f94(a911),x45502)),x45505)))
% 109.14/108.84 [4597]E(f318(f318(f81(a1,x45971),f318(f94(a1),f318(f318(f73(a1),x45972),a88))),f318(f318(f20(a1,x45971,x45971),f318(f318(f9(a1,x45971,f918(x45971,x45971)),f318(f318(f10(a909,f918(x45971,f918(x45971,x45971)),a1),f85(x45971)),a184)),f318(f175(x45971,x45973,x45974),x45975))),f318(f318(f20(a1,x45971,x45971),f318(f318(f10(a911,f918(x45971,x45971),a1),x45974),f318(f318(f9(a1,a911,a911),f318(f318(f10(a911,f918(a911,a911),a1),f73(a911)),a95)),x45975))),f318(f318(f10(a911,x45971,a1),f175(x45971,x45973,x45974)),f318(f318(f9(a1,a911,a911),f318(f318(f10(a911,f918(a911,a911),a1),f73(a911)),a95)),x45975))))),f318(f175(x45971,x45973,x45974),f318(f318(f73(a911),f318(f94(a911),x45972)),x45975)))
% 109.14/108.84 [4629]E(f318(f253(f917(x46291,x46292)),f318(f248(x46291,x46292,a909),f318(f318(f10(f918(x46292,f918(x46293,a909)),f918(x46292,a909),x46291),f318(f10(f918(x46293,a909),a909,x46292),f79(x46293))),f318(f318(f9(x46291,f918(x46292,f918(x46293,a909)),f918(x46292,f918(x46293,a909))),f318(f318(f10(f918(f918(x46293,a909),f918(x46293,a909)),f918(f918(x46292,f918(x46293,a909)),f918(x46292,f918(x46293,a909))),x46291),f10(f918(x46293,a909),f918(x46293,a909),x46292)),f318(f318(f10(f918(x46293,f918(a909,a909)),f918(f918(x46293,a909),f918(x46293,a909)),x46291),f20(x46293,a909,a909)),f318(f318(f10(f918(x46293,a909),f918(x46293,f918(a909,a909)),x46291),f318(f10(a909,f918(a909,a909),x46293),a316)),f318(f318(f9(x46291,f918(f917(x46291,x46293),a909),f918(x46293,a909)),f318(f318(f10(f918(x46293,f918(f918(f917(x46291,x46293),a909),a909)),f918(f918(f917(x46291,x46293),a909),f918(x46293,a909)),x46291),f9(x46293,f918(f917(x46291,x46293),a909),a909)),f318(f318(f10(f918(x46293,f917(x46291,x46293)),f918(x46293,f918(f918(f917(x46291,x46293),a909),a909)),x46291),f318(f10(f917(x46291,x46293),f918(f918(f917(x46291,x46293),a909),a909),x46293),f320(f917(x46291,x46293)))),f243(x46291,x46293)))),x46294))))),f318(f318(f9(x46292,f918(f917(x46293,x46292),a909),f918(x46293,a909)),f318(f318(f10(f918(x46293,f918(f918(f917(x46293,x46292),a909),a909)),f918(f918(f917(x46293,x46292),a909),f918(x46293,a909)),x46292),f9(x46293,f918(f917(x46293,x46292),a909),a909)),f318(f318(f10(f918(x46293,f917(x46293,x46292)),f918(x46293,f918(f918(f917(x46293,x46292),a909),a909)),x46292),f318(f10(f917(x46293,x46292),f918(f918(f917(x46293,x46292),a909),a909),x46293),f320(f917(x46293,x46292)))),f318(f9(x46293,x46292,f917(x46293,x46292)),f243(x46293,x46292))))),x46295))))),f318(f318(f280(x46291,x46293,x46292),x46294),x46295))
% 109.14/108.84 [4233]E(f215(x42331,x42332,x42333,x42334,f211(x42331,x42332,x42335,x42336)),f318(f318(x42334,x42335),x42336))
% 109.14/108.84 [4234]E(f216(x42341,x42342,x42343,x42344,f211(x42341,x42342,x42345,x42346)),f318(f318(x42344,x42345),x42346))
% 109.14/108.84 [4354]E(f118(x43541,x43542,x43543,x43544,f117(x43542,x43545,x43546)),f318(f318(f318(x43544,x43545),x43546),f118(x43541,x43542,x43543,x43544,x43546)))
% 109.14/108.84 [4378]E(f68(x43781,x43782,f68(x43781,x43782,x43783,x43784,x43785),x43784,x43786),f68(x43781,x43782,x43783,x43784,x43786))
% 109.14/108.84 [4485]E(f318(f66(f917(x44851,x44852),x44852,f917(x44853,x44854),f247(x44851,x44852)),f249(x44853,x44851,x44854,x44852,x44855,x44856)),f318(f66(x44854,x44852,f917(x44853,x44854),x44856),f247(x44853,x44854)))
% 109.14/108.84 [4486]E(f318(f66(f917(x44861,x44862),x44861,f917(x44863,x44864),f242(x44861,x44862)),f249(x44863,x44861,x44864,x44862,x44865,x44866)),f318(f66(x44863,x44861,f917(x44863,x44864),x44865),f242(x44863,x44864)))
% 109.14/108.84 [4108]E(f318(f318(f66(x41081,x41082,x41083,x41084),x41085),x41086),f318(x41084,f318(x41085,x41086)))
% 109.14/108.84 [4109]E(f318(f318(f66(x41091,x41092,x41093,x41094),x41095),x41096),f318(x41094,f318(x41095,x41096)))
% 109.14/108.84 [4243]E(f214(x42431,f917(x42432,f913(x42432)),x42433,f318(f248(x42432,f913(x42432),x42431),x42434),f318(f126(x42432),f117(x42432,x42435,x42436))),f318(f318(x42434,x42435),x42436))
% 109.14/108.84 [4291]E(f217(x42911,x42912,x42913,x42914,f211(x42911,x42912,x42915,x42916)),f318(f318(f73(a911),f318(f318(f73(a911),f318(x42913,x42915)),f318(x42914,x42916))),f318(a103,f2(a911))))
% 109.14/108.84 [3910]E(f318(f318(f248(x39101,x39102,x39103),x39104),f318(f318(f243(x39101,x39102),x39105),x39106)),f318(f318(x39104,x39105),x39106))
% 109.14/108.84 [3911]E(f318(f318(f248(x39111,x39112,x39113),x39114),f318(f318(f243(x39111,x39112),x39115),x39116)),f318(f318(x39114,x39115),x39116))
% 109.14/108.84 [3912]E(f318(f318(f248(x39121,x39122,x39123),x39124),f318(f318(f243(x39121,x39122),x39125),x39126)),f318(f318(x39124,x39125),x39126))
% 109.14/108.84 [3975]E(f318(f318(f318(f10(x39751,x39752,x39753),x39754),x39755),x39756),f318(x39754,f318(x39755,x39756)))
% 109.14/108.84 [3976]E(f318(f318(f318(f9(x39761,x39762,x39763),x39764),x39765),x39766),f318(f318(x39764,x39766),x39765))
% 109.14/108.84 [3992]E(f318(f318(f318(f20(x39921,x39922,x39923),x39924),x39925),x39926),f318(f318(x39924,x39926),f318(x39925,x39926)))
% 109.14/108.84 [4013]E(f318(f147(x40131,x40132,x40133,x40134),f318(f318(f142(x40132),x40135),x40136)),f318(f318(x40134,x40135),x40136))
% 109.14/108.84 [4048]E(f160(f917(x40481,x40482),f318(f318(f223(a911),x40483),x40484),f318(f318(f243(x40481,x40482),x40485),x40486)),f318(f318(f172(x40481,x40482),f160(x40481,x40483,x40485)),f160(x40482,x40484,x40486)))
% 109.14/108.84 [4114]E(f318(f318(f142(f917(x41141,x41142)),f318(f318(f243(x41141,x41142),x41143),x41144)),f318(f318(f172(x41141,x41142),x41145),x41146)),f318(f318(f172(x41141,x41142),f318(f318(f142(x41141),x41143),x41145)),f318(f318(f142(x41142),x41144),x41146)))
% 109.14/108.84 [4115]E(f318(f318(f145(x41151,x41152),x41153),f318(f318(f150(x41151,x41154),x41155),x41156)),f318(f318(f150(x41152,f318(f318(f145(x41151,x41152),x41153),x41154)),x41155),f318(x41153,x41156)))
% 109.14/108.84 [4138]E(f318(f318(f246(x41381,x41382,x41383,x41384),x41385),x41386),f318(x41384,f318(f318(f243(x41381,x41382),x41385),x41386)))
% 109.14/108.84 [4139]E(f318(f318(f246(x41391,x41392,x41393,x41394),x41395),x41396),f318(x41394,f318(f318(f243(x41391,x41392),x41395),x41396)))
% 109.14/108.84 [4154]E(f318(f133(x41541,x41542,x41543,x41544),f318(f318(f142(x41542),x41545),x41546)),f318(f133(x41541,x41542,x41543,f318(f318(x41543,x41544),x41545)),x41546))
% 109.14/108.84 [4179]E(f251(x41791,x41792,x41793,x41794,f318(f318(f243(x41791,x41792),x41795),x41796)),f318(f318(x41794,x41795),x41796))
% 109.14/108.84 [4258]E(f318(f318(f33(x42581,f918(x42582,a909)),x42583),f318(f66(x42584,f918(x42582,a909),x42581,x42585),x42586)),f318(f318(f33(x42584,f918(x42582,a909)),f318(f301(x42581,x42584,x42586),x42583)),x42585))
% 109.14/108.84 [4302]E(f318(f318(f145(x43021,x43022),x43023),f318(f318(f145(x43024,x43021),x43025),x43026)),f318(f318(f145(x43024,x43022),f318(f66(x43021,x43022,x43024,x43023),x43025)),x43026))
% 109.14/108.84 [4303]E(f318(f318(f145(x43031,x43032),x43033),f318(f318(f145(x43034,x43031),x43035),x43036)),f318(f318(f145(x43034,x43032),f318(f66(x43031,x43032,x43034,x43033),x43035)),x43036))
% 109.14/108.84 [4309]E(f318(f301(x43091,x43092,f318(f66(x43093,x43092,x43091,x43094),x43095)),x43096),f318(f301(x43093,x43092,x43094),f318(f301(x43091,x43093,x43095),x43096)))
% 109.14/108.84 [4310]E(f318(f302(x43101,x43102,f318(f66(x43103,x43102,x43101,x43104),x43105)),x43106),f318(f302(x43101,x43103,x43105),f318(f302(x43103,x43102,x43104),x43106)))
% 109.14/108.84 [4336]E(f318(f133(x43361,x43362,x43363,f318(f133(x43361,x43362,x43363,x43364),x43365)),x43366),f318(f133(x43361,x43362,x43363,x43364),f318(f318(f125(x43362),x43365),x43366)))
% 109.14/108.84 [4473]E(f318(f249(x44731,x44731,x44732,x44733,f25(x44731),x44734),f318(f318(f243(x44731,x44732),x44735),x44736)),f318(f318(f243(x44731,x44733),x44735),f318(x44734,x44736)))
% 109.14/108.84 [4474]E(f318(f249(x44741,x44742,x44743,x44743,x44744,f25(x44743)),f318(f318(f243(x44741,x44743),x44745),x44746)),f318(f318(f243(x44742,x44743),f318(x44744,x44745)),x44746))
% 109.14/108.84 [4576]E(f318(f318(f145(f917(x45761,x45762),f917(x45761,x45763)),f318(f248(x45761,x45762,f917(x45761,x45763)),f318(f318(f9(x45761,f918(x45762,x45763),f918(x45762,f917(x45761,x45763))),f318(f318(f10(f918(x45763,f917(x45761,x45763)),f918(f918(x45762,x45763),f918(x45762,f917(x45761,x45763))),x45761),f10(x45763,f917(x45761,x45763),x45762)),f243(x45761,x45763))),x45764))),f318(f318(f172(x45761,x45762),x45765),x45766)),f318(f318(f172(x45761,x45763),x45765),f318(f318(f145(x45762,x45763),x45764),x45766)))
% 109.14/108.84 [4164]E(f318(f318(f66(x41641,x41642,x41643,f318(f18(x41642,x41641),x41644)),x41645),x41646),x41644)
% 109.14/108.84 [4195]E(f318(f301(x41951,x41952,x41953),f318(f301(x41954,x41951,x41955),x41956)),f318(f301(x41954,x41952,f318(f318(f10(x41951,x41952,x41954),x41953),x41955)),x41956))
% 109.14/108.84 [4200]E(f318(f318(f33(x42001,f918(x42002,a909)),f318(f301(x42003,x42001,x42004),x42005)),x42006),f318(f318(f33(x42003,f918(x42002,a909)),x42005),f318(f318(f10(x42001,f918(x42002,a909),x42003),x42006),x42004)))
% 109.14/108.84 [4201]E(f318(f318(f34(x42011,f918(x42012,a909)),f318(f301(x42013,x42011,x42014),x42015)),x42016),f318(f318(f34(x42013,f918(x42012,a909)),x42015),f318(f318(f10(x42011,f918(x42012,a909),x42013),x42016),x42014)))
% 109.14/108.84 [4202]E(f318(f318(f33(x42021,f918(x42022,a909)),x42023),f318(f318(f10(x42024,f918(x42022,a909),x42021),x42025),x42026)),f318(f318(f33(x42024,f918(x42022,a909)),f318(f301(x42021,x42024,x42026),x42023)),x42025))
% 109.14/108.84 [4203]E(f318(f318(f34(x42031,f918(x42032,a909)),x42033),f318(f318(f10(x42034,f918(x42032,a909),x42031),x42035),x42036)),f318(f318(f34(x42034,f918(x42032,a909)),f318(f301(x42031,x42034,x42036),x42033)),x42035))
% 109.14/108.84 [4260]E(f318(f318(f33(x42601,f918(x42602,a909)),x42603),f318(f318(f10(f918(x42604,a909),f918(x42602,a909),x42601),f301(x42604,x42602,x42605)),x42606)),f318(f301(x42604,x42602,x42605),f318(f318(f33(x42601,f918(x42604,a909)),x42603),x42606)))
% 109.14/108.84 [4261]E(f318(f318(f33(x42611,f918(x42612,a909)),x42613),f318(f318(f10(f918(x42614,a909),f918(x42612,a909),x42611),f302(x42612,x42614,x42615)),x42616)),f318(f302(x42612,x42614,x42615),f318(f318(f33(x42611,f918(x42614,a909)),x42613),x42616)))
% 109.14/108.84 [4262]E(f318(f318(f34(x42621,f918(x42622,a909)),x42623),f318(f318(f10(f918(x42624,a909),f918(x42622,a909),x42621),f302(x42622,x42624,x42625)),x42626)),f318(f302(x42622,x42624,x42625),f318(f318(f34(x42621,f918(x42624,a909)),x42623),x42626)))
% 109.14/108.84 [4263]E(f318(f318(f33(x42631,f918(x42632,a909)),x42633),f318(f318(f10(f918(x42634,a909),f918(x42632,a909),x42631),f276(x42634,x42632,x42635)),x42636)),f318(f276(x42634,x42632,x42635),f318(f318(f33(x42631,f918(x42634,a909)),x42633),x42636)))
% 109.14/108.84 [4341]E(f318(f133(x43411,x43412,f318(f9(x43412,x43411,x43411),x43413),x43414),f318(f159(x43412),f318(f318(f142(x43412),x43415),x43416))),f318(f318(x43413,x43415),f318(f133(x43411,x43412,f318(f9(x43412,x43411,x43411),x43413),x43414),f318(f159(x43412),x43416))))
% 109.14/108.84 [4405]E(f318(f318(f20(f917(x44051,x44052),x44052,x44053),f318(f318(f10(x44054,f918(x44052,x44053),f917(x44051,x44052)),x44055),f318(f318(f10(x44051,x44054,f917(x44051,x44052)),x44056),f242(x44051,x44052)))),f247(x44051,x44052)),f318(f248(x44051,x44052,x44053),f318(f318(f10(x44054,f918(x44052,x44053),x44051),x44055),x44056)))
% 109.14/108.84 [4411]E(f318(f133(x44111,x44112,f318(f9(x44112,x44111,x44111),x44113),f318(f133(x44111,x44112,f318(f9(x44112,x44111,x44111),x44113),x44114),f318(f159(x44112),x44115))),f318(f159(x44112),x44116)),f318(f133(x44111,x44112,f318(f9(x44112,x44111,x44111),x44113),x44114),f318(f159(x44112),f318(f318(f125(x44112),x44116),x44115))))
% 109.14/108.84 [4413]E(f318(f318(f145(f917(x44131,x44132),f917(x44133,x44132)),f318(f248(x44131,x44132,f917(x44133,x44132)),f318(f318(f10(x44133,f918(x44132,f917(x44133,x44132)),x44131),f243(x44133,x44132)),x44134))),f318(f318(f172(x44131,x44132),x44135),x44136)),f318(f318(f172(x44133,x44132),f318(f318(f145(x44131,x44133),x44134),x44135)),x44136))
% 109.14/108.84 [4461]P1(f318(f318(f225(f918(x44611,a909)),f318(f276(x44612,x44611,x44613),f318(f318(f34(x44614,f918(x44612,a909)),x44615),x44616))),f318(f318(f34(x44614,f918(x44611,a909)),x44615),f318(f318(f10(f918(x44612,a909),f918(x44611,a909),x44614),f276(x44612,x44611,x44613)),x44616))))
% 109.14/108.84 [4272]E(f318(f318(f172(x42721,x42722),f318(f318(f150(x42721,x42723),x42724),f318(f242(x42721,x42722),x42725))),f318(f318(f150(x42722,x42726),x42724),f318(f247(x42721,x42722),x42725))),f318(f318(f150(f917(x42721,x42722),f318(f318(f172(x42721,x42722),x42723),x42726)),x42724),x42725))
% 109.14/108.84 [4324]E(f318(f318(f101(f918(f917(x43241,x43242),a909)),f318(f318(f280(x43241,x43243,x43242),x43244),x43245)),f318(f318(f280(x43241,x43243,x43242),x43244),x43246)),f318(f318(f280(x43241,x43243,x43242),x43244),f318(f318(f101(f918(f917(x43243,x43242),a909)),x43245),x43246)))
% 109.14/108.84 [4425]E(f318(f318(f300(f917(x44251,x44252)),f318(f318(f243(x44251,x44252),x44253),x44254)),f318(f318(f101(f918(f917(x44251,x44252),a909)),f318(f318(f245(x44251,x44252),x44255),f318(f18(f918(x44252,a909),x44251),f318(f318(f300(x44252),x44254),x44256)))),f318(f318(f245(x44251,x44252),f318(f318(f300(x44251),x44253),x44255)),f318(f18(f918(x44252,a909),x44251),x44256)))),f318(f318(f245(x44251,x44252),f318(f318(f300(x44251),x44253),x44255)),f318(f18(f918(x44252,a909),x44251),f318(f318(f300(x44252),x44254),x44256))))
% 109.14/108.84 [4503]E(f318(f318(f92(f918(x45031,a909)),f318(f302(x45031,x45032,f318(f66(f917(x45032,x45033),x45032,x45031,f242(x45032,x45033)),x45034)),x45035)),f318(f302(x45031,x45033,f318(f66(f917(x45032,x45033),x45033,x45031,f247(x45032,x45033)),x45034)),x45036)),f318(f302(x45031,f917(x45032,x45033),x45034),f318(f318(f245(x45032,x45033),x45035),f318(f18(f918(x45033,a909),x45032),x45036))))
% 109.14/108.84 [4347]E(f318(f318(f101(f918(f917(x43471,x43472),a909)),f318(f318(f280(x43471,x43473,x43472),x43474),x43475)),f318(f318(f280(x43471,x43473,x43472),x43476),x43475)),f318(f318(f280(x43471,x43473,x43472),f318(f318(f101(f918(f917(x43471,x43473),a909)),x43474),x43476)),x43475))
% 109.14/108.84 [4480]E(f318(f318(f33(x44801,f918(x44802,a909)),x44803),f318(f318(f9(x44801,f918(x44804,f918(x44802,a909)),f918(x44802,a909)),f318(f318(f10(f918(x44804,a909),f918(f918(x44804,f918(x44802,a909)),f918(x44802,a909)),x44801),f33(x44804,f918(x44802,a909))),x44805)),x44806)),f318(f318(f33(x44804,f918(x44802,a909)),f318(f318(f33(x44801,f918(x44804,a909)),x44803),x44805)),x44806))
% 109.14/108.84 [4481]E(f318(f318(f33(x44811,f918(x44812,a909)),x44813),f318(f318(f9(x44811,f918(x44814,f918(x44812,a909)),f918(x44812,a909)),f318(f318(f10(f918(x44814,a909),f918(f918(x44814,f918(x44812,a909)),f918(x44812,a909)),x44811),f33(x44814,f918(x44812,a909))),x44815)),x44816)),f318(f318(f33(x44814,f918(x44812,a909)),f318(f318(f33(x44811,f918(x44814,a909)),x44813),x44815)),x44816))
% 109.14/108.84 [4482]E(f318(f318(f34(x44821,f918(x44822,a909)),x44823),f318(f318(f9(x44821,f918(x44824,f918(x44822,a909)),f918(x44822,a909)),f318(f318(f10(f918(x44824,a909),f918(f918(x44824,f918(x44822,a909)),f918(x44822,a909)),x44821),f34(x44824,f918(x44822,a909))),x44825)),x44826)),f318(f318(f34(x44824,f918(x44822,a909)),f318(f318(f33(x44821,f918(x44824,a909)),x44823),x44825)),x44826))
% 109.14/108.84 [4483]E(f318(f318(f33(x44831,f918(x44832,a909)),x44833),f318(f318(f9(x44831,f918(x44834,f918(x44832,a909)),f918(x44832,a909)),f318(f318(f10(f918(x44834,a909),f918(f918(x44834,f918(x44832,a909)),f918(x44832,a909)),x44831),f33(x44834,f918(x44832,a909))),x44835)),x44836)),f318(f318(f33(x44834,f918(x44832,a909)),f318(f318(f33(x44831,f918(x44834,a909)),x44833),x44835)),x44836))
% 109.14/108.84 [4484]E(f318(f318(f34(x44841,f918(x44842,a909)),x44843),f318(f318(f9(x44841,f918(x44844,f918(x44842,a909)),f918(x44842,a909)),f318(f318(f10(f918(x44844,a909),f918(f918(x44844,f918(x44842,a909)),f918(x44842,a909)),x44841),f34(x44844,f918(x44842,a909))),x44845)),x44846)),f318(f318(f34(x44844,f918(x44842,a909)),f318(f318(f33(x44841,f918(x44844,a909)),x44843),x44845)),x44846))
% 109.14/108.84 [4540]E(f318(f248(x45401,x45402,f917(x45403,x45404)),f318(f318(f9(x45401,f918(x45402,x45404),f918(x45402,f917(x45403,x45404))),f318(f318(f10(f918(x45404,f917(x45403,x45404)),f918(f918(x45402,x45404),f918(x45402,f917(x45403,x45404))),x45401),f10(x45404,f917(x45403,x45404),x45402)),f318(f318(f10(x45403,f918(x45404,f917(x45403,x45404)),x45401),f243(x45403,x45404)),x45405))),x45406)),f249(x45401,x45403,x45402,x45404,x45405,x45406))
% 109.14/108.84 [4569]E(f318(f301(x45691,x45692,f318(f318(f20(x45691,x45692,x45692),f318(f318(f20(x45691,x45692,f918(x45692,x45692)),f318(f318(f10(a909,f918(x45692,f918(x45692,x45692)),x45691),f85(x45692)),x45693)),x45694)),x45695)),x45696),f318(f318(f101(f918(x45692,a909)),f318(f301(x45691,x45692,x45694),f318(f318(f92(f918(x45691,a909)),x45696),f318(f253(x45691),x45693)))),f318(f301(x45691,x45692,x45695),f318(f318(f92(f918(x45691,a909)),x45696),f318(f253(x45691),f318(f318(f10(a909,a909,x45691),a313),x45693))))))
% 109.14/108.84 [4583]E(f318(f301(x45831,f917(x45832,x45833),f318(f318(f20(x45831,x45833,f917(x45832,x45833)),f318(f318(f10(x45832,f918(x45833,f917(x45832,x45833)),x45831),f243(x45832,x45833)),x45834)),x45835)),x45836),f318(f318(f245(x45832,x45833),f318(f301(x45831,x45832,x45834),x45836)),f318(f318(f10(f918(x45831,a909),f918(x45833,a909),x45832),f301(x45831,x45833,x45835)),f318(f318(f9(x45832,f918(x45831,a909),f918(x45831,a909)),f318(f318(f10(f918(x45831,a909),f918(f918(x45831,a909),f918(x45831,a909)),x45832),f92(f918(x45831,a909))),f318(f318(f10(f918(x45832,a909),f918(x45831,a909),x45832),f302(x45831,x45832,x45834)),f318(f318(f9(x45832,f918(x45832,a909),f918(x45832,a909)),f300(x45832)),f179(f918(x45832,a909)))))),x45836))))
% 109.14/108.84 [4611]E(f237(x46111,x46112,x46113,x46114,x46115,x46116),f318(x46114,f318(f253(x46111),f318(f318(f10(f918(f918(x46113,x46111),a909),a909,x46111),f79(f918(x46113,x46111))),f318(f318(f10(f918(f918(x46113,x46111),a909),f918(f918(x46113,x46111),a909),x46111),f318(f20(f918(x46113,x46111),a909,a909),f318(f318(f10(a909,f918(a909,a909),f918(x46113,x46111)),a316),f318(f318(f9(f918(x46113,x46111),f918(f918(x46113,x46111),a909),a909),f320(f918(x46113,x46111))),x46115)))),f318(f318(f9(x46111,f918(f918(x46113,x46111),x46111),f918(f918(x46113,x46111),a909)),f318(f318(f10(f918(x46111,a909),f918(f918(f918(x46113,x46111),x46111),f918(f918(x46113,x46111),a909)),x46111),f10(x46111,a909,f918(x46113,x46111))),a315)),f318(f318(f9(f918(x46113,x46111),x46113,x46111),f7(f918(x46113,x46111))),x46116)))))))
% 109.14/108.84 [4388]E(f318(f66(x43881,x43882,x43883,x43884),f68(x43883,x43881,x43885,x43886,x43887)),f68(x43883,x43882,f318(f66(x43881,x43882,x43883,x43884),x43885),x43886,f318(x43884,x43887)))
% 109.14/108.84 [4525]E(f318(f247(x45251,x45252),f318(f249(x45253,x45251,x45254,x45252,x45255,x45256),x45257)),f318(x45256,f318(f247(x45253,x45254),x45257)))
% 109.14/108.84 [4526]E(f318(f242(x45261,x45262),f318(f249(x45263,x45261,x45264,x45262,x45265,x45266),x45267)),f318(x45265,f318(f242(x45263,x45264),x45267)))
% 109.14/108.84 [4235]E(f318(f318(f172(x42351,x42352),f318(f318(f150(x42351,x42353),x42354),x42355)),f318(f318(f150(x42352,x42356),x42354),x42357)),f318(f318(f150(f917(x42351,x42352),f318(f318(f172(x42351,x42352),x42353),x42356)),x42354),f318(f318(f243(x42351,x42352),x42355),x42357)))
% 109.14/108.84 [4297]E(f318(f318(f318(f250(x42971,x42972,x42973,x42974),x42975),x42976),x42977),f318(f318(f248(x42972,x42973,x42974),x42976),f318(x42975,x42977)))
% 109.14/108.84 [4298]E(f318(f318(f318(f250(x42981,x42982,x42983,x42984),x42985),x42986),x42987),f318(f318(f248(x42982,x42983,x42984),x42986),f318(x42985,x42987)))
% 109.14/108.84 [4308]E(f318(f318(f318(f250(x43081,x43082,x43083,x43084),x43085),x43086),x43087),f318(f318(x43086,f318(f242(x43082,x43083),f318(x43085,x43087))),f318(f247(x43082,x43083),f318(x43085,x43087))))
% 109.14/108.84 [4362]E(f318(f66(x43621,x43622,x43623,x43624),f318(f66(x43625,x43621,x43623,x43626),x43627)),f318(f66(x43625,x43622,x43623,f318(f66(x43621,x43622,x43625,x43624),x43626)),x43627))
% 109.14/108.84 [4544]E(f318(f249(x45441,x45442,x45443,x45443,x45444,f25(x45443)),f318(f249(x45441,x45441,x45445,x45443,f25(x45441),x45446),x45447)),f318(f318(f243(x45442,x45443),f318(x45444,f318(f242(x45441,x45445),x45447))),f318(x45446,f318(f247(x45441,x45445),x45447))))
% 109.14/108.84 [4545]E(f318(f249(x45451,x45451,x45452,x45453,f25(x45451),x45454),f318(f249(x45455,x45451,x45452,x45452,x45456,f25(x45452)),x45457)),f318(f318(f243(x45451,x45453),f318(x45456,f318(f242(x45455,x45452),x45457))),f318(x45454,f318(f247(x45455,x45452),x45457))))
% 109.14/108.84 [4567]E(f318(f249(x45671,x45672,x45673,x45673,x45674,f25(x45673)),f318(f249(x45675,x45671,x45673,x45673,x45676,f25(x45673)),x45677)),f318(f249(x45675,x45672,x45673,x45673,f318(f66(x45671,x45672,x45675,x45674),x45676),f25(x45673)),x45677))
% 109.14/108.84 [4568]E(f318(f249(x45681,x45681,x45682,x45683,f25(x45681),x45684),f318(f249(x45681,x45681,x45685,x45682,f25(x45681),x45686),x45687)),f318(f249(x45681,x45681,x45685,x45683,f25(x45681),f318(f66(x45682,x45683,x45685,x45684),x45686)),x45687))
% 109.14/108.84 [4580]E(f318(f249(x45801,x45802,x45803,x45803,x45804,f25(x45803)),f318(f249(x45801,x45801,x45805,x45803,f25(x45801),x45806),x45807)),f318(f249(x45802,x45802,x45805,x45803,f25(x45802),x45806),f318(f249(x45801,x45802,x45805,x45805,x45804,f25(x45805)),x45807)))
% 109.14/108.84 [4269]E(f318(f318(f280(x42691,x42692,x42693),f318(f318(f280(x42691,x42694,x42692),x42695),x42696)),x42697),f318(f318(f280(x42691,x42694,x42693),x42695),f318(f318(f280(x42694,x42692,x42693),x42696),x42697)))
% 109.14/108.84 [4330]E(f318(f318(f248(x43301,x43302,x43303),f318(f66(x43304,f918(x43302,x43303),x43301,x43305),x43306)),x43307),f318(f318(x43305,f318(x43306,f318(f242(x43301,x43302),x43307))),f318(f247(x43301,x43302),x43307)))
% 109.14/108.84 [4416]E(f318(f133(x44161,x44162,f318(f9(x44162,x44161,x44161),x44163),x44164),f318(f159(x44162),f318(f318(f145(x44165,x44162),x44166),x44167))),f318(f133(x44161,x44165,f318(f9(x44165,x44161,x44161),f318(f66(x44162,f918(x44161,x44161),x44165,x44163),x44166)),x44164),f318(f159(x44165),x44167)))
% 109.14/108.84 [4363]E(f318(f318(f33(x43631,f918(f917(x43632,x43633),a909)),x43634),f318(f318(f10(f918(f917(x43635,x43633),a909),f918(f917(x43632,x43633),a909),x43631),f318(f280(x43632,x43635,x43633),x43636)),x43637)),f318(f318(f280(x43632,x43635,x43633),x43636),f318(f318(f33(x43631,f918(f917(x43635,x43633),a909)),x43634),x43637)))
% 109.14/108.84 [4508]E(f318(f318(f33(x45081,f918(f917(x45082,x45083),a909)),x45084),f318(f318(f9(x45081,f918(f917(x45085,x45083),a909),f918(f917(x45082,x45083),a909)),f318(f318(f10(f918(f917(x45082,x45085),a909),f918(f918(f917(x45085,x45083),a909),f918(f917(x45082,x45083),a909)),x45081),f280(x45082,x45085,x45083)),x45086)),x45087)),f318(f318(f280(x45082,x45085,x45083),f318(f318(f33(x45081,f918(f917(x45082,x45085),a909)),x45084),x45086)),x45087))
% 109.14/108.84 [4509]E(f318(f133(x45091,x45092,f318(f318(f9(x45091,f918(x45092,x45093),f918(x45092,x45091)),f318(f318(f10(f918(x45093,x45091),f918(f918(x45092,x45093),f918(x45092,x45091)),x45091),f10(x45093,x45091,x45092)),x45094)),x45095),x45096),x45097),f318(f133(x45091,x45093,x45094,x45096),f318(f318(f145(x45092,x45093),x45095),x45097)))
% 109.14/108.84 [4581]E(f318(f318(f34(x45811,f918(x45812,a909)),x45813),f318(f318(f10(f918(x45814,f918(x45812,a909)),f918(x45812,a909),x45811),f318(f34(x45814,f918(x45812,a909)),x45815)),f318(f318(f9(x45811,f918(x45814,f918(x45812,a909)),f918(x45814,f918(x45812,a909))),f318(f318(f10(f918(f918(x45812,a909),f918(x45812,a909)),f918(f918(x45814,f918(x45812,a909)),f918(x45814,f918(x45812,a909))),x45811),f10(f918(x45812,a909),f918(x45812,a909),x45814)),f318(f318(f10(f918(x45812,a909),f918(f918(x45812,a909),f918(x45812,a909)),x45811),f101(f918(x45812,a909))),x45816))),x45817))),f318(f318(f101(f918(x45812,a909)),f318(f318(f34(x45811,f918(x45812,a909)),x45813),x45816)),f318(f318(f34(x45814,f918(x45812,a909)),x45815),x45817)))
% 109.14/108.84 [4582]E(f318(f318(f33(x45821,f918(x45822,a909)),x45823),f318(f318(f10(f918(x45824,f918(x45822,a909)),f918(x45822,a909),x45821),f318(f33(x45824,f918(x45822,a909)),x45825)),f318(f318(f9(x45821,f918(x45824,f918(x45822,a909)),f918(x45824,f918(x45822,a909))),f318(f318(f10(f918(f918(x45822,a909),f918(x45822,a909)),f918(f918(x45824,f918(x45822,a909)),f918(x45824,f918(x45822,a909))),x45821),f10(f918(x45822,a909),f918(x45822,a909),x45824)),f318(f318(f10(f918(x45822,a909),f918(f918(x45822,a909),f918(x45822,a909)),x45821),f92(f918(x45822,a909))),x45826))),x45827))),f318(f318(f92(f918(x45822,a909)),f318(f318(f33(x45821,f918(x45822,a909)),x45823),x45826)),f318(f318(f33(x45824,f918(x45822,a909)),x45825),x45827)))
% 109.14/108.84 [4572]E(f188(x45721,x45722,f318(f318(f318(x45723,x45724),x45725),x45726),f318(f318(f9(x45721,f917(a90,a90),f918(a90,f913(x45722))),f318(f318(f9(x45721,a90,f918(f917(a90,a90),f918(a90,f913(x45722)))),f318(f318(f9(x45721,a90,f918(a90,f918(f917(a90,a90),f918(a90,f913(x45722))))),x45727),x45724)),x45725)),x45726)),f318(f318(f318(f200(x45721,x45722,x45723,x45727),x45724),x45725),x45726))
% 109.14/108.84 [4584]E(f189(x45841,x45842,f318(f318(f318(x45843,x45844),x45845),x45846),f318(f318(f9(x45841,f917(a90,a90),f918(a90,f913(x45842))),f318(f318(f9(x45841,a90,f918(f917(a90,a90),f918(a90,f913(x45842)))),f318(f318(f9(x45841,a90,f918(a90,f918(f917(a90,a90),f918(a90,f913(x45842))))),x45847),x45844)),x45845)),x45846)),f202(x45841,x45842,x45843,x45847,x45844,x45845,x45846))
% 109.14/108.84 [4579]E(f186(x45791,x45792,f318(f318(f318(x45793,x45794),x45795),x45796),f318(f318(f9(x45791,f917(a90,a90),f918(a90,f913(f915(x45792)))),f318(f318(f9(x45791,a90,f918(f917(a90,a90),f918(a90,f913(f915(x45792))))),f318(f318(f9(x45791,a90,f918(a90,f918(f917(a90,a90),f918(a90,f913(f915(x45792)))))),x45797),x45794)),x45795)),x45796)),f318(f318(f318(f196(x45791,x45792,x45793,x45797),x45794),x45795),x45796))
% 109.14/108.84 [4594]E(f187(x45941,x45942,f318(f318(f318(x45943,x45944),x45945),x45946),f318(f318(f9(x45941,f917(a90,a90),f918(a90,f913(f915(x45942)))),f318(f318(f9(x45941,a90,f918(f917(a90,a90),f918(a90,f913(f915(x45942))))),f318(f318(f9(x45941,a90,f918(a90,f918(f917(a90,a90),f918(a90,f913(f915(x45942)))))),x45947),x45944)),x45945)),x45946)),f198(x45941,x45942,x45943,x45947,x45944,x45945,x45946))
% 109.14/108.84 [4475]E(f318(f249(x44751,x44752,x44753,x44754,x44755,x44756),f318(f318(f243(x44751,x44753),x44757),x44758)),f318(f318(f243(x44752,x44754),f318(x44755,x44757)),f318(x44756,x44758)))
% 109.14/108.84 [4596]E(f318(f318(f145(f917(x45961,x45962),f917(x45963,x45964)),f318(f248(x45961,x45962,f917(x45963,x45964)),f318(f318(f9(x45961,f918(x45962,x45964),f918(x45962,f917(x45963,x45964))),f318(f318(f10(f918(x45964,f917(x45963,x45964)),f918(f918(x45962,x45964),f918(x45962,f917(x45963,x45964))),x45961),f10(x45964,f917(x45963,x45964),x45962)),f318(f318(f10(x45963,f918(x45964,f917(x45963,x45964)),x45961),f243(x45963,x45964)),x45965))),x45966))),f318(f318(f172(x45961,x45962),x45967),x45968)),f318(f318(f172(x45963,x45964),f318(f318(f145(x45961,x45963),x45965),x45967)),f318(f318(f145(x45962,x45964),x45966),x45968)))
% 109.14/108.84 [4601]E(f318(f318(f145(f917(x46011,x46012),x46013),f318(f248(x46011,x46012,x46013),f318(f318(f10(f918(x46012,f917(x46011,x46014)),f918(x46012,x46013),x46011),f318(f10(f917(x46011,x46014),x46013,x46012),x46015)),f318(f318(f9(x46011,f918(x46012,x46014),f918(x46012,f917(x46011,x46014))),f318(f318(f10(f918(x46014,f917(x46011,x46014)),f918(f918(x46012,x46014),f918(x46012,f917(x46011,x46014))),x46011),f10(x46014,f917(x46011,x46014),x46012)),f243(x46011,x46014))),x46016)))),f318(f318(f172(x46011,x46012),x46017),x46018)),f318(f318(f145(f917(x46011,x46014),x46013),x46015),f318(f318(f172(x46011,x46014),x46017),f318(f318(f145(x46012,x46014),x46016),x46018))))
% 109.14/108.84 [4517]E(f318(f318(f145(f917(x45171,x45172),x45173),f318(f248(x45171,x45172,x45173),f318(f318(f10(f918(x45172,f917(x45174,x45172)),f918(x45172,x45173),x45171),f318(f10(f917(x45174,x45172),x45173,x45172),x45175)),f318(f318(f10(x45174,f918(x45172,f917(x45174,x45172)),x45171),f243(x45174,x45172)),x45176)))),f318(f318(f172(x45171,x45172),x45177),x45178)),f318(f318(f145(f917(x45174,x45172),x45173),x45175),f318(f318(f172(x45174,x45172),f318(f318(f145(x45171,x45174),x45176),x45177)),x45178)))
% 109.14/108.84 [4466]E(f318(f318(f248(x44661,x44662,x44663),f318(f318(f10(f918(x44662,f917(x44664,x44665)),f918(x44662,x44663),x44661),f318(f10(f917(x44664,x44665),x44663,x44662),f318(f248(x44664,x44665,x44663),x44666))),x44667)),x44668),f318(f318(f248(x44664,x44665,x44663),x44666),f318(f318(f248(x44661,x44662,f917(x44664,x44665)),x44667),x44668)))
% 109.14/108.84 [4602]E(f318(f318(f33(f917(x46021,x46022),f918(f917(x46023,x46024),a909)),f318(f318(f245(x46021,x46022),x46025),f318(f18(f918(x46022,a909),x46021),x46026))),f318(f248(x46021,x46022,f918(f917(x46023,x46024),a909)),f318(f318(f9(x46021,f918(x46022,f918(x46023,f918(x46024,a909))),f918(x46022,f918(f917(x46023,x46024),a909))),f318(f318(f10(f918(f918(x46023,f918(x46024,a909)),f918(f917(x46023,x46024),a909)),f918(f918(x46022,f918(x46023,f918(x46024,a909))),f918(x46022,f918(f917(x46023,x46024),a909))),x46021),f10(f918(x46023,f918(x46024,a909)),f918(f917(x46023,x46024),a909),x46022)),f318(f318(f10(f918(x46023,a909),f918(f918(x46023,f918(x46024,a909)),f918(f917(x46023,x46024),a909)),x46021),f245(x46023,x46024)),x46027))),f318(f318(f10(f918(x46024,a909),f918(x46023,f918(x46024,a909)),x46022),f18(f918(x46024,a909),x46023)),x46028)))),f318(f318(f245(x46023,x46024),f318(f318(f33(x46021,f918(x46023,a909)),x46025),x46027)),f318(f18(f918(x46024,a909),x46023),f318(f318(f33(x46022,f918(x46024,a909)),x46026),x46028))))
% 109.14/108.84 [4531]E(f318(f318(f250(x45311,x45312,x45313,x45314),f318(f318(f250(x45311,x45315,x45316,f917(x45312,x45313)),x45317),x45318)),x45319),f318(f318(f250(x45311,x45315,x45316,x45314),x45317),f318(f318(f9(x45315,f918(x45312,f918(x45313,x45314)),f918(x45316,x45314)),f318(f318(f10(f918(x45316,f917(x45312,x45313)),f918(f918(x45312,f918(x45313,x45314)),f918(x45316,x45314)),x45315),f250(x45316,x45312,x45313,x45314)),x45318)),x45319)))
% 109.14/108.84 [4563]E(f318(f66(f917(x45631,x45632),f917(x45633,x45634),f917(x45635,x45636),f249(x45631,x45633,x45632,x45634,x45637,x45638)),f249(x45635,x45631,x45636,x45632,x45639,x456310)),f249(x45635,x45633,x45636,x45634,f318(f66(x45631,x45633,x45635,x45637),x45639),f318(f66(x45632,x45634,x45636,x45638),x456310)))
% 109.14/108.84 [4564]E(f318(f66(f917(x45641,x45642),f917(x45643,x45644),f917(x45645,x45646),f249(x45641,x45643,x45642,x45644,x45647,x45648)),f249(x45645,x45641,x45646,x45642,x45649,x456410)),f249(x45645,x45643,x45646,x45644,f318(f66(x45641,x45643,x45645,x45647),x45649),f318(f66(x45642,x45644,x45646,x45648),x456410)))
% 109.14/108.84 [4570]E(f318(f249(x45701,x45702,x45703,x45704,x45705,x45706),f318(f249(x45707,x45701,x45708,x45703,x45709,x457010),x457011)),f318(f249(x45707,x45702,x45708,x45704,f318(f66(x45701,x45702,x45707,x45705),x45709),f318(f66(x45703,x45704,x45708,x45706),x457010)),x457011))
% 109.14/108.84 [4702]~P68(x47021)+P68(f915(x47021))
% 109.14/108.84 [4703]~P71(x47031)+P71(f915(x47031))
% 109.14/108.84 [4704]~P111(x47041)+P111(f912(x47041))
% 109.14/108.84 [4706]~P150(x47061)+~E(f71(x47061),f2(x47061))
% 109.14/108.84 [4707]~P150(x47071)+~E(f71(x47071),f2(x47071))
% 109.14/108.84 [4709]~E(x47091,f2(a90))+E(f318(a24,x47091),f2(a1))
% 109.14/108.84 [4710]~E(x47101,f2(a1))+E(f75(a1,x47101),f2(a1))
% 109.14/108.84 [4716]~P114(x47161)+P30(x47161,f2(x47161))
% 109.14/108.84 [4717]~P4(x47171)+P13(x47171,f104(x47171))
% 109.14/108.84 [4718]~P4(x47181)+P13(x47181,f104(x47181))
% 109.14/108.84 [4727]P1(x47271)+P1(f318(a313,x47271))
% 109.14/108.84 [4781]~P114(x47811)+~P30(x47811,f71(x47811))
% 109.14/108.84 [4816]~P1(x48161)+~P1(f318(a313,x48161))
% 109.14/108.84 [4837]E(f318(a95,x48371),f2(a911))+~P1(f318(a184,x48371))
% 109.14/108.84 [4903]~P80(x49031)+P16(x49031,x49031,f74(x49031))
% 109.14/108.84 [4904]~P102(x49041)+P14(x49041,x49041,f101(x49041))
% 109.14/108.84 [4905]~P108(x49051)+P14(x49051,x49051,f92(x49051))
% 109.14/108.84 [4906]~P101(x49061)+P14(x49061,x49061,f74(x49061))
% 109.14/108.84 [4907]~P4(x49071)+P14(x49071,x49071,f223(x49071))
% 109.14/108.84 [4908]~P4(x49081)+P14(x49081,x49081,f224(x49081))
% 109.14/108.84 [4713]~E(x47131,f2(a911))+E(f318(f91(a1),x47131),f2(a1))
% 109.14/108.84 [4719]~P99(x47191)+E(f318(f94(x47191),a76),f2(x47191))
% 109.14/108.84 [4720]~P99(x47201)+E(f318(f94(x47201),a76),f2(x47201))
% 109.14/108.84 [4723]~E(f576(x47231),f2(a911))+E(f318(f156(a911),x47231),f2(a911))
% 109.14/108.84 [4724]~P3(x47241)+E(f227(x47241,f225(x47241)),f223(x47241))
% 109.14/108.84 [4725]~P3(x47251)+E(f228(x47251,f225(x47251)),f224(x47251))
% 109.14/108.84 [4726]~P94(x47261)+E(f75(x47261,f2(x47261)),f2(x47261))
% 109.14/108.84 [4735]~P114(x47351)+E(f318(f91(x47351),f2(a911)),f2(x47351))
% 109.14/108.84 [4736]~P114(x47361)+E(f318(f91(x47361),f71(a911)),f71(x47361))
% 109.14/108.84 [4737]~P144(x47371)+E(f318(f93(x47371),f2(a1)),f2(x47371))
% 109.14/108.84 [4738]~P144(x47381)+E(f318(f93(x47381),f71(a1)),f71(x47381))
% 109.14/108.84 [4739]E(x47391,f2(a911))+~E(f318(f91(a1),x47391),f2(a1))
% 109.14/108.84 [4775]~P96(x47751)+E(f318(f72(x47751),f233(x47751)),f179(x47751))
% 109.14/108.84 [4776]~P96(x47761)+E(f318(f72(x47761),f179(x47761)),f233(x47761))
% 109.14/108.84 [4777]~P66(x47771)+E(f318(f72(x47771),f2(x47771)),f2(x47771))
% 109.14/108.84 [4778]~P91(x47781)+E(f318(f69(x47781),f2(x47781)),f2(x47781))
% 109.14/108.84 [4779]~P116(x47791)+E(f318(f69(x47791),f71(x47791)),f71(x47791))
% 109.14/108.84 [4780]~P86(x47801)+E(f318(f156(x47801),f104(x47801)),f2(x47801))
% 109.14/108.84 [4798]~P38(x47981)+P43(f318(f163(a1),x47981))
% 109.14/108.84 [4820]~P99(x48201)+E(f318(f72(x48201),f71(x48201)),f318(f94(x48201),a88))
% 109.14/108.84 [4821]~P99(x48211)+E(f318(f72(x48211),f71(x48211)),f318(f94(x48211),a88))
% 109.14/108.84 [4836]~P99(x48361)+P30(x48361,f318(f94(x48361),a76))
% 109.14/108.84 [4862]P38(x48621)+~P43(f318(f163(a1),x48621))
% 109.14/108.84 [4909]E(f318(f91(a1),f318(a95,x49091)),x49091)+P1(f318(a184,x49091))
% 109.14/108.84 [4977]~P118(x49771)+E(f236(x49771,f71(x49771),f74(x49771)),f235(x49771))
% 109.14/108.84 [5010]~P99(x50101)+~P30(x50101,f318(f94(x50101),a88))
% 109.14/108.84 [5102]~E(x51021,f2(a911))+P1(f318(f318(f225(a911),x51021),f2(a911)))
% 109.14/108.84 [5103]~E(x51031,f71(a911))+P1(f318(f318(f278(a911),x51031),f71(a911)))
% 109.14/108.84 [5159]E(f318(f69(a1),x51591),x51591)+P1(f318(f318(f226(a1),x51591),f2(a1)))
% 109.14/108.84 [5177]~E(f318(a95,x51771),f2(a911))+P1(f318(f318(f225(a1),x51771),f2(a1)))
% 109.14/108.84 [5246]~P1(f318(a184,x52461))+P1(f318(f318(f226(a1),x52461),f2(a1)))
% 109.14/108.84 [5288]~P130(x52881)+P1(f318(f318(f225(x52881),f2(x52881)),f71(x52881)))
% 109.14/108.84 [5289]~P144(x52891)+P1(f318(f318(f320(x52891),f2(x52891)),f100(x52891)))
% 109.14/108.84 [5290]~P114(x52901)+P1(f318(f318(f320(x52901),f2(x52901)),f177(x52901)))
% 109.14/108.84 [5291]~P144(x52911)+P1(f318(f318(f320(x52911),f71(x52911)),f100(x52911)))
% 109.14/108.84 [5292]~P114(x52921)+P1(f318(f318(f320(x52921),f71(x52921)),f177(x52921)))
% 109.14/108.84 [5293]~P130(x52931)+P1(f318(f318(f226(x52931),f2(x52931)),f71(x52931)))
% 109.14/108.84 [5346]E(x53461,f2(a911))+~P1(f318(f318(f225(a911),x53461),f2(a911)))
% 109.14/108.84 [5347]E(x53471,f71(a911))+~P1(f318(f318(f278(a911),x53471),f71(a911)))
% 109.14/108.84 [5388]E(f318(a95,x53881),f2(a911))+~P1(f318(f318(f225(a1),x53881),f2(a1)))
% 109.14/108.84 [5389]E(f318(a95,x53891),f2(a911))+~P1(f318(f318(f225(a1),x53891),f2(a1)))
% 109.14/108.84 [5446]P1(f318(a184,x54461))+~P1(f318(f318(f226(a1),x54461),f2(a1)))
% 109.14/108.84 [5453]~P4(x54531)+P16(x54531,f912(x54531),f139(x54531,x54531,f7(x54531)))
% 109.14/108.84 [5471]P43(x54711)+~P1(f318(f318(f225(a1),f2(a1)),f324(x54711)))
% 109.14/108.84 [5476]E(f318(f69(a1),x54761),f318(f72(a1),x54761))+~P1(f318(f318(f226(a1),x54761),f2(a1)))
% 109.14/108.84 [5646]~P130(x56461)+~P1(f318(f318(f225(x56461),f71(x56461)),f2(x56461)))
% 109.14/108.84 [5647]~P130(x56471)+~P1(f318(f318(f226(x56471),f71(x56471)),f2(x56471)))
% 109.14/108.84 [5663]~E(x56631,f2(a911))+P1(f318(f318(f225(a1),f318(f91(a1),x56631)),f2(a1)))
% 109.14/108.84 [5664]~E(x56641,f2(a1))+P1(f318(f318(f226(a1),f318(f69(a1),x56641)),f71(a1)))
% 109.14/108.84 [5789]~P86(x57891)+E(f133(x57891,x57891,f73(x57891),f2(x57891)),f156(x57891))
% 109.14/108.84 [5964]~P110(x59641)+P25(a911,x59641,f91(x59641),f233(f918(a911,a909)))
% 109.14/108.84 [6170]E(x61701,f2(a911))+~P1(f318(f318(f225(a1),f318(f91(a1),x61701)),f2(a1)))
% 109.14/108.84 [6171]E(x61711,f2(a1))+~P1(f318(f318(f226(a1),f318(f69(a1),x61711)),f71(a1)))
% 109.14/108.84 [8063]E(x80631,f318(a5,f2(a911)))+P1(f318(f318(f226(a911),f318(f318(f3(a911),f318(a22,x80631)),f318(a103,f2(a911)))),f318(a22,x80631)))
% 109.14/108.84 [8919]~P1(f318(f318(f226(a1),x89191),f2(a1)))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x89191)),x89191)),f2(a1)))
% 109.14/108.84 [8920]~P1(f318(f318(f226(a1),x89201),f2(a1)))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x89201)),x89201)),f2(a1)))
% 109.14/108.84 [9301]P1(f318(f318(f226(a1),x93011),f2(a1)))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x93011)),x93011)),f2(a1)))
% 109.14/108.84 [9302]P1(f318(f318(f226(a1),x93021),f2(a1)))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x93021)),x93021)),f2(a1)))
% 109.14/108.84 [9770]~P1(f318(f318(f226(a1),x97701),f2(a1)))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x97701)),x97701)),a88)),f2(a1)))
% 109.14/108.84 [9941]P1(f318(f318(f226(a1),x99411),f2(a1)))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99411)),x99411)),a88)),f2(a1)))
% 109.14/108.84 [4822]E(x48221,f2(a1))+E(f318(f318(f30(a1),x48221),x48221),f71(a1))
% 109.14/108.84 [4957]~P99(x49571)+E(f318(f93(x49571),f318(f94(a1),a88)),f318(f94(x49571),a88))
% 109.14/108.84 [4967]~P5(x49671)+E(f32(x49671,f233(f918(x49671,a909))),f179(x49671))
% 109.14/108.84 [4968]~P5(x49681)+E(f32(x49681,f179(f918(x49681,a909))),f233(x49681))
% 109.14/108.84 [4969]~P5(x49691)+E(f31(x49691,f233(f918(x49691,a909))),f233(x49691))
% 109.14/108.84 [4970]~P5(x49701)+E(f31(x49701,f179(f918(x49701,a909))),f179(x49701))
% 109.14/108.84 [4971]~P4(x49711)+E(f130(x49711,f179(f918(x49711,a909))),f104(x49711))
% 109.14/108.84 [5114]E(x51141,f2(a911))+P1(f318(f318(f226(a911),f2(a911)),x51141))
% 109.14/108.84 [5115]E(x51151,f2(a911))+P1(f318(f318(f226(a911),f2(a911)),x51151))
% 109.14/108.84 [5134]~P6(x51341)+P1(f318(f318(f225(a1),f2(a1)),x51341))
% 109.14/108.84 [5167]~E(f318(f94(a911),x51671),f2(a911))+P1(f318(f318(f225(a1),x51671),a76))
% 109.14/108.84 [5168]~E(f318(f94(a911),x51681),f2(a911))+P1(f318(f318(f225(a1),x51681),a76))
% 109.14/108.84 [5173]P43(x51731)+P1(f318(f318(f320(a1),f324(x51731)),x51731))
% 109.14/108.84 [5174]E(x51741,f318(a5,f2(a911)))+P1(f318(f318(f225(a90),f71(a90)),x51741))
% 109.14/108.84 [5217]P1(f318(a184,x52171))+P1(f318(f318(f225(a1),f2(a1)),x52171))
% 109.14/108.84 [5270]E(f318(f91(a1),f318(a95,x52701)),f2(a1))+P1(f318(f318(f225(a1),f2(a1)),x52701))
% 109.14/108.84 [5313]~P68(x53131)+P1(f318(f55(x53131),f233(f918(x53131,a909))))
% 109.14/108.84 [5328]E(f318(f91(a1),f318(f94(a911),x53281)),f318(f94(a1),x53281))+P1(f318(a184,f318(f94(a1),x53281)))
% 109.14/108.84 [5331]~E(x53311,f2(a911))+P1(f318(f318(f226(a911),x53311),f318(a103,f2(a911))))
% 109.14/108.84 [5352]E(f318(f94(a911),x53521),f2(a911))+~P1(f318(f318(f225(a1),x53521),a76))
% 109.14/108.84 [5353]E(f318(f94(a911),x53531),f2(a911))+~P1(f318(a184,f318(f94(a1),x53531)))
% 109.14/108.84 [5354]E(f318(f94(a911),x53541),f2(a911))+~P1(f318(f318(f225(a1),x53541),a76))
% 109.14/108.84 [5386]P6(x53861)+~P1(f318(f318(f225(a1),f2(a1)),x53861))
% 109.14/108.84 [5399]~E(x53991,f2(a911))+~P1(f318(f318(f226(a911),f2(a911)),x53991))
% 109.14/108.84 [5456]E(f318(a103,f578(x54561)),x54561)+~P1(f318(f318(f226(a911),f2(a911)),x54561))
% 109.14/108.84 [5465]E(f318(a103,f318(f94(a911),x54651)),f71(a911))+~P1(f318(a184,f318(f94(a1),x54651)))
% 109.14/108.84 [5472]E(f318(f91(a1),f383(x54721)),x54721)+~P1(f318(f318(f226(a1),f2(a1)),x54721))
% 109.14/108.84 [5479]~E(x54791,f318(a5,f2(a911)))+~P1(f318(f318(f225(a90),f71(a90)),x54791))
% 109.14/108.84 [5486]E(f318(f91(a1),f318(f94(a911),x54861)),f2(a1))+~P1(f318(a184,f318(f94(a1),x54861)))
% 109.14/108.84 [5512]E(f318(f156(a911),x55121),f2(a911))+P1(f318(f318(f320(a911),f576(x55121)),f318(f163(a911),x55121)))
% 109.14/108.84 [5532]E(f318(f91(a1),f318(a95,x55321)),x55321)+~P1(f318(f318(f225(a1),f2(a1)),x55321))
% 109.14/108.84 [5533]E(f318(f91(a1),f318(a95,x55331)),x55331)+~P1(f318(f318(f225(a1),f2(a1)),x55331))
% 109.14/108.84 [5541]~P1(f318(a184,x55411))+~P1(f318(f318(f225(a1),f2(a1)),x55411))
% 109.14/108.84 [5639]E(f318(f318(f73(a911),f71(a911)),f318(f94(a911),x56391)),f71(a911))+~P1(f318(f318(f226(a1),x56391),a76))
% 109.14/108.84 [5705]E(x57051,f2(a911))+~P1(f318(f318(f226(a911),x57051),f318(a103,f2(a911))))
% 109.14/108.84 [5747]E(f318(f318(f3(a911),f318(f94(a911),x57471)),f71(a911)),f2(a911))+~P1(f318(f318(f225(a1),x57471),a76))
% 109.14/108.84 [5748]E(f318(f318(f73(a911),f318(f94(a911),x57481)),f71(a911)),f71(a911))+~P1(f318(f318(f226(a1),x57481),a76))
% 109.14/108.84 [5760]~P43(x57601)+E(f318(f29(a911),f318(f301(a1,a911,a95),x57601)),f318(f29(a1),x57601))
% 109.14/108.84 [5790]~P4(x57901)+E(f227(x57901,f318(f9(x57901,x57901,a909),f225(x57901))),f224(x57901))
% 109.14/108.84 [5791]~P4(x57911)+E(f228(x57911,f318(f9(x57911,x57911,a909),f225(x57911))),f223(x57911))
% 109.14/108.84 [5801]E(f39(a911,f318(a103,f2(a911)),f318(f94(a911),x58011)),f318(a103,f2(a911)))+~P1(f318(a184,f318(f94(a1),x58011)))
% 109.14/108.84 [5810]~P1(f318(f318(f226(a1),f2(a1)),x58101))+P1(f318(f318(f225(a1),f71(a1)),x58101))
% 109.14/108.84 [5811]P1(f318(f318(f226(a1),f2(a1)),x58111))+~P1(f318(f318(f225(a1),f71(a1)),x58111))
% 109.14/108.84 [5821]E(f318(a103,f318(f318(f3(a911),x58211),f71(a911))),x58211)+~P1(f318(f318(f226(a911),f2(a911)),x58211))
% 109.14/108.84 [5822]E(f318(a103,f318(f318(f3(a911),x58221),f71(a911))),x58221)+~P1(f318(f318(f226(a911),f2(a911)),x58221))
% 109.14/108.84 [5878]P1(f318(f318(f226(a911),f2(a911)),f383(x58781)))+~P1(f318(f318(f226(a1),f2(a1)),x58781))
% 109.14/108.84 [5939]E(f39(a1,f318(f94(a1),a88),x59391),f318(f318(f3(a1),x59391),f71(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x59391))
% 109.14/108.84 [5977]~P1(f318(f318(f226(a1),a76),x59771))+P1(f318(f318(f226(a911),f2(a911)),f318(f94(a911),x59771)))
% 109.14/108.84 [5983]E(f318(a22,f810(x59831)),x59831)+~P1(f318(f318(f320(a911),x59831),f233(f918(a911,a909))))
% 109.14/108.84 [6036]P1(f318(f318(f226(a911),f2(a911)),f318(a95,x60361)))+~P1(f318(f318(f226(a1),f2(a1)),x60361))
% 109.14/108.84 [6055]E(f318(a22,f318(a5,x60551)),x60551)+~P1(f318(f318(f320(a911),x60551),f233(f918(a911,a909))))
% 109.14/108.84 [6085]~P1(f318(f318(f226(a911),f2(a911)),x60851))+P1(f318(f318(f226(a1),f2(a1)),f318(f91(a1),x60851)))
% 109.14/108.84 [6121]~P1(f318(f318(f226(a911),f2(a911)),f318(a95,x61211)))+P1(f318(f318(f226(a1),f2(a1)),x61211))
% 109.14/108.84 [6139]~P43(x61391)+E(f318(f301(a911,a1,f91(a1)),f318(f301(a1,a911,a95),x61391)),x61391)
% 109.14/108.84 [6150]P1(f318(f318(f226(a1),a76),x61501))+~P1(f318(f318(f226(a911),f2(a911)),f318(f94(a911),x61501)))
% 109.14/108.84 [6208]P1(f318(f318(f226(a911),f2(a911)),x62081))+~P1(f318(f318(f226(a1),f2(a1)),f318(f91(a1),x62081)))
% 109.14/108.84 [6244]E(f170(x62441,f104(f912(x62441))),f104(f912(x62441)))+~P1(f318(f306(f912(f912(x62441)),f171(x62441)),f104(f912(x62441))))
% 109.14/108.84 [6322]E(f318(f301(a911,a1,f91(a1)),f318(f273(a911),f318(a95,x63221))),f318(f293(a1,f2(a1)),x63221))+~P1(f318(f318(f225(a1),f2(a1)),x63221))
% 109.14/108.84 [6339]~P130(x63391)+P1(f318(f318(f226(x63391),f2(x63391)),f318(f318(f73(x63391),f71(x63391)),f71(x63391))))
% 109.14/108.84 [6388]P1(f318(f318(f226(a911),f318(a103,f2(a911))),f318(a95,x63881)))+~P1(f318(f318(f226(a1),f71(a1)),x63881))
% 109.14/108.84 [6485]E(x64851,f2(a1))+P1(f318(f43(f2(a1),x64851),f318(f318(f243(a1,a1),f2(a1)),f2(a1))))
% 109.14/108.84 [6655]~P1(f318(f318(f226(a911),f318(a103,f2(a911))),f318(a95,x66551)))+P1(f318(f318(f226(a1),f71(a1)),x66551))
% 109.14/108.84 [6702]E(f318(a103,f318(f318(f3(a911),f318(f94(a911),x67021)),f71(a911))),f318(f94(a911),x67021))+~P1(f318(f318(f226(a911),f2(a911)),f318(f94(a911),x67021)))
% 109.14/108.84 [7082]~P119(x70821)+P39(x70821,f318(f253(f917(x70821,x70821)),f318(f248(x70821,x70821,a909),f226(x70821))))
% 109.14/108.84 [5692]E(f318(f94(a911),f318(f318(f3(a1),x56921),a88)),f318(a103,f318(f94(a911),x56921)))+P1(f318(a184,f318(f94(a1),x56921)))
% 109.14/108.84 [5708]~P38(x57081)+E(f318(f318(f145(a911,a1),f91(a1)),f318(f318(f145(a1,a911),a95),x57081)),x57081)
% 109.14/108.84 [5722]P28(a908,a813,x57221)+~P1(f318(f318(f320(f910(a908)),x57221),a921))
% 109.14/108.84 [5828]E(f318(f72(a1),f318(f91(a1),f318(a103,f384(x58281)))),x58281)+~P1(f318(f318(f226(a1),x58281),f2(a1)))
% 109.14/108.84 [5838]E(f318(f318(f73(a911),f71(a911)),f318(f94(a911),x58381)),f318(f94(a911),f318(f318(f3(a1),x58381),a88)))+P1(f318(f318(f226(a1),x58381),a76))
% 109.14/108.84 [5880]E(f318(f318(f30(a1),f318(f94(a1),a88)),x58801),f318(f94(a1),a88))+~P1(f318(f318(f226(a1),f2(a1)),x58801))
% 109.14/108.84 [5973]E(f318(f318(f3(a911),f318(f94(a911),x59731)),f71(a911)),f318(f94(a911),f318(f318(f73(a1),x59731),a88)))+P1(f318(f318(f225(a1),x59731),a76))
% 109.14/108.84 [5974]E(f318(f318(f73(a911),f318(f94(a911),x59741)),f71(a911)),f318(f94(a911),f318(f318(f3(a1),x59741),a88)))+P1(f318(f318(f226(a1),x59741),a76))
% 109.14/108.84 [6021]E(f318(a95,f318(f318(f73(a1),f71(a1)),x60211)),f318(a103,f318(a95,x60211)))+~P1(f318(f318(f225(a1),f2(a1)),x60211))
% 109.14/108.84 [6057]E(f318(a103,f318(f318(f3(a911),x60571),f318(a103,f2(a911)))),x60571)+~P1(f318(f318(f226(a911),f2(a911)),x60571))
% 109.14/108.84 [6274]E(f39(a911,f318(a103,f2(a911)),f318(f94(a911),x62741)),f318(a95,f39(a1,f71(a1),f318(f94(a1),x62741))))+P1(f318(a184,f318(f94(a1),x62741)))
% 109.14/108.84 [6498]~P1(f318(f55(x64981),f233(f918(x64981,a909))))+P1(f318(f55(f915(x64981)),f233(f918(f915(x64981),a909))))
% 109.14/108.84 [6586]~P1(f318(f318(f225(a1),f2(a1)),x65861))+P1(f318(f318(f226(a1),f2(a1)),f318(f318(f73(a1),f71(a1)),x65861)))
% 109.14/108.84 [6593]E(f318(f242(a1,a1),f41(f71(a1),f318(f94(a1),x65931))),f318(f318(f30(a1),f71(a1)),f318(f94(a1),x65931)))+~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x65931)))
% 109.14/108.84 [6614]E(f318(f247(a1,a1),f41(f71(a1),f318(f94(a1),x66141))),f39(a1,f71(a1),f318(f94(a1),x66141)))+~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x66141)))
% 109.14/108.84 [6626]P1(f318(f55(x66261),f233(f918(x66261,a909))))+~P1(f318(f55(f915(x66261)),f233(f918(f915(x66261),a909))))
% 109.14/108.84 [6853]~P1(f318(f55(a911),x68531))+P1(f318(f55(a1),f318(f301(a911,a1,f91(a1)),x68531)))
% 109.14/108.84 [6973]~P1(f318(f55(x69731),f233(f918(x69731,a909))))+P1(f318(f318(f226(a911),f2(a911)),f318(f29(x69731),f233(f918(x69731,a909)))))
% 109.14/108.84 [7555]P1(f318(f55(a911),x75551))+~P1(f318(f55(a1),f318(f301(a911,a1,f91(a1)),x75551)))
% 109.14/108.84 [5723]~E(a88,x57231)+E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x57231)),x57231),a88)
% 109.14/108.84 [5724]~E(x57241,a88)+E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x57241)),x57241),a88)
% 109.14/108.84 [6285]E(x62851,a88)+~E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x62851)),x62851),a88)
% 109.14/108.84 [6286]E(a88,x62861)+~E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x62861)),x62861),a88)
% 109.14/108.84 [6554]~E(f318(f94(a911),x65541),f2(a911))+P1(f318(a184,f318(f94(a1),f318(f318(f73(a1),x65541),a88))))
% 109.14/108.84 [7229]E(f318(f94(a911),x72291),f2(a911))+~P1(f318(a184,f318(f94(a1),f318(f318(f73(a1),x72291),a88))))
% 109.14/108.84 [7833]E(f318(a97,f522(x78331)),x78331)+~P1(f318(f318(f320(f918(f917(a911,a911),a909)),x78331),a89))
% 109.14/108.84 [6668]~P99(x66681)+E(f318(f94(x66681),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f71(x66681))
% 109.14/108.84 [6669]~P99(x66691)+E(f318(f94(x66691),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f71(x66691))
% 109.14/108.84 [7100]~P1(f318(a184,f318(f94(a1),x71001)))+E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x71001)),x71001)),f2(a911))
% 109.14/108.84 [8012]~P1(f318(f318(f226(a1),f318(f94(a1),x80121)),f2(a1)))+E(f318(f242(a1,a1),f318(a45,f44(f318(f72(a1),f71(a1)),f318(f72(a1),f318(f94(a1),x80121))))),f318(f318(f30(a1),f71(a1)),f318(f94(a1),x80121)))
% 109.14/108.84 [8021]~P1(f318(f318(f226(a1),f318(f94(a1),x80211)),f2(a1)))+E(f318(f247(a1,a1),f318(a45,f44(f318(f72(a1),f71(a1)),f318(f72(a1),f318(f94(a1),x80211))))),f39(a1,f71(a1),f318(f94(a1),x80211)))
% 109.14/108.84 [8199]~P1(f318(f318(f225(a1),a76),x81991))+P1(f318(f318(f225(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x81991)),x81991)))
% 109.14/108.84 [8200]~P1(f318(f318(f225(a1),a88),x82001))+P1(f318(f318(f225(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x82001)),x82001)))
% 109.14/108.84 [8201]~P1(f318(f318(f225(a1),a76),x82011))+P1(f318(f318(f226(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x82011)),x82011)))
% 109.14/108.84 [8202]~P1(f318(f318(f226(a1),a88),x82021))+P1(f318(f318(f226(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x82021)),x82021)))
% 109.14/108.84 [8539]~P99(x85391)+~P30(x85391,f318(f94(x85391),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))
% 109.14/108.84 [8660]P1(f318(f318(f225(a1),a76),x86601))+~P1(f318(f318(f225(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x86601)),x86601)))
% 109.14/108.84 [8661]P1(f318(f318(f225(a1),a76),x86611))+~P1(f318(f318(f226(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x86611)),x86611)))
% 109.14/108.84 [8662]P1(f318(f318(f225(a1),a88),x86621))+~P1(f318(f318(f225(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x86621)),x86621)))
% 109.14/108.84 [8663]P1(f318(f318(f226(a1),a88),x86631))+~P1(f318(f318(f226(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x86631)),x86631)))
% 109.14/108.84 [8891]E(f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x88911)),x88911)),f318(f318(f81(a911,a911),f318(f94(a911),x88911)),f318(f318(f10(a911,a911,a911),a103),f318(f318(f20(a911,a911,a911),f73(a911)),f7(a911)))))+P1(f318(a184,f318(f94(a1),x88911)))
% 109.14/108.84 [9743]E(x97431,f179(f918(f917(a911,a911),a909)))+P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),x97431),f179(f918(f917(a911,a911),a909)))),a27))
% 109.14/108.84 [7920]~E(a76,x79201)+E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x79201)),x79201)),a88),a76)
% 109.14/108.84 [7921]~E(x79211,a76)+E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x79211)),x79211)),a88),a76)
% 109.14/108.84 [8554]E(x85541,a76)+~E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x85541)),x85541)),a88),a76)
% 109.14/108.84 [8555]E(a76,x85551)+~E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x85551)),x85551)),a88),a76)
% 109.14/108.84 [8906]~P1(f318(a184,f318(f94(a1),x89061)))+P1(f318(a184,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x89061)),x89061))))
% 109.14/108.84 [8907]~P1(f318(f318(f226(a1),x89071),a76))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x89071)),x89071)),a76))
% 109.14/108.84 [8908]~P1(f318(f318(f225(a1),x89081),a88))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x89081)),x89081)),a88))
% 109.14/108.84 [8909]~P1(f318(f318(f226(a1),x89091),a76))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x89091)),x89091)),a76))
% 109.14/108.84 [8910]~P1(f318(f318(f226(a1),x89101),a88))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x89101)),x89101)),a88))
% 109.14/108.84 [8992]~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x89921)))+P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x89921)),x89921))))
% 109.14/108.84 [9294]P1(f318(a184,f318(f94(a1),x92941)))+~P1(f318(a184,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92941)),x92941))))
% 109.14/108.84 [9295]P1(f318(f318(f225(a1),x92951),a88))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92951)),x92951)),a88))
% 109.14/108.84 [9296]P1(f318(f318(f226(a1),x92961),a76))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92961)),x92961)),a76))
% 109.14/108.84 [9297]P1(f318(f318(f226(a1),x92971),a76))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92971)),x92971)),a76))
% 109.14/108.84 [9298]P1(f318(f318(f226(a1),x92981),a88))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92981)),x92981)),a88))
% 109.14/108.84 [9793]~P1(f318(f55(f917(a911,a911)),x97931))+P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),f179(f918(f917(a911,a911),a909))),x97931)),a63))
% 109.14/108.84 [9460]~P1(f318(f318(f225(a1),a76),x94601))+P1(f318(f318(f225(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x94601)),x94601)),a88)))
% 109.14/108.84 [9461]~P1(f318(f318(f226(a1),a88),x94611))+P1(f318(f318(f225(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x94611)),x94611)),a88)))
% 109.14/108.84 [9462]~P1(f318(f318(f226(a1),a76),x94621))+P1(f318(f318(f226(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x94621)),x94621)),a88)))
% 109.14/108.84 [9463]~P1(f318(f318(f226(a1),a88),x94631))+P1(f318(f318(f226(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x94631)),x94631)),a88)))
% 109.14/108.84 [9683]P1(f318(f318(f225(a1),a76),x96831))+~P1(f318(f318(f225(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96831)),x96831)),a88)))
% 109.14/108.84 [9684]P1(f318(f318(f226(a1),a76),x96841))+~P1(f318(f318(f226(a1),a76),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96841)),x96841)),a88)))
% 109.14/108.84 [9685]P1(f318(f318(f226(a1),a88),x96851))+~P1(f318(f318(f225(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96851)),x96851)),a88)))
% 109.14/108.84 [9686]P1(f318(f318(f226(a1),a88),x96861))+~P1(f318(f318(f226(a1),a88),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96861)),x96861)),a88)))
% 109.14/108.84 [9765]~P1(f318(a184,f318(f94(a1),x97651)))+P1(f318(a184,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x97651)),x97651)),a88))))
% 109.14/108.84 [9766]~P1(f318(f318(f225(a1),x97661),a76))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x97661)),x97661)),a88)),a76))
% 109.14/108.84 [9767]~P1(f318(f318(f225(a1),x97671),a88))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x97671)),x97671)),a88)),a88))
% 109.14/108.84 [9768]~P1(f318(f318(f226(a1),x97681),a76))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x97681)),x97681)),a88)),a76))
% 109.14/108.84 [9769]~P1(f318(f318(f225(a1),x97691),a88))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x97691)),x97691)),a88)),a88))
% 109.14/108.84 [9772]~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x97721)))+P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x97721)),x97721)),a88))))
% 109.14/108.84 [9936]P1(f318(a184,f318(f94(a1),x99361)))+~P1(f318(a184,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99361)),x99361)),a88))))
% 109.14/108.84 [9937]P1(f318(f318(f225(a1),x99371),a76))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99371)),x99371)),a88)),a76))
% 109.14/108.84 [9938]P1(f318(f318(f225(a1),x99381),a88))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99381)),x99381)),a88)),a88))
% 109.14/108.84 [9939]P1(f318(f318(f225(a1),x99391),a88))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99391)),x99391)),a88)),a88))
% 109.14/108.84 [9940]P1(f318(f318(f226(a1),x99401),a76))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99401)),x99401)),a88)),a76))
% 109.14/108.84 [10041]~P99(x100411)+E(f318(f318(f73(x100411),f71(x100411)),f71(x100411)),f318(f94(x100411),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))
% 109.14/108.84 [10121]~P114(x101211)+E(f318(f318(f235(x101211),f2(x101211)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f2(x101211))
% 109.14/108.84 [10122]~P114(x101221)+E(f318(f318(f235(x101221),f71(x101221)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f71(x101221))
% 109.14/108.84 [10264]~P1(f318(f318(f226(a911),f71(a911)),x102641))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f30(a911),x102641),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.84 [10268]~P1(f318(f318(f226(a911),f2(a911)),x102681))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f30(a911),f318(f318(f73(a911),x102681),f71(a911))),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.84 [10292]~E(f39(a911,x102921,f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f71(a911))+P1(f318(f318(f226(a911),f2(a911)),f39(a911,x102921,f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.84 [10321]E(f39(a911,x103211,f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f71(a911))+~P1(f318(f318(f226(a911),f2(a911)),f39(a911,x103211,f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.84 [4743]~P7(x47431,x47432)+P51(x47431,x47432)
% 109.14/108.84 [4744]~P7(x47441,x47442)+P51(x47441,x47442)
% 109.14/108.84 [4745]~P39(x47451,x47452)+P61(x47451,x47452)
% 109.14/108.84 [4746]~P46(x47461,x47462)+P61(x47461,x47462)
% 109.14/108.84 [4747]~P7(x47471,x47472)+P53(x47471,x47472)
% 109.14/108.84 [4748]~P7(x47481,x47482)+P53(x47481,x47482)
% 109.14/108.84 [4749]~P15(x47491,x47492)+P53(x47491,x47492)
% 109.14/108.84 [4750]~P15(x47501,x47502)+P53(x47501,x47502)
% 109.14/108.84 [4751]~P7(x47511,x47512)+P54(x47511,x47512)
% 109.14/108.84 [4752]~P7(x47521,x47522)+P54(x47521,x47522)
% 109.14/108.84 [4753]~P15(x47531,x47532)+P54(x47531,x47532)
% 109.14/108.84 [4754]~P15(x47541,x47542)+P54(x47541,x47542)
% 109.14/108.84 [4755]~P7(x47551,x47552)+P15(x47551,x47552)
% 109.14/108.84 [4705]~E(x47051,x47052)+E(f260(x47051,x47052),f71(a90))
% 109.14/108.84 [4708]E(f207(x47081,x47082),x47081)+~E(x47082,f2(a911))
% 109.14/108.84 [4714]~E(x47142,f104(x47141))+E(f143(x47141,x47142),f104(x47141))
% 109.14/108.84 [4715]~E(x47152,f104(x47151))+E(f143(x47151,x47152),f104(x47151))
% 109.14/108.84 [4733]~E(f143(x47332,x47331),f104(x47332))+E(x47331,f104(x47332))
% 109.14/108.84 [4734]~E(f143(x47342,x47341),f104(x47342))+E(x47341,f104(x47342))
% 109.14/108.84 [4759]~P2(x47592)+P2(f918(x47591,x47592))
% 109.14/108.84 [4760]~P3(x47602)+P3(f918(x47601,x47602))
% 109.14/108.84 [4761]~P113(x47612)+P113(f918(x47611,x47612))
% 109.14/108.84 [4762]~P5(x47622)+P5(f918(x47621,x47622))
% 109.14/108.84 [4763]~P64(x47632)+P64(f918(x47631,x47632))
% 109.14/108.84 [4764]~P96(x47642)+P96(f918(x47641,x47642))
% 109.14/108.84 [4765]~P103(x47652)+P102(f918(x47651,x47652))
% 109.14/108.84 [4766]~P103(x47662)+P103(f918(x47661,x47662))
% 109.14/108.84 [4767]~P106(x47672)+P104(f918(x47671,x47672))
% 109.14/108.84 [4768]~P103(x47682)+P108(f918(x47681,x47682))
% 109.14/108.84 [4769]~P115(x47692)+P115(f918(x47691,x47692))
% 109.14/108.84 [4770]~P107(x47702)+P107(f918(x47701,x47702))
% 109.14/108.84 [4771]~P109(x47712)+P109(f918(x47711,x47712))
% 109.14/108.84 [4772]~P106(x47722)+P105(f918(x47721,x47722))
% 109.14/108.84 [4773]~P84(x47732)+P84(f918(x47731,x47732))
% 109.14/108.84 [4774]~P106(x47742)+P106(f918(x47741,x47742))
% 109.14/108.84 [4786]E(x47861,x47862)+~E(f318(a103,x47861),f318(a103,x47862))
% 109.14/108.84 [4787]E(x47871,x47872)+~E(f318(a103,x47871),f318(a103,x47872))
% 109.14/108.84 [4788]E(x47881,x47882)+~E(f318(a97,x47881),f318(a97,x47882))
% 109.14/108.84 [4789]E(x47891,x47892)+~E(f318(a5,x47891),f318(a5,x47892))
% 109.14/108.84 [4790]E(x47901,x47902)+~E(f318(a22,x47901),f318(a22,x47902))
% 109.14/108.84 [4791]E(x47911,x47912)+~E(f318(a22,x47911),f318(a22,x47912))
% 109.14/108.84 [4838]P41(x48381,x48382)+~E(f701(x48382,x48381),f702(x48382,x48381))
% 109.14/108.84 [4868]~P61(x48681,x48682)+P41(x48681,f298(x48681,x48682))
% 109.14/108.84 [4869]~P55(x48691,x48692)+P55(x48691,f298(x48691,x48692))
% 109.14/108.84 [4882]~P69(x48821)+E(f39(x48821,x48822,x48822),f2(x48821))
% 109.14/108.84 [4916]~P39(x49161,x49162)+P39(f912(x49161),f137(x49161,x49162))
% 109.14/108.84 [4917]~P39(x49171,x49172)+P39(f912(x49171),f136(x49171,x49172))
% 109.14/108.84 [4918]~P40(x49181,x49182)+P40(f912(x49181),f138(x49181,x49182))
% 109.14/108.84 [4919]~P40(x49191,x49192)+P40(f912(x49191),f149(x49191,x49192))
% 109.14/108.84 [4920]~P55(x49201,x49202)+P55(f912(x49201),f149(x49201,x49202))
% 109.14/108.84 [5015]~P39(x50151,x50152)+P39(f918(x50151,a909),f309(x50151,x50152))
% 109.14/108.84 [5016]~P39(x50161,x50162)+P39(f918(x50161,a909),f310(x50161,x50162))
% 109.14/108.84 [5143]~P6(x51431)+P43(f294(a1,x51431,x51432))
% 109.14/108.84 [5249]~P39(x52491,x52492)+P63(x52491,f61(x52491,x52491,x52492))
% 109.14/108.84 [5754]~P65(x57541)+P25(x57541,x57541,f72(x57541),x57542)
% 109.14/108.84 [4728]~E(x47282,f104(x47281))+E(f318(f159(x47281),x47282),f104(x47281))
% 109.14/108.84 [4729]~E(x47292,f104(x47291))+E(f318(f158(x47291),x47292),f104(x47291))
% 109.14/108.84 [4730]~E(x47302,f104(x47301))+E(f318(f159(x47301),x47302),f104(x47301))
% 109.14/108.84 [4793]E(x47931,f318(a95,x47932))+~E(f318(f91(a1),x47931),x47932)
% 109.14/108.84 [4795]E(x47951,f104(x47952))+~E(f318(f159(x47952),x47951),f104(x47952))
% 109.14/108.84 [4796]E(x47961,f104(x47962))+~E(f318(f158(x47962),x47961),f104(x47962))
% 109.14/108.84 [4797]E(x47971,f104(x47972))+~E(f318(f159(x47972),x47971),f104(x47972))
% 109.14/108.84 [4809]~P99(x48091)+E(f318(f94(x48091),x48092),f318(f93(x48091),x48092))
% 109.14/108.84 [4814]~P68(x48141)+P1(f318(f55(x48141),x48142))
% 109.14/108.84 [4815]~P68(x48151)+P1(f318(f55(x48151),x48152))
% 109.14/108.84 [4823]~E(f661(x48232,x48231),f104(x48231))+E(f170(x48231,x48232),f104(f912(x48231)))
% 109.14/108.84 [4832]~E(x48322,f104(x48321))+E(f318(f163(x48321),x48322),f179(f918(x48321,a909)))
% 109.14/108.84 [4833]~E(x48332,f104(x48331))+E(f179(f918(x48331,a909)),f318(f163(x48331),x48332))
% 109.14/108.84 [4834]E(x48341,x48342)+~E(f318(f91(a1),x48341),f318(f91(a1),x48342))
% 109.14/108.84 [4835]E(x48351,x48352)+~E(f318(f91(a1),x48351),f318(f91(a1),x48352))
% 109.14/108.84 [4839]E(f205(x48391,x48392),f2(a911))+P1(f318(f55(x48391),x48392))
% 109.14/108.84 [4857]~P116(x48571)+E(f75(x48571,f75(x48571,x48572)),f75(x48571,x48572))
% 109.14/108.84 [4871]~P121(x48711)+E(f318(f318(f235(x48711),x48712),f71(a911)),x48712)
% 109.14/108.84 [4872]~P88(x48721)+E(f318(f318(f235(x48721),x48722),f71(a911)),x48722)
% 109.14/108.84 [4873]~P55(x48731,x48732)+E(f318(f277(x48731,x48731),x48732),x48732)
% 109.14/108.84 [4877]E(x48771,x48772)+E(f260(x48771,x48772),f318(f318(f73(a90),x48772),f71(a90)))
% 109.14/108.84 [4878]E(f318(f29(x48781),x48782),f2(a911))+P1(f318(f55(x48781),x48782))
% 109.14/108.84 [4879]E(f318(f29(x48791),x48792),f2(a911))+P1(f318(f55(x48791),x48792))
% 109.14/108.84 [4880]E(f318(f29(x48801),x48802),f2(a911))+P1(f318(f55(x48801),x48802))
% 109.14/108.84 [4883]~E(f143(x48831,x48832),x48832)+P1(f318(f128(x48831),x48832))
% 109.14/108.84 [4886]~P105(x48861)+E(f318(f318(f101(x48861),x48862),f179(x48861)),x48862)
% 109.14/108.84 [4887]~P104(x48871)+E(f318(f318(f92(x48871),x48872),f233(x48871)),x48872)
% 109.14/108.84 [4888]~P66(x48881)+E(f318(f318(f3(x48881),x48882),f2(x48881)),x48882)
% 109.14/108.84 [4889]~P76(x48891)+E(f318(f318(f73(x48891),x48892),f2(x48891)),x48892)
% 109.14/108.84 [4890]~P86(x48901)+E(f318(f318(f73(x48901),x48902),f2(x48901)),x48902)
% 109.14/108.84 [4891]~P121(x48911)+E(f318(f318(f73(x48911),x48912),f2(x48911)),x48912)
% 109.14/108.84 [4892]~P121(x48921)+E(f318(f318(f74(x48921),x48922),f71(x48921)),x48922)
% 109.14/108.84 [4893]~P88(x48931)+E(f318(f318(f74(x48931),x48932),f71(x48931)),x48932)
% 109.14/108.84 [4894]~P82(x48941)+E(f318(f318(f74(x48941),x48942),f71(x48941)),x48942)
% 109.14/108.84 [4895]~P69(x48951)+E(f318(f318(f30(x48951),x48952),f71(x48951)),x48952)
% 109.14/108.84 [4896]~P125(x48961)+E(f318(f318(f282(x48961),x48962),f71(x48961)),x48962)
% 109.14/108.84 [4897]~P121(x48971)+E(f318(f318(f235(x48971),x48972),f2(a911)),f71(x48971))
% 109.14/108.84 [4898]~P118(x48981)+E(f318(f318(f235(x48981),x48982),f2(a911)),f71(x48981))
% 109.14/108.84 [4899]~E(x48992,f179(f918(x48991,a909)))+E(f318(f29(x48991),x48992),f2(a911))
% 109.14/108.84 [4910]~P69(x49101)+E(f39(x49101,x49102,f2(x49101)),x49102)
% 109.14/108.84 [4921]~P104(x49211)+E(f318(f318(f101(x49211),x49212),f233(x49211)),f233(x49211))
% 109.14/108.84 [4922]~P105(x49221)+E(f318(f318(f92(x49221),x49222),f179(x49221)),f179(x49221))
% 109.14/108.84 [4923]~P121(x49231)+E(f318(f318(f74(x49231),x49232),f2(x49231)),f2(x49231))
% 109.14/108.84 [4924]~P133(x49241)+E(f318(f318(f74(x49241),x49242),f2(x49241)),f2(x49241))
% 109.14/108.84 [4925]~P69(x49251)+E(f318(f318(f30(x49251),x49252),f2(x49251)),f2(x49251))
% 109.14/108.84 [4926]~P126(x49261)+E(f318(f318(f282(x49261),x49262),f2(x49261)),f2(x49261))
% 109.14/108.84 [4928]~P69(x49281)+E(f39(x49281,x49282,f71(x49281)),f2(x49281))
% 109.14/108.84 [4929]~P69(x49291)+E(f39(x49291,f2(x49291),x49292),f2(x49291))
% 109.14/108.84 [4956]E(x49561,f2(a911))+E(f49(x49562,x49561,f104(x49562)),f104(f912(x49562)))
% 109.14/108.84 [4979]P55(x49791,x49792)+~E(f318(f277(x49791,x49791),x49792),x49792)
% 109.14/108.84 [4980]P39(x49801,x49802)+~E(f577(x49802,x49801),f179(f918(x49801,a909)))
% 109.14/108.84 [4981]E(x49811,f104(x49812))+~E(f318(f163(x49812),x49811),f179(f918(x49812,a909)))
% 109.14/108.84 [4982]E(x49821,f104(x49822))+~E(f179(f918(x49822,a909)),f318(f163(x49822),x49821))
% 109.14/108.84 [4985]~E(x49851,x49852)+P1(f318(f318(a315,x49851),x49852))
% 109.14/108.84 [4995]P1(x49951)+P1(f318(f318(a321,x49951),x49952))
% 109.14/108.84 [4996]E(x49961,f104(x49962))+E(f318(f318(f155(x49962),x49961),f2(a911)),f318(f132(x49962),x49961))
% 109.14/108.84 [4998]E(f143(x49981,x49982),x49982)+~P1(f318(f128(x49981),x49982))
% 109.14/108.84 [4999]E(f143(x49991,x49992),x49992)+~P1(f318(f128(x49991),x49992))
% 109.14/108.84 [5006]~P1(x50062)+P1(f318(f318(a321,x50061),x50062))
% 109.14/108.84 [5007]~P1(x50072)+P1(f318(f318(a317,x50071),x50072))
% 109.14/108.84 [5008]~P1(x50081)+P1(f318(f318(a317,x50081),x50082))
% 109.14/108.84 [5018]~E(f662(x50182,x50181),f666(x50182,x50181))+P1(f318(f128(x50181),x50182))
% 109.14/108.84 [5025]E(f318(f253(x50251),x50252),f179(f918(x50251,a909)))+P1(f318(x50252,f539(x50252)))
% 109.14/108.84 [5026]E(f179(f918(x50261,a909)),f318(f253(x50261),x50262))+P1(f318(x50262,f553(x50262)))
% 109.14/108.84 [5096]~P116(x50961)+E(f318(f318(f74(x50961),x50962),f75(x50961,x50962)),f318(f69(x50961),x50962))
% 109.14/108.84 [5107]~E(x51071,f2(a1))+E(f40(x51071,x51072),f318(f318(f243(a1,a1),f2(a1)),f2(a1)))
% 109.14/108.84 [5108]~E(x51081,f2(a1))+E(f40(x51081,x51082),f318(f318(f243(a1,a1),f2(a1)),f2(a1)))
% 109.14/108.84 [5139]~P61(x51391,x51392)+P61(x51391,f318(f277(x51391,x51391),x51392))
% 109.14/108.84 [5140]~P40(x51401,x51402)+P40(x51401,f318(f277(x51401,x51401),x51402))
% 109.14/108.84 [5141]~P41(x51411,x51412)+P41(x51411,f318(f277(x51411,x51411),x51412))
% 109.14/108.84 [5142]~P55(x51421,x51422)+P55(x51421,f318(f277(x51421,x51421),x51422))
% 109.14/108.84 [5164]E(x51641,x51642)+~P1(f318(f318(a315,x51641),x51642))
% 109.14/108.84 [5175]P1(x51751)+~P1(f318(f318(a316,x51752),x51751))
% 109.14/108.84 [5176]P1(x51761)+~P1(f318(f318(a316,x51761),x51762))
% 109.14/108.84 [5181]~P115(x51811)+P1(f318(f318(f225(x51811),x51812),f233(x51811)))
% 109.14/108.84 [5182]~P121(x51821)+P1(f318(f318(f278(x51821),x51822),f2(x51821)))
% 109.14/108.84 [5186]E(x51861,x51862)+~E(f318(x51861,f382(x51862,x51861)),f318(x51862,f382(x51862,x51861)))
% 109.14/108.84 [5219]E(x52191,f2(a911))+E(f207(x52191,f39(a911,x52192,x52191)),f207(x52192,x52191))
% 109.14/108.84 [5224]~P4(x52241)+P13(x52241,f318(f318(f142(x52241),x52242),f104(x52241)))
% 109.14/108.84 [5228]E(x52281,f2(a1))+P1(f318(f43(x52282,x52281),f40(x52282,x52281)))
% 109.14/108.84 [5244]~P15(x52442,x52441)+P1(f318(f318(x52441,f795(x52441)),f795(x52441)))
% 109.14/108.84 [5247]~E(x52471,x52472)+P1(f318(f318(f226(a911),x52471),f318(a103,x52472)))
% 109.14/108.84 [5257]~E(x52571,f2(a911))+P1(f318(f318(f226(a911),x52571),f318(a103,x52572)))
% 109.14/108.84 [5269]P1(f318(x52691,x52692))+P1(f318(f318(f225(a1),f2(a1)),f366(x52691)))
% 109.14/108.84 [5333]P61(x53331,x53332)+~P61(x53331,f318(f277(x53331,x53331),x53332))
% 109.14/108.84 [5334]P40(x53341,x53342)+~P40(x53341,f318(f277(x53341,x53341),x53342))
% 109.14/108.84 [5335]P41(x53351,x53352)+~P41(x53351,f318(f277(x53351,x53351),x53352))
% 109.14/108.84 [5336]P55(x53361,x53362)+~P55(x53361,f318(f277(x53361,x53361),x53362))
% 109.14/108.84 [5339]~E(f39(a911,x53392,x53391),f2(a911))+E(f318(f318(f74(a911),x53391),f370(x53391,x53392)),x53392)
% 109.14/108.84 [5340]~E(f39(a1,x53402,x53401),f2(a1))+E(f318(f318(f74(a1),x53401),f326(x53401,x53402)),x53402)
% 109.14/108.84 [5345]~E(x53451,f318(a103,x53452))+P1(f318(f318(f225(a911),x53451),f318(a103,x53452)))
% 109.14/108.84 [5367]~P1(f318(x53671,x53672))+P1(f318(f318(f225(a1),f2(a1)),f325(x53671)))
% 109.14/108.84 [5378]E(f318(f318(f3(a911),f318(a95,x53781)),f318(a95,x53782)),f318(a95,x53781))+~P1(f318(a184,x53782))
% 109.14/108.84 [5401]E(f263(x54011,x54012),f71(a90))+~P1(f318(f318(f225(a90),x54011),f71(a90)))
% 109.14/108.84 [5498]E(f318(f318(f155(x54981),x54982),f662(x54982,x54981)),f318(f318(f155(x54981),x54982),f666(x54982,x54981)))+P1(f318(f128(x54981),x54982))
% 109.14/108.84 [5542]~P1(f318(x55421,f83(x55422,x55421)))+P1(f318(x55421,f590(x55422,x55421)))
% 109.14/108.84 [5606]P63(x56061,x56062)+~P1(f318(f306(x56061,x56062),f554(x56062,x56061)))
% 109.14/108.84 [5751]~P15(x57512,x57511)+P1(f318(f318(x57511,f797(x57511,x57512)),f797(x57511,x57512)))
% 109.14/108.84 [5752]~P15(x57522,x57521)+P1(f318(f318(x57521,f800(x57521,x57522)),f800(x57521,x57522)))
% 109.14/108.84 [5761]~E(f318(a103,f39(a911,x57611,x57612)),x57612)+E(f39(a911,f318(a103,x57611),x57612),f2(a911))
% 109.14/108.84 [5817]P39(x58171,x58172)+P1(f318(f318(f320(x58171),f593(x58172,x58171)),f594(x58172,x58171)))
% 109.14/108.84 [5824]~P99(x58241)+P1(f318(f318(f320(x58241),f318(f94(x58241),x58242)),f100(x58241)))
% 109.14/108.84 [5825]~P144(x58251)+P1(f318(f318(f320(x58251),f318(f91(x58251),x58252)),f100(x58251)))
% 109.14/108.84 [5826]~P114(x58261)+P1(f318(f318(f320(x58261),f318(f91(x58261),x58262)),f177(x58261)))
% 109.14/108.84 [5827]~P144(x58271)+P1(f318(f318(f320(x58271),f318(f93(x58271),x58272)),f100(x58271)))
% 109.14/108.84 [5961]~P40(x59611,x59612)+E(f318(f318(f280(x59611,x59611,x59611),x59612),f298(x59611,x59612)),x59612)
% 109.14/108.84 [5976]E(f318(a103,f39(a911,x59761,x59762)),x59762)+E(f39(a911,f318(a103,x59761),x59762),f318(a103,f39(a911,x59761,x59762)))
% 109.14/108.84 [6400]P39(x64001,x64002)+~P1(f318(f318(f320(x64001),f555(x64002,x64001)),f307(x64001,x64002)))
% 109.14/108.84 [6437]~P130(x64371)+~P1(f318(f318(f226(x64371),f318(f91(x64371),x64372)),f2(x64371)))
% 109.14/108.84 [6438]~P91(x64381)+~P1(f318(f318(f226(x64381),f318(f69(x64381),x64382)),f2(x64381)))
% 109.14/108.84 [6526]P1(f318(f318(f226(a1),x65261),f39(a1,x65262,x65261)))+~P1(f318(f318(f226(a1),x65261),f2(a1)))
% 109.14/108.84 [6527]P1(f318(f318(f226(a1),x65271),f39(a1,x65272,x65271)))+~P1(f318(f318(f226(a1),x65271),f2(a1)))
% 109.14/108.84 [6628]E(f318(f318(f300(a911),f318(a103,x66281)),f294(a911,x66282,x66281)),f294(a911,x66282,f318(a103,x66281)))+~P1(f318(f318(f225(a911),x66282),f318(a103,x66281)))
% 109.14/108.84 [6716]~P4(x67161)+P13(x67161,f141(x67161,x67161,f7(x67161),x67162))
% 109.14/108.84 [6851]E(f318(f158(x68511),x68512),x68512)+~P1(f318(f318(f225(a911),f318(f180(f912(x68511)),x68512)),f71(a911)))
% 109.14/108.84 [6872]~P91(x68721)+P1(f318(f318(f225(x68721),f318(f72(x68721),f318(f69(x68721),x68722))),f2(x68721)))
% 109.14/108.84 [6905]~P39(x69051,x69052)+P39(x69051,f318(f318(f280(x69051,x69051,x69051),x69052),f298(x69051,x69052)))
% 109.14/108.84 [6906]~P55(x69061,x69062)+P55(x69061,f318(f318(f280(x69061,x69061,x69061),x69062),f298(x69061,x69062)))
% 109.14/108.84 [7123]~P1(f318(f318(f226(a1),x71232),f2(a1)))+P1(f318(f318(f225(a1),f39(a1,x71231,x71232)),f2(a1)))
% 109.14/108.84 [7124]~P1(f318(f318(f226(a1),x71242),f2(a1)))+P1(f318(f318(f225(a1),f39(a1,x71241,x71242)),f2(a1)))
% 109.14/108.84 [7515]~P114(x75151)+E(f181(x75151,f318(f318(f9(x75151,x75151,x75151),f73(x75151)),f71(x75151)),x75152,f2(x75151)),f318(f91(x75151),x75152))
% 109.14/108.84 [7541]~P132(x75411)+~P1(f318(f318(f226(x75411),f318(f318(f74(x75411),x75412),x75412)),f2(x75411)))
% 109.14/108.84 [10357]~P116(x103571)+~P1(f318(f318(f226(x103571),f318(f318(f235(x103571),x103572),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f2(x103571)))
% 109.14/108.84 [4794]~E(x47942,f104(x47941))+E(f318(f180(f912(x47941)),x47942),f2(a911))
% 109.14/108.84 [4824]~E(x48241,f2(a911))+E(f318(f318(f73(a911),x48241),x48242),x48242)
% 109.14/108.84 [4825]~E(x48252,f2(a911))+E(f318(f318(f235(a911),x48251),x48252),f71(a911))
% 109.14/108.84 [4826]~E(x48262,f2(a911))+E(f318(f318(f74(a911),x48261),x48262),f2(a911))
% 109.14/108.84 [4827]~E(x48271,f2(a911))+E(f318(f318(f74(a911),x48271),x48272),f2(a911))
% 109.14/108.84 [4828]~E(x48281,f2(a911))+E(f318(f318(f74(a911),x48281),x48282),f2(a911))
% 109.14/108.84 [4829]~E(x48292,f2(a1))+E(f318(f318(f30(a1),x48291),x48292),f2(a1))
% 109.14/108.84 [4840]E(x48401,f104(x48402))+~E(f318(f180(f912(x48402)),x48401),f2(a911))
% 109.14/108.84 [4841]~P102(x48411)+E(f318(f318(f101(x48411),x48412),x48412),x48412)
% 109.14/108.84 [4842]~P102(x48421)+E(f318(f318(f101(x48421),x48422),x48422),x48422)
% 109.14/108.84 [4843]~P103(x48431)+E(f318(f318(f101(x48431),x48432),x48432),x48432)
% 109.14/108.84 [4844]~P103(x48441)+E(f318(f318(f92(x48441),x48442),x48442),x48442)
% 109.14/108.84 [4845]~P108(x48451)+E(f318(f318(f92(x48451),x48452),x48452),x48452)
% 109.14/108.84 [4846]~P108(x48461)+E(f318(f318(f92(x48461),x48462),x48462),x48462)
% 109.14/108.84 [4847]~P101(x48471)+E(f318(f318(f74(x48471),x48472),x48472),x48472)
% 109.14/108.84 [4848]~P101(x48481)+E(f318(f318(f74(x48481),x48482),x48482),x48482)
% 109.14/108.84 [4849]~P4(x48491)+E(f318(f318(f223(x48491),x48492),x48492),x48492)
% 109.14/108.84 [4850]~P4(x48501)+E(f318(f318(f223(x48501),x48502),x48502),x48502)
% 109.14/108.84 [4851]~P4(x48511)+E(f318(f318(f224(x48511),x48512),x48512),x48512)
% 109.14/108.84 [4852]~P4(x48521)+E(f318(f318(f224(x48521),x48522),x48522),x48522)
% 109.14/108.84 [4870]~P66(x48701)+E(f318(f318(f3(x48701),x48702),x48702),f2(x48701))
% 109.14/108.84 [4884]~P96(x48841)+E(f318(f72(x48841),f318(f72(x48841),x48842)),x48842)
% 109.14/108.84 [4885]~P66(x48851)+E(f318(f72(x48851),f318(f72(x48851),x48852)),x48852)
% 109.14/108.84 [4902]~E(x49022,f2(a911))+E(f318(f318(f235(a911),x49021),x49022),f318(a103,f2(a911)))
% 109.14/108.84 [4937]~P105(x49371)+E(f318(f318(f101(x49371),f179(x49371)),x49372),x49372)
% 109.14/108.84 [4938]~P104(x49381)+E(f318(f318(f92(x49381),f233(x49381)),x49382),x49382)
% 109.14/108.84 [4939]~P76(x49391)+E(f318(f318(f73(x49391),f2(x49391)),x49392),x49392)
% 109.14/108.84 [4940]~P86(x49401)+E(f318(f318(f73(x49401),f2(x49401)),x49402),x49402)
% 109.14/108.84 [4941]~P121(x49411)+E(f318(f318(f73(x49411),f2(x49411)),x49412),x49412)
% 109.14/108.84 [4942]~P121(x49421)+E(f318(f318(f74(x49421),f71(x49421)),x49422),x49422)
% 109.14/108.84 [4943]~P88(x49431)+E(f318(f318(f74(x49431),f71(x49431)),x49432),x49432)
% 109.14/108.84 [4944]~P82(x49441)+E(f318(f318(f74(x49441),f71(x49441)),x49442),x49442)
% 109.14/108.84 [4960]~P104(x49601)+E(f318(f318(f101(x49601),f233(x49601)),x49602),f233(x49601))
% 109.14/108.84 [4961]~P105(x49611)+E(f318(f318(f92(x49611),f179(x49611)),x49612),f179(x49611))
% 109.14/108.84 [4962]~P88(x49621)+E(f318(f318(f235(x49621),f71(x49621)),x49622),f71(x49621))
% 109.14/108.84 [4963]~P121(x49631)+E(f318(f318(f74(x49631),f2(x49631)),x49632),f2(x49631))
% 109.14/108.84 [4964]~P133(x49641)+E(f318(f318(f74(x49641),f2(x49641)),x49642),f2(x49641))
% 109.14/108.84 [4965]~P69(x49651)+E(f318(f318(f30(x49651),f2(x49651)),x49652),f2(x49651))
% 109.14/108.84 [4966]~P125(x49661)+E(f318(f318(f282(x49661),f2(x49661)),x49662),f2(x49661))
% 109.14/108.84 [4974]E(x49741,f104(x49742))+E(f135(x49742,f318(f159(x49742),x49741)),f318(f132(x49742),x49741))
% 109.14/108.84 [4975]E(x49751,f104(x49752))+E(f318(f132(x49752),f318(f159(x49752),x49751)),f135(x49752,x49751))
% 109.14/108.84 [4976]E(x49761,f2(a911))+~E(f318(f318(f73(a911),x49762),x49761),x49762)
% 109.14/108.84 [4983]~P99(x49831)+E(f318(f93(x49831),f318(f94(a1),x49832)),f318(f94(x49831),x49832))
% 109.14/108.84 [4984]~P144(x49841)+E(f318(f93(x49841),f318(f91(a1),x49842)),f318(f91(x49841),x49842))
% 109.14/108.84 [4989]E(x49891,f71(a911))+~E(f318(f318(f74(a911),x49892),x49891),f71(a911))
% 109.14/108.84 [4990]E(x49901,f71(a911))+~E(f318(f318(f74(a911),x49901),x49902),f71(a911))
% 109.14/108.84 [4991]E(x49911,f2(a911))+~E(f318(f318(f73(a911),x49912),x49911),f2(a911))
% 109.14/108.84 [4992]E(x49921,f2(a911))+~E(f318(f318(f73(a911),x49921),x49922),f2(a911))
% 109.14/108.84 [4993]E(x49931,f71(a911))+~E(f318(f318(f74(a911),x49932),x49931),f71(a911))
% 109.14/108.84 [4994]E(x49941,f71(a911))+~E(f318(f318(f74(a911),x49941),x49942),f71(a911))
% 109.14/108.84 [5011]~P91(x50111)+E(f318(f69(x50111),f318(f72(x50111),x50112)),f318(f69(x50111),x50112))
% 109.14/108.84 [5012]~P116(x50121)+E(f318(f69(x50121),f318(f91(x50121),x50122)),f318(f91(x50121),x50122))
% 109.14/108.84 [5013]~P91(x50131)+E(f318(f69(x50131),f318(f69(x50131),x50132)),f318(f69(x50131),x50132))
% 109.14/108.84 [5014]~P76(x50141)+E(f318(f156(x50141),f318(f159(x50141),x50142)),f318(f156(x50141),x50142))
% 109.14/108.84 [5019]~E(x50191,f318(a103,f2(a911)))+E(f318(f318(f235(a911),x50191),x50192),f318(a103,f2(a911)))
% 109.14/108.84 [5028]~P66(x50281)+E(f318(f318(f3(x50281),f2(x50281)),x50282),f318(f72(x50281),x50282))
% 109.14/108.84 [5029]~E(x50292,f2(a911))+E(f130(a911,f318(f293(a911,x50291),x50292)),f104(a911))
% 109.14/108.84 [5038]~P99(x50381)+E(f318(f318(f73(x50381),x50382),f318(f94(x50381),a76)),x50382)
% 109.14/108.84 [5039]E(x50391,f2(a1))+E(f41(f318(f69(a1),x50392),f318(f69(a1),x50391)),f47(x50392,x50391))
% 109.14/108.84 [5053]~E(x50531,x50532)+P1(f318(f318(f225(a911),x50531),x50532))
% 109.14/108.84 [5054]~E(x50541,x50542)+P1(f318(f318(f225(a911),x50541),x50542))
% 109.14/108.84 [5055]~E(x50551,x50552)+P1(f318(f318(f225(a911),x50551),x50552))
% 109.14/108.84 [5062]~E(x50621,f2(a90))+E(f318(f318(f73(a911),f318(a22,x50621)),x50622),x50622)
% 109.14/108.84 [5063]~E(f318(f91(a1),x50631),f318(f94(a1),x50632))+E(x50631,f318(a95,f318(f94(a1),x50632)))
% 109.14/108.84 [5064]~P5(x50641)+E(f86(x50641,f318(f18(x50641,x50641),x50642)),x50642)
% 109.14/108.84 [5077]~P6(x50771)+P6(f318(f318(f235(a1),x50771),x50772))
% 109.14/108.84 [5078]~P96(x50781)+E(f318(f318(f101(x50781),x50782),f318(f72(x50781),x50782)),f233(x50781))
% 109.14/108.84 [5079]~P96(x50791)+E(f318(f318(f92(x50791),x50792),f318(f72(x50791),x50792)),f179(x50791))
% 109.14/108.84 [5080]~P66(x50801)+E(f318(f318(f73(x50801),x50802),f318(f72(x50801),x50802)),f2(x50801))
% 109.14/108.84 [5105]E(x51051,f2(a911))+~E(f318(f72(a1),f318(f91(a1),x51052)),f318(f91(a1),x51051))
% 109.14/108.84 [5106]E(x51061,f2(a911))+~E(f318(f72(a1),f318(f91(a1),x51061)),f318(f91(a1),x51062))
% 109.14/108.84 [5116]E(f185(x51161,x51162),f2(a1))+P1(f318(f318(f225(a1),x51162),x51161))
% 109.14/108.84 [5117]E(f169(x51171,x51172),f104(a1))+P1(f318(f318(f225(a1),x51171),x51172))
% 109.14/108.84 [5118]E(f232(x51181,x51182),f2(a90))+P1(f318(f318(f226(a90),x51181),x51182))
% 109.14/108.84 [5131]E(x51311,f318(a103,f2(a911)))+~E(f318(f318(f74(a911),x51312),x51311),f318(a103,f2(a911)))
% 109.14/108.84 [5132]E(x51321,f318(a103,f2(a911)))+~E(f318(f318(f74(a911),x51321),x51322),f318(a103,f2(a911)))
% 109.14/108.84 [5133]~P2(x51331)+P1(f318(f318(f225(x51331),x51332),x51332))
% 109.14/108.84 [5136]~P99(x51361)+E(f318(f318(f74(x51361),x51362),f318(f94(x51361),a88)),f318(f72(x51361),x51362))
% 109.14/108.84 [5155]~P99(x51551)+E(f318(f72(x51551),f318(f94(x51551),x51552)),f318(f94(x51551),f318(f72(a1),x51552)))
% 109.14/108.84 [5156]~P99(x51561)+E(f318(f72(x51561),f318(f94(x51561),x51562)),f318(f94(x51561),f318(f72(a1),x51562)))
% 109.14/108.84 [5157]~P144(x51571)+E(f318(f72(x51571),f318(f93(x51571),x51572)),f318(f93(x51571),f318(f72(a1),x51572)))
% 109.14/108.84 [5187]~E(x51871,f318(a103,x51872))+P1(f318(f318(f226(a911),f2(a911)),x51871))
% 109.14/108.84 [5205]~P4(x52051)+E(f318(f72(f918(x52051,a909)),f318(f295(x52051),x52052)),f318(f292(x52051),x52052))
% 109.14/108.84 [5206]~P4(x52061)+E(f318(f72(f918(x52061,a909)),f318(f273(x52061),x52062)),f318(f274(x52061),x52062))
% 109.14/108.84 [5207]~P4(x52071)+E(f318(f72(f918(x52071,a909)),f318(f274(x52071),x52072)),f318(f273(x52071),x52072))
% 109.14/108.84 [5208]~P4(x52081)+E(f318(f72(f918(x52081,a909)),f318(f292(x52081),x52082)),f318(f295(x52081),x52082))
% 109.14/108.84 [5218]~E(f318(f91(a1),x52182),x52181)+P1(f318(f318(f225(a1),f2(a1)),x52181))
% 109.14/108.84 [5227]~E(x52272,f2(a1))+E(f47(x52271,x52272),f318(f318(f243(a1,a1),f2(a1)),f318(f69(a1),x52271)))
% 109.14/108.84 [5229]~P109(x52291)+P1(f318(f318(f225(x52291),f179(x52291)),x52292))
% 109.14/108.84 [5268]~P1(f318(x52681,x52682))+P1(f318(x52681,f318(a95,f325(x52681))))
% 109.14/108.84 [5294]~P116(x52941)+E(f318(f318(f74(x52941),f75(x52941,x52942)),f318(f69(x52941),x52942)),x52942)
% 109.14/108.84 [5301]~E(x53012,f2(a911))+E(f78(f917(a911,a911),f42(x53011,x53012)),f318(f318(f243(a911,a911),f2(a911)),x53011))
% 109.14/108.84 [5302]~E(x53021,x53022)+~P1(f318(f318(f226(a911),x53021),x53022))
% 109.14/108.84 [5303]~E(x53031,x53032)+~P1(f318(f318(f226(a911),x53031),x53032))
% 109.14/108.84 [5304]~E(x53041,x53042)+~P1(f318(f318(f226(a911),x53041),x53042))
% 109.14/108.84 [5305]~E(x53051,x53052)+~P1(f318(f318(f226(a911),x53051),x53052))
% 109.14/108.84 [5306]~E(x53061,x53062)+~P1(f318(f318(f226(a911),x53061),x53062))
% 109.14/108.84 [5307]~E(x53071,x53072)+~P1(f318(f318(f226(a1),x53071),x53072))
% 109.14/108.84 [5310]~P114(x53101)+E(f318(f318(f73(x53101),f71(x53101)),f318(f91(x53101),x53102)),f318(f91(x53101),f318(a103,x53102)))
% 109.14/108.84 [5314]~E(x53141,f2(a911))+~P1(f318(f318(f226(a911),x53142),x53141))
% 109.14/108.84 [5329]E(f143(x53291,x53292),x53292)+~E(f318(f180(f912(x53291)),f143(x53291,x53292)),f318(f180(f912(x53291)),x53292))
% 109.14/108.84 [5330]E(f318(f29(x53301),f318(f163(x53301),x53302)),f318(f180(f912(x53301)),x53302))+~P1(f318(f128(x53301),x53302))
% 109.14/108.84 [5344]~P1(f318(x53441,f327(x53441)))+P1(f318(x53441,f318(f91(a1),x53442)))
% 109.14/108.84 [5355]E(f232(x53551,x53552),x53552)+~P1(f318(f318(f226(a90),x53551),x53552))
% 109.14/108.84 [5357]E(f263(x53571,x53572),f71(a90))+~P1(f318(f318(f226(a90),x53572),x53571))
% 109.14/108.84 [5358]E(f169(x53581,x53582),f104(a1))+~P1(f318(f318(f226(a1),x53582),x53581))
% 109.14/108.84 [5359]E(f119(x53591,x53592),f106(a1))+~P1(f318(f318(f226(a1),x53591),x53592))
% 109.14/108.84 [5361]~P113(x53611)+E(f294(x53611,x53612,x53612),f318(f318(f300(x53611),x53612),f179(f918(x53611,a909))))
% 109.14/108.84 [5381]~E(f318(f318(f3(a911),x53811),x53812),f2(a911))+P1(f318(f318(f225(a911),x53811),x53812))
% 109.14/108.84 [5398]~E(x53982,f2(a911))+E(f49(x53981,x53982,f104(x53981)),f318(f318(f142(f912(x53981)),f104(x53981)),f104(f912(x53981))))
% 109.14/108.84 [5402]~P2(x54021)+~P1(f318(f318(f226(x54021),x54022),x54022))
% 109.14/108.84 [5403]~E(f39(a1,x54031,x54032),f2(a1))+E(f39(a1,x54031,f318(f72(a1),x54032)),f2(a1))
% 109.14/108.84 [5404]~E(f39(a1,x54041,x54042),f2(a1))+E(f39(a1,x54041,f318(f72(a1),x54042)),f2(a1))
% 109.14/108.84 [5405]~E(f39(a1,x54051,x54052),f2(a1))+E(f39(a1,f318(f72(a1),x54051),x54052),f2(a1))
% 109.14/108.84 [5406]~E(f39(a1,x54061,x54062),f2(a1))+E(f39(a1,f318(f72(a1),x54061),x54062),f2(a1))
% 109.14/108.84 [5415]E(f318(f293(a911,x54151),f318(a103,x54152)),f179(f918(a911,a909)))+P1(f318(f318(f225(a911),x54151),x54152))
% 109.14/108.84 [5438]E(f130(a911,f318(f293(a911,x54381),x54382)),f104(a911))+P1(f318(f318(f226(a911),x54381),x54382))
% 109.14/108.84 [5443]~E(f318(f29(x54431),f318(f163(x54431),x54432)),f318(f180(f912(x54431)),x54432))+P1(f318(f128(x54431),x54432))
% 109.14/108.84 [5447]~P1(f318(f128(x54471),x54472))+P1(f318(f128(x54471),f318(f158(x54471),x54472)))
% 109.14/108.84 [5448]~P1(f318(f128(x54481),x54482))+P1(f318(f128(x54481),f318(f162(x54481),x54482)))
% 109.14/108.84 [5449]~P1(f318(f128(x54491),x54492))+P1(f318(f128(x54491),f318(f159(x54491),x54492)))
% 109.14/108.84 [5457]P1(f318(x54571,x54572))+~P1(f318(x54571,f318(a95,f366(x54571))))
% 109.14/108.84 [5458]P1(f318(f318(f225(a911),x54582),x54581))+P1(f318(f318(f225(a911),x54581),x54582))
% 109.14/108.84 [5459]P1(f318(f318(f225(a1),x54592),x54591))+P1(f318(f318(f225(a1),x54591),x54592))
% 109.14/108.84 [5463]~P91(x54631)+P1(f318(f318(f225(x54631),x54632),f318(f69(x54631),x54632)))
% 109.14/108.84 [5466]P1(f318(x54661,f356(x54661)))+~P1(f318(x54661,f318(f91(a1),x54662)))
% 109.14/108.84 [5489]E(f318(f318(f3(a911),x54891),x54892),f2(a911))+~P1(f318(f318(f225(a911),x54891),x54892))
% 109.14/108.84 [5490]E(f318(f318(f3(a911),x54901),x54902),f2(a911))+~P1(f318(f318(f225(a911),x54901),x54902))
% 109.14/108.84 [5491]E(f318(f318(f30(a911),x54911),x54912),f2(a911))+~P1(f318(f318(f226(a911),x54911),x54912))
% 109.14/108.84 [5509]E(f39(a911,x55091,x55092),x55091)+~P1(f318(f318(f226(a911),x55091),x55092))
% 109.14/108.84 [5510]E(f39(a911,x55101,x55102),x55101)+~P1(f318(f318(f226(a911),x55101),x55102))
% 109.14/108.84 [5518]E(f39(a1,x55181,f318(f72(a1),x55182)),f283(x55181,x55182))+P1(f318(f318(f225(a1),f2(a1)),x55182))
% 109.14/108.84 [5530]E(f318(f318(f3(a1),x55301),x55302),f185(x55301,x55302))+~P1(f318(f318(f225(a1),x55302),x55301))
% 109.14/108.84 [5531]E(f318(f318(f3(a1),x55311),x55312),f185(x55311,x55312))+~P1(f318(f318(f225(a1),x55312),x55311))
% 109.14/108.84 [5551]P1(f318(f318(f225(a1),f2(a1)),f327(x55511)))+P1(f318(x55511,f318(f91(a1),x55512)))
% 109.14/108.84 [5563]~P130(x55631)+P1(f318(f318(f225(x55631),f2(x55631)),f318(f91(x55631),x55632)))
% 109.14/108.84 [5564]~P130(x55641)+P1(f318(f318(f225(x55641),f2(x55641)),f318(f91(x55641),x55642)))
% 109.14/108.84 [5565]~P91(x55651)+P1(f318(f318(f225(x55651),f2(x55651)),f318(f69(x55651),x55652)))
% 109.14/108.84 [5592]E(f318(f318(f73(a911),x55921),f745(x55922,x55921)),x55922)+~P1(f318(f318(f225(a911),x55921),x55922))
% 109.14/108.84 [5604]~E(f318(f91(a1),x56042),f318(f94(a1),x56041))+P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x56041)))
% 109.14/108.84 [5607]E(f294(a1,x56071,x56072),f179(f918(a1,a909)))+~P1(f318(f318(f226(a1),x56072),x56071))
% 109.14/108.84 [5610]~P116(x56101)+E(f318(f318(f74(x56101),f318(f69(x56101),x56102)),f318(f69(x56101),x56102)),f318(f318(f74(x56101),x56102),x56102))
% 109.14/108.84 [5615]E(f130(a911,f318(f293(a911,x56151),f318(a103,x56152))),f104(a911))+P1(f318(f318(f225(a911),x56151),x56152))
% 109.14/108.84 [5617]E(f318(f318(f30(a1),x56171),x56172),f284(x56171,x56172))+~P1(f318(f318(f225(a1),f2(a1)),x56172))
% 109.14/108.84 [5637]P1(f318(f128(x56371),x56372))+~P1(f318(f128(x56371),f318(f158(x56371),x56372)))
% 109.14/108.84 [5638]P1(f318(f128(x56381),x56382))+~P1(f318(f128(x56381),f318(f159(x56381),x56382)))
% 109.14/108.84 [5665]P1(f318(f55(a911),x56651))+P1(f318(f318(f320(a911),f777(x56651,x56652)),x56651))
% 109.14/108.84 [5666]P1(f318(f55(a911),x56661))+P1(f318(f318(f320(a911),f796(x56661,x56662)),x56661))
% 109.14/108.84 [5669]P1(f318(f318(f226(a911),x56692),f318(a103,x56691)))+P1(f318(f318(f226(a911),x56691),x56692))
% 109.14/108.84 [5670]E(f39(a1,x56701,x56702),f283(x56701,x56702))+~P1(f318(f318(f225(a1),f2(a1)),x56702))
% 109.14/108.84 [5672]E(f130(a911,f318(f293(a911,x56721),x56722)),f104(a911))+~P1(f318(f318(f225(a911),x56722),x56721))
% 109.14/108.84 [5673]E(f130(a911,f318(f293(a911,x56731),x56732)),f104(a911))+~P1(f318(f318(f225(a911),x56732),x56731))
% 109.14/108.84 [5674]~P65(x56741)+E(f318(f301(x56741,x56741,f72(x56741)),f318(f295(x56741),x56742)),f318(f273(x56741),f318(f72(x56741),x56742)))
% 109.14/108.84 [5675]~P65(x56751)+E(f318(f301(x56751,x56751,f72(x56751)),f318(f273(x56751),x56752)),f318(f295(x56751),f318(f72(x56751),x56752)))
% 109.14/108.84 [5676]~P65(x56761)+E(f318(f301(x56761,x56761,f72(x56761)),f318(f274(x56761),x56762)),f318(f292(x56761),f318(f72(x56761),x56762)))
% 109.14/108.84 [5677]~P65(x56771)+E(f318(f301(x56771,x56771,f72(x56771)),f318(f292(x56771),x56772)),f318(f274(x56771),f318(f72(x56771),x56772)))
% 109.14/108.84 [5688]E(x56881,f179(f918(x56882,a909)))+P1(f318(f318(f320(x56882),f667(x56881,x56882)),x56881))
% 109.14/108.84 [5689]E(x56891,f179(f918(x56892,a909)))+P1(f318(f318(f320(x56892),f668(x56891,x56892)),x56891))
% 109.14/108.84 [5696]~P1(f318(f318(f226(a911),x56961),x56962))+P1(f318(f318(f225(a911),x56961),x56962))
% 109.14/108.84 [5697]~P1(f318(f318(f226(a911),x56971),x56972))+P1(f318(f318(f225(a911),x56971),x56972))
% 109.14/108.84 [5698]~P1(f318(f318(f226(a911),x56981),x56982))+P1(f318(f318(f225(a911),x56981),x56982))
% 109.14/108.84 [5699]~P1(f318(f318(f226(a911),x56991),x56992))+P1(f318(f318(f225(a911),x56991),x56992))
% 109.14/108.84 [5700]~P1(f318(f318(f226(a911),x57001),x57002))+P1(f318(f318(f225(a911),x57001),x57002))
% 109.14/108.84 [5701]~P1(f318(f318(f226(a1),x57011),x57012))+P1(f318(f318(f225(a1),x57011),x57012))
% 109.14/108.84 [5717]E(f41(x57171,x57172),f318(f318(f243(a1,a1),f2(a1)),x57171))+~P1(f318(f318(f226(a1),x57171),x57172))
% 109.14/108.84 [5719]E(f206(f318(f72(a1),x57191),f318(f72(a1),x57192)),f206(x57191,x57192))+~P1(f318(f318(f226(a1),x57192),f2(a1)))
% 109.14/108.84 [5733]E(x57331,x57332)+~E(f318(a5,f318(a103,f318(a22,x57331))),f318(a5,f318(a103,f318(a22,x57332))))
% 109.14/108.84 [5738]E(f41(x57381,x57382),f318(f318(f243(a1,a1),f2(a1)),x57381))+~P1(f318(f318(f225(a1),x57382),f2(a1)))
% 109.14/108.84 [5767]E(f39(a911,f318(f94(a911),x57671),f318(f94(a911),x57672)),f2(a911))+~P1(f318(a184,f318(f94(a1),x57671)))
% 109.14/108.84 [5782]P1(f318(f318(f225(a1),f2(a1)),f356(x57821)))+~P1(f318(x57821,f318(f91(a1),x57822)))
% 109.14/108.84 [5815]P43(f294(a1,x58151,x58152))+~P1(f318(f318(f225(a1),f2(a1)),x58151))
% 109.14/108.84 [5820]~P1(f318(f55(x58201),x58202))+P1(f318(f55(f918(x58201,a909)),f318(f299(x58201),x58202)))
% 109.14/108.84 [5833]E(f318(f318(f73(a1),x58331),f318(f91(a1),f359(x58332,x58331))),x58332)+~P1(f318(f318(f225(a1),x58331),x58332))
% 109.14/108.84 [5841]P1(f318(f318(f225(a911),x58411),x58412))+P1(f318(f318(f225(a911),f318(a103,x58412)),x58411))
% 109.14/108.84 [5885]E(f318(f318(f30(a911),f318(f94(a911),x58851)),f318(f94(a911),x58852)),f2(a911))+~P1(f318(a184,f318(f94(a1),x58851)))
% 109.14/108.84 [5886]E(f318(f318(f74(a911),f318(f94(a911),x58861)),f318(f94(a911),x58862)),f2(a911))+~P1(f318(f318(f226(a1),x58861),a76))
% 109.14/108.84 [5887]P1(f318(f318(f225(a911),x58871),f318(a103,x58872)))+~P1(f318(f318(f225(a911),x58871),x58872))
% 109.14/108.84 [5888]P1(f318(f318(f225(a911),x58881),f318(a103,x58882)))+~P1(f318(f318(f225(a911),x58881),x58882))
% 109.14/108.84 [5889]P1(f318(f318(f226(a911),x58891),f318(a103,x58892)))+~P1(f318(f318(f225(a911),x58891),x58892))
% 109.14/108.84 [5890]P1(f318(f318(f226(a911),x58901),f318(a103,x58902)))+~P1(f318(f318(f225(a911),x58901),x58902))
% 109.14/108.84 [5891]P1(f318(f318(f226(a911),x58911),f318(a103,x58912)))+~P1(f318(f318(f226(a911),x58911),x58912))
% 109.14/108.84 [5892]P1(f318(f318(f226(a911),x58921),f318(a103,x58922)))+~P1(f318(f318(f226(a911),x58921),x58922))
% 109.14/108.84 [5895]~E(x58951,x58952)+P1(f318(f318(f226(a1),x58951),f318(f318(f73(a1),x58952),f71(a1))))
% 109.14/108.84 [5898]E(f39(a1,x58981,x58982),f2(a1))+E(f318(f318(f3(a1),x58982),f39(a1,x58981,x58982)),f39(a1,f318(f72(a1),x58981),x58982))
% 109.14/108.84 [5907]E(x59071,f104(x59072))+P1(f318(f318(f320(x59072),f135(x59072,x59071)),f318(f163(x59072),x59071)))
% 109.14/108.84 [5918]E(f78(f917(a911,a911),f42(x59181,x59182)),f318(f318(f243(a911,a911),f2(a911)),x59181))+~P1(f318(f318(f226(a911),x59181),x59182))
% 109.14/108.84 [5919]E(f78(f917(a911,a911),f42(x59191,x59192)),f318(f318(f243(a911,a911),f2(a911)),x59191))+~P1(f318(f318(f226(a911),x59191),x59192))
% 109.14/108.84 [5954]E(f318(f318(f3(a911),f318(f94(a911),x59541)),f318(f94(a911),x59542)),f318(f94(a911),x59541))+~P1(f318(f318(f226(a1),x59542),a76))
% 109.14/108.84 [5955]E(f318(f318(f73(a911),f318(f94(a911),x59551)),f318(f94(a911),x59552)),f318(f94(a911),x59552))+~P1(f318(f318(f226(a1),x59551),a76))
% 109.14/108.84 [5962]E(f318(a103,f318(f318(f73(a911),x59621),f803(x59622,x59621))),x59622)+~P1(f318(f318(f226(a911),x59621),x59622))
% 109.14/108.84 [5982]E(f318(a103,f328(x59821)),x59821)+~P1(f318(f318(f225(a911),f318(a103,x59822)),x59821))
% 109.14/108.84 [5988]P1(f318(x59881,x59882))+~P1(f318(x59881,f318(a82,f580(x59882,x59881))))
% 109.14/108.84 [5989]P1(f318(x59891,x59892))+~P1(f318(x59891,f318(a5,f814(x59892,x59891))))
% 109.14/108.84 [5998]~P1(f318(f318(f226(a911),x59981),f318(a103,x59982)))+P1(f318(f318(f225(a911),x59981),x59982))
% 109.14/108.84 [6035]P1(f318(x60351,x60352))+P1(f318(f318(f320(a911),f814(x60352,x60351)),f233(f918(a911,a909))))
% 109.14/108.84 [6048]E(f318(f318(f300(a911),x60481),f318(f293(a911,x60482),x60481)),f318(f293(a911,x60482),f318(a103,x60481)))+~P1(f318(f318(f225(a911),x60482),x60481))
% 109.14/108.84 [6050]E(x60501,f104(x60502))+E(f318(f318(f125(x60502),f105(x60502,x60501)),f318(f318(f142(x60502),f135(x60502,x60501)),f104(x60502))),x60501)
% 109.14/108.84 [6065]P1(f318(f55(x60651),x60652))+~P1(f318(f318(f226(a911),f2(a911)),f318(f29(x60651),x60652)))
% 109.14/108.84 [6066]P1(f318(f55(x60661),x60662))+~P1(f318(f318(f226(a911),f2(a911)),f318(f29(x60661),x60662)))
% 109.14/108.84 [6070]~E(x60701,f179(f918(x60702,a909)))+~P1(f318(f318(f226(a911),f2(a911)),f318(f29(x60702),x60701)))
% 109.14/108.84 [6080]~P1(f318(f318(f226(a911),x60801),x60802))+P1(f318(f318(f225(a911),f318(a103,x60801)),x60802))
% 109.14/108.84 [6081]~P1(f318(f318(f226(a911),x60811),x60812))+P1(f318(f318(f225(a911),f318(a103,x60811)),x60812))
% 109.14/108.84 [6082]~P1(f318(f318(f226(a911),x60821),x60822))+P1(f318(f318(f225(a911),f318(a103,x60821)),x60822))
% 109.14/108.84 [6086]~P4(x60861)+E(f141(x60861,x60861,f7(x60861),f143(x60861,x60862)),f130(x60861,f318(f163(x60861),x60862)))
% 109.14/108.84 [6089]E(x60891,f104(x60892))+P1(f318(f318(f320(x60892),f318(f132(x60892),x60891)),f318(f163(x60892),x60891)))
% 109.14/108.84 [6095]~P130(x60951)+P1(f318(f318(f226(x60951),x60952),f318(f318(f73(x60951),x60952),f71(x60951))))
% 109.14/108.84 [6097]~P91(x60971)+P1(f318(f318(f225(x60971),f318(f72(x60971),x60972)),f318(f69(x60971),x60972)))
% 109.14/108.84 [6111]~E(x61111,x61112)+E(f281(a911,f278(a911),x61111,x61112),f318(f318(f300(a911),x61111),f179(f918(a911,a909))))
% 109.14/108.84 [6131]P1(f318(f55(a911),x61311))+~P1(f318(f318(f225(a911),f796(x61311,x61312)),x61312))
% 109.14/108.84 [6132]P1(f318(f55(a911),x61321))+~P1(f318(f318(f226(a911),f777(x61321,x61322)),x61322))
% 109.14/108.84 [6136]~P1(f318(f55(f917(x61361,x61361)),x61362))+P1(f318(f55(x61361),f318(f272(x61361),x61362)))
% 109.14/108.84 [6188]E(f281(a911,f278(a911),x61881,x61882),f179(f918(a911,a909)))+P1(f318(f318(f278(a911),x61881),x61882))
% 109.14/108.84 [6189]E(f281(a911,f278(a911),x61891,x61892),f179(f918(a911,a909)))+P1(f318(f318(f278(a911),x61891),x61892))
% 109.14/108.84 [6190]E(f169(f318(f94(a1),x61901),f318(f94(a1),x61902)),f104(a1))+P1(f318(f318(f225(a1),f318(f94(a1),x61901)),f318(f94(a1),x61902)))
% 109.14/108.84 [6192]~P1(f318(f318(f226(a911),x61922),f318(a103,x61921)))+~P1(f318(f318(f226(a911),x61921),x61922))
% 109.14/108.84 [6193]~P113(x61931)+E(f318(f318(f92(f918(x61931,a909)),f318(f292(x61931),x61932)),f318(f274(x61931),x61932)),f318(f318(f300(x61931),x61932),f179(f918(x61931,a909))))
% 109.14/108.84 [6195]E(f318(f318(f235(a911),f318(f94(a911),x61951)),f318(f94(a911),x61952)),f318(f318(f235(a911),f2(a911)),f318(f94(a911),x61952)))+~P1(f318(a184,f318(f94(a1),x61951)))
% 109.14/108.84 [6205]P1(f318(f55(x62051),x62052))+~P1(f318(f55(f918(x62051,a909)),f318(f299(x62051),x62052)))
% 109.14/108.84 [6228]P1(f318(f318(f225(a911),f318(a103,x62281)),f318(a103,x62282)))+~P1(f318(f318(f225(a911),x62281),x62282))
% 109.14/108.84 [6229]P1(f318(f318(f225(a911),f318(a22,x62291)),f318(a22,x62292)))+~P1(f318(f318(f225(a90),x62291),x62292))
% 109.14/108.84 [6230]P1(f318(f318(f225(a90),f318(a5,x62301)),f318(a5,x62302)))+~P1(f318(f318(f225(a911),x62301),x62302))
% 109.14/108.84 [6231]P1(f318(f318(f226(a911),f318(a103,x62311)),f318(a103,x62312)))+~P1(f318(f318(f226(a911),x62311),x62312))
% 109.14/108.84 [6232]P1(f318(f318(f226(a911),f318(a103,x62321)),f318(a103,x62322)))+~P1(f318(f318(f226(a911),x62321),x62322))
% 109.14/108.84 [6233]P1(f318(f318(f226(a911),f318(a22,x62331)),f318(a22,x62332)))+~P1(f318(f318(f226(a90),x62331),x62332))
% 109.14/108.84 [6234]P1(f318(f318(f226(a90),f318(a5,x62341)),f318(a5,x62342)))+~P1(f318(f318(f226(a911),x62341),x62342))
% 109.14/108.84 [6239]E(x62391,x62392)+~E(f318(f301(a911,a1,f91(a1)),x62391),f318(f301(a911,a1,f91(a1)),x62392))
% 109.14/108.84 [6255]P1(f318(f318(f225(a911),x62551),x62552))+~P1(f318(f318(f225(a911),f318(a103,x62551)),x62552))
% 109.14/108.84 [6256]P1(f318(f318(f226(a911),x62561),x62562))+~P1(f318(f318(f225(a911),f318(a103,x62561)),x62562))
% 109.14/108.84 [6257]P1(f318(f318(f226(a911),x62571),x62572))+~P1(f318(f318(f225(a911),f318(a103,x62571)),x62572))
% 109.14/108.84 [6258]P1(f318(f318(f226(a911),x62581),x62582))+~P1(f318(f318(f225(a911),f318(a103,x62581)),x62582))
% 109.14/108.84 [6259]P1(f318(f318(f226(a911),x62591),x62592))+~P1(f318(f318(f226(a911),f318(a103,x62591)),x62592))
% 109.14/108.84 [6277]E(f39(a1,x62771,x62772),f2(a1))+E(f318(f318(f3(a1),f39(a1,x62771,x62772)),x62772),f39(a1,x62771,f318(f72(a1),x62772)))
% 109.14/108.84 [6342]E(f318(f29(f918(x63421,a909)),f318(f299(x63421),x63422)),f318(f318(f235(a911),f318(a103,f318(a103,f2(a911)))),f318(f29(x63421),x63422)))+~P1(f318(f55(x63421),x63422))
% 109.14/108.84 [6345]E(x63451,f104(x63452))+E(f318(f318(f155(x63452),x63451),f318(f318(f3(a911),f318(f180(f912(x63452)),x63451)),f71(a911))),f135(x63452,x63451))
% 109.14/108.84 [6367]E(x63671,f104(x63672))+E(f318(f318(f125(x63672),f318(f162(x63672),x63671)),f318(f318(f142(x63672),f318(f132(x63672),x63671)),f104(x63672))),f318(f158(x63672),x63671))
% 109.14/108.84 [6368]~P1(f318(f179(f918(x63681,a909)),x63682))+P1(f318(f318(f320(x63681),x63682),f179(f918(x63681,a909))))
% 109.14/108.84 [6397]~P1(f318(f55(x63971),f31(f918(x63971,a909),x63972)))+P1(f318(f55(f918(x63971,a909)),x63972))
% 109.14/108.84 [6419]P1(f318(f318(f225(a911),f318(f94(a911),x64191)),f318(f94(a911),x64192)))+~P1(f318(f318(f225(a1),x64191),a76))
% 109.14/108.84 [6440]~P1(f318(f318(f226(a1),x64401),x64402))+P1(f318(f318(f225(a1),x64401),f318(f318(f3(a1),x64402),f71(a1))))
% 109.14/108.84 [6441]~P1(f318(f318(f225(a1),x64411),x64412))+P1(f318(f318(f226(a1),x64411),f318(f318(f73(a1),x64412),f71(a1))))
% 109.14/108.84 [6442]~P1(f318(f318(f226(a1),x64421),x64422))+P1(f318(f318(f226(a1),x64421),f318(f318(f73(a1),x64422),f71(a1))))
% 109.14/108.84 [6444]~P1(f318(f318(f225(a1),x64441),x64442))+P1(f318(f318(f225(a911),f318(f94(a911),x64441)),f318(f94(a911),x64442)))
% 109.14/108.84 [6445]~P1(f318(f318(f225(a1),x64451),x64452))+P1(f318(f318(f225(a1),f318(f94(a1),x64451)),f318(f94(a1),x64452)))
% 109.14/108.84 [6446]~P1(f318(f318(f225(a911),x64461),x64462))+P1(f318(f318(f225(a1),f318(f91(a1),x64461)),f318(f91(a1),x64462)))
% 109.14/108.84 [6447]~P1(f318(f318(f225(a911),x64471),x64472))+P1(f318(f318(f225(a1),f318(f91(a1),x64471)),f318(f91(a1),x64472)))
% 109.14/108.84 [6448]~P1(f318(f318(f226(a1),x64481),x64482))+P1(f318(f318(f226(a1),f318(f94(a1),x64481)),f318(f94(a1),x64482)))
% 109.14/108.84 [6449]~P1(f318(f318(f226(a911),x64491),x64492))+P1(f318(f318(f226(a1),f318(f91(a1),x64491)),f318(f91(a1),x64492)))
% 109.14/108.84 [6450]~P1(f318(f318(f226(a911),x64501),x64502))+P1(f318(f318(f226(a1),f318(f91(a1),x64501)),f318(f91(a1),x64502)))
% 109.14/108.84 [6457]~E(x64572,f179(f918(x64571,a909)))+P1(f318(f318(f225(f918(x64571,a909)),x64572),f179(f918(x64571,a909))))
% 109.14/108.84 [6470]~P1(f318(f318(f225(a911),x64701),x64702))+~P1(f318(f318(f225(a911),f318(a103,x64702)),x64701))
% 109.14/108.84 [6511]~P1(f318(f318(f225(a911),f318(a103,x65111)),f318(a103,x65112)))+P1(f318(f318(f225(a911),x65111),x65112))
% 109.14/108.84 [6512]~P1(f318(f318(f225(a90),f318(a5,x65121)),f318(a5,x65122)))+P1(f318(f318(f225(a911),x65121),x65122))
% 109.14/108.84 [6513]~P1(f318(f318(f225(a911),f318(a22,x65131)),f318(a22,x65132)))+P1(f318(f318(f225(a90),x65131),x65132))
% 109.14/108.84 [6514]~P1(f318(f318(f226(a911),f318(a103,x65141)),f318(a103,x65142)))+P1(f318(f318(f226(a911),x65141),x65142))
% 109.14/108.84 [6515]~P1(f318(f318(f226(a911),f318(a103,x65151)),f318(a103,x65152)))+P1(f318(f318(f226(a911),x65151),x65152))
% 109.14/108.84 [6516]~P1(f318(f318(f226(a90),f318(a5,x65161)),f318(a5,x65162)))+P1(f318(f318(f226(a911),x65161),x65162))
% 109.14/108.84 [6517]~P1(f318(f318(f226(a911),f318(a95,x65171)),f318(a95,x65172)))+P1(f318(f318(f226(a1),x65171),x65172))
% 109.14/108.84 [6518]~P1(f318(f318(f226(a911),f318(a22,x65181)),f318(a22,x65182)))+P1(f318(f318(f226(a90),x65181),x65182))
% 109.14/108.84 [6540]~P1(f318(f318(f320(x65401),x65402),f179(f918(x65401,a909))))+P1(f318(f179(f918(x65401,a909)),x65402))
% 109.14/108.84 [6560]~P1(f318(f318(f226(a911),f318(a95,x65602)),f318(a95,x65601)))+P1(f318(f318(f226(a1),f2(a1)),x65601))
% 109.14/108.84 [6591]P1(f318(f318(f225(a1),f2(a1)),f39(a1,x65911,x65912)))+~P1(f318(f318(f226(a1),f2(a1)),x65912))
% 109.14/108.84 [6592]P1(f318(f318(f225(a1),f2(a1)),f39(a1,x65921,x65922)))+~P1(f318(f318(f226(a1),f2(a1)),x65922))
% 109.14/108.84 [6754]P39(x67541,x67542)+~E(f318(f318(f280(x67541,x67541,x67541),x67542),x67542),f179(f918(f917(x67541,x67541),a909)))
% 109.14/108.84 [6768]~P39(x67681,x67682)+P39(x67681,f318(f318(f280(x67681,x67681,x67681),x67682),x67682))
% 109.14/108.84 [6779]P1(f318(f318(f225(a1),x67791),x67792))+~P1(f318(f318(f226(a1),x67791),f318(f318(f73(a1),x67792),f71(a1))))
% 109.14/108.84 [6780]P1(f318(f318(f226(a1),x67801),x67802))+~P1(f318(f318(f225(a1),x67801),f318(f318(f3(a1),x67802),f71(a1))))
% 109.14/108.84 [6782]P1(f318(f318(f225(a911),x67821),x67822))+~P1(f318(f318(f225(a1),f318(f91(a1),x67821)),f318(f91(a1),x67822)))
% 109.14/108.84 [6783]P1(f318(f318(f225(a911),x67831),x67832))+~P1(f318(f318(f225(a1),f318(f91(a1),x67831)),f318(f91(a1),x67832)))
% 109.14/108.84 [6784]P1(f318(f318(f225(a1),x67841),x67842))+~P1(f318(f318(f225(a1),f318(f94(a1),x67841)),f318(f94(a1),x67842)))
% 109.14/108.84 [6785]P1(f318(f318(f226(a911),x67851),x67852))+~P1(f318(f318(f226(a1),f318(f91(a1),x67851)),f318(f91(a1),x67852)))
% 109.14/108.84 [6786]P1(f318(f318(f226(a911),x67861),x67862))+~P1(f318(f318(f226(a1),f318(f91(a1),x67861)),f318(f91(a1),x67862)))
% 109.14/108.84 [6787]P1(f318(f318(f226(a1),x67871),x67872))+~P1(f318(f318(f226(a911),f318(f94(a911),x67871)),f318(f94(a911),x67872)))
% 109.14/108.84 [6788]P1(f318(f318(f226(a1),x67881),x67882))+~P1(f318(f318(f226(a1),f318(f94(a1),x67881)),f318(f94(a1),x67882)))
% 109.14/108.84 [6861]~E(f281(a911,f278(a911),x68611,x68612),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x68611),x68612))
% 109.14/108.84 [6862]~E(f281(a911,f278(a911),x68621,x68622),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x68621),x68622))
% 109.14/108.84 [6886]~E(f692(x68862,x68861),f104(x68861))+E(f318(f133(f912(x68861),f912(x68861),f125(x68861),f104(x68861)),x68862),f104(x68861))
% 109.14/108.84 [6887]~E(f697(x68872,x68871),f104(x68871))+E(f318(f133(f912(x68871),f912(x68871),f125(x68871),f104(x68871)),x68872),f104(x68871))
% 109.14/108.84 [6892]~P5(x68921)+E(f318(f133(x68921,x68921,f92(x68921),f233(x68921)),x68922),f32(x68921,f318(f163(x68921),x68922)))
% 109.14/108.84 [6893]~P5(x68931)+E(f318(f133(x68931,x68931,f101(x68931),f179(x68931)),x68932),f31(x68931,f318(f163(x68931),x68932)))
% 109.14/108.84 [6907]E(x69071,f2(a90))+E(f318(f318(f73(a911),f318(a22,f318(f318(f3(a90),x69071),f71(a90)))),f318(a103,x69072)),f318(f318(f73(a911),f318(a22,x69071)),x69072))
% 109.14/108.84 [6951]P1(f318(f318(f226(a1),f318(f318(f3(a1),x69511),x69512)),f2(a1)))+~P1(f318(f318(f226(a1),x69511),x69512))
% 109.14/108.84 [6975]~P4(x69751)+E(f318(f318(f101(f918(x69751,a909)),f318(f318(f300(x69751),x69752),f179(f918(x69751,a909)))),f318(f295(x69751),x69752)),f318(f274(x69751),x69752))
% 109.14/108.84 [7052]~P63(x70521,x70522)+P39(x70521,f318(f253(f917(x70521,x70521)),f318(f248(x70521,x70521,a909),x70522)))
% 109.14/108.84 [7053]~P63(x70531,x70532)+P61(x70531,f318(f253(f917(x70531,x70531)),f318(f248(x70531,x70531,a909),x70532)))
% 109.14/108.84 [7054]~P53(x70541,x70542)+P40(x70541,f318(f253(f917(x70541,x70541)),f318(f248(x70541,x70541,a909),x70542)))
% 109.14/108.84 [7055]~P54(x70551,x70552)+P55(x70551,f318(f253(f917(x70551,x70551)),f318(f248(x70551,x70551,a909),x70552)))
% 109.14/108.84 [7056]E(x70561,f179(f918(x70562,a909)))+~P1(f318(f318(f225(f918(x70562,a909)),x70561),f179(f918(x70562,a909))))
% 109.14/108.84 [7139]~P1(f318(f318(f226(a911),f2(a911)),x71392))+P1(f318(f318(f225(a911),f39(a911,x71391,x71392)),x71392))
% 109.14/108.84 [7140]~P1(f318(f318(f225(a1),f2(a1)),x71401))+P1(f318(f318(f225(a1),f39(a1,x71401,x71402)),x71401))
% 109.14/108.84 [7141]~P1(f318(f318(f226(a911),f2(a911)),x71412))+P1(f318(f318(f226(a911),f39(a911,x71411,x71412)),x71412))
% 109.14/108.84 [7142]~P1(f318(f318(f226(a1),f2(a1)),x71422))+P1(f318(f318(f226(a1),f39(a1,x71421,x71422)),x71422))
% 109.14/108.84 [7143]~P1(f318(f318(f226(a1),f2(a1)),x71432))+P1(f318(f318(f226(a1),f39(a1,x71431,x71432)),x71432))
% 109.14/108.84 [7220]~P113(x72201)+E(f318(f318(f3(f918(x72201,a909)),f318(f318(f300(x72201),x72202),f179(f918(x72201,a909)))),f318(f273(x72201),x72202)),f318(f318(f300(x72201),x72202),f179(f918(x72201,a909))))
% 109.14/108.84 [7294]~P51(x72941,x72942)+P56(x72941,f233(f918(x72941,a909)),f318(f253(f917(x72941,x72941)),f318(f248(x72941,x72941,a909),x72942)))
% 109.14/108.84 [7295]P1(f318(x72951,x72952))+P1(f318(f318(f320(f918(f917(a911,a911),a909)),f580(x72952,x72951)),a89))
% 109.14/108.84 [7339]E(f318(f318(f125(a911),f130(a911,f318(f293(a911,x73391),x73392))),f318(f318(f142(a911),x73392),f104(a911))),f130(a911,f318(f293(a911,x73391),f318(a103,x73392))))+~P1(f318(f318(f225(a911),x73391),x73392))
% 109.14/108.84 [7340]E(f318(f318(f125(a911),f130(a911,f318(f293(a911,x73401),x73402))),f318(f318(f142(a911),x73402),f104(a911))),f130(a911,f318(f293(a911,x73401),f318(a103,x73402))))+~P1(f318(f318(f225(a911),x73401),x73402))
% 109.14/108.84 [7482]E(x74821,f2(a911))+~E(f318(f133(a911,a911,f73(a911),x74821),x74822),f2(a911))
% 109.14/108.84 [7507]~P1(f318(f318(f226(a1),f318(f318(f3(a1),x75071),x75072)),f2(a1)))+P1(f318(f318(f226(a1),x75071),x75072))
% 109.14/108.84 [7533]P39(x75331,x75332)+~P39(x75331,f318(f318(f280(x75331,x75331,x75331),x75332),x75332))
% 109.14/108.84 [7558]~P1(f318(f318(f225(a911),f318(a103,x75581)),x75582))+P1(f176(a909,a230,f318(f225(a911),x75581),x75582))
% 109.14/108.84 [7710]P25(a911,a911,f318(f318(f9(a911,a911,a911),f3(a911)),x77101),x77102)+P1(f318(f318(f320(a911),f581(x77101,x77102)),x77102))
% 109.14/108.84 [7765]E(f318(f318(f318(f59(a911,x77651,f73(a911)),f318(f18(a911,x77651),f71(a911))),f2(a911)),x77652),f318(f29(x77651),x77652))+~P1(f318(f55(x77651),x77652))
% 109.14/108.84 [7766]E(f318(f318(f318(f59(a911,x77661,f73(a911)),f318(f18(a911,x77661),f71(a911))),f2(a911)),x77662),f318(f29(x77661),x77662))+~P1(f318(f55(x77661),x77662))
% 109.14/108.84 [7809]P25(a911,a911,f318(f318(f9(a911,a911,a911),f3(a911)),x78091),x78092)+~P1(f318(f318(f225(a911),x78091),f581(x78091,x78092)))
% 109.14/108.84 [7864]P39(x78641,x78642)+P1(f318(f318(f225(f918(x78641,a909)),f577(x78642,x78641)),f318(f276(x78641,x78641,x78642),f577(x78642,x78641))))
% 109.14/108.84 [7869]P63(x78691,x78692)+~P39(x78691,f318(f253(f917(x78691,x78691)),f318(f248(x78691,x78691,a909),x78692)))
% 109.14/108.84 [7870]P53(x78701,x78702)+~P40(x78701,f318(f253(f917(x78701,x78701)),f318(f248(x78701,x78701,a909),x78702)))
% 109.14/108.84 [7871]P54(x78711,x78712)+~P55(x78711,f318(f253(f917(x78711,x78711)),f318(f248(x78711,x78711,a909),x78712)))
% 109.14/108.84 [7940]P1(f318(f318(f225(a911),f318(a103,x79401)),x79402))+~P1(f176(a909,a230,f318(f225(a911),x79401),x79402))
% 109.14/108.84 [8000]P1(f318(f318(f320(f917(a911,a911)),f318(f318(f243(a911,a911),x80001),x80002)),f298(a911,a308)))+~P1(f318(f318(f225(a911),x80001),x80002))
% 109.14/108.84 [8089]P51(x80891,x80892)+~P56(x80891,f233(f918(x80891,a909)),f318(f253(f917(x80891,x80891)),f318(f248(x80891,x80891,a909),x80892)))
% 109.14/108.84 [8142]~P1(f318(f128(x81421),x81422))+P1(f318(f128(f918(x81421,a909)),f318(f318(f145(f912(x81421),f918(x81421,a909)),f163(x81421)),f48(x81421,x81422))))
% 109.14/108.84 [8351]~P39(x83511,f318(f277(x83511,x83511),x83512))+P39(x83511,f318(f277(x83511,x83511),f318(f318(f280(x83511,x83511,x83511),x83512),f298(x83511,x83512))))
% 109.14/108.84 [8446]P26(x84461,a911,f817(x84462,x84461),x84462,f318(f293(a911,f2(a911)),f318(f29(x84461),x84462)))+~P1(f318(f55(x84461),x84462))
% 109.14/108.84 [8447]P26(a911,x84471,f818(x84472,x84471),f318(f293(a911,f2(a911)),f318(f29(x84471),x84472)),x84472)+~P1(f318(f55(x84471),x84472))
% 109.14/108.84 [8465]P26(a911,x84651,f819(x84652,x84651),f294(a911,f71(a911),f318(f29(x84651),x84652)),x84652)+~P1(f318(f55(x84651),x84652))
% 109.14/108.84 [8474]P1(f318(f55(f917(x84741,x84741)),f318(f318(f280(x84741,x84741,x84741),x84742),f298(x84741,x84742))))+~P1(f318(f55(f917(x84741,x84741)),x84742))
% 109.14/108.84 [8498]E(x84981,f2(a1))+P1(f318(f43(x84982,x84981),f318(f318(f243(a1,a1),f318(f318(f30(a1),x84982),x84981)),f39(a1,x84982,x84981))))
% 109.14/108.84 [8511]~P1(f318(f318(f320(f917(a911,a911)),f318(f318(f243(a911,a911),x85111),x85112)),f298(a911,a308)))+P1(f318(f318(f225(a911),x85111),x85112))
% 109.14/108.84 [8528]~P86(x85281)+E(f318(f133(x85281,x85281,f318(f9(x85281,x85281,x85281),f73(x85281)),f2(x85281)),f318(f159(x85281),x85282)),f318(f133(x85281,x85281,f73(x85281),f2(x85281)),x85282))
% 109.14/108.84 [8704]~P4(x87041)+E(f318(f133(f912(x87041),x87041,f318(f9(x87041,f912(x87041),f912(x87041)),f139(x87041,x87041,f7(x87041))),f104(x87041)),x87042),f141(x87041,x87041,f7(x87041),x87042))
% 109.14/108.84 [8809]~P61(x88091,f318(f253(f917(x88091,x88091)),f318(f248(x88091,x88091,a909),x88092)))+P61(x88091,f318(f253(f917(x88091,x88091)),f318(f248(x88091,x88091,a909),f234(x88091,x88091,x88092))))
% 109.14/108.84 [8823]P1(f318(f318(f320(f917(a911,a911)),f318(f318(f243(a911,a911),x88231),x88232)),f318(f318(f280(a911,a911,a911),a308),f298(a911,a308))))+~P1(f318(f318(f226(a911),x88231),x88232))
% 109.14/108.84 [8867]~P1(f318(f55(f917(x88671,x88671)),f318(f318(f280(x88671,x88671,x88671),x88672),f298(x88671,x88672))))+P1(f318(f55(f917(x88671,x88671)),x88672))
% 109.14/108.84 [8925]~P61(x89251,f318(f253(f917(x89251,x89251)),f318(f248(x89251,x89251,a909),f234(x89251,x89251,x89252))))+P61(x89251,f318(f253(f917(x89251,x89251)),f318(f248(x89251,x89251,a909),x89252)))
% 109.14/108.84 [9129]P61(x91291,x91292)+P1(f318(f318(f320(f917(x91291,x91291)),f318(f318(f243(x91291,x91291),f610(x91292,x91291)),f610(x91292,x91291))),f318(f318(f280(x91291,x91291,x91291),x91292),f298(x91291,x91292))))
% 109.14/108.84 [9130]P61(x91301,x91302)+P1(f318(f318(f320(f917(x91301,x91301)),f318(f318(f243(x91301,x91301),f618(x91302,x91301)),f618(x91302,x91301))),f318(f318(f280(x91301,x91301,x91301),x91302),f298(x91301,x91302))))
% 109.14/108.84 [9235]~P1(f318(f318(f320(f917(a911,a911)),f318(f318(f243(a911,a911),x92351),x92352)),f318(f318(f280(a911,a911,a911),a308),f298(a911,a308))))+P1(f318(f318(f226(a911),x92351),x92352))
% 109.14/108.84 [5201]~P99(x52011)+E(f318(f318(f73(x52011),f318(f94(x52011),a76)),x52012),x52012)
% 109.14/108.84 [5234]~P96(x52341)+E(f318(f318(f101(x52341),f318(f72(x52341),x52342)),x52342),f233(x52341))
% 109.14/108.84 [5235]~P96(x52351)+E(f318(f318(f92(x52351),f318(f72(x52351),x52352)),x52352),f179(x52351))
% 109.14/108.84 [5236]~P66(x52361)+E(f318(f318(f73(x52361),f318(f72(x52361),x52362)),x52362),f2(x52361))
% 109.14/108.84 [5237]~P67(x52371)+E(f318(f318(f73(x52371),f318(f72(x52371),x52372)),x52372),f2(x52371))
% 109.14/108.84 [5272]~P99(x52721)+E(f318(f318(f74(x52721),f318(f94(x52721),a88)),x52722),f318(f72(x52721),x52722))
% 109.14/108.84 [5430]~P117(x54301)+E(f318(f318(f74(x54301),f318(f72(x54301),f71(x54301))),x54302),f318(f72(x54301),x54302))
% 109.14/108.84 [5475]E(f318(f69(a1),x54751),f71(a1))+~E(f318(f69(a1),f318(f318(f74(a1),x54751),x54752)),f71(a1))
% 109.14/108.84 [5567]~P99(x55671)+E(f318(f318(f73(x55671),f71(x55671)),f318(f94(x55671),x55672)),f318(f94(x55671),f318(f318(f3(a1),x55672),a88)))
% 109.14/108.84 [5618]~P5(x56181)+E(f32(x56181,f318(f318(f300(x56181),x56182),f179(f918(x56181,a909)))),x56182)
% 109.14/108.84 [5619]~P5(x56191)+E(f31(x56191,f318(f318(f300(x56191),x56192),f179(f918(x56191,a909)))),x56192)
% 109.14/108.84 [5620]~P103(x56201)+E(f12(x56201,f318(f318(f300(x56201),x56202),f179(f918(x56201,a909)))),x56202)
% 109.14/108.84 [5621]~P103(x56211)+E(f15(x56211,f318(f318(f300(x56211),x56212),f179(f918(x56211,a909)))),x56212)
% 109.14/108.84 [5622]~P4(x56221)+E(f16(x56221,f318(f318(f300(x56221),x56222),f179(f918(x56221,a909)))),x56222)
% 109.14/108.84 [5623]~P4(x56231)+E(f17(x56231,f318(f318(f300(x56231),x56232),f179(f918(x56231,a909)))),x56232)
% 109.14/108.84 [5645]E(f318(f318(f73(a911),x56451),f318(f318(f3(a911),x56452),x56451)),x56452)+P1(f318(f318(f226(a911),x56452),x56451))
% 109.14/108.84 [5683]E(x56831,f104(x56832))+P1(f318(f318(f226(a911),f2(a911)),f318(f180(f912(x56832)),x56831)))
% 109.14/108.84 [5812]~P4(x58121)+E(f13(x58121,f223(x58121),f318(f318(f300(x58121),x58122),f179(f918(x58121,a909)))),x58122)
% 109.14/108.84 [5813]~P4(x58131)+E(f14(x58131,f224(x58131),f318(f318(f300(x58131),x58132),f179(f918(x58131,a909)))),x58132)
% 109.14/108.84 [5874]E(f318(f318(f3(a911),x58741),f318(f318(f3(a911),x58741),x58742)),x58742)+~P1(f318(f318(f225(a911),x58742),x58741))
% 109.14/108.84 [5875]E(f318(f318(f73(a911),x58751),f318(f318(f3(a911),x58752),x58751)),x58752)+~P1(f318(f318(f225(a911),x58751),x58752))
% 109.14/108.84 [5896]E(f39(a911,f318(f318(f3(a911),x58961),x58962),x58962),f39(a911,x58961,x58962))+P1(f318(f318(f226(a911),x58961),x58962))
% 109.14/108.84 [5897]E(f39(a911,f318(f318(f3(a911),x58971),x58972),x58972),f39(a911,x58971,x58972))+P1(f318(f318(f226(a911),x58971),x58972))
% 109.14/108.84 [5908]E(f318(f72(a1),f318(f318(f30(a1),x59081),f318(f72(a1),x59082))),f284(x59081,x59082))+P1(f318(f318(f225(a1),f2(a1)),x59082))
% 109.14/108.84 [5910]~E(x59102,f2(a911))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f235(a911),x59101),x59102)))
% 109.14/108.84 [5965]~P99(x59651)+E(f318(f318(f73(x59651),f318(f72(x59651),f71(x59651))),f318(f94(x59651),x59652)),f318(f94(x59651),f318(f318(f73(a1),x59652),a88)))
% 109.14/108.84 [5967]E(f318(f318(f235(a911),f318(f94(a911),x59671)),x59672),f318(f318(f235(a911),f2(a911)),x59672))+~P1(f318(a184,f318(f94(a1),x59671)))
% 109.14/108.84 [6074]E(f318(f132(a911),f130(a911,f318(f293(a911,x60741),x60742))),x60741)+~P1(f318(f318(f226(a911),x60741),x60742))
% 109.14/108.84 [6090]E(f318(f318(f74(a911),f318(f94(a911),x60901)),f318(f94(a911),x60902)),f318(f94(a911),f318(f318(f74(a1),x60901),x60902)))+P1(f318(f318(f226(a1),x60901),a76))
% 109.14/108.84 [6096]~P132(x60961)+P1(f318(f318(f225(x60961),f2(x60961)),f318(f318(f74(x60961),x60962),x60962)))
% 109.14/108.84 [6108]E(f318(f318(f3(a911),f318(a103,x61081)),x61082),f318(a103,f318(f318(f3(a911),x61081),x61082)))+~P1(f318(f318(f225(a911),x61082),x61081))
% 109.14/108.84 [6112]E(f39(a911,f318(f318(f3(a911),x61121),x61122),x61122),f39(a911,x61121,x61122))+~P1(f318(f318(f225(a911),x61122),x61121))
% 109.14/108.84 [6165]E(f318(f318(f235(a911),f318(a95,x61651)),x61652),f318(a95,f318(f318(f235(a1),x61651),x61652)))+~P1(f318(f318(f225(a1),f2(a1)),x61651))
% 109.14/108.84 [6166]E(f318(f318(f235(a911),f318(a95,x61661)),x61662),f318(a95,f318(f318(f235(a1),x61661),x61662)))+~P1(f318(f318(f225(a1),f2(a1)),x61661))
% 109.14/108.84 [6184]P1(f318(f128(x61841),x61842))+P1(f318(f318(f226(a911),f662(x61842,x61841)),f318(f180(f912(x61841)),x61842)))
% 109.14/108.84 [6185]P1(f318(f128(x61851),x61852))+P1(f318(f318(f226(a911),f666(x61852,x61851)),f318(f180(f912(x61851)),x61852)))
% 109.14/108.84 [6199]~E(x61991,f104(x61992))+~P1(f318(f318(f226(a911),f2(a911)),f318(f180(f912(x61992)),x61991)))
% 109.14/108.84 [6210]E(f135(a911,f130(a911,f318(f293(a911,x62101),x62102))),f318(f318(f3(a911),x62102),f71(a911)))+~P1(f318(f318(f226(a911),x62101),x62102))
% 109.14/108.84 [6213]E(f318(f318(f73(a1),x62131),f318(f91(a1),f318(a103,f361(x62132,x62131)))),x62132)+~P1(f318(f318(f226(a1),x62131),x62132))
% 109.14/108.84 [6220]E(x62201,f2(a911))+E(f318(f318(f74(a911),x62202),f318(f318(f235(a911),x62202),f318(f318(f3(a911),x62201),f71(a911)))),f318(f318(f235(a911),x62202),x62201))
% 109.14/108.84 [6249]E(f318(f318(f74(a911),f318(a95,x62491)),f318(a95,x62492)),f318(a95,f318(f318(f74(a1),x62491),x62492)))+~P1(f318(f318(f225(a1),f2(a1)),x62491))
% 109.14/108.84 [6250]E(f318(f318(f30(a911),f318(a95,x62501)),f318(a95,x62502)),f318(a95,f318(f318(f30(a1),x62501),x62502)))+~P1(f318(f318(f225(a1),f2(a1)),x62501))
% 109.14/108.84 [6264]~P121(x62641)+E(f318(f318(f73(x62641),x62642),x62642),f318(f318(f74(x62641),f318(f318(f73(x62641),f71(x62641)),f71(x62641))),x62642))
% 109.14/108.84 [6288]E(f318(f318(f3(a1),f318(f91(a1),x62881)),f318(f91(a1),x62882)),f318(f91(a1),f318(f318(f3(a911),x62881),x62882)))+~P1(f318(f318(f225(a911),x62882),x62881))
% 109.14/108.84 [6290]E(f318(f318(f243(a1,a1),f318(f94(a1),a88)),f318(f318(f73(a1),x62901),x62902)),f44(x62901,x62902))+~P1(f318(f318(f225(a1),x62902),f2(a1)))
% 109.14/108.84 [6319]E(f170(x63191,x63192),f104(f912(x63191)))+P1(f318(f318(f320(f912(x63191)),f661(x63192,x63191)),f318(f163(f912(x63191)),x63192)))
% 109.14/108.84 [6328]E(f107(a1,f318(f120(a1),x63281),f119(x63282,f318(f318(f73(a1),x63281),f71(a1)))),f119(x63282,x63281))+P1(f318(f318(f226(a1),x63282),x63281))
% 109.14/108.84 [6403]E(f318(f318(f142(a1),x64031),f169(f318(f318(f73(a1),x64031),f71(a1)),x64032)),f169(x64031,x64032))+~P1(f318(f318(f225(a1),x64031),x64032))
% 109.14/108.84 [6443]~P1(f318(f318(f226(a911),x64432),x64431))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f3(a911),x64431),x64432)))
% 109.14/108.84 [6473]~P1(f318(f318(f226(a911),x64731),f318(a95,x64732)))+P1(f318(f318(f226(a1),f318(f91(a1),x64731)),x64732))
% 109.14/108.84 [6502]~P4(x65021)+E(f318(f318(f101(f918(x65021,a909)),f318(f273(x65021),x65022)),f318(f318(f300(x65021),x65022),f179(f918(x65021,a909)))),f318(f292(x65021),x65022))
% 109.14/108.84 [6503]~P1(f318(f318(f225(a1),f2(a1)),x65031))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f235(a1),x65031),x65032)))
% 109.14/108.84 [6504]~P1(f318(f318(f226(a911),f2(a911)),x65042))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f73(a911),x65041),x65042)))
% 109.14/108.84 [6505]~P1(f318(f318(f226(a911),f2(a911)),x65051))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f73(a911),x65051),x65052)))
% 109.14/108.84 [6506]~P1(f318(f318(f226(a911),f2(a911)),x65061))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f235(a911),x65061),x65062)))
% 109.14/108.84 [6536]~E(f318(x65361,f2(a911)),f2(a911))+E(f318(f318(f8(a911,a911),x65361),f294(a911,f318(a103,f2(a911)),x65362)),f318(f318(f8(a911,a911),x65361),f294(a911,f2(a911),x65362)))
% 109.14/108.84 [6616]E(f318(f318(f300(a1),x66161),f294(a1,f318(f318(f73(a1),x66161),f71(a1)),x66162)),f294(a1,x66161,x66162))+P1(f318(f318(f226(a1),x66162),x66161))
% 109.14/108.84 [6617]P1(f318(f318(f226(a911),x66171),f318(a95,x66172)))+~P1(f318(f318(f226(a1),f318(f91(a1),x66171)),x66172))
% 109.14/108.84 [6718]E(f318(a95,f318(f318(f235(a1),f318(f94(a1),x67181)),f318(f94(a911),x67182))),f318(f318(f235(a911),f318(f94(a911),x67181)),f318(f94(a911),x67182)))+P1(f318(a184,f318(f94(a1),x67181)))
% 109.14/108.84 [6719]E(f318(a95,f318(f318(f30(a1),f318(f94(a1),x67191)),f318(f94(a1),x67192))),f318(f318(f30(a911),f318(f94(a911),x67191)),f318(f94(a911),x67192)))+P1(f318(a184,f318(f94(a1),x67191)))
% 109.14/108.84 [6781]P1(f318(f318(f226(a911),x67811),x67812))+~P1(f318(f318(f226(a911),f2(a911)),f318(f318(f3(a911),x67812),x67811)))
% 109.14/108.84 [6825]P1(f318(f318(f226(a911),f2(a911)),x68251))+~P1(f318(f318(f226(a911),f2(a911)),f318(f318(f74(a911),x68252),x68251)))
% 109.14/108.84 [6826]P1(f318(f318(f226(a911),f2(a911)),x68261))+~P1(f318(f318(f226(a911),f2(a911)),f318(f318(f74(a911),x68261),x68262)))
% 109.14/108.84 [6844]E(f130(a911,f318(f293(a911,f318(f94(a911),x68441)),f318(f94(a911),x68442))),f104(a911))+P1(f318(f318(f226(a911),f318(f94(a911),x68441)),f318(f94(a911),x68442)))
% 109.14/108.84 [6846]~P1(f318(f318(f225(a1),x68461),f2(a1)))+E(f318(f318(f74(a911),f318(a95,f318(f72(a1),x68461))),f318(a95,f318(f72(a1),x68462))),f318(a95,f318(f318(f74(a1),x68461),x68462)))
% 109.14/108.84 [6904]~E(x69042,f179(f918(x69041,a909)))+P1(f318(f318(f225(f918(x69041,a909)),x69042),f318(f72(f918(x69041,a909)),x69042)))
% 109.14/108.84 [7015]~P1(f318(f318(f226(a1),x70151),x70152))+P1(f318(f318(f225(a1),f318(f318(f73(a1),x70151),f71(a1))),x70152))
% 109.14/108.84 [7016]~P1(f318(f318(f226(a1),x70161),x70162))+P1(f318(f318(f225(a1),f318(f318(f73(a1),x70161),f71(a1))),x70162))
% 109.14/108.84 [7083]E(x70831,f2(a911))+~P1(f318(f318(f225(a1),f318(f91(a1),x70832)),f318(f72(a1),f318(f91(a1),x70831))))
% 109.14/108.84 [7084]E(x70841,f2(a911))+~P1(f318(f318(f225(a1),f318(f91(a1),x70841)),f318(f72(a1),f318(f91(a1),x70842))))
% 109.14/108.84 [7188]E(f318(f318(f243(a1,a1),f318(f94(a1),a88)),f318(f318(f73(a1),x71881),x71882)),f44(x71881,x71882))+~P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),x71881),x71882)))
% 109.14/108.84 [7231]~P27(x72311,x72312)+P39(x72311,f318(f242(f918(f917(x72311,x72311),a909),f918(f917(x72311,x72311),a909)),x72312))
% 109.14/108.84 [7250]~P1(f318(f318(f225(a911),f318(a103,f2(a911))),x72501))+P1(f318(f318(f225(a911),f318(a103,f2(a911))),f318(f318(f235(a911),x72501),x72502)))
% 109.14/108.84 [7483]~P1(f318(f318(f226(a911),f2(a911)),x74831))+P1(f318(f318(f226(a911),f318(f318(f3(a911),x74831),f318(a103,x74832))),x74831))
% 109.14/108.84 [7516]P1(f318(f318(f225(a911),f318(a103,f2(a911))),x75161))+~P1(f318(f318(f225(a911),f318(a103,f2(a911))),f318(f318(f74(a911),x75162),x75161)))
% 109.14/108.84 [7517]P1(f318(f318(f225(a911),f318(a103,f2(a911))),x75171))+~P1(f318(f318(f225(a911),f318(a103,f2(a911))),f318(f318(f74(a911),x75171),x75172)))
% 109.14/108.84 [7520]P1(f318(f318(f225(a911),f318(f318(f155(a911),x75201),x75202)),f318(f156(a911),x75201)))+~P1(f318(f318(f226(a911),x75202),f318(f180(f912(a911)),x75201)))
% 109.14/108.84 [7557]P1(f318(f318(f226(a1),x75571),x75572))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),x75571),f71(a1))),x75572))
% 109.14/108.84 [7566]~P1(f318(f318(f320(a911),x75661),x75662))+P1(f318(f318(f320(a1),f318(f91(a1),x75661)),f318(f301(a911,a1,f91(a1)),x75662)))
% 109.14/108.84 [7599]P1(f318(f55(x75991),f233(f918(x75991,a909))))+~P1(f318(f55(f918(x75992,x75991)),f233(f918(f918(x75992,x75991),a909))))
% 109.14/108.84 [7600]P1(f318(f55(x76001),f233(f918(x76001,a909))))+~P1(f318(f55(f919(x76002,x76001)),f233(f918(f919(x76002,x76001),a909))))
% 109.14/108.84 [7601]P1(f318(f55(x76011),f233(f918(x76011,a909))))+~P1(f318(f55(f919(x76011,x76012)),f233(f918(f919(x76011,x76012),a909))))
% 109.14/108.84 [7639]E(x76391,f179(f918(x76392,a909)))+~P1(f318(f318(f225(f918(x76392,a909)),x76391),f318(f72(f918(x76392,a909)),x76391)))
% 109.14/108.84 [7776]E(f318(f133(f912(x77761),f912(x77761),f125(x77761),f104(x77761)),x77762),f104(x77761))+P1(f318(f318(f320(f912(x77761)),f692(x77762,x77761)),f318(f163(f912(x77761)),x77762)))
% 109.14/108.84 [7777]E(f318(f133(f912(x77771),f912(x77771),f125(x77771),f104(x77771)),x77772),f104(x77771))+P1(f318(f318(f320(f912(x77771)),f697(x77772,x77771)),f318(f163(f912(x77771)),x77772)))
% 109.14/108.84 [7916]E(f170(x79161,f318(f318(f142(f912(x79161)),f104(x79161)),x79162)),f170(x79161,x79162))+~P1(f318(f306(f912(f912(x79161)),f171(x79161)),f318(f318(f142(f912(x79161)),f104(x79161)),x79162)))
% 109.14/108.84 [8108]~P121(x81081)+E(f318(f318(f74(x81081),f318(f318(f73(x81081),f71(x81081)),f71(x81081))),f318(f318(f8(a911,x81081),f91(x81081)),f294(a911,f71(a911),x81082))),f318(f318(f74(x81081),f318(f91(x81081),x81082)),f318(f318(f73(x81081),f318(f91(x81081),x81082)),f71(x81081))))
% 109.14/108.84 [8141]E(f318(f318(f142(a1),f318(f94(a1),x81411)),f169(f318(f318(f73(a1),f318(f94(a1),x81411)),f71(a1)),f318(f94(a1),x81412))),f169(f318(f94(a1),x81411),f318(f94(a1),x81412)))+~P1(f318(f318(f225(a1),f318(f94(a1),x81411)),f318(f94(a1),x81412)))
% 109.14/108.84 [8156]P1(f318(f318(f320(a911),x81561),x81562))+~P1(f318(f318(f320(a1),f318(f91(a1),x81561)),f318(f301(a911,a1,f91(a1)),x81562)))
% 109.14/108.84 [8322]~P1(f318(f55(x83221),x83222))+E(f318(f301(a911,x83221,f558(x83222,x83221)),f318(f253(a911),f318(f318(f9(a911,a911,a909),f226(a911)),f559(x83222,x83221)))),x83222)
% 109.14/108.84 [8597]P57(x85971,x85972)+P1(f318(f318(f320(f917(x85971,x85971)),f318(f318(f243(x85971,x85971),f512(x85972,x85971)),f512(x85972,x85971))),x85972))
% 109.14/108.84 [8598]P40(x85981,x85982)+P1(f318(f318(f320(f917(x85981,x85981)),f318(f318(f243(x85981,x85981),f783(x85982,x85981)),f786(x85982,x85981))),x85982))
% 109.14/108.84 [8599]P40(x85991,x85992)+P1(f318(f318(f320(f917(x85991,x85991)),f318(f318(f243(x85991,x85991),f786(x85992,x85991)),f787(x85992,x85991))),x85992))
% 109.14/108.84 [8600]P41(x86001,x86002)+P1(f318(f318(f320(f917(x86001,x86001)),f318(f318(f243(x86001,x86001),f702(x86002,x86001)),f701(x86002,x86001))),x86002))
% 109.14/108.84 [8601]P41(x86011,x86012)+P1(f318(f318(f320(f917(x86011,x86011)),f318(f318(f243(x86011,x86011),f701(x86012,x86011)),f702(x86012,x86011))),x86012))
% 109.14/108.84 [8602]P55(x86021,x86022)+P1(f318(f318(f320(f917(x86021,x86021)),f318(f318(f243(x86021,x86021),f798(x86022,x86021)),f799(x86022,x86021))),x86022))
% 109.14/108.84 [8863]~P1(f318(f318(f225(f918(a911,a909)),x88631),x88632))+P1(f318(f318(f225(f918(a1,a909)),f318(f301(a911,a1,f91(a1)),x88631)),f318(f301(a911,a1,f91(a1)),x88632)))
% 109.14/108.84 [8864]~P1(f318(f318(f226(f918(a911,a909)),x88641),x88642))+P1(f318(f318(f226(f918(a1,a909)),f318(f301(a911,a1,f91(a1)),x88641)),f318(f301(a911,a1,f91(a1)),x88642)))
% 109.14/108.84 [8899]~P99(x88991)+E(f318(f318(f3(x88991),f71(x88991)),f318(f94(x88991),x88992)),f318(f94(x88991),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f318(f72(a1),x88992))))
% 109.14/108.84 [8975]~P1(f318(f318(f320(a911),x89751),f318(f163(a911),x89752)))+P1(f318(f318(f225(a911),x89751),f318(f133(a911,a911,f73(a911),f2(a911)),x89752)))
% 109.14/108.84 [9069]P48(x90691,x90692)+~P1(f318(f318(f320(f917(x90691,x90691)),f318(f318(f243(x90691,x90691),f486(x90692,x90691)),f486(x90692,x90691))),x90692))
% 109.14/108.84 [9070]P40(x90701,x90702)+~P1(f318(f318(f320(f917(x90701,x90701)),f318(f318(f243(x90701,x90701),f783(x90702,x90701)),f787(x90702,x90701))),x90702))
% 109.14/108.84 [9071]P55(x90711,x90712)+~P1(f318(f318(f320(f917(x90711,x90711)),f318(f318(f243(x90711,x90711),f799(x90712,x90711)),f798(x90712,x90711))),x90712))
% 109.14/108.84 [9206]~P1(f318(f318(f225(f918(a1,a909)),f318(f301(a911,a1,f91(a1)),x92061)),f318(f301(a911,a1,f91(a1)),x92062)))+P1(f318(f318(f225(f918(a911,a909)),x92061),x92062))
% 109.14/108.84 [9207]~P1(f318(f318(f226(f918(a1,a909)),f318(f301(a911,a1,f91(a1)),x92071)),f318(f301(a911,a1,f91(a1)),x92072)))+P1(f318(f318(f226(f918(a911,a909)),x92071),x92072))
% 109.14/108.84 [10200]~P111(x102001)+E(f107(f912(x102001),f318(f120(f912(x102001)),f104(x102001)),f318(f318(f318(f85(f913(f912(x102001))),f318(f318(f226(a1),f2(a1)),x102002)),f318(f109(f917(x102001,f912(x102001)),f912(x102001),f122(x102001,f912(x102001),f123(x102001,f318(f318(f3(a1),x102002),f71(a1))),f123(f912(x102001),f318(f318(f3(a1),x102002),f71(a1))))),f318(f248(x102001,f912(x102001),f913(f912(x102001))),f318(f318(f10(f918(f912(x102001),f912(x102001)),f918(f912(x102001),f913(f912(x102001))),x102001),f318(f10(f912(x102001),f913(f912(x102001)),f912(x102001)),f120(f912(x102001)))),f142(x102001))))),f106(f912(x102001)))),f123(f912(x102001),x102002))
% 109.14/108.84 [10221]~P1(f318(f55(x102211),x102212))+E(f318(f180(f912(x102211)),f83(f912(x102211),f318(f318(f20(f912(x102211),a909,a909),f318(f318(f10(a909,f918(a909,a909),f912(x102211)),a316),f318(f318(f9(f912(x102211),f918(x102211,a909),a909),f318(f318(f10(f918(x102211,a909),f918(f918(x102211,a909),a909),f912(x102211)),a315),f163(x102211))),x102212))),f128(x102211)))),f205(x102211,x102212))
% 109.14/108.84 [6209]E(f318(f318(f73(a911),f318(f318(f3(a911),x62091),x62092)),x62092),x62091)+~P1(f318(f318(f225(a911),x62092),x62091))
% 109.14/108.84 [6282]E(f318(f318(f30(a911),f318(f318(f74(a911),x62821),x62822)),x62822),x62821)+~P1(f318(f318(f226(a911),f2(a911)),x62822))
% 109.14/108.84 [6283]E(f318(f318(f30(a911),f318(f318(f74(a911),x62831),x62832)),x62831),x62832)+~P1(f318(f318(f226(a911),f2(a911)),x62831))
% 109.14/108.84 [6289]~P76(x62891)+E(f318(f318(f8(a911,x62891),f318(f155(x62891),x62892)),f318(f293(a911,f2(a911)),f318(f180(f912(x62891)),x62892))),f318(f156(x62891),x62892))
% 109.14/108.84 [6395]E(f39(a911,f318(a103,f318(f318(f74(a911),x63951),x63952)),x63951),f71(a911))+~P1(f318(f318(f226(a911),f71(a911)),x63951))
% 109.14/108.84 [6401]E(f318(a103,f318(f318(f73(a911),f318(f94(a911),x64011)),x64012)),f318(f318(f73(a911),f71(a911)),x64012))+~P1(f318(a184,f318(f94(a1),x64011)))
% 109.14/108.84 [6430]E(f318(a95,f318(f318(f235(a1),f318(f94(a1),x64301)),x64302)),f318(f318(f235(a911),f318(f94(a911),x64301)),x64302))+P1(f318(a184,f318(f94(a1),x64301)))
% 109.14/108.84 [6667]E(f318(f318(f3(a911),x66671),f318(f94(a911),f318(f318(f73(a1),x66672),a88))),f318(f318(f3(a911),f318(a103,x66671)),f318(f94(a911),x66672)))+~P1(f318(f318(f226(a1),a76),x66672))
% 109.14/108.84 [6753]E(x67531,f2(a911))+E(f318(a103,f318(f318(f73(a911),f318(f318(f3(a911),x67531),f71(a911))),x67532)),f318(f318(f73(a911),x67531),x67532))
% 109.14/108.84 [6794]E(x67941,f2(a1))+P1(f318(f318(f226(a1),f2(a1)),f318(f318(f235(a1),f318(f69(a1),x67941)),x67942)))
% 109.14/108.84 [6810]~E(x68102,f2(a911))+P1(f318(f318(f226(a1),f2(a1)),f318(f318(f235(a1),f318(f69(a1),x68101)),x68102)))
% 109.14/108.84 [6849]E(x68491,f2(a911))+E(f318(f318(f73(a911),x68492),f318(f318(f74(a911),f318(f318(f3(a911),x68491),f71(a911))),x68492)),f318(f318(f74(a911),x68491),x68492))
% 109.14/108.84 [6897]~P1(f318(f318(f225(a1),x68971),x68972))+P1(f318(f318(f226(a1),f318(f318(f73(a1),x68971),a88)),x68972))
% 109.14/108.84 [7019]E(f318(f318(f142(a911),x70191),f130(a911,f318(f293(a911,f318(a103,x70191)),x70192))),f130(a911,f318(f293(a911,x70191),x70192)))+~P1(f318(f318(f226(a911),x70191),x70192))
% 109.14/108.84 [7020]E(f318(f318(f142(a911),x70201),f130(a911,f318(f293(a911,f318(a103,x70201)),x70202))),f130(a911,f318(f293(a911,x70201),x70202)))+~P1(f318(f318(f226(a911),x70201),x70202))
% 109.14/108.84 [7225]E(x72251,f104(x72252))+E(f257(x72252,f318(f318(f145(x72252,f917(a90,x72252)),f318(f243(a90,x72252),f71(a90))),x72251)),f266(x72252,x72251))
% 109.14/108.84 [7459]P1(f318(f318(f225(a1),x74591),x74592))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),x74591),a88)),x74592))
% 109.14/108.84 [7460]E(x74601,x74602)+~E(f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x74601)),x74601),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x74602)),x74602))
% 109.14/108.84 [7918]~P1(f318(f318(f226(a911),x79181),x79182))+P1(f318(f318(f320(f917(a911,a911)),f318(f318(f243(a911,a911),x79181),x79182)),a231))
% 109.14/108.84 [8133]~P1(f318(f318(f226(a90),f2(a90)),x81331))+P1(f318(f318(f226(a90),f318(f242(a90,f917(a90,a90)),f318(f258(x81331),x81332))),x81331))
% 109.14/108.84 [8401]~P40(x84011,x84012)+P40(x84011,f318(f318(f101(f918(f917(x84011,x84011),a909)),x84012),f298(x84011,f179(f918(f917(x84011,x84011),a909)))))
% 109.14/108.84 [8402]~P41(x84021,x84022)+P41(x84021,f318(f318(f101(f918(f917(x84021,x84021),a909)),x84022),f298(x84021,f179(f918(f917(x84021,x84021),a909)))))
% 109.14/108.84 [8451]~P91(x84511)+P1(f318(f318(f225(x84511),f318(f69(x84511),f318(f156(x84511),x84512))),f318(f156(x84511),f318(f318(f145(x84511,x84511),f69(x84511)),x84512))))
% 109.14/108.84 [8476]P1(f318(f318(f226(a911),x84761),x84762))+~P1(f318(f318(f320(f917(a911,a911)),f318(f318(f243(a911,a911),x84761),x84762)),a231))
% 109.14/108.84 [8623]E(f318(f318(f243(x86231,x86231),f636(x86232,x86231)),f636(x86232,x86231)),x86232)+~P1(f318(f318(f320(f917(x86231,x86231)),x86232),f298(x86231,f179(f918(f917(x86231,x86231),a909)))))
% 109.14/108.84 [8668]E(f318(f293(a911,x86681),f318(f318(f73(a911),x86681),f318(f29(a911),x86682))),x86682)+~P1(f318(f318(f225(f918(a911,a909)),x86682),f318(f293(a911,x86681),f318(f318(f73(a911),x86681),f318(f29(a911),x86682)))))
% 109.14/108.84 [8689]E(f318(f318(f142(a911),f318(f94(a911),x86891)),f130(a911,f318(f293(a911,f318(a103,f318(f94(a911),x86891))),f318(f94(a911),x86892)))),f130(a911,f318(f293(a911,f318(f94(a911),x86891)),f318(f94(a911),x86892))))+~P1(f318(f318(f226(a911),f318(f94(a911),x86891)),f318(f94(a911),x86892)))
% 109.14/108.84 [8893]P41(x88931,x88932)+~P41(x88931,f318(f318(f101(f918(f917(x88931,x88931),a909)),x88932),f298(x88931,f179(f918(f917(x88931,x88931),a909)))))
% 109.14/108.84 [9114]~P40(x91141,x91142)+P1(f318(f318(f225(f918(f917(x91141,x91141),a909)),f318(f318(f280(x91141,x91141,x91141),x91142),x91142)),x91142))
% 109.14/108.84 [9140]E(f168(f912(x91401),f318(f318(f10(a909,a909,f912(x91401)),a313),f318(f318(f9(f912(x91401),f912(x91401),a909),a315),f104(x91401))),x91402),f170(x91401,f170(x91401,x91402)))+~P13(a911,f318(f159(a911),f318(f318(f145(f912(x91401),a911),f180(f912(x91401))),x91402)))
% 109.14/108.84 [10021]P1(f318(a184,x100212))+E(f318(f318(f81(a1,a911),f318(f318(f3(a1),x100211),x100212)),f318(f318(f20(a1,a911,a911),f318(f318(f9(a1,a911,f918(a911,a911)),f318(f318(f10(a909,f918(a911,f918(a911,a911)),a1),f85(a911)),a184)),f2(a911))),a95)),f318(f318(f3(a911),f318(a95,x100211)),f318(a95,x100212)))
% 109.14/108.84 [10033]E(f318(f318(f81(a1,a911),f318(f94(a1),f318(f318(f73(a1),x100331),f318(f72(a1),x100332)))),f318(f318(f20(a1,a911,a911),f318(f318(f9(a1,a911,f918(a911,a911)),f318(f318(f10(a909,f918(a911,f918(a911,a911)),a1),f85(a911)),a184)),f2(a911))),a95)),f318(f318(f3(a911),f318(f94(a911),x100331)),f318(f94(a911),x100332)))+P1(f318(f318(f226(a1),x100332),a76))
% 109.14/108.84 [10034]~P27(x100341,x100342)+P1(f318(f318(f225(f918(f917(x100341,x100341),a909)),f318(f318(f280(x100341,x100341,x100341),f318(f242(f918(f917(x100341,x100341),a909),f918(f917(x100341,x100341),a909)),x100342)),f318(f247(f918(f917(x100341,x100341),a909),f918(f917(x100341,x100341),a909)),x100342))),f318(f242(f918(f917(x100341,x100341),a909),f918(f917(x100341,x100341),a909)),x100342)))
% 109.14/108.84 [10078]~E(f318(f29(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),f318(f318(f9(a911,f918(a911,a909),a909),f320(a911)),x100781))),f318(f318(f9(a911,a911,a909),f226(a911)),f318(a103,x100782))))),f2(a911))+~P1(f318(f318(f320(a911),f2(a911)),x100781))
% 109.14/108.84 [10086]E(f290(a911,f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100861,x100862),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x100862),x100861))
% 109.14/108.84 [10089]E(f288(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100891,x100892),f179(f918(a911,a909)))+P1(f318(f318(f278(a911),x100891),x100892))
% 109.14/108.84 [10090]E(f291(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100901,x100902),f179(f918(a911,a909)))+P1(f318(f318(f278(a911),x100901),x100902))
% 109.14/108.84 [10091]E(f288(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100911,x100912),f179(f918(a911,a909)))+P1(f318(f318(f278(a911),x100911),x100912))
% 109.14/108.84 [10092]E(f291(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100921,x100922),f179(f918(a911,a909)))+P1(f318(f318(f278(a911),x100921),x100922))
% 109.14/108.84 [10093]E(f288(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100931,x100932),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x100932),x100931))
% 109.14/108.84 [10094]E(f291(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100941,x100942),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x100942),x100941))
% 109.14/108.84 [10095]E(f288(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100951,x100952),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x100952),x100951))
% 109.14/108.84 [10096]E(f288(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100961,x100962),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x100962),x100961))
% 109.14/108.84 [10097]E(f291(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100971,x100972),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x100972),x100971))
% 109.14/108.84 [10098]E(f291(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x100981,x100982),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x100982),x100981))
% 109.14/108.84 [10190]~P5(x101901)+E(f31(x101901,f318(f253(x101901),f318(f318(f10(f918(x101901,a909),a909,x101901),f80(x101901)),f318(f318(f10(f918(x101901,a909),f918(x101901,a909),x101901),f318(f20(x101901,a909,a909),f318(f318(f10(a909,f918(a909,a909),x101901),a321),f318(f318(f9(x101901,f918(x101901,a909),a909),f320(x101901)),x101902)))),f225(x101901))))),f32(x101901,x101902))
% 109.14/108.84 [10216]~P39(x102161,x102162)+P63(x102161,f318(f318(f9(x102161,f918(f917(x102161,x102161),a909),f918(x102161,a909)),f318(f318(f10(f918(x102161,f918(f918(f917(x102161,x102161),a909),a909)),f918(f918(f917(x102161,x102161),a909),f918(x102161,a909)),x102161),f9(x102161,f918(f917(x102161,x102161),a909),a909)),f318(f318(f10(f918(x102161,f917(x102161,x102161)),f918(x102161,f918(f918(f917(x102161,x102161),a909),a909)),x102161),f318(f10(f917(x102161,x102161),f918(f918(f917(x102161,x102161),a909),a909),x102161),f320(f917(x102161,x102161)))),f243(x102161,x102161)))),x102162))
% 109.14/108.84 [10217]~P8(x102171,f233(f918(x102171,a909)),x102172)+P7(x102171,f318(f318(f9(x102171,f918(f917(x102171,x102171),a909),f918(x102171,a909)),f318(f318(f10(f918(x102171,f918(f918(f917(x102171,x102171),a909),a909)),f918(f918(f917(x102171,x102171),a909),f918(x102171,a909)),x102171),f9(x102171,f918(f917(x102171,x102171),a909),a909)),f318(f318(f10(f918(x102171,f917(x102171,x102171)),f918(x102171,f918(f918(f917(x102171,x102171),a909),a909)),x102171),f318(f10(f917(x102171,x102171),f918(f918(f917(x102171,x102171),a909),a909),x102171),f320(f917(x102171,x102171)))),f243(x102171,x102171)))),x102172))
% 109.14/108.84 [10253]P39(x102531,x102532)+~P63(x102531,f318(f318(f9(x102531,f918(f917(x102531,x102531),a909),f918(x102531,a909)),f318(f318(f10(f918(x102531,f918(f918(f917(x102531,x102531),a909),a909)),f918(f918(f917(x102531,x102531),a909),f918(x102531,a909)),x102531),f9(x102531,f918(f917(x102531,x102531),a909),a909)),f318(f318(f10(f918(x102531,f917(x102531,x102531)),f918(x102531,f918(f918(f917(x102531,x102531),a909),a909)),x102531),f318(f10(f917(x102531,x102531),f918(f918(f917(x102531,x102531),a909),a909),x102531),f320(f917(x102531,x102531)))),f243(x102531,x102531)))),x102532))
% 109.14/108.84 [10254]P8(x102541,f233(f918(x102541,a909)),x102542)+~P7(x102541,f318(f318(f9(x102541,f918(f917(x102541,x102541),a909),f918(x102541,a909)),f318(f318(f10(f918(x102541,f918(f918(f917(x102541,x102541),a909),a909)),f918(f918(f917(x102541,x102541),a909),f918(x102541,a909)),x102541),f9(x102541,f918(f917(x102541,x102541),a909),a909)),f318(f318(f10(f918(x102541,f917(x102541,x102541)),f918(x102541,f918(f918(f917(x102541,x102541),a909),a909)),x102541),f318(f10(f917(x102541,x102541),f918(f918(f917(x102541,x102541),a909),a909),x102541),f320(f917(x102541,x102541)))),f243(x102541,x102541)))),x102542))
% 109.14/108.84 [7410]E(f318(f318(f73(a911),f318(f94(a911),f318(f318(f3(a1),x74101),a88))),x74102),f318(a103,f318(f318(f73(a911),f318(f94(a911),x74101)),x74102)))+P1(f318(a184,f318(f94(a1),x74101)))
% 109.14/108.84 [7899]~P99(x78991)+E(f318(f318(f73(x78991),f318(f318(f73(x78991),f71(x78991)),f318(f94(x78991),x78992))),f318(f94(x78991),x78992)),f318(f94(x78991),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x78992)),x78992)))
% 109.14/108.84 [9262]~P1(f318(f318(f225(a1),x92621),x92622))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92621)),x92621)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92622)),x92622)))
% 109.14/108.84 [9263]~P1(f318(f318(f225(a1),x92631),x92632))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92631)),x92631)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92632)),x92632)))
% 109.14/108.84 [9264]~P1(f318(f318(f226(a1),x92641),x92642))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92641)),x92641)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92642)),x92642)))
% 109.14/108.84 [9265]~P1(f318(f318(f226(a1),x92651),x92652))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92651)),x92651)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92652)),x92652)))
% 109.14/108.84 [9506]~P1(f318(f55(x95061),x95062))+P1(f318(f55(f918(x95061,a909)),f318(f253(f918(x95061,a909)),f318(f318(f9(f918(x95061,a909),f918(x95061,a909),a909),f225(f918(x95061,a909))),x95062))))
% 109.14/108.84 [9532]P1(f318(f318(f225(a1),x95321),x95322))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95321)),x95321)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95322)),x95322)))
% 109.14/108.84 [9533]P1(f318(f318(f225(a1),x95331),x95332))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95331)),x95331)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95332)),x95332)))
% 109.14/108.84 [9534]P1(f318(f318(f226(a1),x95341),x95342))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95341)),x95341)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95342)),x95342)))
% 109.14/108.84 [9535]P1(f318(f318(f226(a1),x95351),x95352))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95351)),x95351)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95352)),x95352)))
% 109.14/108.84 [9562]~E(f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),x95621),f179(f918(f917(a911,a911),a909)))),f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),x95622),f179(f918(f917(a911,a911),a909)))))+P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),x95621),x95622)),a99))
% 109.14/108.84 [9640]E(f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),x96401),f179(f918(f917(a911,a911),a909)))),f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),x96402),f179(f918(f917(a911,a911),a909)))))+~P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),x96401),x96402)),a99))
% 109.14/108.84 [9688]P1(f318(f318(f225(a1),f2(a1)),f639(x96881,x96882)))+E(f318(f253(a1),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),x96881)),f318(f253(a1),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),x96882)))
% 109.14/108.84 [9803]~P1(f318(f318(f225(a1),x98031),x98032))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98031)),x98031)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98032)),x98032)))
% 109.14/108.84 [9804]~P1(f318(f318(f225(a1),x98041),x98042))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98041)),x98041)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98042)),x98042)))
% 109.14/108.84 [9805]~P1(f318(f318(f225(a1),x98051),x98052))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98051)),x98051)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98052)),x98052)))
% 109.14/108.84 [9806]~P1(f318(f318(f225(a1),x98061),x98062))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98061)),x98061)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98062)),x98062)))
% 109.14/108.84 [9963]P1(f318(f318(f225(a1),x99631),x99632))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99631)),x99631)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99632)),x99632)))
% 109.14/108.84 [9964]P1(f318(f318(f225(a1),x99641),x99642))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99641)),x99641)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99642)),x99642)))
% 109.14/108.84 [9965]P1(f318(f318(f225(a1),x99651),x99652))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99651)),x99651)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99652)),x99652)))
% 109.14/108.84 [9966]P1(f318(f318(f225(a1),x99661),x99662))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99661)),x99661)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99662)),x99662)))
% 109.14/108.84 [10199]~P5(x101991)+E(f32(x101991,f318(f253(x101991),f318(f318(f10(f918(x101991,a909),a909,x101991),f80(x101991)),f318(f318(f10(f918(x101991,a909),f918(x101991,a909),x101991),f318(f20(x101991,a909,a909),f318(f318(f10(a909,f918(a909,a909),x101991),a321),f318(f318(f9(x101991,f918(x101991,a909),a909),f320(x101991)),x101992)))),f318(f9(x101991,x101991,a909),f225(x101991)))))),f31(x101991,x101992))
% 109.14/108.84 [10220]P1(f318(f318(f320(a911),f2(a911)),x102201))+E(f318(f29(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),f318(f318(f9(a911,f918(a911,a909),a909),f318(f318(f10(a911,f918(f918(a911,a909),a909),a911),f320(a911)),a103)),x102201))),f318(f318(f9(a911,a911,a909),f226(a911)),x102202)))),f318(f29(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),f318(f318(f9(a911,f918(a911,a909),a909),f320(a911)),x102201))),f318(f318(f9(a911,a911,a909),f226(a911)),f318(a103,x102202))))))
% 109.14/108.84 [7964]~P99(x79641)+E(f318(f318(f74(x79641),x79642),f318(f94(x79641),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),x79642)
% 109.14/108.84 [8191]~P99(x81911)+E(f318(f318(f73(x81911),f318(f94(x81911),x81912)),f71(x81911)),f318(f94(x81911),f318(f318(f73(a1),x81912),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))))
% 109.14/108.84 [8235]P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x82352)))+E(f318(f318(f235(a1),x82351),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x82352)),x82352))),f71(a1))
% 109.14/108.84 [9271]E(x92711,x92712)+~E(f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92711)),x92711)),a88),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x92712)),x92712)),a88))
% 109.14/108.84 [9545]~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x95452)))+E(f318(f318(f235(a1),x95451),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95452)),x95452))),f318(f318(f81(a1,a1),f318(f318(f235(a1),x95451),f318(f94(a911),x95452))),f318(f318(f20(a1,a1,a1),f318(f318(f10(a1,f918(a1,a1),a1),f74(a1)),f318(f74(a1),x95451))),f7(a1))))
% 109.14/108.84 [9930]~P1(f318(f318(f225(a911),f643(x99302,x99301)),f318(x99301,f643(x99302,x99301))))+P1(f318(f55(a911),f318(f253(a911),f318(f318(f9(a911,a911,a909),f318(f318(f10(a911,f918(a911,a909),a911),f225(a911)),x99301)),x99302))))
% 109.14/108.84 [10069]~P1(f318(f318(f225(a911),f318(f94(a911),x100691)),f318(a103,x100692)))+P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x100691),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f9(a1,a911,a909),f318(f318(f10(a911,f918(a911,a909),a1),f225(a911)),a95)),x100692))))
% 109.14/108.84 [10070]~P1(f318(f318(f226(a911),f318(f94(a911),x100701)),f318(a103,x100702)))+P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x100701),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f9(a1,a911,a909),f318(f318(f10(a911,f918(a911,a909),a1),f226(a911)),a95)),x100702))))
% 109.14/108.84 [10114]P1(f318(f318(f225(a911),f318(f94(a911),x101141)),f318(a103,x101142)))+~P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x101141),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f9(a1,a911,a909),f318(f318(f10(a911,f918(a911,a909),a1),f225(a911)),a95)),x101142))))
% 109.14/108.84 [10115]P1(f318(f318(f226(a911),f318(f94(a911),x101151)),f318(a103,x101152)))+~P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x101151),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f9(a1,a911,a909),f318(f318(f10(a911,f918(a911,a909),a1),f226(a911)),a95)),x101152))))
% 109.14/108.84 [10144]~P1(f318(f318(f225(a911),f318(a103,x101442)),f318(f94(a911),x101441)))+P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x101441),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f10(a911,a909,a1),f318(f225(a911),x101442)),a95)))))
% 109.14/108.84 [10145]~P1(f318(f318(f226(a911),f318(a103,x101452)),f318(f94(a911),x101451)))+P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x101451),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f10(a911,a909,a1),f318(f226(a911),x101452)),a95)))))
% 109.14/108.84 [10188]P1(f318(f318(f225(a911),f318(a103,x101881)),f318(f94(a911),x101882)))+~P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x101882),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f10(a911,a909,a1),f318(f225(a911),x101881)),a95)))))
% 109.14/108.84 [10189]P1(f318(f318(f226(a911),f318(a103,x101891)),f318(f94(a911),x101892)))+~P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x101892),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f10(a911,a909,a1),f318(f226(a911),x101891)),a95)))))
% 109.14/108.84 [10272]~P1(f318(f318(f320(a911),f2(a911)),x102721))+E(f318(a103,f318(f29(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),f318(f318(f9(a911,f918(a911,a909),a909),f318(f318(f10(a911,f918(f918(a911,a909),a909),a911),f320(a911)),a103)),x102721))),f318(f318(f9(a911,a911,a909),f226(a911)),x102722))))),f318(f29(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),f318(f318(f9(a911,f918(a911,a909),a909),f320(a911)),x102721))),f318(f318(f9(a911,a911,a909),f226(a911)),f318(a103,x102722))))))
% 109.14/108.84 [8829]~P99(x88291)+E(f318(f318(f74(x88291),f318(f94(x88291),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),x88292),x88292)
% 109.14/108.84 [8873]~P99(x88731)+E(f318(f318(f73(x88731),f71(x88731)),f318(f94(x88731),x88732)),f318(f94(x88731),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),x88732)))
% 109.14/108.84 [8914]~P99(x89141)+E(f318(f318(f3(x89141),f318(f94(x89141),x89142)),f71(x89141)),f318(f94(x89141),f318(f318(f73(a1),x89142),f318(f72(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))))
% 109.14/108.84 [9007]~P99(x90071)+E(f318(f318(f74(x90071),f318(f318(f73(x90071),f71(x90071)),f71(x90071))),f318(f94(x90071),x90072)),f318(f94(x90071),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x90072)),x90072)),a88)))
% 109.14/108.84 [9037]~P1(f318(f318(f226(a911),f318(f94(a911),a76)),x90372))+E(f318(f318(f3(a911),x90371),f318(f318(f3(a911),x90372),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),f318(f318(f3(a911),f318(a103,x90371)),x90372))
% 109.14/108.84 [9058]~P99(x90581)+E(f318(f94(x90581),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x90582)),x90582)),a88)),f318(f318(f73(x90581),f318(f318(f73(x90581),f2(x90581)),f318(f94(x90581),x90582))),f318(f94(x90581),x90582)))
% 109.14/108.84 [9654]~P1(f318(f318(f226(a1),x96541),x96542))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96541)),x96541)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96542)),x96542)),a88)))
% 109.14/108.84 [9655]~P1(f318(f318(f226(a1),x96551),x96552))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96551)),x96551)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96552)),x96552)),a88)))
% 109.14/108.84 [9656]~P1(f318(f318(f226(a1),x96561),x96562))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96561)),x96561)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96562)),x96562)),a88)))
% 109.14/108.84 [9657]~P1(f318(f318(f226(a1),x96571),x96572))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96571)),x96571)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96572)),x96572)),a88)))
% 109.14/108.84 [9817]P1(f318(f318(f226(a1),x98171),x98172))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98171)),x98171)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98172)),x98172)),a88)))
% 109.14/108.84 [9818]P1(f318(f318(f226(a1),x98181),x98182))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98181)),x98181)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98182)),x98182)),a88)))
% 109.14/108.84 [9819]P1(f318(f318(f226(a1),x98191),x98192))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98191)),x98191)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98192)),x98192)),a88)))
% 109.14/108.84 [9820]P1(f318(f318(f226(a1),x98201),x98202))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98201)),x98201)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x98202)),x98202)),a88)))
% 109.14/108.84 [9875]~P88(x98751)+E(f318(f318(f235(x98751),x98752),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))),f318(f318(f74(x98751),f318(f318(f74(x98751),x98752),x98752)),x98752))
% 109.14/108.84 [9924]~P1(f318(f318(f225(a1),x99241),x99242))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99241)),x99241)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99242)),x99242)),a88)))
% 109.14/108.84 [9925]~P1(f318(f318(f225(a1),x99251),x99252))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99251)),x99251)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99252)),x99252)),a88)))
% 109.14/108.84 [9926]~P1(f318(f318(f226(a1),x99261),x99262))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99261)),x99261)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99262)),x99262)),a88)))
% 109.14/108.84 [9927]~P1(f318(f318(f226(a1),x99271),x99272))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99271)),x99271)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x99272)),x99272)),a88)))
% 109.14/108.84 [10029]P1(f318(f318(f225(a1),x100291),x100292))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x100291)),x100291)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x100292)),x100292)),a88)))
% 109.14/108.84 [10030]P1(f318(f318(f225(a1),x100301),x100302))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x100301)),x100301)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x100302)),x100302)),a88)))
% 109.14/108.84 [10031]P1(f318(f318(f226(a1),x100311),x100312))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x100311)),x100311)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x100312)),x100312)),a88)))
% 109.14/108.84 [10032]P1(f318(f318(f226(a1),x100321),x100322))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x100321)),x100321)),a88)),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x100322)),x100322)),a88)))
% 109.14/108.84 [9672]~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x96722)))+E(f318(f318(f30(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96721)),x96721))),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96722)),x96722)),a88))),f318(f318(f30(a1),f318(f94(a1),x96721)),f318(f94(a1),x96722)))
% 109.14/108.84 [9695]P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x96952)))+E(f318(f318(f30(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96951)),x96951))),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96952)),x96952)),a88))),f318(f318(f30(a1),f318(f318(f73(a1),f318(f94(a1),x96951)),f71(a1))),f318(f94(a1),x96952)))
% 109.14/108.84 [10178]~E(f318(a103,x101782),f318(f94(a911),x101781))+P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x101781),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f9(a1,a911,a909),f318(f318(f10(a911,f918(a911,a909),a1),a315),a95)),x101782)))))
% 109.14/108.84 [10179]~E(f318(f94(a911),x101791),f318(a103,x101792))+P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x101791),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f9(a1,a911,a909),f318(f318(f10(a911,f918(a911,a909),a1),a315),a95)),x101792)))))
% 109.14/108.84 [10223]E(f318(a103,x102231),f318(f94(a911),x102232))+~P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x102232),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f9(a1,a911,a909),f318(f318(f10(a911,f918(a911,a909),a1),a315),a95)),x102231)))))
% 109.14/108.84 [10224]E(f318(f94(a911),x102241),f318(a103,x102242))+~P1(f318(f318(f81(a1,a909),f318(f94(a1),f318(f318(f73(a1),x102241),a88))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a321),f318(f318(f10(a909,a909,a1),a313),a184))),f318(f318(f9(a1,a911,a909),f318(f318(f10(a911,f918(a911,a909),a1),a315),a95)),x102242)))))
% 109.14/108.84 [10273]~P15(x102731,x102732)+P1(f318(f318(f320(f918(x102731,a909)),f805(x102732,x102731)),f318(f318(f10(f918(x102731,a909),a909,f918(x102731,a909)),f79(x102731)),f318(f318(f10(f918(x102731,a909),f918(x102731,a909),f918(x102731,a909)),f318(f20(x102731,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102731),a316),f318(f318(f20(x102731,x102731,a909),x102732),f7(x102731))))),f318(f318(f9(f918(x102731,a909),f918(x102731,f918(x102731,a909)),f918(x102731,a909)),f318(f318(f10(f918(f918(x102731,a909),a909),f918(f918(x102731,f918(x102731,a909)),f918(x102731,a909)),f918(x102731,a909)),f10(f918(x102731,a909),a909,x102731)),a315)),x102732)))))
% 109.14/108.84 [10343]~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x103432)))+E(f39(a1,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x103431)),x103431)),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x103432)),x103432)),a88))),f318(f318(f73(a1),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f39(a1,f318(f94(a1),x103431),f318(f94(a1),x103432)))),f71(a1)))
% 109.14/108.84 [10345]P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x103452)))+E(f39(a1,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x103451)),x103451)),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x103452)),x103452)),a88))),f318(f318(f3(a1),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f39(a1,f318(f318(f73(a1),f318(f94(a1),x103451)),f71(a1)),f318(f94(a1),x103452)))),f71(a1)))
% 109.14/108.84 [10124]~P121(x101241)+E(f318(f318(f74(x101241),x101242),x101242),f318(f318(f235(x101241),x101242),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.84 [10125]~P88(x101251)+E(f318(f318(f235(x101251),x101252),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f318(f74(x101251),x101252),x101252))
% 109.14/108.84 [10126]~P99(x101261)+E(f318(f318(f74(x101261),x101262),f318(f94(x101261),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f318(f73(x101261),x101262),x101262))
% 109.14/108.84 [10204]~P144(x102041)+E(f318(f318(f235(x102041),f318(f72(x102041),x102042)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f318(f235(x102041),x102042),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.84 [10205]~P116(x102051)+E(f318(f318(f235(x102051),f318(f69(x102051),x102052)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f318(f235(x102051),x102052),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.84 [10203]~P99(x102031)+E(f318(f318(f74(x102031),f318(f94(x102031),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x102032),f318(f318(f73(x102031),x102032),x102032))
% 109.14/108.84 [10243]~P116(x102431)+E(f318(f69(x102431),f318(f318(f235(x102431),x102432),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x102431),x102432),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.84 [10262]~P116(x102621)+P1(f318(f318(f225(x102621),f2(x102621)),f318(f318(f235(x102621),x102622),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.84 [10260]~P99(x102601)+E(f318(f318(f235(x102601),f318(f94(x102601),a88)),f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x102602)),f71(x102601))
% 109.14/108.84 [10261]~P144(x102611)+E(f318(f318(f235(x102611),f318(f72(x102611),f71(x102611))),f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x102612)),f71(x102611))
% 109.14/108.84 [10367]~P1(f318(f318(f225(a1),f2(a1)),x103672))+E(f39(a1,f318(f318(f73(a1),f71(a1)),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103671)),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103672)),f318(f318(f73(a1),f71(a1)),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f39(a1,x103671,x103672))))
% 109.14/108.84 [10380]~P1(f318(f318(f225(a1),f2(a1)),x103802))+E(f318(f318(f30(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103801))),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103802)),f318(f318(f30(a1),x103801),x103802))
% 109.14/108.84 [10381]~P1(f318(f318(f225(a1),x103812),f2(a1)))+E(f318(f318(f30(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103811))),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103812)),f318(f318(f30(a1),f318(f318(f73(a1),x103811),f71(a1))),x103812))
% 109.14/108.84 [10382]~P1(f318(f318(f225(a1),x103822),f2(a1)))+E(f39(a1,f318(f318(f73(a1),f71(a1)),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103821)),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103822)),f318(f318(f3(a1),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f39(a1,f318(f318(f73(a1),x103821),f71(a1)),x103822))),f71(a1)))
% 109.14/108.84 [10326]~P99(x103261)+E(f318(f318(f235(x103261),f318(f94(x103261),a88)),f318(a103,f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103262))),f318(f94(x103261),a88))
% 109.14/108.84 [10328]~P144(x103281)+E(f318(f318(f235(x103281),f318(f72(x103281),f71(x103281))),f318(a103,f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103282))),f318(f72(x103281),f71(x103281)))
% 109.14/108.84 [5065]P40(x50651,x50652)+~P8(x50651,x50653,x50652)
% 109.14/108.84 [5066]P40(x50661,x50662)+~P8(x50661,x50663,x50662)
% 109.14/108.84 [5067]P55(x50671,x50672)+~P8(x50671,x50673,x50672)
% 109.14/108.84 [5068]P55(x50681,x50682)+~P8(x50681,x50683,x50682)
% 109.14/108.84 [5242]~P8(x52421,x52422,x52423)+P56(x52421,x52422,x52423)
% 109.14/108.84 [5243]~P8(x52431,x52432,x52433)+P56(x52431,x52432,x52433)
% 109.14/108.84 [8171]~E(x81712,x81713)+P36(x81711,x81711,a315,x81712,x81713)
% 109.14/108.84 [8725]E(x87251,x87252)+~P36(x87253,x87253,a315,x87251,x87252)
% 109.14/108.84 [4874]E(f160(x48741,x48742,x48743),f104(x48741))+~E(x48742,f2(a911))
% 109.14/108.84 [4875]E(f160(x48751,x48752,x48753),f104(x48751))+~E(x48752,f2(a911))
% 109.14/108.84 [5040]~E(f160(x50402,x50401,x50403),f104(x50402))+E(x50401,f2(a911))
% 109.14/108.84 [5041]~E(f160(x50412,x50411,x50413),f104(x50412))+E(x50411,f2(a911))
% 109.14/108.84 [5248]~P39(x52481,x52483)+P39(x52481,f312(x52481,x52482,x52483))
% 109.14/108.84 [5360]~P31(x53601,x53602,x53603)+P33(a1,x53601,f169(x53602,x53603))
% 109.14/108.84 [5409]P28(x54091,x54092,x54093)+~P28(x54091,f318(a103,x54092),x54093)
% 109.14/108.84 [5428]P31(x54281,x54282,x54283)+~P33(a1,x54281,f169(x54282,x54283))
% 109.14/108.84 [5499]~P8(x54991,x54992,x54993)+P8(f912(x54991),f152(x54991,x54992),f149(x54991,x54993))
% 109.14/108.84 [5500]~P56(x55001,x55002,x55003)+P56(f912(x55001),f152(x55001,x55002),f149(x55001,x55003))
% 109.14/108.84 [5612]P58(x56121,x56122,x56123)+~E(f591(x56123,x56122,x56121),f592(x56123,x56122,x56121))
% 109.14/108.84 [5613]P59(x56131,x56132,x56133)+~E(f613(x56133,x56132,x56131),f614(x56133,x56132,x56131))
% 109.14/108.84 [6574]P29(x65741,x65742,x65743)+~P28(x65741,f634(x65743,x65742,x65741),f770(x65743,x65742,x65741))
% 109.14/108.84 [8177]~E(x81772,x81773)+P26(x81771,x81771,f25(x81771),x81772,x81773)
% 109.14/108.84 [8733]E(x87331,x87332)+~P26(x87333,x87333,f25(x87333),x87331,x87332)
% 109.14/108.84 [4830]~E(f318(f159(x48302),x48301),x48303)+E(x48301,f318(f159(x48302),x48303))
% 109.14/108.84 [4831]~E(x48312,f318(f159(x48311),x48313))+E(f318(f159(x48311),x48312),x48313)
% 109.14/108.84 [4881]E(x48811,x48812)+~E(f318(f159(x48813),x48811),f318(f159(x48813),x48812))
% 109.14/108.84 [5092]~P7(x50923,x50921)+P1(f318(f318(x50921,x50922),x50922))
% 109.14/108.84 [5093]~P51(x50933,x50931)+P1(f318(f318(x50931,x50932),x50932))
% 109.14/108.84 [5094]~P63(x50941,x50942)+P1(f318(f306(x50941,x50942),x50943))
% 109.14/108.84 [5095]~P63(x50951,x50952)+P1(f318(f306(x50951,x50952),x50953))
% 109.14/108.84 [5160]~P39(x51601,x51602)+P39(f912(x51601),f318(f134(x51601,x51602),x51603))
% 109.14/108.84 [5165]~P1(f318(x51652,x51653))+~E(f318(f253(x51651),x51652),f179(f918(x51651,a909)))
% 109.14/108.84 [5166]~P1(f318(x51662,x51663))+~E(f179(f918(x51661,a909)),f318(f253(x51661),x51662))
% 109.14/108.84 [5178]E(x51781,f2(a911))+E(f135(x51782,f160(x51782,x51781,x51783)),x51783)
% 109.14/108.84 [5194]~P1(f318(x51941,x51943))+P1(f318(x51941,f83(x51942,x51941)))
% 109.14/108.84 [5195]~P1(f318(x51951,x51953))+P1(f318(x51951,f83(x51952,x51951)))
% 109.14/108.84 [5196]~P1(f318(x51961,x51963))+P1(f318(x51961,f83(x51962,x51961)))
% 109.14/108.84 [5197]~P1(f318(x51971,x51973))+P1(f318(x51971,f83(x51972,x51971)))
% 109.14/108.84 [5198]~P1(f318(x51981,x51983))+P1(f318(x51981,f732(x51981,x51982)))
% 109.14/108.84 [5210]E(x52101,f2(a911))+E(f318(f132(x52102),f160(x52102,x52101,x52103)),x52103)
% 109.14/108.84 [5322]~E(x53222,x53223)+P1(f318(f318(f320(x53221),x53222),f318(a315,x53223)))
% 109.14/108.84 [5337]~E(x53372,f2(a911))+E(f318(f163(x53371),f160(x53371,x53372,x53373)),f179(f918(x53371,a909)))
% 109.14/108.84 [5382]E(f318(f159(x53821),x53822),f318(f318(f142(x53821),x53823),f104(x53821)))+~E(x53822,f318(f318(f142(x53821),x53823),f104(x53821)))
% 109.14/108.84 [5383]~E(x53833,f318(f318(f142(x53831),x53832),f104(x53831)))+E(f318(f318(f142(x53831),x53832),f104(x53831)),f318(f159(x53831),x53833))
% 109.14/108.84 [5424]~P35(x54241,x54242,x54243)+P35(x54241,x54242,f318(f159(x54241),x54243))
% 109.14/108.84 [5425]~P33(x54251,x54252,x54253)+P33(x54251,x54252,f318(f159(x54251),x54253))
% 109.14/108.84 [5429]E(f318(f29(x54291),f852(x54292,x54293,x54291)),x54292)+~E(f318(f29(x54291),x54293),f318(a103,x54292))
% 109.14/108.84 [5435]~P39(x54351,x54353)+P1(f318(f318(f320(x54351),x54352),f307(x54351,x54353)))
% 109.14/108.84 [5436]~P39(x54361,x54363)+P1(f318(f318(f320(x54361),x54362),f307(x54361,x54363)))
% 109.14/108.84 [5440]~E(f318(f159(x54402),x54401),f318(f318(f142(x54402),x54403),f104(x54402)))+E(x54401,f318(f318(f142(x54402),x54403),f104(x54402)))
% 109.14/108.84 [5441]~E(f318(f318(f142(x54412),x54413),f104(x54412)),f318(f159(x54412),x54411))+E(x54411,f318(f318(f142(x54412),x54413),f104(x54412)))
% 109.14/108.84 [5464]E(f78(f917(a911,a911),f42(x54641,x54642)),x54643)+~P1(f318(f42(x54641,x54642),x54643))
% 109.14/108.84 [5503]P35(x55031,x55032,x55033)+~P35(x55031,x55032,f318(f159(x55031),x55033))
% 109.14/108.84 [5504]P33(x55041,x55042,x55043)+~P33(x55041,x55042,f318(f159(x55041),x55043))
% 109.14/108.84 [5543]P1(f318(f318(x55431,x55432),x55432))+~P1(f318(f261(x55433,x55431),x55432))
% 109.14/108.84 [5544]~P1(f318(f318(x55442,x55443),x55443))+P1(f318(f261(x55441,x55442),x55443))
% 109.14/108.84 [5566]~E(x55662,f104(x55661))+P1(f318(f318(f320(f912(x55661)),x55662),f152(x55661,x55663)))
% 109.14/108.84 [5575]~P56(x55751,x55752,x55753)+P56(x55751,x55752,f318(f277(x55751,x55751),x55753))
% 109.14/108.84 [5576]~P59(x55761,x55762,x55763)+P59(x55761,x55762,f318(f277(x55761,x55761),x55763))
% 109.14/108.84 [5593]~P69(x55931)+E(f39(x55931,f39(x55931,x55932,x55933),x55933),f39(x55931,x55932,x55933))
% 109.14/108.84 [5694]E(x56941,x56942)+~P1(f318(f318(f320(x56943),x56941),f318(a315,x56942)))
% 109.14/108.84 [5743]~P114(x57431)+E(f181(x57431,x57432,f2(a911),x57433),x57433)
% 109.14/108.84 [5765]P56(x57651,x57652,x57653)+~P56(x57651,x57652,f318(f277(x57651,x57651),x57653))
% 109.14/108.84 [5766]P59(x57661,x57662,x57663)+~P59(x57661,x57662,f318(f277(x57661,x57661),x57663))
% 109.14/108.84 [5770]~P4(x57702)+E(f141(x57701,x57702,x57703,f104(x57701)),f104(x57701))
% 109.14/108.84 [5783]E(f161(x57831,x57832,f143(x57831,x57833)),f143(x57831,f161(x57831,x57832,x57833)))+~P1(f318(f128(x57831),x57833))
% 109.14/108.84 [5882]~P1(f318(f318(x58823,x58822),x58822))+P1(f318(f318(f320(x58821),x58822),f261(x58821,x58823)))
% 109.14/108.84 [5884]E(f318(f127(x58841,x58842),x58843),f104(x58841))+P1(f318(x58842,f678(x58843,x58842,x58841)))
% 109.14/108.84 [5943]E(f62(x59431,x59432,x59433),x59432)+P1(f318(x59433,f733(x59432,x59431,x59433)))
% 109.14/108.84 [6041]~P1(f318(f128(x60411),x60412))+P1(f318(f128(x60411),f167(x60411,x60412,x60413)))
% 109.14/108.84 [6042]~P1(f318(f128(x60421),x60423))+P1(f318(f128(x60421),f161(x60421,x60422,x60423)))
% 109.14/108.84 [6043]~P1(f318(f128(x60431),x60433))+P1(f318(f128(x60431),f168(x60431,x60432,x60433)))
% 109.14/108.84 [6044]~P1(f318(f128(x60441),x60443))+P1(f318(f128(x60441),f131(x60441,x60442,x60443)))
% 109.14/108.84 [6045]~P151(x60451,x60452,x60453)+P1(f318(x60451,f39(a1,x60452,x60453)))
% 109.14/108.84 [6060]~P35(x60603,x60601,x60602)+P1(f318(x60601,f746(x60602,x60601,x60603)))
% 109.14/108.84 [6061]~P37(x60613,x60611,x60612)+P1(f318(x60611,f759(x60612,x60611,x60613)))
% 109.14/108.84 [6062]~P37(x60623,x60621,x60622)+P1(f318(x60621,f769(x60622,x60621,x60623)))
% 109.14/108.84 [6063]~P35(x60633,x60631,x60632)+P1(f318(x60631,f790(x60632,x60631,x60633)))
% 109.14/108.84 [6064]~P35(x60643,x60641,x60642)+P1(f318(x60641,f791(x60641,x60642,x60643)))
% 109.14/108.84 [6069]P1(f318(f318(x60691,x60692),x60692))+~P1(f318(f318(f320(x60693),x60692),f261(x60693,x60691)))
% 109.14/108.84 [6084]E(f318(f127(x60841,x60842),x60843),f168(x60841,x60842,x60843))+P1(f318(x60842,f717(x60843,x60842,x60841)))
% 109.14/108.84 [6126]~P1(f318(f128(x61261),x61263))+P1(f318(f128(f912(x61261)),f49(x61261,x61262,x61263)))
% 109.14/108.84 [6160]~P113(x61601)+E(f318(f318(f92(f918(x61601,a909)),f318(f273(x61601),x61602)),f294(x61601,x61602,x61603)),f179(f918(x61601,a909)))
% 109.14/108.84 [6161]~P113(x61611)+E(f318(f318(f92(f918(x61611,a909)),f318(f292(x61611),x61612)),f296(x61611,x61612,x61613)),f179(f918(x61611,a909)))
% 109.14/108.84 [6162]~P113(x61621)+E(f318(f318(f92(f918(x61621,a909)),f318(f292(x61621),x61622)),f297(x61621,x61622,x61623)),f179(f918(x61621,a909)))
% 109.14/108.84 [6391]E(f318(f127(x63911,x63912),x63913),x63913)+~P1(f318(x63912,f679(x63913,x63912,x63911)))
% 109.14/108.84 [6393]E(f318(f318(f300(x63931),f854(x63932,x63933,x63931)),f852(x63932,x63933,x63931)),x63933)+~E(f318(f29(x63931),x63933),f318(a103,x63932))
% 109.14/108.84 [6408]P151(x64081,x64082,x64083)+~P1(f318(x64081,f39(a1,x64082,x64083)))
% 109.14/108.84 [6458]P32(x64581,x64582,x64583)+~P1(f318(x64581,f520(x64583,x64582,x64581)))
% 109.14/108.84 [6459]P33(x64591,x64592,x64593)+~P1(f318(x64592,f760(x64593,x64592,x64591)))
% 109.14/108.84 [6460]P33(x64601,x64602,x64603)+~P1(f318(x64602,f761(x64602,x64603,x64601)))
% 109.14/108.84 [6461]P33(x64611,x64612,x64613)+~P1(f318(x64612,f762(x64613,x64612,x64611)))
% 109.14/108.84 [6462]P31(x64621,x64622,x64623)+~P1(f318(x64621,f781(x64623,x64622,x64621)))
% 109.14/108.84 [6464]E(f168(x64641,x64642,x64643),x64643)+~P1(f318(x64642,f712(x64643,x64642,x64641)))
% 109.14/108.84 [6543]~P1(f318(x65432,f465(x65433,x65432,x65431)))+P1(f318(f239(x65431,x65432),x65433))
% 109.14/108.84 [6544]~P1(f318(x65442,f680(x65443,x65442,x65441)))+P1(f318(f151(x65441,x65442),x65443))
% 109.14/108.84 [6795]~P1(f318(f306(x67951,x67952),f491(x67953,x67952,x67951)))+P1(f318(f306(x67951,x67952),x67953))
% 109.14/108.84 [6796]~P1(f318(f306(x67961,x67962),f494(x67963,x67962,x67961)))+P1(f318(f306(x67961,x67962),x67963))
% 109.14/108.84 [7411]~P69(x74111)+E(f318(f318(f73(x74111),f318(f318(f74(x74111),x74112),f318(f318(f30(x74111),x74113),x74112))),f39(x74111,x74113,x74112)),x74113)
% 109.14/108.84 [7437]P31(x74371,x74372,x74373)+P1(f318(f318(f320(a1),f781(x74373,x74372,x74371)),f294(a1,x74372,x74373)))
% 109.14/108.84 [7856]E(f318(f318(f243(x78561,x78561),f523(x78562,x78563,x78561)),f523(x78562,x78563,x78561)),x78563)+~P1(f318(f318(f320(f917(x78561,x78561)),x78563),f254(x78561,x78562)))
% 109.14/108.84 [7978]~P1(f318(f318(f320(x79781),f532(x79783,x79782,x79781)),f307(x79781,x79783)))+P1(f318(f318(f320(x79781),x79782),f307(x79781,x79783)))
% 109.14/108.84 [7979]~P1(f318(f318(f320(x79791),f596(x79793,x79792,x79791)),f307(x79791,x79793)))+P1(f318(f318(f320(x79791),x79792),f307(x79791,x79793)))
% 109.14/108.84 [7980]~P1(f318(f318(f320(x79801),f598(x79803,x79802,x79801)),f307(x79801,x79803)))+P1(f318(f318(f320(x79801),x79802),f307(x79801,x79803)))
% 109.14/108.84 [8070]P35(a1,x80701,f169(x80702,x80703))+P31(f318(f66(a909,a909,a1,a313),x80701),x80702,x80703)
% 109.14/108.84 [8151]~P69(x81511)+E(f318(f318(f73(x81511),f318(f318(f74(x81511),f318(f318(f30(x81511),x81512),x81513)),x81513)),f39(x81511,x81512,x81513)),x81512)
% 109.14/108.84 [8152]~P69(x81521)+E(f318(f318(f73(x81521),f318(f318(f74(x81521),f318(f318(f30(x81521),x81522),x81523)),x81523)),f39(x81521,x81522,x81523)),x81522)
% 109.14/108.84 [8203]~E(f318(f29(x82031),x82032),f318(a103,x82033))+~P1(f318(f318(f320(x82031),f854(x82033,x82032,x82031)),f852(x82033,x82032,x82031)))
% 109.14/108.84 [8640]~P35(a1,x86401,f169(x86402,x86403))+~P31(f318(f66(a909,a909,a1,a313),x86401),x86402,x86403)
% 109.14/108.84 [8824]P1(f318(f318(f225(f918(f917(x88241,x88241),a909)),f298(x88241,x88242)),f298(x88241,x88243)))+~P1(f318(f318(f225(f918(f917(x88241,x88241),a909)),x88242),f298(x88241,x88243)))
% 109.14/108.84 [8959]~P26(x89591,x89592,x89593,f233(f918(x89591,a909)),f233(f918(x89592,a909)))+P25(x89591,x89592,x89593,f233(f918(x89591,a909)))
% 109.14/108.84 [8960]~P26(x89601,x89602,x89603,f233(f918(x89601,a909)),f233(f918(x89602,a909)))+P25(x89601,x89602,x89603,f233(f918(x89601,a909)))
% 109.14/108.84 [9110]E(x91101,f104(x91102))+~P1(f318(f318(f320(f917(f912(x91102),f912(x91102))),f318(f318(f243(f912(x91102),f912(x91102)),x91101),f104(x91102))),f149(x91102,x91103)))
% 109.14/108.84 [9134]E(x91341,f104(x91342))+~P1(f318(f318(f320(f917(f912(x91342),f912(x91342))),f318(f318(f243(f912(x91342),f912(x91342)),f104(x91342)),x91341)),f149(x91342,x91343)))
% 109.14/108.84 [9247]E(f318(f318(f142(x92471),f686(x92472,x92473,x92471)),f687(x92472,x92473,x92471)),x92473)+~P1(f318(f318(f320(f917(f912(x92471),f912(x92471))),f318(f318(f243(f912(x92471),f912(x92471)),f104(x92471)),x92473)),f138(x92471,x92472)))
% 109.14/108.84 [9499]~P132(x94991)+~P1(f318(f318(f226(x94991),f318(f318(f73(x94991),f318(f318(f74(x94991),x94992),x94992)),f318(f318(f74(x94991),x94993),x94993))),f2(x94991)))
% 109.14/108.84 [9555]P1(f318(f55(x95551),x95552))+~P1(f318(f318(f320(f917(f918(x95551,a909),f918(x95551,a909))),f318(f318(f243(f918(x95551,a909),f918(x95551,a909)),x95553),x95552)),f305(x95551)))
% 109.14/108.84 [9867]~P49(x98671,x98672,x98673)+P1(f318(f318(f225(a1),f318(f318(f66(f917(a1,a1),a1,x98671,f242(a1,a1)),f203(x98671)),f221(x98671,x98672,f218(x98671,x98673)))),f2(a1)))
% 109.14/108.84 [9868]~P50(x98681,x98682,x98683)+P1(f318(f318(f226(a1),f318(f318(f66(f917(a1,a1),a1,x98681,f242(a1,a1)),f203(x98681)),f221(x98681,x98682,f218(x98681,x98683)))),f2(a1)))
% 109.14/108.84 [10003]P50(x100031,x100032,x100033)+~P1(f318(f318(f226(a1),f318(f318(f66(f917(a1,a1),a1,x100031,f242(a1,a1)),f203(x100031)),f221(x100031,x100032,f218(x100031,x100033)))),f2(a1)))
% 109.14/108.84 [10004]P49(x100041,x100042,x100043)+~P1(f318(f318(f225(a1),f318(f318(f66(f917(a1,a1),a1,x100041,f242(a1,a1)),f203(x100041)),f221(x100041,x100042,f218(x100041,x100043)))),f2(a1)))
% 109.14/108.84 [10427]~P116(x104271)+~P1(f318(f318(f226(x104271),f318(f318(f73(x104271),f318(f318(f235(x104271),x104272),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x104271),x104273),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))),f2(x104271)))
% 109.14/108.84 [4858]~E(x48583,f104(x48581))+E(f318(f318(f125(x48581),x48582),x48583),x48582)
% 109.14/108.84 [4859]~E(x48592,f104(x48591))+E(f318(f318(f125(x48591),x48592),x48593),x48593)
% 109.14/108.84 [4860]~E(x48603,f104(x48601))+E(f318(f318(f125(x48601),x48602),x48603),x48602)
% 109.14/108.84 [4861]~E(x48612,f104(x48611))+E(f318(f318(f125(x48611),x48612),x48613),x48613)
% 109.14/108.84 [4867]~E(x48672,f2(a911))+E(f318(f318(f166(x48671),x48672),x48673),f104(x48671))
% 109.14/108.84 [4876]~E(x48763,f104(x48761))+E(f318(f318(f166(x48761),x48762),x48763),f104(x48761))
% 109.14/108.84 [4915]~E(x49151,x49153)+E(x49151,f318(f318(f125(x49152),f104(x49152)),x49153))
% 109.14/108.84 [5003]~P115(x50032)+E(f318(f233(f918(x50031,x50032)),x50033),f233(x50032))
% 109.14/108.84 [5004]~P109(x50042)+E(f318(f179(f918(x50041,x50042)),x50043),f179(x50042))
% 109.14/108.84 [5005]~P109(x50052)+E(f318(f179(f918(x50051,x50052)),x50053),f179(x50052))
% 109.14/108.84 [5021]E(x50211,f104(x50212))+~E(f318(f318(f125(x50212),x50211),x50213),x50213)
% 109.14/108.84 [5022]E(x50221,f104(x50222))+~E(f318(f318(f125(x50222),x50223),x50221),x50223)
% 109.14/108.84 [5023]E(x50231,f104(x50232))+~E(f318(f318(f125(x50232),x50233),x50231),x50233)
% 109.14/108.84 [5024]E(x50241,f104(x50242))+~E(f318(f318(f125(x50242),x50241),x50243),x50243)
% 109.14/108.84 [5030]E(x50301,f104(x50302))+~E(f318(f318(f125(x50302),x50303),x50301),f104(x50302))
% 109.14/108.84 [5031]E(x50311,f104(x50312))+~E(f318(f318(f125(x50312),x50311),x50313),f104(x50312))
% 109.14/108.84 [5032]E(x50321,f104(x50322))+~E(f318(f318(f125(x50322),x50323),x50321),f104(x50322))
% 109.14/108.84 [5033]E(x50331,f104(x50332))+~E(f318(f318(f125(x50332),x50331),x50333),f104(x50332))
% 109.14/108.84 [5058]~E(x50582,f2(a911))+E(f318(f318(f74(a911),x50581),x50582),f318(f318(f74(a911),x50583),x50582))
% 109.14/108.84 [5059]~E(x50591,f2(a911))+E(f318(f318(f74(a911),x50591),x50592),f318(f318(f74(a911),x50591),x50593))
% 109.14/108.84 [5060]~E(x50601,f2(a911))+E(f318(f318(f74(a911),x50601),x50602),f318(f318(f74(a911),x50601),x50603))
% 109.14/108.84 [5119]~P102(x51191)+E(f318(f318(f101(x51191),x51192),x51193),f318(f318(f101(x51191),x51193),x51192))
% 109.14/108.84 [5120]~P102(x51201)+E(f318(f318(f101(x51201),x51202),x51203),f318(f318(f101(x51201),x51203),x51202))
% 109.14/108.84 [5121]~P103(x51211)+E(f318(f318(f101(x51211),x51212),x51213),f318(f318(f101(x51211),x51213),x51212))
% 109.14/108.84 [5122]~P103(x51221)+E(f318(f318(f92(x51221),x51222),x51223),f318(f318(f92(x51221),x51223),x51222))
% 109.14/108.84 [5123]~P108(x51231)+E(f318(f318(f92(x51231),x51232),x51233),f318(f318(f92(x51231),x51233),x51232))
% 109.14/108.84 [5124]~P108(x51241)+E(f318(f318(f92(x51241),x51242),x51243),f318(f318(f92(x51241),x51243),x51242))
% 109.14/108.84 [5125]~P121(x51251)+E(f318(f318(f73(x51251),x51252),x51253),f318(f318(f73(x51251),x51253),x51252))
% 109.14/108.84 [5126]~P121(x51261)+E(f318(f318(f74(x51261),x51262),x51263),f318(f318(f74(x51261),x51263),x51262))
% 109.14/108.84 [5127]~P4(x51271)+E(f318(f318(f223(x51271),x51272),x51273),f318(f318(f223(x51271),x51273),x51272))
% 109.14/108.84 [5128]~P4(x51281)+E(f318(f318(f223(x51281),x51282),x51283),f318(f318(f223(x51281),x51283),x51282))
% 109.14/108.84 [5129]~P4(x51291)+E(f318(f318(f224(x51291),x51292),x51293),f318(f318(f224(x51291),x51293),x51292))
% 109.14/108.84 [5130]~P4(x51301)+E(f318(f318(f224(x51301),x51302),x51303),f318(f318(f224(x51301),x51303),x51302))
% 109.14/108.84 [5192]E(f39(a911,x51921,x51922),f2(a911))+~E(x51921,f318(f318(f74(a911),x51922),x51923))
% 109.14/108.84 [5193]E(f39(a1,x51931,x51932),f2(a1))+~E(x51931,f318(f318(f74(a1),x51932),x51933))
% 109.14/108.84 [5260]E(x52601,x52602)+~E(f318(f318(f73(a911),x52603),x52601),f318(f318(f73(a911),x52603),x52602))
% 109.14/108.84 [5261]E(x52611,x52612)+~E(f318(f318(f73(a911),x52611),x52613),f318(f318(f73(a911),x52612),x52613))
% 109.14/108.84 [5273]~P96(x52731)+E(f318(f318(f92(x52731),x52732),f318(f72(x52731),x52733)),f318(f318(f3(x52731),x52732),x52733))
% 109.14/108.84 [5274]~P66(x52741)+E(f318(f318(f73(x52741),x52742),f318(f72(x52741),x52743)),f318(f318(f3(x52741),x52742),x52743))
% 109.14/108.84 [5275]~P67(x52751)+E(f318(f318(f73(x52751),x52752),f318(f72(x52751),x52753)),f318(f318(f3(x52751),x52752),x52753))
% 109.14/108.84 [5276]~P117(x52761)+E(f318(f318(f73(x52761),x52762),f318(f72(x52761),x52763)),f318(f318(f3(x52761),x52762),x52763))
% 109.14/108.84 [5277]~P66(x52771)+E(f318(f318(f3(x52771),x52772),f318(f72(x52771),x52773)),f318(f318(f73(x52771),x52772),x52773))
% 109.14/108.84 [5315]~P1(f318(x53153,x53152))+P1(f318(f318(f320(x53151),x53152),x53153))
% 109.14/108.84 [5316]~P76(x53162)+E(f318(f318(f8(x53161,x53162),x53163),f179(f918(x53161,a909))),f2(x53162))
% 109.14/108.84 [5317]~P76(x53172)+E(f318(f318(f8(x53171,x53172),x53173),f179(f918(x53171,a909))),f2(x53172))
% 109.14/108.84 [5318]~P82(x53182)+E(f318(f318(f11(x53181,x53182),x53183),f179(f918(x53181,a909))),f71(x53182))
% 109.14/108.84 [5319]~P82(x53192)+E(f318(f318(f11(x53191,x53192),x53193),f179(f918(x53191,a909))),f71(x53192))
% 109.14/108.84 [5372]~E(x53722,f318(f318(f73(a911),x53721),x53723))+P1(f318(f318(f225(a911),x53721),x53722))
% 109.14/108.84 [5375]~E(x53752,f179(f918(x53751,a909)))+E(f318(f318(f54(x53751),x53752),x53753),f179(f918(f918(x53751,a909),a909)))
% 109.14/108.84 [5376]~E(x53762,f179(f918(x53761,a909)))+E(f179(f918(f918(x53761,a909),a909)),f318(f318(f54(x53761),x53762),x53763))
% 109.14/108.84 [5444]~E(f318(f275(x54442,x54443),x54441),f179(f918(x54443,a909)))+E(x54441,f179(f918(f917(x54442,x54443),a909)))
% 109.14/108.84 [5445]~E(f318(f255(x54452,x54453),x54451),f179(f918(x54452,a909)))+E(x54451,f179(f918(f917(x54452,x54453),a909)))
% 109.14/108.84 [5477]E(f318(f275(x54771,x54772),x54773),f179(f918(x54772,a909)))+~E(x54773,f179(f918(f917(x54771,x54772),a909)))
% 109.14/108.84 [5478]E(f318(f255(x54781,x54782),x54783),f179(f918(x54781,a909)))+~E(x54783,f179(f918(f917(x54781,x54782),a909)))
% 109.14/108.84 [5481]E(f265(x54811,x54812,x54813),f318(f318(f3(a90),x54812),x54813))+P1(f318(f318(f226(a90),x54812),x54813))
% 109.14/108.84 [5497]P1(f318(x54971,x54972))+~P1(f318(f318(f320(x54973),x54972),x54971))
% 109.14/108.84 [5536]E(x55361,x55362)+~E(f318(f72(f918(x55363,a909)),x55361),f318(f72(f918(x55363,a909)),x55362))
% 109.14/108.84 [5545]~E(x55451,f179(f918(x55452,a909)))+~P1(f318(f318(f320(x55452),x55453),x55451))
% 109.14/108.84 [5546]~E(x55461,f179(f918(x55462,a909)))+~P1(f318(f318(f320(x55462),x55463),x55461))
% 109.14/108.84 [5547]~E(x55471,f179(f918(x55472,a909)))+~P1(f318(f318(f320(x55472),x55473),x55471))
% 109.14/108.84 [5577]~E(x55772,f318(f318(f73(a1),x55771),f318(f91(a1),x55773)))+P1(f318(f318(f225(a1),x55771),x55772))
% 109.14/108.84 [5591]E(f318(f318(f300(x55911),x55912),x55913),x55913)+~P1(f318(f318(f320(x55911),x55912),x55913))
% 109.14/108.84 [5602]E(x56021,f179(f918(x56022,a909)))+~E(f318(f318(f54(x56022),x56021),x56023),f179(f918(f918(x56022,a909),a909)))
% 109.14/108.84 [5603]E(x56031,f179(f918(x56032,a909)))+~E(f179(f918(f918(x56032,a909),a909)),f318(f318(f54(x56032),x56031),x56033))
% 109.14/108.84 [5609]~P129(x56091)+E(f318(f318(f74(x56091),f318(f72(x56091),x56092)),f318(f72(x56091),x56093)),f318(f318(f74(x56091),x56092),x56093))
% 109.14/108.84 [5611]~P72(x56111)+E(f318(f318(f282(x56111),f318(f72(x56111),x56112)),f318(f72(x56111),x56113)),f318(f318(f282(x56111),x56112),x56113))
% 109.14/108.84 [5640]~P1(f318(x56403,x56402))+P1(f318(f318(f320(x56401),x56402),f318(f253(x56401),x56403)))
% 109.14/108.84 [5641]~P1(f318(x56413,x56412))+P1(f318(f318(f320(x56411),x56412),f318(f253(x56411),x56413)))
% 109.14/108.84 [5667]E(x56671,f2(a911))+E(f318(f163(x56672),f160(x56672,x56671,x56673)),f318(f318(f300(x56672),x56673),f179(f918(x56672,a909))))
% 109.14/108.84 [5668]E(x56681,f2(a911))+E(f318(f163(x56682),f160(x56682,x56681,x56683)),f318(f318(f300(x56682),x56683),f179(f918(x56682,a909))))
% 109.14/108.84 [5687]E(f161(x56871,x56872,x56873),x56873)+P1(f318(f318(f320(x56871),x56872),f318(f163(x56871),x56873)))
% 109.14/108.84 [5774]~P1(f318(f128(x57741),x57743))+P1(f318(f128(x57741),f318(f127(x57741,x57742),x57743)))
% 109.14/108.84 [5818]~P69(x58181)+E(f318(f318(f30(x58181),f39(x58181,x58182,x58183)),x58183),f2(x58181))
% 109.14/108.84 [5837]E(f167(x58371,f318(f318(f142(x58371),x58372),f104(x58371)),x58373),f104(x58371))+P1(f318(f318(f320(a911),f2(a911)),x58373))
% 109.14/108.84 [5843]E(x58431,f2(a911))+E(f318(f162(x58432),f160(x58432,x58431,x58433)),f160(x58432,f318(f318(f3(a911),x58431),f71(a911)),x58433))
% 109.14/108.84 [5893]E(f318(f318(f142(x58931),x58932),x58933),f131(x58931,x58932,x58933))+P1(f318(f318(f320(x58931),x58932),f318(f163(x58931),x58933)))
% 109.14/108.84 [5894]E(f318(f318(f142(x58941),x58942),x58943),f131(x58941,x58942,x58943))+P1(f318(f318(f320(x58941),x58942),f318(f163(x58941),x58943)))
% 109.14/108.84 [5903]E(x59031,x59032)+~E(f318(f318(f74(a911),f318(a103,x59033)),x59031),f318(f318(f74(a911),f318(a103,x59033)),x59032))
% 109.14/108.84 [5904]~E(x59042,f318(f318(f73(a1),x59041),f318(f91(a1),f318(a103,x59043))))+P1(f318(f318(f226(a1),x59041),x59042))
% 109.14/108.84 [5966]~P32(x59661,x59662,x59663)+P33(a911,x59661,f130(a911,f318(f293(a911,x59662),x59663)))
% 109.14/108.84 [6020]~E(x60203,f104(x60201))+E(f318(f318(f318(f174(f912(x60201),f912(x60201)),x60202),f158(x60201)),x60203),f104(x60201))
% 109.14/108.84 [6022]P1(f318(x60221,x60222))+~P1(f318(f318(f320(x60223),x60222),f318(f253(x60223),x60221)))
% 109.14/108.84 [6023]P1(f318(x60231,x60232))+~P1(f318(f318(f320(x60233),x60232),f318(f253(x60233),x60231)))
% 109.14/108.84 [6024]P1(f318(x60241,x60242))+~P1(f318(f318(f320(x60243),x60242),f318(f253(x60243),x60241)))
% 109.14/108.84 [6056]E(x60561,x60562)+~E(f318(f318(f300(x60563),x60561),f179(f918(x60563,a909))),f318(f318(f300(x60563),x60562),f179(f918(x60563,a909))))
% 109.14/108.84 [6071]~P113(x60711)+E(f318(f318(f92(f918(x60711,a909)),f318(f273(x60711),x60712)),f318(f293(x60711,x60712),x60713)),f179(f918(x60711,a909)))
% 109.14/108.84 [6109]E(f131(x61091,x61092,x61093),x61093)+~P1(f318(f318(f320(x61091),x61092),f318(f163(x61091),x61093)))
% 109.14/108.84 [6110]E(f131(x61101,x61102,x61103),x61103)+~P1(f318(f318(f320(x61101),x61102),f318(f163(x61101),x61103)))
% 109.14/108.84 [6135]~P65(x61351)+E(f318(f301(x61351,x61351,f72(x61351)),f318(f293(x61351,x61352),x61353)),f296(x61351,f318(f72(x61351),x61353),f318(f72(x61351),x61352)))
% 109.14/108.84 [6140]P1(f318(f318(f320(x61401),x61402),f318(f163(x61401),x61403)))+~P1(f318(f318(f163(x61401),x61403),x61402))
% 109.14/108.84 [6141]P1(f318(f318(f320(x61411),x61412),f318(f163(x61411),x61413)))+~P1(f318(f318(f163(x61411),x61413),x61412))
% 109.14/108.84 [6146]E(f318(f180(f912(x61461)),f161(x61461,x61462,x61463)),f318(f180(f912(x61461)),x61463))+P1(f318(f318(f320(x61461),x61462),f318(f163(x61461),x61463)))
% 109.14/108.84 [6163]P1(f318(x61631,x61632))+~P1(f318(f318(f320(x61633),x61632),f179(f918(x61633,a909))))
% 109.14/108.84 [6164]~P1(f318(x61642,x61643))+P1(f318(f318(f320(x61641),f732(x61642,x61641)),f233(f918(x61641,a909))))
% 109.14/108.84 [6198]~P113(x61981)+E(f318(f318(f92(f918(x61981,a909)),f318(f293(x61981,x61982),x61983)),f318(f274(x61981),x61983)),f179(f918(x61981,a909)))
% 109.14/108.84 [6218]~P65(x62181)+E(f318(f301(x62181,x62181,f72(x62181)),f294(x62181,x62182,x62183)),f294(x62181,f318(f72(x62181),x62183),f318(f72(x62181),x62182)))
% 109.14/108.84 [6219]~P65(x62191)+E(f318(f301(x62191,x62191,f72(x62191)),f297(x62191,x62192,x62193)),f297(x62191,f318(f72(x62191),x62193),f318(f72(x62191),x62192)))
% 109.14/108.84 [6225]~P1(f318(x62251,x62252))+~P1(f318(f318(f320(x62253),x62252),f179(f918(x62253,a909))))
% 109.14/108.84 [6279]~P1(f318(f318(f320(x62791),x62793),f318(f163(x62791),x62792)))+P1(f318(f318(f163(x62791),x62792),x62793))
% 109.14/108.84 [6280]~P1(f318(f318(f320(x62801),x62803),f318(f163(x62801),x62802)))+P1(f318(f318(f163(x62801),x62802),x62803))
% 109.14/108.84 [6284]E(f167(x62841,f318(f318(f142(x62841),x62842),f104(x62841)),x62843),f318(f318(f142(x62841),x62842),f104(x62841)))+~P1(f318(f318(f320(a911),f2(a911)),x62843))
% 109.14/108.84 [6291]P32(x62911,x62912,x62913)+~P33(a911,x62911,f130(a911,f318(f293(a911,x62912),x62913)))
% 109.14/108.84 [6294]~P65(x62941)+E(f318(f301(x62941,x62941,f72(x62941)),f296(x62941,x62942,x62943)),f318(f293(x62941,f318(f72(x62941),x62943)),f318(f72(x62941),x62942)))
% 109.14/108.84 [6315]~P70(x63151)+E(f39(x63151,f318(f72(x63151),f39(x63151,x63152,x63153)),x63153),f39(x63151,f318(f72(x63151),x63152),x63153))
% 109.14/108.84 [6406]~P1(f318(f55(f917(x64062,x64061)),x64063))+P1(f318(f55(x64061),f318(f275(x64062,x64061),x64063)))
% 109.14/108.84 [6407]~P1(f318(f55(f917(x64071,x64072)),x64073))+P1(f318(f55(x64071),f318(f255(x64071,x64072),x64073)))
% 109.14/108.84 [6412]~P113(x64121)+E(f318(f318(f92(f918(x64121,a909)),f294(x64121,x64122,x64123)),f318(f295(x64121),x64123)),f179(f918(x64121,a909)))
% 109.14/108.84 [6413]~P113(x64131)+E(f318(f318(f92(f918(x64131,a909)),f296(x64131,x64132,x64133)),f318(f295(x64131),x64133)),f179(f918(x64131,a909)))
% 109.14/108.84 [6414]~P113(x64141)+E(f318(f318(f92(f918(x64141,a909)),f297(x64141,x64142,x64143)),f318(f274(x64141),x64143)),f179(f918(x64141,a909)))
% 109.14/108.84 [6483]E(f318(f318(f155(x64831),x64832),f633(x64832,x64833,x64831)),x64833)+~P1(f318(f318(f320(x64831),x64833),f318(f163(x64831),x64832)))
% 109.14/108.84 [6627]E(x66271,f104(x66272))+~E(f318(f318(f318(f174(f912(x66272),f912(x66272)),x66273),f158(x66272)),x66271),f104(x66272))
% 109.14/108.84 [6733]~P1(f318(f55(f917(x67332,x67331)),x67333))+P1(f318(f55(f917(x67331,x67332)),f318(f277(x67332,x67331),x67333)))
% 109.14/108.84 [6756]E(x67561,x67562)+~E(f281(a911,f278(a911),x67563,x67561),f318(f318(f300(a911),x67562),f179(f918(a911,a909))))
% 109.14/108.84 [6757]E(x67571,x67572)+~E(f281(a911,f278(a911),x67571,x67572),f318(f318(f300(a911),x67573),f179(f918(a911,a909))))
% 109.14/108.84 [6888]P59(x68881,x68882,x68883)+P1(f318(f318(f320(x68881),f614(x68883,x68882,x68881)),x68882))
% 109.14/108.84 [6889]P59(x68891,x68892,x68893)+P1(f318(f318(f320(x68891),f613(x68893,x68892,x68891)),x68892))
% 109.14/108.84 [6900]P1(f318(f306(x69001,x69002),x69003))+P1(f318(f318(x69002,f491(x69003,x69002,x69001)),x69003))
% 109.14/108.84 [6901]P1(f318(f306(x69011,x69012),x69013))+P1(f318(f318(x69012,f494(x69013,x69012,x69011)),x69013))
% 109.14/108.84 [6927]E(f318(f180(f912(x69271)),f161(x69271,x69272,x69273)),f318(f318(f3(a911),f318(f180(f912(x69271)),x69273)),f71(a911)))+~P1(f318(f318(f320(x69271),x69272),f318(f163(x69271),x69273)))
% 109.14/108.84 [6964]P1(f318(f239(x69641,x69642),x69643))+P1(f318(f318(f320(x69641),f465(x69643,x69642,x69641)),x69643))
% 109.14/108.84 [6974]~P1(f318(f55(f917(x69742,x69741)),f318(f277(x69741,x69742),x69743)))+P1(f318(f55(f917(x69741,x69742)),x69743))
% 109.14/108.84 [7032]~P1(f318(f318(f320(x70321),x70322),f318(f163(x70321),f105(x70321,x70323))))+P1(f318(f318(f320(x70321),x70322),f318(f163(x70321),x70323)))
% 109.14/108.84 [7037]P29(x70371,x70372,x70373)+P1(f318(f318(f320(f910(x70371)),f770(x70373,x70372,x70371)),x70373))
% 109.14/108.84 [7067]E(f318(f127(x70671,x70672),x70673),x70673)+P1(f318(f318(f320(x70671),f679(x70673,x70672,x70671)),f318(f163(x70671),x70673)))
% 109.14/108.84 [7081]E(f318(f127(x70811,x70812),x70813),f104(x70811))+P1(f318(f318(f320(x70811),f678(x70813,x70812,x70811)),f318(f163(x70811),x70813)))
% 109.14/108.84 [7108]P33(x71081,x71082,x71083)+P1(f318(f318(f320(x71081),f760(x71083,x71082,x71081)),f318(f163(x71081),x71083)))
% 109.14/108.84 [7109]P33(x71091,x71092,x71093)+P1(f318(f318(f320(x71091),f762(x71093,x71092,x71091)),f318(f163(x71091),x71093)))
% 109.14/108.84 [7110]P33(x71101,x71102,x71103)+P1(f318(f318(f320(x71101),f761(x71102,x71103,x71101)),f318(f163(x71101),x71103)))
% 109.14/108.84 [7113]E(f168(x71131,x71132,x71133),x71133)+P1(f318(f318(f320(x71131),f712(x71133,x71132,x71131)),f318(f163(x71131),x71133)))
% 109.14/108.84 [7189]P1(f318(f151(x71891,x71892),x71893))+P1(f318(f318(f320(x71891),f680(x71893,x71892,x71891)),f318(f163(x71891),x71893)))
% 109.14/108.84 [7198]~P35(x71981,x71983,x71982)+P1(f318(f318(f320(x71981),f746(x71982,x71983,x71981)),f318(f163(x71981),x71982)))
% 109.14/108.84 [7199]~P37(x71991,x71993,x71992)+P1(f318(f318(f320(x71991),f759(x71992,x71993,x71991)),f318(f163(x71991),x71992)))
% 109.14/108.84 [7200]~P37(x72001,x72003,x72002)+P1(f318(f318(f320(x72001),f769(x72002,x72003,x72001)),f318(f163(x72001),x72002)))
% 109.14/108.84 [7201]~P35(x72011,x72013,x72012)+P1(f318(f318(f320(x72011),f790(x72012,x72013,x72011)),f318(f163(x72011),x72012)))
% 109.14/108.84 [7202]~P35(x72021,x72022,x72023)+P1(f318(f318(f320(x72021),f791(x72022,x72023,x72021)),f318(f163(x72021),x72023)))
% 109.14/108.84 [7235]P1(f318(f318(f320(x72351),x72352),f329(x72353,x72352,x72351)))+~P1(f318(f318(f320(x72351),x72352),f31(f918(x72351,a909),x72353)))
% 109.14/108.84 [7236]~P76(x72361)+E(f318(f318(f73(x72361),f318(f318(f8(a911,x72361),x72362),f318(f273(a911),x72363))),f318(x72362,x72363)),f318(f318(f8(a911,x72361),x72362),f318(f273(a911),f318(a103,x72363))))
% 109.14/108.84 [7248]P32(x72481,x72482,x72483)+P1(f318(f318(f320(a911),f520(x72483,x72482,x72481)),f318(f293(a911,x72482),x72483)))
% 109.14/108.84 [7328]~P35(x73282,x73281,x73283)+P1(f318(x73281,f318(f318(f155(x73282),x73283),f750(x73283,x73281,x73282))))
% 109.14/108.84 [7341]~P1(f318(f318(f320(x73411),x73412),f905(x73412,x73413,x73411)))+P1(f318(f318(f320(x73411),x73412),f32(f918(x73411,a909),x73413)))
% 109.14/108.84 [7374]~P76(x73741)+E(f318(f318(f73(x73741),f318(f318(f8(a911,x73741),x73742),f318(f292(a911),x73743))),f318(x73742,f318(a103,x73743))),f318(f318(f8(a911,x73741),x73742),f318(f292(a911),f318(a103,x73743))))
% 109.14/108.84 [7505]P1(f318(f318(f320(f912(x75051)),x75052),f152(x75051,x75053)))+P1(f318(f318(f320(x75051),f657(x75053,x75052,x75051)),f318(f163(x75051),x75052)))
% 109.14/108.84 [7518]~P1(f318(f318(f320(f912(x75181)),x75182),f152(x75181,f307(x75181,x75183))))+P1(f318(f318(f320(f912(x75181)),x75182),f307(f912(x75181),f148(x75181,x75183))))
% 109.14/108.84 [7542]~P1(f318(f318(f320(f912(x75421)),x75422),f307(f912(x75421),f148(x75421,x75423))))+P1(f318(f318(f320(f912(x75421)),x75422),f152(x75421,f307(x75421,x75423))))
% 109.14/108.84 [7575]E(f318(f318(f318(f174(f912(x75751),f912(x75751)),x75752),f158(x75751)),x75753),x75753)+~P1(f318(f318(f225(a911),f318(f180(f912(x75751)),x75753)),f71(a911)))
% 109.14/108.84 [7608]E(f318(f318(f125(x76081),f754(x76082,x76083,x76081)),f318(f318(f142(x76081),x76083),f755(x76082,x76083,x76081))),x76082)+~P1(f318(f318(f320(x76081),x76083),f318(f163(x76081),x76082)))
% 109.14/108.84 [7609]E(f318(f318(f125(x76091),f751(x76092,x76093,x76091)),f318(f318(f142(x76091),x76093),f752(x76092,x76093,x76091))),x76092)+~P1(f318(f318(f320(x76091),x76093),f318(f163(x76091),x76092)))
% 109.14/108.84 [7610]E(f318(f318(f125(x76101),f756(x76102,x76103,x76101)),f318(f318(f142(x76101),x76103),f757(x76102,x76103,x76101))),x76102)+~P1(f318(f318(f320(x76101),x76103),f318(f163(x76101),x76102)))
% 109.14/108.84 [7630]~P25(x76301,x76302,x76303,f233(f918(x76301,a909)))+P25(f912(x76301),f912(x76302),f318(f145(x76301,x76302),x76303),f233(f918(f912(x76301),a909)))
% 109.14/108.84 [7631]~P25(x76311,x76312,x76313,f233(f918(x76311,a909)))+P25(f912(x76311),f912(x76312),f318(f145(x76311,x76312),x76313),f233(f918(f912(x76311),a909)))
% 109.14/108.84 [7778]E(x77781,f318(f318(f73(a911),f318(f318(f74(a911),f318(f242(a911,a911),x77782)),x77783)),f318(f247(a911,a911),x77782)))+~P1(f318(f42(x77781,x77783),x77782))
% 109.14/108.84 [7785]P25(x77851,x77852,x77853,f233(f918(x77851,a909)))+~P25(f912(x77851),f912(x77852),f318(f145(x77851,x77852),x77853),f233(f918(f912(x77851),a909)))
% 109.14/108.84 [7786]P25(x77861,x77862,x77863,f233(f918(x77861,a909)))+~P25(f912(x77861),f912(x77862),f318(f145(x77861,x77862),x77863),f233(f918(f912(x77861),a909)))
% 109.14/108.84 [7832]P1(f318(f318(f320(f918(x78321,a909)),f905(x78322,x78323,x78321)),x78323))+P1(f318(f318(f320(x78321),x78322),f32(f918(x78321,a909),x78323)))
% 109.14/108.84 [7923]P1(f318(f318(f320(f912(x79231)),x79232),f152(x79231,x79233)))+~P1(f318(f318(f320(x79231),f657(x79233,x79232,x79231)),x79233))
% 109.14/108.84 [8023]P33(x80231,x80232,x80233)+~P1(f318(x80232,f318(f318(f155(x80231),x80233),f753(x80233,x80232,x80231))))
% 109.14/108.84 [8048]E(x80481,x80482)+~E(f318(f318(f9(x80483,f918(x80483,a909),a909),f320(x80483)),x80481),f318(f318(f9(x80483,f918(x80483,a909),a909),f320(x80483)),x80482))
% 109.14/108.84 [8056]~P1(f318(f318(f320(f917(x80561,x80561)),x80563),f254(x80561,x80562)))+P1(f318(f318(f320(x80561),f523(x80562,x80563,x80561)),x80562))
% 109.14/108.84 [8058]~P1(f318(f318(f320(x80581),x80583),f31(f918(x80581,a909),x80582)))+P1(f318(f318(f320(f918(x80581,a909)),f329(x80582,x80583,x80581)),x80582))
% 109.14/108.84 [8172]P25(x81721,x81722,f84(x81722,x81721,f233(f918(x81722,a909)),x81723),f233(f918(x81721,a909)))+~E(f318(f301(x81722,x81721,x81723),f233(f918(x81722,a909))),f233(f918(x81721,a909)))
% 109.14/108.84 [8230]~P1(f318(f318(f320(x82301),x82302),f318(f163(x82301),f751(x82303,x82302,x82301))))+~P1(f318(f318(f320(x82301),x82302),f318(f163(x82301),x82303)))
% 109.14/108.84 [8231]~P1(f318(f318(f320(x82311),x82312),f318(f163(x82311),f757(x82313,x82312,x82311))))+~P1(f318(f318(f320(x82311),x82312),f318(f163(x82311),x82313)))
% 109.14/108.84 [8261]P32(f318(f66(a909,a909,a911,a313),x82611),x82612,x82613)+P35(a911,x82611,f130(a911,f318(f293(a911,x82612),x82613)))
% 109.14/108.84 [8421]E(x84211,f104(x84212))+P1(f318(f318(f320(x84212),f318(f242(x84212,f917(a90,a90)),f318(f266(x84212,x84211),x84213))),f318(f163(x84212),x84211)))
% 109.14/108.84 [8517]~P77(x85171)+E(f318(f133(x85171,x85171,f318(f9(x85171,x85171,x85171),f73(x85171)),x85172),f318(f159(x85171),x85173)),f318(f133(x85171,x85171,f73(x85171),x85172),x85173))
% 109.14/108.84 [8713]~P25(x87132,x87131,x87133,f233(f918(x87132,a909)))+E(f318(f301(x87131,x87132,f84(x87132,x87131,f233(f918(x87132,a909)),x87133)),f233(f918(x87131,a909))),f233(f918(x87132,a909)))
% 109.14/108.84 [8783]~P32(f318(f66(a909,a909,a911,a313),x87831),x87832,x87833)+~P35(a911,x87831,f130(a911,f318(f293(a911,x87832),x87833)))
% 109.14/108.84 [8917]~P26(x89171,x89172,x89173,f233(f918(x89171,a909)),f233(f918(x89172,a909)))+E(f318(f301(x89171,x89172,x89173),f233(f918(x89171,a909))),f233(f918(x89172,a909)))
% 109.14/108.84 [8918]~P26(x89181,x89182,x89183,f233(f918(x89181,a909)),f233(f918(x89182,a909)))+E(f318(f301(x89181,x89182,x89183),f233(f918(x89181,a909))),f233(f918(x89182,a909)))
% 109.14/108.84 [9028]~P4(x90281)+E(f318(f163(x90281),f140(x90281,x90281,f7(x90281),x90282,x90283)),f318(f318(f300(x90281),x90282),f318(f163(x90281),x90283)))
% 109.14/108.84 [9038]~E(f318(x90383,f318(f84(x90381,x90382,f233(f918(x90381,a909)),x90383),f804(x90383,x90382,x90381))),f804(x90383,x90382,x90381))+E(f318(f301(x90381,x90382,x90383),f233(f918(x90381,a909))),f233(f918(x90382,a909)))
% 109.14/108.84 [9040]P1(f318(f318(f226(a911),f2(a911)),f619(x90401,x90402,x90403)))+~P1(f318(f318(f320(f917(x90403,x90403)),x90402),f318(f318(f280(x90403,x90403,x90403),x90401),f298(x90403,x90401))))
% 109.14/108.84 [9314]~P61(x93141,x93142)+~P1(f318(f318(f320(f917(x93141,x93141)),f318(f318(f243(x93141,x93141),x93143),x93143)),f318(f318(f280(x93141,x93141,x93141),x93142),f298(x93141,x93142))))
% 109.14/108.84 [9417]~P26(x94172,x94171,x94173,f233(f918(x94172,a909)),f233(f918(x94171,a909)))+P26(x94171,x94172,f84(x94172,x94171,f233(f918(x94172,a909)),x94173),f233(f918(x94171,a909)),f233(f918(x94172,a909)))
% 109.14/108.84 [9454]~E(f318(f318(f92(f918(f917(x94541,x94541),a909)),f318(f277(x94541,x94541),x94542)),f298(x94541,x94542)),f179(f918(f917(x94541,x94541),a909)))+~P1(f318(f318(f320(f917(x94541,x94541)),f318(f318(f243(x94541,x94541),x94543),x94543)),f318(f318(f280(x94541,x94541,x94541),x94542),f298(x94541,x94542))))
% 109.14/108.84 [9633]~P1(f318(f55(x96331),x96332))+P1(f318(f318(f225(a911),f318(f29(x96331),f318(f318(f3(f918(x96331,a909)),x96332),f318(f318(f300(x96331),x96333),f179(f918(x96331,a909)))))),f318(f29(x96331),x96332)))
% 109.14/108.84 [5179]~E(x51793,f104(x51791))+E(f135(x51791,f318(f318(f142(x51791),x51792),x51793)),x51792)
% 109.14/108.84 [5180]~E(x51803,f104(x51801))+E(f135(x51801,f318(f318(f142(x51801),x51802),x51803)),x51802)
% 109.14/108.84 [5189]~E(x51893,f104(x51891))+E(f105(x51891,f318(f318(f142(x51891),x51892),x51893)),f104(x51891))
% 109.14/108.84 [5220]E(x52201,f104(x52202))+E(f135(x52202,f318(f318(f142(x52202),x52203),x52201)),f135(x52202,x52201))
% 109.14/108.84 [5221]E(x52211,f104(x52212))+E(f135(x52212,f318(f318(f142(x52212),x52213),x52211)),f135(x52212,x52211))
% 109.14/108.84 [5222]E(x52221,f104(x52222))+E(f135(x52222,f318(f318(f125(x52222),x52223),x52221)),f135(x52222,x52221))
% 109.14/108.84 [5223]E(x52231,f104(x52232))+E(f135(x52232,f318(f318(f125(x52232),x52233),x52231)),f135(x52232,x52231))
% 109.14/108.84 [5230]~E(x52303,f104(x52301))+E(f105(x52301,f318(f318(f125(x52301),x52302),x52303)),f105(x52301,x52302))
% 109.14/108.84 [5231]~E(x52313,f104(x52311))+E(f135(x52311,f318(f318(f125(x52311),x52312),x52313)),f135(x52311,x52312))
% 109.14/108.84 [5232]~E(x52323,f104(x52321))+E(f135(x52321,f318(f318(f125(x52321),x52322),x52323)),f135(x52321,x52322))
% 109.14/108.84 [5266]E(x52661,f104(x52662))+E(f318(f132(x52662),f318(f318(f125(x52662),x52661),x52663)),f318(f132(x52662),x52661))
% 109.14/108.84 [5267]E(x52671,f104(x52672))+E(f318(f132(x52672),f318(f318(f125(x52672),x52671),x52673)),f318(f132(x52672),x52671))
% 109.14/108.84 [5295]~E(x52952,f104(x52951))+E(f318(f132(x52951),f318(f318(f125(x52951),x52952),x52953)),f318(f132(x52951),x52953))
% 109.14/108.84 [5348]~P103(x53481)+E(f318(f318(f101(x53481),x53482),f318(f318(f92(x53481),x53482),x53483)),x53482)
% 109.14/108.84 [5349]~P103(x53491)+E(f318(f318(f92(x53491),x53492),f318(f318(f101(x53491),x53492),x53493)),x53492)
% 109.14/108.84 [5350]~P4(x53501)+E(f318(f318(f223(x53501),x53502),f318(f318(f224(x53501),x53502),x53503)),x53502)
% 109.14/108.84 [5351]~P4(x53511)+E(f318(f318(f224(x53511),x53512),f318(f318(f223(x53511),x53512),x53513)),x53512)
% 109.14/108.84 [5370]~P69(x53701)+E(f39(x53701,f318(f318(f74(x53701),x53702),x53703),x53703),f2(x53701))
% 109.14/108.84 [5371]~P69(x53711)+E(f39(x53711,f318(f318(f74(x53711),x53712),x53713),x53712),f2(x53711))
% 109.14/108.84 [5439]~P67(x54391)+E(f318(f72(x54391),f318(f318(f3(x54391),x54392),x54393)),f318(f318(f3(x54391),x54393),x54392))
% 109.14/108.84 [5501]E(x55011,f104(x55012))+E(f105(x55012,f318(f318(f142(x55012),x55013),x55011)),f318(f318(f142(x55012),x55013),f105(x55012,x55011)))
% 109.14/108.84 [5502]E(x55021,f104(x55022))+E(f105(x55022,f318(f318(f125(x55022),x55023),x55021)),f318(f318(f125(x55022),x55023),f105(x55022,x55021)))
% 109.14/108.84 [5505]~P5(x55051)+E(f32(x55051,f318(f318(f300(x55051),x55052),x55053)),f318(f318(f92(x55051),x55052),f32(x55051,x55053)))
% 109.14/108.84 [5506]~P5(x55061)+E(f31(x55061,f318(f318(f300(x55061),x55062),x55063)),f318(f318(f101(x55061),x55062),f31(x55061,x55063)))
% 109.14/108.84 [5552]~P102(x55521)+E(f318(f318(f101(x55521),x55522),f318(f318(f101(x55521),x55522),x55523)),f318(f318(f101(x55521),x55522),x55523))
% 109.14/108.84 [5553]~P102(x55531)+E(f318(f318(f101(x55531),x55532),f318(f318(f101(x55531),x55532),x55533)),f318(f318(f101(x55531),x55532),x55533))
% 109.14/108.84 [5554]~P103(x55541)+E(f318(f318(f101(x55541),x55542),f318(f318(f101(x55541),x55542),x55543)),f318(f318(f101(x55541),x55542),x55543))
% 109.14/108.84 [5555]~P103(x55551)+E(f318(f318(f92(x55551),x55552),f318(f318(f92(x55551),x55552),x55553)),f318(f318(f92(x55551),x55552),x55553))
% 109.14/108.84 [5556]~P108(x55561)+E(f318(f318(f92(x55561),x55562),f318(f318(f92(x55561),x55562),x55563)),f318(f318(f92(x55561),x55562),x55563))
% 109.14/108.84 [5557]~P108(x55571)+E(f318(f318(f92(x55571),x55572),f318(f318(f92(x55571),x55572),x55573)),f318(f318(f92(x55571),x55572),x55573))
% 109.14/108.84 [5558]~P101(x55581)+E(f318(f318(f74(x55581),x55582),f318(f318(f74(x55581),x55582),x55583)),f318(f318(f74(x55581),x55582),x55583))
% 109.14/108.84 [5559]~P4(x55591)+E(f318(f318(f223(x55591),x55592),f318(f318(f223(x55591),x55592),x55593)),f318(f318(f223(x55591),x55592),x55593))
% 109.14/108.84 [5560]~P4(x55601)+E(f318(f318(f223(x55601),x55602),f318(f318(f223(x55601),x55602),x55603)),f318(f318(f223(x55601),x55602),x55603))
% 109.14/108.84 [5561]~P4(x55611)+E(f318(f318(f224(x55611),x55612),f318(f318(f224(x55611),x55612),x55613)),f318(f318(f224(x55611),x55612),x55613))
% 109.14/108.84 [5562]~P4(x55621)+E(f318(f318(f224(x55621),x55622),f318(f318(f224(x55621),x55622),x55623)),f318(f318(f224(x55621),x55622),x55623))
% 109.14/108.84 [5569]~P69(x55691)+E(f39(x55691,f318(f318(f73(x55691),x55692),x55693),x55693),f39(x55691,x55692,x55693))
% 109.14/108.84 [5570]~P69(x55701)+E(f39(x55701,f318(f318(f73(x55701),x55702),x55703),x55702),f39(x55701,x55703,x55702))
% 109.14/108.84 [5578]~P129(x55781)+E(f318(f318(f74(x55781),x55782),f318(f72(x55781),x55783)),f318(f72(x55781),f318(f318(f74(x55781),x55782),x55783)))
% 109.14/108.84 [5579]~P72(x55791)+E(f318(f318(f282(x55791),x55792),f318(f72(x55791),x55793)),f318(f72(x55791),f318(f318(f282(x55791),x55792),x55793)))
% 109.14/108.84 [5580]~P86(x55801)+E(f318(f318(f73(x55801),x55802),f318(f156(x55801),x55803)),f318(f156(x55801),f318(f318(f142(x55801),x55802),x55803)))
% 109.14/108.84 [5608]~P129(x56081)+E(f318(f318(f74(x56081),f318(f72(x56081),x56082)),x56083),f318(f318(f74(x56081),x56082),f318(f72(x56081),x56083)))
% 109.14/108.84 [5614]~P8(x56141,x56142,x56143)+E(f31(f918(x56141,a909),f318(f318(f54(x56141),x56142),x56143)),x56142)
% 109.14/108.84 [5678]~P121(x56781)+E(f318(f318(f74(x56781),x56782),f318(f318(f235(x56781),x56782),x56783)),f318(f318(f235(x56781),x56782),f318(a103,x56783)))
% 109.14/108.84 [5679]~P118(x56791)+E(f318(f318(f74(x56791),x56792),f318(f318(f235(x56791),x56792),x56793)),f318(f318(f235(x56791),x56792),f318(a103,x56793)))
% 109.14/108.84 [5680]~P121(x56801)+E(f318(f318(f74(x56801),x56802),f318(f318(f235(x56801),x56802),x56803)),f318(f318(f235(x56801),x56802),f318(a103,x56803)))
% 109.14/108.84 [5690]~P66(x56901)+E(f318(f318(f73(x56901),f318(f72(x56901),x56902)),f318(f318(f73(x56901),x56902),x56903)),x56903)
% 109.14/108.84 [5713]~P114(x57131)+E(f318(f318(f235(x57131),f318(f91(x57131),x57132)),x57133),f318(f91(x57131),f318(f318(f235(a911),x57132),x57133)))
% 109.14/108.84 [5714]~P144(x57141)+E(f318(f318(f235(x57141),f318(f93(x57141),x57142)),x57143),f318(f93(x57141),f318(f318(f235(a1),x57142),x57143)))
% 109.14/108.84 [5720]~P91(x57201)+E(f318(f69(x57201),f318(f318(f3(x57201),x57202),x57203)),f318(f69(x57201),f318(f318(f3(x57201),x57203),x57202)))
% 109.14/108.84 [5725]~P116(x57251)+E(f318(f318(f74(x57251),f75(x57251,x57252)),f75(x57251,x57253)),f75(x57251,f318(f318(f74(x57251),x57252),x57253)))
% 109.14/108.84 [5729]E(x57291,f104(x57292))+E(f318(f318(f125(x57292),f318(f162(x57292),x57291)),x57293),f318(f162(x57292),f318(f318(f125(x57292),x57291),x57293)))
% 109.14/108.84 [5734]~E(x57342,f318(a103,f318(f318(f73(a911),x57341),x57343)))+P1(f318(f318(f226(a911),x57341),x57342))
% 109.14/108.84 [5735]~P129(x57351)+E(f318(f318(f74(x57351),f318(f72(x57351),x57352)),x57353),f318(f72(x57351),f318(f318(f74(x57351),x57352),x57353)))
% 109.14/108.84 [5736]~P125(x57361)+E(f318(f318(f282(x57361),f318(f72(x57361),x57362)),x57363),f318(f72(x57361),f318(f318(f282(x57361),x57362),x57363)))
% 109.14/108.84 [5737]~P116(x57371)+E(f318(f318(f235(x57371),f318(f69(x57371),x57372)),x57373),f318(f69(x57371),f318(f318(f235(x57371),x57372),x57373)))
% 109.14/108.84 [5836]E(f436(x58361,x58362,x58363),f447(x58361,x58362,x58363))+E(f318(f318(f92(f918(x58363,a909)),x58362),x58361),f179(f918(x58363,a909)))
% 109.14/108.84 [5851]~P76(x58512)+E(f318(f318(f8(x58511,x58512),f318(f18(x58512,x58511),f2(x58512))),x58513),f2(x58512))
% 109.14/108.84 [5852]~P82(x58522)+E(f318(f318(f11(x58521,x58522),f318(f18(x58522,x58521),f71(x58522))),x58523),f71(x58522))
% 109.14/108.84 [5854]~P99(x58541)+E(f318(f318(f3(x58541),f318(f94(x58541),x58542)),f318(f94(x58541),x58543)),f318(f94(x58541),f318(f318(f3(a1),x58542),x58543)))
% 109.14/108.84 [5855]~P99(x58551)+E(f318(f318(f73(x58551),f318(f94(x58551),x58552)),f318(f94(x58551),x58553)),f318(f94(x58551),f318(f318(f73(a1),x58552),x58553)))
% 109.14/108.84 [5856]~P99(x58561)+E(f318(f318(f74(x58561),f318(f94(x58561),x58562)),f318(f94(x58561),x58563)),f318(f94(x58561),f318(f318(f74(a1),x58562),x58563)))
% 109.14/108.84 [5857]~P114(x58571)+E(f318(f318(f73(x58571),f318(f91(x58571),x58572)),f318(f91(x58571),x58573)),f318(f91(x58571),f318(f318(f73(a911),x58572),x58573)))
% 109.14/108.84 [5858]~P114(x58581)+E(f318(f318(f74(x58581),f318(f91(x58581),x58582)),f318(f91(x58581),x58583)),f318(f91(x58581),f318(f318(f74(a911),x58582),x58583)))
% 109.14/108.84 [5859]~P144(x58591)+E(f318(f318(f3(x58591),f318(f93(x58591),x58592)),f318(f93(x58591),x58593)),f318(f93(x58591),f318(f318(f3(a1),x58592),x58593)))
% 109.14/108.84 [5860]~P144(x58601)+E(f318(f318(f73(x58601),f318(f93(x58601),x58602)),f318(f93(x58601),x58603)),f318(f93(x58601),f318(f318(f73(a1),x58602),x58603)))
% 109.14/108.84 [5861]~P144(x58611)+E(f318(f318(f74(x58611),f318(f93(x58611),x58612)),f318(f93(x58611),x58613)),f318(f93(x58611),f318(f318(f74(a1),x58612),x58613)))
% 109.14/108.84 [5862]~P99(x58621)+E(f318(f318(f73(x58621),f318(f94(x58621),x58622)),f318(f94(x58621),x58623)),f318(f94(x58621),f318(f318(f73(a1),x58622),x58623)))
% 109.14/108.84 [5863]~P99(x58631)+E(f318(f318(f74(x58631),f318(f94(x58631),x58632)),f318(f94(x58631),x58633)),f318(f94(x58631),f318(f318(f74(a1),x58632),x58633)))
% 109.14/108.84 [5911]~E(x59113,x59112)+P1(f318(f318(f225(f918(x59111,a909)),x59112),x59113))
% 109.14/108.84 [5912]~E(x59122,x59123)+P1(f318(f318(f225(f918(x59121,a909)),x59122),x59123))
% 109.14/108.84 [5913]~E(x59132,x59133)+P1(f318(f318(f225(f918(x59131,a909)),x59132),x59133))
% 109.14/108.84 [5914]~E(x59142,x59143)+P1(f318(f318(f225(f918(x59141,a909)),x59142),x59143))
% 109.14/108.84 [5915]~E(x59152,x59153)+P1(f318(f318(f225(f918(x59151,a909)),x59152),x59153))
% 109.14/108.84 [5916]~E(x59162,x59163)+P1(f318(f318(f225(f918(x59161,a909)),x59162),x59163))
% 109.14/108.84 [5917]~E(x59172,x59173)+P1(f318(f318(f225(f918(x59171,a909)),x59172),x59173))
% 109.14/108.84 [5922]~P96(x59221)+E(f318(f318(f92(x59221),f318(f72(x59221),x59222)),f318(f72(x59221),x59223)),f318(f72(x59221),f318(f318(f101(x59221),x59222),x59223)))
% 109.14/108.84 [5923]~P96(x59231)+E(f318(f318(f101(x59231),f318(f72(x59231),x59232)),f318(f72(x59231),x59233)),f318(f72(x59231),f318(f318(f92(x59231),x59232),x59233)))
% 109.14/108.84 [5924]~P66(x59241)+E(f318(f318(f73(x59241),f318(f72(x59241),x59242)),f318(f72(x59241),x59243)),f318(f72(x59241),f318(f318(f73(x59241),x59243),x59242)))
% 109.14/108.84 [5925]~P67(x59251)+E(f318(f318(f73(x59251),f318(f72(x59251),x59252)),f318(f72(x59251),x59253)),f318(f72(x59251),f318(f318(f73(x59251),x59252),x59253)))
% 109.14/108.84 [5926]~P83(x59261)+E(f318(f318(f224(x59261),f318(f72(x59261),x59262)),f318(f72(x59261),x59263)),f318(f72(x59261),f318(f318(f223(x59261),x59262),x59263)))
% 109.14/108.84 [5927]~P83(x59271)+E(f318(f318(f223(x59271),f318(f72(x59271),x59272)),f318(f72(x59271),x59273)),f318(f72(x59271),f318(f318(f224(x59271),x59272),x59273)))
% 109.14/108.84 [5928]~P116(x59281)+E(f318(f318(f74(x59281),f318(f69(x59281),x59282)),f318(f69(x59281),x59283)),f318(f69(x59281),f318(f318(f74(x59281),x59282),x59283)))
% 109.14/108.84 [5929]~P74(x59291)+E(f318(f318(f282(x59291),f318(f69(x59291),x59292)),f318(f69(x59291),x59293)),f318(f69(x59291),f318(f318(f282(x59291),x59292),x59293)))
% 109.14/108.84 [5930]~P86(x59301)+E(f318(f318(f73(x59301),f318(f156(x59301),x59302)),f318(f156(x59301),x59303)),f318(f156(x59301),f318(f318(f125(x59301),x59302),x59303)))
% 109.14/108.84 [5931]E(x59311,f179(f918(x59312,a909)))+~E(f318(f318(f101(f918(x59312,a909)),x59313),x59311),f179(f918(x59312,a909)))
% 109.14/108.84 [5932]E(x59321,f179(f918(x59322,a909)))+~E(f318(f318(f101(f918(x59322,a909)),x59321),x59323),f179(f918(x59322,a909)))
% 109.14/108.84 [5933]~P152(x59331,x59332,x59333)+P1(f318(x59331,f318(f318(f30(a1),x59332),x59333)))
% 109.14/108.84 [5990]~P1(f318(f55(x59901),x59903))+P1(f318(f55(x59901),f318(f318(f300(x59901),x59902),x59903)))
% 109.14/108.84 [5991]~P1(f318(f55(x59911),x59913))+P1(f318(f55(x59911),f318(f318(f300(x59911),x59912),x59913)))
% 109.14/108.84 [5992]~P1(f318(f128(x59921),x59923))+P1(f318(f128(x59921),f318(f318(f166(x59921),x59922),x59923)))
% 109.14/108.84 [5993]~P1(f318(f128(x59931),x59933))+P1(f318(f128(x59931),f318(f318(f129(x59931),x59932),x59933)))
% 109.14/108.84 [6025]~P102(x60251)+P1(f318(f318(f225(x60251),x60252),f318(f318(f101(x60251),x60253),x60252)))
% 109.14/108.84 [6026]~P103(x60261)+P1(f318(f318(f225(x60261),x60262),f318(f318(f101(x60261),x60263),x60262)))
% 109.14/108.84 [6027]~P102(x60271)+P1(f318(f318(f225(x60271),x60272),f318(f318(f101(x60271),x60272),x60273)))
% 109.14/108.84 [6028]~P103(x60281)+P1(f318(f318(f225(x60281),x60282),f318(f318(f101(x60281),x60282),x60283)))
% 109.14/108.84 [6029]~P4(x60291)+P1(f318(f318(f225(x60291),x60292),f318(f318(f224(x60291),x60293),x60292)))
% 109.14/108.84 [6030]~P4(x60301)+P1(f318(f318(f225(x60301),x60302),f318(f318(f224(x60301),x60302),x60303)))
% 109.14/108.84 [6031]~P121(x60311)+P1(f318(f318(f278(x60311),x60312),f318(f318(f74(x60311),x60313),x60312)))
% 109.14/108.84 [6032]~P121(x60321)+P1(f318(f318(f278(x60321),x60322),f318(f318(f74(x60321),x60322),x60323)))
% 109.14/108.84 [6046]~E(x60461,f2(a911))+E(f318(f318(f30(a911),f318(f318(f74(a911),x60461),x60462)),f318(f318(f74(a911),x60461),x60463)),f2(a911))
% 109.14/108.84 [6128]~P99(x61281)+E(f318(f318(f3(x61281),f318(f94(x61281),x61282)),f318(f94(x61281),x61283)),f318(f94(x61281),f318(f318(f73(a1),x61282),f318(f72(a1),x61283))))
% 109.14/108.84 [6186]E(x61861,f2(a911))+E(f318(f318(f30(a911),f318(f318(f74(a911),x61861),x61862)),f318(f318(f74(a911),x61861),x61863)),f318(f318(f30(a911),x61862),x61863))
% 109.14/108.84 [6216]E(f143(x62161,f318(f318(f142(x62161),x62162),x62163)),f318(f318(f142(x62161),x62162),f143(x62161,x62163)))+P1(f318(f318(f320(x62161),x62162),f318(f163(x62161),x62163)))
% 109.14/108.84 [6253]P152(x62531,x62532,x62533)+~P1(f318(x62531,f318(f318(f30(a1),x62532),x62533)))
% 109.14/108.84 [6324]E(x63241,f104(x63242))+E(f318(f318(f142(x63242),f318(f132(x63242),x63241)),f318(f318(f166(x63242),x63243),f318(f162(x63242),x63241))),f318(f318(f166(x63242),f318(a103,x63243)),x63241))
% 109.14/108.84 [6331]E(f318(f318(f3(f918(x63311,a909)),x63312),x63313),x63312)+~E(f318(f318(f92(f918(x63311,a909)),x63312),x63313),f179(f918(x63311,a909)))
% 109.14/108.84 [6346]E(f143(x63461,f318(f318(f142(x63461),x63462),x63463)),f143(x63461,x63463))+~P1(f318(f318(f320(x63461),x63462),f318(f163(x63461),x63463)))
% 109.14/108.84 [6375]~P1(f318(f318(f225(a911),x63751),x63753))+P1(f318(f318(f225(a911),x63751),f318(f318(f73(a911),x63752),x63753)))
% 109.14/108.84 [6376]~P1(f318(f318(f225(a911),x63761),x63763))+P1(f318(f318(f225(a911),x63761),f318(f318(f73(a911),x63762),x63763)))
% 109.14/108.84 [6377]~P1(f318(f318(f225(a911),x63771),x63772))+P1(f318(f318(f225(a911),x63771),f318(f318(f73(a911),x63772),x63773)))
% 109.14/108.84 [6378]~P1(f318(f318(f225(a911),x63781),x63782))+P1(f318(f318(f225(a911),x63781),f318(f318(f73(a911),x63782),x63783)))
% 109.14/108.84 [6379]~P1(f318(f318(f226(a911),x63791),x63793))+P1(f318(f318(f226(a911),x63791),f318(f318(f73(a911),x63792),x63793)))
% 109.14/108.84 [6380]~P1(f318(f318(f226(a911),x63801),x63803))+P1(f318(f318(f226(a911),x63801),f318(f318(f73(a911),x63802),x63803)))
% 109.14/108.84 [6381]~P1(f318(f318(f226(a911),x63811),x63812))+P1(f318(f318(f226(a911),x63811),f318(f318(f73(a911),x63812),x63813)))
% 109.14/108.84 [6382]~P1(f318(f318(f226(a911),x63821),x63822))+P1(f318(f318(f226(a911),x63821),f318(f318(f73(a911),x63822),x63823)))
% 109.14/108.84 [6420]P1(f318(f55(x64201),x64202))+~P1(f318(f55(x64201),f318(f318(f300(x64201),x64203),x64202)))
% 109.14/108.84 [6421]P1(f318(f128(x64211),x64212))+~P1(f318(f128(x64211),f318(f318(f142(x64211),x64213),x64212)))
% 109.14/108.84 [6422]P1(f318(f128(x64221),x64222))+~P1(f318(f128(x64221),f318(f318(f125(x64221),x64223),x64222)))
% 109.14/108.84 [6423]P1(f318(f128(x64231),x64232))+~P1(f318(f128(x64231),f318(f318(f125(x64231),x64232),x64233)))
% 109.14/108.84 [6472]~P121(x64721)+E(f318(f318(f73(x64721),x64722),f318(f318(f74(x64721),x64723),x64722)),f318(f318(f74(x64721),f318(f318(f73(x64721),x64723),f71(x64721))),x64722))
% 109.14/108.84 [6519]~E(x65191,x65192)+~P1(f318(f318(f226(f918(x65193,a909)),x65191),x65192))
% 109.14/108.84 [6564]P1(f318(f318(f320(x65641),x65642),x65643))+P1(f318(f318(f320(x65641),x65642),f318(f72(f918(x65641,a909)),x65643)))
% 109.14/108.84 [6565]P1(f318(f318(f320(x65651),x65652),x65653))+P1(f318(f318(f320(x65651),x65652),f318(f72(f918(x65651,a909)),x65653)))
% 109.14/108.84 [6571]E(f135(x65711,f318(f318(f129(x65711),x65712),x65713)),f135(x65711,x65713))+~P1(f318(f318(f226(a911),x65712),f318(f180(f912(x65711)),x65713)))
% 109.14/108.84 [6572]E(f318(f318(f166(x65721),x65722),f105(x65721,x65723)),f318(f318(f166(x65721),x65722),x65723))+~P1(f318(f318(f226(a911),x65722),f318(f180(f912(x65721)),x65723)))
% 109.14/108.84 [6629]E(f318(f318(f318(f174(f912(x66291),f912(x66291)),x66292),f158(x66291)),x66293),x66293)+~E(f39(a911,x66292,f318(f180(f912(x66291)),x66293)),f2(a911))
% 109.14/108.84 [6636]~P8(x66361,x66363,x66362)+E(f318(f318(f280(x66361,x66361,x66361),f318(f277(x66361,x66361),x66362)),x66362),x66362)
% 109.14/108.84 [6677]~E(f318(f318(f101(f918(x66771,a909)),x66772),x66773),x66773)+P1(f318(f318(f225(f918(x66771,a909)),x66772),x66773))
% 109.14/108.84 [6682]~P58(x66821,x66821,x66823)+P58(x66821,x66821,f318(f318(f174(f917(x66821,x66821),a909),x66822),x66823))
% 109.14/108.84 [6685]~P1(f318(f318(f320(x66851),x66853),f318(f163(x66851),x66852)))+P1(f318(f318(f226(a911),f2(a911)),f318(f180(f912(x66851)),x66852)))
% 109.14/108.84 [6701]~E(x67012,x67013)+P1(f318(f318(f320(x67011),x67012),f318(f318(f300(x67011),x67013),f179(f918(x67011,a909)))))
% 109.14/108.84 [6712]~P91(x67121)+E(f318(f69(x67121),f318(f318(f73(x67121),f318(f69(x67121),x67122)),f318(f69(x67121),x67123))),f318(f318(f73(x67121),f318(f69(x67121),x67122)),f318(f69(x67121),x67123)))
% 109.14/108.84 [6722]E(f318(f318(f30(a911),f318(f318(f74(a911),x67221),x67222)),f318(f318(f74(a911),x67221),x67223)),f318(f318(f30(a911),x67222),x67223))+~P1(f318(f318(f226(a911),f2(a911)),x67221))
% 109.14/108.84 [6868]~P1(f318(f55(x68681),x68683))+E(f318(f318(f58(x68681,f918(x68681,a909),f300(x68681)),x68682),x68683),f318(f318(f101(f918(x68681,a909)),x68683),x68682))
% 109.14/108.84 [6920]E(f318(f318(f101(f918(x69201,a909)),x69202),x69203),x69202)+~P1(f318(f318(f225(f918(x69201,a909)),x69203),x69202))
% 109.14/108.84 [6921]E(f318(f318(f101(f918(x69211,a909)),x69212),x69213),x69213)+~P1(f318(f318(f225(f918(x69211,a909)),x69212),x69213))
% 109.14/108.84 [6922]E(f318(f318(f101(f918(x69221,a909)),x69222),x69223),x69223)+~P1(f318(f318(f225(f918(x69221,a909)),x69222),x69223))
% 109.14/108.84 [6923]E(f318(f318(f92(f918(x69231,a909)),x69232),x69233),x69233)+~P1(f318(f318(f225(f918(x69231,a909)),x69233),x69232))
% 109.14/108.84 [6924]E(f318(f318(f92(f918(x69241,a909)),x69242),x69243),x69242)+~P1(f318(f318(f225(f918(x69241,a909)),x69242),x69243))
% 109.14/108.84 [6972]~P1(f318(f128(x69721),x69722))+E(f318(f318(f3(f918(x69721,a909)),f318(f163(x69721),x69722)),f318(f318(f300(x69721),x69723),f179(f918(x69721,a909)))),f318(f163(x69721),f161(x69721,x69723,x69722)))
% 109.14/108.84 [7027]P39(x70271,x70272)+~P39(x70271,f318(f318(f174(f917(x70271,x70271),a909),x70273),x70272))
% 109.14/108.84 [7044]~E(x70441,f2(a911))+P1(f318(f318(f278(a911),f318(f318(f74(a911),x70441),x70442)),f318(f318(f74(a911),x70441),x70443)))
% 109.14/108.84 [7093]P1(f318(f43(x70931,x70932),f318(a45,x70933)))+~P1(f318(f43(f318(f72(a1),x70931),f318(f72(a1),x70932)),x70933))
% 109.14/108.84 [7098]E(f318(f318(f3(f918(x70981,a909)),f318(f318(f300(x70981),x70982),x70983)),f318(f318(f300(x70981),x70982),f179(f918(x70981,a909)))),x70983)+P1(f318(f318(f320(x70981),x70982),x70983))
% 109.14/108.84 [7122]E(f318(f318(f92(f918(x71221,a909)),f318(f163(x71221),x71222)),f318(f163(x71221),x71223)),f179(f918(x71221,a909)))+~P1(f318(f128(x71221),f318(f318(f125(x71221),x71222),x71223)))
% 109.14/108.84 [7137]~P1(f318(f318(f320(x71371),x71372),f318(f163(x71371),x71373)))+~P1(f318(f128(x71371),f318(f318(f142(x71371),x71372),x71373)))
% 109.14/108.84 [7208]P33(x72081,x72082,x72083)+P1(f318(f318(f226(a911),f753(x72083,x72082,x72081)),f318(f180(f912(x72081)),x72083)))
% 109.14/108.84 [7218]E(f318(f318(f92(f918(x72181,a909)),x72182),x72183),f179(f918(x72181,a909)))+P1(f318(f318(f320(x72181),f436(x72183,x72182,x72181)),x72182))
% 109.14/108.84 [7219]E(f318(f318(f92(f918(x72191,a909)),x72192),x72193),f179(f918(x72191,a909)))+P1(f318(f318(f320(x72191),f447(x72193,x72192,x72191)),x72193))
% 109.14/108.84 [7222]E(f105(x72221,f318(f318(f166(x72221),x72222),x72223)),f318(f318(f166(x72221),f318(f318(f3(a911),x72222),f71(a911))),x72223))+~P1(f318(f318(f225(a911),x72222),f318(f180(f912(x72221)),x72223)))
% 109.14/108.84 [7281]~P35(x72813,x72812,x72811)+P1(f318(f318(f226(a911),f750(x72811,x72812,x72813)),f318(f180(f912(x72813)),x72811)))
% 109.14/108.84 [7301]P1(f318(f318(f226(a911),f2(a911)),x73011))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x73012),x73011)),f318(f318(f74(a911),x73013),x73011)))
% 109.14/108.84 [7302]P1(f318(f318(f226(a911),f2(a911)),x73021))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x73021),x73022)),f318(f318(f74(a911),x73021),x73023)))
% 109.14/108.84 [7303]~P1(f318(f318(f320(x73031),x73032),x73033))+~P1(f318(f318(f320(x73031),x73032),f318(f72(f918(x73031,a909)),x73033)))
% 109.14/108.84 [7304]~P1(f318(f318(f320(x73041),x73042),x73043))+~P1(f318(f318(f320(x73041),x73042),f318(f72(f918(x73041,a909)),x73043)))
% 109.14/108.84 [7305]~P1(f318(f318(f320(x73051),x73052),x73053))+~P1(f318(f318(f320(x73051),x73052),f318(f72(f918(x73051,a909)),x73053)))
% 109.14/108.84 [7309]~P1(f318(f318(f226(f918(x73091,a909)),x73092),x73093))+P1(f318(f318(f225(f918(x73091,a909)),x73092),x73093))
% 109.14/108.84 [7310]~P1(f318(f318(f226(f918(x73101,a909)),x73102),x73103))+P1(f318(f318(f225(f918(x73101,a909)),x73102),x73103))
% 109.14/108.84 [7311]~P1(f318(f318(f226(f918(x73111,a909)),x73112),x73113))+P1(f318(f318(f225(f918(x73111,a909)),x73112),x73113))
% 109.14/108.84 [7419]~P1(f318(f318(f225(a911),x74193),x74192))+P1(f318(f318(f225(a911),f318(f318(f3(a911),x74191),x74192)),f318(f318(f3(a911),x74191),x74193)))
% 109.14/108.84 [7420]~P1(f318(f318(f225(a911),x74201),x74203))+P1(f318(f318(f225(a911),f318(f318(f3(a911),x74201),x74202)),f318(f318(f3(a911),x74203),x74202)))
% 109.14/108.84 [7421]~P1(f318(f318(f225(a911),x74212),x74213))+P1(f318(f318(f225(a911),f318(f318(f73(a911),x74211),x74212)),f318(f318(f73(a911),x74211),x74213)))
% 109.14/108.84 [7422]~P1(f318(f318(f225(a911),x74221),x74223))+P1(f318(f318(f225(a911),f318(f318(f73(a911),x74221),x74222)),f318(f318(f73(a911),x74223),x74222)))
% 109.14/108.84 [7423]~P1(f318(f318(f225(a911),x74232),x74233))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x74231),x74232)),f318(f318(f74(a911),x74231),x74233)))
% 109.14/108.84 [7424]~P1(f318(f318(f225(a911),x74242),x74243))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x74241),x74242)),f318(f318(f74(a911),x74241),x74243)))
% 109.14/108.84 [7425]~P1(f318(f318(f225(a911),x74251),x74253))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x74251),x74252)),f318(f318(f74(a911),x74253),x74252)))
% 109.14/108.84 [7426]~P1(f318(f318(f225(a911),x74261),x74263))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x74261),x74262)),f318(f318(f74(a911),x74263),x74262)))
% 109.14/108.84 [7427]~P1(f318(f318(f225(a911),x74271),x74273))+P1(f318(f318(f225(a911),f318(f318(f30(a911),x74271),x74272)),f318(f318(f30(a911),x74273),x74272)))
% 109.14/108.84 [7428]~P1(f318(f318(f225(a1),x74282),x74283))+P1(f318(f318(f225(a1),f318(f318(f73(a1),x74281),x74282)),f318(f318(f73(a1),x74281),x74283)))
% 109.14/108.84 [7429]~P1(f318(f318(f226(a911),x74292),x74293))+P1(f318(f318(f226(a911),f318(f318(f73(a911),x74291),x74292)),f318(f318(f73(a911),x74291),x74293)))
% 109.14/108.84 [7430]~P1(f318(f318(f226(a911),x74301),x74303))+P1(f318(f318(f226(a911),f318(f318(f73(a911),x74301),x74302)),f318(f318(f73(a911),x74303),x74302)))
% 109.14/108.84 [7431]~P1(f318(f318(f226(a1),x74311),x74313))+P1(f318(f318(f226(a1),f318(f318(f73(a1),x74311),x74312)),f318(f318(f73(a1),x74313),x74312)))
% 109.14/108.84 [7432]~P1(f318(f318(f278(a911),x74322),x74323))+P1(f318(f318(f278(a911),f318(f318(f74(a911),x74321),x74322)),f318(f318(f74(a911),x74321),x74323)))
% 109.14/108.84 [7503]E(x75031,x75032)+~P1(f318(f318(f320(x75033),x75031),f318(f318(f300(x75033),x75032),f179(f918(x75033,a909)))))
% 109.14/108.84 [7504]E(x75041,x75042)+~P1(f318(f318(f320(x75043),x75041),f318(f318(f300(x75043),x75042),f179(f918(x75043,a909)))))
% 109.14/108.84 [7506]~E(f318(f318(f92(f918(x75061,a909)),x75062),x75063),f179(f918(x75061,a909)))+P1(f318(f318(f225(f918(x75061,a909)),x75062),f318(f72(f918(x75061,a909)),x75063)))
% 109.14/108.84 [7510]P1(f318(f318(f320(f918(x75101,a909)),x75102),f318(f299(x75101),x75103)))+~P1(f318(f318(f225(f918(x75101,a909)),x75102),x75103))
% 109.14/108.84 [7511]P1(f318(f318(f320(f918(x75111,a909)),x75112),f318(f299(x75111),x75113)))+~P1(f318(f318(f225(f918(x75111,a909)),x75112),x75113))
% 109.14/108.84 [7559]E(f318(f318(f142(x75591),f318(f318(f155(x75591),x75592),x75593)),f318(f318(f129(x75591),f318(a103,x75593)),x75592)),f318(f318(f129(x75591),x75593),x75592))+~P1(f318(f318(f226(a911),x75593),f318(f180(f912(x75591)),x75592)))
% 109.14/108.84 [7585]P1(f318(f318(f320(f917(x75851,x75851)),x75852),f298(x75851,x75853)))+~P1(f318(f318(f320(f917(x75851,x75851)),x75852),x75853))
% 109.14/108.84 [7593]~P1(f318(f318(f320(f918(x75931,a909)),x75932),f318(f299(x75931),x75933)))+P1(f318(f318(f225(f918(x75931,a909)),x75932),x75933))
% 109.14/108.84 [7594]~P1(f318(f318(f320(f918(x75941,a909)),x75942),f318(f299(x75941),x75943)))+P1(f318(f318(f225(f918(x75941,a909)),x75942),x75943))
% 109.14/108.84 [7637]P1(f318(f318(f225(f918(x76371,a909)),x76372),f31(f918(x76371,a909),x76373)))+~P1(f318(f318(f320(f918(x76371,a909)),x76372),x76373))
% 109.14/108.84 [7661]~P144(x76611)+E(f318(f318(f74(x76611),f318(f318(f235(x76611),f318(f72(x76611),f71(x76611))),x76612)),f318(f318(f235(x76611),x76613),x76612)),f318(f318(f235(x76611),f318(f72(x76611),x76613)),x76612))
% 109.14/108.84 [7683]E(f318(f318(f155(x76831),x76832),f318(f318(f3(a911),f318(f180(f912(x76831)),x76832)),f318(a103,x76833))),f318(f318(f155(x76831),f318(f159(x76831),x76832)),x76833))+~P1(f318(f318(f226(a911),x76833),f318(f180(f912(x76831)),x76832)))
% 109.14/108.84 [7700]~E(f318(f318(f92(f918(x77001,a909)),f434(x77003,x77002,x77001)),x77003),f179(f918(x77001,a909)))+E(f318(f318(f92(f918(x77001,a909)),f31(f918(x77001,a909),x77002)),x77003),f179(f918(x77001,a909)))
% 109.14/108.84 [7761]~P1(f318(f318(f320(x77613),x77612),f318(f163(x77613),x77611)))+P1(f318(f318(f226(a911),f633(x77611,x77612,x77613)),f318(f180(f912(x77613)),x77611)))
% 109.14/108.84 [7769]P1(f318(f318(f320(x77691),f318(f318(f155(x77691),x77692),x77693)),f318(f163(x77691),x77692)))+~P1(f318(f318(f226(a911),x77693),f318(f180(f912(x77691)),x77692)))
% 109.14/108.84 [7867]~P1(f318(x78672,f713(x78673,x78672,x78671)))+E(f318(f318(f129(x78671),f318(f180(f912(x78671)),f168(x78671,x78672,x78673))),x78673),f104(x78671))
% 109.14/108.84 [7880]P1(f318(f318(f225(f918(f912(x78801),a909)),f152(x78801,x78802)),f152(x78801,x78803)))+~P1(f318(f318(f225(f918(x78801,a909)),x78802),x78803))
% 109.14/108.84 [7881]P1(f318(f318(f225(f918(f912(x78811),a909)),f151(x78811,x78812)),f151(x78811,x78813)))+~P1(f318(f318(f225(f918(x78811,a909)),x78812),x78813))
% 109.14/108.84 [7908]E(f318(f318(f92(f918(x79081,a909)),f31(f918(x79081,a909),x79082)),x79083),f179(f918(x79081,a909)))+P1(f318(f318(f320(f918(x79081,a909)),f434(x79083,x79082,x79081)),x79082))
% 109.14/108.84 [7910]~P1(f318(f318(f320(f918(x79101,a909)),x79103),x79102))+P1(f318(f318(f225(f918(x79101,a909)),f32(f918(x79101,a909),x79102)),x79103))
% 109.14/108.84 [7912]E(f318(f318(f92(f918(x79121,a909)),x79122),x79123),f179(f918(x79121,a909)))+~P1(f318(f318(f225(f918(x79121,a909)),x79122),f318(f72(f918(x79121,a909)),x79123)))
% 109.14/108.84 [7963]E(f318(f318(f3(a911),f318(f318(f73(a911),f318(f156(a911),x79631)),x79632)),f318(f318(f155(a911),x79631),x79633)),f318(f156(a911),f318(f318(f150(a911,x79631),x79633),x79632)))+~P1(f318(f318(f226(a911),x79633),f318(f180(f912(a911)),x79631)))
% 109.14/108.84 [8016]P1(f318(f318(f225(a911),x80161),x80162))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),x80163),x80161)),f318(f318(f73(a911),x80163),x80162)))
% 109.14/108.84 [8017]P1(f318(f318(f226(a911),x80171),x80172))+~P1(f318(f318(f226(a911),f318(f318(f73(a911),x80173),x80171)),f318(f318(f73(a911),x80173),x80172)))
% 109.14/108.84 [8018]P1(f318(f318(f226(a911),x80181),x80182))+~P1(f318(f318(f226(a911),f318(f318(f74(a911),x80183),x80181)),f318(f318(f74(a911),x80183),x80182)))
% 109.14/108.84 [8019]P1(f318(f318(f226(a911),x80191),x80192))+~P1(f318(f318(f226(a911),f318(f318(f74(a911),x80191),x80193)),f318(f318(f74(a911),x80192),x80193)))
% 109.14/108.84 [8046]P1(f318(f318(f226(a911),f2(a911)),x80461))+~P1(f318(f318(f226(a911),f318(f318(f74(a911),x80462),x80461)),f318(f318(f74(a911),x80463),x80461)))
% 109.14/108.84 [8047]P1(f318(f318(f226(a911),f2(a911)),x80471))+~P1(f318(f318(f226(a911),f318(f318(f74(a911),x80471),x80472)),f318(f318(f74(a911),x80471),x80473)))
% 109.14/108.84 [8116]E(f238(x81161,x81162,x81163),x81162)+~P1(f318(f318(f225(f918(x81161,a909)),x81163),f318(f318(f300(x81161),x81162),f179(f918(x81161,a909)))))
% 109.14/108.84 [8165]~P1(f318(f128(x81651),x81653))+E(f318(f127(x81651,f318(f318(f10(a909,a909,x81651),a313),f318(a315,x81652))),x81653),f161(x81651,x81652,x81653))
% 109.14/108.84 [8190]E(f318(f318(f129(x81901),f318(f180(f912(x81901)),f168(x81901,x81902,x81903))),x81903),f104(x81901))+P1(f318(f318(f320(x81901),f713(x81903,x81902,x81901)),f318(f163(x81901),x81903)))
% 109.14/108.84 [8195]E(f318(f318(f125(x81951),f318(f318(f166(x81951),x81952),x81953)),f318(f318(f142(x81951),f318(f318(f155(x81951),x81953),x81952)),f104(x81951))),f318(f318(f166(x81951),f318(a103,x81952)),x81953))+~P1(f318(f318(f226(a911),x81952),f318(f180(f912(x81951)),x81953)))
% 109.14/108.84 [8267]E(f318(f127(x82671,f318(f318(f10(a909,a909,x82671),a313),f318(a315,x82672))),x82673),x82673)+P1(f318(f318(f320(x82671),x82672),f318(f163(x82671),x82673)))
% 109.14/108.84 [8273]P1(f318(f318(f225(f918(f918(x82731,a909),a909)),f239(x82731,x82732)),f239(x82731,x82733)))+~P1(f318(f318(f225(f918(x82731,a909)),x82732),x82733))
% 109.14/108.84 [8313]~P1(f318(f128(x83131),x83133))+P1(f318(f128(x83131),f318(f318(f318(f174(f912(x83131),f912(x83131)),x83132),f158(x83131)),x83133)))
% 109.14/108.84 [8318]~P1(f318(f318(f225(a911),x83182),x83183))+P1(f318(f318(f225(a911),f318(f318(f74(a911),f318(a103,x83181)),x83182)),f318(f318(f74(a911),f318(a103,x83181)),x83183)))
% 109.14/108.84 [8319]~P1(f318(f318(f226(a911),x83192),x83193))+P1(f318(f318(f226(a911),f318(f318(f74(a911),f318(a103,x83191)),x83192)),f318(f318(f74(a911),f318(a103,x83191)),x83193)))
% 109.14/108.84 [8339]P1(f318(f318(f225(f918(f918(x83391,a909),a909)),f318(f299(x83391),x83392)),f318(f299(x83391),x83393)))+~P1(f318(f318(f225(f918(x83391,a909)),x83392),x83393))
% 109.14/108.84 [8406]~E(f318(f301(x84061,x84062,x84063),f233(f918(x84061,a909))),f233(f918(x84062,a909)))+E(f318(f66(x84061,x84062,x84062,x84063),f84(x84061,x84062,f233(f918(x84061,a909)),x84063)),f25(x84062))
% 109.14/108.84 [8496]~P1(f318(f318(f225(f918(x84961,a909)),x84963),x84962))+P1(f318(f318(f225(f918(x84961,a909)),f318(f72(f918(x84961,a909)),x84962)),f318(f72(f918(x84961,a909)),x84963)))
% 109.14/108.84 [8497]~P1(f318(f318(f225(f918(x84971,a909)),x84973),x84972))+P1(f318(f318(f225(f918(x84971,a909)),f318(f72(f918(x84971,a909)),x84972)),f318(f72(f918(x84971,a909)),x84973)))
% 109.14/108.84 [8531]E(f318(f301(a911,a911,f318(f318(f9(a911,a911,a911),f3(a911)),x85311)),f318(f293(a911,x85312),x85313)),f318(f293(a911,f318(f318(f3(a911),x85312),x85311)),f318(f318(f3(a911),x85313),x85311)))+~P1(f318(f318(f226(a911),x85311),x85313))
% 109.14/108.84 [8553]~P86(x85531)+E(f318(f318(f73(x85531),x85532),f318(f133(x85531,x85531,f73(x85531),f2(x85531)),x85533)),f318(f133(x85531,x85531,f73(x85531),x85532),x85533))
% 109.14/108.84 [8634]~P91(x86341)+P1(f318(f318(f225(x86341),f318(f69(x86341),f318(f318(f3(x86341),x86342),x86343))),f318(f318(f73(x86341),f318(f69(x86341),x86342)),f318(f69(x86341),x86343))))
% 109.14/108.84 [8635]~P91(x86351)+P1(f318(f318(f225(x86351),f318(f69(x86351),f318(f318(f73(x86351),x86352),x86353))),f318(f318(f73(x86351),f318(f69(x86351),x86352)),f318(f69(x86351),x86353))))
% 109.14/108.84 [8646]E(f318(f318(f73(a1),f318(f318(f74(a1),x86461),f39(a1,f318(f318(f30(a1),x86462),x86461),x86463))),f39(a1,x86462,x86461)),f39(a1,x86462,f318(f318(f74(a1),x86461),x86463)))+~P1(f318(f318(f226(a1),f2(a1)),x86463))
% 109.14/108.84 [8651]E(f318(f318(f125(x86511),f318(f318(f166(x86511),x86512),x86513)),f318(f318(f142(x86511),f318(f132(x86511),f318(f318(f129(x86511),x86512),x86513))),f104(x86511))),f318(f318(f166(x86511),f318(a103,x86512)),x86513))+~P1(f318(f318(f226(a911),x86512),f318(f180(f912(x86511)),x86513)))
% 109.14/108.84 [8675]E(f318(f259(x86751,f318(f318(f145(x86751,f917(a90,x86751)),f318(f243(a90,x86751),f71(a90))),x86752)),f318(a5,x86753)),f318(f318(f155(x86751),x86752),x86753))+~P1(f318(f318(f226(a911),x86753),f318(f180(f912(x86751)),x86752)))
% 109.14/108.84 [8743]P1(f318(f318(f320(f917(x87431,x87431)),x87432),f318(f318(f280(x87431,x87431,x87431),x87433),f298(x87431,x87433))))+~P1(f318(f318(f320(f917(x87431,x87431)),x87432),x87433))
% 109.14/108.84 [8753]E(f318(f301(x87531,x87532,x87533),f233(f918(x87531,a909))),f233(f918(x87532,a909)))+~E(f318(f66(x87531,x87532,x87532,x87533),f84(x87531,x87532,f233(f918(x87531,a909)),x87533)),f25(x87532))
% 109.14/108.84 [8764]P1(f318(f318(f225(a911),x87641),x87642))+~P1(f318(f318(f225(a911),f318(f318(f74(a911),f318(a103,x87643)),x87641)),f318(f318(f74(a911),f318(a103,x87643)),x87642)))
% 109.14/108.84 [8765]P1(f318(f318(f226(a911),x87651),x87652))+~P1(f318(f318(f226(a911),f318(f318(f74(a911),f318(a103,x87653)),x87651)),f318(f318(f74(a911),f318(a103,x87653)),x87652)))
% 109.14/108.84 [8779]P1(f318(f318(f225(f918(x87791,a909)),x87792),x87793))+~P1(f318(f318(f225(f918(x87791,a909)),f318(f72(f918(x87791,a909)),x87793)),f318(f72(f918(x87791,a909)),x87792)))
% 109.14/108.84 [8802]P1(f318(f128(x88021),x88022))+~P1(f318(f128(x88021),f318(f318(f318(f174(f912(x88021),f912(x88021)),x88023),f158(x88021)),x88022)))
% 109.14/108.84 [8868]E(f318(f276(x88681,x88681,f298(x88681,x88682)),x88683),x88683)+~P1(f318(f318(f225(f918(x88681,a909)),f318(f276(x88681,x88681,x88682),x88683)),x88683))
% 109.14/108.84 [8916]~P4(x89161)+P13(x89161,f318(f127(x89161,f318(f318(f9(x89161,x89161,a909),a315),f318(x89162,x89163))),x89163))
% 109.14/108.84 [8923]~P1(f318(f318(f225(a911),x89231),x89232))+P1(f318(f318(f225(a911),x89231),f318(f133(a911,a911,f73(a911),x89232),x89233)))
% 109.14/108.84 [9014]~P1(f318(f318(f320(f917(x90141,x90141)),x90142),f298(x90141,x90143)))+P1(f318(f318(f320(f917(x90141,x90141)),x90142),f318(f318(f174(f917(x90141,x90141),a909),f617(x90143,x90142,x90141)),x90143)))
% 109.14/108.84 [9096]~P86(x90961)+E(f318(f318(f73(x90961),x90962),f318(f133(x90961,x90961,f318(f9(x90961,x90961,x90961),f73(x90961)),f2(x90961)),f318(f159(x90961),x90963))),f318(f133(x90961,x90961,f73(x90961),x90962),x90963))
% 109.14/108.84 [9208]~P26(x92082,x92081,x92083,f233(f918(x92082,a909)),f233(f918(x92081,a909)))+E(f84(x92081,x92082,f233(f918(x92081,a909)),f84(x92082,x92081,f233(f918(x92082,a909)),x92083)),x92083)
% 109.14/108.84 [9366]P58(x93661,x93662,x93663)+P1(f318(f318(f320(f917(x93661,x93662)),f318(f318(f243(x93661,x93662),f611(x93663,x93662,x93661)),f592(x93663,x93662,x93661))),x93663))
% 109.14/108.84 [9367]P58(x93671,x93672,x93673)+P1(f318(f318(f320(f917(x93671,x93672)),f318(f318(f243(x93671,x93672),f611(x93673,x93672,x93671)),f591(x93673,x93672,x93671))),x93673))
% 109.14/108.84 [9436]~P1(f318(f318(f320(f917(x94361,x94361)),x94362),f318(f318(f280(x94361,x94361,x94361),x94363),f298(x94361,x94363))))+P1(f318(f318(f320(f917(x94361,x94361)),x94362),f318(f318(f174(f917(x94361,x94361),a909),f619(x94363,x94362,x94361)),x94363)))
% 109.14/108.84 [9437]~P1(f318(x94371,f318(f318(f155(x94372),x94373),f318(f180(f912(x94372)),f168(x94372,x94371,x94373)))))+~P1(f318(f318(f226(a911),f318(f180(f912(x94372)),f168(x94372,x94371,x94373))),f318(f180(f912(x94372)),x94373)))
% 109.14/108.84 [9531]~P1(f318(f318(f225(f918(x95311,a909)),x95312),x95313))+P1(f318(f318(f225(f918(x95311,a909)),f318(f318(f9(x95311,f918(x95311,a909),a909),f320(x95311)),x95312)),f318(f318(f9(x95311,f918(x95311,a909),a909),f320(x95311)),x95313)))
% 109.14/108.84 [9587]~P1(f318(f318(f320(f917(f918(x95871,a909),f918(x95871,a909))),f318(f318(f243(f918(x95871,a909),f918(x95871,a909)),x95872),x95873)),f305(x95871)))+P1(f318(f318(f226(f918(x95871,a909)),x95872),x95873))
% 109.14/108.84 [9611]P59(x96111,x96112,x96113)+~P1(f318(f318(f320(f917(x96111,x96111)),f318(f318(f243(x96111,x96111),f614(x96113,x96112,x96111)),f613(x96113,x96112,x96111))),x96113))
% 109.14/108.84 [9612]P59(x96121,x96122,x96123)+~P1(f318(f318(f320(f917(x96121,x96121)),f318(f318(f243(x96121,x96121),f613(x96123,x96122,x96121)),f614(x96123,x96122,x96121))),x96123))
% 109.14/108.84 [9647]~P1(f318(f318(f320(f917(f912(x96471),f912(x96471))),f318(f318(f243(f912(x96471),f912(x96471)),x96472),x96472)),f138(x96471,x96473)))+P1(f318(f318(f320(f917(x96471,x96471)),f318(f318(f243(x96471,x96471),f642(x96472,x96473,x96471)),f642(x96472,x96473,x96471))),x96473))
% 109.14/108.84 [9710]P1(f318(f318(f225(f918(x97101,a909)),x97102),x97103))+~P1(f318(f318(f225(f918(x97101,a909)),f318(f318(f9(x97101,f918(x97101,a909),a909),f320(x97101)),x97102)),f318(f318(f9(x97101,f918(x97101,a909),a909),f320(x97101)),x97103)))
% 109.14/108.84 [9797]E(f318(f318(f3(a911),f318(f318(f8(a911,a911),x97971),f318(f273(a911),x97972))),f318(f318(f8(a911,a911),x97973),f318(f273(a911),x97972))),f318(f318(f8(a911,a911),f318(f318(f20(a911,a911,a911),f318(f318(f10(a911,f918(a911,a911),a911),f3(a911)),x97971)),x97973)),f318(f273(a911),x97972)))+~P1(f318(f318(f225(a911),f318(x97973,f502(x97972,x97971,x97973))),f318(x97971,f502(x97972,x97971,x97973))))
% 109.14/108.84 [5771]~P66(x57711)+E(f318(f318(f3(x57711),f318(f318(f73(x57711),x57712),x57713)),x57713),x57712)
% 109.14/108.84 [5772]~P66(x57721)+E(f318(f318(f73(x57721),f318(f318(f3(x57721),x57722),x57723)),x57723),x57722)
% 109.14/108.84 [6000]~P66(x60001)+E(f318(f318(f73(x60001),x60002),f318(f318(f73(x60001),f318(f72(x60001),x60002)),x60003)),x60003)
% 109.14/108.84 [6087]~P88(x60871)+E(f318(f318(f74(x60871),f318(f318(f235(x60871),x60872),x60873)),x60872),f318(f318(f235(x60871),x60872),f318(a103,x60873)))
% 109.14/108.84 [6088]~P121(x60881)+E(f318(f318(f74(x60881),f318(f318(f235(x60881),x60882),x60883)),x60882),f318(f318(f235(x60881),x60882),f318(a103,x60883)))
% 109.14/108.84 [6312]~P116(x63121)+E(f318(f69(x63121),f318(f318(f235(x63121),f318(f72(x63121),x63122)),x63123)),f318(f69(x63121),f318(f318(f235(x63121),x63122),x63123)))
% 109.14/108.84 [6358]~P88(x63581)+E(f318(f318(f74(x63581),f318(f318(f235(x63581),x63582),x63583)),x63582),f318(f318(f74(x63581),x63582),f318(f318(f235(x63581),x63582),x63583)))
% 109.14/108.84 [6411]E(f318(f318(f3(a90),f318(f318(f73(a90),x64111),x64112)),x64113),f265(x64111,x64112,x64113))+~P1(f318(f318(f226(a90),x64112),x64113))
% 109.14/108.84 [6434]~E(f318(f318(f129(x64341),x64343),x64342),f104(x64341))+P1(f318(f318(f225(a911),f318(f180(f912(x64341)),x64342)),x64343))
% 109.14/108.84 [6570]E(f318(f318(f74(a911),f318(f94(a911),x65701)),f318(f318(f74(a911),f318(f94(a911),x65702)),x65703)),f2(a911))+~P1(f318(f318(f226(a1),x65701),a76))
% 109.14/108.84 [6587]~P72(x65871)+E(f318(f318(f235(x65871),f318(f318(f282(x65871),f71(x65871)),x65872)),x65873),f318(f318(f282(x65871),f71(x65871)),f318(f318(f235(x65871),x65872),x65873)))
% 109.14/108.84 [6661]E(f318(f318(f3(a911),f318(f318(f73(a911),x66611),x66612)),x66613),f318(f318(f3(a911),x66611),f318(f318(f3(a911),x66613),x66612)))+~P1(f318(f318(f225(a911),x66612),x66613))
% 109.14/108.84 [6662]E(f318(f318(f3(a911),f318(f318(f73(a911),x66621),x66622)),x66623),f318(f318(f73(a911),x66621),f318(f318(f3(a911),x66622),x66623)))+~P1(f318(f318(f225(a911),x66623),x66622))
% 109.14/108.84 [6663]E(f318(f318(f3(a911),f318(f318(f73(a911),x66631),x66632)),x66633),f318(f318(f73(a911),x66631),f318(f318(f3(a911),x66632),x66633)))+~P1(f318(f318(f225(a911),x66633),x66632))
% 109.14/108.84 [6703]~P103(x67031)+P1(f318(f318(f225(x67031),f318(f318(f92(x67031),x67032),x67033)),x67033))
% 109.14/108.84 [6704]~P108(x67041)+P1(f318(f318(f225(x67041),f318(f318(f92(x67041),x67042),x67043)),x67043))
% 109.14/108.84 [6705]~P103(x67051)+P1(f318(f318(f225(x67051),f318(f318(f92(x67051),x67052),x67053)),x67052))
% 109.14/108.84 [6706]~P108(x67061)+P1(f318(f318(f225(x67061),f318(f318(f92(x67061),x67062),x67063)),x67062))
% 109.14/108.84 [6707]~P4(x67071)+P1(f318(f318(f225(x67071),f318(f318(f223(x67071),x67072),x67073)),x67073))
% 109.14/108.84 [6708]~P4(x67081)+P1(f318(f318(f225(x67081),f318(f318(f223(x67081),x67082),x67083)),x67082))
% 109.14/108.84 [6721]E(f318(f318(f30(a1),f318(f318(f30(a1),x67211),x67212)),x67213),f318(f318(f30(a1),x67211),f318(f318(f74(a1),x67212),x67213)))+~P1(f318(f318(f226(a1),f2(a1)),x67213))
% 109.14/108.84 [6777]~P121(x67771)+E(f318(f318(f73(x67771),f318(f318(f74(x67771),x67772),x67773)),x67773),f318(f318(f74(x67771),f318(f318(f73(x67771),x67772),f71(x67771))),x67773))
% 109.14/108.84 [6778]~P99(x67781)+E(f318(f318(f74(x67781),f318(f72(x67781),f318(f94(x67781),x67782))),x67783),f318(f318(f74(x67781),f318(f94(x67781),f318(f72(a1),x67782))),x67783))
% 109.14/108.84 [6852]~P86(x68521)+E(f318(f156(x68521),f318(f318(f145(x68522,x68521),f318(f18(x68521,x68522),f2(x68521))),x68523)),f2(x68521))
% 109.14/108.84 [6869]E(f318(f318(f73(a911),f318(f94(a911),x68691)),f318(f318(f73(a911),f318(f94(a911),x68692)),x68693)),f318(f318(f73(a911),f318(f94(a911),x68692)),x68693))+~P1(f318(a184,f318(f94(a1),x68691)))
% 109.14/108.84 [6884]~P5(x68841)+E(f32(x68841,f318(f318(f300(x68841),x68842),f318(f318(f300(x68841),x68843),f179(f918(x68841,a909))))),f318(f318(f92(x68841),x68842),x68843))
% 109.14/108.84 [6885]~P5(x68851)+E(f31(x68851,f318(f318(f300(x68851),x68852),f318(f318(f300(x68851),x68853),f179(f918(x68851,a909))))),f318(f318(f101(x68851),x68852),x68853))
% 109.14/108.84 [6908]E(f318(f318(f166(x69081),x69082),x69083),x69083)+~P1(f318(f318(f225(a911),f318(f180(f912(x69081)),x69083)),x69082))
% 109.14/108.84 [6914]E(f318(f318(f129(x69141),x69142),x69143),f104(x69141))+~P1(f318(f318(f225(a911),f318(f180(f912(x69141)),x69143)),x69142))
% 109.14/108.84 [6915]E(f318(f318(f129(x69151),x69152),x69153),f104(x69151))+~P1(f318(f318(f225(a911),f318(f180(f912(x69151)),x69153)),x69152))
% 109.14/108.84 [6925]E(f318(f318(f73(a911),f318(f318(f3(a911),x69251),x69252)),x69253),f318(f318(f3(a911),f318(f318(f73(a911),x69251),x69253)),x69252))+~P1(f318(f318(f225(a911),x69252),x69251))
% 109.14/108.84 [6926]E(f318(f318(f73(a911),f318(f318(f3(a911),x69261),x69262)),x69263),f318(f318(f3(a911),f318(f318(f73(a911),x69261),x69263)),x69262))+~P1(f318(f318(f225(a911),x69262),x69261))
% 109.14/108.84 [6940]~P1(f318(f318(f226(a911),x69401),x69403))+P1(f318(f318(f226(a911),f318(f318(f3(a911),x69401),x69402)),x69403))
% 109.14/108.84 [6965]~P4(x69651)+E(f161(x69651,x69652,f318(f318(f139(x69651,x69651,f7(x69651)),x69652),x69653)),x69653)
% 109.14/108.84 [7057]E(f318(f318(f3(a911),f318(f318(f73(a911),x70571),x70572)),f318(a103,x70573)),f318(f318(f3(a911),x70571),f318(a103,f318(f318(f3(a911),x70573),x70572))))+~P1(f318(f318(f225(a911),x70572),x70573))
% 109.14/108.84 [7058]~P116(x70581)+P1(f318(f318(f225(x70581),f2(x70581)),f318(f318(f235(x70581),f318(f69(x70581),x70582)),x70583)))
% 109.14/108.84 [7106]P24(x71061,x71062,x71063)+~P1(f318(f318(f225(f918(f910(x71061),a909)),x71063),x71062))
% 109.14/108.84 [7148]~P1(f318(f55(x71481),x71483))+P1(f318(f55(x71481),f318(f318(f92(f918(x71481,a909)),x71482),x71483)))
% 109.14/108.84 [7149]~P1(f318(f55(x71491),x71492))+P1(f318(f55(x71491),f318(f318(f92(f918(x71491,a909)),x71492),x71493)))
% 109.14/108.84 [7150]~P1(f318(f55(x71501),x71502))+P1(f318(f55(x71501),f318(f318(f3(f918(x71501,a909)),x71502),x71503)))
% 109.14/108.84 [7291]~P39(x72911,x72913)+P39(x72911,f318(f318(f92(f918(f917(x72911,x72911),a909)),x72912),x72913))
% 109.14/108.84 [7292]~P39(x72921,x72922)+P39(x72921,f318(f318(f92(f918(f917(x72921,x72921),a909)),x72922),x72923))
% 109.14/108.84 [7415]~P103(x74151)+E(f12(x74151,f318(f163(x74151),f318(f318(f142(x74151),x74152),x74153))),f318(f133(x74151,x74151,f92(x74151),x74152),x74153))
% 109.14/108.84 [7416]~P103(x74161)+E(f15(x74161,f318(f163(x74161),f318(f318(f142(x74161),x74162),x74163))),f318(f133(x74161,x74161,f101(x74161),x74162),x74163))
% 109.14/108.84 [7417]~P4(x74171)+E(f16(x74171,f318(f163(x74171),f318(f318(f142(x74171),x74172),x74173))),f318(f133(x74171,x74171,f223(x74171),x74172),x74173))
% 109.14/108.84 [7418]~P4(x74181)+E(f17(x74181,f318(f163(x74181),f318(f318(f142(x74181),x74182),x74183))),f318(f133(x74181,x74181,f224(x74181),x74182),x74183))
% 109.14/108.84 [7478]~P1(f318(f55(x74781),x74782))+P1(f318(f318(f225(a911),f318(f29(x74781),x74782)),f318(f29(x74781),f318(f318(f300(x74781),x74783),x74782))))
% 109.14/108.84 [7479]E(f318(f318(f101(f918(a911,a909)),f318(f293(a911,x74791),x74792)),f318(f293(a911,x74792),f318(f318(f73(a911),x74792),x74793))),f318(f293(a911,x74791),f318(f318(f73(a911),x74792),x74793)))+~P1(f318(f318(f225(a911),x74791),x74792))
% 109.14/108.84 [7486]P1(f318(f318(f225(a911),x74861),x74862))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),x74863),x74861)),x74862))
% 109.14/108.84 [7487]P1(f318(f318(f225(a911),x74871),x74872))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),x74871),x74873)),x74872))
% 109.14/108.84 [7488]P1(f318(f318(f225(a911),x74881),x74882))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),x74883),x74881)),x74882))
% 109.14/108.84 [7489]P1(f318(f318(f225(a911),x74891),x74892))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),x74891),x74893)),x74892))
% 109.14/108.84 [7490]P1(f318(f318(f226(a911),x74901),x74902))+~P1(f318(f318(f226(a911),f318(f318(f73(a911),x74901),x74903)),x74902))
% 109.14/108.84 [7527]~P4(x75271)+E(f13(x75271,f223(x75271),f318(f163(x75271),f318(f318(f142(x75271),x75272),x75273))),f318(f133(x75271,x75271,f223(x75271),x75272),x75273))
% 109.14/108.84 [7528]~P4(x75281)+E(f14(x75281,f224(x75281),f318(f163(x75281),f318(f318(f142(x75281),x75282),x75283))),f318(f133(x75281,x75281,f224(x75281),x75282),x75283))
% 109.14/108.84 [7532]~E(x75322,f179(f918(f917(x75321,x75321),a909)))+P1(f318(f318(f225(f918(f917(x75321,x75321),a909)),x75322),x75323))
% 109.14/108.84 [7632]E(f318(f318(f101(f918(x76321,a909)),x76322),f318(f318(f3(f918(x76321,a909)),x76323),x76322)),x76323)+~P1(f318(f318(f225(f918(x76321,a909)),x76322),x76323))
% 109.14/108.84 [7633]~P1(f318(f318(f225(a911),x76331),f318(f318(f73(a911),x76333),x76332)))+P1(f318(f318(f225(a911),f318(f318(f3(a911),x76331),x76332)),x76333))
% 109.14/108.84 [7634]~P1(f318(f318(f226(a911),x76341),f318(f318(f3(a911),x76343),x76342)))+P1(f318(f318(f226(a911),f318(f318(f73(a911),x76341),x76342)),x76343))
% 109.14/108.84 [7690]E(x76901,f104(x76902))+E(f318(f132(x76902),f318(f318(f318(f174(f912(x76902),f912(x76902)),x76903),f158(x76902)),x76901)),f318(f318(f155(x76902),x76901),f39(a911,x76903,f318(f180(f912(x76902)),x76901))))
% 109.14/108.84 [7699]E(f318(f318(f300(x76991),x76992),f318(f318(f3(f918(x76991,a909)),x76993),f318(f318(f300(x76991),x76992),f179(f918(x76991,a909))))),x76993)+~P1(f318(f318(f320(x76991),x76992),x76993))
% 109.14/108.84 [7858]P1(f318(f318(f225(a911),x78581),f318(f318(f73(a911),x78582),x78583)))+~P1(f318(f318(f225(a911),f318(f318(f3(a911),x78581),x78583)),x78582))
% 109.14/108.84 [7859]P1(f318(f318(f226(a911),x78591),f318(f318(f3(a911),x78592),x78593)))+~P1(f318(f318(f226(a911),f318(f318(f73(a911),x78591),x78593)),x78592))
% 109.14/108.84 [7884]P1(f318(f55(x78841),x78842))+~P1(f318(f55(x78841),f318(f318(f101(f918(x78841,a909)),x78843),x78842)))
% 109.14/108.84 [7885]P1(f318(f55(x78851),x78852))+~P1(f318(f55(x78851),f318(f318(f101(f918(x78851,a909)),x78852),x78853)))
% 109.14/108.84 [7961]~P48(x79611,x79613)+P1(f318(f318(f320(f917(x79611,x79611)),f318(f318(f243(x79611,x79611),x79612),x79612)),x79613))
% 109.14/108.84 [8090]E(f318(f318(f155(a911),f130(a911,f318(f293(a911,x80901),x80902))),x80903),f318(f318(f73(a911),x80901),x80903))+~P1(f318(f318(f226(a911),f318(f318(f73(a911),x80901),x80903)),x80902))
% 109.14/108.84 [8154]E(f318(f318(f166(a911),x81541),f130(a911,f318(f293(a911,x81542),x81543))),f130(a911,f318(f293(a911,x81542),f318(f318(f73(a911),x81542),x81541))))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),x81542),x81541)),x81543))
% 109.14/108.84 [8477]E(f318(f318(f125(x84771),f318(f318(f166(x84771),x84772),x84773)),f318(f318(f142(x84771),f318(f318(f155(x84771),x84773),x84772)),f318(f318(f129(x84771),f318(a103,x84772)),x84773))),x84773)+~P1(f318(f318(f226(a911),x84772),f318(f180(f912(x84771)),x84773)))
% 109.14/108.84 [8485]P1(f318(f318(f225(f918(x84851,a909)),f306(x84851,x84852)),f306(x84851,x84853)))+~P1(f318(f318(f225(f918(x84851,f918(x84851,a909))),x84853),x84852))
% 109.14/108.84 [8486]~P59(x84861,x84862,x84863)+P59(x84861,x84862,f318(f318(f3(f918(f917(x84861,x84861),a909)),x84863),f298(x84861,f179(f918(f917(x84861,x84861),a909)))))
% 109.14/108.84 [8505]P1(f318(f318(f225(f918(x85051,a909)),f307(x85051,x85052)),f307(x85051,x85053)))+~P1(f318(f318(f225(f918(f917(x85051,x85051),a909)),x85053),x85052))
% 109.14/108.84 [8512]~P132(x85121)+P1(f318(f318(f225(x85121),f2(x85121)),f318(f318(f73(x85121),f318(f318(f74(x85121),x85122),x85122)),f318(f318(f74(x85121),x85123),x85123))))
% 109.14/108.84 [8546]P1(f318(f318(f225(f918(x85461,a909)),f318(f272(x85461),x85462)),f318(f272(x85461),x85463)))+~P1(f318(f318(f225(f918(f917(x85461,x85461),a909)),x85462),x85463))
% 109.14/108.84 [8575]~P57(x85751,x85752)+~P1(f318(f318(f320(f917(x85751,x85751)),f318(f318(f243(x85751,x85751),x85753),x85753)),x85752))
% 109.14/108.84 [8576]~P39(x85761,x85762)+~P1(f318(f318(f320(f917(x85761,x85761)),f318(f318(f243(x85761,x85761),x85763),x85763)),x85762))
% 109.14/108.84 [8577]~P39(x85771,x85772)+~P1(f318(f318(f320(f917(x85771,x85771)),f318(f318(f243(x85771,x85771),x85773),x85773)),x85772))
% 109.14/108.84 [8620]~E(x86202,x86203)+P1(f318(f318(f320(f917(x86201,x86201)),f318(f318(f243(x86201,x86201),x86202),x86203)),f298(x86201,f179(f918(f917(x86201,x86201),a909)))))
% 109.14/108.84 [8636]P1(f318(f318(f225(f918(x86361,a909)),f32(f918(x86361,a909),x86362)),f32(f918(x86361,a909),x86363)))+~P1(f318(f318(f225(f918(f918(x86361,a909),a909)),x86363),x86362))
% 109.14/108.84 [8637]P1(f318(f318(f225(f918(x86371,a909)),f31(f918(x86371,a909),x86372)),f31(f918(x86371,a909),x86373)))+~P1(f318(f318(f225(f918(f918(x86371,a909),a909)),x86372),x86373))
% 109.14/108.84 [8694]~P8(x86941,x86943,x86942)+P1(f318(f318(f225(f918(f917(x86941,x86941),a909)),x86942),f318(f318(f245(x86941,x86941),x86943),f318(f18(f918(x86941,a909),x86941),x86943))))
% 109.14/108.84 [8695]~P56(x86951,x86953,x86952)+P1(f318(f318(f225(f918(f917(x86951,x86951),a909)),x86952),f318(f318(f245(x86951,x86951),x86953),f318(f18(f918(x86951,a909),x86951),x86953))))
% 109.14/108.84 [8744]~P91(x87441)+P1(f318(f318(f225(x87441),f318(f318(f3(x87441),f318(f69(x87441),x87442)),f318(f69(x87441),x87443))),f318(f69(x87441),f318(f318(f3(x87441),x87443),x87442))))
% 109.14/108.84 [8745]~P91(x87451)+P1(f318(f318(f225(x87451),f318(f318(f3(x87451),f318(f69(x87451),x87452)),f318(f69(x87451),x87453))),f318(f69(x87451),f318(f318(f3(x87451),x87452),x87453))))
% 109.14/108.84 [8777]P1(f318(f318(f225(f918(f917(x87771,x87771),a909)),f298(x87771,x87772)),f298(x87771,x87773)))+~P1(f318(f318(f225(f918(f917(x87771,x87771),a909)),x87772),x87773))
% 109.14/108.84 [8880]~P25(x88802,x88801,x88803,f233(f918(x88802,a909)))+E(f318(f66(x88801,x88802,x88802,f84(x88802,x88801,f233(f918(x88802,a909)),x88803)),x88803),f25(x88802))
% 109.14/108.84 [8881]~P25(x88812,x88811,x88813,f233(f918(x88812,a909)))+E(f318(f66(x88811,x88812,x88812,f84(x88812,x88811,f233(f918(x88812,a909)),x88813)),x88813),f25(x88812))
% 109.14/108.84 [8941]P59(x89411,x89412,x89413)+~P59(x89411,x89412,f318(f318(f3(f918(f917(x89411,x89411),a909)),x89413),f298(x89411,f179(f918(f917(x89411,x89411),a909)))))
% 109.14/108.84 [8961]P1(f318(f318(f225(f918(f917(f912(x89611),f912(x89611)),a909)),f148(x89611,x89612)),f148(x89611,x89613)))+~P1(f318(f318(f225(f918(f917(x89611,x89611),a909)),x89612),x89613))
% 109.14/108.84 [8962]P1(f318(f318(f225(f918(f917(f912(x89621),f912(x89621)),a909)),f149(x89621,x89622)),f149(x89621,x89623)))+~P1(f318(f318(f225(f918(f917(x89621,x89621),a909)),x89622),x89623))
% 109.14/108.84 [8985]~P56(x89851,x89853,x89852)+P1(f318(f318(f225(f918(f917(x89851,x89851),a909)),x89852),f318(f318(f280(x89851,x89851,x89851),f318(f277(x89851,x89851),x89852)),x89852)))
% 109.14/108.84 [9023]~P1(f318(f128(x90231),x90233))+P1(f318(f128(x90231),f318(f318(f129(x90231),f318(f180(f912(x90231)),f168(x90231,x90232,x90233))),x90233)))
% 109.14/108.84 [9041]~P1(f318(f128(x90411),x90412))+E(f318(f127(x90411,f318(f318(f9(x90411,f918(x90411,a909),a909),f320(x90411)),f318(f163(x90411),f167(x90411,x90412,x90413)))),x90412),f167(x90411,x90412,x90413))
% 109.14/108.84 [9094]E(x90941,x90942)+~P1(f318(f318(f320(f917(x90943,x90943)),f318(f318(f243(x90943,x90943),x90941),x90942)),f298(x90943,f179(f918(f917(x90943,x90943),a909)))))
% 109.14/108.84 [9177]P1(f318(f318(f320(x91771),x91772),f307(x91771,x91773)))+P1(f318(f318(f320(f917(x91771,x91771)),f318(f318(f243(x91771,x91771),f532(x91773,x91772,x91771)),x91772)),x91773))
% 109.14/108.84 [9178]P1(f318(f318(f320(x91781),x91782),f307(x91781,x91783)))+P1(f318(f318(f320(f917(x91781,x91781)),f318(f318(f243(x91781,x91781),f596(x91783,x91782,x91781)),x91782)),x91783))
% 109.14/108.84 [9179]P1(f318(f318(f320(x91791),x91792),f307(x91791,x91793)))+P1(f318(f318(f320(f917(x91791,x91791)),f318(f318(f243(x91791,x91791),f598(x91793,x91792,x91791)),x91792)),x91793))
% 109.14/108.84 [9209]P25(x92091,x92092,x92093,f233(f918(x92091,a909)))+~E(f318(f66(x92092,x92091,x92091,f84(x92091,x92092,f233(f918(x92091,a909)),x92093)),x92093),f25(x92091))
% 109.14/108.84 [9256]~P1(f318(f318(f320(f912(x92561)),x92563),f152(x92561,x92562)))+P1(f318(f151(x92561,f318(f318(f9(x92561,f918(x92561,a909),a909),f320(x92561)),x92562)),x92563))
% 109.14/108.84 [9286]P1(f318(x92863,x92862))+E(f318(f253(x92861),f318(f318(f20(x92861,a909,a909),f318(f318(f10(a909,f918(a909,a909),x92861),a316),f318(a315,x92862))),x92863)),f179(f918(x92861,a909)))
% 109.14/108.84 [9304]~P91(x93041)+P1(f318(f318(f225(x93041),f318(f69(x93041),f318(f318(f3(x93041),f318(f69(x93041),x93042)),f318(f69(x93041),x93043)))),f318(f69(x93041),f318(f318(f3(x93041),x93042),x93043))))
% 109.14/108.84 [9321]~P1(f318(x93213,x93212))+E(f318(f253(x93211),f318(f318(f20(x93211,a909,a909),f318(f318(f10(a909,f918(a909,a909),x93211),a316),f318(a315,x93212))),x93213)),f318(f318(f300(x93211),x93212),f179(f918(x93211,a909))))
% 109.14/108.84 [9330]~P1(f318(f318(f320(f918(x93301,a909)),x93303),f318(f299(x93301),x93302)))+P1(f318(f239(x93301,f318(f318(f9(x93301,f918(x93301,a909),a909),f320(x93301)),x93302)),x93303))
% 109.14/108.84 [9365]P39(x93651,x93652)+P1(f318(f318(f320(f917(x93651,x93651)),f318(f318(f243(x93651,x93651),f318(f568(x93652,x93651),f318(a103,x93653))),f318(f568(x93652,x93651),x93653))),x93652))
% 109.14/108.84 [9468]~P1(f318(f128(x94681),x94683))+P1(f318(f128(x94681),f318(f127(x94681,f318(f318(f10(a909,a909,x94681),a313),f318(a315,x94682))),x94683)))
% 109.14/108.84 [9508]P1(f318(f318(f320(f912(x95081)),x95082),f152(x95081,x95083)))+~P1(f318(f151(x95081,f318(f318(f9(x95081,f918(x95081,a909),a909),f320(x95081)),x95083)),x95082))
% 109.14/108.84 [9523]P1(f318(f318(f320(f918(x95231,a909)),x95232),f318(f299(x95231),x95233)))+~P1(f318(f239(x95231,f318(f318(f9(x95231,f918(x95231,a909),a909),f320(x95231)),x95233)),x95232))
% 109.14/108.84 [9582]P1(f318(f318(f320(x95821),f318(f259(x95821,x95822),x95823)),f318(f163(x95821),f318(f318(f145(f917(a90,x95821),x95821),f247(a90,x95821)),x95822))))+~P1(f318(f318(f226(a90),x95823),f318(f156(a90),f318(f318(f145(f917(a90,x95821),a90),f242(a90,x95821)),x95822))))
% 109.14/108.84 [9626]P1(f318(f318(f225(f918(f917(f912(x96261),f912(x96261)),a909)),f149(x96261,x96262)),f318(f318(f245(f912(x96261),f912(x96261)),f152(x96261,x96263)),f318(f18(f918(f912(x96261),a909),f912(x96261)),f152(x96261,x96263)))))+~P1(f318(f318(f225(f918(f917(x96261,x96261),a909)),x96262),f318(f318(f245(x96261,x96261),x96263),f318(f18(f918(x96261,a909),x96261),x96263))))
% 109.14/108.84 [9650]P1(f318(f318(f320(x96501),f318(f242(x96501,f917(a90,a90)),f318(f257(x96501,x96502),x96503))),f318(f163(x96501),f318(f318(f145(f917(a90,x96501),x96501),f247(a90,x96501)),x96502))))+~P1(f318(f318(f226(a90),f2(a90)),f318(f156(a90),f318(f318(f145(f917(a90,x96501),a90),f242(a90,x96501)),x96502))))
% 109.14/108.84 [9673]~P1(f318(f318(f225(f918(f917(x96731,x96731),a909)),x96732),f318(f318(f245(x96731,x96731),x96733),f318(f18(f918(x96731,a909),x96731),x96733))))+P1(f318(f318(f225(f918(f917(x96731,x96731),a909)),f318(f318(f280(x96731,x96731,x96731),x96732),f298(x96731,x96732))),f318(f318(f245(x96731,x96731),x96733),f318(f18(f918(x96731,a909),x96731),x96733))))
% 109.14/108.84 [10006]~P39(x100061,x100062)+~P1(f318(f318(f320(f917(x100061,x100061)),f318(f318(f243(x100061,x100061),f318(x100063,f318(a103,f569(x100062,x100061,x100063)))),f318(x100063,f569(x100062,x100061,x100063)))),x100062))
% 109.14/108.84 [10007]~P39(x100071,x100072)+~P1(f318(f318(f320(f917(x100071,x100071)),f318(f318(f243(x100071,x100071),f318(x100073,f318(a103,f605(x100073,x100072,x100071)))),f318(x100073,f605(x100073,x100072,x100071)))),x100072))
% 109.14/108.84 [10235]P1(f318(f318(f225(f918(f917(f918(x102351,a909),f918(x102351,a909)),a909)),f318(f318(f280(f918(x102351,a909),f918(x102351,a909),f918(x102351,a909)),f309(x102351,x102352)),f318(f318(f101(f918(f917(f918(x102351,a909),f918(x102351,a909)),a909)),f309(x102351,x102353)),f318(f318(f300(f917(f918(x102351,a909),f918(x102351,a909))),f318(f318(f243(f918(x102351,a909),f918(x102351,a909)),f179(f918(x102351,a909))),f179(f918(x102351,a909)))),f179(f918(f917(f918(x102351,a909),f918(x102351,a909)),a909)))))),f309(x102351,x102352)))+~P1(f318(f318(f225(f918(f917(x102351,x102351),a909)),f318(f318(f280(x102351,x102351,x102351),x102352),x102353)),x102352))
% 109.14/108.84 [10236]P1(f318(f318(f225(f918(f917(f918(x102361,a909),f918(x102361,a909)),a909)),f318(f318(f280(f918(x102361,a909),f918(x102361,a909),f918(x102361,a909)),f310(x102361,x102362)),f318(f318(f101(f918(f917(f918(x102361,a909),f918(x102361,a909)),a909)),f310(x102361,x102363)),f318(f318(f300(f917(f918(x102361,a909),f918(x102361,a909))),f318(f318(f243(f918(x102361,a909),f918(x102361,a909)),f179(f918(x102361,a909))),f179(f918(x102361,a909)))),f179(f918(f917(f918(x102361,a909),f918(x102361,a909)),a909)))))),f310(x102361,x102362)))+~P1(f318(f318(f225(f918(f917(x102361,x102361),a909)),f318(f318(f280(x102361,x102361,x102361),x102362),x102363)),x102362))
% 109.14/108.84 [7414]~P1(f318(f318(f225(a911),x74142),x74141))+E(f318(f318(f3(a911),f318(a103,f318(f318(f3(a911),x74141),x74142))),x74143),f318(f318(f3(a911),f318(a103,x74141)),f318(f318(f73(a911),x74142),x74143)))
% 109.14/108.84 [7450]~P69(x74501)+E(f318(f318(f73(x74501),f39(x74501,x74502,x74503)),f318(f318(f74(x74501),f318(f318(f30(x74501),x74502),x74503)),x74503)),x74502)
% 109.14/108.84 [7638]E(f318(f318(f74(a911),f318(f94(a911),x76381)),f318(f318(f74(a911),f318(f94(a911),x76382)),x76383)),f318(f318(f74(a911),f318(f94(a911),f318(f318(f74(a1),x76381),x76382))),x76383))+P1(f318(f318(f226(a1),x76381),a76))
% 109.14/108.84 [8099]~P1(f318(f318(f225(a911),x80993),x80992))+P1(f318(f318(f225(a911),x80991),f318(f318(f3(a911),f318(f318(f73(a911),x80992),x80991)),x80993)))
% 109.14/108.84 [8304]~P1(f318(f318(f225(a911),x83041),x83042))+E(f318(f318(f125(a911),f130(a911,f318(f293(a911,x83041),x83042))),f130(a911,f318(f293(a911,x83042),f318(f318(f73(a911),x83042),x83043)))),f130(a911,f318(f293(a911,x83041),f318(f318(f73(a911),x83042),x83043))))
% 109.14/108.84 [8550]~P1(f318(f55(x85501),x85502))+E(f318(a103,f318(f29(x85501),f318(f318(f3(f918(x85501,a909)),x85502),f318(f318(f300(x85501),x85503),f179(f918(x85501,a909)))))),f318(f29(x85501),f318(f318(f300(x85501),x85503),x85502)))
% 109.14/108.84 [8594]~P1(f318(f55(x85941),x85942))+E(f318(f318(f73(a911),f71(a911)),f318(f29(x85941),f318(f318(f3(f918(x85941,a909)),x85942),f318(f318(f300(x85941),x85943),f179(f918(x85941,a909)))))),f318(f29(x85941),f318(f318(f300(x85941),x85943),x85942)))
% 109.14/108.84 [8786]E(f318(f318(f3(a911),f318(f29(x87861),x87862)),f318(f29(x87861),f318(f318(f92(f918(x87861,a909)),x87862),x87863))),f318(f29(x87861),f318(f318(f3(f918(x87861,a909)),x87862),x87863)))+~P1(f318(f55(x87861),f318(f318(f92(f918(x87861,a909)),x87862),x87863)))
% 109.14/108.84 [9035]~P6(f318(x90352,f496(x90352,x90353,x90351)))+E(f318(f91(a1),f318(f318(f8(x90351,a911),f318(f318(f10(a1,a911,x90351),a95),x90352)),x90353)),f318(f318(f8(x90351,a1),x90352),x90353))
% 109.14/108.84 [9036]~P6(f318(x90362,f493(x90362,x90363,x90361)))+E(f318(f91(a1),f318(f318(f11(x90361,a911),f318(f318(f10(a1,a911,x90361),a95),x90362)),x90363)),f318(f318(f11(x90361,a1),x90362),x90363))
% 109.14/108.84 [9077]~P1(f318(f55(x90771),x90773))+P1(f318(f318(f225(a911),f318(f318(f3(a911),f318(f29(x90771),x90772)),f318(f29(x90771),x90773))),f318(f29(x90771),f318(f318(f3(f918(x90771,a909)),x90772),x90773))))
% 109.14/108.84 [9105]P1(f318(f318(f320(x91051),f496(x91052,x91053,x91051)),x91053))+E(f318(f91(a1),f318(f318(f8(x91051,a911),f318(f318(f10(a1,a911,x91051),a95),x91052)),x91053)),f318(f318(f8(x91051,a1),x91052),x91053))
% 109.14/108.84 [9106]P1(f318(f318(f320(x91061),f493(x91062,x91063,x91061)),x91063))+E(f318(f91(a1),f318(f318(f11(x91061,a911),f318(f318(f10(a1,a911,x91061),a95),x91062)),x91063)),f318(f318(f11(x91061,a1),x91062),x91063))
% 109.14/108.84 [9169]E(f78(x91691,f318(f318(f9(x91691,f918(x91691,a909),a909),f320(x91691)),f318(f318(f3(f918(x91691,a909)),x91692),f318(f318(f300(x91691),x91693),f179(f918(x91691,a909)))))),f238(x91691,x91693,x91692))+P1(f318(f318(f225(f918(x91691,a909)),x91692),f318(f318(f300(x91691),x91693),f179(f918(x91691,a909)))))
% 109.14/108.84 [9524]E(f318(f318(f145(f912(x95241),x95241),f318(f318(f9(f912(x95241),a911,x95241),f155(x95241)),x95242)),f318(f127(f912(x95241),f318(f318(f10(a911,a909,f912(x95241)),f318(f226(a911),x95242)),f180(f912(x95241)))),x95243)),f318(f318(f155(f912(x95241)),f170(x95241,x95243)),x95242))+~P1(f318(f318(f226(a911),x95242),f318(f180(f912(f912(x95241))),f170(x95241,x95243))))
% 109.14/108.84 [9600]E(f318(f127(x96001,x96002),x96003),f168(x96001,x96002,x96003))+P1(f318(f318(f320(x96001),f717(x96003,x96002,x96001)),f318(f163(x96001),f318(f318(f129(x96001),f318(f180(f912(x96001)),f168(x96001,x96002,x96003))),x96003))))
% 109.14/108.84 [9750]E(f318(f318(f129(x97501),f318(f180(f912(x97501)),f168(x97501,x97502,x97503))),x97503),f104(x97501))+~P1(f318(x97502,f318(f132(x97501),f318(f318(f129(x97501),f318(f180(f912(x97501)),f168(x97501,x97502,x97503))),x97503))))
% 109.14/108.84 [9856]~P1(f318(f318(f320(f917(x98561,x98561)),x98562),f298(x98561,x98563)))+P1(f318(f318(f320(f917(x98561,x98561)),x98562),f318(f318(f33(a911,f918(f917(x98561,x98561),a909)),f233(f918(a911,a909))),f318(f318(f9(a911,f918(f917(x98561,x98561),a909),f918(f917(x98561,x98561),a909)),f174(f917(x98561,x98561),a909)),x98563))))
% 109.14/108.84 [9918]~P1(f318(f318(f225(f918(x99181,a909)),f318(f318(f33(a911,f918(x99181,a909)),f318(f293(a911,f2(a911)),f505(x99183,x99182,x99181))),x99182)),x99183))+P1(f318(f318(f225(f918(x99181,a909)),f318(f318(f33(a911,f918(x99181,a909)),f233(f918(a911,a909))),x99182)),x99183))
% 109.14/108.84 [9981]~P1(f318(f318(f226(a1),f2(a1)),x99813))+P1(f318(f318(f226(a1),x99811),f318(f318(f73(a1),x99812),f318(f318(f74(a1),f318(f318(f73(a1),f318(f69(a1),f318(f318(f3(a1),x99812),x99811))),f71(a1))),x99813))))
% 109.14/108.84 [9993]~P39(x99931,f318(f318(f101(f918(f917(x99931,x99931),a909)),x99932),x99933))+P39(x99931,f318(f318(f101(f918(f917(x99931,x99931),a909)),f318(f318(f101(f918(f917(x99931,x99931),a909)),f318(f318(f280(x99931,x99931,x99931),x99932),x99932)),f318(f318(f280(x99931,x99931,x99931),x99933),x99932))),x99933))
% 109.14/108.84 [10063]P39(x100631,f318(f318(f101(f918(f917(x100631,x100631),a909)),x100632),x100633))+~P39(x100631,f318(f318(f101(f918(f917(x100631,x100631),a909)),f318(f318(f101(f918(f917(x100631,x100631),a909)),f318(f318(f280(x100631,x100631,x100631),x100632),x100632)),f318(f318(f280(x100631,x100631,x100631),x100633),x100632))),x100633))
% 109.14/108.84 [9605]~P144(x96051)+E(f318(f93(x96051),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x96052),x96053)),f179(f918(f917(a911,a911),a909)))))),f318(f318(f3(x96051),f318(f91(x96051),x96052)),f318(f91(x96051),x96053)))
% 109.14/108.84 [9698]P1(f318(x96983,x96982))+E(f318(f253(x96981),f318(f318(f20(x96981,a909,a909),f318(f318(f10(a909,f918(a909,a909),x96981),a316),f318(f318(f9(x96981,x96981,a909),a315),x96982))),x96983)),f179(f918(x96981,a909)))
% 109.14/108.84 [9700]~P1(f318(x97003,x97002))+E(f318(f253(x97001),f318(f318(f20(x97001,a909,a909),f318(f318(f10(a909,f918(a909,a909),x97001),a316),f318(f318(f9(x97001,x97001,a909),a315),x97002))),x97003)),f318(f318(f300(x97001),x97002),f179(f918(x97001,a909))))
% 109.14/108.84 [9958]E(x99581,x99582)+P1(f318(f318(f234(x99583,x99583,f318(f318(f10(f918(x99583,a909),f918(x99583,a909),x99583),f318(f10(a909,a909,x99583),a313)),a315)),x99581),x99582))
% 109.14/108.84 [10043]~E(x100431,x100432)+~P1(f318(f318(f234(x100433,x100433,f318(f318(f10(f918(x100433,a909),f918(x100433,a909),x100433),f318(f10(a909,a909,x100433),a313)),a315)),x100431),x100432))
% 109.14/108.84 [10055]~P1(f318(f55(x100551),x100553))+E(f318(f318(f58(x100551,f918(x100551,a909),f318(f318(f10(f918(x100551,a909),f918(f918(x100551,a909),f918(x100551,a909)),x100551),f318(f9(f918(x100551,a909),f918(x100551,a909),f918(x100551,a909)),f3(f918(x100551,a909)))),f318(f318(f9(x100551,f918(x100551,a909),f918(x100551,a909)),f300(x100551)),f179(f918(x100551,a909))))),x100552),x100553),f318(f318(f3(f918(x100551,a909)),x100552),x100553))
% 109.14/108.84 [10082]~P1(f318(f318(f226(a1),f2(a1)),x100823))+P1(f318(f318(f226(a1),f318(f318(f3(a1),x100821),f318(f318(f74(a1),f318(f318(f73(a1),f318(f69(a1),f318(f318(f3(a1),x100821),x100822))),f71(a1))),x100823))),x100822))
% 109.14/108.84 [10348]~P1(f318(f318(f320(x103481),x103483),f307(x103481,x103482)))+P1(f318(f306(x103481,f318(f318(f9(x103481,f918(f917(x103481,x103481),a909),f918(x103481,a909)),f318(f318(f10(f918(x103481,f918(f918(f917(x103481,x103481),a909),a909)),f918(f918(f917(x103481,x103481),a909),f918(x103481,a909)),x103481),f9(x103481,f918(f917(x103481,x103481),a909),a909)),f318(f318(f10(f918(x103481,f917(x103481,x103481)),f918(x103481,f918(f918(f917(x103481,x103481),a909),a909)),x103481),f318(f10(f917(x103481,x103481),f918(f918(f917(x103481,x103481),a909),a909),x103481),f320(f917(x103481,x103481)))),f243(x103481,x103481)))),x103482)),x103483))
% 109.14/108.84 [10362]P1(f318(f318(f320(x103621),x103622),f307(x103621,x103623)))+~P1(f318(f306(x103621,f318(f318(f9(x103621,f918(f917(x103621,x103621),a909),f918(x103621,a909)),f318(f318(f10(f918(x103621,f918(f918(f917(x103621,x103621),a909),a909)),f918(f918(f917(x103621,x103621),a909),f918(x103621,a909)),x103621),f9(x103621,f918(f917(x103621,x103621),a909),a909)),f318(f318(f10(f918(x103621,f917(x103621,x103621)),f918(x103621,f918(f918(f917(x103621,x103621),a909),a909)),x103621),f318(f10(f917(x103621,x103621),f918(f918(f917(x103621,x103621),a909),a909),x103621),f320(f917(x103621,x103621)))),f243(x103621,x103621)))),x103623)),x103622))
% 109.14/108.84 [9916]~P1(f318(f55(x99161),f318(f253(x99161),x99163)))+P1(f318(f55(x99161),f318(f253(x99161),f318(f318(f20(x99161,a909,a909),f318(f318(f10(a909,f918(a909,a909),x99161),a316),x99162)),x99163))))
% 109.14/108.84 [9917]~P1(f318(f55(x99171),f318(f253(x99171),x99172)))+P1(f318(f55(x99171),f318(f253(x99171),f318(f318(f20(x99171,a909,a909),f318(f318(f10(a909,f918(a909,a909),x99171),a316),x99172)),x99173))))
% 109.14/108.84 [10027]P1(f318(f55(x100271),f318(f253(x100271),x100272)))+~P1(f318(f55(x100271),f318(f253(x100271),f318(f318(f20(x100271,a909,a909),f318(f318(f10(a909,f918(a909,a909),x100271),a317),x100273)),x100272))))
% 109.14/108.84 [10028]P1(f318(f55(x100281),f318(f253(x100281),x100282)))+~P1(f318(f55(x100281),f318(f253(x100281),f318(f318(f20(x100281,a909,a909),f318(f318(f10(a909,f918(a909,a909),x100281),a317),x100282)),x100283))))
% 109.14/108.84 [10304]~P1(f318(f55(x103041),x103042))+P1(f318(f55(f912(x103041)),f318(f253(f912(x103041)),f318(f318(f20(f912(x103041),a909,a909),f318(f318(f10(a909,f918(a909,a909),f912(x103041)),a316),f318(f318(f9(f912(x103041),f918(x103041,a909),a909),f318(f318(f10(f918(x103041,a909),f918(f918(x103041,a909),a909),f912(x103041)),f225(f918(x103041,a909))),f163(x103041))),x103042))),f318(f318(f9(f912(x103041),a911,a909),f318(f318(f10(a911,f918(a911,a909),f912(x103041)),a315),f180(f912(x103041)))),x103043)))))
% 109.14/108.84 [10305]~P1(f318(f55(x103051),x103052))+P1(f318(f55(f912(x103051)),f318(f253(f912(x103051)),f318(f318(f20(f912(x103051),a909,a909),f318(f318(f10(a909,f918(a909,a909),f912(x103051)),a316),f318(f318(f9(f912(x103051),f918(x103051,a909),a909),f318(f318(f10(f918(x103051,a909),f918(f918(x103051,a909),a909),f912(x103051)),f225(f918(x103051,a909))),f163(x103051))),x103052))),f318(f318(f9(f912(x103051),a911,a909),f318(f318(f10(a911,f918(a911,a909),f912(x103051)),f225(a911)),f180(f912(x103051)))),x103053)))))
% 109.14/108.84 [9566]~P99(x95661)+E(f318(f318(f235(x95661),x95662),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x95663)),x95663)),a88))),f318(f318(f81(x95661,x95661),f318(f318(f235(x95661),x95662),f318(f94(a911),x95663))),f318(f318(f20(x95661,x95661,x95661),f74(x95661)),f7(x95661))))
% 109.14/108.84 [9603]~P99(x96031)+E(f318(f318(f235(x96031),f318(f94(x96031),x96032)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96033)),x96033)),a88))),f318(f318(f81(x96031,x96031),f318(f318(f235(x96031),f318(f94(x96031),x96032)),f318(f94(a911),x96033))),f318(f318(f20(x96031,x96031,x96031),f74(x96031)),f7(x96031))))
% 109.14/108.84 [10265]~P121(x102651)+E(f318(f318(f235(x102651),x102652),f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x102653)),f318(f318(f74(x102651),f318(f318(f235(x102651),x102652),x102653)),f318(f318(f235(x102651),x102652),x102653)))
% 109.14/108.84 [10281]~P88(x102811)+E(f318(f318(f235(x102811),f318(f318(f235(x102811),x102812),x102813)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f318(f235(x102811),x102812),f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x102813)))
% 109.14/108.84 [10327]~P144(x103271)+E(f318(f318(f235(x103271),f318(f72(x103271),x103272)),f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103273)),f318(f318(f235(x103271),x103272),f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103273)))
% 109.14/108.84 [10386]~P116(x103861)+P1(f318(f318(f225(x103861),f2(x103861)),f318(f318(f73(x103861),f318(f318(f235(x103861),x103862),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x103861),x103863),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))))
% 109.14/108.84 [10335]~P121(x103351)+E(f318(f318(f235(x103351),x103352),f318(a103,f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103353))),f318(f318(f74(x103351),x103352),f318(f318(f74(x103351),f318(f318(f235(x103351),x103352),x103353)),f318(f318(f235(x103351),x103352),x103353))))
% 109.14/108.84 [10354]~P88(x103541)+E(f318(f318(f74(x103541),x103542),f318(f318(f235(x103541),f318(f318(f235(x103541),x103542),x103543)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x103541),x103542),f318(a103,f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103543))))
% 109.14/108.84 [10366]~P116(x103661)+P1(f318(f318(f225(x103661),f2(x103661)),f318(f318(f235(x103661),x103662),f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103663))))
% 109.14/108.84 [10407]~P99(x104071)+E(f318(f318(f3(x104071),f318(f318(f73(x104071),f318(f318(f235(x104071),x104072),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x104071),x104073),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))),f318(f318(f74(x104071),f318(f318(f74(x104071),f318(f94(x104071),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x104072)),x104073)),f318(f318(f235(x104071),f318(f318(f3(x104071),x104072),x104073)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.84 [10408]~P99(x104081)+E(f318(f318(f73(x104081),f318(f318(f73(x104081),f318(f318(f235(x104081),x104082),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x104081),x104083),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))),f318(f318(f74(x104081),f318(f318(f74(x104081),f318(f94(x104081),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x104082)),x104083)),f318(f318(f235(x104081),f318(f318(f73(x104081),x104082),x104083)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.84 [7902]P25(x79021,x79022,x79023,x79024)+~E(f531(x79024,x79023,x79022,x79021),f540(x79024,x79023,x79022,x79021))
% 109.14/108.84 [8188]P36(x81881,x81882,x81883,x81884,f104(x81882))+~E(x81884,f104(x81881))
% 109.14/108.84 [8189]P36(x81891,x81892,x81893,f104(x81891),x81894)+~E(x81894,f104(x81892))
% 109.14/108.84 [8734]~P36(x87342,x87343,x87344,x87341,f104(x87343))+E(x87341,f104(x87342))
% 109.14/108.84 [8735]~P36(x87353,x87352,x87354,f104(x87353),x87351)+E(x87351,f104(x87352))
% 109.14/108.84 [5185]~P17(x51853,x51851,x51854)+E(f318(f318(x51851,x51852),x51852),x51852)
% 109.14/108.84 [5437]P1(f318(x54372,x54374))+E(f318(f127(x54371,x54372),f160(x54371,x54373,x54374)),f104(x54371))
% 109.14/108.84 [5473]~E(x54734,f179(f918(x54731,a909)))+E(f318(f301(x54731,x54732,x54733),x54734),f179(f918(x54732,a909)))
% 109.14/108.84 [5474]~E(x54744,f179(f918(x54741,a909)))+E(f318(f301(x54741,x54742,x54743),x54744),f179(f918(x54742,a909)))
% 109.14/108.84 [5718]~P1(f318(x57182,x57184))+E(f318(f127(x57181,x57182),f160(x57181,x57183,x57184)),f160(x57181,x57183,x57184))
% 109.14/108.84 [5749]~E(f318(f301(x57492,x57493,x57494),x57491),f179(f918(x57493,a909)))+E(x57491,f179(f918(x57492,a909)))
% 109.14/108.84 [5750]~E(f318(f301(x57502,x57503,x57504),x57501),f179(f918(x57503,a909)))+E(x57501,f179(f918(x57502,a909)))
% 109.14/108.84 [5938]~P7(x59381,x59383)+E(f262(x59381,x59382,f261(x59381,x59383),x59384),x59384)
% 109.14/108.84 [6047]~P4(x60472)+E(f318(f318(f139(x60471,x60472,x60473),x60474),f104(x60471)),f318(f318(f142(x60471),x60474),f104(x60471)))
% 109.14/108.84 [6405]~E(x64051,f179(f918(x64052,a909)))+~P1(f318(f56(x64052,x64053,x64051),x64054))
% 109.14/108.84 [6426]~P62(x64261,x64263,x64264,x64262)+P1(f318(f55(x64261),x64262))
% 109.14/108.84 [6427]~P62(x64271,x64273,x64274,x64272)+P1(f318(f55(x64271),x64272))
% 109.14/108.84 [6428]~P62(x64281,x64283,x64282,x64284)+P1(f318(f55(x64281),x64282))
% 109.14/108.84 [6429]~P62(x64291,x64293,x64292,x64294)+P1(f318(f55(x64291),x64292))
% 109.14/108.84 [6435]~P62(x64352,x64353,x64354,x64351)+~E(x64351,f179(f918(x64352,a909)))
% 109.14/108.84 [6436]~P62(x64362,x64363,x64364,x64361)+~E(x64361,f179(f918(x64362,a909)))
% 109.14/108.84 [6469]~P113(x64691)+E(f318(f318(f92(f918(x64691,a909)),f318(f293(x64691,x64692),x64693)),f294(x64691,x64693,x64694)),f179(f918(x64691,a909)))
% 109.14/108.84 [6494]~P1(f318(f318(x64943,x64944),x64942))+P1(f318(f318(f320(x64941),x64942),f285(x64941,x64943,x64944)))
% 109.14/108.84 [6495]~P1(f318(f318(x64953,x64954),x64952))+P1(f318(f318(f320(x64951),x64952),f286(x64951,x64953,x64954)))
% 109.14/108.84 [6496]~P1(f318(f318(x64963,x64962),x64964))+P1(f318(f318(f320(x64961),x64962),f287(x64961,x64963,x64964)))
% 109.14/108.84 [6497]~P1(f318(f318(x64973,x64972),x64974))+P1(f318(f318(f320(x64971),x64972),f289(x64971,x64973,x64974)))
% 109.14/108.84 [6640]~P113(x66401)+E(f318(f318(f92(f918(x66401,a909)),f294(x66401,x66402,x66403)),f296(x66401,x66403,x66404)),f179(f918(x66401,a909)))
% 109.14/108.84 [6641]~P113(x66411)+E(f318(f318(f92(f918(x66411,a909)),f294(x66411,x66412,x66413)),f297(x66411,x66413,x66414)),f179(f918(x66411,a909)))
% 109.14/108.84 [6642]~P113(x66421)+E(f318(f318(f92(f918(x66421,a909)),f296(x66421,x66422,x66423)),f296(x66421,x66423,x66424)),f179(f918(x66421,a909)))
% 109.14/108.84 [6643]~P113(x66431)+E(f318(f318(f92(f918(x66431,a909)),f296(x66431,x66432,x66433)),f297(x66431,x66433,x66434)),f179(f918(x66431,a909)))
% 109.14/108.84 [6644]~P113(x66441)+E(f318(f318(f92(f918(x66441,a909)),f297(x66441,x66442,x66443)),f294(x66441,x66443,x66444)),f179(f918(x66441,a909)))
% 109.14/108.84 [6680]P1(f318(f318(x66801,x66802),f566(x66802,x66801)))+~P1(f318(f240(x66803,x66804,x66801),x66802))
% 109.14/108.84 [6764]~P4(x67642)+E(f318(f163(x67641),f141(x67641,x67642,x67643,x67644)),f318(f163(x67641),x67644))
% 109.14/108.84 [6815]~P114(x68151)+E(f181(x68151,x68152,f318(a103,x68153),x68154),f181(x68151,x68152,x68153,f318(x68152,x68154)))
% 109.14/108.84 [6878]~P1(f318(f318(f320(x68784),x68783),f285(x68784,x68781,x68782)))+P1(f318(f318(x68781,x68782),x68783))
% 109.14/108.84 [6879]~P1(f318(f318(f320(x68794),x68793),f286(x68794,x68791,x68792)))+P1(f318(f318(x68791,x68792),x68793))
% 109.14/108.84 [6880]~P1(f318(f318(f320(x68804),x68802),f287(x68804,x68801,x68803)))+P1(f318(f318(x68801,x68802),x68803))
% 109.14/108.84 [6881]~P1(f318(f318(f320(x68814),x68812),f289(x68814,x68811,x68813)))+P1(f318(f318(x68811,x68812),x68813))
% 109.14/108.84 [6952]E(f318(f29(f919(x69521,x69522)),f304(x69521,x69522,x69523,x69524)),f2(a911))+P1(f318(f55(x69522),x69524))
% 109.14/108.84 [6953]E(f318(f29(f919(x69531,x69532)),f304(x69531,x69532,x69533,x69534)),f2(a911))+P1(f318(f55(x69531),x69533))
% 109.14/108.84 [7157]~P14(x71574,x71571,x71572)+E(f318(f66(x71571,x71571,x71571,f318(x71572,x71573)),f318(x71572,x71573)),f318(x71572,x71573))
% 109.14/108.84 [7399]E(f268(x73991,x73992,x73993,x73994),f318(f243(f918(a90,f918(a909,f915(f913(x73991)))),f917(a90,a90)),f35(x73991)))+~P1(f318(f318(f225(a90),x73993),f2(a90)))
% 109.14/108.84 [8025]~E(x80252,x80253)+P1(f318(f318(f320(f917(x80251,x80251)),f318(f318(f243(x80251,x80251),x80252),x80253)),f298(x80251,x80254)))
% 109.14/108.84 [8054]~P25(x80541,x80542,x80543,f233(f918(x80541,a909)))+E(f318(f70(x80541,x80542,f233(f918(x80541,a909)),x80543),f318(x80543,x80544)),x80544)
% 109.14/108.84 [8055]~P25(x80551,x80552,x80553,f233(f918(x80551,a909)))+E(f318(f84(x80551,x80552,f233(f918(x80551,a909)),x80553),f318(x80553,x80554)),x80554)
% 109.14/108.84 [8137]~P1(f318(f318(f320(f912(x81371)),f318(f318(f142(x81371),x81374),x81372)),f152(x81371,x81373)))+P1(f318(f318(f320(f912(x81371)),x81372),f152(x81371,x81373)))
% 109.14/108.84 [8138]~P1(f318(f318(f320(f912(x81381)),f318(f318(f125(x81381),x81384),x81382)),f152(x81381,x81383)))+P1(f318(f318(f320(f912(x81381)),x81382),f152(x81381,x81383)))
% 109.14/108.84 [8139]~P1(f318(f318(f320(f912(x81391)),f318(f318(f125(x81391),x81392),x81394)),f152(x81391,x81393)))+P1(f318(f318(f320(f912(x81391)),x81392),f152(x81391,x81393)))
% 109.14/108.84 [8150]~P4(x81501)+P13(x81501,f318(f318(f145(x81502,x81501),x81503),f141(x81502,x81501,x81503,x81504)))
% 109.14/108.84 [8260]P25(x82604,x82603,x82601,x82602)+E(f318(x82601,f531(x82602,x82601,x82603,x82604)),f318(x82601,f540(x82602,x82601,x82603,x82604)))
% 109.14/108.84 [8367]~P25(x83672,x83671,x83674,x83673)+P25(x83671,x83672,f70(x83672,x83671,x83673,x83674),f318(f301(x83672,x83671,x83674),x83673))
% 109.14/108.84 [8503]P39(f917(x85032,x85034),f271(x85032,x85034,x85031,x85033))+P1(f318(x85031,f572(x85032,x85033,x85034,x85031)))
% 109.14/108.84 [8621]E(x86211,x86212)+~P1(f318(f318(f320(f917(x86213,x86213)),f318(f318(f243(x86213,x86213),x86211),x86212)),f254(x86213,x86214)))
% 109.14/108.84 [8684]~P1(f318(f55(f919(x86843,x86841)),f304(x86843,x86841,x86844,x86842)))+P1(f318(f55(x86841),x86842))
% 109.14/108.84 [8685]~P1(f318(f55(f919(x86851,x86853)),f304(x86851,x86853,x86852,x86854)))+P1(f318(f55(x86851),x86852))
% 109.14/108.84 [8686]~P1(f318(f55(f919(x86863,x86861)),f304(x86863,x86861,x86864,x86862)))+P1(f318(f55(x86861),x86862))
% 109.14/108.84 [8687]~P1(f318(f55(f919(x86871,x86873)),f304(x86871,x86873,x86872,x86874)))+P1(f318(f55(x86871),x86872))
% 109.14/108.84 [8696]~P25(x86961,x86962,x86963,x86964)+P26(x86961,x86962,x86963,x86964,f318(f301(x86961,x86962,x86963),x86964))
% 109.14/108.84 [8698]P11(x86981,x86982,x86983,x86984)+~E(f318(x86984,f845(x86982,x86984,x86983,x86981)),f318(x86984,f834(x86982,x86984,x86983,x86981)))
% 109.14/108.84 [8787]~P26(x87872,x87873,x87874,x87871,f179(f918(x87873,a909)))+E(x87871,f179(f918(x87872,a909)))
% 109.14/108.84 [8788]~P26(x87883,x87882,x87884,f179(f918(x87883,a909)),x87881)+E(x87881,f179(f918(x87882,a909)))
% 109.14/108.84 [8872]P39(f917(x88721,x88722),f271(x88721,x88722,x88723,x88724))+~P39(x88722,f318(x88724,f572(x88721,x88724,x88722,x88723)))
% 109.14/108.84 [9441]E(f318(f318(f150(x94411,x94412),f664(x94413,x94414,x94412,x94411)),f665(x94413,x94414,x94412,x94411)),x94414)+~P1(f318(f318(f320(f917(f912(x94411),f912(x94411))),f318(f318(f243(f912(x94411),f912(x94411)),x94412),x94414)),f148(x94411,x94413)))
% 109.14/108.84 [9449]~P1(f318(f318(f320(f917(f912(x94491),f912(x94491))),f318(f318(f243(f912(x94491),f912(x94491)),x94492),x94493)),f136(x94491,x94494)))+P1(f318(f318(f320(f917(f912(x94491),f912(x94491))),f318(f318(f243(f912(x94491),f912(x94491)),x94492),x94493)),f138(x94491,x94494)))
% 109.14/108.84 [9563]P1(f318(f55(x95631),x95632))+~P1(f318(f318(f320(f917(f918(x95631,a909),f918(x95631,a909))),f318(f318(f243(f918(x95631,a909),f918(x95631,a909)),x95633),x95632)),f310(x95631,x95634)))
% 109.14/108.84 [9564]P1(f318(f55(x95641),x95642))+~P1(f318(f318(f320(f917(f918(x95641,a909),f918(x95641,a909))),f318(f318(f243(f918(x95641,a909),f918(x95641,a909)),x95642),x95643)),f310(x95641,x95644)))
% 109.14/108.84 [9565]~E(x95651,f179(f918(x95652,a909)))+~P1(f318(f318(f320(f917(f918(x95652,a909),f918(x95652,a909))),f318(f318(f243(f918(x95652,a909),f918(x95652,a909)),x95653),x95651)),f310(x95652,x95654)))
% 109.14/108.84 [10215]P11(x102151,x102152,x102153,x102154)+~P1(f318(f318(f248(x102151,x102151,a909),f318(f318(f9(x102151,f918(x102151,x102152),f918(x102151,a909)),f318(f318(f10(f918(x102152,a909),f918(f918(x102151,x102152),f918(x102151,a909)),x102151),f10(x102152,a909,x102151)),f318(f318(f10(x102152,f918(x102152,a909),x102151),a315),x102154))),x102154)),f521(x102154,x102153,x102152,x102151)))
% 109.14/108.84 [5083]~E(x50834,f104(x50831))+E(f318(f318(f145(x50831,x50832),x50833),x50834),f104(x50832))
% 109.14/108.84 [5084]~E(x50842,f104(x50841))+E(f318(f318(f150(x50841,x50842),x50843),x50844),f104(x50841))
% 109.14/108.84 [5085]~E(x50854,f104(x50851))+E(f318(f318(f145(x50851,x50852),x50853),x50854),f104(x50852))
% 109.14/108.84 [5323]E(x53231,f104(x53232))+~E(f318(f318(f145(x53232,x53233),x53234),x53231),f104(x53233))
% 109.14/108.84 [5324]E(x53241,f104(x53242))+~E(f318(f318(f145(x53242,x53243),x53244),x53241),f104(x53243))
% 109.14/108.84 [5325]E(x53251,f104(x53252))+~E(f318(f318(f150(x53252,x53251),x53253),x53254),f104(x53252))
% 109.14/108.84 [5362]E(x53621,x53622)+~E(f318(f318(f125(x53623),x53624),x53621),f318(f318(f125(x53623),x53624),x53622))
% 109.14/108.84 [5363]E(x53631,x53632)+~E(f318(f318(f125(x53633),x53631),x53634),f318(f318(f125(x53633),x53632),x53634))
% 109.14/108.84 [5511]P1(f318(x55113,x55112))+E(f161(x55111,x55112,f318(f127(x55111,x55113),x55114)),f318(f127(x55111,x55113),x55114))
% 109.14/108.84 [5513]~P1(f318(x55132,x55133))+P35(x55131,x55132,f318(f318(f142(x55131),x55133),x55134))
% 109.14/108.84 [5523]E(x55231,x55232)+~E(f130(a911,f318(f293(a911,x55231),x55233)),f318(f318(f142(a911),x55232),x55234))
% 109.14/108.84 [5571]~P27(x55712,x55713)+P27(x55711,f318(f318(f67(x55712,x55711),x55713),x55714))
% 109.14/108.84 [5572]~P39(x55722,x55723)+P39(x55721,f318(f318(f279(x55722,x55721),x55723),x55724))
% 109.14/108.84 [5573]~P40(x55732,x55733)+P40(x55731,f318(f318(f279(x55732,x55731),x55733),x55734))
% 109.14/108.84 [5574]~P55(x55742,x55743)+P55(x55741,f318(f318(f279(x55742,x55741),x55743),x55744))
% 109.14/108.84 [5702]~P35(x57021,x57022,x57024)+P35(x57021,x57022,f318(f318(f142(x57021),x57023),x57024))
% 109.14/108.84 [5703]~P35(x57031,x57032,x57034)+P35(x57031,x57032,f318(f318(f125(x57031),x57033),x57034))
% 109.14/108.84 [5704]~P35(x57041,x57042,x57043)+P35(x57041,x57042,f318(f318(f125(x57041),x57043),x57044))
% 109.14/108.84 [5794]~E(x57941,f104(x57942))+~E(f318(f318(f125(x57942),x57943),f318(f318(f142(x57942),x57944),f104(x57942))),x57941)
% 109.14/108.84 [5819]~P33(x58193,x58191,f318(f318(f142(x58193),x58192),x58194))+P1(f318(x58191,x58192))
% 109.14/108.84 [5829]E(f105(x58291,x58292),x58293)+~E(f318(f318(f125(x58291),x58293),f318(f318(f142(x58291),x58294),f104(x58291))),x58292)
% 109.14/108.84 [5830]E(f135(x58301,x58302),x58303)+~E(f318(f318(f125(x58301),x58304),f318(f318(f142(x58301),x58303),f104(x58301))),x58302)
% 109.14/108.84 [5940]~E(f130(a911,f318(f293(a911,x59401),x59402)),f318(f318(f142(a911),x59403),x59404))+P1(f318(f318(f226(a911),x59401),x59402))
% 109.14/108.84 [5949]P33(x59491,x59492,x59493)+~P33(x59491,x59492,f318(f318(f142(x59491),x59494),x59493))
% 109.14/108.84 [5950]P33(x59501,x59502,x59503)+~P33(x59501,x59502,f318(f318(f125(x59501),x59504),x59503))
% 109.14/108.84 [5951]P33(x59511,x59512,x59513)+~P33(x59511,x59512,f318(f318(f125(x59511),x59513),x59514))
% 109.14/108.84 [6037]~E(f318(f94(a911),x60374),f2(a911))+E(f318(f318(f155(x60371),f318(f318(f142(x60371),x60372),x60373)),f318(f94(a911),x60374)),x60372)
% 109.14/108.84 [6151]E(x61511,f318(f318(f125(x61512),f318(f159(x61512),x61513)),f318(f318(f142(x61512),x61514),f104(x61512))))+~E(f318(f159(x61512),x61511),f318(f318(f142(x61512),x61514),x61513))
% 109.14/108.84 [6326]~P113(x63261)+E(f318(f318(f92(f918(x63261,a909)),f318(f293(x63261,x63262),x63263)),f318(f293(x63261,x63263),x63264)),f179(f918(x63261,a909)))
% 109.14/108.84 [6338]E(f318(f318(f155(x63381),f160(x63381,x63382,x63383)),x63384),x63383)+~P1(f318(f318(f226(a911),x63384),x63382))
% 109.14/108.84 [6365]~P76(x63651)+E(f318(f156(x63651),f318(f318(f145(a1,x63651),x63652),f169(x63653,x63654))),f318(f318(f8(a1,x63651),x63652),f318(f163(a1),f169(x63653,x63654))))
% 109.14/108.84 [6366]~P76(x63661)+E(f318(f318(f8(a1,x63661),x63662),f318(f163(a1),f169(x63663,x63664))),f318(f156(x63661),f318(f318(f145(a1,x63661),x63662),f169(x63663,x63664))))
% 109.14/108.84 [6507]~E(x65072,f318(f318(f125(x65071),f318(f159(x65071),x65074)),f318(f318(f142(x65071),x65073),f104(x65071))))+E(f318(f159(x65071),x65072),f318(f318(f142(x65071),x65073),x65074))
% 109.14/108.84 [6525]~P19(x65252,x65253,x65254,x65251)+E(f318(x65251,f179(f918(x65252,a909))),f25(x65253))
% 109.14/108.84 [6551]~P113(x65511)+E(f318(f318(f92(f918(x65511,a909)),f297(x65511,x65512,x65513)),f318(f293(x65511,x65513),x65514)),f179(f918(x65511,a909)))
% 109.14/108.84 [6765]E(x67651,f179(f918(x67652,a909)))+~E(f304(x67653,x67652,x67654,x67651),f179(f918(f919(x67653,x67652),a909)))
% 109.14/108.84 [6766]E(x67661,f179(f918(x67662,a909)))+~E(f304(x67662,x67663,x67661,x67664),f179(f918(f919(x67662,x67663),a909)))
% 109.14/108.84 [6837]~P4(x68372)+E(f318(f180(f912(x68371)),f141(x68371,x68372,x68373,x68374)),f318(f180(f912(x68371)),x68374))
% 109.14/108.84 [6848]~P1(f318(f241(x68483,x68484,x68481),x68482))+P1(f318(f318(x68481,f556(x68482,x68481)),x68482))
% 109.14/108.84 [6874]E(f318(f94(a911),x68741),f2(a911))+E(f318(f318(f155(x68742),f318(f318(f142(x68742),x68743),x68744)),f318(f94(a911),x68741)),f318(f318(f155(x68742),x68744),f318(f318(f3(a911),f318(f94(a911),x68741)),f71(a911))))
% 109.14/108.84 [6890]~P1(f318(f55(x68902),x68904))+P1(f318(f55(x68901),f318(f301(x68902,x68901,x68903),x68904)))
% 109.14/108.84 [7118]~P25(x71182,x71181,x71183,x71184)+E(f318(f29(x71181),f318(f301(x71182,x71181,x71183),x71184)),f318(f29(x71182),x71184))
% 109.14/108.84 [7136]E(f318(f301(x71361,x71362,x71363),f318(f302(x71361,x71362,x71363),x71364)),x71364)+~E(f318(f301(x71361,x71362,x71363),f233(f918(x71361,a909))),f233(f918(x71362,a909)))
% 109.14/108.84 [7540]~P25(x75401,x75402,x75403,f233(f918(x75401,a909)))+E(f318(f302(x75401,x75402,x75403),f318(f301(x75401,x75402,x75403),x75404)),x75404)
% 109.14/108.84 [7820]E(x78201,x78202)+~P1(f318(f318(f320(x78203),x78201),f318(f163(x78203),f160(x78203,x78204,x78202))))
% 109.14/108.84 [7829]~E(x78291,f2(a911))+~P1(f318(f318(f320(x78292),x78293),f318(f163(x78292),f160(x78292,x78291,x78294))))
% 109.14/108.84 [7861]P1(f318(x78611,x78612))+~P1(f318(f318(f320(x78613),x78612),f318(f163(x78613),f168(x78613,x78611,x78614))))
% 109.14/108.84 [7975]~P1(f318(f318(f320(f912(x79751)),f318(f318(f142(x79751),x79752),x79754)),f152(x79751,x79753)))+P1(f318(f318(f320(x79751),x79752),x79753))
% 109.14/108.84 [8095]~P1(f318(f318(f320(x80951),x80952),f318(f163(x80951),f167(x80951,x80953,x80954))))+P1(f318(f318(f320(x80951),x80952),f318(f163(x80951),x80953)))
% 109.14/108.84 [8096]~P1(f318(f318(f320(x80961),x80962),f318(f163(x80961),f167(x80961,x80963,x80964))))+P1(f318(f318(f320(x80961),x80962),f318(f163(x80961),x80963)))
% 109.14/108.84 [8097]~P1(f318(f318(f320(x80971),x80972),f318(f163(x80971),f161(x80971,x80974,x80973))))+P1(f318(f318(f320(x80971),x80972),f318(f163(x80971),x80973)))
% 109.14/108.84 [8098]~P1(f318(f318(f320(x80981),x80982),f318(f163(x80981),f168(x80981,x80984,x80983))))+P1(f318(f318(f320(x80981),x80982),f318(f163(x80981),x80983)))
% 109.14/108.84 [8107]E(f318(f180(f912(x81071)),x81072),x81073)+~P1(f318(f318(f320(f912(x81071)),x81072),f318(f163(f912(x81071)),f49(x81071,x81073,x81074))))
% 109.14/108.84 [8206]P1(f318(x82063,x82062))+E(f318(f127(x82061,f318(f318(f10(a909,a909,x82061),a313),f318(a315,x82062))),f318(f127(x82061,x82063),x82064)),f318(f127(x82061,x82063),x82064))
% 109.14/108.84 [8320]E(f318(f318(f155(x83201),f168(x83201,x83202,x83203)),x83204),f318(f318(f155(x83201),x83203),x83204))+~P1(f318(f318(f226(a911),x83204),f318(f180(f912(x83201)),f168(x83201,x83202,x83203))))
% 109.14/108.84 [8404]~P76(x84041)+E(f318(f318(f8(a911,x84041),f318(f318(f10(a911,x84041,a911),x84042),a103)),f318(f293(a911,x84043),x84044)),f318(f318(f8(a911,x84041),x84042),f318(f293(a911,f318(a103,x84043)),f318(a103,x84044))))
% 109.14/108.84 [8413]~P76(x84131)+E(f318(f318(f8(a911,x84131),f318(f318(f10(a911,x84131,a911),x84132),a103)),f294(a911,x84133,x84134)),f318(f318(f8(a911,x84131),x84132),f294(a911,f318(a103,x84133),f318(a103,x84134))))
% 109.14/108.84 [8540]~P25(x85401,x85403,x85404,f233(f918(x85401,a909)))+P25(x85401,f918(x85402,x85403),f318(f318(f10(x85403,f918(x85402,x85403),x85401),f18(x85403,x85402)),x85404),f233(f918(x85401,a909)))
% 109.14/108.84 [8625]~P25(x86252,x86251,x86254,x86253)+E(f318(f301(x86251,x86252,f70(x86252,x86251,x86253,x86254)),f318(f301(x86252,x86251,x86254),x86253)),x86253)
% 109.14/108.84 [8688]~P1(f318(f318(f320(f917(x86881,x86881)),f318(f318(f243(x86881,x86881),x86882),x86884)),f254(x86881,x86883)))+P1(f318(f318(f320(x86881),x86882),x86883))
% 109.14/108.84 [8805]~P25(x88052,x88051,x88053,f233(f918(x88052,a909)))+E(f318(f301(x88051,x88052,f84(x88052,x88051,f233(f918(x88052,a909)),x88053)),f318(f301(x88052,x88051,x88053),x88054)),x88054)
% 109.14/108.84 [8806]~P25(x88062,x88061,x88063,f233(f918(x88062,a909)))+E(f318(f301(x88061,x88062,f84(x88062,x88061,f233(f918(x88062,a909)),x88063)),f318(f301(x88062,x88061,x88063),x88064)),x88064)
% 109.14/108.84 [8879]~P26(x88791,x88792,x88793,x88794,f233(f918(x88792,a909)))+E(f318(f301(x88791,x88792,x88793),f233(f918(x88791,a909))),f233(f918(x88792,a909)))
% 109.14/108.84 [8911]~E(f318(f318(f8(x89111,a911),x89114),x89113),f318(a103,x89112))+P1(f318(f318(f320(x89111),f749(x89112,x89113,x89114,x89111)),x89113))
% 109.14/108.84 [8933]~E(f318(f318(f8(x89334,a911),x89331),x89333),f318(a103,x89332))+P1(f318(f318(f226(a911),f2(a911)),f318(x89331,f749(x89332,x89333,x89331,x89334))))
% 109.14/108.84 [8944]~P1(f318(f55(x89442),x89444))+P1(f318(f318(f225(a911),f318(f29(x89441),f318(f301(x89442,x89441,x89443),x89444))),f318(f29(x89442),x89444)))
% 109.14/108.84 [8945]E(f318(f318(f243(x89451,x89452),f637(x89453,x89454,x89452,x89451)),f638(x89453,x89454,x89452,x89451)),x89454)+~P1(f318(f318(f320(f917(x89451,x89452)),x89454),f318(f277(x89452,x89451),x89453)))
% 109.14/108.84 [8953]P25(x89531,x89532,x89533,x89534)+P1(f318(f318(f320(x89531),f531(x89534,x89533,x89532,x89531)),x89534))
% 109.14/108.84 [8954]P25(x89541,x89542,x89543,x89544)+P1(f318(f318(f320(x89541),f540(x89544,x89543,x89542,x89541)),x89544))
% 109.14/108.84 [9027]P11(x90271,x90272,x90273,x90274)+P1(f318(f318(f320(f917(x90271,x90271)),f521(x90274,x90273,x90272,x90271)),x90273))
% 109.14/108.84 [9082]P1(f318(x90821,x90822))+~P1(f318(x90821,f318(f318(f243(x90823,x90824),f487(x90824,x90823,x90821)),f488(x90824,x90823,x90821))))
% 109.14/108.84 [9099]E(f318(f180(f912(x90991)),x90992),f318(f180(f912(x90991)),x90993))+~P1(f318(f318(f320(f917(f912(x90991),f912(x90991))),f318(f318(f243(f912(x90991),f912(x90991)),x90992),x90993)),f136(x90991,x90994)))
% 109.14/108.84 [9100]E(f318(f180(f912(x91001)),x91002),f318(f180(f912(x91001)),x91003))+~P1(f318(f318(f320(f917(f912(x91001),f912(x91001))),f318(f318(f243(f912(x91001),f912(x91001)),x91002),x91003)),f148(x91001,x91004)))
% 109.14/108.84 [9101]E(f318(f180(f912(x91011)),x91012),f318(f180(f912(x91011)),x91013))+~P1(f318(f318(f320(f917(f912(x91011),f912(x91011))),f318(f318(f243(f912(x91011),f912(x91011)),x91012),x91013)),f149(x91011,x91014)))
% 109.14/108.84 [9102]E(f318(f180(f912(x91021)),x91022),f318(f180(f912(x91021)),x91023))+~P1(f318(f318(f320(f917(f912(x91021),f912(x91021))),f318(f318(f243(f912(x91021),f912(x91021)),x91022),x91023)),f149(x91021,x91024)))
% 109.14/108.84 [9103]E(f318(f180(f912(x91031)),x91032),f318(f180(f912(x91031)),x91033))+~P1(f318(f318(f320(f917(f912(x91031),f912(x91031))),f318(f318(f243(f912(x91031),f912(x91031)),x91032),x91033)),f149(x91031,x91034)))
% 109.14/108.84 [9173]P1(f318(f318(f225(a911),f146(x91731,x91732,x91733)),f146(x91731,x91734,x91733)))+P1(f318(f318(f320(x91731),f663(x91734,x91732,x91733,x91731)),f318(f163(x91731),x91733)))
% 109.14/108.84 [9176]E(f318(f180(f912(x91761)),x91762),f318(f180(f912(x91761)),x91763))+~P1(f318(f318(f320(f917(f912(x91761),f912(x91761))),f318(f318(f243(f912(x91761),f912(x91761)),x91762),x91763)),f298(f912(x91761),f148(x91761,x91764))))
% 109.14/108.84 [9411]~P25(x94111,x94112,x94113,x94114)+~P1(f318(f318(f226(a911),f318(f29(x94112),f318(f301(x94111,x94112,x94113),x94114))),f318(f29(x94111),x94114)))
% 109.14/108.84 [9466]~P1(f318(f318(f320(f917(f912(x94661),f912(x94661))),f318(f318(f243(f912(x94661),f912(x94661)),x94662),x94663)),f148(x94661,x94664)))+P1(f318(f318(f320(f917(f912(x94661),f912(x94661))),f318(f318(f243(f912(x94661),f912(x94661)),x94662),x94663)),f149(x94661,f298(x94661,x94664))))
% 109.14/108.84 [9470]~P1(f318(f318(f320(f917(f912(x94701),f912(x94701))),f318(f318(f243(f912(x94701),f912(x94701)),x94702),x94703)),f149(x94701,x94704)))+P1(f318(f318(f320(f917(f912(x94701),f912(x94701))),f318(f318(f243(f912(x94701),f912(x94701)),x94702),x94703)),f298(f912(x94701),f148(x94701,x94704))))
% 109.14/108.84 [9482]P1(f318(f318(f320(f917(x94821,x94821)),f318(f318(f243(x94821,x94821),x94822),x94823)),f298(x94821,x94824)))+~P1(f318(f318(f320(f917(x94821,x94821)),f318(f318(f243(x94821,x94821),x94822),x94823)),f318(f318(f280(x94821,x94821,x94821),x94824),f298(x94821,x94824))))
% 109.14/108.84 [9674]E(f318(f318(f125(x96741),f682(x96742,x96743,x96744,x96741)),f318(f318(f142(x96741),f676(x96742,x96743,x96744,x96741)),f683(x96742,x96743,x96744,x96741))),x96744)+~P1(f318(f318(f320(f917(f912(x96741),f912(x96741))),f318(f318(f243(f912(x96741),f912(x96741)),x96744),x96743)),f148(x96741,x96742)))
% 109.14/108.84 [9675]E(f318(f318(f125(x96751),f682(x96752,x96753,x96754,x96751)),f318(f318(f142(x96751),f677(x96752,x96753,x96754,x96751)),f683(x96752,x96753,x96754,x96751))),x96753)+~P1(f318(f318(f320(f917(f912(x96751),f912(x96751))),f318(f318(f243(f912(x96751),f912(x96751)),x96754),x96753)),f148(x96751,x96752)))
% 109.14/108.84 [9757]P1(f318(f318(f320(f917(x97571,x97571)),f318(f318(f243(x97571,x97571),x97572),f625(x97573,x97574,x97572,x97571))),f298(x97571,x97573)))+~P1(f318(f318(f320(f917(x97571,x97571)),f318(f318(f243(x97571,x97571),x97572),x97574)),f318(f318(f280(x97571,x97571,x97571),x97573),f298(x97571,x97573))))
% 109.14/108.84 [9840]P1(f318(f318(f225(a911),f146(x98401,x98402,x98403)),f146(x98401,x98404,x98403)))+~P1(f318(f318(f226(a911),f318(x98402,f663(x98404,x98402,x98403,x98401))),f318(x98404,f663(x98404,x98402,x98403,x98401))))
% 109.14/108.84 [9912]P1(f318(f318(f320(f917(x99121,x99121)),f318(f318(f243(x99121,x99121),f624(x99122,x99123,x99124,x99121)),x99123)),f298(x99121,x99122)))+~P1(f318(f318(f320(f917(x99121,x99121)),f318(f318(f243(x99121,x99121),x99124),x99123)),f318(f318(f280(x99121,x99121,x99121),x99122),f298(x99121,x99122))))
% 109.14/108.84 [5343]~E(x53432,x53433)+E(f161(x53431,x53432,f318(f318(f142(x53431),x53433),x53434)),x53434)
% 109.14/108.84 [5356]~E(x53562,f2(a911))+E(f318(f318(f166(x53561),x53562),f318(f318(f142(x53561),x53563),x53564)),f104(x53561))
% 109.14/108.84 [5467]P1(f318(x54672,x54673))+E(f168(x54671,x54672,f318(f318(f142(x54671),x54673),x54674)),f104(x54671))
% 109.14/108.84 [5534]~P64(x55342)+E(f318(f318(f72(f918(x55341,x55342)),x55343),x55344),f318(f72(x55342),f318(x55343,x55344)))
% 109.14/108.84 [5535]~P64(x55352)+E(f318(f318(f72(f918(x55351,x55352)),x55353),x55354),f318(f72(x55352),f318(x55353,x55354)))
% 109.14/108.84 [5548]~E(x55482,f2(a911))+E(f318(f318(f129(x55481),x55482),f318(f318(f142(x55481),x55483),x55484)),f318(f318(f142(x55481),x55483),x55484))
% 109.14/108.84 [5549]P1(f318(x55492,x55493))+E(f318(f127(x55491,x55492),f318(f318(f142(x55491),x55493),x55494)),f318(f127(x55491,x55492),x55494))
% 109.14/108.84 [5685]~E(x56852,x56854)+P1(f318(f318(f318(f300(x56851),x56852),x56853),x56854))
% 109.14/108.84 [5693]E(x56931,f104(x56932))+E(f135(x56933,f318(f318(f145(x56932,x56933),x56934),x56931)),f318(x56934,f135(x56932,x56931)))
% 109.14/108.84 [5707]~E(x57071,f57(x57072,x57074))+E(f318(x57071,f318(f318(f300(x57072),x57073),f179(f918(x57072,a909)))),x57073)
% 109.14/108.84 [5726]~E(f318(f94(a911),x57262),f2(a911))+E(f318(f318(f166(x57261),f318(f94(a911),x57262)),f318(f318(f142(x57261),x57263),x57264)),f104(x57261))
% 109.14/108.84 [5745]E(x57451,f104(x57452))+E(f318(f132(x57453),f318(f318(f145(x57452,x57453),x57454),x57451)),f318(x57454,f318(f132(x57452),x57451)))
% 109.14/108.84 [5849]~P1(f318(x58493,x58494))+P1(f318(f318(f318(f300(x58491),x58492),x58493),x58494))
% 109.14/108.84 [5952]~E(f318(f94(a911),x59522),f2(a911))+E(f318(f318(f129(x59521),f318(f94(a911),x59522)),f318(f318(f142(x59521),x59523),x59524)),f318(f318(f142(x59521),x59523),x59524))
% 109.14/108.84 [5969]~P18(x59692,x59694,x59691)+E(f318(x59691,f318(f318(f300(x59692),x59693),f179(f918(x59692,a909)))),x59693)
% 109.14/108.84 [5995]~E(x59952,x59953)+P1(f318(f318(f320(x59951),x59952),f318(f318(f300(x59951),x59953),x59954)))
% 109.14/108.84 [5996]~E(x59962,x59963)+P1(f318(f318(f320(x59961),x59962),f318(f318(f300(x59961),x59963),x59964)))
% 109.14/108.84 [6001]~P102(x60011)+E(f318(f318(f101(x60011),x60012),f318(f318(f101(x60011),x60013),x60014)),f318(f318(f101(x60011),x60013),f318(f318(f101(x60011),x60012),x60014)))
% 109.14/108.84 [6002]~P102(x60021)+E(f318(f318(f101(x60021),x60022),f318(f318(f101(x60021),x60023),x60024)),f318(f318(f101(x60021),x60023),f318(f318(f101(x60021),x60022),x60024)))
% 109.14/108.84 [6003]~P103(x60031)+E(f318(f318(f101(x60031),x60032),f318(f318(f101(x60031),x60033),x60034)),f318(f318(f101(x60031),x60033),f318(f318(f101(x60031),x60032),x60034)))
% 109.14/108.84 [6004]~P103(x60041)+E(f318(f318(f92(x60041),x60042),f318(f318(f92(x60041),x60043),x60044)),f318(f318(f92(x60041),x60043),f318(f318(f92(x60041),x60042),x60044)))
% 109.14/108.84 [6005]~P108(x60051)+E(f318(f318(f92(x60051),x60052),f318(f318(f92(x60051),x60053),x60054)),f318(f318(f92(x60051),x60053),f318(f318(f92(x60051),x60052),x60054)))
% 109.14/108.84 [6006]~P108(x60061)+E(f318(f318(f92(x60061),x60062),f318(f318(f92(x60061),x60063),x60064)),f318(f318(f92(x60061),x60063),f318(f318(f92(x60061),x60062),x60064)))
% 109.14/108.84 [6007]~P121(x60071)+E(f318(f318(f73(x60071),x60072),f318(f318(f73(x60071),x60073),x60074)),f318(f318(f73(x60071),x60073),f318(f318(f73(x60071),x60072),x60074)))
% 109.14/108.84 [6008]~P121(x60081)+E(f318(f318(f74(x60081),x60082),f318(f318(f74(x60081),x60083),x60084)),f318(f318(f74(x60081),x60083),f318(f318(f74(x60081),x60082),x60084)))
% 109.14/108.84 [6009]~P4(x60091)+E(f318(f318(f223(x60091),x60092),f318(f318(f223(x60091),x60093),x60094)),f318(f318(f223(x60091),x60093),f318(f318(f223(x60091),x60092),x60094)))
% 109.14/108.84 [6010]~P4(x60101)+E(f318(f318(f223(x60101),x60102),f318(f318(f223(x60101),x60103),x60104)),f318(f318(f223(x60101),x60103),f318(f318(f223(x60101),x60102),x60104)))
% 109.14/108.84 [6011]~P4(x60111)+E(f318(f318(f224(x60111),x60112),f318(f318(f224(x60111),x60113),x60114)),f318(f318(f224(x60111),x60113),f318(f318(f224(x60111),x60112),x60114)))
% 109.14/108.84 [6012]~P4(x60121)+E(f318(f318(f224(x60121),x60122),f318(f318(f224(x60121),x60123),x60124)),f318(f318(f224(x60121),x60123),f318(f318(f224(x60121),x60122),x60124)))
% 109.14/108.84 [6019]E(x60191,x60192)+E(f161(x60193,x60191,f318(f318(f142(x60193),x60192),x60194)),f318(f318(f142(x60193),x60192),f161(x60193,x60191,x60194)))
% 109.14/108.84 [6034]~P1(f318(x60342,x60343))+E(f318(f127(x60341,x60342),f318(f318(f142(x60341),x60343),x60344)),f318(f318(f142(x60341),x60343),f318(f127(x60341,x60342),x60344)))
% 109.14/108.84 [6127]~E(x61274,f179(f918(x61271,a909)))+E(f318(f301(x61271,x61272,f318(f18(x61272,x61271),x61273)),x61274),f179(f918(x61272,a909)))
% 109.14/108.84 [6172]~P1(f318(x61722,x61723))+E(f168(x61721,x61722,f318(f318(f142(x61721),x61723),x61724)),f318(f318(f142(x61721),x61723),f168(x61721,x61722,x61724)))
% 109.14/108.84 [6221]P24(x62211,x62212,x62213)+~P24(x62211,x62212,f318(f318(f300(f910(x62211)),x62214),x62213))
% 109.14/108.84 [6237]E(x62371,f179(f918(x62372,a909)))+E(f318(f318(f33(x62372,f918(x62373,a909)),x62371),f318(f18(f918(x62373,a909),x62372),x62374)),x62374)
% 109.14/108.84 [6238]E(x62381,f179(f918(x62382,a909)))+E(f318(f318(f34(x62382,f918(x62383,a909)),x62381),f318(f18(f918(x62383,a909),x62382),x62384)),x62384)
% 109.14/108.84 [6247]~E(x62474,f179(f918(x62472,a909)))+E(f318(f318(f245(x62471,x62472),x62473),f318(f18(f918(x62472,a909),x62471),x62474)),f179(f918(f917(x62471,x62472),a909)))
% 109.14/108.84 [6248]~E(x62483,f179(f918(x62481,a909)))+E(f318(f318(f245(x62481,x62482),x62483),f318(f18(f918(x62482,a909),x62481),x62484)),f179(f918(f917(x62481,x62482),a909)))
% 109.14/108.84 [6303]E(x63031,f2(a911))+E(f318(f318(f129(x63032),x63031),f318(f318(f142(x63032),x63033),x63034)),f318(f318(f129(x63032),f318(f318(f3(a911),x63031),f71(a911))),x63034))
% 109.14/108.84 [6320]E(x63201,f179(f918(x63202,a909)))+E(f318(f301(x63202,x63203,f318(f18(x63203,x63202),x63204)),x63201),f318(f318(f300(x63203),x63204),f179(f918(x63203,a909))))
% 109.14/108.84 [6323]E(f318(f302(x63231,x63232,f318(f18(x63232,x63231),x63233)),x63234),f179(f918(x63231,a909)))+P1(f318(f318(f320(x63232),x63233),x63234))
% 109.14/108.84 [6389]~E(x63893,f179(f918(x63891,a909)))+E(f318(f318(f33(x63891,f918(x63892,a909)),x63893),f318(f18(f918(x63892,a909),x63891),x63894)),f179(f918(x63892,a909)))
% 109.14/108.84 [6390]~E(x63903,f179(f918(x63901,a909)))+E(f318(f318(f34(x63901,f918(x63902,a909)),x63903),f318(f18(f918(x63902,a909),x63901),x63904)),f233(f918(x63902,a909)))
% 109.14/108.84 [6392]~P69(x63921)+E(f39(x63921,f318(f318(f74(x63921),x63922),x63923),f318(f318(f74(x63921),x63922),x63924)),f318(f318(f74(x63921),x63922),f39(x63921,x63923,x63924)))
% 109.14/108.84 [6561]E(f318(f302(x65611,x65612,f318(f18(x65612,x65611),x65613)),x65614),f233(f918(x65611,a909)))+~P1(f318(f318(f320(x65612),x65613),x65614))
% 109.14/108.84 [6583]~P1(f318(f318(f320(x65831),x65832),x65834))+P1(f318(f318(f320(x65831),x65832),f318(f318(f300(x65831),x65833),x65834)))
% 109.14/108.84 [6584]~P1(f318(f318(f320(x65841),x65842),x65844))+P1(f318(f318(f320(x65841),x65842),f318(f318(f300(x65841),x65843),x65844)))
% 109.14/108.84 [6585]~P1(f318(f318(f320(x65851),x65852),x65854))+P1(f318(f318(f320(x65851),x65852),f318(f318(f300(x65851),x65853),x65854)))
% 109.14/108.84 [6590]P1(f318(x65901,x65902))+~P1(f318(f151(x65903,x65901),f318(f318(f142(x65903),x65902),x65904)))
% 109.14/108.84 [6599]~E(x65993,f318(f318(f3(a911),f318(f180(f912(x65991)),x65992)),f71(a911)))+E(f105(x65991,f318(f318(f150(x65991,x65992),x65993),x65994)),f105(x65991,x65992))
% 109.14/108.84 [6618]~P4(x66181)+E(f318(f318(f92(f918(x66181,a909)),f318(f292(x66181),x66182)),f294(x66181,x66183,x66184)),f294(x66181,x66183,f318(f318(f223(x66181),x66182),x66184)))
% 109.14/108.84 [6619]~P4(x66191)+E(f318(f318(f92(f918(x66191,a909)),f318(f274(x66191),x66192)),f294(x66191,x66193,x66194)),f294(x66191,f318(f318(f224(x66191),x66192),x66193),x66194))
% 109.14/108.84 [6634]E(f318(f318(f92(f918(x66341,a909)),x66342),f318(f318(f300(x66341),x66343),x66344)),f318(f318(f92(f918(x66341,a909)),x66342),x66344))+P1(f318(f318(f320(x66341),x66343),x66342))
% 109.14/108.84 [6635]E(f318(f318(f92(f918(x66351,a909)),x66352),f318(f318(f300(x66351),x66353),x66354)),f318(f318(f92(f918(x66351,a909)),x66352),x66354))+P1(f318(f318(f320(x66351),x66353),x66352))
% 109.14/108.84 [6647]E(f161(x66471,x66472,f318(f318(f125(x66471),x66473),x66474)),f318(f318(f125(x66471),x66473),f161(x66471,x66472,x66474)))+P1(f318(f318(f320(x66471),x66472),f318(f163(x66471),x66473)))
% 109.14/108.85 [6652]~P88(x66521)+E(f318(f318(f74(x66521),f318(f318(f235(x66521),x66522),x66523)),f318(f318(f235(x66521),x66522),x66524)),f318(f318(f235(x66521),x66522),f318(f318(f73(a911),x66523),x66524)))
% 109.14/108.85 [6653]~P121(x66531)+E(f318(f318(f74(x66531),f318(f318(f235(x66531),x66532),x66533)),f318(f318(f235(x66531),x66532),x66534)),f318(f318(f235(x66531),x66532),f318(f318(f73(a911),x66533),x66534)))
% 109.14/108.85 [6688]~P107(x66881)+E(f318(f318(f92(x66881),f318(f318(f101(x66881),x66882),x66883)),f318(f318(f101(x66881),x66882),x66884)),f318(f318(f101(x66881),x66882),f318(f318(f92(x66881),x66883),x66884)))
% 109.14/108.85 [6689]~P107(x66891)+E(f318(f318(f101(x66891),f318(f318(f92(x66891),x66892),x66893)),f318(f318(f92(x66891),x66892),x66894)),f318(f318(f92(x66891),x66892),f318(f318(f101(x66891),x66893),x66894)))
% 109.14/108.85 [6690]~P121(x66901)+E(f318(f318(f73(x66901),f318(f318(f74(x66901),x66902),x66903)),f318(f318(f74(x66901),x66902),x66904)),f318(f318(f74(x66901),x66902),f318(f318(f73(x66901),x66903),x66904)))
% 109.14/108.85 [6691]~P4(x66911)+E(f318(f318(f224(x66911),f318(f318(f223(x66911),x66912),x66913)),f318(f318(f223(x66911),x66912),x66914)),f318(f318(f223(x66911),x66912),f318(f318(f224(x66911),x66913),x66914)))
% 109.14/108.85 [6692]~P4(x66921)+E(f318(f318(f223(x66921),f318(f318(f224(x66921),x66922),x66923)),f318(f318(f224(x66921),x66922),x66924)),f318(f318(f224(x66921),x66922),f318(f318(f223(x66921),x66923),x66924)))
% 109.14/108.85 [6728]~P69(x67281)+E(f39(x67281,f318(f318(f74(x67281),x67282),x67283),f318(f318(f74(x67281),x67284),x67283)),f318(f318(f74(x67281),f39(x67281,x67282,x67284)),x67283))
% 109.14/108.85 [6731]~E(f318(f180(f912(x67311)),x67313),f318(f180(f912(x67312)),x67314))+E(f318(f318(f145(f917(x67311,x67312),x67312),f247(x67311,x67312)),f318(f318(f172(x67311,x67312),x67313),x67314)),x67314)
% 109.14/108.85 [6732]~E(f318(f180(f912(x67321)),x67323),f318(f180(f912(x67322)),x67324))+E(f318(f318(f145(f917(x67321,x67322),x67321),f242(x67321,x67322)),f318(f318(f172(x67321,x67322),x67323),x67324)),x67323)
% 109.14/108.85 [6737]P1(f318(f151(x67371,x67372),x67373))+~P1(f318(f151(x67371,x67372),f318(f318(f142(x67371),x67374),x67373)))
% 109.14/108.85 [6738]P1(f318(f151(x67381,x67382),x67383))+~P1(f318(f151(x67381,x67382),f318(f318(f125(x67381),x67384),x67383)))
% 109.14/108.85 [6739]P1(f318(f151(x67391,x67392),x67393))+~P1(f318(f151(x67391,x67392),f318(f318(f125(x67391),x67393),x67394)))
% 109.14/108.85 [6744]~P70(x67441)+E(f39(x67441,f318(f318(f3(x67441),x67442),f39(x67441,x67443,x67444)),x67444),f39(x67441,f318(f318(f3(x67441),x67442),x67443),x67444))
% 109.14/108.85 [6745]~P69(x67451)+E(f39(x67451,f318(f318(f73(x67451),x67452),f39(x67451,x67453,x67454)),x67454),f39(x67451,f318(f318(f73(x67451),x67452),x67453),x67454))
% 109.14/108.85 [6746]~P69(x67461)+E(f39(x67461,f318(f318(f74(x67461),x67462),f39(x67461,x67463,x67464)),x67464),f39(x67461,f318(f318(f74(x67461),x67462),x67463),x67464))
% 109.14/108.85 [6747]~P69(x67471)+E(f39(x67471,f318(f318(f73(x67471),x67472),f39(x67471,x67473,x67474)),x67474),f39(x67471,f318(f318(f73(x67471),x67472),x67473),x67474))
% 109.14/108.85 [6828]~P4(x68281)+E(f318(f318(f92(f918(x68281,a909)),f294(x68281,x68282,x68283)),f318(f292(x68281),x68284)),f294(x68281,x68282,f318(f318(f223(x68281),x68283),x68284)))
% 109.14/108.85 [6829]~P4(x68291)+E(f318(f318(f92(f918(x68291,a909)),f294(x68291,x68292,x68293)),f318(f274(x68291),x68294)),f294(x68291,f318(f318(f224(x68291),x68292),x68294),x68293))
% 109.14/108.85 [6832]~E(f318(f180(f912(x68321)),x68323),f318(f180(f912(x68322)),x68324))+E(f318(f318(f172(x68321,x68322),f318(f159(x68321),x68323)),f318(f159(x68322),x68324)),f318(f159(f917(x68321,x68322)),f318(f318(f172(x68321,x68322),x68323),x68324)))
% 109.14/108.85 [6845]E(x68451,f318(f318(f3(a911),f318(f180(f912(x68452)),x68453)),f71(a911)))+E(f105(x68452,f318(f318(f150(x68452,x68453),x68451),x68454)),f318(f318(f150(x68452,f105(x68452,x68453)),x68451),x68454))
% 109.14/108.85 [6859]~P1(f318(f128(x68592),x68594))+P1(f318(f128(f917(x68591,x68592)),f318(f318(f172(x68591,x68592),x68593),x68594)))
% 109.14/108.85 [6860]~P1(f318(f128(x68601),x68603))+P1(f318(f128(f917(x68601,x68602)),f318(f318(f172(x68601,x68602),x68603),x68604)))
% 109.14/108.85 [7121]E(f318(f318(f30(a911),x71211),x71212),x71213)+~P1(f318(f42(x71211,x71212),f318(f318(f243(a911,a911),x71213),x71214)))
% 109.14/108.85 [7144]E(f39(a911,x71441,x71442),x71443)+~P1(f318(f42(x71441,x71442),f318(f318(f243(a911,a911),x71444),x71443)))
% 109.14/108.85 [7147]P1(f318(f128(x71471),x71472))+~P1(f318(f128(x71473),f318(f318(f145(x71471,x71473),x71474),x71472)))
% 109.14/108.85 [7155]~P24(x71551,x71552,f318(f318(f300(f910(x71551)),x71553),x71554))+P24(x71551,x71552,f318(f318(f300(f910(x71551)),x71553),f179(f918(f910(x71551),a909))))
% 109.14/108.85 [7230]E(f161(x72301,x72302,f318(f318(f125(x72301),x72303),x72304)),f318(f318(f125(x72301),f161(x72301,x72302,x72303)),x72304))+~P1(f318(f318(f320(x72301),x72302),f318(f163(x72301),x72303)))
% 109.14/108.85 [7296]E(f318(f94(a911),x72961),f2(a911))+E(f318(f318(f129(x72962),f318(f94(a911),x72961)),f318(f318(f142(x72962),x72963),x72964)),f318(f318(f129(x72962),f318(f318(f3(a911),f318(f94(a911),x72961)),f71(a911))),x72964))
% 109.14/108.85 [7323]~P70(x73231)+E(f39(x73231,f318(f318(f3(x73231),f39(x73231,x73232,x73233)),x73234),x73233),f39(x73231,f318(f318(f3(x73231),x73232),x73234),x73233))
% 109.14/108.85 [7324]~P69(x73241)+E(f39(x73241,f318(f318(f73(x73241),f39(x73241,x73242,x73243)),x73244),x73243),f39(x73241,f318(f318(f73(x73241),x73242),x73244),x73243))
% 109.14/108.85 [7325]~P69(x73251)+E(f39(x73251,f318(f318(f74(x73251),f39(x73251,x73252,x73253)),x73254),x73253),f39(x73251,f318(f318(f74(x73251),x73252),x73254),x73253))
% 109.14/108.85 [7326]~P69(x73261)+E(f39(x73261,f318(f318(f73(x73261),f39(x73261,x73262,x73263)),x73264),x73263),f39(x73261,f318(f318(f73(x73261),x73262),x73264),x73263))
% 109.14/108.85 [7327]~P69(x73271)+E(f39(x73271,f318(f318(f74(x73271),f39(x73271,x73272,x73273)),x73274),x73273),f39(x73271,f318(f318(f74(x73271),x73272),x73274),x73273))
% 109.14/108.85 [7513]~E(x75131,f318(f318(f142(x75132),x75133),x75134))+~P1(f318(f318(f225(a911),f318(f180(f912(x75132)),x75131)),f318(f180(f912(x75132)),x75134)))
% 109.14/108.85 [7711]P25(x77111,x77112,x77113,f318(f163(x77111),x77114))+~P1(f318(f128(x77112),f318(f318(f145(x77111,x77112),x77113),x77114)))
% 109.14/108.85 [7784]~P1(f318(f318(f225(f918(x77841,a909)),x77842),x77844))+P1(f318(f318(f225(f918(x77841,a909)),x77842),f318(f318(f300(x77841),x77843),x77844)))
% 109.14/108.85 [7821]~P70(x78211)+E(f39(x78211,f318(f318(f3(x78211),f39(x78211,x78212,x78213)),f39(x78211,x78214,x78213)),x78213),f39(x78211,f318(f318(f3(x78211),x78212),x78214),x78213))
% 109.14/108.85 [7822]~P69(x78221)+E(f39(x78221,f318(f318(f73(x78221),f39(x78221,x78222,x78223)),f39(x78221,x78224,x78223)),x78223),f39(x78221,f318(f318(f73(x78221),x78222),x78224),x78223))
% 109.14/108.85 [7823]~P69(x78231)+E(f39(x78231,f318(f318(f74(x78231),f39(x78231,x78232,x78233)),f39(x78231,x78234,x78233)),x78233),f39(x78231,f318(f318(f74(x78231),x78232),x78234),x78233))
% 109.14/108.85 [7927]~E(f318(x79274,f468(x79274,x79273,x79271,x79272)),f233(f918(x79272,a909)))+E(f318(f318(f34(x79271,f918(x79272,a909)),x79273),x79274),f233(f918(x79272,a909)))
% 109.14/108.85 [7928]~E(f318(x79284,f471(x79284,x79283,x79281,x79282)),f179(f918(x79282,a909)))+E(f318(f318(f33(x79281,f918(x79282,a909)),x79283),x79284),f179(f918(x79282,a909)))
% 109.14/108.85 [7929]~E(f318(x79294,f472(x79294,x79293,x79292,x79291)),f179(f918(x79292,a909)))+E(f318(f318(f33(x79291,f918(x79292,a909)),x79293),x79294),f179(f918(x79292,a909)))
% 109.14/108.85 [7930]~E(f318(x79304,f469(x79304,x79303,x79302,x79301)),f233(f918(x79302,a909)))+E(f318(f318(f34(x79301,f918(x79302,a909)),x79303),x79304),f233(f918(x79302,a909)))
% 109.14/108.85 [8321]P1(f318(x83211,x83212))+~P1(f318(f318(f320(x83213),x83212),f318(f318(f92(f918(x83213,a909)),x83214),f318(f253(x83213),x83211))))
% 109.14/108.85 [8357]~P1(f318(f318(f225(f918(x83571,a909)),x83573),x83574))+P1(f318(f318(f225(f918(x83571,a909)),f318(f318(f300(x83571),x83572),x83573)),f318(f318(f300(x83571),x83572),x83574)))
% 109.14/108.85 [8400]P1(f318(f318(f320(x84001),x84002),x84003))+~P1(f318(f318(f320(x84001),x84002),f318(f318(f92(f918(x84001,a909)),x84003),f318(f253(x84001),x84004))))
% 109.14/108.85 [8532]P1(f318(x85322,x85323))+E(f318(f318(f129(x85321),f318(f180(f912(x85321)),f168(x85321,x85322,f318(f318(f142(x85321),x85323),x85324)))),f318(f318(f142(x85321),x85323),x85324)),f318(f318(f142(x85321),x85323),x85324))
% 109.14/108.85 [8639]~P1(f318(f318(f226(a911),f318(x86394,x86392)),f318(x86394,x86393)))+P1(f318(f318(f320(f917(x86391,x86391)),f318(f318(f243(x86391,x86391),x86392),x86393)),f318(f318(f279(a911,x86391),a231),x86394)))
% 109.14/108.85 [8738]~P1(f318(x87382,f736(x87384,x87382,x87383,x87381)))+E(f168(x87381,x87382,f318(f318(f125(x87381),x87383),x87384)),f318(f318(f125(x87381),x87383),f168(x87381,x87382,x87384)))
% 109.14/108.85 [8810]P25(f912(x88101),f912(x88102),f318(f145(x88101,x88102),x88103),x88104)+~P25(x88101,x88102,x88103,f31(f918(x88101,a909),f318(f301(f912(x88101),f918(x88101,a909),f163(x88101)),x88104)))
% 109.14/108.85 [8883]~P1(f318(x88832,x88833))+E(f318(f318(f129(x88831),f318(f180(f912(x88831)),f168(x88831,x88832,f318(f318(f142(x88831),x88833),x88834)))),f318(f318(f142(x88831),x88833),x88834)),f318(f318(f129(x88831),f318(f180(f912(x88831)),f168(x88831,x88832,x88834))),x88834))
% 109.14/108.85 [8924]~E(x89242,x89243)+E(f318(f127(x89241,f318(f318(f10(a909,a909,x89241),a313),f318(a315,x89242))),f318(f318(f142(x89241),x89243),x89244)),f318(f127(x89241,f318(f318(f10(a909,a909,x89241),a313),f318(a315,x89242))),x89244))
% 109.14/108.85 [8934]E(f318(f318(f34(x89341,f918(x89342,a909)),x89343),x89344),f233(f918(x89342,a909)))+P1(f318(f318(f320(x89341),f468(x89344,x89343,x89341,x89342)),x89343))
% 109.14/108.85 [8935]E(f318(f318(f33(x89351,f918(x89352,a909)),x89353),x89354),f179(f918(x89352,a909)))+P1(f318(f318(f320(x89351),f471(x89354,x89353,x89351,x89352)),x89353))
% 109.14/108.85 [8936]E(f318(f318(f33(x89361,f918(x89362,a909)),x89363),x89364),f179(f918(x89362,a909)))+P1(f318(f318(f320(x89361),f472(x89364,x89363,x89362,x89361)),x89363))
% 109.14/108.85 [8937]E(f318(f318(f34(x89371,f918(x89372,a909)),x89373),x89374),f233(f918(x89372,a909)))+P1(f318(f318(f320(x89371),f469(x89374,x89373,x89372,x89371)),x89373))
% 109.14/108.85 [8977]P1(f318(f318(f226(a911),f318(x89771,x89772)),f318(x89771,x89773)))+~P1(f318(f318(f320(f917(x89774,x89774)),f318(f318(f243(x89774,x89774),x89772),x89773)),f318(f318(f279(a911,x89774),a231),x89771)))
% 109.14/108.85 [9005]E(f168(x90051,x90052,f318(f318(f125(x90051),x90053),x90054)),f318(f318(f125(x90051),x90053),f168(x90051,x90052,x90054)))+P1(f318(f318(f320(x90051),f736(x90054,x90052,x90053,x90051)),f318(f163(x90051),x90053)))
% 109.14/108.85 [9059]~P26(x90591,x90592,x90593,f233(f918(x90591,a909)),f233(f918(x90592,a909)))+E(f318(f301(x90591,x90592,x90593),f318(f72(f918(x90591,a909)),x90594)),f318(f72(f918(x90592,a909)),f318(f301(x90591,x90592,x90593),x90594)))
% 109.14/108.85 [9162]P1(f318(f318(f320(x91621),f517(x91622,x91623,x91624,x91621)),x91623))+~P1(f318(f318(f320(f918(x91621,a909)),x91624),f318(f318(f54(x91621),x91623),x91622)))
% 109.14/108.85 [9165]E(x91651,x91652)+~P1(f318(f318(f320(f917(x91653,x91653)),f318(f318(f243(x91653,x91653),x91651),x91652)),f318(f318(f174(f917(x91653,x91653),a909),f2(a911)),x91654)))
% 109.14/108.85 [9234]E(f318(f276(x92341,x92341,x92342),f318(f318(f300(x92341),f517(x92342,x92343,x92344,x92341)),f179(f918(x92341,a909)))),x92344)+~P1(f318(f318(f320(f918(x92341,a909)),x92344),f318(f318(f54(x92341),x92343),x92342)))
% 109.14/108.85 [9239]~P1(f318(f318(f320(f917(x92391,x92391)),f318(f318(f243(x92391,x92391),x92393),x92392)),f298(x92391,x92394)))+P1(f318(f318(f320(f917(x92391,x92391)),f318(f318(f243(x92391,x92391),x92392),x92393)),f298(x92391,f318(f277(x92391,x92391),x92394))))
% 109.14/108.85 [9252]~P69(x92521)+E(f318(f318(f73(x92521),f318(f318(f73(x92521),f318(f318(f74(x92521),x92522),f318(f318(f30(x92521),x92523),x92522))),f39(x92521,x92523,x92522))),x92524),f318(f318(f73(x92521),x92523),x92524))
% 109.14/108.85 [9269]~P1(f318(f318(f320(x92691),x92693),x92694))+P1(f318(f318(f320(f918(x92691,a909)),f318(f276(x92691,x92691,x92692),f318(f318(f300(x92691),x92693),f179(f918(x92691,a909))))),f318(f318(f54(x92691),x92694),x92692)))
% 109.14/108.85 [9282]P1(f318(f318(f320(f917(x92821,x92821)),f318(f318(f243(x92821,x92821),x92822),x92823)),f298(x92821,x92824)))+~P1(f318(f318(f320(f917(x92821,x92821)),f318(f318(f243(x92821,x92821),x92823),x92822)),f298(x92821,f318(f277(x92821,x92821),x92824))))
% 109.14/108.85 [9370]E(f318(f318(f150(x93701,f318(f159(x93701),x93702)),f318(f318(f3(a911),f318(f318(f3(a911),f318(f180(f912(x93701)),x93702)),x93703)),f71(a911))),x93704),f318(f159(x93701),f318(f318(f150(x93701,x93702),x93703),x93704)))+~P1(f318(f318(f226(a911),x93703),f318(f180(f912(x93701)),x93702)))
% 109.14/108.85 [9374]~P1(f318(x93742,f730(x93744,x93742,x93743,x93741)))+E(f318(f318(f129(x93741),f318(f180(f912(x93741)),f168(x93741,x93742,f318(f318(f125(x93741),x93743),x93744)))),f318(f318(f125(x93741),x93743),x93744)),f318(f318(f129(x93741),f318(f180(f912(x93741)),f168(x93741,x93742,x93744))),x93744))
% 109.14/108.85 [9419]~P25(x94192,x94191,x94193,f233(f918(x94192,a909)))+P1(f318(f318(f225(f918(x94191,a909)),f318(f301(x94192,x94191,x94193),f318(f72(f918(x94192,a909)),x94194))),f318(f72(f918(x94191,a909)),f318(f301(x94192,x94191,x94193),x94194))))
% 109.14/108.85 [9432]~P5(x94321)+E(f318(f133(x94321,x94322,f318(f9(x94322,x94321,x94321),f318(f318(f10(x94321,f918(x94321,x94321),x94322),f101(x94321)),x94323)),f179(x94321)),x94324),f318(f318(f33(x94322,x94321),f318(f163(x94322),x94324)),x94323))
% 109.14/108.85 [9433]~P5(x94331)+E(f318(f133(x94331,x94332,f318(f9(x94332,x94331,x94331),f318(f318(f10(x94331,f918(x94331,x94331),x94332),f92(x94331)),x94333)),f233(x94331)),x94334),f318(f318(f34(x94332,x94331),f318(f163(x94332),x94334)),x94333))
% 109.14/108.85 [9445]E(f318(f318(f129(x94451),f318(f180(f912(x94451)),f168(x94451,x94452,f318(f318(f125(x94451),x94453),x94454)))),f318(f318(f125(x94451),x94453),x94454)),f318(f318(f129(x94451),f318(f180(f912(x94451)),f168(x94451,x94452,x94454))),x94454))+P1(f318(f318(f320(x94451),f730(x94454,x94452,x94453,x94451)),f318(f163(x94451),x94453)))
% 109.14/108.85 [9516]~P1(f318(f318(f320(f917(f912(x95164),f912(x95164))),f318(f318(f243(f912(x95164),f912(x95164)),x95163),x95162)),f148(x95164,x95161)))+P1(f318(f318(f226(a911),f664(x95161,x95162,x95163,x95164)),f318(f180(f912(x95164)),x95163)))
% 109.14/108.85 [9517]~P69(x95171)+E(f318(f318(f73(x95171),f318(f318(f73(x95171),f318(f318(f74(x95171),f318(f318(f30(x95171),x95172),x95173)),x95173)),f39(x95171,x95172,x95173))),x95174),f318(f318(f73(x95171),x95172),x95174))
% 109.14/108.85 [9551]~P1(f318(f318(f320(f917(f912(x95511),f912(x95511))),f318(f318(f243(f912(x95511),f912(x95511)),x95512),x95513)),f318(f277(f912(x95511),f912(x95511)),f148(x95511,x95514))))+P1(f318(f318(f320(f917(f912(x95511),f912(x95511))),f318(f318(f243(f912(x95511),f912(x95511)),x95512),x95513)),f148(x95511,f318(f277(x95511,x95511),x95514))))
% 109.14/108.85 [9552]P1(f318(f318(f320(f917(f912(x95521),f912(x95521))),f318(f318(f243(f912(x95521),f912(x95521)),x95522),x95523)),f318(f277(f912(x95521),f912(x95521)),f148(x95521,x95524))))+~P1(f318(f318(f320(f917(f912(x95521),f912(x95521))),f318(f318(f243(f912(x95521),f912(x95521)),x95522),x95523)),f148(x95521,f318(f277(x95521,x95521),x95524))))
% 109.14/108.85 [9585]~P1(f318(f318(f320(x95851),x95853),f318(f255(x95851,x95852),x95854)))+P1(f318(f318(f320(f917(x95851,x95852)),f318(f318(f243(x95851,x95852),x95853),f570(x95854,x95852,x95853,x95851))),x95854))
% 109.14/108.85 [9586]~P1(f318(f318(f320(x95861),x95863),f318(f255(x95861,x95862),x95864)))+P1(f318(f318(f320(f917(x95861,x95862)),f318(f318(f243(x95861,x95862),x95863),f571(x95864,x95862,x95863,x95861))),x95864))
% 109.14/108.85 [9752]~P1(f318(f318(f320(f917(x97521,x97521)),f318(f318(f243(x97521,x97521),x97522),x97524)),f318(f318(f280(x97521,x97521,x97521),x97523),f298(x97521,x97523))))+P1(f318(f318(f320(f917(x97521,x97521)),f318(f318(f243(x97521,x97521),x97522),f624(x97523,x97524,x97522,x97521))),x97523))
% 109.14/108.85 [9931]P11(x99311,x99312,x99313,x99314)+P1(f318(f318(f320(f917(x99311,x99311)),f318(f318(f243(x99311,x99311),f834(x99312,x99314,x99313,x99311)),f845(x99312,x99314,x99313,x99311))),x99313))
% 109.14/108.85 [9946]~P1(f318(f318(f320(f917(x99462,x99461)),x99464),f318(f277(x99461,x99462),x99463)))+P1(f318(f318(f320(f917(x99461,x99462)),f318(f318(f243(x99461,x99462),f638(x99463,x99464,x99461,x99462)),f637(x99463,x99464,x99461,x99462))),x99463))
% 109.14/108.85 [9975]~P1(f318(f318(f320(f917(f912(x99751),f912(x99751))),f318(f318(f243(f912(x99751),f912(x99751)),x99754),x99753)),f148(x99751,x99752)))+P1(f318(f318(f320(f917(x99751,x99751)),f318(f318(f243(x99751,x99751),f676(x99752,x99753,x99754,x99751)),f677(x99752,x99753,x99754,x99751))),x99752))
% 109.14/108.85 [10057]~P1(f318(f318(f320(f917(f912(x100571),f912(x100571))),f318(f318(f243(f912(x100571),f912(x100571)),x100572),x100574)),f148(x100571,x100573)))+P1(f318(f318(f320(f917(x100571,x100571)),f318(f318(f243(x100571,x100571),f318(f318(f155(x100571),x100572),f664(x100573,x100574,x100572,x100571))),f665(x100573,x100574,x100572,x100571))),x100573))
% 109.14/108.85 [10076]~P1(f318(f55(x100762),x100764))+E(f318(f318(f318(f59(f918(x100761,a909),x100762,f101(f918(x100761,a909))),f318(f318(f9(x100762,f918(x100761,a909),f918(x100761,a909)),f318(f318(f10(x100761,f918(f918(x100761,a909),f918(x100761,a909)),x100762),f300(x100761)),x100763)),f179(f918(x100761,a909)))),f179(f918(x100761,a909))),x100764),f318(f301(x100762,x100761,x100763),x100764))
% 109.14/108.85 [10167]~P25(x101671,x101672,x101673,f233(f918(x101671,a909)))+P1(f318(f318(f225(f918(x101671,a909)),f318(f302(x101671,x101672,x101673),f318(f318(f300(x101672),x101674),f179(f918(x101672,a909))))),f318(f318(f300(x101671),f78(x101671,f318(f318(f9(x101671,x101672,a909),f318(f318(f10(x101672,f918(x101672,a909),x101671),a315),x101673)),x101674))),f179(f918(x101671,a909)))))
% 109.14/108.85 [5756]~E(f318(f318(f125(x57561),x57562),x57564),x57563)+E(f318(f318(f166(x57561),f318(f180(f912(x57561)),x57562)),x57563),x57562)
% 109.14/108.85 [5757]~E(f318(f318(f125(x57572),x57573),x57571),x57574)+E(x57571,f318(f318(f129(x57572),f318(f180(f912(x57572)),x57573)),x57574))
% 109.14/108.85 [5768]~E(x57684,f2(a911))+E(f318(f318(f155(x57681),f318(f318(f142(x57681),x57682),x57683)),x57684),x57682)
% 109.14/108.85 [6316]~P121(x63161)+E(f318(f318(f235(x63161),f318(f318(f235(x63161),x63162),x63163)),x63164),f318(f318(f235(x63161),x63162),f318(f318(f74(a911),x63163),x63164)))
% 109.14/108.85 [6317]~P88(x63171)+E(f318(f318(f235(x63171),f318(f318(f235(x63171),x63172),x63173)),x63174),f318(f318(f235(x63171),x63172),f318(f318(f74(a911),x63173),x63174)))
% 109.14/108.85 [6321]E(x63211,f2(a911))+E(f318(f318(f155(x63212),f318(f318(f142(x63212),x63213),x63214)),x63211),f318(f318(f155(x63212),x63214),f318(f318(f3(a911),x63211),f71(a911))))
% 109.14/108.85 [6347]~P121(x63471)+E(f318(f318(f73(x63471),f318(f318(f73(x63471),x63472),x63473)),x63474),f318(f318(f73(x63471),x63472),f318(f318(f73(x63471),x63473),x63474)))
% 109.14/108.85 [6348]~P121(x63481)+E(f318(f318(f74(x63481),f318(f318(f74(x63481),x63482),x63483)),x63484),f318(f318(f74(x63481),x63482),f318(f318(f74(x63481),x63483),x63484)))
% 109.14/108.85 [6349]~P125(x63491)+E(f318(f318(f282(x63491),f318(f318(f74(x63491),x63492),x63493)),x63494),f318(f318(f74(x63491),x63492),f318(f318(f282(x63491),x63493),x63494)))
% 109.14/108.85 [6350]~P102(x63501)+E(f318(f318(f101(x63501),f318(f318(f101(x63501),x63502),x63503)),x63504),f318(f318(f101(x63501),x63502),f318(f318(f101(x63501),x63503),x63504)))
% 109.14/108.85 [6351]~P102(x63511)+E(f318(f318(f101(x63511),f318(f318(f101(x63511),x63512),x63513)),x63514),f318(f318(f101(x63511),x63512),f318(f318(f101(x63511),x63513),x63514)))
% 109.14/108.85 [6352]~P103(x63521)+E(f318(f318(f101(x63521),f318(f318(f101(x63521),x63522),x63523)),x63524),f318(f318(f101(x63521),x63522),f318(f318(f101(x63521),x63523),x63524)))
% 109.14/108.85 [6353]~P103(x63531)+E(f318(f318(f92(x63531),f318(f318(f92(x63531),x63532),x63533)),x63534),f318(f318(f92(x63531),x63532),f318(f318(f92(x63531),x63533),x63534)))
% 109.14/108.85 [6354]~P108(x63541)+E(f318(f318(f92(x63541),f318(f318(f92(x63541),x63542),x63543)),x63544),f318(f318(f92(x63541),x63542),f318(f318(f92(x63541),x63543),x63544)))
% 109.14/108.85 [6355]~P108(x63551)+E(f318(f318(f92(x63551),f318(f318(f92(x63551),x63552),x63553)),x63554),f318(f318(f92(x63551),x63552),f318(f318(f92(x63551),x63553),x63554)))
% 109.14/108.85 [6356]~P77(x63561)+E(f318(f318(f73(x63561),f318(f318(f73(x63561),x63562),x63563)),x63564),f318(f318(f73(x63561),x63562),f318(f318(f73(x63561),x63563),x63564)))
% 109.14/108.85 [6357]~P121(x63571)+E(f318(f318(f73(x63571),f318(f318(f73(x63571),x63572),x63573)),x63574),f318(f318(f73(x63571),x63572),f318(f318(f73(x63571),x63573),x63574)))
% 109.14/108.85 [6359]~P121(x63591)+E(f318(f318(f74(x63591),f318(f318(f74(x63591),x63592),x63593)),x63594),f318(f318(f74(x63591),x63592),f318(f318(f74(x63591),x63593),x63594)))
% 109.14/108.85 [6360]~P80(x63601)+E(f318(f318(f74(x63601),f318(f318(f74(x63601),x63602),x63603)),x63604),f318(f318(f74(x63601),x63602),f318(f318(f74(x63601),x63603),x63604)))
% 109.14/108.85 [6361]~P4(x63611)+E(f318(f318(f223(x63611),f318(f318(f223(x63611),x63612),x63613)),x63614),f318(f318(f223(x63611),x63612),f318(f318(f223(x63611),x63613),x63614)))
% 109.14/108.85 [6362]~P4(x63621)+E(f318(f318(f223(x63621),f318(f318(f223(x63621),x63622),x63623)),x63624),f318(f318(f223(x63621),x63622),f318(f318(f223(x63621),x63623),x63624)))
% 109.14/108.85 [6363]~P4(x63631)+E(f318(f318(f224(x63631),f318(f318(f224(x63631),x63632),x63633)),x63634),f318(f318(f224(x63631),x63632),f318(f318(f224(x63631),x63633),x63634)))
% 109.14/108.85 [6364]~P4(x63641)+E(f318(f318(f224(x63641),f318(f318(f224(x63641),x63642),x63643)),x63644),f318(f318(f224(x63641),x63642),f318(f318(f224(x63641),x63643),x63644)))
% 109.14/108.85 [6373]~P69(x63731)+E(f39(x63731,f318(f318(f73(x63731),x63732),f318(f318(f74(x63731),x63733),x63734)),x63734),f39(x63731,x63732,x63734))
% 109.14/108.85 [6374]~P69(x63741)+E(f39(x63741,f318(f318(f73(x63741),x63742),f318(f318(f74(x63741),x63743),x63744)),x63743),f39(x63741,x63742,x63743))
% 109.14/108.85 [6508]E(f318(f318(f155(x65081),f318(f318(f166(x65081),x65082),x65083)),x65084),f318(f318(f155(x65081),x65083),x65084))+~P1(f318(f318(f226(a911),x65084),x65082))
% 109.14/108.85 [6684]~E(x66842,x66844)+P1(f318(f318(f163(x66841),f318(f318(f142(x66841),x66842),x66843)),x66844))
% 109.14/108.85 [6686]~P121(x66861)+E(f318(f318(f73(x66861),f318(f318(f73(x66861),x66862),x66863)),x66864),f318(f318(f73(x66861),f318(f318(f73(x66861),x66862),x66864)),x66863))
% 109.14/108.85 [6687]~P121(x66871)+E(f318(f318(f74(x66871),f318(f318(f74(x66871),x66872),x66873)),x66874),f318(f318(f74(x66871),f318(f318(f74(x66871),x66872),x66874)),x66873))
% 109.14/108.85 [6750]~P114(x67502)+E(f318(f318(f8(x67501,x67502),f318(f18(x67502,x67501),x67503)),x67504),f318(f318(f74(x67502),f318(f91(x67502),f318(f29(x67501),x67504))),x67503))
% 109.14/108.85 [6917]E(f318(f318(f92(f918(x69171,a909)),f318(f318(f300(x69171),x69172),x69173)),x69174),f318(f318(f92(f918(x69171,a909)),x69173),x69174))+P1(f318(f318(f320(x69171),x69172),x69174))
% 109.14/108.85 [6918]E(f318(f318(f92(f918(x69181,a909)),f318(f318(f300(x69181),x69182),x69183)),x69184),f318(f318(f92(f918(x69181,a909)),x69183),x69184))+P1(f318(f318(f320(x69181),x69182),x69184))
% 109.14/108.85 [6986]~P107(x69861)+E(f318(f318(f92(x69861),f318(f318(f101(x69861),x69862),x69863)),f318(f318(f101(x69861),x69864),x69863)),f318(f318(f101(x69861),f318(f318(f92(x69861),x69862),x69864)),x69863))
% 109.14/108.85 [6987]~P107(x69871)+E(f318(f318(f101(x69871),f318(f318(f92(x69871),x69872),x69873)),f318(f318(f92(x69871),x69874),x69873)),f318(f318(f92(x69871),f318(f318(f101(x69871),x69872),x69874)),x69873))
% 109.14/108.85 [6988]~P65(x69881)+E(f318(f318(f223(x69881),f318(f318(f3(x69881),x69882),x69883)),f318(f318(f3(x69881),x69884),x69883)),f318(f318(f3(x69881),f318(f318(f223(x69881),x69882),x69884)),x69883))
% 109.14/108.85 [6989]~P65(x69891)+E(f318(f318(f224(x69891),f318(f318(f3(x69891),x69892),x69893)),f318(f318(f3(x69891),x69894),x69893)),f318(f318(f3(x69891),f318(f318(f224(x69891),x69892),x69894)),x69893))
% 109.14/108.85 [6990]~P89(x69901)+E(f318(f318(f223(x69901),f318(f318(f73(x69901),x69902),x69903)),f318(f318(f73(x69901),x69904),x69903)),f318(f318(f73(x69901),f318(f318(f223(x69901),x69902),x69904)),x69903))
% 109.14/108.85 [6991]~P89(x69911)+E(f318(f318(f224(x69911),f318(f318(f73(x69911),x69912),x69913)),f318(f318(f73(x69911),x69914),x69913)),f318(f318(f73(x69911),f318(f318(f224(x69911),x69912),x69914)),x69913))
% 109.14/108.85 [6992]~P121(x69921)+E(f318(f318(f74(x69921),f318(f318(f235(x69921),x69922),x69923)),f318(f318(f235(x69921),x69924),x69923)),f318(f318(f235(x69921),f318(f318(f74(x69921),x69922),x69924)),x69923))
% 109.14/108.85 [6993]~P82(x69931)+E(f318(f318(f74(x69931),f318(f318(f235(x69931),x69932),x69933)),f318(f318(f235(x69931),x69934),x69933)),f318(f318(f235(x69931),f318(f318(f74(x69931),x69932),x69934)),x69933))
% 109.14/108.85 [6994]~P72(x69941)+E(f318(f318(f282(x69941),f318(f318(f235(x69941),x69942),x69943)),f318(f318(f235(x69941),x69944),x69943)),f318(f318(f235(x69941),f318(f318(f282(x69941),x69942),x69944)),x69943))
% 109.14/108.85 [6995]~P121(x69951)+E(f318(f318(f73(x69951),f318(f318(f74(x69951),x69952),x69953)),f318(f318(f74(x69951),x69954),x69953)),f318(f318(f74(x69951),f318(f318(f73(x69951),x69952),x69954)),x69953))
% 109.14/108.85 [6996]~P122(x69961)+E(f318(f318(f73(x69961),f318(f318(f74(x69961),x69962),x69963)),f318(f318(f74(x69961),x69964),x69963)),f318(f318(f74(x69961),f318(f318(f73(x69961),x69962),x69964)),x69963))
% 109.14/108.85 [6997]~P125(x69971)+E(f318(f318(f3(x69971),f318(f318(f282(x69971),x69972),x69973)),f318(f318(f282(x69971),x69974),x69973)),f318(f318(f282(x69971),f318(f318(f3(x69971),x69972),x69974)),x69973))
% 109.14/108.85 [6998]~P125(x69981)+E(f318(f318(f73(x69981),f318(f318(f282(x69981),x69982),x69983)),f318(f318(f282(x69981),x69984),x69983)),f318(f318(f282(x69981),f318(f318(f73(x69981),x69982),x69984)),x69983))
% 109.14/108.85 [6999]~P4(x69991)+E(f318(f318(f224(x69991),f318(f318(f223(x69991),x69992),x69993)),f318(f318(f223(x69991),x69994),x69993)),f318(f318(f223(x69991),f318(f318(f224(x69991),x69992),x69994)),x69993))
% 109.14/108.85 [7000]~P4(x70001)+E(f318(f318(f223(x70001),f318(f318(f224(x70001),x70002),x70003)),f318(f318(f224(x70001),x70004),x70003)),f318(f318(f224(x70001),f318(f318(f223(x70001),x70002),x70004)),x70003))
% 109.14/108.85 [7001]~P121(x70011)+E(f318(f318(f73(x70011),f318(f318(f74(x70011),x70012),x70013)),f318(f318(f74(x70011),x70014),x70013)),f318(f318(f74(x70011),f318(f318(f73(x70011),x70012),x70014)),x70013))
% 109.14/108.85 [7033]E(f318(f318(f150(x70331,x70332),x70333),x70334),x70332)+~P1(f318(f318(f225(a911),f318(f180(f912(x70331)),x70332)),x70333))
% 109.14/108.85 [7059]~P1(f318(x70593,x70594))+P1(f318(f318(f318(f101(f918(x70591,a909)),x70592),x70593),x70594))
% 109.14/108.85 [7060]~P1(f318(x70603,x70604))+P1(f318(f318(f318(f101(f918(x70601,a909)),x70602),x70603),x70604))
% 109.14/108.85 [7061]~P1(f318(x70612,x70614))+P1(f318(f318(f318(f101(f918(x70611,a909)),x70612),x70613),x70614))
% 109.14/108.85 [7062]~P1(f318(x70622,x70624))+P1(f318(f318(f318(f101(f918(x70621,a909)),x70622),x70623),x70624))
% 109.14/108.85 [7080]E(f318(f318(f155(x70801),f318(f318(f125(x70801),x70802),x70803)),x70804),f318(f318(f155(x70801),x70802),x70804))+~P1(f318(f318(f226(a911),x70804),f318(f180(f912(x70801)),x70802)))
% 109.14/108.85 [7090]E(f318(f318(f3(f918(x70901,a909)),f318(f318(f300(x70901),x70902),x70903)),x70904),f318(f318(f3(f918(x70901,a909)),x70903),x70904))+~P1(f318(f318(f320(x70901),x70902),x70904))
% 109.14/108.85 [7091]E(f318(f318(f3(f918(x70911,a909)),f318(f318(f300(x70911),x70912),x70913)),x70914),f318(f318(f3(f918(x70911,a909)),x70913),x70914))+~P1(f318(f318(f320(x70911),x70912),x70914))
% 109.14/108.85 [7134]~E(f130(a911,f318(f293(a911,x71341),x71342)),f318(f318(f142(a911),x71344),x71343))+E(f130(a911,f318(f293(a911,f318(f318(f73(a911),x71341),f71(a911))),x71342)),x71343)
% 109.14/108.85 [7156]~P1(f318(f318(f163(x71561),x71563),x71564))+P1(f318(f318(f163(x71561),f318(f318(f142(x71561),x71562),x71563)),x71564))
% 109.14/108.85 [7206]E(x72061,f2(a911))+E(f318(f318(f142(x72062),x72063),f318(f318(f166(x72062),f318(f318(f3(a911),x72061),f71(a911))),x72064)),f318(f318(f166(x72062),x72061),f318(f318(f142(x72062),x72063),x72064)))
% 109.14/108.85 [7307]E(f318(f318(f155(x73071),x73072),f318(f318(f3(a911),x73073),f318(f180(f912(x73071)),x73074))),f318(f318(f155(x73071),f318(f318(f125(x73071),x73074),x73072)),x73073))+P1(f318(f318(f226(a911),x73073),f318(f180(f912(x73071)),x73074)))
% 109.14/108.85 [7336]E(f318(f318(f92(f918(x73361,a909)),x73362),f318(f318(f300(x73361),x73363),x73364)),f318(f318(f300(x73361),x73363),f318(f318(f92(f918(x73361,a909)),x73362),x73364)))+~P1(f318(f318(f320(x73361),x73363),x73362))
% 109.14/108.85 [7337]E(f318(f318(f92(f918(x73371,a909)),x73372),f318(f318(f300(x73371),x73373),x73374)),f318(f318(f300(x73371),x73373),f318(f318(f92(f918(x73371,a909)),x73372),x73374)))+~P1(f318(f318(f320(x73371),x73373),x73372))
% 109.14/108.85 [7375]E(f318(f318(f155(x73751),f318(f318(f150(x73751,x73752),x73753),x73754)),x73753),x73754)+~P1(f318(f318(f226(a911),x73753),f318(f180(f912(x73751)),x73752)))
% 109.14/108.85 [7397]E(x73971,f179(f918(x73972,a909)))+E(f318(f301(f917(x73973,x73972),x73973,f242(x73973,x73972)),f318(f318(f245(x73973,x73972),x73974),f318(f18(f918(x73972,a909),x73973),x73971))),x73974)
% 109.14/108.85 [7398]E(x73981,f179(f918(x73982,a909)))+E(f318(f301(f917(x73982,x73983),x73983,f247(x73982,x73983)),f318(f318(f245(x73982,x73983),x73981),f318(f18(f918(x73983,a909),x73982),x73984))),x73984)
% 109.14/108.85 [7469]E(f318(f318(f3(f918(x74691,a909)),f318(f318(f300(x74691),x74692),x74693)),x74694),f318(f318(f300(x74691),x74692),f318(f318(f3(f918(x74691,a909)),x74693),x74694)))+P1(f318(f318(f320(x74691),x74692),x74694))
% 109.14/108.85 [7499]~E(x74994,f179(f918(x74992,a909)))+E(f318(f301(f917(x74991,x74992),x74991,f242(x74991,x74992)),f318(f318(f245(x74991,x74992),x74993),f318(f18(f918(x74992,a909),x74991),x74994))),f179(f918(x74991,a909)))
% 109.14/108.85 [7500]~E(x75003,f179(f918(x75001,a909)))+E(f318(f301(f917(x75001,x75002),x75002,f247(x75001,x75002)),f318(f318(f245(x75001,x75002),x75003),f318(f18(f918(x75002,a909),x75001),x75004))),f179(f918(x75002,a909)))
% 109.14/108.85 [7547]~P1(f318(f318(f320(x75471),x75472),x75474))+P1(f318(f318(f320(x75471),x75472),f318(f318(f101(f918(x75471,a909)),x75473),x75474)))
% 109.14/108.85 [7548]~P1(f318(f318(f320(x75481),x75482),x75484))+P1(f318(f318(f320(x75481),x75482),f318(f318(f101(f918(x75481,a909)),x75483),x75484)))
% 109.14/108.85 [7549]~P1(f318(f318(f320(x75491),x75492),x75494))+P1(f318(f318(f320(x75491),x75492),f318(f318(f101(f918(x75491,a909)),x75493),x75494)))
% 109.14/108.85 [7550]~P1(f318(f318(f320(x75501),x75502),x75503))+P1(f318(f318(f320(x75501),x75502),f318(f318(f101(f918(x75501,a909)),x75503),x75504)))
% 109.14/108.85 [7551]~P1(f318(f318(f320(x75511),x75512),x75513))+P1(f318(f318(f320(x75511),x75512),f318(f318(f101(f918(x75511,a909)),x75513),x75514)))
% 109.14/108.85 [7552]~P1(f318(f318(f320(x75521),x75522),x75523))+P1(f318(f318(f320(x75521),x75522),f318(f318(f101(f918(x75521,a909)),x75523),x75524)))
% 109.14/108.85 [7569]E(f318(f318(f92(f918(x75691,a909)),f318(f318(f300(x75691),x75692),x75693)),x75694),f318(f318(f300(x75691),x75692),f318(f318(f92(f918(x75691,a909)),x75693),x75694)))+~P1(f318(f318(f320(x75691),x75692),x75694))
% 109.14/108.85 [7570]E(f318(f318(f92(f918(x75701,a909)),f318(f318(f300(x75701),x75702),x75703)),x75704),f318(f318(f300(x75701),x75702),f318(f318(f92(f918(x75701,a909)),x75703),x75704)))+~P1(f318(f318(f320(x75701),x75702),x75704))
% 109.14/108.85 [7840]P1(f318(x78401,x78402))+~P1(f318(f318(f318(f92(f918(x78403,a909)),x78404),x78401),x78402))
% 109.14/108.85 [7841]P1(f318(x78411,x78412))+~P1(f318(f318(f318(f92(f918(x78413,a909)),x78411),x78414),x78412))
% 109.14/108.85 [7842]P1(f318(x78421,x78422))+~P1(f318(f318(f318(f92(f918(x78423,a909)),x78424),x78421),x78422))
% 109.14/108.85 [7843]P1(f318(x78431,x78432))+~P1(f318(f318(f318(f92(f918(x78433,a909)),x78431),x78434),x78432))
% 109.14/108.85 [7844]E(f318(f318(f8(x78441,a911),x78442),f318(f318(f3(f918(x78441,a909)),x78443),f318(f318(f300(x78441),x78444),f179(f918(x78441,a909))))),f318(f318(f8(x78441,a911),x78442),x78443))+P1(f318(f318(f320(x78441),x78444),x78443))
% 109.14/108.85 [7849]~P76(x78491)+E(f318(f156(x78491),f318(f318(f145(a911,x78491),x78492),f130(a911,f318(f293(a911,x78493),x78494)))),f318(f318(f8(a911,x78491),x78492),f318(f163(a911),f130(a911,f318(f293(a911,x78493),x78494)))))
% 109.14/108.85 [7850]~P76(x78501)+E(f318(f318(f8(a911,x78501),x78502),f318(f163(a911),f130(a911,f318(f293(a911,x78503),x78504)))),f318(f156(x78501),f318(f318(f145(a911,x78501),x78502),f130(a911,f318(f293(a911,x78503),x78504)))))
% 109.14/108.85 [7967]~E(x79673,x79674)+P1(f318(f56(x79671,x79672,f318(f318(f300(x79671),x79673),f179(f918(x79671,a909)))),x79674))
% 109.14/108.85 [8061]P1(f318(f318(f320(x80611),x80612),f318(f163(x80611),x80613)))+~P1(f318(f318(f320(x80611),x80612),f318(f163(x80611),f318(f318(f166(x80611),x80614),x80613))))
% 109.14/108.85 [8062]P1(f318(f318(f320(x80621),x80622),f318(f163(x80621),x80623)))+~P1(f318(f318(f320(x80621),x80622),f318(f163(x80621),f318(f318(f129(x80621),x80624),x80623))))
% 109.14/108.85 [8124]P1(f318(f318(f320(x81241),x81242),x81243))+~P1(f318(f318(f320(x81241),x81242),f318(f318(f92(f918(x81241,a909)),x81244),x81243)))
% 109.14/108.85 [8125]P1(f318(f318(f320(x81251),x81252),x81253))+~P1(f318(f318(f320(x81251),x81252),f318(f318(f92(f918(x81251,a909)),x81254),x81253)))
% 109.14/108.85 [8126]P1(f318(f318(f320(x81261),x81262),x81263))+~P1(f318(f318(f320(x81261),x81262),f318(f318(f92(f918(x81261,a909)),x81264),x81263)))
% 109.14/108.85 [8127]P1(f318(f318(f320(x81271),x81272),x81273))+~P1(f318(f318(f320(x81271),x81272),f318(f318(f92(f918(x81271,a909)),x81273),x81274)))
% 109.14/108.85 [8128]P1(f318(f318(f320(x81281),x81282),x81283))+~P1(f318(f318(f320(x81281),x81282),f318(f318(f92(f918(x81281,a909)),x81283),x81284)))
% 109.14/108.85 [8129]P1(f318(f318(f320(x81291),x81292),x81293))+~P1(f318(f318(f320(x81291),x81292),f318(f318(f92(f918(x81291,a909)),x81293),x81294)))
% 109.14/108.85 [8130]P1(f318(f318(f320(x81301),x81302),x81303))+~P1(f318(f318(f320(x81301),x81302),f318(f318(f3(f918(x81301,a909)),x81303),x81304)))
% 109.14/108.85 [8131]P1(f318(f318(f320(x81311),x81312),x81313))+~P1(f318(f318(f320(x81311),x81312),f318(f318(f3(f918(x81311,a909)),x81313),x81314)))
% 109.14/108.85 [8132]P1(f318(f318(f320(x81321),x81322),x81323))+~P1(f318(f318(f320(x81321),x81322),f318(f318(f3(f918(x81321,a909)),x81323),x81324)))
% 109.14/108.85 [8147]E(f318(f318(f125(x81471),f318(f318(f166(x81471),x81472),x81473)),f318(f318(f142(x81471),x81474),f318(f318(f129(x81471),f318(a103,x81472)),x81473))),f318(f318(f150(x81471,x81473),x81472),x81474))+~P1(f318(f318(f226(a911),x81472),f318(f180(f912(x81471)),x81473)))
% 109.14/108.85 [8170]P1(f318(f318(f320(x81701),x81702),x81703))+~P1(f318(f318(f225(f918(x81701,a909)),f318(f318(f300(x81701),x81702),x81704)),x81703))
% 109.14/108.85 [8210]~P1(f318(f318(f320(x82101),x82102),x82103))+~P1(f318(f318(f320(x82101),x82102),f318(f318(f3(f918(x82101,a909)),x82104),x82103)))
% 109.14/108.85 [8211]~P1(f318(f318(f320(x82111),x82112),x82113))+~P1(f318(f318(f320(x82111),x82112),f318(f318(f3(f918(x82111,a909)),x82114),x82113)))
% 109.14/108.85 [8212]~P1(f318(f318(f320(x82121),x82122),x82123))+~P1(f318(f318(f320(x82121),x82122),f318(f318(f3(f918(x82121,a909)),x82124),x82123)))
% 109.14/108.85 [8245]~P1(f318(f318(f226(a911),x82454),f318(f180(f912(x82451)),x82453)))+P1(f318(f318(f320(x82451),x82452),f318(f163(x82451),f318(f318(f150(x82451,x82453),x82454),x82452))))
% 109.14/108.85 [8291]E(f318(f94(a911),x82911),f2(a911))+E(f318(f318(f142(x82912),x82913),f318(f318(f166(x82912),f318(f318(f3(a911),f318(f94(a911),x82911)),f71(a911))),x82914)),f318(f318(f166(x82912),f318(f94(a911),x82911)),f318(f318(f142(x82912),x82913),x82914)))
% 109.14/108.85 [8300]E(f318(f318(f155(x83001),f318(f318(f129(x83001),x83002),x83003)),x83004),f318(f318(f155(x83001),x83003),f318(f318(f73(a911),x83002),x83004)))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),x83002),x83004)),f318(f180(f912(x83001)),x83003)))
% 109.14/108.85 [8309]~P114(x83092)+E(f318(f318(f8(x83091,x83092),f318(f318(f10(a911,x83092,x83091),f91(x83092)),x83093)),x83094),f318(f91(x83092),f318(f318(f8(x83091,a911),x83093),x83094)))
% 109.14/108.85 [8310]~P144(x83102)+E(f318(f318(f8(x83101,x83102),f318(f318(f10(a1,x83102,x83101),f93(x83102)),x83103)),x83104),f318(f93(x83102),f318(f318(f8(x83101,a1),x83103),x83104)))
% 109.14/108.85 [8359]~P75(x83592)+E(f318(f318(f11(x83591,x83592),f318(f318(f10(x83592,x83592,x83591),f69(x83592)),x83593)),x83594),f318(f69(x83592),f318(f318(f11(x83591,x83592),x83593),x83594)))
% 109.14/108.85 [8360]~P67(x83602)+E(f318(f318(f8(x83601,x83602),f318(f318(f10(x83602,x83602,x83601),f72(x83602)),x83603)),x83604),f318(f72(x83602),f318(f318(f8(x83601,x83602),x83603),x83604)))
% 109.14/108.85 [8362]E(f318(f318(f8(x83621,a911),x83622),f318(f318(f3(f918(x83621,a909)),x83623),f318(f318(f300(x83621),x83624),f179(f918(x83621,a909))))),f318(f318(f3(a911),f318(f318(f8(x83621,a911),x83622),x83623)),f318(x83622,x83624)))+~P1(f318(f318(f320(x83621),x83624),x83623))
% 109.14/108.85 [8380]P1(f318(f318(f225(f918(x83801,a909)),x83802),x83803))+~P1(f318(f318(f225(f918(x83801,a909)),f318(f318(f300(x83801),x83804),x83802)),x83803))
% 109.14/108.85 [8500]~E(f318(f301(x85002,x85003,x85001),f233(f918(x85002,a909))),f233(f918(x85003,a909)))+E(f318(x85001,f318(f84(x85002,x85003,f233(f918(x85002,a909)),x85001),x85004)),x85004)
% 109.14/108.85 [8501]~E(f318(f301(x85012,x85013,x85011),f233(f918(x85012,a909))),f233(f918(x85013,a909)))+E(f318(x85011,f318(f84(x85012,x85013,f233(f918(x85012,a909)),x85011),x85014)),x85014)
% 109.14/108.85 [8585]P39(x85851,x85852)+~P39(x85851,f318(f318(f300(f917(x85851,x85851)),f318(f318(f243(x85851,x85851),x85853),x85854)),x85852))
% 109.14/108.85 [8586]P61(x85861,x85862)+~P61(x85861,f318(f318(f300(f917(x85861,x85861)),f318(f318(f243(x85861,x85861),x85863),x85864)),x85862))
% 109.14/108.85 [8591]~P4(x85911)+E(f318(f318(f139(x85911,x85911,f7(x85911)),x85912),f318(f318(f139(x85911,x85911,f7(x85911)),x85913),x85914)),f318(f318(f139(x85911,x85911,f7(x85911)),x85913),f318(f318(f139(x85911,x85911,f7(x85911)),x85912),x85914)))
% 109.14/108.85 [8606]E(x86061,x86062)+~P1(f318(f56(x86063,x86064,f318(f318(f300(x86063),x86061),f179(f918(x86063,a909)))),x86062))
% 109.14/108.85 [8617]E(f318(f318(f125(x86171),f318(f318(f166(x86171),x86172),x86173)),f318(f318(f166(x86171),x86174),f318(f318(f129(x86171),x86172),x86173))),f318(f318(f166(x86171),f318(f318(f73(a911),x86172),x86174)),x86173))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),x86172),x86174)),f318(f180(f912(x86171)),x86173)))
% 109.14/108.85 [8653]P1(f318(f55(x86531),x86532))+~E(x86532,f318(f301(a911,x86531,x86533),f318(f253(a911),f318(f318(f9(a911,a911,a909),f226(a911)),x86534))))
% 109.14/108.85 [8654]P1(f318(f55(x86541),x86542))+~E(x86542,f318(f301(a911,x86541,x86543),f318(f253(a911),f318(f318(f9(a911,a911,a909),f226(a911)),x86544))))
% 109.14/108.85 [8678]~P95(x86781)+E(f318(f133(x86781,x86781,f73(x86781),f318(f318(f73(x86781),x86782),x86783)),x86784),f318(f318(f73(x86781),x86782),f318(f133(x86781,x86781,f73(x86781),x86783),x86784)))
% 109.14/108.85 [8714]P1(f318(f318(f225(f918(x87141,a909)),f318(f255(x87141,x87142),x87143)),f318(f255(x87141,x87142),x87144)))+~P1(f318(f318(f225(f918(f917(x87141,x87142),a909)),x87143),x87144))
% 109.14/108.85 [8726]~P1(f318(f318(f225(a911),x87262),x87264))+P1(f318(f318(f225(f918(x87261,a909)),f318(f163(x87261),f318(f318(f166(x87261),x87262),x87263))),f318(f163(x87261),f318(f318(f166(x87261),x87264),x87263))))
% 109.14/108.85 [8727]~P1(f318(f318(f225(a911),x87274),x87272))+P1(f318(f318(f225(f918(x87271,a909)),f318(f163(x87271),f318(f318(f129(x87271),x87272),x87273))),f318(f163(x87271),f318(f318(f129(x87271),x87274),x87273))))
% 109.14/108.85 [8784]~P1(f318(f55(x87841),f318(f318(f3(f918(x87841,a909)),x87842),x87844)))+P1(f318(f55(x87841),f318(f318(f3(f918(x87841,a909)),x87842),f318(f318(f300(x87841),x87843),x87844))))
% 109.14/108.85 [8820]P1(f318(f318(f320(f917(x88201,x88201)),x88202),f298(x88201,x88203)))+~P1(f318(f318(f320(f917(x88201,x88201)),x88202),f318(f318(f174(f917(x88201,x88201),a909),x88204),x88203)))
% 109.14/108.85 [8821]P1(f318(f318(f320(f917(x88211,x88211)),x88212),f298(x88211,x88213)))+~P1(f318(f318(f320(f917(x88211,x88211)),x88212),f318(f318(f174(f917(x88211,x88211),a909),x88214),x88213)))
% 109.14/108.85 [8900]~P1(f318(f55(x89001),f318(f318(f3(f918(x89001,a909)),x89002),f318(f318(f300(x89001),x89004),x89003))))+P1(f318(f55(x89001),f318(f318(f3(f918(x89001,a909)),x89002),x89003)))
% 109.14/108.85 [8982]P1(f318(f318(f320(f917(x89821,x89822)),f318(f318(f243(x89821,x89822),x89823),x89824)),f179(f918(f917(x89821,x89822),a909))))+~P1(f318(f318(f179(f918(x89821,f918(x89822,a909))),x89823),x89824))
% 109.14/108.85 [9123]~P103(x91231)+P1(f318(f318(f225(x91231),f318(f318(f101(x91231),x91232),f318(f318(f92(x91231),x91233),x91234))),f318(f318(f92(x91231),f318(f318(f101(x91231),x91232),x91233)),f318(f318(f101(x91231),x91232),x91234))))
% 109.14/108.85 [9124]~P4(x91241)+P1(f318(f318(f225(x91241),f318(f318(f224(x91241),x91242),f318(f318(f223(x91241),x91243),x91244))),f318(f318(f223(x91241),f318(f318(f224(x91241),x91242),x91243)),f318(f318(f224(x91241),x91242),x91244))))
% 109.14/108.85 [9141]~P1(f318(f318(f320(f917(x91411,x91412)),f318(f318(f243(x91411,x91412),x91413),x91414)),f179(f918(f917(x91411,x91412),a909))))+P1(f318(f318(f179(f918(x91411,f918(x91412,a909))),x91413),x91414))
% 109.14/108.85 [9260]E(x92601,x92602)+~P1(f318(f318(f320(f917(x92603,x92603)),f318(f318(f243(x92603,x92603),x92601),x92602)),f318(f163(f917(x92603,x92603)),f318(f318(f172(x92603,x92603),x92604),x92604))))
% 109.14/108.85 [9292]~P1(f318(f318(f320(f917(x92921,x92921)),f318(f318(f243(x92921,x92921),x92923),x92922)),f298(x92921,x92924)))+~P39(x92921,f318(f318(f300(f917(x92921,x92921)),f318(f318(f243(x92921,x92921),x92922),x92923)),x92924))
% 109.14/108.85 [9293]~P1(f318(f318(f320(f917(x92931,x92931)),f318(f318(f243(x92931,x92931),x92933),x92932)),f298(x92931,x92934)))+~P61(x92931,f318(f318(f300(f917(x92931,x92931)),f318(f318(f243(x92931,x92931),x92932),x92933)),x92934))
% 109.14/108.85 [9303]E(x93031,x93032)+E(f318(f127(x93033,f318(f318(f10(a909,a909,x93033),a313),f318(a315,x93031))),f318(f318(f142(x93033),x93032),x93034)),f318(f318(f142(x93033),x93032),f318(f127(x93033,f318(f318(f10(a909,a909,x93033),a313),f318(a315,x93031))),x93034)))
% 109.14/108.85 [9313]P1(f318(f318(f320(x93131),x93132),f318(f163(x93131),x93133)))+~P1(f318(f318(f320(f917(x93131,x93131)),f318(f318(f243(x93131,x93131),x93132),x93134)),f318(f163(f917(x93131,x93131)),f318(f318(f172(x93131,x93131),x93133),x93133))))
% 109.14/108.85 [9336]~P26(x93362,x93361,x93363,f233(f918(x93362,a909)),f233(f918(x93361,a909)))+E(f318(f301(x93361,x93362,f84(x93362,x93361,f233(f918(x93362,a909)),x93363)),x93364),f318(f302(x93362,x93361,x93363),x93364))
% 109.14/108.85 [9351]~P103(x93511)+P1(f318(f318(f225(x93511),f318(f318(f101(x93511),f318(f318(f92(x93511),x93512),x93513)),f318(f318(f92(x93511),x93512),x93514))),f318(f318(f92(x93511),x93512),f318(f318(f101(x93511),x93513),x93514))))
% 109.14/108.85 [9352]~P4(x93521)+P1(f318(f318(f225(x93521),f318(f318(f224(x93521),f318(f318(f223(x93521),x93522),x93523)),f318(f318(f223(x93521),x93522),x93524))),f318(f318(f223(x93521),x93522),f318(f318(f224(x93521),x93523),x93524))))
% 109.14/108.85 [9388]P1(f318(f318(f320(f917(x93881,x93881)),f318(f318(f243(x93881,x93881),x93882),x93883)),f318(f318(f280(x93881,x93881,x93881),x93884),f298(x93881,x93884))))+~P1(f318(f318(f320(f917(x93881,x93881)),f318(f318(f243(x93881,x93881),x93882),x93883)),x93884))
% 109.14/108.85 [9413]~P26(x94132,x94131,x94134,f233(f918(x94132,a909)),f233(f918(x94131,a909)))+E(f318(f253(x94131),f318(f318(f10(x94132,a909,x94131),x94133),f84(x94132,x94131,f233(f918(x94132,a909)),x94134))),f318(f301(x94132,x94131,x94134),f318(f253(x94132),x94133)))
% 109.14/108.85 [9427]~E(f318(f301(x94272,x94271,x94273),f233(f918(x94272,a909))),f233(f918(x94271,a909)))+P1(f318(f318(f225(f918(x94271,a909)),f318(f72(f918(x94271,a909)),f318(f301(x94272,x94271,x94273),x94274))),f318(f301(x94272,x94271,x94273),f318(f72(f918(x94272,a909)),x94274))))
% 109.14/108.85 [9771]P1(f318(f318(f320(f917(x97711,x97711)),f318(f318(f243(x97711,x97711),x97712),x97713)),f318(f277(x97711,x97711),f318(f318(f280(x97711,x97711,x97711),x97714),f298(x97711,x97714)))))+~P1(f318(f318(f320(f917(x97711,x97711)),f318(f318(f243(x97711,x97711),x97712),x97713)),f318(f318(f280(x97711,x97711,x97711),f318(f277(x97711,x97711),x97714)),f298(x97711,f318(f277(x97711,x97711),x97714)))))
% 109.14/108.85 [9773]~P1(f318(f318(f320(f917(x97731,x97731)),f318(f318(f243(x97731,x97731),x97732),x97733)),f318(f277(x97731,x97731),f318(f318(f280(x97731,x97731,x97731),x97734),f298(x97731,x97734)))))+P1(f318(f318(f320(f917(x97731,x97731)),f318(f318(f243(x97731,x97731),x97732),x97733)),f318(f318(f280(x97731,x97731,x97731),f318(f277(x97731,x97731),x97734)),f298(x97731,f318(f277(x97731,x97731),x97734)))))
% 109.14/108.85 [9794]~P1(f318(f318(f320(x97942),x97944),f318(f275(x97941,x97942),x97943)))+P1(f318(f318(f320(f917(x97941,x97942)),f318(f318(f243(x97941,x97942),f563(x97943,x97941,x97944,x97942)),x97944)),x97943))
% 109.14/108.85 [9795]~P1(f318(f318(f320(x97952),x97954),f318(f275(x97951,x97952),x97953)))+P1(f318(f318(f320(f917(x97951,x97952)),f318(f318(f243(x97951,x97952),f564(x97953,x97951,x97954,x97952)),x97954)),x97953))
% 109.14/108.85 [9829]~P1(f318(f318(f320(x98291),x98294),f318(f318(f101(f918(x98291,a909)),x98292),x98293)))+P1(f318(f318(f318(f101(f918(x98291,a909)),f318(f318(f9(x98291,f918(x98291,a909),a909),f320(x98291)),x98292)),f318(f318(f9(x98291,f918(x98291,a909),a909),f320(x98291)),x98293)),x98294))
% 109.14/108.85 [9830]~P1(f318(f318(f320(x98301),x98304),f318(f318(f92(f918(x98301,a909)),x98302),x98303)))+P1(f318(f318(f318(f92(f918(x98301,a909)),f318(f318(f9(x98301,f918(x98301,a909),a909),f320(x98301)),x98302)),f318(f318(f9(x98301,f918(x98301,a909),a909),f320(x98301)),x98303)),x98304))
% 109.14/108.85 [9910]~P1(f318(f318(f320(f917(x99101,x99101)),f318(f318(f243(x99101,x99101),x99104),x99103)),f318(f318(f280(x99101,x99101,x99101),x99102),f298(x99101,x99102))))+P1(f318(f318(f320(f917(x99101,x99101)),f318(f318(f243(x99101,x99101),f625(x99102,x99103,x99104,x99101)),x99103)),x99102))
% 109.14/108.85 [9959]P1(f318(f318(f320(x99591),x99592),f318(f318(f101(f918(x99591,a909)),x99593),x99594)))+~P1(f318(f318(f318(f101(f918(x99591,a909)),f318(f318(f9(x99591,f918(x99591,a909),a909),f320(x99591)),x99593)),f318(f318(f9(x99591,f918(x99591,a909),a909),f320(x99591)),x99594)),x99592))
% 109.14/108.85 [9960]P1(f318(f318(f320(x99601),x99602),f318(f318(f92(f918(x99601,a909)),x99603),x99604)))+~P1(f318(f318(f318(f92(f918(x99601,a909)),f318(f318(f9(x99601,f918(x99601,a909),a909),f320(x99601)),x99603)),f318(f318(f9(x99601,f918(x99601,a909),a909),f320(x99601)),x99604)),x99602))
% 109.14/108.85 [10218]P34(x102181,f318(f318(f9(x102181,f918(f917(x102181,x102181),a909),f918(x102181,a909)),f318(f318(f10(f918(x102181,f918(f918(f917(x102181,x102181),a909),a909)),f918(f918(f917(x102181,x102181),a909),f918(x102181,a909)),x102181),f9(x102181,f918(f917(x102181,x102181),a909),a909)),f318(f318(f10(f918(x102181,f917(x102181,x102181)),f918(x102181,f918(f918(f917(x102181,x102181),a909),a909)),x102181),f318(f10(f917(x102181,x102181),f918(f918(f917(x102181,x102181),a909),a909),x102181),f320(f917(x102181,x102181)))),f243(x102181,x102181)))),x102182),x102183,x102184)+~P1(f318(f318(f320(f917(f912(x102181),f912(x102181))),f318(f318(f243(f912(x102181),f912(x102181)),x102183),x102184)),f149(x102181,x102182)))
% 109.14/108.85 [10222]P62(x102221,f318(f318(f9(x102221,f918(f917(x102221,x102221),a909),f918(x102221,a909)),f318(f318(f10(f918(x102221,f918(f918(f917(x102221,x102221),a909),a909)),f918(f918(f917(x102221,x102221),a909),f918(x102221,a909)),x102221),f9(x102221,f918(f917(x102221,x102221),a909),a909)),f318(f318(f10(f918(x102221,f917(x102221,x102221)),f918(x102221,f918(f918(f917(x102221,x102221),a909),a909)),x102221),f318(f10(f917(x102221,x102221),f918(f918(f917(x102221,x102221),a909),a909),x102221),f320(f917(x102221,x102221)))),f243(x102221,x102221)))),x102222),x102223,x102224)+~P1(f318(f318(f320(f917(f918(x102221,a909),f918(x102221,a909))),f318(f318(f243(f918(x102221,a909),f918(x102221,a909)),x102223),x102224)),f310(x102221,x102222)))
% 109.14/108.85 [10252]E(x102521,x102522)+~E(f318(f318(f9(x102523,f918(f917(x102523,x102524),a909),f918(x102524,a909)),f318(f318(f10(f918(x102524,f918(f918(f917(x102523,x102524),a909),a909)),f918(f918(f917(x102523,x102524),a909),f918(x102524,a909)),x102523),f9(x102524,f918(f917(x102523,x102524),a909),a909)),f318(f318(f10(f918(x102524,f917(x102523,x102524)),f918(x102524,f918(f918(f917(x102523,x102524),a909),a909)),x102523),f318(f10(f917(x102523,x102524),f918(f918(f917(x102523,x102524),a909),a909),x102524),f320(f917(x102523,x102524)))),f243(x102523,x102524)))),x102521),f318(f318(f9(x102523,f918(f917(x102523,x102524),a909),f918(x102524,a909)),f318(f318(f10(f918(x102524,f918(f918(f917(x102523,x102524),a909),a909)),f918(f918(f917(x102523,x102524),a909),f918(x102524,a909)),x102523),f9(x102524,f918(f917(x102523,x102524),a909),a909)),f318(f318(f10(f918(x102524,f917(x102523,x102524)),f918(x102524,f918(f918(f917(x102523,x102524),a909),a909)),x102523),f318(f10(f917(x102523,x102524),f918(f918(f917(x102523,x102524),a909),a909),x102524),f320(f917(x102523,x102524)))),f243(x102523,x102524)))),x102522))
% 109.14/108.85 [10255]~P34(x102551,f318(f318(f9(x102551,f918(f917(x102551,x102551),a909),f918(x102551,a909)),f318(f318(f10(f918(x102551,f918(f918(f917(x102551,x102551),a909),a909)),f918(f918(f917(x102551,x102551),a909),f918(x102551,a909)),x102551),f9(x102551,f918(f917(x102551,x102551),a909),a909)),f318(f318(f10(f918(x102551,f917(x102551,x102551)),f918(x102551,f918(f918(f917(x102551,x102551),a909),a909)),x102551),f318(f10(f917(x102551,x102551),f918(f918(f917(x102551,x102551),a909),a909),x102551),f320(f917(x102551,x102551)))),f243(x102551,x102551)))),x102554),x102552,x102553)+P1(f318(f318(f320(f917(f912(x102551),f912(x102551))),f318(f318(f243(f912(x102551),f912(x102551)),x102552),x102553)),f149(x102551,x102554)))
% 109.14/108.85 [10256]~P62(x102561,f318(f318(f9(x102561,f918(f917(x102561,x102561),a909),f918(x102561,a909)),f318(f318(f10(f918(x102561,f918(f918(f917(x102561,x102561),a909),a909)),f918(f918(f917(x102561,x102561),a909),f918(x102561,a909)),x102561),f9(x102561,f918(f917(x102561,x102561),a909),a909)),f318(f318(f10(f918(x102561,f917(x102561,x102561)),f918(x102561,f918(f918(f917(x102561,x102561),a909),a909)),x102561),f318(f10(f917(x102561,x102561),f918(f918(f917(x102561,x102561),a909),a909),x102561),f320(f917(x102561,x102561)))),f243(x102561,x102561)))),x102564),x102562,x102563)+P1(f318(f318(f320(f917(f918(x102561,a909),f918(x102561,a909))),f318(f318(f243(f918(x102561,a909),f918(x102561,a909)),x102562),x102563)),f310(x102561,x102564)))
% 109.14/108.85 [7619]~P99(x76191)+E(f318(f318(f73(x76191),f318(f94(x76191),x76192)),f318(f318(f3(x76191),f318(f94(x76191),x76193)),x76194)),f318(f318(f3(x76191),f318(f94(x76191),f318(f318(f73(a1),x76192),x76193))),x76194))
% 109.14/108.85 [7620]~P99(x76201)+E(f318(f318(f73(x76201),f318(f94(x76201),x76202)),f318(f318(f73(x76201),f318(f94(x76201),x76203)),x76204)),f318(f318(f73(x76201),f318(f94(x76201),f318(f318(f73(a1),x76202),x76203))),x76204))
% 109.14/108.85 [7621]~P99(x76211)+E(f318(f318(f74(x76211),f318(f94(x76211),x76212)),f318(f318(f74(x76211),f318(f94(x76211),x76213)),x76214)),f318(f318(f74(x76211),f318(f94(x76211),f318(f318(f74(a1),x76212),x76213))),x76214))
% 109.14/108.85 [7662]~P114(x76621)+E(f318(f156(x76621),f318(f318(f145(x76622,x76621),f318(f18(x76621,x76622),x76623)),x76624)),f318(f318(f74(x76621),f318(f91(x76621),f318(f180(f912(x76622)),x76624))),x76623))
% 109.14/108.85 [7898]E(f318(f259(x78981,f318(f318(f142(f917(a90,x78981)),x78982),x78983)),x78984),f318(f247(a90,x78981),x78982))+~P1(f318(f318(f226(a90),x78984),f318(f242(a90,x78981),x78982)))
% 109.14/108.85 [7941]~P99(x79411)+E(f318(f318(f73(x79411),f318(f94(x79411),x79412)),f318(f318(f3(x79411),x79413),f318(f94(x79411),x79414))),f318(f318(f73(x79411),f318(f94(x79411),f318(f318(f73(a1),x79412),f318(f72(a1),x79414)))),x79413))
% 109.14/108.85 [8071]E(f318(f259(x80711,x80712),f318(f318(f3(a90),x80713),f318(f242(a90,x80711),x80714))),f318(f259(x80711,f318(f318(f142(f917(a90,x80711)),x80714),x80712)),x80713))+P1(f318(f318(f226(a90),x80713),f318(f242(a90,x80711),x80714)))
% 109.14/108.85 [8507]~P1(f318(f318(f320(x85071),x85072),f318(f163(x85071),f105(x85071,x85074))))+P1(f318(f318(f320(x85071),x85072),f318(f163(x85071),f105(x85071,f318(f318(f125(x85071),x85073),x85074)))))
% 109.14/108.85 [8508]~P1(f318(f318(f320(x85081),x85082),f318(f163(x85081),f105(x85081,x85083))))+P1(f318(f318(f320(x85081),x85082),f318(f163(x85081),f105(x85081,f318(f318(f125(x85081),x85083),x85084)))))
% 109.14/108.85 [8527]E(f318(f318(f101(f918(x85271,a909)),f318(f318(f92(f918(x85271,a909)),x85272),x85273)),x85274),f318(f318(f92(f918(x85271,a909)),x85272),f318(f318(f101(f918(x85271,a909)),x85273),x85274)))+~P1(f318(f318(f225(f918(x85271,a909)),x85274),x85272))
% 109.14/108.85 [8833]~E(f318(f318(f101(f918(x88331,a909)),f318(f318(f92(f918(x88331,a909)),x88333),x88334)),x88332),f318(f318(f92(f918(x88331,a909)),x88333),f318(f318(f101(f918(x88331,a909)),x88334),x88332)))+P1(f318(f318(f225(f918(x88331,a909)),x88332),x88333))
% 109.14/108.85 [9128]~P1(f318(f318(f225(f918(x91281,a909)),x91282),f318(f318(f101(f918(x91281,a909)),x91283),x91284)))+P1(f318(f318(f225(f918(x91281,a909)),f318(f318(f3(f918(x91281,a909)),x91282),x91283)),x91284))
% 109.14/108.85 [9232]~E(f318(f301(x92321,x92322,x92323),f233(f918(x92321,a909))),f233(f918(x92322,a909)))+E(f318(f301(x92321,x92322,x92323),f318(f301(x92322,x92321,f84(x92321,x92322,f233(f918(x92321,a909)),x92323)),x92324)),x92324)
% 109.14/108.85 [9236]P1(f318(f318(f225(f918(x92361,a909)),x92362),f318(f318(f101(f918(x92361,a909)),x92363),x92364)))+~P1(f318(f318(f225(f918(x92361,a909)),f318(f318(f3(f918(x92361,a909)),x92362),x92363)),x92364))
% 109.14/108.85 [9332]~P91(x93321)+E(f318(f69(x93321),f318(f318(f8(x93322,x93321),f318(f318(f10(x93321,x93321,x93322),f69(x93321)),x93323)),x93324)),f318(f318(f8(x93322,x93321),f318(f318(f10(x93321,x93321,x93322),f69(x93321)),x93323)),x93324))
% 109.14/108.85 [9507]~P91(x95071)+P1(f318(f318(f225(x95071),f2(x95071)),f318(f318(f8(x95072,x95071),f318(f318(f10(x95071,x95071,x95072),f69(x95071)),x95073)),x95074)))
% 109.14/108.85 [9511]~P67(x95111)+E(f318(f156(x95111),f318(f318(f145(x95112,x95111),f318(f66(x95111,x95111,x95112,f72(x95111)),x95113)),x95114)),f318(f72(x95111),f318(f156(x95111),f318(f318(f145(x95112,x95111),x95113),x95114))))
% 109.14/108.85 [9649]~P91(x96491)+P1(f318(f318(f225(x96491),f318(f69(x96491),f318(f318(f8(x96492,x96491),x96493),x96494))),f318(f318(f8(x96492,x96491),f318(f318(f10(x96491,x96491,x96492),f69(x96491)),x96493)),x96494)))
% 109.14/108.85 [9690]~E(f318(f318(f73(a911),x96901),x96904),f318(f318(f73(a911),x96903),x96902))+P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),f318(f318(f243(a911,a911),x96901),x96902)),f318(f318(f243(a911,a911),x96903),x96904))),a99))
% 109.14/108.85 [9691]~P1(f318(f318(f226(a911),x96911),x96913))+P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),f318(f318(f243(a911,a911),x96911),x96912)),f318(f318(f243(a911,a911),x96913),x96914))),a26))
% 109.14/108.85 [9692]~P1(f318(f318(f226(a911),x96921),x96923))+P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),f318(f318(f243(a911,a911),x96921),x96922)),f318(f318(f243(a911,a911),x96923),x96924))),a64))
% 109.14/108.85 [9852]E(f318(f318(f73(a911),x98521),x98522),f318(f318(f73(a911),x98523),x98524))+~P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),f318(f318(f243(a911,a911),x98521),x98524)),f318(f318(f243(a911,a911),x98523),x98522))),a99))
% 109.14/108.85 [9884]E(f318(f318(f155(x98841),f318(f318(f129(x98841),f318(f180(f912(x98841)),f168(x98841,x98842,x98843))),x98843)),x98844),f318(f318(f155(x98841),x98843),f318(f318(f73(a911),x98844),f318(f180(f912(x98841)),f168(x98841,x98842,x98843)))))+~P1(f318(f318(f226(a911),x98844),f318(f180(f912(x98841)),f318(f318(f129(x98841),f318(f180(f912(x98841)),f168(x98841,x98842,x98843))),x98843))))
% 109.14/108.85 [9901]~P1(f318(f318(f320(x99012),x99014),f318(f318(f33(x99011,f918(x99012,a909)),f233(f918(x99011,a909))),x99013)))+P1(f318(f318(f318(f33(x99011,f918(x99012,a909)),f233(f918(x99011,a909))),f318(f318(f10(f918(x99012,a909),f918(x99012,a909),x99011),f318(f9(x99012,f918(x99012,a909),a909),f320(x99012))),x99013)),x99014))
% 109.14/108.85 [9902]~P1(f318(f318(f320(x99022),x99024),f318(f318(f34(x99021,f918(x99022,a909)),f233(f918(x99021,a909))),x99023)))+P1(f318(f318(f318(f34(x99021,f918(x99022,a909)),f233(f918(x99021,a909))),f318(f318(f10(f918(x99022,a909),f918(x99022,a909),x99021),f318(f9(x99022,f918(x99022,a909),a909),f320(x99022))),x99023)),x99024))
% 109.14/108.85 [9987]~P1(f318(f43(x99871,x99872),f318(f318(f243(a1,a1),x99874),x99873)))+P1(f318(f43(f318(f72(a1),x99871),x99872),f318(f318(f243(a1,a1),f318(f318(f318(f85(a1),f318(f318(a315,x99873),f2(a1))),f318(f72(a1),x99874)),f318(f318(f3(a1),f318(f72(a1),x99874)),f71(a1)))),f318(f318(f318(f85(a1),f318(f318(a315,x99873),f2(a1))),f2(a1)),f318(f318(f3(a1),x99872),x99873)))))
% 109.14/108.85 [9998]P1(f318(f318(f320(x99981),x99982),f318(f318(f33(x99983,f918(x99981,a909)),f233(f918(x99983,a909))),x99984)))+~P1(f318(f318(f318(f33(x99983,f918(x99981,a909)),f233(f918(x99983,a909))),f318(f318(f10(f918(x99981,a909),f918(x99981,a909),x99983),f318(f9(x99981,f918(x99981,a909),a909),f320(x99981))),x99984)),x99982))
% 109.14/108.85 [9999]P1(f318(f318(f320(x99991),x99992),f318(f318(f34(x99993,f918(x99991,a909)),f233(f918(x99993,a909))),x99994)))+~P1(f318(f318(f318(f34(x99993,f918(x99991,a909)),f233(f918(x99993,a909))),f318(f318(f10(f918(x99991,a909),f918(x99991,a909),x99993),f318(f9(x99991,f918(x99991,a909),a909),f320(x99991))),x99994)),x99992))
% 109.14/108.85 [10011]E(f318(f318(f33(a911,f918(x100111,a909)),f233(f918(a911,a909))),x100112),f318(f318(f33(a911,f918(x100111,a909)),f233(f918(a911,a909))),x100113))+~E(f318(f318(f33(a911,f918(x100111,a909)),f318(f293(a911,f2(a911)),f506(x100112,x100114,x100113,x100111))),x100113),f318(f318(f33(a911,f918(x100111,a909)),f318(f293(a911,f2(a911)),f318(f318(f73(a911),f506(x100112,x100114,x100113,x100111)),x100114))),x100112))
% 109.14/108.85 [10360]~P1(f318(f318(f225(f918(f917(x103601,x103602),a909)),x103603),x103604))+P1(f318(f318(f225(f918(x103601,f918(x103602,a909))),f318(f318(f9(x103601,f918(f917(x103601,x103602),a909),f918(x103602,a909)),f318(f318(f10(f918(x103602,f918(f918(f917(x103601,x103602),a909),a909)),f918(f918(f917(x103601,x103602),a909),f918(x103602,a909)),x103601),f9(x103602,f918(f917(x103601,x103602),a909),a909)),f318(f318(f10(f918(x103602,f917(x103601,x103602)),f918(x103602,f918(f918(f917(x103601,x103602),a909),a909)),x103601),f318(f10(f917(x103601,x103602),f918(f918(f917(x103601,x103602),a909),a909),x103602),f320(f917(x103601,x103602)))),f243(x103601,x103602)))),x103603)),f318(f318(f9(x103601,f918(f917(x103601,x103602),a909),f918(x103602,a909)),f318(f318(f10(f918(x103602,f918(f918(f917(x103601,x103602),a909),a909)),f918(f918(f917(x103601,x103602),a909),f918(x103602,a909)),x103601),f9(x103602,f918(f917(x103601,x103602),a909),a909)),f318(f318(f10(f918(x103602,f917(x103601,x103602)),f918(x103602,f918(f918(f917(x103601,x103602),a909),a909)),x103601),f318(f10(f917(x103601,x103602),f918(f918(f917(x103601,x103602),a909),a909),x103602),f320(f917(x103601,x103602)))),f243(x103601,x103602)))),x103604)))
% 109.14/108.85 [10383]P1(f318(f318(f225(f918(f917(x103831,x103832),a909)),x103833),x103834))+~P1(f318(f318(f225(f918(x103831,f918(x103832,a909))),f318(f318(f9(x103831,f918(f917(x103831,x103832),a909),f918(x103832,a909)),f318(f318(f10(f918(x103832,f918(f918(f917(x103831,x103832),a909),a909)),f918(f918(f917(x103831,x103832),a909),f918(x103832,a909)),x103831),f9(x103832,f918(f917(x103831,x103832),a909),a909)),f318(f318(f10(f918(x103832,f917(x103831,x103832)),f918(x103832,f918(f918(f917(x103831,x103832),a909),a909)),x103831),f318(f10(f917(x103831,x103832),f918(f918(f917(x103831,x103832),a909),a909),x103832),f320(f917(x103831,x103832)))),f243(x103831,x103832)))),x103833)),f318(f318(f9(x103831,f918(f917(x103831,x103832),a909),f918(x103832,a909)),f318(f318(f10(f918(x103832,f918(f918(f917(x103831,x103832),a909),a909)),f918(f918(f917(x103831,x103832),a909),f918(x103832,a909)),x103831),f9(x103832,f918(f917(x103831,x103832),a909),a909)),f318(f318(f10(f918(x103832,f917(x103831,x103832)),f918(x103832,f918(f918(f917(x103831,x103832),a909),a909)),x103831),f318(f10(f917(x103831,x103832),f918(f918(f917(x103831,x103832),a909),a909),x103832),f320(f917(x103831,x103832)))),f243(x103831,x103832)))),x103834)))
% 109.14/108.85 [9377]~P1(f318(f318(f320(f917(x93771,x93771)),x93772),f298(x93771,x93774)))+P1(f318(f318(f320(f917(x93771,x93771)),x93772),f298(x93771,f318(f318(f101(f918(f917(x93771,x93771),a909)),x93773),x93774))))
% 109.14/108.85 [9378]~P1(f318(f318(f320(f917(x93781,x93781)),x93782),f298(x93781,x93783)))+P1(f318(f318(f320(f917(x93781,x93781)),x93782),f298(x93781,f318(f318(f101(f918(f917(x93781,x93781),a909)),x93783),x93784))))
% 109.14/108.85 [10087]~P1(f318(f318(f225(a911),f318(f318(f73(a911),x100871),x100874)),f318(f318(f73(a911),x100873),x100872)))+P1(f318(f318(f225(a1),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x100871),x100872)),f179(f918(f917(a911,a911),a909)))))),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x100873),x100874)),f179(f918(f917(a911,a911),a909)))))))
% 109.14/108.85 [10088]~P1(f318(f318(f226(a911),f318(f318(f73(a911),x100881),x100884)),f318(f318(f73(a911),x100883),x100882)))+P1(f318(f318(f226(a1),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x100881),x100882)),f179(f918(f917(a911,a911),a909)))))),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x100883),x100884)),f179(f918(f917(a911,a911),a909)))))))
% 109.14/108.85 [10161]P1(f318(f318(f225(a911),f318(f318(f73(a911),x101611),x101612)),f318(f318(f73(a911),x101613),x101614)))+~P1(f318(f318(f225(a1),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x101611),x101614)),f179(f918(f917(a911,a911),a909)))))),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x101613),x101612)),f179(f918(f917(a911,a911),a909)))))))
% 109.14/108.85 [10162]P1(f318(f318(f226(a911),f318(f318(f73(a911),x101621),x101622)),f318(f318(f73(a911),x101623),x101624)))+~P1(f318(f318(f226(a1),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x101621),x101624)),f179(f918(f917(a911,a911),a909)))))),f318(a82,f318(f276(f917(a911,a911),f917(a911,a911),a99),f318(f318(f300(f917(a911,a911)),f318(f318(f243(a911,a911),x101623),x101622)),f179(f918(f917(a911,a911),a909)))))))
% 109.14/108.85 [10206]P1(f318(f318(f225(f918(x102061,a909)),f318(f318(f33(a911,f918(x102061,a909)),f233(f918(a911,a909))),x102062)),f318(f318(f33(a911,f918(x102061,a909)),f233(f918(a911,a909))),x102063)))+~P1(f318(f318(f225(f918(x102061,a909)),f318(f318(f33(a911,f918(x102061,a909)),f318(f293(a911,f2(a911)),f499(x102063,x102064,x102062,x102061))),x102062)),f318(f318(f33(a911,f918(x102061,a909)),f318(f293(a911,f2(a911)),f318(f318(f73(a911),f499(x102063,x102064,x102062,x102061)),x102064))),x102063)))
% 109.14/108.85 [10259]P1(f318(f318(f225(a90),x102594),f2(a90)))+E(f318(f318(f250(f917(a90,a90),f917(x102591,f918(a914,a314)),f917(a90,a90),f917(f918(a90,f918(a909,f915(f913(x102591)))),f917(a90,a90))),f318(x102592,x102593)),f318(f318(f10(f918(f918(a90,f918(a909,f915(f913(x102591)))),f918(f917(a90,a90),f917(f918(a90,f918(a909,f915(f913(x102591)))),f917(a90,a90)))),f918(f917(a90,a90),f917(f918(a90,f918(a909,f915(f913(x102591)))),f917(a90,a90))),f917(x102591,f918(a914,a314))),f318(f250(f917(a90,a90),f918(a90,f918(a909,f915(f913(x102591)))),f917(a90,a90),f917(f918(a90,f918(a909,f915(f913(x102591)))),f917(a90,a90))),f268(x102591,x102592,f318(f318(f3(a90),x102594),f71(a90)),x102593))),f318(f318(f10(f918(f918(a90,f918(a909,f915(f913(x102591)))),f918(a90,f918(a909,f915(f913(x102591))))),f918(f918(a90,f918(a909,f915(f913(x102591)))),f918(f917(a90,a90),f917(f918(a90,f918(a909,f915(f913(x102591)))),f917(a90,a90)))),f917(x102591,f918(a914,a314))),f318(f10(f918(a90,f918(a909,f915(f913(x102591)))),f918(f917(a90,a90),f917(f918(a90,f918(a909,f915(f913(x102591)))),f917(a90,a90))),f918(a90,f918(a909,f915(f913(x102591))))),f243(f918(a90,f918(a909,f915(f913(x102591)))),f917(a90,a90)))),f318(f318(f10(f918(a90,f918(a909,f915(f913(x102591)))),f918(f918(a90,f918(a909,f915(f913(x102591)))),f918(a90,f918(a909,f915(f913(x102591))))),f917(x102591,f918(a914,a314))),f38(x102591)),f318(f318(f10(x102591,f918(a90,f918(a909,f915(f913(x102591)))),f917(x102591,f918(a914,a314))),f36(x102591)),f242(x102591,f918(a914,a314))))))),f268(x102591,x102592,x102594,x102593))
% 109.14/108.85 [10349]~P1(f318(f318(f320(x103492),x103494),f318(f275(x103491,x103492),x103493)))+P1(f318(f241(x103491,x103492,f318(f318(f9(x103491,f918(f917(x103491,x103492),a909),f918(x103492,a909)),f318(f318(f10(f918(x103492,f918(f918(f917(x103491,x103492),a909),a909)),f918(f918(f917(x103491,x103492),a909),f918(x103492,a909)),x103491),f9(x103492,f918(f917(x103491,x103492),a909),a909)),f318(f318(f10(f918(x103492,f917(x103491,x103492)),f918(x103492,f918(f918(f917(x103491,x103492),a909),a909)),x103491),f318(f10(f917(x103491,x103492),f918(f918(f917(x103491,x103492),a909),a909),x103492),f320(f917(x103491,x103492)))),f243(x103491,x103492)))),x103493)),x103494))
% 109.14/108.85 [10350]~P1(f318(f318(f320(x103501),x103504),f318(f255(x103501,x103502),x103503)))+P1(f318(f240(x103501,x103502,f318(f318(f9(x103501,f918(f917(x103501,x103502),a909),f918(x103502,a909)),f318(f318(f10(f918(x103502,f918(f918(f917(x103501,x103502),a909),a909)),f918(f918(f917(x103501,x103502),a909),f918(x103502,a909)),x103501),f9(x103502,f918(f917(x103501,x103502),a909),a909)),f318(f318(f10(f918(x103502,f917(x103501,x103502)),f918(x103502,f918(f918(f917(x103501,x103502),a909),a909)),x103501),f318(f10(f917(x103501,x103502),f918(f918(f917(x103501,x103502),a909),a909),x103502),f320(f917(x103501,x103502)))),f243(x103501,x103502)))),x103503)),x103504))
% 109.14/108.85 [10363]P1(f318(f318(f320(x103631),x103632),f318(f275(x103633,x103631),x103634)))+~P1(f318(f241(x103633,x103631,f318(f318(f9(x103633,f918(f917(x103633,x103631),a909),f918(x103631,a909)),f318(f318(f10(f918(x103631,f918(f918(f917(x103633,x103631),a909),a909)),f918(f918(f917(x103633,x103631),a909),f918(x103631,a909)),x103633),f9(x103631,f918(f917(x103633,x103631),a909),a909)),f318(f318(f10(f918(x103631,f917(x103633,x103631)),f918(x103631,f918(f918(f917(x103633,x103631),a909),a909)),x103633),f318(f10(f917(x103633,x103631),f918(f918(f917(x103633,x103631),a909),a909),x103631),f320(f917(x103633,x103631)))),f243(x103633,x103631)))),x103634)),x103632))
% 109.14/108.85 [10364]P1(f318(f318(f320(x103641),x103642),f318(f255(x103641,x103643),x103644)))+~P1(f318(f240(x103641,x103643,f318(f318(f9(x103641,f918(f917(x103641,x103643),a909),f918(x103643,a909)),f318(f318(f10(f918(x103643,f918(f918(f917(x103641,x103643),a909),a909)),f918(f918(f917(x103641,x103643),a909),f918(x103643,a909)),x103641),f9(x103643,f918(f917(x103641,x103643),a909),a909)),f318(f318(f10(f918(x103643,f917(x103641,x103643)),f918(x103643,f918(f918(f917(x103641,x103643),a909),a909)),x103641),f318(f10(f917(x103641,x103643),f918(f918(f917(x103641,x103643),a909),a909),x103643),f320(f917(x103641,x103643)))),f243(x103641,x103643)))),x103644)),x103642))
% 109.14/108.85 [10022]P1(f318(f151(x100221,x100222),x100223))+~P1(f318(f151(x100221,f318(f318(f20(x100221,a909,a909),f318(f318(f10(a909,f918(a909,a909),x100221),a316),x100224)),x100222)),x100223))
% 109.14/108.85 [10023]P1(f318(f151(x100231,x100232),x100233))+~P1(f318(f151(x100231,f318(f318(f20(x100231,a909,a909),f318(f318(f10(a909,f918(a909,a909),x100231),a316),x100232)),x100234)),x100233))
% 109.14/108.85 [10099]~P121(x100991)+E(f318(f318(f74(x100991),f318(f318(f73(x100991),f71(x100991)),f71(x100991))),f318(f318(f8(a911,x100991),f318(f318(f10(x100991,x100991,a911),f318(f73(x100991),x100992)),f318(f318(f9(a911,x100991,x100991),f318(f318(f10(x100991,f918(x100991,x100991),a911),f74(x100991)),f91(x100991))),x100993))),f318(f273(a911),x100994))),f318(f318(f74(x100991),f318(f91(x100991),x100994)),f318(f318(f73(x100991),x100992),f318(f318(f73(x100991),x100992),f318(f318(f74(x100991),f318(f91(x100991),f318(f318(f3(a911),x100994),f71(a911)))),x100993)))))
% 109.14/108.85 [10225]P1(f318(x102251,f573(x102252,x102253,x102254,x102251)))+P39(x102252,f318(f253(f917(x102252,x102252)),f318(f248(x102252,x102252,a909),f318(f318(f10(f918(x102252,a909),f918(x102252,a909),x102252),f318(f20(x102252,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102252),a316),x102251))),f318(f318(f9(x102252,f918(x102252,x102252),f918(x102252,a909)),f318(f318(f10(f918(x102252,a909),f918(f918(x102252,x102252),f918(x102252,a909)),x102252),f10(x102252,a909,x102252)),a315)),x102253)))))
% 109.14/108.85 [10237]~P1(f318(f318(f226(a911),f318(x102374,f318(x102373,f573(x102371,x102373,x102374,x102372)))),f318(x102374,f573(x102371,x102373,x102374,x102372))))+P39(x102371,f318(f253(f917(x102371,x102371)),f318(f248(x102371,x102371,a909),f318(f318(f10(f918(x102371,a909),f918(x102371,a909),x102371),f318(f20(x102371,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102371),a316),x102372))),f318(f318(f9(x102371,f918(x102371,x102371),f918(x102371,a909)),f318(f318(f10(f918(x102371,a909),f918(f918(x102371,x102371),f918(x102371,a909)),x102371),f10(x102371,a909,x102371)),a315)),x102373)))))
% 109.14/108.85 [10315]~P5(x103151)+E(f32(x103151,f318(f253(x103151),f318(f318(f10(f918(f918(x103152,x103151),a909),a909,x103151),f79(f918(x103152,x103151))),f318(f318(f10(f918(f918(x103152,x103151),a909),f918(f918(x103152,x103151),a909),x103151),f318(f20(f918(x103152,x103151),a909,a909),f318(f318(f10(a909,f918(a909,a909),f918(x103152,x103151)),a316),f318(f318(f9(f918(x103152,x103151),f918(f918(x103152,x103151),a909),a909),f320(f918(x103152,x103151))),x103153)))),f318(f318(f9(x103151,f918(f918(x103152,x103151),x103151),f918(f918(x103152,x103151),a909)),f318(f318(f10(f918(x103151,a909),f918(f918(f918(x103152,x103151),x103151),f918(f918(x103152,x103151),a909)),x103151),f10(x103151,a909,f918(x103152,x103151))),a315)),f318(f318(f9(f918(x103152,x103151),x103152,x103151),f7(f918(x103152,x103151))),x103154)))))),f318(f32(f918(x103152,x103151),x103153),x103154))
% 109.14/108.85 [10316]~P5(x103161)+E(f32(x103161,f318(f253(x103161),f318(f318(f10(f918(f918(x103162,x103161),a909),a909,x103161),f79(f918(x103162,x103161))),f318(f318(f10(f918(f918(x103162,x103161),a909),f918(f918(x103162,x103161),a909),x103161),f318(f20(f918(x103162,x103161),a909,a909),f318(f318(f10(a909,f918(a909,a909),f918(x103162,x103161)),a316),f318(f318(f9(f918(x103162,x103161),f918(f918(x103162,x103161),a909),a909),f320(f918(x103162,x103161))),x103163)))),f318(f318(f9(x103161,f918(f918(x103162,x103161),x103161),f918(f918(x103162,x103161),a909)),f318(f318(f10(f918(x103161,a909),f918(f918(f918(x103162,x103161),x103161),f918(f918(x103162,x103161),a909)),x103161),f10(x103161,a909,f918(x103162,x103161))),a315)),f318(f318(f9(f918(x103162,x103161),x103162,x103161),f7(f918(x103162,x103161))),x103164)))))),f318(f32(f918(x103162,x103161),x103163),x103164))
% 109.14/108.85 [10317]~P5(x103171)+E(f31(x103171,f318(f253(x103171),f318(f318(f10(f918(f918(x103172,x103171),a909),a909,x103171),f79(f918(x103172,x103171))),f318(f318(f10(f918(f918(x103172,x103171),a909),f918(f918(x103172,x103171),a909),x103171),f318(f20(f918(x103172,x103171),a909,a909),f318(f318(f10(a909,f918(a909,a909),f918(x103172,x103171)),a316),f318(f318(f9(f918(x103172,x103171),f918(f918(x103172,x103171),a909),a909),f320(f918(x103172,x103171))),x103173)))),f318(f318(f9(x103171,f918(f918(x103172,x103171),x103171),f918(f918(x103172,x103171),a909)),f318(f318(f10(f918(x103171,a909),f918(f918(f918(x103172,x103171),x103171),f918(f918(x103172,x103171),a909)),x103171),f10(x103171,a909,f918(x103172,x103171))),a315)),f318(f318(f9(f918(x103172,x103171),x103172,x103171),f7(f918(x103172,x103171))),x103174)))))),f318(f31(f918(x103172,x103171),x103173),x103174))
% 109.14/108.85 [10318]~P5(x103181)+E(f31(x103181,f318(f253(x103181),f318(f318(f10(f918(f918(x103182,x103181),a909),a909,x103181),f79(f918(x103182,x103181))),f318(f318(f10(f918(f918(x103182,x103181),a909),f918(f918(x103182,x103181),a909),x103181),f318(f20(f918(x103182,x103181),a909,a909),f318(f318(f10(a909,f918(a909,a909),f918(x103182,x103181)),a316),f318(f318(f9(f918(x103182,x103181),f918(f918(x103182,x103181),a909),a909),f320(f918(x103182,x103181))),x103183)))),f318(f318(f9(x103181,f918(f918(x103182,x103181),x103181),f918(f918(x103182,x103181),a909)),f318(f318(f10(f918(x103181,a909),f918(f918(f918(x103182,x103181),x103181),f918(f918(x103182,x103181),a909)),x103181),f10(x103181,a909,f918(x103182,x103181))),a315)),f318(f318(f9(f918(x103182,x103181),x103182,x103181),f7(f918(x103182,x103181))),x103184)))))),f318(f31(f918(x103182,x103181),x103183),x103184))
% 109.14/108.85 [10402]~P1(f318(f318(f320(f917(x104021,x104021)),f318(f318(f243(x104021,x104021),x104023),x104024)),f318(f318(f101(f918(f917(x104021,x104021),a909)),x104022),f298(x104021,f179(f918(f917(x104021,x104021),a909))))))+P1(f318(f318(f318(f318(f101(f918(x104021,f918(x104021,a909))),f318(f318(f9(x104021,f918(f917(x104021,x104021),a909),f918(x104021,a909)),f318(f318(f10(f918(x104021,f918(f918(f917(x104021,x104021),a909),a909)),f918(f918(f917(x104021,x104021),a909),f918(x104021,a909)),x104021),f9(x104021,f918(f917(x104021,x104021),a909),a909)),f318(f318(f10(f918(x104021,f917(x104021,x104021)),f918(x104021,f918(f918(f917(x104021,x104021),a909),a909)),x104021),f318(f10(f917(x104021,x104021),f918(f918(f917(x104021,x104021),a909),a909),x104021),f320(f917(x104021,x104021)))),f243(x104021,x104021)))),x104022)),a315),x104023),x104024))
% 109.14/108.85 [10418]P1(f318(f318(f320(f917(x104181,x104181)),f318(f318(f243(x104181,x104181),x104182),x104183)),f318(f318(f101(f918(f917(x104181,x104181),a909)),x104184),f298(x104181,f179(f918(f917(x104181,x104181),a909))))))+~P1(f318(f318(f318(f318(f101(f918(x104181,f918(x104181,a909))),f318(f318(f9(x104181,f918(f917(x104181,x104181),a909),f918(x104181,a909)),f318(f318(f10(f918(x104181,f918(f918(f917(x104181,x104181),a909),a909)),f918(f918(f917(x104181,x104181),a909),f918(x104181,a909)),x104181),f9(x104181,f918(f917(x104181,x104181),a909),a909)),f318(f318(f10(f918(x104181,f917(x104181,x104181)),f918(x104181,f918(f918(f917(x104181,x104181),a909),a909)),x104181),f318(f10(f917(x104181,x104181),f918(f918(f917(x104181,x104181),a909),a909),x104181),f320(f917(x104181,x104181)))),f243(x104181,x104181)))),x104184)),a315),x104182),x104183))
% 109.14/108.85 [10346]E(f318(f318(f142(f912(x103461)),f318(f318(f142(x103461),x103462),f318(f133(f912(x103461),f912(x103461),f125(x103461),f104(x103461)),f318(f318(f145(f912(x103461),f912(x103461)),f147(f912(x103461),x103461,f104(x103461),f318(f318(f10(f912(x103461),f918(f912(x103461),f912(x103461)),x103461),f18(f912(x103461),f912(x103461))),f318(f318(f9(x103461,f912(x103461),f912(x103461)),f142(x103461)),f104(x103461))))),x103463)))),f170(x103461,f318(f318(f142(f912(x103461)),x103464),f318(f133(f912(f912(x103461)),f912(f912(x103461)),f125(f912(x103461)),f104(f912(x103461))),f318(f318(f145(f912(x103461),f912(f912(x103461))),f147(f912(f912(x103461)),x103461,f104(f912(x103461)),f318(f18(f918(f912(x103461),f912(f912(x103461))),x103461),f318(f318(f9(f912(x103461),f912(f912(x103461)),f912(f912(x103461))),f142(f912(x103461))),f104(f912(x103461)))))),x103463))))),f170(x103461,f318(f318(f142(f912(x103461)),f318(f318(f142(x103461),x103462),x103464)),x103463)))+~P1(f318(f306(f912(f912(x103461)),f171(x103461)),f318(f318(f142(f912(x103461)),f318(f318(f142(x103461),x103462),x103464)),x103463)))
% 109.14/108.85 [10401]~P1(f318(f55(x104012),f318(f253(x104012),x104014)))+P1(f318(f55(x104011),f318(f253(x104011),f318(f318(f10(f918(x104012,a909),a909,x104011),f79(x104012)),f318(f318(f9(x104011,f918(x104012,a909),f918(x104012,a909)),f318(f318(f10(f918(x104012,f918(a909,a909)),f918(f918(x104012,a909),f918(x104012,a909)),x104011),f20(x104012,a909,a909)),f318(f318(f10(f918(x104012,a909),f918(x104012,f918(a909,a909)),x104011),f318(f10(a909,f918(a909,a909),x104012),a316)),f318(f318(f9(x104011,f918(x104012,x104011),f918(x104012,a909)),f318(f318(f10(f918(x104011,a909),f918(f918(x104012,x104011),f918(x104012,a909)),x104011),f10(x104011,a909,x104012)),a315)),x104013)))),x104014)))))
% 109.14/108.85 [8869]P25(x88691,x88692,x88693,x88694)+~P26(x88691,x88692,x88693,x88694,x88695)
% 109.14/108.85 [8870]P25(x88701,x88702,x88703,x88704)+~P26(x88701,x88702,x88703,x88704,x88705)
% 109.14/108.85 [5390]E(x53901,x53902)+~E(f160(x53903,x53901,x53904),f160(x53903,x53902,x53905))
% 109.14/108.85 [5391]E(x53911,x53912)+~E(f117(x53913,x53914,x53911),f117(x53913,x53915,x53912))
% 109.14/108.85 [5392]E(x53921,x53922)+~E(f117(x53923,x53921,x53924),f117(x53923,x53922,x53925))
% 109.14/108.85 [8204]~E(f318(x82043,x82044),x82045)+E(f68(x82041,x82042,x82043,x82044,x82045),x82043)
% 109.14/108.85 [8205]~E(f318(x82053,x82054),x82055)+E(f68(x82051,x82052,x82053,x82054,x82055),x82053)
% 109.14/108.85 [8736]~E(f68(x87364,x87365,x87361,x87362,x87363),x87361)+E(f318(x87361,x87362),x87363)
% 109.14/108.85 [9349]~P26(x93492,x93491,x93494,x93493,x93495)+P26(x93491,x93492,f70(x93492,x93491,x93493,x93494),x93495,x93493)
% 109.14/108.85 [9350]~P26(x93502,x93501,x93504,x93503,x93505)+P26(x93501,x93502,f84(x93502,x93501,x93503,x93504),x93505,x93503)
% 109.14/108.85 [6201]P1(f318(f241(x62011,x62012,x62013),x62014))+~P1(f318(f318(x62013,x62015),x62014))
% 109.14/108.85 [6202]P1(f318(f241(x62021,x62022,x62023),x62024))+~P1(f318(f318(x62023,x62025),x62024))
% 109.14/108.85 [6203]P1(f318(f240(x62031,x62032,x62033),x62034))+~P1(f318(f318(x62033,x62034),x62035))
% 109.14/108.85 [6204]P1(f318(f240(x62041,x62042,x62043),x62044))+~P1(f318(f318(x62043,x62044),x62045))
% 109.14/108.85 [6675]~E(x66755,f2(a90))+E(f318(f187(x66751,x66752,x66753,x66754),x66755),f115(x66752))
% 109.14/108.85 [6676]~E(x66765,f2(a90))+E(f318(f189(x66761,x66762,x66763,x66764),x66765),f106(x66762))
% 109.14/108.85 [6817]~E(x68173,f2(a90))+E(f318(f264(x68171,x68172,x68173,x68174),x68175),f318(f243(x68171,x68172),x68175))
% 109.14/108.85 [7854]~P20(x78544,x78541,x78542,x78545)+E(f318(f66(x78541,x78541,x78541,f318(x78542,x78543)),f318(x78542,x78543)),f318(x78542,x78543))
% 109.14/108.85 [8246]~P16(x82465,x82461,x82462)+E(f318(f66(x82461,x82461,x82461,f318(x82462,x82463)),f318(x82462,x82464)),f318(f66(x82461,x82461,x82461,f318(x82462,x82464)),f318(x82462,x82463)))
% 109.14/108.85 [8567]P1(f318(f318(f320(f917(x85671,x85671)),f318(f318(f243(x85671,x85671),x85672),x85673)),f312(x85671,x85674,x85675)))+~P1(f318(f318(f226(a911),f318(x85674,x85672)),f318(x85674,x85673)))
% 109.14/108.85 [8664]~P1(f318(f318(f320(x86644),x86643),f281(x86644,x86641,x86642,x86645)))+P1(f318(f318(x86641,x86642),x86643))
% 109.14/108.85 [8665]~P1(f318(f318(f320(x86654),x86653),f290(x86654,x86651,x86652,x86655)))+P1(f318(f318(x86651,x86652),x86653))
% 109.14/108.85 [8666]~P1(f318(f318(f320(x86664),x86662),f281(x86664,x86661,x86665,x86663)))+P1(f318(f318(x86661,x86662),x86663))
% 109.14/108.85 [8667]~P1(f318(f318(f320(x86674),x86672),f290(x86674,x86671,x86675,x86673)))+P1(f318(f318(x86671,x86672),x86673))
% 109.14/108.85 [8747]~P26(x87471,x87473,x87475,x87472,x87474)+E(f318(f29(x87471),x87472),f318(f29(x87473),x87474))
% 109.14/108.85 [8796]~P26(x87961,x87962,x87963,x87964,x87965)+E(f318(f301(x87961,x87962,x87963),x87964),x87965)
% 109.14/108.85 [8811]~P60(x88112,x88111,x88115,x88113,x88114)+E(f318(f301(x88111,x88112,x88113),x88114),f233(f918(x88112,a909)))
% 109.14/108.85 [9248]~P36(x92481,x92482,x92483,x92484,x92485)+P36(x92481,x92482,x92483,f318(f159(x92481),x92484),f318(f159(x92482),x92485))
% 109.14/108.85 [9250]~P36(x92501,x92502,x92503,f318(f159(x92501),x92504),x92505)+P36(x92501,x92502,x92503,x92504,f318(f159(x92502),x92505))
% 109.14/108.85 [9251]~P36(x92511,x92512,x92513,x92514,f318(f159(x92512),x92515))+P36(x92511,x92512,x92513,f318(f159(x92511),x92514),x92515)
% 109.14/108.85 [9257]P36(x92571,x92572,x92573,x92574,x92575)+~P36(x92571,x92572,x92573,f318(f159(x92571),x92574),f318(f159(x92572),x92575))
% 109.14/108.85 [9676]P1(f318(f318(f320(f917(f912(x96761),f912(x96761))),f318(f318(f243(f912(x96761),f912(x96761)),f318(f318(f142(x96761),x96762),x96763)),f318(f318(f142(x96761),x96762),x96764))),f148(x96761,x96765)))+~P1(f318(f318(f320(f917(f912(x96761),f912(x96761))),f318(f318(f243(f912(x96761),f912(x96761)),x96763),x96764)),f148(x96761,x96765)))
% 109.14/108.85 [9677]P1(f318(f318(f320(f917(f912(x96771),f912(x96771))),f318(f318(f243(f912(x96771),f912(x96771)),f318(f318(f125(x96771),x96772),x96773)),f318(f318(f125(x96771),x96772),x96774))),f138(x96771,x96775)))+~P1(f318(f318(f320(f917(f912(x96771),f912(x96771))),f318(f318(f243(f912(x96771),f912(x96771)),x96773),x96774)),f138(x96771,x96775)))
% 109.14/108.85 [9891]E(f318(f318(f142(x98911),f648(x98912,x98913,x98914,x98915,x98911)),f649(x98912,x98913,x98914,x98915,x98911)),x98915)+~P1(f318(f318(f320(f917(f912(x98911),f912(x98911))),f318(f318(f243(f912(x98911),f912(x98911)),x98915),f318(f318(f142(x98911),x98914),x98913))),f149(x98911,x98912)))
% 109.14/108.85 [9913]E(f318(f318(f142(x99131),f650(x99132,x99133,x99134,x99135,x99131)),f651(x99132,x99133,x99134,x99135,x99131)),x99133)+~P1(f318(f318(f320(f917(f912(x99131),f912(x99131))),f318(f318(f243(f912(x99131),f912(x99131)),f318(f318(f142(x99131),x99135),x99134)),x99133)),f149(x99131,x99132)))
% 109.14/108.85 [10066]~P1(f318(f318(f320(f917(f912(x100661),f912(x100661))),f318(f318(f243(f912(x100661),f912(x100661)),f318(f318(f142(x100661),x100665),x100662)),x100664)),f149(x100661,x100663)))+P1(f318(f318(f320(f917(f912(x100661),f912(x100661))),f318(f318(f243(f912(x100661),f912(x100661)),x100662),f651(x100663,x100664,x100662,x100665,x100661))),f149(x100661,x100663)))
% 109.14/108.85 [10133]~P1(f318(f318(f320(f917(f912(x101331),f912(x101331))),f318(f318(f243(f912(x101331),f912(x101331)),x101335),f318(f318(f142(x101331),x101334),x101333))),f149(x101331,x101332)))+P1(f318(f318(f320(f917(f912(x101331),f912(x101331))),f318(f318(f243(f912(x101331),f912(x101331)),f649(x101332,x101333,x101334,x101335,x101331)),x101333)),f149(x101331,x101332)))
% 109.14/108.85 [10320]P1(f318(f318(f320(f917(x103201,x103201)),f318(f318(f243(x103201,x103201),f318(x103202,f318(f318(f73(a911),x103203),x103204))),f318(x103202,x103203))),f298(x103201,x103205)))+~P1(f318(f318(f320(f917(x103201,x103201)),f318(f318(f243(x103201,x103201),f318(x103202,f318(a103,f612(x103204,x103203,x103205,x103202,x103201)))),f318(x103202,f612(x103204,x103203,x103205,x103202,x103201)))),f298(x103201,x103205)))
% 109.14/108.85 [5364]E(x53641,x53642)+~E(f318(f318(f142(x53643),x53644),x53641),f318(f318(f142(x53643),x53645),x53642))
% 109.14/108.85 [5365]E(x53651,x53652)+~E(f318(f318(f142(x53653),x53651),x53654),f318(f318(f142(x53653),x53652),x53655))
% 109.14/108.85 [5407]P1(f318(x54071,x54072))+~E(f318(f127(x54073,x54071),x54074),f318(f318(f142(x54073),x54072),x54075))
% 109.14/108.85 [5408]P1(f318(x54081,x54082))+~E(f318(f318(f142(x54083),x54082),x54084),f318(f127(x54083,x54081),x54085))
% 109.14/108.85 [5568]~E(f318(f318(f129(x55681),x55683),x55682),f318(f318(f142(x55681),x55684),x55685))+E(f318(f318(f155(x55681),x55682),x55683),x55684)
% 109.14/108.85 [5706]~P14(x57064,x57065,x57061)+E(f318(f318(x57061,x57062),f318(f318(x57061,x57062),x57063)),f318(f318(x57061,x57062),x57063))
% 109.14/108.85 [6261]~E(x62614,f2(a90))+E(f318(f318(f108(x62611,x62612,x62613),x62614),x62615),f318(f318(f243(f912(x62612),x62611),f104(x62612)),x62615))
% 109.14/108.85 [6330]~P4(x63302)+~E(f318(f318(f139(x63301,x63302,x63303),x63304),x63305),f104(x63301))
% 109.14/108.85 [6714]E(x67141,x67142)+~E(f318(f318(f125(x67143),x67144),f318(f318(f142(x67143),x67141),f104(x67143))),f318(f318(f125(x67143),x67145),f318(f318(f142(x67143),x67142),f104(x67143))))
% 109.14/108.85 [6715]E(x67151,x67152)+~E(f318(f318(f125(x67153),x67151),f318(f318(f142(x67153),x67154),f104(x67153))),f318(f318(f125(x67153),x67152),f318(f318(f142(x67153),x67155),f104(x67153))))
% 109.14/108.85 [7031]E(f318(f318(f300(x70311),f318(x70312,x70313)),f318(f301(x70314,x70311,x70312),x70315)),f318(f301(x70314,x70311,x70312),x70315))+~P1(f318(f318(f320(x70314),x70313),x70315))
% 109.14/108.85 [7038]~P1(f318(x70384,f318(x70383,x70385)))+P1(f318(f318(f302(x70381,x70382,x70383),x70384),x70385))
% 109.14/108.85 [7039]~P1(f318(f318(x70393,x70395),x70394))+P1(f318(f318(f234(x70391,x70392,x70393),x70394),x70395))
% 109.14/108.85 [7040]~P1(f318(f318(x70403,x70405),x70404))+P1(f318(f318(f234(x70401,x70402,x70403),x70404),x70405))
% 109.14/108.85 [7041]~P1(f318(f318(x70413,x70415),x70414))+P1(f318(f318(f234(x70411,x70412,x70413),x70414),x70415))
% 109.14/108.85 [7138]~E(f318(f301(x71381,x71382,x71383),x71384),x71385)+E(f318(f301(f918(x71381,a909),f918(x71382,a909),f301(x71381,x71382,x71383)),f318(f299(x71381),x71384)),f318(f299(x71382),x71385))
% 109.14/108.85 [7166]E(f318(f262(x71661,x71662,x71663,x71664),x71665),f318(x71664,x71665))+~P1(f318(f318(f320(x71661),x71665),x71663))
% 109.14/108.85 [7477]P25(x74771,x74772,x74773,x74774)+~P25(x74771,x74772,x74773,f318(f318(f300(x74771),x74775),x74774))
% 109.14/108.85 [7574]~P1(f318(f318(f320(x75744),x75743),x75745))+P1(f318(f318(f320(x75741),f318(x75742,x75743)),f318(f301(x75744,x75741,x75742),x75745)))
% 109.14/108.85 [7595]~P4(x75952)+E(f141(x75951,x75952,x75953,f318(f127(x75951,x75954),x75955)),f318(f127(x75951,x75954),f141(x75951,x75952,x75953,x75955)))
% 109.14/108.85 [7626]P1(f318(x76261,f318(x76262,x76263)))+~P1(f318(f318(f302(x76264,x76265,x76262),x76261),x76263))
% 109.14/108.85 [7627]P1(f318(f318(x76271,x76272),x76273))+~P1(f318(f318(f234(x76274,x76275,x76271),x76273),x76272))
% 109.14/108.85 [7628]P1(f318(f318(x76281,x76282),x76283))+~P1(f318(f318(f234(x76284,x76285,x76281),x76283),x76282))
% 109.14/108.85 [7629]P1(f318(f318(x76291,x76292),x76293))+~P1(f318(f318(f234(x76294,x76295,x76291),x76293),x76292))
% 109.14/108.85 [7691]~P1(f318(f318(f320(x76913),f318(x76914,x76912)),x76915))+P1(f318(f318(f320(x76911),x76912),f318(f302(x76911,x76913,x76914),x76915)))
% 109.14/108.85 [7692]~P1(f318(f318(f320(x76923),f318(x76924,x76922)),x76925))+P1(f318(f318(f320(x76921),x76922),f318(f302(x76921,x76923,x76924),x76925)))
% 109.14/108.85 [8083]~P1(f318(f318(f320(x80835),x80833),f318(f302(x80835,x80831,x80832),x80834)))+P1(f318(f318(f320(x80831),f318(x80832,x80833)),x80834))
% 109.14/108.85 [8084]~P1(f318(f318(f320(x80845),x80843),f318(f302(x80845,x80841,x80842),x80844)))+P1(f318(f318(f320(x80841),f318(x80842,x80843)),x80844))
% 109.14/108.85 [8385]~P16(x83852,x83851,x83853)+E(f318(f133(x83851,x83852,f318(f9(x83852,x83851,x83851),x83853),x83854),f143(x83852,x83855)),f318(f318(f58(x83852,x83851,x83853),x83854),f318(f163(x83852),x83855)))
% 109.14/108.85 [8407]E(f318(x84071,f689(x84072,x84071,x84073,x84074)),x84074)+~P1(f318(f318(f320(x84075),x84074),f318(f301(x84073,x84075,x84071),x84072)))
% 109.14/108.85 [8712]~E(x87122,f318(f318(f142(x87121),x87124),x87125))+P1(f318(f318(f320(f917(f912(x87121),f912(x87121))),f318(f318(f243(f912(x87121),f912(x87121)),f104(x87121)),x87122)),f138(x87121,x87123)))
% 109.14/108.85 [8756]E(f318(x87561,f318(f84(x87562,x87563,x87564,x87561),x87565)),x87565)+~P1(f318(f318(f320(x87563),x87565),f318(f301(x87562,x87563,x87561),x87564)))
% 109.14/108.85 [8759]P25(x87591,x87592,f84(x87592,x87591,x87593,x87594),x87595)+~P1(f318(f318(f225(f918(x87591,a909)),x87595),f318(f301(x87592,x87591,x87594),x87593)))
% 109.14/108.85 [8766]~P36(x87661,x87663,x87665,x87662,x87664)+E(f318(f180(f912(x87661)),x87662),f318(f180(f912(x87663)),x87664))
% 109.14/108.85 [8767]~P36(x87671,x87673,x87675,x87672,x87674)+E(f318(f180(f912(x87671)),x87672),f318(f180(f912(x87673)),x87674))
% 109.14/108.85 [8768]~P36(x87681,x87683,x87685,x87682,x87684)+E(f318(f180(f912(x87681)),x87682),f318(f180(f912(x87683)),x87684))
% 109.14/108.85 [8778]P1(f318(f318(f225(f918(x87781,a909)),f318(f318(f34(x87782,f918(x87781,a909)),x87783),x87784)),f318(x87784,x87785)))+~P1(f318(f318(f320(x87782),x87785),x87783))
% 109.14/108.85 [8826]~P60(x88261,x88262,x88263,x88265,x88264)+E(f318(f301(x88261,x88262,x88263),f233(f918(x88261,a909))),x88264)
% 109.14/108.85 [9056]E(f318(f127(x90561,x90562),f737(x90563,x90564,x90565,x90562,x90561)),x90563)+~E(f318(f127(x90561,x90562),x90565),f318(f318(f142(x90561),x90564),x90563))
% 109.14/108.85 [9057]E(f318(f127(x90571,x90572),f740(x90573,x90572,x90574,x90575,x90571)),x90574)+~E(f318(f318(f142(x90571),x90575),x90574),f318(f127(x90571,x90572),x90573))
% 109.14/108.85 [9149]E(f318(f180(f912(x91491)),x91492),x91493)+~P1(f318(f318(f320(f917(f912(x91491),f912(x91491))),f318(f318(f243(f912(x91491),f912(x91491)),x91494),x91492)),f318(f134(x91491,x91495),x91493)))
% 109.14/108.85 [9150]E(f318(f180(f912(x91501)),x91502),x91503)+~P1(f318(f318(f320(f917(f912(x91501),f912(x91501))),f318(f318(f243(f912(x91501),f912(x91501)),x91502),x91504)),f318(f134(x91501,x91505),x91503)))
% 109.14/108.85 [9213]P1(f318(f318(f320(x92131),f689(x92132,x92133,x92131,x92134)),x92132))+~P1(f318(f318(f320(x92135),x92134),f318(f301(x92131,x92135,x92133),x92132)))
% 109.14/108.85 [9373]~P42(f918(x93733,a909),f918(x93731,a909),x93732)+P1(f318(f318(f225(f918(x93731,a909)),f318(x93732,f318(f318(f92(f918(x93733,a909)),x93734),x93735))),f318(f318(f92(f918(x93731,a909)),f318(x93732,x93734)),f318(x93732,x93735))))
% 109.14/108.85 [9375]E(f318(f301(x93751,x93752,x93753),f428(x93754,x93753,x93751,x93755,x93752)),x93755)+~P1(f318(f318(f225(f918(x93752,a909)),x93755),f318(f301(x93751,x93752,x93753),x93754)))
% 109.14/108.85 [9699]P1(f318(f318(f320(f917(f912(x96991),f912(x96991))),f318(f318(f243(f912(x96991),f912(x96991)),f318(f318(f142(x96991),x96992),x96993)),f318(f318(f142(x96991),x96992),x96994))),f298(f912(x96991),f148(x96991,x96995))))+~P1(f318(f318(f320(f917(f912(x96991),f912(x96991))),f318(f318(f243(f912(x96991),f912(x96991)),x96993),x96994)),f298(f912(x96991),f148(x96991,x96995))))
% 109.14/108.85 [9730]~E(f318(x97303,f690(x97305,x97304,x97303,x97302,x97301)),f318(x97305,f690(x97305,x97304,x97303,x97302,x97301)))+E(f318(f318(f145(x97301,x97302),x97303),x97304),f318(f318(f145(x97301,x97302),x97305),x97304))
% 109.14/108.85 [9815]~E(f318(f127(x98151,x98155),x98154),f318(f318(f142(x98151),x98153),x98152))+E(f318(f318(f125(x98151),f738(x98152,x98153,x98154,x98155,x98151)),f318(f318(f142(x98151),x98153),f737(x98152,x98153,x98154,x98155,x98151))),x98154)
% 109.14/108.85 [9816]~E(f318(f318(f142(x98161),x98165),x98164),f318(f127(x98161,x98163),x98162))+E(f318(f318(f125(x98161),f741(x98162,x98163,x98164,x98165,x98161)),f318(f318(f142(x98161),x98165),f740(x98162,x98163,x98164,x98165,x98161))),x98162)
% 109.14/108.85 [9824]E(f318(f318(f145(x98241,x98242),x98243),x98244),f318(f318(f145(x98241,x98242),x98245),x98244))+P1(f318(f318(f320(x98241),f690(x98243,x98244,x98245,x98242,x98241)),f318(f163(x98241),x98244)))
% 109.14/108.85 [9853]~P1(f318(f318(f320(x98535),x98534),f318(f276(x98531,x98535,x98533),x98532)))+P1(f318(f318(f320(x98531),f514(x98532,x98533,x98531,x98534,x98535)),x98532))
% 109.14/108.85 [9854]~P1(f318(f318(f320(x98545),x98544),f318(f276(x98541,x98545,x98543),x98542)))+P1(f318(f318(f320(x98541),f518(x98542,x98543,x98541,x98544,x98545)),x98542))
% 109.14/108.85 [9885]~P1(f318(f318(f225(f918(x98855,a909)),x98854),f318(f301(x98851,x98855,x98853),x98852)))+P1(f318(f318(f225(f918(x98851,a909)),f428(x98852,x98853,x98851,x98854,x98855)),x98852))
% 109.14/108.85 [10322]E(x103221,f2(a90))+E(f214(f917(f912(x103222),x103223),f917(x103222,x103223),f318(f318(f243(f912(x103222),x103223),f104(x103222)),x103224),f318(f248(x103222,x103223,f917(f912(x103222),x103223)),f318(f318(f9(x103222,f918(x103223,f917(f912(x103222),x103223)),f918(x103223,f917(f912(x103222),x103223))),f318(f318(f10(f918(f917(f912(x103222),x103223),f917(f912(x103222),x103223)),f918(f918(x103223,f917(f912(x103222),x103223)),f918(x103223,f917(f912(x103222),x103223))),x103222),f10(f917(f912(x103222),x103223),f917(f912(x103222),x103223),x103223)),f318(f318(f10(f918(f912(x103222),f918(x103223,f917(f912(x103222),x103223))),f918(f917(f912(x103222),x103223),f917(f912(x103222),x103223)),x103222),f248(f912(x103222),x103223,f917(f912(x103222),x103223))),f318(f318(f10(f918(f912(x103222),f912(x103222)),f918(f912(x103222),f918(x103223,f917(f912(x103222),x103223))),x103222),f318(f10(f912(x103222),f918(x103223,f917(f912(x103222),x103223)),f912(x103222)),f243(f912(x103222),x103223))),f142(x103222))))),f318(f108(x103223,x103222,x103225),f318(f318(f3(a90),x103221),f71(a90))))),f318(x103225,x103224)),f318(f318(f108(x103223,x103222,x103225),x103221),x103224))
% 109.14/108.85 [6142]E(x61421,x61422)+~E(f318(f247(x61423,x61424),f318(f318(f243(x61423,x61424),x61425),x61421)),x61422)
% 109.14/108.85 [6143]E(x61431,x61432)+~E(f318(f242(x61433,x61434),f318(f318(f243(x61433,x61434),x61431),x61435)),x61432)
% 109.14/108.85 [6404]~E(x64043,f318(f318(f125(x64041),x64044),f318(f318(f142(x64041),x64042),x64045)))+P1(f318(f318(f320(x64041),x64042),f318(f163(x64041),x64043)))
% 109.14/108.85 [6803]E(f318(f301(x68031,x68032,f318(f18(x68032,x68031),x68033)),x68034),f318(f318(f300(x68032),x68033),f179(f918(x68032,a909))))+~P1(f318(f318(f320(x68031),x68035),x68034))
% 109.14/108.85 [6877]E(f318(f318(f101(f918(x68771,a909)),f318(f163(x68771),x68772)),f318(f163(x68771),x68773)),f318(f163(x68771),x68774))+~E(f157(x68771,x68775,x68774),f318(f318(f243(f912(x68771),f912(x68771)),x68772),x68773))
% 109.14/108.85 [6969]~P4(x69692)+E(f318(f180(f912(x69691)),f318(f318(f139(x69691,x69692,x69693),x69694),x69695)),f318(a103,f318(f180(f912(x69691)),x69695)))
% 109.14/108.85 [6985]~P4(x69852)+E(f318(f163(x69851),f318(f318(f139(x69851,x69852,x69853),x69854),x69855)),f318(f318(f300(x69851),x69854),f318(f163(x69851),x69855)))
% 109.14/108.85 [7259]~P121(x72591)+E(f318(f318(f73(x72591),f318(f318(f73(x72591),x72592),x72593)),f318(f318(f73(x72591),x72594),x72595)),f318(f318(f73(x72591),f318(f318(f73(x72591),x72592),x72594)),f318(f318(f73(x72591),x72593),x72595)))
% 109.14/108.85 [7260]~P121(x72601)+E(f318(f318(f74(x72601),f318(f318(f74(x72601),x72602),x72603)),f318(f318(f74(x72601),x72604),x72605)),f318(f318(f74(x72601),f318(f318(f74(x72601),x72602),x72604)),f318(f318(f74(x72601),x72603),x72605)))
% 109.14/108.85 [7261]~P72(x72611)+E(f318(f318(f282(x72611),f318(f318(f74(x72611),x72612),x72613)),f318(f318(f74(x72611),x72614),x72615)),f318(f318(f74(x72611),f318(f318(f282(x72611),x72612),x72614)),f318(f318(f282(x72611),x72613),x72615)))
% 109.14/108.85 [7275]~P4(x72751)+E(f294(x72751,f318(f318(f224(x72751),x72752),x72753),f318(f318(f223(x72751),x72754),x72755)),f318(f318(f92(f918(x72751,a909)),f294(x72751,x72752,x72754)),f294(x72751,x72753,x72755)))
% 109.14/108.85 [7276]~P4(x72761)+E(f296(x72761,f318(f318(f224(x72761),x72762),x72763),f318(f318(f223(x72761),x72764),x72765)),f318(f318(f92(f918(x72761,a909)),f296(x72761,x72762,x72764)),f296(x72761,x72763,x72765)))
% 109.14/108.85 [7277]~P4(x72771)+E(f297(x72771,f318(f318(f224(x72771),x72772),x72773),f318(f318(f223(x72771),x72774),x72775)),f318(f318(f92(f918(x72771,a909)),f297(x72771,x72772,x72774)),f297(x72771,x72773,x72775)))
% 109.14/108.85 [7278]~P4(x72781)+E(f318(f318(f92(f918(x72781,a909)),f318(f293(x72781,x72782),x72783)),f318(f293(x72781,x72784),x72785)),f318(f293(x72781,f318(f318(f224(x72781),x72782),x72784)),f318(f318(f223(x72781),x72783),x72785)))
% 109.14/108.85 [7400]~P1(f318(x74001,f481(x74003,x74002,x74001)))+P1(f318(x74001,f318(f318(f243(x74002,x74003),x74004),x74005)))
% 109.14/108.85 [7502]~E(x75022,f318(x75024,x75025))+P1(f318(f318(f320(x75021),x75022),f318(f301(x75023,x75021,x75024),f233(f918(x75023,a909)))))
% 109.14/108.85 [7571]~P16(x75713,x75712,x75714)+P16(x75711,x75712,f318(f318(f10(x75713,f918(x75712,x75712),x75711),x75714),x75715))
% 109.14/108.85 [7572]~P14(x75723,x75722,x75724)+P14(x75721,x75722,f318(f318(f10(x75723,f918(x75722,x75722),x75721),x75724),x75725))
% 109.14/108.85 [7708]~P25(x77081,x77082,x77083,x77084)+P25(x77081,x77082,x77083,f318(f318(f3(f918(x77081,a909)),x77084),x77085))
% 109.14/108.85 [7862]~P1(f318(f318(x78623,x78624),x78625))+P1(f318(f318(f248(x78621,x78622,a909),x78623),f318(f318(f243(x78621,x78622),x78624),x78625)))
% 109.14/108.85 [7863]~P1(f318(f318(x78633,x78634),x78635))+P1(f318(f318(f248(x78631,x78632,a909),x78633),f318(f318(f243(x78631,x78632),x78634),x78635)))
% 109.14/108.85 [7981]~P1(f318(x79812,x79814))+~E(f318(f318(f129(x79811),f318(f180(f912(x79811)),f168(x79811,x79812,x79813))),x79813),f318(f318(f142(x79811),x79814),x79815))
% 109.14/108.85 [8001]P25(x80011,x80012,x80013,x80014)+~P25(x80011,x80012,x80013,f318(f318(f101(f918(x80011,a909)),x80015),x80014))
% 109.14/108.85 [8002]P25(x80021,x80022,x80023,x80024)+~P25(x80021,x80022,x80023,f318(f318(f101(f918(x80021,a909)),x80024),x80025))
% 109.14/108.85 [8045]~P4(x80452)+E(f318(f318(f139(x80451,x80452,x80453),x80454),f141(x80451,x80452,x80453,x80455)),f141(x80451,x80452,x80453,f318(f318(f142(x80451),x80454),x80455)))
% 109.14/108.85 [8363]~P14(x83632,x83631,x83633)+E(f318(f133(x83631,x83632,f318(f9(x83632,x83631,x83631),x83633),x83634),x83635),f318(f318(f58(x83632,x83631,x83633),x83634),f318(f163(x83632),x83635)))
% 109.14/108.85 [8390]~E(f318(f318(f129(x83901),f318(f180(f912(x83901)),f168(x83901,x83902,x83903))),x83903),f318(f318(f142(x83901),x83904),x83905))+E(f318(f318(f125(x83901),f168(x83901,x83902,x83903)),f318(f318(f142(x83901),x83904),x83905)),x83903)
% 109.14/108.85 [8417]P1(f318(f318(x84171,x84172),x84173))+~P1(f318(f318(f248(x84174,x84175,a909),x84171),f318(f318(f243(x84174,x84175),x84172),x84173)))
% 109.14/108.85 [8889]P1(f318(f318(f225(f918(x88891,a909)),f318(f301(x88892,x88891,x88893),x88894)),f318(f301(x88892,x88891,x88893),x88895)))+~P1(f318(f318(f225(f918(x88892,a909)),x88894),x88895))
% 109.14/108.85 [8890]P1(f318(f318(f225(f918(x88901,a909)),f318(f302(x88901,x88902,x88903),x88904)),f318(f302(x88901,x88902,x88903),x88905)))+~P1(f318(f318(f225(f918(x88902,a909)),x88904),x88905))
% 109.14/108.85 [8970]E(x89701,f2(a90))+E(f318(f318(f250(x89702,x89703,x89702,f917(x89703,x89702)),f318(x89704,x89705)),f264(x89703,x89702,f318(f318(f3(a90),x89701),f71(a90)),x89704)),f318(f264(x89703,x89702,x89701,x89704),x89705))
% 109.14/108.85 [9081]P1(f318(f318(f246(x90811,x90812,a909,x90813),x90814),x90815))+~P1(f318(x90813,f318(f318(f243(x90811,x90812),x90814),x90815)))
% 109.14/108.85 [9354]~P1(f318(f318(f246(x93542,x93543,a909,x93541),x93544),x93545))+P1(f318(x93541,f318(f318(f243(x93542,x93543),x93544),x93545)))
% 109.14/108.85 [9355]~P1(f318(f318(f246(x93552,x93553,a909,x93551),x93554),x93555))+P1(f318(x93551,f318(f318(f243(x93552,x93553),x93554),x93555)))
% 109.14/108.85 [9546]~P1(f318(f318(f320(x95462),x95465),f318(f301(x95461,x95462,x95464),x95463)))+P1(f318(f318(f320(x95461),f318(f84(x95461,x95462,x95463,x95464),x95465)),x95463))
% 109.14/108.85 [9628]~P1(f318(f55(x96283),f318(f301(x96282,x96283,x96285),f233(f918(x96282,a909)))))+P1(f318(f55(x96281),f318(f301(x96282,x96281,f318(f318(f10(x96283,x96281,x96282),x96284),x96285)),f233(f918(x96282,a909)))))
% 109.14/108.85 [9653]P1(f318(f318(f225(f918(f918(x96531,a909),a909)),f318(f301(f918(x96532,a909),f918(x96531,a909),f301(x96532,x96531,x96533)),f318(f299(x96532),x96534))),f318(f299(x96531),x96535)))+~P1(f318(f318(f225(f918(x96531,a909)),f318(f301(x96532,x96531,x96533),x96534)),x96535))
% 109.14/108.85 [9738]E(x97381,x97382)+~P1(f318(f60(x97383,x97384,x97385,x97381,f179(f918(x97383,a909))),x97382))
% 109.14/108.85 [9753]E(f318(f318(f243(x97531,x97532),f548(x97533,x97534,x97535,x97532,x97531)),f549(x97533,x97534,x97535,x97532,x97531)),x97535)+~P1(f318(f318(f320(f917(x97531,x97532)),x97535),f318(f318(f245(x97531,x97532),x97534),x97533)))
% 109.14/108.85 [9859]P1(f318(f318(f320(x98591),f548(x98592,x98593,x98594,x98595,x98591)),x98593))+~P1(f318(f318(f320(f917(x98591,x98595)),x98594),f318(f318(f245(x98591,x98595),x98593),x98592)))
% 109.14/108.85 [10035]P1(f318(f318(f320(x100351),f549(x100352,x100353,x100354,x100351,x100355)),f318(x100352,f548(x100352,x100353,x100354,x100351,x100355))))+~P1(f318(f318(f320(f917(x100355,x100351)),x100354),f318(f318(f245(x100355,x100351),x100353),x100352)))
% 109.14/108.85 [10046]P1(f318(f318(f320(f917(x100461,x100461)),f318(f318(f243(x100461,x100461),x100462),f630(x100463,x100464,x100465,x100462,x100461))),x100463))+~P1(f318(f318(f320(f917(x100461,x100461)),f318(f318(f243(x100461,x100461),x100462),x100465)),f318(f318(f174(f917(x100461,x100461),a909),f318(a103,x100464)),x100463)))
% 109.14/108.85 [10047]P1(f318(f318(f320(f917(x100471,x100471)),f318(f318(f243(x100471,x100471),x100472),f632(x100473,x100474,x100475,x100472,x100471))),x100473))+~P1(f318(f318(f320(f917(x100471,x100471)),f318(f318(f243(x100471,x100471),x100472),x100475)),f318(f318(f174(f917(x100471,x100471),a909),f318(a103,x100474)),x100473)))
% 109.14/108.85 [10064]~P1(f318(f318(f320(f917(f912(x100641),f912(x100641))),f318(f318(f243(f912(x100641),f912(x100641)),f318(f318(f142(x100641),x100642),x100645)),x100644)),f149(x100641,x100643)))+P1(f318(f318(f320(f917(x100641,x100641)),f318(f318(f243(x100641,x100641),x100642),f650(x100643,x100644,x100645,x100642,x100641))),x100643))
% 109.14/108.85 [6480]P1(f318(x64802,x64804))+E(f168(x64801,x64802,f318(f318(f125(x64801),x64803),f318(f318(f142(x64801),x64804),x64805))),f168(x64801,x64802,x64803))
% 109.14/108.85 [6529]~P103(x65292)+E(f318(f318(f318(f101(f918(x65291,x65292)),x65293),x65294),x65295),f318(f318(f101(x65292),f318(x65293,x65295)),f318(x65294,x65295)))
% 109.14/108.85 [6530]~P103(x65302)+E(f318(f318(f318(f101(f918(x65301,x65302)),x65303),x65304),x65305),f318(f318(f101(x65302),f318(x65303,x65305)),f318(x65304,x65305)))
% 109.14/108.85 [6531]~P103(x65312)+E(f318(f318(f318(f92(f918(x65311,x65312)),x65313),x65314),x65315),f318(f318(f92(x65312),f318(x65313,x65315)),f318(x65314,x65315)))
% 109.14/108.85 [6532]~P103(x65322)+E(f318(f318(f318(f92(f918(x65321,x65322)),x65323),x65324),x65325),f318(f318(f92(x65322),f318(x65323,x65325)),f318(x65324,x65325)))
% 109.14/108.85 [6533]~P84(x65332)+E(f318(f318(f318(f3(f918(x65331,x65332)),x65333),x65334),x65335),f318(f318(f3(x65332),f318(x65333,x65335)),f318(x65334,x65335)))
% 109.14/108.85 [6534]~P84(x65342)+E(f318(f318(f318(f3(f918(x65341,x65342)),x65343),x65344),x65345),f318(f318(f3(x65342),f318(x65343,x65345)),f318(x65344,x65345)))
% 109.14/108.85 [6552]E(x65521,x65522)+E(f318(f318(f155(x65523),f318(f318(f150(x65523,x65524),x65521),x65525)),x65522),f318(f318(f155(x65523),x65524),x65522))
% 109.14/108.85 [6822]~E(x68224,f179(f918(x68223,a909)))+E(f318(f318(f101(f918(x68221,a909)),x68222),f318(f318(f33(x68223,f918(x68221,a909)),x68224),x68225)),x68222)
% 109.14/108.85 [6823]~E(x68234,f179(f918(x68233,a909)))+E(f318(f318(f92(f918(x68231,a909)),x68232),f318(f318(f34(x68233,f918(x68231,a909)),x68234),x68235)),x68232)
% 109.14/108.85 [6824]~E(x68244,f179(f918(x68243,a909)))+E(f318(f318(f3(f918(x68241,a909)),x68242),f318(f318(f33(x68243,f918(x68241,a909)),x68244),x68245)),x68242)
% 109.14/108.85 [6841]~E(x68414,f179(f918(x68413,a909)))+E(f318(f318(f300(x68411),x68412),f318(f318(f33(x68413,f918(x68411,a909)),x68414),x68415)),f318(f318(f300(x68411),x68412),f179(f918(x68411,a909))))
% 109.14/108.85 [7258]~P121(x72581)+E(f318(f318(f74(x72581),f318(f318(f74(x72581),x72582),x72583)),f318(f318(f74(x72581),x72584),x72585)),f318(f318(f74(x72581),x72582),f318(f318(f74(x72581),x72583),f318(f318(f74(x72581),x72584),x72585))))
% 109.14/108.85 [7617]E(f318(f318(f155(x76171),f318(f318(f145(x76172,x76171),x76173),x76174)),x76175),f318(x76173,f318(f318(f155(x76172),x76174),x76175)))+~P1(f318(f318(f226(a911),x76175),f318(f180(f912(x76172)),x76174)))
% 109.14/108.85 [7680]E(f318(f318(f101(f918(x76801,a909)),f318(x76802,x76803)),f318(f318(f33(x76804,f918(x76801,a909)),x76805),x76802)),f318(f318(f33(x76804,f918(x76801,a909)),x76805),x76802))+~P1(f318(f318(f320(x76804),x76803),x76805))
% 109.14/108.85 [7681]E(f318(f318(f92(f918(x76811,a909)),f318(x76812,x76813)),f318(f318(f34(x76814,f918(x76811,a909)),x76815),x76812)),f318(f318(f34(x76814,f918(x76811,a909)),x76815),x76812))+~P1(f318(f318(f320(x76814),x76813),x76815))
% 109.14/108.85 [8287]~E(x82873,f179(f918(x82871,a909)))+E(f318(f318(f33(x82871,f918(x82872,a909)),x82873),f318(f318(f10(f918(x82872,a909),f918(x82872,a909),x82871),f318(f300(x82872),x82874)),x82875)),f179(f918(x82872,a909)))
% 109.14/108.85 [8292]~P1(f318(f318(f320(x82924),x82923),x82925))+P1(f318(f318(f225(f918(x82921,a909)),f318(x82922,x82923)),f318(f318(f33(x82924,f918(x82921,a909)),x82925),x82922)))
% 109.14/108.85 [8416]~E(f318(x84164,x84162),x84165)+P1(f318(f318(f320(x84161),x84162),f318(f302(x84161,x84163,x84164),f318(f318(f300(x84163),x84165),f179(f918(x84163,a909))))))
% 109.14/108.85 [8464]~P58(x84641,x84642,f318(f277(x84642,x84641),x84643))+E(f318(f318(f92(f918(x84641,a909)),f318(f276(x84642,x84641,x84643),x84644)),f318(f276(x84642,x84641,x84643),x84645)),f318(f276(x84642,x84641,x84643),f318(f318(f92(f918(x84642,a909)),x84644),x84645)))
% 109.14/108.85 [8536]E(x85361,f2(a90))+E(f318(f109(x85362,x85363,f318(x85364,f318(f318(f3(a90),x85361),f71(a90)))),f318(f318(f9(x85362,a90,f913(x85363)),x85365),x85361)),f318(f189(x85362,x85363,x85364,x85365),x85361))
% 109.14/108.85 [8573]E(x85731,f179(f918(x85732,a909)))+E(f318(f318(f33(x85732,f918(x85733,a909)),x85731),f318(f318(f10(f918(x85733,a909),f918(x85733,a909),x85732),f318(f300(x85733),x85734)),x85735)),f318(f318(f300(x85733),x85734),f318(f318(f33(x85732,f918(x85733,a909)),x85731),x85735)))
% 109.14/108.85 [8574]E(x85741,f179(f918(x85742,a909)))+E(f318(f318(f33(x85742,f918(x85743,a909)),x85741),f318(f318(f10(f918(x85743,a909),f918(x85743,a909),x85742),f318(f300(x85743),x85744)),x85745)),f318(f318(f300(x85743),x85744),f318(f318(f33(x85742,f918(x85743,a909)),x85741),x85745)))
% 109.14/108.85 [8626]~P25(x86262,x86261,x86263,f233(f918(x86262,a909)))+E(f318(f318(f92(f918(x86261,a909)),f318(f301(x86262,x86261,x86263),x86264)),f318(f301(x86262,x86261,x86263),x86265)),f318(f301(x86262,x86261,x86263),f318(f318(f92(f918(x86262,a909)),x86264),x86265)))
% 109.14/108.85 [8627]~P25(x86272,x86271,x86273,f233(f918(x86272,a909)))+E(f318(f318(f3(f918(x86271,a909)),f318(f301(x86272,x86271,x86273),x86274)),f318(f301(x86272,x86271,x86273),x86275)),f318(f301(x86272,x86271,x86273),f318(f318(f3(f918(x86272,a909)),x86274),x86275)))
% 109.14/108.85 [8699]~P1(f318(f318(f61(x86991,x86992,x86995),x86993),x86994))+P1(f318(f318(f320(f917(x86991,x86992)),f318(f318(f243(x86991,x86992),x86993),x86994)),x86995))
% 109.14/108.85 [8729]P1(f318(f318(f320(x87291),x87292),f318(f275(x87293,x87291),x87294)))+~P1(f318(f318(f320(f917(x87293,x87291)),f318(f318(f243(x87293,x87291),x87295),x87292)),x87294))
% 109.14/108.85 [8730]P1(f318(f318(f320(x87301),x87302),f318(f275(x87303,x87301),x87304)))+~P1(f318(f318(f320(f917(x87303,x87301)),f318(f318(f243(x87303,x87301),x87305),x87302)),x87304))
% 109.14/108.85 [8731]P1(f318(f318(f320(x87311),x87312),f318(f255(x87311,x87313),x87314)))+~P1(f318(f318(f320(f917(x87311,x87313)),f318(f318(f243(x87311,x87313),x87312),x87315)),x87314))
% 109.14/108.85 [8732]P1(f318(f318(f320(x87321),x87322),f318(f255(x87321,x87323),x87324)))+~P1(f318(f318(f320(f917(x87321,x87323)),f318(f318(f243(x87321,x87323),x87322),x87325)),x87324))
% 109.14/108.85 [8871]P1(f318(f318(f61(x88711,x88712,x88713),x88714),x88715))+~P1(f318(f318(f320(f917(x88711,x88712)),f318(f318(f243(x88711,x88712),x88714),x88715)),x88713))
% 109.14/108.85 [8905]E(f318(x89051,x89052),x89053)+~P1(f318(f318(f320(x89054),x89052),f318(f302(x89054,x89055,x89051),f318(f318(f300(x89055),x89053),f179(f918(x89055,a909))))))
% 109.14/108.85 [9145]P1(f318(f318(f320(f917(x91451,x91452)),f318(f318(f243(x91451,x91452),x91453),x91454)),f318(f277(x91452,x91451),x91455)))+~P1(f318(f318(f320(f917(x91452,x91451)),f318(f318(f243(x91452,x91451),x91454),x91453)),x91455))
% 109.14/108.85 [9146]P1(f318(f318(f320(f917(x91461,x91462)),f318(f318(f243(x91461,x91462),x91463),x91464)),f318(f277(x91462,x91461),x91465)))+~P1(f318(f318(f320(f917(x91462,x91461)),f318(f318(f243(x91462,x91461),x91464),x91463)),x91465))
% 109.14/108.85 [9164]~P1(f318(f318(x91641,x91645),x91644))+P1(f318(f318(x91641,f318(f247(x91642,x91643),f318(f318(f243(x91642,x91643),x91644),x91645))),f318(f242(x91642,x91643),f318(f318(f243(x91642,x91643),x91644),x91645))))
% 109.14/108.85 [9193]~P1(f318(f318(f320(f917(x91932,x91931)),f318(f318(f243(x91932,x91931),x91934),x91933)),f318(f277(x91931,x91932),x91935)))+P1(f318(f318(f320(f917(x91931,x91932)),f318(f318(f243(x91931,x91932),x91933),x91934)),x91935))
% 109.14/108.85 [9194]~P1(f318(f318(f320(f917(x91942,x91941)),f318(f318(f243(x91942,x91941),x91944),x91943)),f318(f277(x91941,x91942),x91945)))+P1(f318(f318(f320(f917(x91941,x91942)),f318(f318(f243(x91941,x91942),x91943),x91944)),x91945))
% 109.14/108.85 [9220]~P1(f318(f318(f320(f917(x92203,x92201)),f318(f318(f243(x92203,x92201),x92205),x92202)),x92204))+P1(f318(f318(f320(x92201),x92202),f318(f276(x92203,x92201,x92204),f318(f318(f300(x92203),x92205),f179(f918(x92203,a909))))))
% 109.14/108.85 [9267]P1(f318(f318(f320(f917(x92671,x92672)),f318(f318(f243(x92671,x92672),x92673),x92674)),x92675))+~P1(f318(f318(f320(x92672),x92674),f318(f276(x92671,x92672,x92675),f318(f318(f300(x92671),x92673),f179(f918(x92671,a909))))))
% 109.14/108.85 [9362]~P76(x93621)+E(f318(f318(f8(a911,x93621),x93622),f294(a911,f318(f318(f73(a911),x93623),x93624),f318(f318(f73(a911),x93625),x93624))),f318(f318(f8(a911,x93621),f318(f318(f10(a911,x93621,a911),x93622),f318(f318(f9(a911,a911,a911),f73(a911)),x93624))),f294(a911,x93623,x93625)))
% 109.14/108.85 [9380]~P76(x93801)+E(f318(f318(f8(a911,x93801),x93802),f318(f293(a911,f318(f318(f73(a911),x93803),x93804)),f318(f318(f73(a911),x93805),x93804))),f318(f318(f8(a911,x93801),f318(f318(f10(a911,x93801,a911),x93802),f318(f318(f9(a911,a911,a911),f73(a911)),x93804))),f318(f293(a911,x93803),x93805)))
% 109.14/108.85 [9438]~P25(x94381,x94382,x94383,f233(f918(x94381,a909)))+E(f318(f318(f145(x94381,x94382),x94383),f318(f127(x94381,f318(f318(f10(a909,a909,x94381),a313),f318(a315,x94384))),x94385)),f318(f127(x94382,f318(f318(f10(a909,a909,x94382),a313),f318(a315,f318(x94383,x94384)))),f318(f318(f145(x94381,x94382),x94383),x94385)))
% 109.14/108.85 [9459]~P25(x94591,x94592,x94593,f318(f318(f300(x94591),x94594),f318(f163(x94591),x94595)))+E(f318(f318(f145(x94591,x94592),x94593),f318(f127(x94591,f318(f318(f10(a909,a909,x94591),a313),f318(a315,x94594))),x94595)),f318(f127(x94592,f318(f318(f10(a909,a909,x94592),a313),f318(a315,f318(x94593,x94594)))),f318(f318(f145(x94591,x94592),x94593),x94595)))
% 109.14/108.85 [9616]P1(f318(f318(f320(f917(f912(x96161),f912(x96161))),f318(f318(f243(f912(x96161),f912(x96161)),f318(f318(f142(x96161),x96162),x96163)),f318(f318(f142(x96161),x96164),x96163))),f148(x96161,x96165)))+~P1(f318(f318(f320(f917(x96161,x96161)),f318(f318(f243(x96161,x96161),x96162),x96164)),x96165))
% 109.14/108.85 [9748]E(f318(f318(f300(x97481),f402(x97482,x97483,x97484,x97485,x97481)),f403(x97482,x97483,x97484,x97485,x97481)),f318(f318(f300(x97481),x97484),x97483))+~P1(f318(f56(x97481,x97485,f318(f318(f300(x97481),x97484),x97483)),x97482))
% 109.14/108.85 [9749]E(f318(f318(f300(x97491),f404(x97492,x97493,x97494,x97495,x97491)),f405(x97492,x97493,x97494,x97495,x97491)),f318(f318(f300(x97491),x97494),x97493))+~P1(f318(f56(x97491,x97495,f318(f318(f300(x97491),x97494),x97493)),x97492))
% 109.14/108.85 [9843]P1(f318(f318(f320(x98431),f482(x98432,x98433,x98434,x98435,x98431)),x98434))+P1(f318(f318(f318(f34(x98431,f918(x98435,a909)),x98434),x98433),x98432))
% 109.14/108.85 [9848]P1(f318(f318(f320(x98481),f474(x98482,x98483,x98481,x98484,x98485)),x98483))+P1(f318(f318(f320(x98485),x98484),f318(f318(f34(x98481,f918(x98485,a909)),x98483),x98482)))
% 109.14/108.85 [9857]P1(f318(f318(f320(x98571),f477(x98572,x98573,x98571,x98574,x98575)),x98573))+P1(f318(f318(f225(f918(x98575,a909)),x98574),f318(f318(f34(x98571,f918(x98575,a909)),x98573),x98572)))
% 109.14/108.85 [9858]P1(f318(f318(f320(x98581),f830(x98582,x98583,x98584,x98585,x98581)),x98585))+P1(f318(f318(f225(f918(x98584,a909)),x98583),f318(f318(f34(x98581,f918(x98584,a909)),x98585),x98582)))
% 109.14/108.85 [9860]P1(f318(f318(x98601,f470(x98602,x98601,x98603,x98604,x98605)),x98602))+~P1(f318(f318(f318(f33(x98605,f918(x98604,a909)),x98603),x98601),x98602))
% 109.14/108.85 [9864]P1(f318(f318(f320(x98641),f470(x98642,x98643,x98644,x98645,x98641)),x98644))+~P1(f318(f318(f318(f33(x98641,f918(x98645,a909)),x98644),x98643),x98642))
% 109.14/108.85 [9865]P56(x98654,f318(f318(f34(x98651,f918(x98654,a909)),x98655),x98653),f318(f318(f34(x98651,f918(f917(x98654,x98654),a909)),x98655),x98652))+P1(f318(f318(f320(x98651),f768(x98652,x98653,x98654,x98655,x98651)),x98655))
% 109.14/108.85 [9866]P56(x98664,f318(f318(f33(x98661,f918(x98664,a909)),x98665),x98663),f318(f318(f33(x98661,f918(f917(x98664,x98664),a909)),x98665),x98662))+P1(f318(f318(f320(x98661),f824(x98662,x98663,x98664,x98665,x98661)),x98665))
% 109.14/108.85 [9877]P1(f318(f318(f320(x98771),f476(x98772,x98773,x98771,x98774,x98775)),x98773))+~P1(f318(f318(f320(x98775),x98774),f318(f318(f33(x98771,f918(x98775,a909)),x98773),x98772)))
% 109.14/108.85 [9883]P1(f318(f318(f320(x98831),x98832),f318(x98833,f476(x98833,x98834,x98835,x98832,x98831))))+~P1(f318(f318(f320(x98831),x98832),f318(f318(f33(x98835,f918(x98831,a909)),x98834),x98833)))
% 109.14/108.85 [9982]~P1(f318(f318(x99824,f482(x99825,x99824,x99823,x99822,x99821)),x99825))+P1(f318(f318(f318(f34(x99821,f918(x99822,a909)),x99823),x99824),x99825))
% 109.14/108.85 [9985]~P1(f318(f318(f320(x99851),x99852),f318(x99855,f474(x99855,x99854,x99853,x99852,x99851))))+P1(f318(f318(f320(x99851),x99852),f318(f318(f34(x99853,f918(x99851,a909)),x99854),x99855)))
% 109.14/108.85 [9988]~P56(x99881,f318(x99884,f824(x99885,x99884,x99881,x99883,x99882)),f318(x99885,f824(x99885,x99884,x99881,x99883,x99882)))+P56(x99881,f318(f318(f33(x99882,f918(x99881,a909)),x99883),x99884),f318(f318(f33(x99882,f918(f917(x99881,x99881),a909)),x99883),x99885))
% 109.14/108.85 [9989]~P56(x99891,f318(x99894,f768(x99895,x99894,x99891,x99893,x99892)),f318(x99895,f768(x99895,x99894,x99891,x99893,x99892)))+P56(x99891,f318(f318(f34(x99892,f918(x99891,a909)),x99893),x99894),f318(f318(f34(x99892,f918(f917(x99891,x99891),a909)),x99893),x99895))
% 109.14/108.85 [9990]~P1(f318(f318(f225(f918(x99901,a909)),x99902),f318(x99905,f477(x99905,x99904,x99903,x99902,x99901))))+P1(f318(f318(f225(f918(x99901,a909)),x99902),f318(f318(f34(x99903,f918(x99901,a909)),x99904),x99905)))
% 109.14/108.85 [9991]~P1(f318(f318(f225(f918(x99911,a909)),x99912),f318(x99915,f830(x99915,x99912,x99911,x99914,x99913))))+P1(f318(f318(f225(f918(x99911,a909)),x99912),f318(f318(f34(x99913,f918(x99911,a909)),x99914),x99915)))
% 109.14/108.85 [10050]~P1(f318(f318(f320(x100501),f402(x100505,x100504,x100503,x100502,x100501)),f403(x100505,x100504,x100503,x100502,x100501)))+~P1(f318(f56(x100501,x100502,f318(f318(f300(x100501),x100503),x100504)),x100505))
% 109.14/108.85 [10051]~P1(f318(f318(f320(x100511),f404(x100515,x100514,x100513,x100512,x100511)),f405(x100515,x100514,x100513,x100512,x100511)))+~P1(f318(f56(x100511,x100512,f318(f318(f300(x100511),x100513),x100514)),x100515))
% 109.14/108.85 [10052]~P1(f318(f318(f320(f917(x100521,x100521)),f318(f318(f243(x100521,x100521),x100522),x100525)),f318(f318(f174(f917(x100521,x100521),a909),f318(a103,x100524)),x100523)))+P1(f318(f318(f320(f917(x100521,x100521)),f318(f318(f243(x100521,x100521),x100522),f631(x100523,x100524,x100525,x100522,x100521))),f318(f318(f174(f917(x100521,x100521),a909),x100524),x100523)))
% 109.14/108.85 [10058]P1(f318(f60(x100581,x100581,x100582,f402(x100583,x100584,x100585,x100582,x100581),f403(x100583,x100584,x100585,x100582,x100581)),x100583))+~P1(f318(f56(x100581,x100582,f318(f318(f300(x100581),x100585),x100584)),x100583))
% 109.14/108.85 [10059]P1(f318(f60(x100591,x100591,x100592,f404(x100593,x100594,x100595,x100592,x100591),f405(x100593,x100594,x100595,x100592,x100591)),x100593))+~P1(f318(f56(x100591,x100592,f318(f318(f300(x100591),x100595),x100594)),x100593))
% 109.14/108.85 [10068]~P4(x100681)+P13(x100681,f318(f318(f145(x100682,x100681),x100683),f318(f127(x100682,f318(f318(f9(x100682,x100681,a909),f318(f318(f10(x100681,f918(x100681,a909),x100682),a315),x100683)),f318(x100684,x100685))),x100685)))
% 109.14/108.85 [10112]~P1(f318(f318(f320(x101122),x101125),f318(f276(x101121,x101122,x101124),x101123)))+P1(f318(f318(f320(f917(x101121,x101122)),f318(f318(f243(x101121,x101122),f514(x101123,x101124,x101121,x101125,x101122)),x101125)),x101124))
% 109.14/108.85 [10113]~P1(f318(f318(f320(x101132),x101135),f318(f276(x101131,x101132,x101134),x101133)))+P1(f318(f318(f320(f917(x101131,x101132)),f318(f318(f243(x101131,x101132),f518(x101133,x101134,x101131,x101135,x101132)),x101135)),x101134))
% 109.14/108.85 [10118]~P1(f318(f318(f320(f917(x101181,x101181)),f318(f318(f243(x101181,x101181),x101185),x101184)),f318(f318(f174(f917(x101181,x101181),a909),f318(a103,x101183)),x101182)))+P1(f318(f318(f320(f917(x101181,x101181)),f318(f318(f243(x101181,x101181),f631(x101182,x101183,x101184,x101185,x101181)),x101184)),x101182))
% 109.14/108.85 [10130]~P1(f318(f318(f320(f917(x101301,x101301)),f318(f318(f243(x101301,x101301),x101305),x101304)),f318(f318(f174(f917(x101301,x101301),a909),f318(a103,x101303)),x101302)))+P1(f318(f318(f320(f917(x101301,x101301)),f318(f318(f243(x101301,x101301),f630(x101302,x101303,x101304,x101305,x101301)),x101304)),f318(f318(f174(f917(x101301,x101301),a909),x101303),x101302)))
% 109.14/108.85 [10131]~P1(f318(f318(f320(f917(x101311,x101311)),f318(f318(f243(x101311,x101311),x101315),x101314)),f318(f318(f174(f917(x101311,x101311),a909),f318(a103,x101313)),x101312)))+P1(f318(f318(f320(f917(x101311,x101311)),f318(f318(f243(x101311,x101311),f632(x101312,x101313,x101314,x101315,x101311)),x101314)),f318(f318(f174(f917(x101311,x101311),a909),x101313),x101312)))
% 109.14/108.85 [10132]~P1(f318(f318(f320(f917(f912(x101321),f912(x101321))),f318(f318(f243(f912(x101321),f912(x101321)),x101325),f318(f318(f142(x101321),x101324),x101323))),f149(x101321,x101322)))+P1(f318(f318(f320(f917(x101321,x101321)),f318(f318(f243(x101321,x101321),f648(x101322,x101323,x101324,x101325,x101321)),x101324)),x101322))
% 109.14/108.85 [7701]~E(x77013,f179(f918(x77012,a909)))+E(f318(f318(f101(f918(x77011,a909)),f318(f318(f33(x77012,f918(x77011,a909)),x77013),x77014)),x77015),x77015)
% 109.14/108.85 [7702]~E(x77023,f179(f918(x77022,a909)))+E(f318(f318(f92(f918(x77021,a909)),f318(f318(f34(x77022,f918(x77021,a909)),x77023),x77024)),x77025),x77025)
% 109.14/108.85 [7752]~P121(x77521)+E(f318(f318(f74(x77521),f318(f318(f74(x77521),x77522),x77523)),f318(f318(f74(x77521),x77524),x77525)),f318(f318(f74(x77521),x77524),f318(f318(f74(x77521),f318(f318(f74(x77521),x77522),x77523)),x77525)))
% 109.14/108.85 [8121]~E(x81213,f179(f918(x81212,a909)))+E(f318(f318(f3(f918(x81211,a909)),f318(f318(f34(x81212,f918(x81211,a909)),x81213),x81214)),x81215),f318(f318(f3(f918(x81211,a909)),f233(f918(x81211,a909))),x81215))
% 109.14/108.85 [8258]E(f318(f318(f150(x82581,f318(f318(f125(x82581),x82582),x82583)),x82584),x82585),f318(f318(f125(x82581),f318(f318(f150(x82581,x82582),x82584),x82585)),x82583))+~P1(f318(f318(f226(a911),x82584),f318(f180(f912(x82581)),x82582)))
% 109.14/108.85 [8259]E(f318(f318(f150(x82591,f318(f318(f125(x82591),x82592),x82593)),x82594),x82595),f318(f318(f125(x82591),f318(f318(f150(x82591,x82592),x82594),x82595)),x82593))+~P1(f318(f318(f226(a911),x82594),f318(f180(f912(x82591)),x82592)))
% 109.14/108.85 [8526]E(f318(f318(f155(x85261),f318(f318(f145(a911,x85261),x85262),f130(a911,f318(f293(a911,x85263),x85264)))),x85265),f318(x85262,f318(f318(f73(a911),x85263),x85265)))+~P1(f318(f318(f226(a911),x85265),f318(f318(f3(a911),x85264),x85263)))
% 109.14/108.85 [8541]E(x85411,f2(a90))+E(f113(x85412,x85413,f318(x85414,f318(f318(f3(a90),x85411),f71(a90))),f318(f318(f9(x85412,a90,f913(f915(x85413))),x85415),x85411)),f318(f187(x85412,x85413,x85414,x85415),x85411))
% 109.14/108.85 [8564]~E(x85643,f179(f918(x85641,a909)))+E(f318(f318(f33(x85641,f918(x85642,a909)),x85643),f318(f318(f10(f918(x85642,a909),f918(x85642,a909),x85641),f318(f101(f918(x85642,a909)),x85644)),x85645)),f179(f918(x85642,a909)))
% 109.14/108.85 [8565]~E(x85653,f179(f918(x85651,a909)))+E(f318(f318(f34(x85651,f918(x85652,a909)),x85653),f318(f318(f10(f918(x85652,a909),f918(x85652,a909),x85651),f318(f92(f918(x85652,a909)),x85654)),x85655)),f233(f918(x85652,a909)))
% 109.14/108.85 [8566]~E(x85663,f179(f918(x85661,a909)))+E(f318(f318(f34(x85661,f918(x85662,a909)),x85663),f318(f318(f10(f918(x85662,a909),f918(x85662,a909),x85661),f318(f3(f918(x85662,a909)),x85664)),x85665)),f233(f918(x85662,a909)))
% 109.14/108.85 [8568]~P146(x85682)+E(f318(f318(f8(x85681,x85682),f318(f318(f10(x85682,x85682,x85681),f318(f74(x85682),x85683)),x85684)),x85685),f318(f318(f74(x85682),x85683),f318(f318(f8(x85681,x85682),x85684),x85685)))
% 109.14/108.85 [8853]E(x88531,f179(f918(x88532,a909)))+E(f318(f318(f33(x88532,f918(x88533,a909)),x88531),f318(f318(f10(f918(x88533,a909),f918(x88533,a909),x88532),f318(f101(f918(x88533,a909)),x88534)),x88535)),f318(f318(f101(f918(x88533,a909)),x88534),f318(f318(f33(x88532,f918(x88533,a909)),x88531),x88535)))
% 109.14/108.85 [8854]E(x88541,f179(f918(x88542,a909)))+E(f318(f318(f34(x88542,f918(x88543,a909)),x88541),f318(f318(f10(f918(x88543,a909),f918(x88543,a909),x88542),f318(f92(f918(x88543,a909)),x88544)),x88545)),f318(f318(f92(f918(x88543,a909)),x88544),f318(f318(f34(x88542,f918(x88543,a909)),x88541),x88545)))
% 109.14/108.85 [8855]E(x88551,f179(f918(x88552,a909)))+E(f318(f318(f34(x88552,f918(x88553,a909)),x88551),f318(f318(f10(f918(x88553,a909),f918(x88553,a909),x88552),f318(f3(f918(x88553,a909)),x88554)),x88555)),f318(f318(f3(f918(x88553,a909)),x88554),f318(f318(f33(x88552,f918(x88553,a909)),x88551),x88555)))
% 109.14/108.85 [8856]E(x88561,f179(f918(x88562,a909)))+E(f318(f318(f33(x88562,f918(x88563,a909)),x88561),f318(f318(f10(f918(x88563,a909),f918(x88563,a909),x88562),f318(f101(f918(x88563,a909)),x88564)),x88565)),f318(f318(f101(f918(x88563,a909)),x88564),f318(f318(f33(x88562,f918(x88563,a909)),x88561),x88565)))
% 109.14/108.85 [8857]E(x88571,f179(f918(x88572,a909)))+E(f318(f318(f34(x88572,f918(x88573,a909)),x88571),f318(f318(f10(f918(x88573,a909),f918(x88573,a909),x88572),f318(f92(f918(x88573,a909)),x88574)),x88575)),f318(f318(f92(f918(x88573,a909)),x88574),f318(f318(f34(x88572,f918(x88573,a909)),x88571),x88575)))
% 109.14/108.85 [8858]E(x88581,f179(f918(x88582,a909)))+E(f318(f318(f34(x88582,f918(x88583,a909)),x88581),f318(f318(f10(f918(x88583,a909),f918(x88583,a909),x88582),f318(f3(f918(x88583,a909)),x88584)),x88585)),f318(f318(f3(f918(x88583,a909)),x88584),f318(f318(f33(x88582,f918(x88583,a909)),x88581),x88585)))
% 109.14/108.85 [9063]~P1(f318(f318(f226(a911),f318(x90634,x90632)),f318(x90634,x90633)))+P1(f318(f318(f320(f917(x90631,x90631)),f318(f318(f243(x90631,x90631),x90632),x90633)),f144(x90631,f318(f318(f142(f918(x90631,a911)),x90634),x90635))))
% 109.14/108.85 [9064]~P1(f318(f318(f226(a911),f318(x90644,x90642)),f318(x90644,x90643)))+P1(f318(f318(f320(f917(x90641,x90641)),f318(f318(f243(x90641,x90641),x90642),x90643)),f144(x90641,f318(f318(f142(f918(x90641,a911)),x90644),x90645))))
% 109.14/108.85 [9307]~P42(f918(x93075,a909),f918(x93071,a909),x93072)+P1(f318(f318(f225(f918(x93071,a909)),f318(f318(f101(f918(x93071,a909)),f318(x93072,x93073)),f318(x93072,x93074))),f318(x93072,f318(f318(f101(f918(x93075,a909)),x93073),x93074))))
% 109.14/108.85 [9328]~P25(x93282,x93281,x93283,f318(f318(f101(f918(x93282,a909)),x93284),x93285))+E(f318(f318(f92(f918(x93281,a909)),f318(f301(x93282,x93281,x93283),f318(f318(f3(f918(x93282,a909)),x93284),x93285))),f318(f301(x93282,x93281,x93283),f318(f318(f3(f918(x93282,a909)),x93285),x93284))),f179(f918(x93281,a909)))
% 109.14/108.85 [9584]~P25(x95843,x95841,x95845,f233(f918(x95843,a909)))+E(f318(f66(x95841,x95842,x95843,f318(f66(x95843,x95842,x95841,x95844),f84(x95843,x95841,f233(f918(x95843,a909)),x95845))),x95845),x95844)
% 109.14/108.85 [9614]~P1(f318(f318(f225(f918(x96143,a909)),f318(f276(x96141,x96143,x96144),x96142)),x96145))+P1(f318(f318(f225(f918(x96141,a909)),x96142),f318(f72(f918(x96141,a909)),f318(f276(x96143,x96141,f318(f277(x96141,x96143),x96144)),f318(f72(f918(x96143,a909)),x96145)))))
% 109.14/108.85 [9637]~P25(x96371,x96372,x96373,f318(f318(f300(x96371),x96374),x96375))+~P1(f318(f318(f320(x96372),f318(x96373,x96374)),f318(f301(x96371,x96372,x96373),f318(f318(f3(f918(x96371,a909)),x96375),f318(f318(f300(x96371),x96374),f179(f918(x96371,a909)))))))
% 109.14/108.85 [9703]P1(f318(f318(f225(f918(x97031,a909)),f318(f276(x97032,x97031,x97033),x97034)),x97035))+~P1(f318(f318(f225(f918(x97032,a909)),x97034),f318(f72(f918(x97032,a909)),f318(f276(x97031,x97032,f318(f277(x97032,x97031),x97033)),f318(f72(f918(x97031,a909)),x97035)))))
% 109.14/108.85 [9782]~P91(x97821)+P1(f318(f318(f225(x97821),f318(f69(x97821),f318(f318(f3(x97821),f318(f318(f73(x97821),x97822),x97823)),f318(f318(f73(x97821),x97824),x97825)))),f318(f318(f73(x97821),f318(f69(x97821),f318(f318(f3(x97821),x97822),x97824))),f318(f69(x97821),f318(f318(f3(x97821),x97823),x97825)))))
% 109.14/108.85 [9898]P1(f318(f318(f320(x98981),f479(x98982,x98983,x98984,x98981,x98985)),x98984))+P1(f318(f318(f225(f918(x98985,a909)),f318(f318(f33(x98981,f918(x98985,a909)),x98984),x98983)),x98982))
% 109.14/108.85 [10084]~P1(f318(f318(f225(f918(x100841,a909)),f318(x100844,f479(x100845,x100844,x100843,x100842,x100841))),x100845))+P1(f318(f318(f225(f918(x100841,a909)),f318(f318(f33(x100842,f918(x100841,a909)),x100843),x100844)),x100845))
% 109.14/108.85 [8677]E(f318(f318(f125(x86771),x86772),f318(f318(f150(x86771,x86773),f318(f318(f3(a911),x86774),f318(f180(f912(x86771)),x86772))),x86775)),f318(f318(f150(x86771,f318(f318(f125(x86771),x86772),x86773)),x86774),x86775))+P1(f318(f318(f226(a911),x86774),f318(f180(f912(x86771)),x86772)))
% 109.14/108.85 [8706]~P148(x87061)+E(f318(f318(f73(x87061),f318(f318(f74(x87061),x87062),x87063)),f318(f318(f73(x87061),f318(f318(f74(x87061),x87064),x87063)),x87065)),f318(f318(f73(x87061),f318(f318(f74(x87061),f318(f318(f73(x87061),x87062),x87064)),x87063)),x87065))
% 109.14/108.85 [9277]~P146(x92771)+E(f318(f156(x92771),f318(f318(f145(x92772,x92771),f318(f318(f10(x92771,x92771,x92772),f318(f74(x92771),x92773)),x92774)),x92775)),f318(f318(f74(x92771),x92773),f318(f156(x92771),f318(f318(f145(x92772,x92771),x92774),x92775))))
% 109.14/108.85 [9458]E(f318(f180(f912(x94581)),f318(f318(f166(x94581),f318(f318(f223(a911),f318(f180(f912(x94581)),x94582)),f318(f180(f912(x94583)),x94584))),x94582)),f318(f180(f912(x94583)),f318(f318(f166(x94583),f318(f318(f223(a911),f318(f180(f912(x94581)),x94582)),f318(f180(f912(x94583)),x94584))),x94584)))+P1(f318(x94585,f318(f318(f172(x94581,x94583),x94582),x94584)))
% 109.14/108.85 [9713]~P146(x97132)+E(f318(f318(f8(x97131,x97132),f318(f318(f9(x97131,x97132,x97132),f318(f318(f10(x97132,f918(x97132,x97132),x97131),f74(x97132)),x97133)),x97134)),x97135),f318(f318(f74(x97132),f318(f318(f8(x97131,x97132),x97133),x97135)),x97134))
% 109.14/108.85 [9714]~P73(x97142)+E(f318(f318(f8(x97141,x97142),f318(f318(f9(x97141,x97142,x97142),f318(f318(f10(x97142,f918(x97142,x97142),x97141),f282(x97142)),x97143)),x97144)),x97145),f318(f318(f282(x97142),f318(f318(f8(x97141,x97142),x97143),x97145)),x97144))
% 109.14/108.85 [9721]~P67(x97212)+E(f318(f318(f8(x97211,x97212),f318(f318(f20(x97211,x97212,x97212),f318(f318(f10(x97212,f918(x97212,x97212),x97211),f3(x97212)),x97213)),x97214)),x97215),f318(f318(f3(x97212),f318(f318(f8(x97211,x97212),x97213),x97215)),f318(f318(f8(x97211,x97212),x97214),x97215)))
% 109.14/108.85 [9722]~P76(x97222)+E(f318(f318(f8(x97221,x97222),f318(f318(f20(x97221,x97222,x97222),f318(f318(f10(x97222,f918(x97222,x97222),x97221),f73(x97222)),x97223)),x97224)),x97225),f318(f318(f73(x97222),f318(f318(f8(x97221,x97222),x97223),x97225)),f318(f318(f8(x97221,x97222),x97224),x97225)))
% 109.14/108.85 [9723]~P82(x97232)+E(f318(f318(f11(x97231,x97232),f318(f318(f20(x97231,x97232,x97232),f318(f318(f10(x97232,f918(x97232,x97232),x97231),f74(x97232)),x97233)),x97234)),x97235),f318(f318(f74(x97232),f318(f318(f11(x97231,x97232),x97233),x97235)),f318(f318(f11(x97231,x97232),x97234),x97235)))
% 109.14/108.85 [9760]~E(x97603,f179(f918(x97601,a909)))+E(f318(f318(f33(x97601,f918(x97602,a909)),x97603),f318(f318(f9(x97601,f918(x97602,a909),f918(x97602,a909)),f318(f318(f10(f918(x97602,a909),f918(f918(x97602,a909),f918(x97602,a909)),x97601),f101(f918(x97602,a909))),x97604)),x97605)),f179(f918(x97602,a909)))
% 109.14/108.85 [9761]~E(x97613,f179(f918(x97611,a909)))+E(f318(f318(f34(x97611,f918(x97612,a909)),x97613),f318(f318(f9(x97611,f918(x97612,a909),f918(x97612,a909)),f318(f318(f10(f918(x97612,a909),f918(f918(x97612,a909),f918(x97612,a909)),x97611),f92(f918(x97612,a909))),x97614)),x97615)),f233(f918(x97612,a909)))
% 109.14/108.85 [9762]~E(x97623,f179(f918(x97621,a909)))+E(f318(f318(f34(x97621,f918(x97622,a909)),x97623),f318(f318(f9(x97621,f918(x97622,a909),f918(x97622,a909)),f318(f318(f10(f918(x97622,a909),f918(f918(x97622,a909),f918(x97622,a909)),x97621),f3(f918(x97622,a909))),x97624)),x97625)),f233(f918(x97622,a909)))
% 109.14/108.85 [9787]E(x97871,f179(f918(x97872,a909)))+E(f318(f318(f33(x97872,f918(x97873,a909)),x97871),f318(f318(f9(x97872,f918(x97873,a909),f918(x97873,a909)),f318(f318(f10(f918(x97873,a909),f918(f918(x97873,a909),f918(x97873,a909)),x97872),f101(f918(x97873,a909))),x97874)),x97875)),f318(f318(f101(f918(x97873,a909)),f318(f318(f33(x97872,f918(x97873,a909)),x97871),x97874)),x97875))
% 109.14/108.85 [9788]E(x97881,f179(f918(x97882,a909)))+E(f318(f318(f34(x97882,f918(x97883,a909)),x97881),f318(f318(f9(x97882,f918(x97883,a909),f918(x97883,a909)),f318(f318(f10(f918(x97883,a909),f918(f918(x97883,a909),f918(x97883,a909)),x97882),f92(f918(x97883,a909))),x97884)),x97885)),f318(f318(f92(f918(x97883,a909)),f318(f318(f34(x97882,f918(x97883,a909)),x97881),x97884)),x97885))
% 109.14/108.85 [9789]E(x97891,f179(f918(x97892,a909)))+E(f318(f318(f34(x97892,f918(x97893,a909)),x97891),f318(f318(f9(x97892,f918(x97893,a909),f918(x97893,a909)),f318(f318(f10(f918(x97893,a909),f918(f918(x97893,a909),f918(x97893,a909)),x97892),f3(f918(x97893,a909))),x97894)),x97895)),f318(f318(f3(f918(x97893,a909)),f318(f318(f34(x97892,f918(x97893,a909)),x97891),x97894)),x97895))
% 109.14/108.85 [9790]E(x97901,f179(f918(x97902,a909)))+E(f318(f318(f33(x97902,f918(x97903,a909)),x97901),f318(f318(f9(x97902,f918(x97903,a909),f918(x97903,a909)),f318(f318(f10(f918(x97903,a909),f918(f918(x97903,a909),f918(x97903,a909)),x97902),f101(f918(x97903,a909))),x97904)),x97905)),f318(f318(f101(f918(x97903,a909)),f318(f318(f33(x97902,f918(x97903,a909)),x97901),x97904)),x97905))
% 109.14/108.85 [9791]E(x97911,f179(f918(x97912,a909)))+E(f318(f318(f34(x97912,f918(x97913,a909)),x97911),f318(f318(f9(x97912,f918(x97913,a909),f918(x97913,a909)),f318(f318(f10(f918(x97913,a909),f918(f918(x97913,a909),f918(x97913,a909)),x97912),f92(f918(x97913,a909))),x97914)),x97915)),f318(f318(f92(f918(x97913,a909)),f318(f318(f34(x97912,f918(x97913,a909)),x97911),x97914)),x97915))
% 109.14/108.85 [9792]E(x97921,f179(f918(x97922,a909)))+E(f318(f318(f34(x97922,f918(x97923,a909)),x97921),f318(f318(f9(x97922,f918(x97923,a909),f918(x97923,a909)),f318(f318(f10(f918(x97923,a909),f918(f918(x97923,a909),f918(x97923,a909)),x97922),f3(f918(x97923,a909))),x97924)),x97925)),f318(f318(f3(f918(x97923,a909)),f318(f318(f34(x97922,f918(x97923,a909)),x97921),x97924)),x97925))
% 109.14/108.85 [9333]~P1(f318(f318(f225(a911),x93331),x93334))+E(f318(f318(f3(a911),f318(f318(f73(a911),f318(f318(f74(a911),x93331),x93332)),x93333)),f318(f318(f73(a911),f318(f318(f74(a911),x93334),x93332)),x93335)),f318(f318(f3(a911),x93333),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x93334),x93331)),x93332)),x93335)))
% 109.14/108.85 [9962]~P146(x99621)+E(f318(f156(x99621),f318(f318(f145(x99622,x99621),f318(f318(f9(x99622,x99621,x99621),f318(f318(f10(x99621,f918(x99621,x99621),x99622),f74(x99621)),x99623)),x99624)),x99625)),f318(f318(f74(x99621),f318(f156(x99621),f318(f318(f145(x99622,x99621),x99623),x99625))),x99624))
% 109.14/108.85 [9972]~P67(x99721)+E(f318(f156(x99721),f318(f318(f145(x99722,x99721),f318(f318(f20(x99722,x99721,x99721),f318(f318(f10(x99721,f918(x99721,x99721),x99722),f3(x99721)),x99723)),x99724)),x99725)),f318(f318(f3(x99721),f318(f156(x99721),f318(f318(f145(x99722,x99721),x99723),x99725))),f318(f156(x99721),f318(f318(f145(x99722,x99721),x99724),x99725))))
% 109.14/108.85 [9973]~P76(x99731)+E(f318(f156(x99731),f318(f318(f145(x99732,x99731),f318(f318(f20(x99732,x99731,x99731),f318(f318(f10(x99731,f918(x99731,x99731),x99732),f73(x99731)),x99733)),x99734)),x99735)),f318(f318(f73(x99731),f318(f156(x99731),f318(f318(f145(x99732,x99731),x99733),x99735))),f318(f156(x99731),f318(f318(f145(x99732,x99731),x99734),x99735))))
% 109.14/108.85 [10105]P1(f318(x101051,f318(f318(f172(x101052,x101053),x101054),x101055)))+~P1(f318(x101051,f318(f318(f172(x101052,x101053),f318(f318(f166(x101052),f318(f318(f223(a911),f318(f180(f912(x101052)),x101054)),f318(f180(f912(x101053)),x101055))),x101054)),f318(f318(f166(x101053),f318(f318(f223(a911),f318(f180(f912(x101052)),x101054)),f318(f180(f912(x101053)),x101055))),x101055))))
% 109.14/108.85 [10377]~P1(f318(f318(f320(f917(x103772,x103771)),f318(f318(f243(x103772,x103771),x103774),x103775)),f318(f277(x103771,x103772),x103773)))+P1(f318(f318(f234(x103771,x103772,f318(f318(f9(x103771,f918(f917(x103771,x103772),a909),f918(x103772,a909)),f318(f318(f10(f918(x103772,f918(f918(f917(x103771,x103772),a909),a909)),f918(f918(f917(x103771,x103772),a909),f918(x103772,a909)),x103771),f9(x103772,f918(f917(x103771,x103772),a909),a909)),f318(f318(f10(f918(x103772,f917(x103771,x103772)),f918(x103772,f918(f918(f917(x103771,x103772),a909),a909)),x103771),f318(f10(f917(x103771,x103772),f918(f918(f917(x103771,x103772),a909),a909),x103772),f320(f917(x103771,x103772)))),f243(x103771,x103772)))),x103773)),x103774),x103775))
% 109.14/108.85 [10398]P1(f318(f318(f320(f917(x103981,x103982)),f318(f318(f243(x103981,x103982),x103983),x103984)),f318(f277(x103982,x103981),x103985)))+~P1(f318(f318(f234(x103982,x103981,f318(f318(f9(x103982,f918(f917(x103982,x103981),a909),f918(x103981,a909)),f318(f318(f10(f918(x103981,f918(f918(f917(x103982,x103981),a909),a909)),f918(f918(f917(x103982,x103981),a909),f918(x103981,a909)),x103982),f9(x103981,f918(f917(x103982,x103981),a909),a909)),f318(f318(f10(f918(x103981,f917(x103982,x103981)),f918(x103981,f918(f918(f917(x103982,x103981),a909),a909)),x103982),f318(f10(f917(x103982,x103981),f918(f918(f917(x103982,x103981),a909),a909),x103981),f320(f917(x103982,x103981)))),f243(x103982,x103981)))),x103985)),x103983),x103984))
% 109.14/108.85 [9583]~P1(f318(f318(f225(a911),x95834),x95831))+E(f318(f318(f3(a911),f318(f318(f73(a911),f318(f318(f74(a911),x95831),x95832)),x95833)),f318(f318(f73(a911),f318(f318(f74(a911),x95834),x95832)),x95835)),f318(f318(f3(a911),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x95831),x95834)),x95832)),x95833)),x95835))
% 109.14/108.85 [7408]E(x74081,x74082)+~E(f211(x74083,x74084,x74085,x74081),f211(x74083,x74084,x74086,x74082))
% 109.14/108.85 [7409]E(x74091,x74092)+~E(f211(x74093,x74094,x74091,x74095),f211(x74093,x74094,x74092,x74096))
% 109.14/108.85 [8510]~P19(x85105,x85101,x85102,x85106)+E(f318(f66(x85101,x85101,x85101,f318(x85102,x85103)),f318(x85102,x85104)),f318(f66(x85101,x85101,x85101,f318(x85102,x85104)),f318(x85102,x85103)))
% 109.14/108.85 [8748]~P60(x87484,x87485,x87482,x87481,x87486)+E(f318(x87481,f318(x87482,x87483)),x87483)
% 109.14/108.85 [8904]P25(x89041,x89042,x89043,x89044)+~P25(x89041,x89045,f318(f66(x89042,x89045,x89041,x89046),x89043),x89044)
% 109.14/108.85 [8983]~E(x89836,x89834)+E(f318(f68(x89831,x89832,x89833,x89834,x89835),x89836),x89835)
% 109.14/108.85 [8984]~E(x89846,x89844)+E(f318(f68(x89841,x89842,x89843,x89844,x89845),x89846),x89845)
% 109.14/108.85 [8989]E(x89891,x89892)+E(f318(f68(x89893,x89894,x89895,x89892,x89896),x89891),f318(x89895,x89891))
% 109.14/108.85 [8990]E(x89901,x89902)+E(f318(f68(x89903,x89904,x89905,x89902,x89906),x89901),f318(x89905,x89901))
% 109.14/108.85 [8991]E(x89911,x89912)+E(f318(f68(x89913,x89914,x89915,x89912,x89916),x89911),f318(x89915,x89911))
% 109.14/108.85 [9004]~P25(x90044,x90042,f318(f66(x90041,x90042,x90044,x90043),x90045),x90046)+P25(x90041,x90042,x90043,f318(f301(x90044,x90041,x90045),x90046))
% 109.14/108.85 [9724]P1(f318(f55(x97241),x97242))+~P1(f318(f60(x97241,x97243,x97244,x97245,x97242),x97246))
% 109.14/108.85 [9733]~P1(f318(f318(f320(x97334),x97333),f288(x97334,x97331,x97335,x97332,x97336)))+P1(f318(f318(x97331,x97332),x97333))
% 109.14/108.85 [9734]~P1(f318(f318(f320(x97344),x97343),f291(x97344,x97345,x97341,x97342,x97346)))+P1(f318(f318(x97341,x97342),x97343))
% 109.14/108.85 [9735]~P1(f318(f318(f320(x97354),x97352),f288(x97354,x97355,x97351,x97356,x97353)))+P1(f318(f318(x97351,x97352),x97353))
% 109.14/108.85 [9736]~P1(f318(f318(f320(x97364),x97362),f291(x97364,x97361,x97365,x97366,x97363)))+P1(f318(f318(x97361,x97362),x97363))
% 109.14/108.85 [10238]P12(x102381,x102382,x102383,x102384,x102385,x102386)+~E(f318(f318(x102386,f846(x102383,x102386,x102385,x102382,x102384,x102381)),f848(x102383,x102386,x102385,x102382,x102384,x102381)),f318(f318(x102386,f847(x102383,x102386,x102385,x102382,x102384,x102381)),f849(x102383,x102386,x102385,x102382,x102384,x102381)))
% 109.14/108.85 [5899]E(x58991,x58992)+~E(f318(f318(f243(x58993,x58994),x58995),x58991),f318(f318(f243(x58993,x58994),x58996),x58992))
% 109.14/108.85 [5900]E(x59001,x59002)+~E(f318(f318(f243(x59003,x59004),x59005),x59001),f318(f318(f243(x59003,x59004),x59006),x59002))
% 109.14/108.85 [5901]E(x59011,x59012)+~E(f318(f318(f243(x59013,x59014),x59011),x59015),f318(f318(f243(x59013,x59014),x59012),x59016))
% 109.14/108.85 [5902]E(x59021,x59022)+~E(f318(f318(f243(x59023,x59024),x59021),x59025),f318(f318(f243(x59023,x59024),x59022),x59026))
% 109.14/108.85 [6040]~P16(x60405,x60406,x60401)+E(f318(f318(x60401,x60402),f318(f318(x60401,x60403),x60404)),f318(f318(x60401,x60403),f318(f318(x60401,x60402),x60404)))
% 109.14/108.85 [7471]~P34(x74714,x74711,f318(f318(f142(x74714),x74712),x74715),f318(f318(f142(x74714),x74713),x74716))+P1(f318(f318(x74711,x74712),x74713))
% 109.14/108.85 [7817]P34(x78171,x78172,x78173,x78174)+~P34(x78171,x78172,f318(f318(f142(x78171),x78175),x78173),f318(f318(f142(x78171),x78176),x78174))
% 109.14/108.85 [8846]~P60(x88465,x88461,x88462,x88466,x88464)+P1(f318(f318(f320(x88461),f318(x88462,x88463)),x88464))
% 109.14/108.85 [9054]~E(x90543,f318(f318(f142(x90541),x90545),x90546))+P1(f318(f318(f320(f917(f912(x90541),f912(x90541))),f318(f318(f243(f912(x90541),f912(x90541)),x90542),f318(f318(f125(x90541),x90542),x90543))),f138(x90541,x90544)))
% 109.14/108.85 [9283]~P36(x92831,x92832,x92833,x92835,x92836)+P36(x92831,x92832,x92833,f318(f318(f166(x92831),x92834),x92835),f318(f318(f166(x92832),x92834),x92836))
% 109.14/108.85 [9284]~P36(x92841,x92842,x92843,x92845,x92846)+P36(x92841,x92842,x92843,f318(f318(f129(x92841),x92844),x92845),f318(f318(f129(x92842),x92844),x92846))
% 109.14/108.85 [9556]E(f318(f301(x95561,x95562,f68(x95561,x95562,x95563,x95564,x95565)),x95566),f318(f301(x95561,x95562,x95563),x95566))+P1(f318(f318(f320(x95561),x95564),x95566))
% 109.14/108.85 [9559]E(f318(f318(f145(x95591,x95592),f68(x95591,x95592,x95593,x95594,x95595)),x95596),f318(f318(f145(x95591,x95592),x95593),x95596))+P1(f318(f318(f320(x95591),x95594),f318(f163(x95591),x95596)))
% 109.14/108.85 [9802]~P23(x98024,x98022,x98025,x98023,x98026,x98021)+E(f318(x98021,f179(f918(x98022,a909))),x98023)
% 109.14/108.85 [10053]~E(f318(x100534,f318(f242(x100531,x100533),x100535)),f318(x100536,f318(f242(x100531,x100533),x100535)))+E(f318(f249(x100531,x100532,x100533,x100533,x100534,f25(x100533)),x100535),f318(f249(x100531,x100532,x100533,x100533,x100536,f25(x100533)),x100535))
% 109.14/108.85 [10054]~E(f318(x100544,f318(f247(x100541,x100542),x100545)),f318(x100546,f318(f247(x100541,x100542),x100545)))+E(f318(f249(x100541,x100541,x100542,x100543,f25(x100541),x100544),x100545),f318(f249(x100541,x100541,x100542,x100543,f25(x100541),x100546),x100545))
% 109.14/108.85 [10102]~E(f318(f249(x101022,x101026,x101023,x101023,x101021,f25(x101023)),x101024),f318(f249(x101022,x101026,x101023,x101023,x101025,f25(x101023)),x101024))+E(f318(x101021,f318(f242(x101022,x101023),x101024)),f318(x101025,f318(f242(x101022,x101023),x101024)))
% 109.14/108.85 [10103]~E(f318(f249(x101032,x101032,x101033,x101036,f25(x101032),x101031),x101034),f318(f249(x101032,x101032,x101033,x101036,f25(x101032),x101035),x101034))+E(f318(x101031,f318(f247(x101032,x101033),x101034)),f318(x101035,f318(f247(x101032,x101033),x101034)))
% 109.14/108.85 [8947]P1(f318(f318(f320(x89471),x89472),x89473))+~P1(f318(f318(f320(f917(x89471,x89474)),f318(f318(f243(x89471,x89474),x89472),x89475)),f318(f318(f245(x89471,x89474),x89473),x89476)))
% 109.14/108.85 [8948]P1(f318(f318(f320(x89481),x89482),x89483))+~P1(f318(f318(f320(f917(x89481,x89484)),f318(f318(f243(x89481,x89484),x89482),x89485)),f318(f318(f245(x89481,x89484),x89483),x89486)))
% 109.14/108.85 [8949]P1(f318(f318(f320(x89491),x89492),x89493))+~P1(f318(f318(f320(f917(x89491,x89494)),f318(f318(f243(x89491,x89494),x89492),x89495)),f318(f318(f245(x89491,x89494),x89493),x89496)))
% 109.14/108.85 [8963]P1(f318(f318(f320(x89631),x89632),f318(x89633,x89634)))+~P1(f318(f318(f320(f917(x89635,x89631)),f318(f318(f243(x89635,x89631),x89634),x89632)),f318(f318(f245(x89635,x89631),x89636),x89633)))
% 109.14/108.85 [8964]P1(f318(f318(f320(x89641),x89642),f318(x89643,x89644)))+~P1(f318(f318(f320(f917(x89645,x89641)),f318(f318(f243(x89645,x89641),x89644),x89642)),f318(f318(f245(x89645,x89641),x89646),x89643)))
% 109.14/108.85 [8965]P1(f318(f318(f320(x89651),x89652),f318(x89653,x89654)))+~P1(f318(f318(f320(f917(x89655,x89651)),f318(f318(f243(x89655,x89651),x89654),x89652)),f318(f318(f245(x89655,x89651),x89656),x89653)))
% 109.14/108.85 [9404]P1(f318(f318(f320(f917(x94041,x94041)),f318(f318(f243(x94041,x94041),f318(x94042,x94043)),f318(x94042,x94044))),x94045))+~P1(f318(f318(f320(f917(x94046,x94046)),f318(f318(f243(x94046,x94046),x94043),x94044)),f318(f318(f279(x94041,x94046),x94045),x94042)))
% 109.14/108.85 [9424]~P1(f318(f318(f320(f917(x94244,x94244)),f318(f318(f243(x94244,x94244),f318(x94246,x94242)),f318(x94246,x94243))),x94245))+P1(f318(f318(f320(f917(x94241,x94241)),f318(f318(f243(x94241,x94241),x94242),x94243)),f318(f318(f279(x94244,x94241),x94245),x94246)))
% 109.14/108.85 [10104]E(f318(f318(f243(x101041,x101042),f644(x101043,x101044,x101045,x101046,x101042,x101041)),f645(x101043,x101044,x101045,x101046,x101042,x101041)),x101046)+~P1(f318(f318(f320(f917(x101041,x101042)),x101046),f318(f318(f280(x101041,x101045,x101042),x101044),x101043)))
% 109.14/108.85 [10311]~P1(f318(f318(f320(f917(x103111,x103116)),x103115),f318(f318(f280(x103111,x103112,x103116),x103114),x103113)))+P1(f318(f318(f320(f917(x103111,x103112)),f318(f318(f243(x103111,x103112),f644(x103113,x103114,x103112,x103115,x103116,x103111)),f646(x103113,x103114,x103112,x103115,x103116,x103111))),x103114))
% 109.14/108.85 [10312]~P1(f318(f318(f320(f917(x103126,x103122)),x103125),f318(f318(f280(x103126,x103121,x103122),x103124),x103123)))+P1(f318(f318(f320(f917(x103121,x103122)),f318(f318(f243(x103121,x103122),f646(x103123,x103124,x103121,x103125,x103122,x103126)),f645(x103123,x103124,x103121,x103125,x103122,x103126))),x103123))
% 109.14/108.85 [10313]P12(x103131,x103132,x103133,x103134,x103135,x103136)+P1(f318(f318(f320(f917(x103132,x103132)),f318(f318(f243(x103132,x103132),f849(x103133,x103136,x103135,x103132,x103134,x103131)),f848(x103133,x103136,x103135,x103132,x103134,x103131))),x103135))
% 109.14/108.85 [10314]P12(x103141,x103142,x103143,x103144,x103145,x103146)+P1(f318(f318(f320(f917(x103141,x103141)),f318(f318(f243(x103141,x103141),f847(x103143,x103146,x103145,x103142,x103144,x103141)),f846(x103143,x103146,x103145,x103142,x103144,x103141))),x103144))
% 109.14/108.85 [7886]~P5(x78862)+E(f318(f318(f33(x78861,x78862),x78863),f318(f318(f9(x78861,x78864,x78862),x78865),x78866)),f318(f318(f318(f33(x78861,f918(x78864,x78862)),x78863),x78865),x78866))
% 109.14/108.85 [7887]~P5(x78872)+E(f318(f318(f34(x78871,x78872),x78873),f318(f318(f9(x78871,x78874,x78872),x78875),x78876)),f318(f318(f318(f34(x78871,f918(x78874,x78872)),x78873),x78875),x78876))
% 109.14/108.85 [8655]E(f318(f318(f33(x86551,f918(x86552,a909)),x86553),f318(f318(f10(f918(x86552,a909),f918(x86552,a909),x86551),f318(f300(x86552),x86554)),x86555)),f318(f318(f300(x86552),x86554),f318(f318(f33(x86551,f918(x86552,a909)),x86553),x86555)))+~P1(f318(f318(f320(x86551),x86556),x86553))
% 109.14/108.85 [8656]E(f318(f318(f34(x86561,f918(x86562,a909)),x86563),f318(f318(f10(f918(x86562,a909),f918(x86562,a909),x86561),f318(f300(x86562),x86564)),x86565)),f318(f318(f300(x86562),x86564),f318(f318(f34(x86561,f918(x86562,a909)),x86563),x86565)))+~P1(f318(f318(f320(x86561),x86566),x86563))
% 109.14/108.85 [9108]~P5(x91082)+E(f318(f318(f33(x91081,x91082),x91083),f318(f318(f10(f918(x91084,x91082),x91082,x91081),f318(f33(x91084,x91082),x91085)),f318(f9(x91084,x91081,x91082),x91086))),f318(f318(f33(x91084,x91082),x91085),f318(f318(f10(f918(x91081,x91082),x91082,x91084),f318(f33(x91081,x91082),x91083)),x91086)))
% 109.14/108.85 [9109]~P5(x91092)+E(f318(f318(f34(x91091,x91092),x91093),f318(f318(f10(f918(x91094,x91092),x91092,x91091),f318(f34(x91094,x91092),x91095)),f318(f9(x91094,x91091,x91092),x91096))),f318(f318(f34(x91094,x91092),x91095),f318(f318(f10(f918(x91091,x91092),x91092,x91094),f318(f34(x91091,x91092),x91093)),x91096)))
% 109.14/108.85 [9309]P1(f318(f318(f320(x93091),x93092),f318(f163(x93091),x93093)))+~P1(f318(f318(f320(f917(x93094,x93091)),f318(f318(f243(x93094,x93091),x93095),x93092)),f318(f163(f917(x93094,x93091)),f318(f318(f172(x93094,x93091),x93096),x93093))))
% 109.14/108.85 [9310]P1(f318(f318(f320(x93101),x93102),f318(f163(x93101),x93103)))+~P1(f318(f318(f320(f917(x93101,x93104)),f318(f318(f243(x93101,x93104),x93102),x93105)),f318(f163(f917(x93101,x93104)),f318(f318(f172(x93101,x93104),x93103),x93106))))
% 109.14/108.85 [9311]P1(f318(f318(f320(x93111),x93112),f318(f163(x93111),x93113)))+~P1(f318(f318(f320(f917(x93114,x93111)),f318(f318(f243(x93114,x93111),x93115),x93112)),f318(f163(f917(x93114,x93111)),f318(f318(f172(x93114,x93111),x93116),x93113))))
% 109.14/108.85 [9312]P1(f318(f318(f320(x93121),x93122),f318(f163(x93121),x93123)))+~P1(f318(f318(f320(f917(x93121,x93124)),f318(f318(f243(x93121,x93124),x93122),x93125)),f318(f163(f917(x93121,x93124)),f318(f318(f172(x93121,x93124),x93123),x93126))))
% 109.14/108.85 [9420]P1(f318(f318(f225(f918(x94201,a909)),f318(f276(x94202,x94201,x94203),x94204)),x94205))+~P1(f318(f318(f225(f918(f917(x94202,x94201),a909)),x94203),f318(f318(f245(x94202,x94201),x94206),f318(f18(f918(x94201,a909),x94202),x94205))))
% 109.14/108.85 [9425]~P26(x94254,x94252,x94255,f233(f918(x94254,a909)),f233(f918(x94252,a909)))+E(f318(f318(f34(x94251,f918(x94252,a909)),x94253),f318(f318(f10(f918(x94254,a909),f918(x94252,a909),x94251),f301(x94254,x94252,x94255)),x94256)),f318(f301(x94254,x94252,x94255),f318(f318(f34(x94251,f918(x94254,a909)),x94253),x94256)))
% 109.14/108.85 [9615]P1(f318(f318(f320(f917(f912(x96151),f912(x96151))),f318(f318(f243(f912(x96151),f912(x96151)),f318(f318(f142(x96151),x96152),x96153)),f318(f318(f142(x96151),x96154),x96155))),f138(x96151,x96156)))+~P1(f318(f318(f320(f917(x96151,x96151)),f318(f318(f243(x96151,x96151),x96152),x96154)),x96156))
% 109.14/108.85 [10101]E(f318(f318(f243(x101011,x101012),f586(x101013,x101014,x101015,x101012,x101011,x101016)),f589(x101013,x101014,x101015,x101012,x101011,x101016)),x101016)+P1(f318(f318(f320(x101015),x101014),f318(f318(f248(x101011,x101012,f918(x101015,a909)),x101013),x101016)))
% 109.14/108.85 [10106]E(f318(f318(f243(x101061,x101062),f587(x101063,x101064,x101062,x101061,x101065,x101066)),f588(x101063,x101064,x101062,x101061,x101065,x101066)),x101063)+~P1(f318(f318(f320(x101066),x101065),f318(f318(f248(x101061,x101062,f918(x101066,a909)),x101064),x101063)))
% 109.14/108.85 [10250]P1(f318(f318(f320(x102501),x102502),f318(f318(x102503,f587(x102504,x102503,x102505,x102506,x102502,x102501)),f588(x102504,x102503,x102505,x102506,x102502,x102501))))+~P1(f318(f318(f320(x102501),x102502),f318(f318(f248(x102506,x102505,f918(x102501,a909)),x102503),x102504)))
% 109.14/108.85 [10282]~P1(f318(f318(f320(x102821),x102822),f318(f318(x102825,f586(x102825,x102822,x102821,x102824,x102823,x102826)),f589(x102825,x102822,x102821,x102824,x102823,x102826))))+P1(f318(f318(f320(x102821),x102822),f318(f318(f248(x102823,x102824,f918(x102821,a909)),x102825),x102826)))
% 109.14/108.85 [8552]E(x85521,x85522)+E(f318(f318(f150(x85523,f318(f318(f150(x85523,x85524),x85521),x85525)),x85522),x85526),f318(f318(f150(x85523,f318(f318(f150(x85523,x85524),x85522),x85526)),x85521),x85525))
% 109.14/108.85 [9687]~P1(f318(f318(f320(x96873),x96876),x96875))+E(f318(f318(f300(x96871),x96872),f318(f301(x96873,x96871,x96874),f318(f318(f3(f918(x96873,a909)),x96875),f318(f318(f300(x96873),x96876),f179(f918(x96873,a909)))))),f318(f301(x96873,x96871,f68(x96873,x96871,x96874,x96876,x96872)),x96875))
% 109.14/108.85 [9186]~P1(f318(f318(x91864,x91865),x91866))+P1(f318(f318(f318(f318(f101(f918(x91861,f918(x91862,a909))),x91863),x91864),x91865),x91866))
% 109.14/108.85 [9187]~P1(f318(f318(x91874,x91875),x91876))+P1(f318(f318(f318(f318(f101(f918(x91871,f918(x91872,a909))),x91873),x91874),x91875),x91876))
% 109.14/108.85 [9188]~P1(f318(f318(x91883,x91885),x91886))+P1(f318(f318(f318(f318(f101(f918(x91881,f918(x91882,a909))),x91883),x91884),x91885),x91886))
% 109.14/108.85 [9189]~P1(f318(f318(x91893,x91895),x91896))+P1(f318(f318(f318(f318(f101(f918(x91891,f918(x91892,a909))),x91893),x91894),x91895),x91896))
% 109.14/108.85 [9477]P1(f318(f318(x94771,x94772),x94773))+~P1(f318(f318(f318(f318(f92(f918(x94774,f918(x94775,a909))),x94776),x94771),x94772),x94773))
% 109.14/108.85 [9478]P1(f318(f318(x94781,x94782),x94783))+~P1(f318(f318(f318(f318(f92(f918(x94784,f918(x94785,a909))),x94781),x94786),x94782),x94783))
% 109.14/108.85 [9479]P1(f318(f318(x94791,x94792),x94793))+~P1(f318(f318(f318(f318(f92(f918(x94794,f918(x94795,a909))),x94796),x94791),x94792),x94793))
% 109.14/108.85 [9480]P1(f318(f318(x94801,x94802),x94803))+~P1(f318(f318(f318(f318(f92(f918(x94804,f918(x94805,a909))),x94801),x94806),x94802),x94803))
% 109.14/108.85 [9950]~P76(x99502)+E(f318(f318(f8(x99501,x99502),f318(f318(f9(x99501,f918(x99503,a909),x99502),f318(f318(f10(f918(x99503,x99502),f918(f918(x99503,a909),x99502),x99501),f8(x99503,x99502)),x99504)),x99505)),x99506),f318(f318(f8(f917(x99501,x99503),x99502),f318(f248(x99501,x99503,x99502),x99504)),f318(f318(f245(x99501,x99503),x99506),f318(f18(f918(x99503,a909),x99501),x99505))))
% 109.14/108.85 [9951]~P82(x99512)+E(f318(f318(f11(x99511,x99512),f318(f318(f9(x99511,f918(x99513,a909),x99512),f318(f318(f10(f918(x99513,x99512),f918(f918(x99513,a909),x99512),x99511),f11(x99513,x99512)),x99514)),x99515)),x99516),f318(f318(f11(f917(x99511,x99513),x99512),f318(f248(x99511,x99513,x99512),x99514)),f318(f318(f245(x99511,x99513),x99516),f318(f18(f918(x99513,a909),x99511),x99515))))
% 109.14/108.85 [10077]~P76(x100772)+E(f318(f318(f8(x100771,x100772),f318(f318(f9(x100771,f918(x100773,a909),x100772),f318(f318(f10(f918(x100773,x100772),f918(f918(x100773,a909),x100772),x100771),f8(x100773,x100772)),f318(f9(x100773,x100771,x100772),x100774))),x100775)),x100776),f318(f318(f8(x100773,x100772),f318(f318(f9(x100773,f918(x100771,a909),x100772),f318(f318(f10(f918(x100771,x100772),f918(f918(x100771,a909),x100772),x100773),f8(x100771,x100772)),x100774)),x100776)),x100775))
% 109.14/108.85 [10415]~P1(f318(f318(f320(f917(x104151,x104152)),f318(f318(f243(x104151,x104152),x104155),x104156)),f318(f318(f101(f918(f917(x104151,x104152),a909)),x104153),x104154)))+P1(f318(f318(f318(f318(f101(f918(x104151,f918(x104152,a909))),f318(f318(f9(x104151,f918(f917(x104151,x104152),a909),f918(x104152,a909)),f318(f318(f10(f918(x104152,f918(f918(f917(x104151,x104152),a909),a909)),f918(f918(f917(x104151,x104152),a909),f918(x104152,a909)),x104151),f9(x104152,f918(f917(x104151,x104152),a909),a909)),f318(f318(f10(f918(x104152,f917(x104151,x104152)),f918(x104152,f918(f918(f917(x104151,x104152),a909),a909)),x104151),f318(f10(f917(x104151,x104152),f918(f918(f917(x104151,x104152),a909),a909),x104152),f320(f917(x104151,x104152)))),f243(x104151,x104152)))),x104153)),f318(f318(f9(x104151,f918(f917(x104151,x104152),a909),f918(x104152,a909)),f318(f318(f10(f918(x104152,f918(f918(f917(x104151,x104152),a909),a909)),f918(f918(f917(x104151,x104152),a909),f918(x104152,a909)),x104151),f9(x104152,f918(f917(x104151,x104152),a909),a909)),f318(f318(f10(f918(x104152,f917(x104151,x104152)),f918(x104152,f918(f918(f917(x104151,x104152),a909),a909)),x104151),f318(f10(f917(x104151,x104152),f918(f918(f917(x104151,x104152),a909),a909),x104152),f320(f917(x104151,x104152)))),f243(x104151,x104152)))),x104154)),x104155),x104156))
% 109.14/108.85 [10416]~P1(f318(f318(f320(f917(x104161,x104162)),f318(f318(f243(x104161,x104162),x104165),x104166)),f318(f318(f92(f918(f917(x104161,x104162),a909)),x104163),x104164)))+P1(f318(f318(f318(f318(f92(f918(x104161,f918(x104162,a909))),f318(f318(f9(x104161,f918(f917(x104161,x104162),a909),f918(x104162,a909)),f318(f318(f10(f918(x104162,f918(f918(f917(x104161,x104162),a909),a909)),f918(f918(f917(x104161,x104162),a909),f918(x104162,a909)),x104161),f9(x104162,f918(f917(x104161,x104162),a909),a909)),f318(f318(f10(f918(x104162,f917(x104161,x104162)),f918(x104162,f918(f918(f917(x104161,x104162),a909),a909)),x104161),f318(f10(f917(x104161,x104162),f918(f918(f917(x104161,x104162),a909),a909),x104162),f320(f917(x104161,x104162)))),f243(x104161,x104162)))),x104163)),f318(f318(f9(x104161,f918(f917(x104161,x104162),a909),f918(x104162,a909)),f318(f318(f10(f918(x104162,f918(f918(f917(x104161,x104162),a909),a909)),f918(f918(f917(x104161,x104162),a909),f918(x104162,a909)),x104161),f9(x104162,f918(f917(x104161,x104162),a909),a909)),f318(f318(f10(f918(x104162,f917(x104161,x104162)),f918(x104162,f918(f918(f917(x104161,x104162),a909),a909)),x104161),f318(f10(f917(x104161,x104162),f918(f918(f917(x104161,x104162),a909),a909),x104162),f320(f917(x104161,x104162)))),f243(x104161,x104162)))),x104164)),x104165),x104166))
% 109.14/108.85 [10430]P1(f318(f318(f320(f917(x104301,x104302)),f318(f318(f243(x104301,x104302),x104303),x104304)),f318(f318(f101(f918(f917(x104301,x104302),a909)),x104305),x104306)))+~P1(f318(f318(f318(f318(f101(f918(x104301,f918(x104302,a909))),f318(f318(f9(x104301,f918(f917(x104301,x104302),a909),f918(x104302,a909)),f318(f318(f10(f918(x104302,f918(f918(f917(x104301,x104302),a909),a909)),f918(f918(f917(x104301,x104302),a909),f918(x104302,a909)),x104301),f9(x104302,f918(f917(x104301,x104302),a909),a909)),f318(f318(f10(f918(x104302,f917(x104301,x104302)),f918(x104302,f918(f918(f917(x104301,x104302),a909),a909)),x104301),f318(f10(f917(x104301,x104302),f918(f918(f917(x104301,x104302),a909),a909),x104302),f320(f917(x104301,x104302)))),f243(x104301,x104302)))),x104305)),f318(f318(f9(x104301,f918(f917(x104301,x104302),a909),f918(x104302,a909)),f318(f318(f10(f918(x104302,f918(f918(f917(x104301,x104302),a909),a909)),f918(f918(f917(x104301,x104302),a909),f918(x104302,a909)),x104301),f9(x104302,f918(f917(x104301,x104302),a909),a909)),f318(f318(f10(f918(x104302,f917(x104301,x104302)),f918(x104302,f918(f918(f917(x104301,x104302),a909),a909)),x104301),f318(f10(f917(x104301,x104302),f918(f918(f917(x104301,x104302),a909),a909),x104302),f320(f917(x104301,x104302)))),f243(x104301,x104302)))),x104306)),x104303),x104304))
% 109.14/108.85 [10431]P1(f318(f318(f320(f917(x104311,x104312)),f318(f318(f243(x104311,x104312),x104313),x104314)),f318(f318(f92(f918(f917(x104311,x104312),a909)),x104315),x104316)))+~P1(f318(f318(f318(f318(f92(f918(x104311,f918(x104312,a909))),f318(f318(f9(x104311,f918(f917(x104311,x104312),a909),f918(x104312,a909)),f318(f318(f10(f918(x104312,f918(f918(f917(x104311,x104312),a909),a909)),f918(f918(f917(x104311,x104312),a909),f918(x104312,a909)),x104311),f9(x104312,f918(f917(x104311,x104312),a909),a909)),f318(f318(f10(f918(x104312,f917(x104311,x104312)),f918(x104312,f918(f918(f917(x104311,x104312),a909),a909)),x104311),f318(f10(f917(x104311,x104312),f918(f918(f917(x104311,x104312),a909),a909),x104312),f320(f917(x104311,x104312)))),f243(x104311,x104312)))),x104315)),f318(f318(f9(x104311,f918(f917(x104311,x104312),a909),f918(x104312,a909)),f318(f318(f10(f918(x104312,f918(f918(f917(x104311,x104312),a909),a909)),f918(f918(f917(x104311,x104312),a909),f918(x104312,a909)),x104311),f9(x104312,f918(f917(x104311,x104312),a909),a909)),f318(f318(f10(f918(x104312,f917(x104311,x104312)),f918(x104312,f918(f918(f917(x104311,x104312),a909),a909)),x104311),f318(f10(f917(x104311,x104312),f918(f918(f917(x104311,x104312),a909),a909),x104312),f320(f917(x104311,x104312)))),f243(x104311,x104312)))),x104316)),x104313),x104314))
% 109.14/108.85 [10404]~P1(f318(f318(f320(f917(x104042,x104043)),f318(f318(f243(x104042,x104043),x104045),x104046)),f318(f318(f33(x104041,f918(f917(x104042,x104043),a909)),f233(f918(x104041,a909))),x104044)))+P1(f318(f318(f318(f318(f33(x104041,f918(x104042,f918(x104043,a909))),f233(f918(x104041,a909))),f318(f318(f10(f918(f917(x104042,x104043),a909),f918(x104042,f918(x104043,a909)),x104041),f318(f9(x104042,f918(f917(x104042,x104043),a909),f918(x104043,a909)),f318(f318(f10(f918(x104043,f918(f918(f917(x104042,x104043),a909),a909)),f918(f918(f917(x104042,x104043),a909),f918(x104043,a909)),x104042),f9(x104043,f918(f917(x104042,x104043),a909),a909)),f318(f318(f10(f918(x104043,f917(x104042,x104043)),f918(x104043,f918(f918(f917(x104042,x104043),a909),a909)),x104042),f318(f10(f917(x104042,x104043),f918(f918(f917(x104042,x104043),a909),a909),x104043),f320(f917(x104042,x104043)))),f243(x104042,x104043))))),x104044)),x104045),x104046))
% 109.14/108.85 [10405]~P1(f318(f318(f320(f917(x104052,x104053)),f318(f318(f243(x104052,x104053),x104055),x104056)),f318(f318(f34(x104051,f918(f917(x104052,x104053),a909)),f233(f918(x104051,a909))),x104054)))+P1(f318(f318(f318(f318(f34(x104051,f918(x104052,f918(x104053,a909))),f233(f918(x104051,a909))),f318(f318(f10(f918(f917(x104052,x104053),a909),f918(x104052,f918(x104053,a909)),x104051),f318(f9(x104052,f918(f917(x104052,x104053),a909),f918(x104053,a909)),f318(f318(f10(f918(x104053,f918(f918(f917(x104052,x104053),a909),a909)),f918(f918(f917(x104052,x104053),a909),f918(x104053,a909)),x104052),f9(x104053,f918(f917(x104052,x104053),a909),a909)),f318(f318(f10(f918(x104053,f917(x104052,x104053)),f918(x104053,f918(f918(f917(x104052,x104053),a909),a909)),x104052),f318(f10(f917(x104052,x104053),f918(f918(f917(x104052,x104053),a909),a909),x104053),f320(f917(x104052,x104053)))),f243(x104052,x104053))))),x104054)),x104055),x104056))
% 109.14/108.85 [10420]P1(f318(f318(f320(f917(x104201,x104202)),f318(f318(f243(x104201,x104202),x104203),x104204)),f318(f318(f33(x104205,f918(f917(x104201,x104202),a909)),f233(f918(x104205,a909))),x104206)))+~P1(f318(f318(f318(f318(f33(x104205,f918(x104201,f918(x104202,a909))),f233(f918(x104205,a909))),f318(f318(f10(f918(f917(x104201,x104202),a909),f918(x104201,f918(x104202,a909)),x104205),f318(f9(x104201,f918(f917(x104201,x104202),a909),f918(x104202,a909)),f318(f318(f10(f918(x104202,f918(f918(f917(x104201,x104202),a909),a909)),f918(f918(f917(x104201,x104202),a909),f918(x104202,a909)),x104201),f9(x104202,f918(f917(x104201,x104202),a909),a909)),f318(f318(f10(f918(x104202,f917(x104201,x104202)),f918(x104202,f918(f918(f917(x104201,x104202),a909),a909)),x104201),f318(f10(f917(x104201,x104202),f918(f918(f917(x104201,x104202),a909),a909),x104202),f320(f917(x104201,x104202)))),f243(x104201,x104202))))),x104206)),x104203),x104204))
% 109.14/108.85 [10421]P1(f318(f318(f320(f917(x104211,x104212)),f318(f318(f243(x104211,x104212),x104213),x104214)),f318(f318(f34(x104215,f918(f917(x104211,x104212),a909)),f233(f918(x104215,a909))),x104216)))+~P1(f318(f318(f318(f318(f34(x104215,f918(x104211,f918(x104212,a909))),f233(f918(x104215,a909))),f318(f318(f10(f918(f917(x104211,x104212),a909),f918(x104211,f918(x104212,a909)),x104215),f318(f9(x104211,f918(f917(x104211,x104212),a909),f918(x104212,a909)),f318(f318(f10(f918(x104212,f918(f918(f917(x104211,x104212),a909),a909)),f918(f918(f917(x104211,x104212),a909),f918(x104212,a909)),x104211),f9(x104212,f918(f917(x104211,x104212),a909),a909)),f318(f318(f10(f918(x104212,f917(x104211,x104212)),f918(x104212,f918(f918(f917(x104211,x104212),a909),a909)),x104211),f318(f10(f917(x104211,x104212),f918(f918(f917(x104211,x104212),a909),a909),x104212),f320(f917(x104211,x104212)))),f243(x104211,x104212))))),x104216)),x104213),x104214))
% 109.14/108.85 [7567]E(f318(x75671,f318(x75672,x75673)),f318(x75674,x75673))+~E(f318(f66(x75675,x75676,x75677,x75671),x75672),x75674)
% 109.14/108.85 [9704]E(x97041,x97042)+E(f68(x97043,x97044,f68(x97043,x97044,x97045,x97041,x97046),x97042,x97047),f68(x97043,x97044,f68(x97043,x97044,x97045,x97042,x97047),x97041,x97046))
% 109.14/108.85 [9801]~P22(x98013,x98014,x98011,x98015,x98016,x98017)+E(f318(f318(x98011,x98012),x98012),x98012)
% 109.14/108.85 [6144]~E(f318(f318(f145(x61441,x61445),x61446),x61442),f318(f318(f145(x61443,x61445),x61447),x61444))+E(f318(f180(f912(x61441)),x61442),f318(f180(f912(x61443)),x61444))
% 109.14/108.85 [8588]E(f318(x85881,f318(x85882,x85883)),f318(x85884,x85883))+~E(f318(f66(x85885,x85886,x85887,x85881),x85882),f318(f66(x85886,x85886,x85887,f25(x85886)),x85884))
% 109.14/108.85 [8938]~P36(x89384,x89385,x89381,f318(f318(f142(x89384),x89382),x89386),f318(f318(f142(x89385),x89383),x89387))+P1(f318(f318(x89381,x89382),x89383))
% 109.14/108.85 [9320]P36(x93201,x93202,x93203,x93204,x93205)+~P36(x93201,x93202,x93203,f318(f318(f142(x93201),x93206),x93204),f318(f318(f142(x93202),x93207),x93205))
% 109.14/108.85 [9986]P1(f318(f318(x99861,x99862),f565(x99863,x99862,x99864,x99861)))+~P1(f318(f318(f244(x99865,x99866,x99867,x99861,x99864),x99862),x99863))
% 109.14/108.85 [10008]P1(f318(f318(x100081,f565(x100082,x100083,x100081,x100084)),x100082))+~P1(f318(f318(f244(x100085,x100086,x100087,x100084,x100081),x100083),x100082))
% 109.14/108.85 [9062]~P20(x90626,x90621,x90623,x90627)+E(f318(f66(x90621,x90621,x90622,f318(x90623,x90624)),f318(f66(x90621,x90621,x90622,f318(x90623,x90624)),x90625)),f318(f66(x90621,x90621,x90622,f318(x90623,x90624)),x90625))
% 109.14/108.85 [9428]~P36(x94283,x94282,x94284,f318(f318(f145(x94281,x94283),x94285),x94286),x94287)+P36(x94281,x94282,f318(f318(f10(x94283,f918(x94282,a909),x94281),x94284),x94285),x94286,x94287)
% 109.14/108.85 [9455]P36(x94551,x94552,x94553,f318(f318(f145(x94554,x94551),x94555),x94556),x94557)+~P36(x94554,x94552,f318(f318(f10(x94551,f918(x94552,a909),x94554),x94553),x94555),x94556,x94557)
% 109.14/108.85 [9061]~P1(f318(f318(f320(x90611),x90612),f318(f318(x90615,x90616),x90617)))+P1(f318(f318(f320(x90611),x90612),f318(f318(f248(x90613,x90614,f918(x90611,a909)),x90615),f318(f318(f243(x90613,x90614),x90616),x90617))))
% 109.14/108.85 [9345]P1(f318(f318(f318(x93451,x93452),x93453),x93454))+~P1(f318(f318(f318(f248(x93455,x93456,f918(x93457,a909)),x93451),f318(f318(f243(x93455,x93456),x93452),x93453)),x93454))
% 109.14/108.85 [9494]P1(f318(f318(f320(x94941),f318(f318(x94942,x94943),x94944)),f318(f301(f917(x94945,x94946),x94941,f318(f248(x94945,x94946,x94941),x94942)),x94947)))+~P1(f318(f318(f320(f917(x94945,x94946)),f318(f318(f243(x94945,x94946),x94943),x94944)),x94947))
% 109.14/108.85 [9855]P1(f318(f318(f320(f917(f912(x98551),f912(x98551))),f318(f318(f243(f912(x98551),f912(x98551)),f318(f318(f125(x98551),x98552),f318(f318(f142(x98551),x98553),x98554))),f318(f318(f125(x98551),x98552),f318(f318(f142(x98551),x98555),x98556)))),f138(x98551,x98557)))+~P1(f318(f318(f320(f917(x98551,x98551)),f318(f318(f243(x98551,x98551),x98553),x98555)),x98557))
% 109.14/108.85 [9922]~P36(x99221,x99223,x99224,x99226,f318(f318(f145(x99222,x99223),x99225),x99227))+P36(x99221,x99222,f318(f318(f9(x99221,f918(x99222,x99223),f918(x99222,a909)),f318(f318(f10(f918(x99223,a909),f918(f918(x99222,x99223),f918(x99222,a909)),x99221),f10(x99223,a909,x99222)),x99224)),x99225),x99226,x99227)
% 109.14/108.85 [10012]P36(x100121,x100122,x100123,x100124,f318(f318(f145(x100125,x100122),x100126),x100127))+~P36(x100121,x100125,f318(f318(f9(x100121,f918(x100125,x100122),f918(x100125,a909)),f318(f318(f10(f918(x100122,a909),f918(f918(x100125,x100122),f918(x100125,a909)),x100121),f10(x100122,a909,x100125)),x100123)),x100126),x100124,x100127)
% 109.14/108.85 [10297]P1(f318(f318(f320(x102971),f483(x102972,x102973,x102974,x102975,x102976,x102977,x102971)),x102975))+P1(f318(f318(f318(f318(f34(x102971,f918(x102977,f918(x102976,a909))),x102975),x102974),x102973),x102972))
% 109.14/108.85 [10298]P1(f318(f318(f320(x102981),f778(x102982,x102983,x102984,x102985,x102986,x102987,x102981)),x102987))+P1(f318(f318(f318(f318(f34(x102981,f918(x102983,f918(x102982,a909))),x102987),x102986),x102985),x102984))
% 109.14/108.85 [10299]P1(f318(f318(f320(x102991),f484(x102992,x102993,x102994,x102995,x102996,x102997,x102991)),x102995))+~P1(f318(f318(f318(f318(f33(x102991,f918(x102997,f918(x102996,a909))),x102995),x102994),x102993),x102992))
% 109.14/108.85 [10300]P1(f318(f318(f320(x103001),f779(x103002,x103003,x103004,x103005,x103006,x103007,x103001)),x103005))+~P1(f318(f318(f318(f318(f33(x103001,f918(x103007,f918(x103006,a909))),x103005),x103004),x103003),x103002))
% 109.14/108.85 [10355]P1(f318(f318(f318(x103551,f484(x103552,x103553,x103551,x103554,x103555,x103556,x103557)),x103553),x103552))+~P1(f318(f318(f318(f318(f33(x103557,f918(x103556,f918(x103555,a909))),x103554),x103551),x103553),x103552))
% 109.14/108.85 [10356]P1(f318(f318(f318(x103561,f779(x103562,x103563,x103561,x103564,x103565,x103566,x103567)),x103563),x103562))+~P1(f318(f318(f318(f318(f33(x103567,f918(x103566,f918(x103565,a909))),x103564),x103561),x103563),x103562))
% 109.14/108.85 [10374]~P1(f318(f318(f318(x103745,f483(x103747,x103746,x103745,x103744,x103743,x103742,x103741)),x103746),x103747))+P1(f318(f318(f318(f318(f34(x103741,f918(x103742,f918(x103743,a909))),x103744),x103745),x103746),x103747))
% 109.14/108.85 [10375]~P1(f318(f318(f318(x103755,f778(x103753,x103752,x103757,x103756,x103755,x103754,x103751)),x103756),x103757))+P1(f318(f318(f318(f318(f34(x103751,f918(x103752,f918(x103753,a909))),x103754),x103755),x103756),x103757))
% 109.14/108.85 [10403]~P1(f318(f318(f320(f917(x104031,x104033)),f318(f318(f243(x104031,x104033),x104036),x104037)),f318(f318(f280(x104031,x104032,x104033),x104034),x104035)))+P1(f318(f318(f244(x104031,x104032,x104033,f318(f318(f9(x104031,f918(f917(x104031,x104032),a909),f918(x104032,a909)),f318(f318(f10(f918(x104032,f918(f918(f917(x104031,x104032),a909),a909)),f918(f918(f917(x104031,x104032),a909),f918(x104032,a909)),x104031),f9(x104032,f918(f917(x104031,x104032),a909),a909)),f318(f318(f10(f918(x104032,f917(x104031,x104032)),f918(x104032,f918(f918(f917(x104031,x104032),a909),a909)),x104031),f318(f10(f917(x104031,x104032),f918(f918(f917(x104031,x104032),a909),a909),x104032),f320(f917(x104031,x104032)))),f243(x104031,x104032)))),x104034),f318(f318(f9(x104032,f918(f917(x104032,x104033),a909),f918(x104033,a909)),f318(f318(f10(f918(x104033,f918(f918(f917(x104032,x104033),a909),a909)),f918(f918(f917(x104032,x104033),a909),f918(x104033,a909)),x104032),f9(x104033,f918(f917(x104032,x104033),a909),a909)),f318(f318(f10(f918(x104033,f917(x104032,x104033)),f918(x104033,f918(f918(f917(x104032,x104033),a909),a909)),x104032),f318(f10(f917(x104032,x104033),f918(f918(f917(x104032,x104033),a909),a909),x104033),f320(f917(x104032,x104033)))),f243(x104032,x104033)))),x104035)),x104036),x104037))
% 109.14/108.85 [10419]P1(f318(f318(f320(f917(x104191,x104192)),f318(f318(f243(x104191,x104192),x104193),x104194)),f318(f318(f280(x104191,x104195,x104192),x104196),x104197)))+~P1(f318(f318(f244(x104191,x104195,x104192,f318(f318(f9(x104191,f918(f917(x104191,x104195),a909),f918(x104195,a909)),f318(f318(f10(f918(x104195,f918(f918(f917(x104191,x104195),a909),a909)),f918(f918(f917(x104191,x104195),a909),f918(x104195,a909)),x104191),f9(x104195,f918(f917(x104191,x104195),a909),a909)),f318(f318(f10(f918(x104195,f917(x104191,x104195)),f918(x104195,f918(f918(f917(x104191,x104195),a909),a909)),x104191),f318(f10(f917(x104191,x104195),f918(f918(f917(x104191,x104195),a909),a909),x104195),f320(f917(x104191,x104195)))),f243(x104191,x104195)))),x104196),f318(f318(f9(x104195,f918(f917(x104195,x104192),a909),f918(x104192,a909)),f318(f318(f10(f918(x104192,f918(f918(f917(x104195,x104192),a909),a909)),f918(f918(f917(x104195,x104192),a909),f918(x104192,a909)),x104195),f9(x104192,f918(f917(x104195,x104192),a909),a909)),f318(f318(f10(f918(x104192,f917(x104195,x104192)),f918(x104192,f918(f918(f917(x104195,x104192),a909),a909)),x104195),f318(f10(f917(x104195,x104192),f918(f918(f917(x104195,x104192),a909),a909),x104192),f320(f917(x104195,x104192)))),f243(x104195,x104192)))),x104197)),x104193),x104194))
% 109.14/108.85 [10308]~P146(x103082)+E(f318(f318(f8(x103081,x103082),f318(f318(f9(x103081,f918(x103083,a909),x103082),f318(f318(f10(f918(x103083,x103082),f918(f918(x103083,a909),x103082),x103081),f8(x103083,x103082)),f318(f318(f9(x103081,f918(x103083,x103082),f918(x103083,x103082)),f318(f318(f10(f918(x103082,x103082),f918(f918(x103083,x103082),f918(x103083,x103082)),x103081),f10(x103082,x103082,x103083)),f318(f318(f10(x103082,f918(x103082,x103082),x103081),f74(x103082)),x103084))),x103085))),x103086)),x103087),f318(f318(f74(x103082),f318(f318(f8(x103081,x103082),x103084),x103087)),f318(f318(f8(x103083,x103082),x103085),x103086)))
% 109.14/108.85 [9376]~P19(x93767,x93761,x93763,x93768)+E(f318(f66(x93761,x93761,x93762,f318(x93763,x93764)),f318(f66(x93761,x93761,x93762,f318(x93763,x93765)),x93766)),f318(f66(x93761,x93761,x93762,f318(x93763,x93765)),f318(f66(x93761,x93761,x93762,f318(x93763,x93764)),x93766)))
% 109.14/108.85 [10411]E(f318(f318(f243(x104111,x104112),f318(x104113,f551(x104114,x104115,x104113,x104116,x104117,x104118,x104112,x104111))),f318(x104115,f552(x104114,x104115,x104113,x104116,x104117,x104118,x104112,x104111))),x104118)+~P1(f318(f318(f320(f917(x104111,x104112)),x104118),f318(f301(f917(x104117,x104116),f917(x104111,x104112),f249(x104117,x104111,x104116,x104112,x104113,x104115)),x104114)))
% 109.14/108.85 [10436]~P1(f318(f318(f320(f917(x104368,x104367)),x104366),f318(f301(f917(x104361,x104362),f917(x104368,x104367),f249(x104361,x104368,x104362,x104367,x104365,x104364)),x104363)))+P1(f318(f318(f320(f917(x104361,x104362)),f318(f318(f243(x104361,x104362),f551(x104363,x104364,x104365,x104362,x104361,x104366,x104367,x104368)),f552(x104363,x104364,x104365,x104362,x104361,x104366,x104367,x104368))),x104363))
% 109.14/108.85 [9844]P1(f318(f318(f320(f917(f917(x98441,x98442),f917(x98441,x98442))),f318(f318(f243(f917(x98441,x98442),f917(x98441,x98442)),f318(f318(f243(x98441,x98442),x98443),x98444)),f318(f318(f243(x98441,x98442),x98445),x98446))),f311(x98441,x98442,x98447,x98448)))+~P1(f318(f318(f320(f917(x98441,x98441)),f318(f318(f243(x98441,x98441),x98443),x98445)),x98447))
% 109.14/108.85 [10397]E(f318(f133(x103971,x103972,f318(f9(x103972,x103971,x103971),x103973),f318(x103974,x103975)),x103976),f318(x103974,f318(f133(x103977,x103972,f318(f9(x103972,x103977,x103977),x103978),x103975),x103976)))+P1(f318(f318(f320(x103972),f728(x103975,x103978,x103974,x103973,x103977,x103971,x103976,x103972)),f318(f163(x103972),x103976)))
% 109.14/108.85 [10423]~E(f318(f66(x104231,x104231,x104237,f318(x104233,f728(x104235,x104238,x104234,x104233,x104237,x104231,x104236,x104232))),x104234),f318(f66(x104237,x104231,x104237,x104234),f318(x104238,f728(x104235,x104238,x104234,x104233,x104237,x104231,x104236,x104232))))+E(f318(f133(x104231,x104232,f318(f9(x104232,x104231,x104231),x104233),f318(x104234,x104235)),x104236),f318(x104234,f318(f133(x104237,x104232,f318(f9(x104232,x104237,x104237),x104238),x104235),x104236)))
% 109.14/108.85 [8592]E(f318(x85921,f318(x85922,x85923)),f318(x85924,f318(x85925,x85923)))+~E(f318(f66(x85926,x85927,x85928,x85921),x85922),f318(f66(x85929,x85927,x85928,x85924),x85925))
% 109.14/108.85 [8593]E(f318(x85931,f318(x85932,x85933)),f318(x85934,f318(x85935,x85933)))+~E(f318(f66(x85936,x85937,x85938,x85931),x85932),f318(f66(x85939,x85937,x85938,x85934),x85935))
% 109.14/108.85 [10219]P1(f318(f318(f320(f917(x102191,x102192)),f318(f318(f243(x102191,x102192),f318(x102193,x102194)),f318(x102195,x102196))),f318(f301(f917(x102197,x102198),f917(x102191,x102192),f249(x102197,x102191,x102198,x102192,x102193,x102195)),x102199)))+~P1(f318(f318(f320(f917(x102197,x102198)),f318(f318(f243(x102197,x102198),x102194),x102196)),x102199))
% 109.14/108.85 [8884]~E(f318(x88844,f318(x88845,x88846)),f318(x88849,f318(x888410,x888411)))+E(f318(f318(f66(x88841,x88842,x88843,x88844),x88845),x88846),f318(f318(f66(x88847,x88842,x88848,x88849),x888410),x888411))
% 109.14/108.85 [9469]~P19(x94698,x94699,x946910,x946911)+E(f318(f66(x94691,x94692,x94693,x94694),f318(f66(x94695,x94691,x94693,x94696),x94697)),f318(f66(x94695,x94692,x94693,f318(f66(x94691,x94692,x94695,x94694),x94696)),x94697))
% 109.14/108.85 [4711]~P4(x47111)+~P108(x47111)+E(f92(x47111),f223(x47111))
% 109.14/108.85 [4712]~P4(x47121)+~P102(x47121)+E(f101(x47121),f224(x47121))
% 109.14/108.85 [4955]~P116(x49551)+~P99(x49551)+E(f318(f69(x49551),f318(f94(x49551),a88)),f71(x49551))
% 109.14/108.85 [5245]E(x52451,f2(a1))+E(f75(a1,x52451),f318(f72(a1),f71(a1)))+P1(f318(f318(f226(a1),f2(a1)),x52451))
% 109.14/108.85 [5452]E(x54521,f2(a1))+E(f75(a1,x54521),f71(a1))+~P1(f318(f318(f226(a1),f2(a1)),x54521))
% 109.14/108.85 [6774]~P43(x67741)+~P1(f318(f55(a1),x67741))+P1(f318(f55(a911),f318(f301(a1,a911,a95),x67741)))
% 109.14/108.85 [7135]E(f41(f71(a1),f318(f94(a1),x71351)),f318(f318(f243(a1,a1),f2(a1)),f71(a1)))+~P1(f318(f318(f226(a1),f2(a1)),f318(f94(a1),x71351)))+~P1(f318(f318(f226(a1),f71(a1)),f318(f94(a1),x71351)))
% 109.14/108.85 [7475]~P43(x74751)+P1(f318(f55(a1),x74751))+~P1(f318(f55(a911),f318(f301(a1,a911,a95),x74751)))
% 109.14/108.85 [8302]E(f318(f318(f243(a1,a1),f318(f94(a1),a88)),f318(f318(f73(a1),f71(a1)),f318(f94(a1),x83021))),f44(f71(a1),f318(f94(a1),x83021)))+~P1(f318(f318(f226(a1),f2(a1)),f318(f94(a1),x83021)))+~P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),f71(a1)),f318(f94(a1),x83021))))
% 109.14/108.85 [10334]E(f318(f37(f318(f94(a1),x103341)),f41(f71(a1),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f94(a1),x103341)))),f41(f71(a1),f318(f94(a1),x103341)))+~P1(f318(f318(f226(a1),f2(a1)),f318(f94(a1),x103341)))+P1(f318(f318(f226(a1),f71(a1)),f318(f94(a1),x103341)))
% 109.14/108.85 [10338]E(f318(f37(f318(f94(a1),x103381)),f44(f71(a1),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f94(a1),x103381)))),f44(f71(a1),f318(f94(a1),x103381)))+~P1(f318(f318(f226(a1),f2(a1)),f318(f94(a1),x103381)))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),f71(a1)),f318(f94(a1),x103381))))
% 109.14/108.85 [9800]E(x98001,f179(f918(f917(a911,a911),a909)))+~P1(f318(f55(f917(a911,a911)),x98001))+P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),f179(f918(f917(a911,a911),a909))),x98001)),a28))
% 109.14/108.85 [10246]E(x102461,f2(a911))+E(x102461,f318(a103,f2(a911)))+~P1(f318(f318(f226(a911),x102461),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.85 [10391]E(x103911,f2(a90))+E(f318(f318(f73(a1),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(a24,f318(f318(f30(a90),x103911),f318(f94(a90),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))),f71(a1)),f318(a24,x103911))+E(f39(a90,x103911,f318(f94(a90),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f2(a90))
% 109.14/108.85 [10323]E(x103231,f2(a90))+~E(f39(a90,x103231,f318(f94(a90),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f2(a90))+E(f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(a24,f318(f318(f30(a90),x103231),f318(f94(a90),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))),f318(a24,x103231))
% 109.14/108.85 [4792]~P61(x47921,x47922)+P46(x47921,x47922)+~P47(a909)
% 109.14/108.85 [4721]~P114(x47211)+P30(x47211,x47212)+~E(x47212,f2(x47211))
% 109.14/108.85 [4722]~P4(x47221)+P13(x47221,x47222)+~E(x47222,f104(x47221))
% 109.14/108.85 [4731]~P116(x47311)+~E(x47312,f2(x47311))+E(f75(x47311,x47312),f2(x47311))
% 109.14/108.85 [4732]~P94(x47321)+~E(x47322,f2(x47321))+E(f75(x47321,x47322),f2(x47321))
% 109.14/108.85 [4740]~P114(x47402)+~P30(x47402,x47401)+E(x47401,f2(x47402))
% 109.14/108.85 [4785]~P116(x47852)+~E(f75(x47852,x47851),f2(x47852))+E(x47851,f2(x47852))
% 109.14/108.85 [4799]~P68(x47992)+~P68(x47991)+P68(f918(x47991,x47992))
% 109.14/108.85 [4800]~P68(x48002)+~P68(x48001)+P68(f917(x48001,x48002))
% 109.14/108.85 [4801]~P68(x48012)+~P68(x48011)+P68(f919(x48011,x48012))
% 109.14/108.85 [4802]~P6(x48022)+~P6(x48021)+P6(f185(x48021,x48022))
% 109.14/108.85 [4803]~P71(x48032)+~P71(x48031)+P71(f918(x48031,x48032))
% 109.14/108.85 [4804]~P71(x48042)+~P71(x48041)+P71(f917(x48041,x48042))
% 109.14/108.85 [4805]~P71(x48052)+~P71(x48051)+P71(f919(x48051,x48052))
% 109.14/108.85 [4806]~P111(x48062)+~P111(x48061)+P111(f917(x48061,x48062))
% 109.14/108.85 [4927]~P4(x49271)+~P13(x49271,x49272)+P13(x49271,f143(x49271,x49272))
% 109.14/108.85 [5169]~P6(x51692)+~P6(x51691)+P6(f39(a1,x51691,x51692))
% 109.14/108.85 [4741]~P83(x47411)+~E(x47412,f2(x47411))+E(f318(f72(x47411),x47412),x47412)
% 109.14/108.85 [4742]~P83(x47421)+~E(x47422,f2(x47421))+E(f318(f72(x47421),x47422),x47422)
% 109.14/108.85 [4756]~P98(x47561)+~E(x47562,f2(a1))+E(f318(f93(x47561),x47562),f2(x47561))
% 109.14/108.85 [4757]~P144(x47571)+~E(x47572,f2(a1))+E(f318(f93(x47571),x47572),f2(x47571))
% 109.14/108.85 [4758]~P98(x47581)+~E(x47582,f2(a1))+E(f318(f93(x47581),x47582),f2(x47581))
% 109.14/108.85 [4782]~P66(x47821)+~E(f2(x47821),x47822)+E(f318(f72(x47821),x47822),f2(x47821))
% 109.14/108.85 [4783]~P66(x47831)+~E(x47832,f2(x47831))+E(f318(f72(x47831),x47832),f2(x47831))
% 109.14/108.85 [4784]~P91(x47841)+~E(x47842,f2(x47841))+E(f318(f69(x47841),x47842),f2(x47841))
% 109.14/108.85 [4807]~P83(x48072)+E(x48071,f2(x48072))+~E(f318(f72(x48072),x48071),x48071)
% 109.14/108.85 [4808]~P83(x48082)+E(x48081,f2(x48082))+~E(f318(f72(x48082),x48081),x48081)
% 109.14/108.85 [4810]E(x48101,f318(a95,x48102))+~E(x48101,f2(a911))+~E(x48102,f318(f91(a1),x48101))
% 109.14/108.85 [4811]E(f318(a95,x48111),x48112)+~E(x48112,f2(a911))+~E(x48111,f318(f91(a1),x48112))
% 109.14/108.85 [4812]~P98(x48122)+E(x48121,f2(a1))+~E(f318(f93(x48122),x48121),f2(x48122))
% 109.14/108.85 [4813]~P98(x48132)+E(x48131,f2(a1))+~E(f318(f93(x48132),x48131),f2(x48132))
% 109.14/108.85 [4817]~P66(x48172)+E(x48171,f2(x48172))+~E(f318(f72(x48172),x48171),f2(x48172))
% 109.14/108.85 [4818]~P91(x48182)+E(x48181,f2(x48182))+~E(f318(f69(x48182),x48181),f2(x48182))
% 109.14/108.85 [4819]~P66(x48191)+E(f2(x48191),x48192)+~E(f318(f72(x48191),x48192),f2(x48191))
% 109.14/108.85 [5000]~P4(x50001)+~P13(x50001,x50002)+P13(x50001,f318(f162(x50001),x50002))
% 109.14/108.85 [5027]~P1(x50272)+~P1(x50271)+P1(f318(f318(a316,x50271),x50272))
% 109.14/108.85 [5061]~E(f71(a911),f2(a911))+E(f318(f29(x50611),x50612),f2(a911))+~P1(f318(f55(x50611),x50612))
% 109.14/108.85 [5098]~P118(x50981)+~P146(x50981)+E(f318(f318(f235(x50981),f2(x50981)),f318(a103,x50982)),f2(x50981))
% 109.14/108.85 [5137]~P4(x51371)+P13(x51371,f130(x51371,x51372))+~P1(f318(f55(x51371),x51372))
% 109.14/108.85 [5138]~P4(x51381)+P13(x51381,f720(x51382,x51381))+~P1(f318(f55(x51381),x51382))
% 109.14/108.85 [5161]~P4(x51611)+E(f318(f163(x51611),f130(x51611,x51612)),x51612)+~P1(f318(f55(x51611),x51612))
% 109.14/108.85 [5162]~P4(x51621)+E(f318(f163(x51621),f720(x51622,x51621)),x51622)+~P1(f318(f55(x51621),x51622))
% 109.14/108.85 [5191]P1(x51911)+P1(x51912)+~P1(f318(f318(a317,x51912),x51911))
% 109.14/108.85 [5204]E(x52041,f179(f918(x52042,a909)))+~E(f318(f29(x52042),x52041),f2(a911))+~P1(f318(f55(x52042),x52041))
% 109.14/108.85 [5209]P1(x52091)+~P1(x52092)+~P1(f318(f318(a321,x52092),x52091))
% 109.14/108.85 [5263]~P81(x52631)+E(f318(f69(x52631),x52632),x52632)+P1(f318(f318(f226(x52631),x52632),f2(x52631)))
% 109.14/108.85 [5264]~P5(x52642)+~P42(x52642,x52642,x52641)+E(f318(x52641,f87(x52642,x52641)),f87(x52642,x52641))
% 109.14/108.85 [5265]~P5(x52652)+~P42(x52652,x52652,x52651)+E(f318(x52651,f86(x52652,x52651)),f86(x52652,x52651))
% 109.14/108.85 [5326]~P71(x53262)+~P1(f318(f50(x53262),x53261))+P1(f318(x53261,f721(x53261,x53262)))
% 109.14/108.85 [5327]~P71(x53272)+~P1(f318(f50(x53272),x53271))+P1(f318(x53271,f729(x53271,x53272)))
% 109.14/108.85 [5368]E(x53681,f104(x53682))+P1(f318(f128(x53682),f105(x53682,x53681)))+~P1(f318(f128(x53682),x53681))
% 109.14/108.85 [5373]~P4(x53731)+~P1(f318(f55(x53731),x53732))+P1(f318(f128(x53731),f130(x53731,x53732)))
% 109.14/108.85 [5374]~P4(x53741)+~P1(f318(f55(x53741),x53742))+P1(f318(f128(x53741),f720(x53742,x53741)))
% 109.14/108.85 [5379]~P144(x53791)+E(f318(f91(x53791),f318(a95,x53792)),f318(f93(x53791),x53792))+P1(f318(f318(f226(a1),x53792),f2(a1)))
% 109.14/108.85 [5400]P7(x54002,x54001)+E(f318(x54001,f516(x54001)),f318(x54001,f519(x54001)))+P1(f318(f318(x54001,f516(x54001)),f519(x54001)))
% 109.14/108.85 [5414]E(f318(f91(a1),f371(x54141,x54142)),x54141)+P1(f318(x54142,f318(a95,x54141)))+~P1(f318(x54142,f2(a911)))
% 109.14/108.85 [5426]~P71(x54261)+~P1(f318(x54262,f734(x54262,x54261)))+P1(f318(f51(x54261),x54262))
% 109.14/108.85 [5427]~P71(x54271)+~P1(f318(x54272,f744(x54272,x54271)))+P1(f318(f51(x54271),x54272))
% 109.14/108.85 [5462]~P116(x54621)+~E(f75(x54621,x54622),f318(f72(x54621),f71(x54621)))+P1(f318(f318(f226(x54621),x54622),f2(x54621)))
% 109.14/108.85 [5537]~E(x55372,f2(a1))+E(f206(x55371,x55372),f318(f318(f243(a1,a1),f2(a1)),f71(a1)))+P1(f318(f318(f226(a1),x55372),f2(a1)))
% 109.14/108.85 [5538]~E(x55381,f2(a1))+E(f206(x55381,x55382),f318(f318(f243(a1,a1),f2(a1)),f71(a1)))+P1(f318(f318(f226(a1),x55382),f2(a1)))
% 109.14/108.85 [5590]E(f318(f91(a1),f371(x55901,x55902)),x55901)+P1(f318(x55902,f318(a95,x55901)))+P1(f318(f318(f226(a1),x55901),f2(a1)))
% 109.14/108.85 [5656]~P116(x56561)+E(f75(x56561,x56562),f318(f72(x56561),f71(x56561)))+~P1(f318(f318(f226(x56561),x56562),f2(x56561)))
% 109.14/108.85 [5657]~P116(x56571)+E(f75(x56571,x56572),f318(f72(x56571),f71(x56571)))+~P1(f318(f318(f226(x56571),x56572),f2(x56571)))
% 109.14/108.85 [5658]~P91(x56581)+E(f318(f69(x56581),x56582),f318(f72(x56581),x56582))+~P1(f318(f318(f225(x56581),x56582),f2(x56581)))
% 109.14/108.85 [5659]~P91(x56591)+E(f318(f69(x56591),x56592),f318(f72(x56591),x56592))+~P1(f318(f318(f226(x56591),x56592),f2(x56591)))
% 109.14/108.85 [5660]~P81(x56601)+E(f318(f69(x56601),x56602),f318(f72(x56601),x56602))+~P1(f318(f318(f226(x56601),x56602),f2(x56601)))
% 109.14/108.85 [5762]~P1(f318(x57621,f371(x57622,x57621)))+P1(f318(x57621,f318(a95,x57622)))+~P1(f318(x57621,f2(a911)))
% 109.14/108.85 [5769]E(x57691,f2(a911))+E(f318(a103,f579(x57692,x57691)),x57691)+~P1(f318(f318(f226(a911),x57691),f318(a103,x57692)))
% 109.14/108.85 [5773]P7(x57731,x57732)+~E(f318(x57732,f516(x57732)),f318(x57732,f519(x57732)))+~P1(f318(f318(x57732,f516(x57732)),f519(x57732)))
% 109.14/108.85 [5792]~P4(x57921)+P13(x57921,x57922)+P1(f318(f318(f225(a911),f704(x57922,x57921)),f705(x57922,x57921)))
% 109.14/108.85 [5793]~P4(x57931)+P13(x57931,x57932)+P1(f318(f318(f225(a911),f711(x57932,x57931)),f716(x57932,x57931)))
% 109.14/108.85 [5879]~P91(x58791)+~E(x58792,f2(x58791))+P1(f318(f318(f225(x58791),f318(f69(x58791),x58792)),f2(x58791)))
% 109.14/108.85 [5968]~P1(f318(x59681,f371(x59682,x59681)))+P1(f318(x59681,f318(a95,x59682)))+P1(f318(f318(f226(a1),x59682),f2(a1)))
% 109.14/108.85 [5994]~P1(f318(x59941,f318(a95,x59942)))+P1(f318(x59941,f2(a911)))+~P1(f318(f318(f226(a1),x59942),f2(a1)))
% 109.14/108.85 [6341]~P116(x63411)+~P1(f318(f318(f226(x63411),x63412),f2(x63411)))+P1(f318(f318(f226(x63411),f75(x63411,x63412)),f2(x63411)))
% 109.14/108.85 [6455]~P116(x64551)+P1(f318(f318(f225(x64551),f318(f93(x64551),x64552)),f2(x64551)))+~P1(f318(f318(f225(a1),x64552),f2(a1)))
% 109.14/108.85 [6456]~P116(x64561)+P1(f318(f318(f226(x64561),f318(f93(x64561),x64562)),f2(x64561)))+~P1(f318(f318(f226(a1),x64562),f2(a1)))
% 109.14/108.85 [6465]~P91(x64652)+E(x64651,f2(x64652))+~P1(f318(f318(f225(x64652),f318(f69(x64652),x64651)),f2(x64652)))
% 109.14/108.85 [6541]~P144(x65411)+~P1(f318(f318(f320(x65411),x65412),f100(x65411)))+P1(f318(f318(f320(x65411),f318(f72(x65411),x65412)),f100(x65411)))
% 109.14/108.85 [6573]~P116(x65731)+~P1(f318(f318(f226(x65731),f75(x65731,x65732)),f2(x65731)))+P1(f318(f318(f226(x65731),x65732),f2(x65731)))
% 109.14/108.85 [6748]~P116(x67482)+~P1(f318(f318(f225(x67482),f318(f93(x67482),x67481)),f2(x67482)))+P1(f318(f318(f225(a1),x67481),f2(a1)))
% 109.14/108.85 [6749]~P116(x67492)+~P1(f318(f318(f226(x67492),f318(f93(x67492),x67491)),f2(x67492)))+P1(f318(f318(f226(a1),x67491),f2(a1)))
% 109.14/108.85 [6834]~P5(x68341)+~P42(x68341,x68341,x68342)+P1(f318(f318(f225(x68341),f318(x68342,f87(x68341,x68342))),f87(x68341,x68342)))
% 109.14/108.85 [6835]~P5(x68351)+~P42(x68351,x68351,x68352)+P1(f318(f318(f225(x68351),f318(x68352,f86(x68351,x68352))),f86(x68351,x68352)))
% 109.14/108.85 [7251]~P83(x72511)+~P1(f318(f318(f225(x72511),x72512),f2(x72511)))+P1(f318(f318(f225(x72511),f318(f318(f73(x72511),x72512),x72512)),f2(x72511)))
% 109.14/108.85 [7253]~P83(x72531)+~P1(f318(f318(f226(x72531),x72532),f2(x72531)))+P1(f318(f318(f226(x72531),f318(f318(f73(x72531),x72532),x72532)),f2(x72531)))
% 109.14/108.85 [7254]~P116(x72541)+~P1(f318(f318(f226(x72541),x72542),f2(x72541)))+P1(f318(f318(f226(x72541),f318(f318(f73(x72541),x72542),x72542)),f2(x72541)))
% 109.14/108.85 [7810]~P83(x78101)+~P1(f318(f318(f225(x78101),f318(f318(f73(x78101),x78102),x78102)),f2(x78101)))+P1(f318(f318(f225(x78101),x78102),f2(x78101)))
% 109.14/108.85 [7811]~P83(x78111)+~P1(f318(f318(f226(x78111),f318(f318(f73(x78111),x78112),x78112)),f2(x78111)))+P1(f318(f318(f226(x78111),x78112),f2(x78111)))
% 109.14/108.85 [7812]~P116(x78121)+~P1(f318(f318(f226(x78121),f318(f318(f73(x78121),x78122),x78122)),f2(x78121)))+P1(f318(f318(f226(x78121),x78122),f2(x78121)))
% 109.14/108.85 [4853]~E(x48532,f71(a911))+~E(x48531,f71(a911))+E(f318(f318(f74(a911),x48531),x48532),f71(a911))
% 109.14/108.85 [4854]~E(x48542,f2(a911))+~E(x48541,f2(a911))+E(f318(f318(f73(a911),x48541),x48542),f2(a911))
% 109.14/108.85 [4855]~E(x48552,f71(a911))+~E(x48551,f71(a911))+E(f318(f318(f74(a911),x48551),x48552),f71(a911))
% 109.14/108.85 [4856]~E(x48562,f71(a1))+~E(x48561,f71(a1))+E(f318(f318(f74(a1),x48561),x48562),f71(a1))
% 109.14/108.85 [4911]~P69(x49112)+E(x49111,f2(x49112))+E(f318(f318(f30(x49112),x49111),x49111),f71(x49112))
% 109.14/108.85 [4912]~P125(x49122)+E(x49121,f2(x49122))+E(f318(f318(f282(x49122),x49121),x49121),f71(x49122))
% 109.14/108.85 [4913]~P126(x49132)+E(x49131,f2(x49132))+E(f318(f318(f282(x49132),x49131),x49131),f71(x49132))
% 109.14/108.85 [4930]~P83(x49301)+~E(x49302,f2(x49301))+E(f318(f318(f73(x49301),x49302),x49302),f2(x49301))
% 109.14/108.85 [4931]~P83(x49311)+~E(x49312,f2(x49311))+E(f318(f318(f73(x49311),x49312),x49312),f2(x49311))
% 109.14/108.85 [4934]~P145(x49341)+~E(x49342,f71(x49341))+E(f318(f318(f74(x49341),x49342),x49342),f71(x49341))
% 109.14/108.85 [4935]~P126(x49351)+~E(x49352,f2(x49351))+E(f318(f318(f282(x49351),x49352),x49352),f2(x49351))
% 109.14/108.85 [4978]~E(x49782,f2(a911))+~E(x49781,f2(a911))+E(f318(f72(a1),f318(f91(a1),x49781)),f318(f91(a1),x49782))
% 109.14/108.85 [4997]E(x49971,f71(a911))+E(x49972,f2(a911))+~E(f318(f318(f74(a911),x49972),x49971),x49972)
% 109.14/108.85 [5009]E(x50091,f2(a911))+E(x50092,f2(a911))+~E(f318(f318(f74(a911),x50092),x50091),f2(a911))
% 109.14/108.85 [5034]~E(x50342,f2(a911))+~E(x50341,f318(a103,f2(a911)))+E(f318(f318(f73(a911),x50341),x50342),f318(a103,f2(a911)))
% 109.14/108.85 [5035]~E(x50351,f2(a911))+~E(x50352,f318(a103,f2(a911)))+E(f318(f318(f73(a911),x50351),x50352),f318(a103,f2(a911)))
% 109.14/108.85 [5036]~E(x50362,f2(a911))+~E(x50361,f318(a103,f2(a911)))+E(f318(f318(f73(a911),x50361),x50362),f318(a103,f2(a911)))
% 109.14/108.85 [5037]~E(x50371,f2(a911))+~E(x50372,f318(a103,f2(a911)))+E(f318(f318(f73(a911),x50371),x50372),f318(a103,f2(a911)))
% 109.14/108.85 [5044]E(x50441,f71(a1))+E(x50442,f318(f94(a1),a88))+~E(f318(f318(f74(a1),x50441),x50442),f71(a1))
% 109.14/108.85 [5045]E(x50451,f71(a1))+E(x50452,f318(f94(a1),a88))+~E(f318(f318(f74(a1),x50452),x50451),f71(a1))
% 109.14/108.85 [5046]E(x50461,f71(a1))+E(x50461,f318(f94(a1),a88))+~E(f318(f318(f74(a1),x50462),x50461),f71(a1))
% 109.14/108.85 [5047]E(x50471,f71(a1))+E(x50471,f318(f94(a1),a88))+~E(f318(f318(f74(a1),x50471),x50472),f71(a1))
% 109.14/108.85 [5048]E(x50481,f71(a1))+E(x50481,f318(f94(a1),a88))+~E(f318(f318(f74(a1),x50481),x50482),f71(a1))
% 109.14/108.85 [5069]~P83(x50692)+E(x50691,f2(x50692))+~E(f318(f318(f73(x50692),x50691),x50691),f2(x50692))
% 109.14/108.85 [5070]~P83(x50702)+E(x50701,f2(x50702))+~E(f318(f318(f73(x50702),x50701),x50701),f2(x50702))
% 109.14/108.85 [5076]~E(x50761,f318(f94(a1),a88))+~E(x50762,f318(f94(a1),a88))+E(f318(f318(f74(a1),x50761),x50762),f71(a1))
% 109.14/108.85 [5086]E(x50861,f2(a911))+E(x50862,f2(a911))+~E(f318(f318(f73(a911),x50862),x50861),f318(a103,f2(a911)))
% 109.14/108.85 [5087]E(x50871,f2(a911))+E(x50872,f2(a911))+~E(f318(f318(f73(a911),x50872),x50871),f318(a103,f2(a911)))
% 109.14/108.85 [5097]~P99(x50971)+~P72(x50971)+E(f318(f318(f282(x50971),x50972),f318(f94(x50971),a76)),f2(x50971))
% 109.14/108.85 [5104]~P145(x51041)+~E(x51042,f318(f72(x51041),f71(x51041)))+E(f318(f318(f74(x51041),x51042),x51042),f71(x51041))
% 109.14/108.85 [5109]~P6(x51092)+~P6(x51091)+P6(f318(f318(f73(a1),x51091),x51092))
% 109.14/108.85 [5110]~P6(x51102)+~P6(x51101)+P6(f318(f318(f74(a1),x51101),x51102))
% 109.14/108.85 [5111]~P6(x51112)+~P6(x51111)+P6(f318(f318(f30(a1),x51111),x51112))
% 109.14/108.85 [5112]~E(x51122,f2(a1))+E(x51121,f2(a1))+E(f40(x51121,x51122),f318(f318(f243(a1,a1),f2(a1)),x51121))
% 109.14/108.85 [5113]~E(x51132,f2(a1))+E(x51131,f2(a1))+E(f40(x51131,x51132),f318(f318(f243(a1,a1),f2(a1)),x51131))
% 109.14/108.85 [5135]~E(x51352,f318(a103,f2(a911)))+~E(x51351,f318(a103,f2(a911)))+E(f318(f318(f74(a911),x51351),x51352),f318(a103,f2(a911)))
% 109.14/108.85 [5150]E(x51501,f2(a911))+E(x51501,f318(a103,f2(a911)))+~E(f318(f318(f73(a911),x51502),x51501),f318(a103,f2(a911)))
% 109.14/108.85 [5151]E(x51511,f2(a911))+E(x51511,f318(a103,f2(a911)))+~E(f318(f318(f73(a911),x51511),x51512),f318(a103,f2(a911)))
% 109.14/108.85 [5152]E(x51521,f2(a911))+E(x51522,f318(a103,f2(a911)))+~E(f318(f318(f235(a911),x51522),x51521),f318(a103,f2(a911)))
% 109.14/108.85 [5153]E(x51531,f2(a911))+E(x51531,f318(a103,f2(a911)))+~E(f318(f318(f73(a911),x51532),x51531),f318(a103,f2(a911)))
% 109.14/108.85 [5154]E(x51541,f2(a911))+E(x51541,f318(a103,f2(a911)))+~E(f318(f318(f73(a911),x51541),x51542),f318(a103,f2(a911)))
% 109.14/108.85 [5163]~P99(x51631)+~P72(x51631)+E(f318(f318(f282(x51631),x51632),f318(f94(x51631),a88)),f318(f72(x51631),x51632))
% 109.14/108.85 [5183]E(x51831,f318(a95,x51832))+~E(x51831,f2(a911))+P1(f318(f318(f225(a1),f2(a1)),x51832))
% 109.14/108.85 [5184]E(f318(a95,x51841),x51842)+~E(x51842,f2(a911))+P1(f318(f318(f225(a1),f2(a1)),x51841))
% 109.14/108.85 [5199]E(x51991,f318(a103,f2(a911)))+E(x51992,f318(a103,f2(a911)))+~E(f318(f318(f73(a911),x51991),x51992),f318(a103,f2(a911)))
% 109.14/108.85 [5200]E(x52001,f318(a103,f2(a911)))+E(x52002,f318(a103,f2(a911)))+~E(f318(f318(f73(a911),x52001),x52002),f318(a103,f2(a911)))
% 109.14/108.85 [5211]~E(x52111,f318(a95,x52112))+E(x52111,f2(a911))+P1(f318(f318(f225(a1),f2(a1)),x52112))
% 109.14/108.85 [5212]~E(f318(a95,x52122),x52121)+E(x52121,f2(a911))+P1(f318(f318(f225(a1),f2(a1)),x52122))
% 109.14/108.85 [5238]~P103(x52381)+E(f318(f57(x52381,f92(x52381)),x52382),f12(x52381,x52382))+~P1(f318(f55(x52381),x52382))
% 109.14/108.85 [5239]~P103(x52391)+E(f318(f57(x52391,f101(x52391)),x52392),f15(x52391,x52392))+~P1(f318(f55(x52391),x52392))
% 109.14/108.85 [5240]~P4(x52401)+E(f318(f57(x52401,f223(x52401)),x52402),f16(x52401,x52402))+~P1(f318(f55(x52401),x52402))
% 109.14/108.85 [5241]~P4(x52411)+E(f318(f57(x52411,f224(x52411)),x52412),f17(x52411,x52412))+~P1(f318(f55(x52411),x52412))
% 109.14/108.85 [5321]E(x53211,x53212)+~E(f318(f318(f3(a911),x53212),x53211),f2(a911))+~E(f318(f318(f3(a911),x53211),x53212),f2(a911))
% 109.14/108.85 [5338]P6(x53381)+~P43(x53382)+~P1(f318(f318(f320(a1),x53381),x53382))
% 109.14/108.85 [5369]~P116(x53691)+~E(f75(x53691,x53692),f71(x53691))+P1(f318(f318(f226(x53691),f2(x53691)),x53692))
% 109.14/108.85 [5380]~P99(x53801)+E(f318(f91(x53801),f318(f94(a911),x53802)),f318(f94(x53801),x53802))+P1(f318(a184,f318(f94(a1),x53802)))
% 109.14/108.85 [5385]~P46(x53851,x53852)+P47(a909)+P1(f318(f55(f917(x53851,x53851)),x53852))
% 109.14/108.85 [5454]~P4(x54541)+E(f318(f57(x54541,f223(x54541)),x54542),f13(x54541,f223(x54541),x54542))+~P1(f318(f55(x54541),x54542))
% 109.14/108.85 [5455]~P4(x54551)+E(f318(f57(x54551,f224(x54551)),x54552),f14(x54551,f224(x54551),x54552))+~P1(f318(f55(x54551),x54552))
% 109.14/108.85 [5468]E(x54681,x54682)+P1(f318(f318(f226(a911),x54682),x54681))+P1(f318(f318(f226(a911),x54681),x54682))
% 109.14/108.85 [5469]E(x54691,x54692)+P1(f318(f318(f226(a911),x54692),x54691))+P1(f318(f318(f226(a911),x54691),x54692))
% 109.14/108.85 [5470]E(x54701,x54702)+P1(f318(f318(f226(a1),x54702),x54701))+P1(f318(f318(f226(a1),x54701),x54702))
% 109.14/108.85 [5524]~P99(x55241)+E(f318(f91(x55241),f318(f94(a911),x55242)),f2(x55241))+~P1(f318(a184,f318(f94(a1),x55242)))
% 109.14/108.85 [5527]~E(x55272,f318(a95,x55271))+E(x55271,f318(f91(a1),x55272))+~P1(f318(f318(f225(a1),f2(a1)),x55271))
% 109.14/108.85 [5528]~E(f318(a95,x55281),x55282)+E(x55281,f318(f91(a1),x55282))+~P1(f318(f318(f225(a1),f2(a1)),x55281))
% 109.14/108.85 [5529]~E(x55291,f318(a95,x55292))+E(f318(f91(a1),x55291),x55292)+~P1(f318(f318(f225(a1),f2(a1)),x55292))
% 109.14/108.85 [5539]E(x55391,f318(a95,x55392))+~E(x55392,f318(f91(a1),x55391))+~P1(f318(f318(f225(a1),f2(a1)),x55392))
% 109.14/108.85 [5540]E(f318(a95,x55401),x55402)+~E(x55401,f318(f91(a1),x55402))+~P1(f318(f318(f225(a1),f2(a1)),x55401))
% 109.14/108.85 [5581]~P91(x55812)+E(x55811,f2(x55812))+P1(f318(f318(f226(x55812),f2(x55812)),f318(f69(x55812),x55811)))
% 109.14/108.85 [5643]~P116(x56431)+E(f75(x56431,x56432),f71(x56431))+~P1(f318(f318(f226(x56431),f2(x56431)),x56432))
% 109.14/108.85 [5644]~P116(x56441)+E(f75(x56441,x56442),f71(x56441))+~P1(f318(f318(f226(x56441),f2(x56441)),x56442))
% 109.14/108.85 [5650]~P99(x56501)+E(f318(f91(x56501),f318(f94(a911),x56502)),f2(x56501))+P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x56502)))
% 109.14/108.85 [5661]~P91(x56611)+E(f318(f69(x56611),x56612),x56612)+~P1(f318(f318(f225(x56611),f2(x56611)),x56612))
% 109.14/108.85 [5662]~P91(x56621)+E(f318(f69(x56621),x56622),x56622)+~P1(f318(f318(f226(x56621),f2(x56621)),x56622))
% 109.14/108.85 [5671]E(x56711,f2(a911))+~E(f130(a911,f318(f293(a911,x56712),x56711)),f104(a911))+P1(f318(f318(f225(a911),x56711),x56712))
% 109.14/108.85 [5681]~P76(x56811)+E(f318(f318(f8(x56811,x56811),f7(x56811)),f318(f163(x56811),x56812)),f318(f156(x56811),x56812))+~P1(f318(f128(x56811),x56812))
% 109.14/108.85 [5684]~P144(x56841)+E(f318(f91(x56841),f318(a95,x56842)),f318(f93(x56841),x56842))+~P1(f318(f318(f225(a1),f2(a1)),x56842))
% 109.14/108.85 [5686]~E(x56861,x56862)+P1(f318(f318(f226(a911),x56861),f318(a103,x56862)))+P1(f318(f318(f226(a911),x56861),x56862))
% 109.14/108.85 [5709]E(x57091,x57092)+P1(f318(f318(f226(a911),x57091),x57092))+~P1(f318(f318(f225(a911),x57091),x57092))
% 109.14/108.85 [5710]E(x57101,x57102)+P1(f318(f318(f226(a911),x57101),x57102))+~P1(f318(f318(f225(a911),x57101),x57102))
% 109.14/108.85 [5711]E(x57111,x57112)+P1(f318(f318(f226(a911),x57111),x57112))+~P1(f318(f318(f225(a911),x57111),x57112))
% 109.14/108.85 [5712]E(x57121,x57122)+P1(f318(f318(f226(a1),x57121),x57122))+~P1(f318(f318(f225(a1),x57121),x57122))
% 109.14/108.85 [5715]E(x57151,f71(a1))+~E(f318(f318(f74(a1),x57152),x57151),f71(a1))+~P1(f318(f318(f226(a1),f2(a1)),x57152))
% 109.14/108.85 [5716]E(x57161,f71(a1))+~E(f318(f318(f74(a1),x57161),x57162),f71(a1))+~P1(f318(f318(f226(a1),f2(a1)),x57161))
% 109.14/108.85 [5758]~P43(x57582)+P1(f318(f318(f225(a1),f2(a1)),x57581))+~P1(f318(f318(f320(a1),x57581),x57582))
% 109.14/108.85 [5759]~P43(x57592)+P1(f318(f318(f225(a1),f2(a1)),x57591))+~P1(f318(f318(f320(a1),x57591),x57592))
% 109.14/108.85 [5778]~P61(x57781,x57782)+P39(x57781,x57782)+~P1(f318(f55(f917(x57781,x57781)),x57782))
% 109.14/108.85 [5779]~P61(x57791,x57792)+P39(x57791,x57792)+~P1(f318(f55(f917(x57791,x57791)),x57792))
% 109.14/108.85 [5780]~P39(x57801,x57802)+P61(x57801,x57802)+~P1(f318(f55(f917(x57801,x57801)),x57802))
% 109.14/108.85 [5781]~P61(x57811,x57812)+P46(x57811,x57812)+~P1(f318(f55(f917(x57811,x57811)),x57812))
% 109.14/108.85 [5823]E(x58231,f179(f918(x58232,a909)))+~P1(f318(f55(x58232),x58231))+P1(f318(f318(f226(a911),f2(a911)),f318(f29(x58232),x58231)))
% 109.14/108.85 [5850]~P1(f318(x58501,x58502))+P1(f318(x58501,f2(a911)))+P1(f318(f318(f226(a911),f887(x58502,x58501)),x58502))
% 109.14/108.85 [5873]E(x58731,f2(a911))+~E(f318(f156(a911),x58732),f2(a911))+~P1(f318(f318(f320(a911),x58731),f318(f163(a911),x58732)))
% 109.14/108.85 [5909]~E(x59091,x59092)+P1(f318(f318(f226(a911),x59091),f318(a103,x59092)))+~P1(f318(f318(f225(a911),x59092),x59091))
% 109.14/108.85 [5941]E(x59411,x59412)+~P1(f318(f318(f225(a911),x59412),x59411))+~P1(f318(f318(f225(a911),x59411),x59412))
% 109.14/108.85 [5942]E(x59421,x59422)+~P1(f318(f318(f225(a1),x59422),x59421))+~P1(f318(f318(f225(a1),x59421),x59422))
% 109.14/108.85 [5944]E(f318(f29(x59441),x59442),f2(a911))+~P1(f318(f55(x59441),x59442))+P1(f318(f318(f320(x59441),f895(x59442,x59441)),x59442))
% 109.14/108.85 [5953]E(f44(x59531,x59532),f40(x59531,x59532))+P1(f318(f318(f225(a1),f2(a1)),x59531))+~P1(f318(f318(f226(a1),f2(a1)),x59532))
% 109.14/108.85 [5980]~P1(f318(x59801,f367(x59801)))+P1(f318(x59801,f318(a95,x59802)))+~P1(f318(f318(f225(a1),f2(a1)),x59802))
% 109.14/108.85 [5984]P1(f318(f318(f225(a911),x59841),f789(x59842)))+~P1(f318(f55(a911),x59842))+~P1(f318(f318(f320(a911),x59841),x59842))
% 109.14/108.85 [5985]P1(f318(f318(f226(a911),x59851),f758(x59852)))+~P1(f318(f55(a911),x59852))+~P1(f318(f318(f320(a911),x59851),x59852))
% 109.14/108.85 [6013]E(x60131,x60132)+~P1(f318(f318(f226(a911),x60131),f318(a103,x60132)))+P1(f318(f318(f226(a911),x60131),x60132))
% 109.14/108.85 [6014]E(x60141,x60142)+~P1(f318(f318(f226(a911),x60141),f318(a103,x60142)))+P1(f318(f318(f226(a911),x60141),x60142))
% 109.14/108.85 [6015]E(x60151,x60152)+~P1(f318(f318(f226(a911),x60151),f318(a103,x60152)))+P1(f318(f318(f226(a911),x60151),x60152))
% 109.14/108.85 [6016]E(x60161,x60162)+~P1(f318(f318(f226(a911),x60161),f318(a103,x60162)))+P1(f318(f318(f226(a911),x60161),x60162))
% 109.14/108.85 [6051]E(x60511,f318(a103,x60512))+~P1(f318(f318(f225(a911),x60511),f318(a103,x60512)))+P1(f318(f318(f225(a911),x60511),x60512))
% 109.14/108.85 [6052]E(x60521,f318(a103,x60522))+~P1(f318(f318(f225(a911),x60521),f318(a103,x60522)))+P1(f318(f318(f225(a911),x60521),x60522))
% 109.14/108.85 [6067]P1(f318(x60671,f368(x60671)))+~P1(f318(x60671,f318(a95,x60672)))+~P1(f318(f318(f225(a1),f2(a1)),x60672))
% 109.14/108.85 [6083]~P1(f318(x60831,x60832))+~P1(f318(f318(f225(a1),f2(a1)),x60832))+P1(f318(x60831,f318(f91(a1),f357(x60831))))
% 109.14/108.85 [6094]~P91(x60942)+~E(x60941,f2(x60942))+~P1(f318(f318(f226(x60942),f2(x60942)),f318(f69(x60942),x60941)))
% 109.14/108.85 [6119]~P61(x61191,x61192)+P39(x61191,f318(f277(x61191,x61191),x61192))+~P1(f318(f55(f917(x61191,x61191)),x61192))
% 109.14/108.85 [6130]~P99(x61301)+E(f318(f91(x61301),f318(f94(a911),x61302)),f318(f94(x61301),x61302))+~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x61302)))
% 109.14/108.85 [6133]E(f318(a103,x61331),x61332)+~P1(f318(f318(f226(a911),x61331),x61332))+P1(f318(f318(f226(a911),f318(a103,x61331)),x61332))
% 109.14/108.85 [6147]E(f318(f318(f30(a1),x61471),x61472),f2(a1))+~P1(f318(f318(f225(a1),x61471),f2(a1)))+~P1(f318(f318(f226(a1),x61472),x61471))
% 109.14/108.85 [6148]E(f318(f318(f30(a1),x61481),x61482),f2(a1))+~P1(f318(f318(f225(a1),x61481),f2(a1)))+~P1(f318(f318(f226(a1),x61482),x61481))
% 109.14/108.85 [6159]E(f39(a1,x61591,x61592),x61591)+~P1(f318(f318(f225(a1),x61591),f2(a1)))+~P1(f318(f318(f226(a1),x61592),x61591))
% 109.14/108.85 [6173]E(f41(x61731,x61732),f40(x61731,x61732))+~P1(f318(f318(f225(a1),f2(a1)),x61731))+~P1(f318(f318(f225(a1),f2(a1)),x61732))
% 109.14/108.85 [6181]E(f318(f318(f30(a911),x61811),x61812),f2(a911))+~P1(f318(f318(f226(a911),f2(a911)),x61812))+~P1(f318(f318(f226(a911),x61811),x61812))
% 109.14/108.85 [6182]E(f318(f318(f30(a1),x61821),x61822),f2(a1))+~P1(f318(f318(f225(a1),f2(a1)),x61821))+~P1(f318(f318(f226(a1),x61821),x61822))
% 109.14/108.85 [6183]E(f318(f318(f30(a1),x61831),x61832),f2(a1))+~P1(f318(f318(f225(a1),f2(a1)),x61831))+~P1(f318(f318(f226(a1),x61831),x61832))
% 109.14/108.85 [6194]E(f39(a911,f318(f94(a911),x61941),f318(f94(a911),x61942)),f318(f94(a911),x61941))+P1(f318(a184,f318(f94(a1),x61941)))+~P1(f318(a184,f318(f94(a1),x61942)))
% 109.14/108.85 [6196]E(f39(a1,x61961,x61962),x61961)+~P1(f318(f318(f225(a1),f2(a1)),x61961))+~P1(f318(f318(f226(a1),x61961),x61962))
% 109.14/108.85 [6197]E(x61971,x61972)+~P1(f318(f318(f226(a911),x61971),f318(a103,x61972)))+~P1(f318(f318(f225(a911),x61972),x61971))
% 109.14/108.85 [6207]E(f318(f91(a1),x62071),f318(f94(a1),x62072))+~E(x62071,f318(a95,f318(f94(a1),x62072)))+~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x62072)))
% 109.14/108.85 [6211]~P83(x62111)+~P1(f318(f318(f225(x62111),x62112),f2(x62111)))+P1(f318(f318(f225(x62111),x62112),f318(f72(x62111),x62112)))
% 109.14/108.85 [6212]~P116(x62121)+~P1(f318(f318(f226(x62121),x62122),f2(x62121)))+P1(f318(f318(f226(x62121),x62122),f318(f72(x62121),x62122)))
% 109.14/108.85 [6222]~P5(x62221)+E(f318(f318(f58(x62221,x62221,f92(x62221)),f233(x62221)),x62222),f32(x62221,x62222))+~P1(f318(f55(x62221),x62222))
% 109.14/108.85 [6223]~P5(x62231)+E(f318(f318(f58(x62231,x62231,f101(x62231)),f179(x62231)),x62232),f31(x62231,x62232))+~P1(f318(f55(x62231),x62232))
% 109.14/108.85 [6240]~P116(x62401)+~P1(f318(f318(f225(a1),f2(a1)),x62402))+P1(f318(f318(f225(x62401),f2(x62401)),f318(f93(x62401),x62402)))
% 109.14/108.85 [6241]~P130(x62411)+~P1(f318(f318(f226(a911),f2(a911)),x62412))+P1(f318(f318(f226(x62411),f2(x62411)),f318(f91(x62411),x62412)))
% 109.14/108.85 [6242]~P116(x62421)+~P1(f318(f318(f226(a1),f2(a1)),x62422))+P1(f318(f318(f226(x62421),f2(x62421)),f318(f93(x62421),x62422)))
% 109.14/108.85 [6245]~P6(x62452)+~P6(x62451)+E(f318(f301(a911,a1,f91(a1)),f294(a911,f318(a95,x62451),f318(a95,x62452))),f294(a1,x62451,x62452))
% 109.14/108.85 [6251]P1(f318(x62511,x62512))+~P1(f318(f318(f225(a1),f2(a1)),x62512))+~P1(f318(x62511,f318(f91(a1),f358(x62511))))
% 109.14/108.85 [6281]E(f318(f318(f73(a911),f318(f94(a911),x62811)),f318(f94(a911),x62812)),f318(f94(a911),x62811))+P1(f318(f318(f226(a1),x62811),a76))+~P1(f318(f318(f226(a1),x62812),a76))
% 109.14/108.85 [6287]~P116(x62871)+P1(f318(f318(f226(x62871),f2(x62871)),f75(x62871,x62872)))+~P1(f318(f318(f226(x62871),f2(x62871)),x62872))
% 109.14/108.85 [6300]~P65(x63001)+~P1(f318(f318(f225(x63001),x63002),f2(x63001)))+P1(f318(f318(f225(x63001),f2(x63001)),f318(f72(x63001),x63002)))
% 109.14/108.85 [6301]~P65(x63011)+~P1(f318(f318(f226(x63011),x63012),f2(x63011)))+P1(f318(f318(f226(x63011),f2(x63011)),f318(f72(x63011),x63012)))
% 109.14/108.85 [6304]E(x63041,f233(f918(x63042,a909)))+~E(f318(f29(x63042),x63041),f318(f29(x63042),f233(f918(x63042,a909))))+~P1(f318(f55(x63042),f233(f918(x63042,a909))))
% 109.14/108.85 [6332]~P83(x63321)+P1(f318(f318(f225(x63321),x63322),f2(x63321)))+~P1(f318(f318(f225(x63321),x63322),f318(f72(x63321),x63322)))
% 109.14/108.85 [6333]~P116(x63331)+P1(f318(f318(f226(x63331),x63332),f2(x63331)))+~P1(f318(f318(f226(x63331),x63332),f318(f72(x63331),x63332)))
% 109.14/108.85 [6340]E(f41(x63401,x63402),f318(f318(f243(a1,a1),f2(a1)),x63401))+~P1(f318(f318(f226(a1),f2(a1)),x63402))+~P1(f318(f318(f226(a1),x63401),x63402))
% 109.14/108.85 [6343]~P99(x63431)+P1(f318(f318(f320(x63431),f318(f94(x63431),x63432)),f177(x63431)))+~P1(f318(f318(f225(a1),a76),x63432))
% 109.14/108.85 [6372]E(x63721,f2(a911))+~P1(f318(f318(f226(a911),x63721),f318(a103,x63722)))+P1(f318(f318(f226(a911),f579(x63722,x63721)),x63722))
% 109.14/108.85 [6394]~P116(x63941)+~P1(f318(f318(f226(x63941),f2(x63941)),f75(x63941,x63942)))+P1(f318(f318(f226(x63941),f2(x63941)),x63942))
% 109.14/108.85 [6396]~E(f318(f94(a911),x63962),f318(f94(a911),x63961))+P1(f318(f318(f225(a1),f318(f94(a1),x63961)),f2(a1)))+~P1(f318(a184,f318(f94(a1),x63962)))
% 109.14/108.85 [6425]E(f318(f242(a1,a1),f44(x64251,x64252)),f318(f318(f30(a1),x64251),x64252))+~P1(f318(f318(f226(a1),x64251),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x64252))
% 109.14/108.85 [6463]E(f318(f247(a1,a1),f44(x64631,x64632)),f39(a1,x64631,x64632))+~P1(f318(f318(f226(a1),x64631),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x64632))
% 109.14/108.85 [6466]~P116(x64662)+~P1(f318(f318(f225(x64662),f2(x64662)),f318(f93(x64662),x64661)))+P1(f318(f318(f225(a1),f2(a1)),x64661))
% 109.14/108.85 [6467]~P130(x64672)+~P1(f318(f318(f226(x64672),f2(x64672)),f318(f91(x64672),x64671)))+P1(f318(f318(f226(a911),f2(a911)),x64671))
% 109.14/108.85 [6468]~P116(x64682)+~P1(f318(f318(f226(x64682),f2(x64682)),f318(f93(x64682),x64681)))+P1(f318(f318(f226(a1),f2(a1)),x64681))
% 109.14/108.85 [6471]E(f318(f242(a1,a1),f41(x64711,x64712)),f318(f318(f30(a1),x64711),x64712))+~P1(f318(f318(f225(a1),f2(a1)),x64712))+~P1(f318(f318(f226(a1),f2(a1)),x64711))
% 109.14/108.85 [6484]E(f318(f247(a1,a1),f41(x64841,x64842)),f39(a1,x64841,x64842))+~P1(f318(f318(f225(a1),f2(a1)),x64842))+~P1(f318(f318(f226(a1),f2(a1)),x64841))
% 109.14/108.85 [6499]~P65(x64991)+P1(f318(f318(f225(x64991),x64992),f2(x64991)))+~P1(f318(f318(f225(x64991),f2(x64991)),f318(f72(x64991),x64992)))
% 109.14/108.85 [6500]~P65(x65001)+P1(f318(f318(f226(x65001),x65002),f2(x65001)))+~P1(f318(f318(f226(x65001),f2(x65001)),f318(f72(x65001),x65002)))
% 109.14/108.85 [6523]~P5(x65231)+~P42(x65231,x65231,x65232)+P1(f318(f318(f225(x65231),f87(x65231,x65232)),f318(x65232,f87(x65231,x65232))))
% 109.14/108.85 [6524]~P5(x65241)+~P42(x65241,x65241,x65242)+P1(f318(f318(f225(x65241),f86(x65241,x65242)),f318(x65242,f86(x65241,x65242))))
% 109.14/108.85 [6528]P1(f318(f43(x65281,x65282),f44(x65281,x65282)))+~P1(f318(f318(f226(a1),x65281),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x65282))
% 109.14/108.85 [6553]P1(f318(f43(x65531,x65532),f41(x65531,x65532)))+~P1(f318(f318(f225(a1),f2(a1)),x65531))+~P1(f318(f318(f226(a1),f2(a1)),x65532))
% 109.14/108.85 [6597]~P65(x65971)+P1(f318(f318(f225(x65971),f318(f72(x65971),x65972)),f2(x65971)))+~P1(f318(f318(f225(x65971),f2(x65971)),x65972))
% 109.14/108.85 [6598]~P65(x65981)+P1(f318(f318(f226(x65981),f318(f72(x65981),x65982)),f2(x65981)))+~P1(f318(f318(f226(x65981),f2(x65981)),x65982))
% 109.14/108.85 [6615]E(f318(f318(f3(a911),f318(a95,x66151)),f318(a95,x66152)),f318(a95,f185(x66151,x66152)))+~P1(f318(f318(f225(a1),f2(a1)),x66152))+~P1(f318(f318(f225(a1),f2(a1)),x66151))
% 109.14/108.85 [6633]P1(f318(f318(f225(a1),f2(a1)),f185(x66331,x66332)))+~P1(f318(f318(f225(a1),f2(a1)),x66332))+~P1(f318(f318(f225(a1),f2(a1)),x66331))
% 109.14/108.85 [6666]~P1(f318(x66661,x66662))+P1(f318(x66661,f2(a911)))+P1(f318(x66661,f318(f318(f73(a911),f887(x66662,x66661)),f71(a911))))
% 109.14/108.85 [6674]E(f281(a911,f278(a911),x66741,x66742),f179(f918(a911,a909)))+P1(f318(f318(f278(a911),x66741),x66742))+~P1(f318(f318(f278(a911),x66742),x66741))
% 109.14/108.85 [6755]E(f318(f94(a911),x67551),f318(f94(a911),x67552))+~P1(f318(f318(f225(a1),f318(f94(a1),x67552)),f2(a1)))+~P1(f318(a184,f318(f94(a1),x67551)))
% 109.14/108.85 [6767]~E(x67671,f2(a911))+~E(f681(x67672,x67671),f2(a911))+E(f318(f133(a911,a911,f73(a911),x67671),x67672),f2(a911))
% 109.14/108.85 [6791]~P1(f318(f55(x67911),f863(x67912,x67911)))+~P1(f318(f55(f918(x67911,a909)),x67912))+P1(f318(f55(x67911),f31(f918(x67911,a909),x67912)))
% 109.14/108.85 [6797]E(x67971,x67972)+P1(f318(f318(f226(a1),x67971),x67972))+~P1(f318(f318(f226(a1),x67971),f318(f318(f73(a1),x67972),f71(a1))))
% 109.14/108.85 [6798]P1(f318(f318(f225(a911),f318(a95,x67981)),f318(a95,x67982)))+~P1(f318(f318(f225(a1),f2(a1)),x67982))+~P1(f318(f318(f225(a1),x67981),x67982))
% 109.14/108.85 [6799]P1(f318(f318(f225(a911),f318(a95,x67991)),f318(a95,x67992)))+~P1(f318(f318(f226(a1),f2(a1)),x67991))+~P1(f318(f318(f225(a1),x67991),x67992))
% 109.14/108.85 [6800]P1(f318(f318(f226(a911),f318(a95,x68001)),f318(a95,x68002)))+~P1(f318(f318(f226(a1),f2(a1)),x68002))+~P1(f318(f318(f226(a1),x68001),x68002))
% 109.14/108.85 [6801]P1(f318(f318(f226(a911),f318(a95,x68011)),f318(a95,x68012)))+~P1(f318(f318(f225(a1),f2(a1)),x68011))+~P1(f318(f318(f226(a1),x68011),x68012))
% 109.14/108.85 [6802]P1(f318(f318(f226(a911),f318(a95,x68021)),f318(a95,x68022)))+~P1(f318(f318(f226(a1),f2(a1)),x68022))+~P1(f318(f318(f226(a1),x68021),x68022))
% 109.14/108.85 [6813]E(f39(a911,f318(a95,x68131),f318(a95,x68132)),f318(a95,f39(a1,x68131,x68132)))+~P1(f318(f318(f225(a1),f2(a1)),x68132))+~P1(f318(f318(f225(a1),f2(a1)),x68131))
% 109.14/108.85 [6814]E(f39(a911,f318(a95,x68141),f318(a95,x68142)),f318(a95,f39(a1,x68141,x68142)))+~P1(f318(f318(f225(a1),f2(a1)),x68142))+~P1(f318(f318(f225(a1),f2(a1)),x68141))
% 109.14/108.85 [6839]~P65(x68391)+~P1(f318(f318(f225(x68391),f318(f72(x68391),x68392)),f2(x68391)))+P1(f318(f318(f225(x68391),f2(x68391)),x68392))
% 109.14/108.85 [6840]~P65(x68401)+~P1(f318(f318(f226(x68401),f318(f72(x68401),x68402)),f2(x68401)))+P1(f318(f318(f226(x68401),f2(x68401)),x68402))
% 109.14/108.85 [6854]~P1(f318(f318(f226(a1),a76),x68542))+~P1(f318(f318(f226(a1),x68541),x68542))+P1(f318(f318(f226(a911),f318(f94(a911),x68541)),f318(f94(a911),x68542)))
% 109.14/108.85 [6941]~P1(f318(f318(f225(a1),f2(a1)),x69411))+P1(f318(f318(f226(a911),f318(a95,x69411)),x69412))+~P1(f318(f318(f226(a1),x69411),f318(f91(a1),x69412)))
% 109.14/108.85 [6946]P1(f318(x69461,x69462))+~P1(f318(x69461,f318(a22,f811(x69461,x69462))))+~P1(f318(f318(f320(a911),x69462),f233(f918(a911,a909))))
% 109.14/108.85 [6956]E(x69561,f2(a1))+E(f39(a1,x69562,x69561),f2(a1))+E(f318(f318(f3(a1),f318(f72(a1),f318(f318(f30(a1),x69562),x69561))),f71(a1)),f318(f318(f30(a1),x69562),f318(f72(a1),x69561)))
% 109.14/108.85 [6968]~P1(f318(f318(f225(a1),f2(a1)),x69681))+~P1(f318(f318(f226(a911),f318(a95,x69681)),x69682))+P1(f318(f318(f226(a1),x69681),f318(f91(a1),x69682)))
% 109.14/108.85 [7006]~P1(f318(f318(f225(a911),f318(a95,x70061)),f318(a95,x70062)))+~P1(f318(f318(f225(a1),f2(a1)),x70062))+P1(f318(f318(f225(a1),x70061),x70062))
% 109.14/108.85 [7007]~P1(f318(f318(f225(a911),f318(a95,x70071)),f318(a95,x70072)))+~P1(f318(f318(f226(a1),f2(a1)),x70071))+P1(f318(f318(f225(a1),x70071),x70072))
% 109.14/108.85 [7008]~P1(f318(f318(f226(a911),f318(a95,x70081)),f318(a95,x70082)))+~P1(f318(f318(f225(a1),f2(a1)),x70081))+P1(f318(f318(f226(a1),x70081),x70082))
% 109.14/108.85 [7009]~P1(f318(f318(f226(a911),f318(a95,x70091)),f318(a95,x70092)))+~P1(f318(f318(f226(a1),f2(a1)),x70092))+P1(f318(f318(f226(a1),x70091),x70092))
% 109.14/108.85 [7036]P1(f318(f318(f225(a1),x70361),x70362))+~P1(f318(f318(f225(a911),f318(f94(a911),x70361)),f318(f94(a911),x70362)))+P1(f318(f318(f225(a1),x70361),a76))
% 109.14/108.85 [7063]P1(f318(f318(f225(a1),f2(a1)),f39(a1,x70631,x70632)))+~P1(f318(f318(f225(a1),f2(a1)),x70632))+~P1(f318(f318(f225(a1),f2(a1)),x70631))
% 109.14/108.85 [7161]P1(f318(f318(f226(a1),a76),x71611))+~P1(f318(f318(f226(a1),x71612),x71611))+~P1(f318(f318(f226(a911),f318(f94(a911),x71612)),f318(f94(a911),x71611)))
% 109.14/108.85 [7215]E(f318(f318(f243(a1,a1),f318(f318(f30(a1),x72151),x72152)),f39(a1,x72151,x72152)),f44(x72151,x72152))+~P1(f318(f318(f226(a1),x72151),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x72152))
% 109.14/108.85 [7234]E(f318(f318(f243(a1,a1),f318(f318(f30(a1),x72341),x72342)),f39(a1,x72341,x72342)),f41(x72341,x72342))+~P1(f318(f318(f225(a1),f2(a1)),x72342))+~P1(f318(f318(f225(a1),f2(a1)),x72341))
% 109.14/108.85 [7288]~P101(x72882)+E(x72881,f104(x72882))+E(f318(f133(x72882,x72882,f74(x72882),f318(f132(x72882),x72881)),f318(f162(x72882),x72881)),f318(f57(x72882,f74(x72882)),f318(f163(x72882),x72881)))
% 109.14/108.85 [7405]~E(x74051,f2(a911))+E(f318(f133(a911,a911,f73(a911),x74051),x74052),f2(a911))+P1(f318(f318(f320(a911),f681(x74052,x74051)),f318(f163(a911),x74052)))
% 109.14/108.85 [7454]~P1(f318(f318(f225(a1),x74541),f2(a1)))+P1(f318(f318(f225(a1),f318(f318(f30(a1),x74541),x74542)),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x74542))
% 109.14/108.85 [7455]~P1(f318(f318(f226(a1),x74552),f2(a1)))+P1(f318(f318(f225(a1),f318(f318(f30(a1),x74551),x74552)),f2(a1)))+~P1(f318(f318(f225(a1),f2(a1)),x74551))
% 109.14/108.85 [7456]~P1(f318(f318(f226(a1),x74562),f2(a1)))+P1(f318(f318(f226(a1),f318(f318(f30(a1),x74561),x74562)),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x74561))
% 109.14/108.85 [7457]~P1(f318(f318(f226(a1),x74571),f2(a1)))+P1(f318(f318(f226(a1),f318(f318(f30(a1),x74571),x74572)),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x74572))
% 109.14/108.85 [7458]~P1(f318(f318(f226(a1),x74581),f2(a1)))+P1(f318(f318(f226(a1),f318(f318(f30(a1),x74581),x74582)),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x74582))
% 109.14/108.85 [7465]P1(f318(f318(f320(f918(x74651,a909)),f863(x74652,x74651)),x74652))+~P1(f318(f55(f918(x74651,a909)),x74652))+P1(f318(f55(x74651),f31(f918(x74651,a909),x74652)))
% 109.14/108.85 [7546]P25(x75461,x75461,x75462,f233(f918(x75461,a909)))+~E(f318(f301(x75461,x75461,x75462),f233(f918(x75461,a909))),f233(f918(x75461,a909)))+~P1(f318(f55(x75461),f233(f918(x75461,a909))))
% 109.14/108.85 [7666]~P25(x76661,x76661,x76662,f233(f918(x76661,a909)))+E(f318(f301(x76661,x76661,x76662),f233(f918(x76661,a909))),f233(f918(x76661,a909)))+~P1(f318(f55(x76661),f233(f918(x76661,a909))))
% 109.14/108.85 [7689]E(f41(f318(f94(a1),x76891),f318(f94(a1),x76892)),f318(f318(f243(a1,a1),f2(a1)),f318(f94(a1),x76891)))+~P1(f318(f318(f226(a1),f2(a1)),f318(f94(a1),x76892)))+~P1(f318(f318(f226(a1),f318(f94(a1),x76891)),f318(f94(a1),x76892)))
% 109.14/108.85 [7803]E(f318(f318(f30(a1),x78031),x78032),f318(f94(a1),a88))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),x78031),x78032)),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x78031))
% 109.14/108.85 [7860]~P1(f318(f318(f226(a1),x78602),f2(a1)))+~P1(f318(f318(f226(a1),f318(f318(f30(a1),x78601),x78602)),f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x78601))
% 109.14/108.85 [7865]E(f318(f318(f73(a1),x78651),x78652),f39(a1,x78651,x78652))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),x78651),x78652)),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x78651))
% 109.14/108.85 [7868]P1(f318(f318(f226(a1),x78681),f2(a1)))+~P1(f318(f318(f226(a1),f318(f318(f30(a1),x78681),x78682)),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x78682))
% 109.14/108.85 [8559]~P4(x85591)+P13(x85591,x85592)+~P1(f318(f318(f225(x85591),f318(f318(f155(x85591),x85592),f704(x85592,x85591))),f318(f318(f155(x85591),x85592),f705(x85592,x85591))))
% 109.14/108.85 [8560]~P4(x85601)+P13(x85601,x85602)+~P1(f318(f318(f225(x85601),f318(f318(f155(x85601),x85602),f711(x85602,x85601))),f318(f318(f155(x85601),x85602),f716(x85602,x85601))))
% 109.14/108.85 [5816]E(x58161,f2(a1))+~E(f39(a1,x58162,x58161),f2(a1))+E(f318(f318(f30(a1),x58162),f318(f72(a1),x58161)),f318(f72(a1),f318(f318(f30(a1),x58162),x58161)))
% 109.14/108.85 [5834]~P43(x58342)+~P43(x58341)+P43(f318(f318(f101(f918(a1,a909)),x58341),x58342))
% 109.14/108.85 [5835]~P43(x58352)+~P43(x58351)+P43(f318(f318(f92(f918(a1,a909)),x58351),x58352))
% 109.14/108.85 [5853]~P99(x58531)+~P72(x58531)+E(f318(f72(x58531),f318(f318(f282(x58531),f71(x58531)),x58532)),f318(f318(f282(x58531),f318(f94(x58531),a88)),x58532))
% 109.14/108.85 [5972]E(x59721,f2(a1))+~E(f39(a1,x59722,x59721),f2(a1))+E(f318(f318(f30(a1),f318(f72(a1),x59722)),x59721),f318(f72(a1),f318(f318(f30(a1),x59722),x59721)))
% 109.14/108.85 [6113]~P4(x61131)+P13(x61131,x61132)+P1(f318(f318(f226(a911),f705(x61132,x61131)),f318(f180(f912(x61131)),x61132)))
% 109.14/108.85 [6114]~P4(x61141)+P13(x61141,x61142)+P1(f318(f318(f226(a911),f716(x61142,x61141)),f318(f180(f912(x61141)),x61142)))
% 109.14/108.85 [6275]~P99(x62751)+~E(f318(f94(x62751),x62752),f2(x62751))+P30(x62751,f318(f94(x62751),f318(f318(f73(a1),x62752),f318(f72(a1),a76))))
% 109.14/108.85 [6276]~P99(x62761)+~E(f318(f94(x62761),x62762),f2(x62761))+P30(x62761,f318(f94(x62761),f318(f318(f73(a1),a76),f318(f72(a1),x62762))))
% 109.14/108.85 [6278]E(f318(a45,f41(f318(f72(a1),x62781),f318(f72(a1),x62782))),f40(x62781,x62782))+P1(f318(f318(f225(a1),f2(a1)),x62781))+P1(f318(f318(f226(a1),f2(a1)),x62782))
% 109.14/108.85 [6402]~E(x64022,f2(a911))+~E(x64021,f2(a911))+P1(f318(f318(f225(a1),f318(f91(a1),x64021)),f318(f72(a1),f318(f91(a1),x64022))))
% 109.14/108.85 [6431]E(f318(f318(f73(a911),f318(f94(a911),x64311)),f318(f94(a911),x64312)),f318(f94(a911),f318(f318(f73(a1),x64311),x64312)))+P1(f318(f318(f226(a1),x64311),a76))+P1(f318(f318(f226(a1),x64312),a76))
% 109.14/108.85 [6562]~P83(x65621)+~P1(f318(f318(f225(x65621),f2(x65621)),x65622))+P1(f318(f318(f225(x65621),f318(f72(x65621),x65622)),x65622))
% 109.14/108.85 [6563]~P83(x65631)+~P1(f318(f318(f226(x65631),f2(x65631)),x65632))+P1(f318(f318(f226(x65631),f318(f72(x65631),x65632)),x65632))
% 109.14/108.85 [6741]E(f318(f318(f3(a911),f318(a95,x67411)),f318(a95,x67412)),f318(a95,f318(f318(f3(a1),x67411),x67412)))+~P1(f318(f318(f225(a1),f2(a1)),x67412))+~P1(f318(f318(f225(a1),x67412),x67411))
% 109.14/108.85 [6775]E(f318(a95,f39(a1,f318(f94(a1),x67751),f318(f94(a1),x67752))),f39(a911,f318(f94(a911),x67751),f318(f94(a911),x67752)))+P1(f318(a184,f318(f94(a1),x67751)))+P1(f318(a184,f318(f94(a1),x67752)))
% 109.14/108.85 [6792]~P83(x67921)+P1(f318(f318(f225(x67921),f2(x67921)),x67922))+~P1(f318(f318(f225(x67921),f318(f72(x67921),x67922)),x67922))
% 109.14/108.85 [6793]~P83(x67931)+P1(f318(f318(f226(x67931),f2(x67931)),x67932))+~P1(f318(f318(f226(x67931),f318(f72(x67931),x67932)),x67932))
% 109.14/108.85 [6805]~P83(x68051)+~P1(f318(f318(f225(x68051),f2(x68051)),x68052))+P1(f318(f318(f225(x68051),f2(x68051)),f318(f318(f73(x68051),x68052),x68052)))
% 109.14/108.85 [6808]~P83(x68081)+~P1(f318(f318(f226(x68081),f2(x68081)),x68082))+P1(f318(f318(f226(x68081),f2(x68081)),f318(f318(f73(x68081),x68082),x68082)))
% 109.14/108.85 [6818]E(f318(f318(f73(a911),f318(a95,x68181)),f318(a95,x68182)),f318(a95,f318(f318(f73(a1),x68181),x68182)))+~P1(f318(f318(f225(a1),f2(a1)),x68182))+~P1(f318(f318(f225(a1),f2(a1)),x68181))
% 109.14/108.85 [6819]E(f318(f318(f73(a911),f318(a95,x68191)),f318(a95,x68192)),f318(a95,f318(f318(f73(a1),x68191),x68192)))+~P1(f318(f318(f225(a1),f2(a1)),x68192))+~P1(f318(f318(f225(a1),f2(a1)),x68191))
% 109.14/108.85 [6820]E(f318(f318(f74(a911),f318(a95,x68201)),f318(a95,x68202)),f318(a95,f318(f318(f74(a1),x68201),x68202)))+~P1(f318(f318(f225(a1),f2(a1)),x68202))+~P1(f318(f318(f225(a1),f2(a1)),x68201))
% 109.14/108.85 [6821]E(f318(f318(f30(a911),f318(a95,x68211)),f318(a95,x68212)),f318(a95,f318(f318(f30(a1),x68211),x68212)))+~P1(f318(f318(f225(a1),f2(a1)),x68212))+~P1(f318(f318(f225(a1),f2(a1)),x68211))
% 109.14/108.85 [6831]E(x68311,f2(a911))+P1(f318(f318(f226(a911),f2(a911)),x68312))+~P1(f318(f318(f226(a911),f2(a911)),f318(f318(f235(a911),x68312),x68311)))
% 109.14/108.85 [6866]~P99(x68661)+E(f318(f94(x68661),x68662),f2(x68661))+~P30(x68661,f318(f94(x68661),f318(f318(f73(a1),a76),f318(f72(a1),x68662))))
% 109.14/108.85 [6867]~P99(x68671)+E(f318(f94(x68671),x68672),f2(x68671))+~P30(x68671,f318(f94(x68671),f318(f318(f73(a1),x68672),f318(f72(a1),a76))))
% 109.14/108.85 [6919]~P1(f318(f55(x69191),x69192))+~P1(f318(f55(x69191),f233(f918(x69191,a909))))+P1(f318(f55(x69191),f318(f72(f918(x69191,a909)),x69192)))
% 109.14/108.85 [6942]~P1(f318(f318(f226(a1),f2(a1)),x69422))+~P1(f318(f318(f225(a1),x69422),x69421))+P1(f318(f318(f226(a1),f2(a1)),f318(f318(f30(a1),x69421),x69422)))
% 109.14/108.85 [6943]~P1(f318(f318(f225(a1),x69431),f2(a1)))+~P1(f318(f318(f226(a1),x69432),f2(a1)))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f30(a1),x69431),x69432)))
% 109.14/108.85 [6980]~P1(f318(f318(f225(a1),f2(a1)),x69802))+~P1(f318(f318(f225(a1),f2(a1)),x69801))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),x69801),x69802)))
% 109.14/108.85 [6981]~P1(f318(f318(f225(a1),f2(a1)),x69812))+~P1(f318(f318(f225(a1),f2(a1)),x69811))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f74(a1),x69811),x69812)))
% 109.14/108.85 [6982]~P1(f318(f318(f225(a1),f2(a1)),x69822))+~P1(f318(f318(f225(a1),f2(a1)),x69821))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f30(a1),x69821),x69822)))
% 109.14/108.85 [6983]~P1(f318(f318(f225(a1),f2(a1)),x69831))+~P1(f318(f318(f226(a1),f2(a1)),x69832))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f30(a1),x69831),x69832)))
% 109.14/108.85 [6984]~P1(f318(f318(f226(a911),f2(a911)),x69842))+~P1(f318(f318(f226(a911),f2(a911)),x69841))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f74(a911),x69841),x69842)))
% 109.14/108.85 [7050]E(x70501,f2(a1))+E(f39(a1,x70502,x70501),f2(a1))+E(f318(f318(f3(a1),f318(f72(a1),f318(f318(f30(a1),x70502),x70501))),f71(a1)),f318(f318(f30(a1),f318(f72(a1),x70502)),x70501))
% 109.14/108.85 [7107]P1(f318(f318(f226(a911),f2(a911)),x71071))+P1(f318(f318(f226(a911),f2(a911)),x71072))+~P1(f318(f318(f226(a911),f2(a911)),f318(f318(f73(a911),x71072),x71071)))
% 109.14/108.85 [7111]~P83(x71111)+P1(f318(f318(f225(x71111),f2(x71111)),x71112))+~P1(f318(f318(f225(x71111),f2(x71111)),f318(f318(f73(x71111),x71112),x71112)))
% 109.14/108.85 [7112]~P83(x71121)+P1(f318(f318(f226(x71121),f2(x71121)),x71122))+~P1(f318(f318(f226(x71121),f2(x71121)),f318(f318(f73(x71121),x71122),x71122)))
% 109.14/108.85 [7162]~P1(f318(f55(x71621),x71622))+P1(f318(f55(x71621),f233(f918(x71621,a909))))+~P1(f318(f55(x71621),f318(f72(f918(x71621,a909)),x71622)))
% 109.14/108.85 [7226]P1(f318(f318(f225(a1),x72261),f2(a1)))+~P1(f318(f318(f226(a1),x72262),f2(a1)))+~P1(f318(f318(f225(a1),f2(a1)),f318(f318(f30(a1),x72261),x72262)))
% 109.14/108.85 [7232]~P1(f318(f318(f226(a1),f2(a1)),x72321))+P1(f318(f318(f225(a1),x72321),x72322))+~P1(f318(f318(f226(a1),f2(a1)),f318(f318(f30(a1),x72322),x72321)))
% 109.14/108.85 [7233]~P1(f318(f318(f225(a1),f2(a1)),x72332))+P1(f318(f318(f225(a1),x72331),x72332))+~P1(f318(f318(f226(a1),f2(a1)),f318(f318(f30(a1),x72332),x72331)))
% 109.14/108.85 [7263]P1(f318(f318(f225(a1),f2(a1)),x72631))+~P1(f318(f318(f226(a1),f2(a1)),x72632))+~P1(f318(f318(f225(a1),f2(a1)),f318(f318(f30(a1),x72631),x72632)))
% 109.14/108.85 [7264]P1(f318(f318(f226(a1),f2(a1)),x72641))+~P1(f318(f318(f225(a1),f2(a1)),x72642))+~P1(f318(f318(f226(a1),f2(a1)),f318(f318(f30(a1),x72642),x72641)))
% 109.14/108.85 [7367]E(f207(x73671,x73672),x73671)+~E(x73672,f2(a911))+~P1(f318(f306(f917(a911,a911),a210),f318(f318(f243(a911,a911),x73671),x73672)))
% 109.14/108.85 [7565]E(f169(x75651,x75652),f104(a1))+P1(f318(f318(f225(a1),x75651),x75652))+~P1(f318(f306(f917(a1,a1),a173),f318(f318(f243(a1,a1),x75651),x75652)))
% 109.14/108.85 [7586]E(f318(f318(f243(a1,a1),f318(f94(a1),a88)),f318(f318(f73(a1),x75861),x75862)),f44(x75861,x75862))+~P1(f318(f318(f226(a1),f2(a1)),x75862))+~P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),x75861),x75862)))
% 109.14/108.85 [7616]E(x76161,f2(a911))+E(f207(x76161,f39(a911,x76162,x76161)),f207(x76162,x76161))+~P1(f318(f306(f917(a911,a911),a210),f318(f318(f243(a911,a911),x76162),x76161)))
% 109.14/108.85 [7668]E(f119(x76681,x76682),f106(a1))+~P1(f318(f318(f226(a1),x76681),x76682))+~P1(f318(f306(f917(a1,a1),a124),f318(f318(f243(a1,a1),x76681),x76682)))
% 109.14/108.85 [7697]~P1(f318(f55(x76972),f233(f918(x76972,a909))))+~P1(f318(f55(x76971),f233(f918(x76971,a909))))+P1(f318(f55(f917(x76971,x76972)),f233(f918(f917(x76971,x76972),a909))))
% 109.14/108.85 [7698]~P1(f318(f55(x76982),f233(f918(x76982,a909))))+~P1(f318(f55(x76981),f233(f918(x76981,a909))))+P1(f318(f55(f919(x76981,x76982)),f233(f918(f919(x76981,x76982),a909))))
% 109.14/108.85 [7767]~P1(f318(f318(f226(a911),f318(a103,f2(a911))),x77671))+~P1(f318(f318(f226(a911),f318(a103,f2(a911))),x77672))+P1(f318(f318(f226(a911),x77671),f318(f318(f74(a911),x77672),x77671)))
% 109.14/108.85 [7768]~P1(f318(f318(f226(a911),f318(a103,f2(a911))),x77681))+~P1(f318(f318(f226(a911),f318(a103,f2(a911))),x77682))+P1(f318(f318(f226(a911),x77681),f318(f318(f74(a911),x77681),x77682)))
% 109.14/108.85 [7802]E(f318(f29(x78021),f233(f918(x78021,a909))),f318(a103,f2(a911)))+P1(f318(f55(x78022),f233(f918(x78022,a909))))+~P1(f318(f55(f918(x78022,x78021)),f233(f918(f918(x78022,x78021),a909))))
% 109.14/108.85 [7853]E(f41(x78531,x78532),f318(f318(f243(a1,a1),f2(a1)),x78531))+~P1(f318(f318(f226(a1),x78531),x78532))+~P1(f318(f306(f917(a1,a1),a52),f318(f318(f243(a1,a1),x78531),x78532)))
% 109.14/108.85 [7857]E(f206(f318(f72(a1),x78571),f318(f72(a1),x78572)),f206(x78571,x78572))+~P1(f318(f318(f226(a1),x78572),f2(a1)))+~P1(f318(f306(f917(a1,a1),a212),f318(f318(f243(a1,a1),x78571),x78572)))
% 109.14/108.85 [7878]E(f41(x78781,x78782),f318(f318(f243(a1,a1),f2(a1)),x78781))+~P1(f318(f318(f225(a1),x78782),f2(a1)))+~P1(f318(f306(f917(a1,a1),a52),f318(f318(f243(a1,a1),x78781),x78782)))
% 109.14/108.85 [7931]~P1(f318(f318(f225(a911),f318(a103,f2(a911))),x79311))+~P1(f318(f318(f225(a911),f318(a103,f2(a911))),x79312))+P1(f318(f318(f225(a911),f318(a103,f2(a911))),f318(f318(f74(a911),x79311),x79312)))
% 109.14/108.85 [7932]~P1(f318(f318(f226(a911),f318(a103,f2(a911))),x79322))+~P1(f318(f318(f226(a911),f318(a103,f2(a911))),x79321))+P1(f318(f318(f226(a911),f318(a103,f2(a911))),f318(f318(f74(a911),x79321),x79322)))
% 109.14/108.85 [8088]E(f318(f318(f243(a1,a1),f318(f94(a1),a88)),f318(f318(f73(a1),x80881),x80882)),f44(x80881,x80882))+~P1(f318(f318(f225(a1),x80882),f2(a1)))+~P1(f318(f306(f917(a1,a1),a46),f318(f318(f243(a1,a1),x80881),x80882)))
% 109.14/108.85 [8110]E(f107(a1,f318(f120(a1),x81101),f119(x81102,f318(f318(f73(a1),x81101),f71(a1)))),f119(x81102,x81101))+P1(f318(f318(f226(a1),x81102),x81101))+~P1(f318(f306(f917(a1,a1),a124),f318(f318(f243(a1,a1),x81102),x81101)))
% 109.14/108.85 [8122]E(f318(f318(f142(a1),x81221),f169(f318(f318(f73(a1),x81221),f71(a1)),x81222)),f169(x81221,x81222))+~P1(f318(f318(f225(a1),x81221),x81222))+~P1(f318(f306(f917(a1,a1),a173),f318(f318(f243(a1,a1),x81221),x81222)))
% 109.14/108.85 [8276]~P113(x82761)+P42(a911,x82761,x82762)+~P1(f318(f318(f225(x82761),f318(x82762,f906(x82762,x82761))),f318(x82762,f318(a103,f906(x82762,x82761)))))
% 109.14/108.85 [8409]E(f318(f318(f243(a1,a1),f318(f94(a1),a88)),f318(f318(f73(a1),x84091),x84092)),f44(x84091,x84092))+~P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),x84091),x84092)))+~P1(f318(f306(f917(a1,a1),a46),f318(f318(f243(a1,a1),x84091),x84092)))
% 109.14/108.85 [8609]E(x86091,f104(x86092))+~P1(f318(f128(x86092),x86091))+E(f168(x86092,f318(f318(f10(a909,a909,x86092),a313),f318(f318(f9(x86092,x86092,a909),a315),f135(x86092,x86091))),x86091),f105(x86092,x86091))
% 109.14/108.85 [8683]E(f318(f318(f243(a1,a1),f318(f94(a1),a88)),f318(f318(f73(a1),f318(f94(a1),x86831)),f318(f94(a1),x86832))),f44(f318(f94(a1),x86831),f318(f94(a1),x86832)))+~P1(f318(f318(f226(a1),f2(a1)),f318(f94(a1),x86832)))+~P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),f318(f94(a1),x86831)),f318(f94(a1),x86832))))
% 109.14/108.85 [8708]~P43(x87082)+~P43(x87081)+E(f318(f301(a911,a1,f91(a1)),f318(f318(f101(f918(a911,a909)),f318(f301(a1,a911,a95),x87081)),f318(f301(a1,a911,a95),x87082))),f318(f318(f101(f918(a1,a909)),x87081),x87082))
% 109.14/108.85 [8709]~P43(x87092)+~P43(x87091)+E(f318(f301(a911,a1,f91(a1)),f318(f318(f92(f918(a911,a909)),f318(f301(a1,a911,a95),x87091)),f318(f301(a1,a911,a95),x87092))),f318(f318(f92(f918(a1,a909)),x87091),x87092))
% 109.14/108.85 [9444]~P99(x94441)+~E(f318(f94(x94441),x94442),f71(x94441))+P30(x94441,f318(f94(x94441),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f318(f72(a1),x94442))))
% 109.14/108.85 [9669]~P99(x96691)+E(f318(f94(x96691),x96692),f71(x96691))+~P30(x96691,f318(f94(x96691),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),f318(f72(a1),x96692))))
% 109.14/108.85 [10433]E(x104331,f2(a1))+E(x104332,f2(a1))+E(f318(f249(a1,a1,a1,a1,f25(a1),f318(f74(a1),f75(a1,x104332))),f318(f318(f318(f85(f917(a1,a1)),f318(f318(a315,f75(a1,x104331)),f75(a1,x104332))),f47(x104331,x104332)),f318(f318(f248(a1,a1,f917(a1,a1)),f318(f318(f20(a1,f918(a1,f917(a1,a1)),f918(a1,f917(a1,a1))),f318(f318(f10(f918(a1,f918(f917(a1,a1),f917(a1,a1))),f918(f918(a1,f917(a1,a1)),f918(a1,f917(a1,a1))),a1),f20(a1,f917(a1,a1),f917(a1,a1))),f318(f318(f10(f917(a1,a1),f918(a1,f918(f917(a1,a1),f917(a1,a1))),a1),f318(f9(a1,f917(a1,a1),f918(f917(a1,a1),f917(a1,a1))),f318(f318(f10(a909,f918(f917(a1,a1),f918(f917(a1,a1),f917(a1,a1))),a1),f85(f917(a1,a1))),f318(f318(f9(a1,a1,a909),a315),f2(a1))))),f318(f318(f9(a1,a1,f917(a1,a1)),f318(f318(f10(a1,f918(a1,f917(a1,a1)),a1),f243(a1,a1)),f72(a1))),f2(a1))))),f318(f318(f9(a1,f918(a1,a1),f918(a1,f917(a1,a1))),f318(f318(f10(f918(a1,f917(a1,a1)),f918(f918(a1,a1),f918(a1,f917(a1,a1))),a1),f10(a1,f917(a1,a1),a1)),f318(f318(f10(a1,f918(a1,f917(a1,a1)),a1),f243(a1,a1)),f318(f318(f9(a1,a1,a1),f318(f318(f10(a1,f918(a1,a1),a1),f3(a1)),f72(a1))),f71(a1))))),f318(f3(a1),f318(f69(a1),x104332))))),f47(x104331,x104332)))),f40(x104331,x104332))
% 109.14/108.85 [10434]E(x104341,f2(a1))+E(x104342,f2(a1))+E(f318(f249(a1,a1,a1,a1,f25(a1),f318(f74(a1),f75(a1,x104342))),f318(f318(f318(f85(f917(a1,a1)),f318(f318(a317,f318(f318(a316,f318(f318(f226(a1),f2(a1)),x104342)),f318(f318(f225(a1),f2(a1)),x104341))),f318(f318(a316,f318(f318(f226(a1),x104342),f2(a1))),f318(f318(f226(a1),x104341),f2(a1))))),f47(x104341,x104342)),f318(f318(f248(a1,a1,f917(a1,a1)),f318(f318(f20(a1,f918(a1,f917(a1,a1)),f918(a1,f917(a1,a1))),f318(f318(f10(f918(a1,f918(f917(a1,a1),f917(a1,a1))),f918(f918(a1,f917(a1,a1)),f918(a1,f917(a1,a1))),a1),f20(a1,f917(a1,a1),f917(a1,a1))),f318(f318(f10(f917(a1,a1),f918(a1,f918(f917(a1,a1),f917(a1,a1))),a1),f318(f9(a1,f917(a1,a1),f918(f917(a1,a1),f917(a1,a1))),f318(f318(f10(a909,f918(f917(a1,a1),f918(f917(a1,a1),f917(a1,a1))),a1),f85(f917(a1,a1))),f318(f318(f9(a1,a1,a909),a315),f2(a1))))),f318(f318(f9(a1,a1,f917(a1,a1)),f318(f318(f10(a1,f918(a1,f917(a1,a1)),a1),f243(a1,a1)),f72(a1))),f2(a1))))),f318(f318(f9(a1,f918(a1,a1),f918(a1,f917(a1,a1))),f318(f318(f10(f918(a1,f917(a1,a1)),f918(f918(a1,a1),f918(a1,f917(a1,a1))),a1),f10(a1,f917(a1,a1),a1)),f318(f318(f10(a1,f918(a1,f917(a1,a1)),a1),f243(a1,a1)),f318(f318(f9(a1,a1,a1),f318(f318(f10(a1,f918(a1,a1),a1),f3(a1)),f72(a1))),f71(a1))))),f318(f3(a1),f318(f69(a1),x104342))))),f47(x104341,x104342)))),f40(x104341,x104342))
% 109.14/108.85 [5842]~P116(x58421)+~P99(x58421)+E(f318(f69(x58421),f318(f318(f235(x58421),f318(f94(x58421),a88)),x58422)),f71(x58421))
% 109.14/108.85 [6344]~P144(x63441)+~P1(f318(f318(f226(a1),x63442),f2(a1)))+E(f318(f72(x63441),f318(f91(x63441),f318(a95,f318(f72(a1),x63442)))),f318(f93(x63441),x63442))
% 109.14/108.85 [6546]P1(f318(f318(f225(a90),x65461),f71(a90)))+E(f318(f318(f73(a90),f71(a90)),f263(x65461,f318(f318(f30(a90),x65462),x65461))),f263(x65461,x65462))+P1(f318(f318(f226(a90),x65462),x65461))
% 109.14/108.85 [7151]~P98(x71511)+~P1(f318(f318(f320(x71511),x71512),f100(x71511)))+~E(f318(f318(f73(x71511),f318(f318(f73(x71511),f71(x71511)),x71512)),x71512),f2(x71511))
% 109.14/108.85 [7265]~P1(f318(f318(f225(a1),x72652),f2(a1)))+~P1(f318(f318(f226(a1),x72651),f2(a1)))+E(f318(f242(a1,a1),f318(a45,f41(f318(f72(a1),x72651),f318(f72(a1),x72652)))),f318(f318(f30(a1),x72651),x72652))
% 109.14/108.85 [7282]~P1(f318(f318(f225(a1),x72822),f2(a1)))+~P1(f318(f318(f226(a1),x72821),f2(a1)))+E(f318(f247(a1,a1),f318(a45,f41(f318(f72(a1),x72821),f318(f72(a1),x72822)))),f39(a1,x72821,x72822))
% 109.14/108.85 [7290]~P1(f318(f318(f226(a1),x72902),f2(a1)))+E(f318(f242(a1,a1),f318(a45,f44(f318(f72(a1),x72901),f318(f72(a1),x72902)))),f318(f318(f30(a1),x72901),x72902))+~P1(f318(f318(f226(a1),f2(a1)),x72901))
% 109.14/108.85 [7308]~P1(f318(f318(f226(a1),x73082),f2(a1)))+E(f318(f247(a1,a1),f318(a45,f44(f318(f72(a1),x73081),f318(f72(a1),x73082)))),f39(a1,x73081,x73082))+~P1(f318(f318(f226(a1),f2(a1)),x73081))
% 109.14/108.85 [7361]E(f318(f318(f30(a1),f318(f318(f235(a1),x73611),x73612)),x73611),f318(f318(f235(a1),x73611),f318(f318(f3(a911),x73612),f318(a103,f2(a911)))))+~P1(f318(f318(f226(a911),f2(a911)),x73612))+~P1(f318(f318(f226(a1),f2(a1)),x73611))
% 109.14/108.85 [7462]~P1(f318(f318(f226(a911),f2(a911)),x74621))+~P1(f318(f318(f226(a911),f2(a911)),x74622))+P1(f318(f318(f226(a911),f318(f318(f3(a911),x74621),x74622)),x74621))
% 109.14/108.85 [7463]~P1(f318(f318(f226(a911),f2(a911)),x74631))+~P1(f318(f318(f226(a911),f71(a911)),x74632))+P1(f318(f318(f226(a911),f318(f318(f30(a911),x74631),x74632)),x74631))
% 109.14/108.85 [7464]~P1(f318(f318(f226(a1),f2(a1)),x74641))+~P1(f318(f318(f226(a1),f71(a1)),x74642))+P1(f318(f318(f226(a1),f318(f318(f30(a1),x74641),x74642)),x74641))
% 109.14/108.85 [7592]E(x75921,f2(a911))+~E(x75922,f2(a1))+~P1(f318(f318(f226(a1),f2(a1)),f318(f318(f235(a1),f318(f69(a1),x75922)),x75921)))
% 109.14/108.85 [7962]~P1(f318(x79621,x79622))+P1(f318(x79621,f2(a911)))+E(f318(a103,f229(a911,f318(f318(f10(a911,a909,a911),x79621),a103))),f229(a911,x79621))
% 109.14/108.85 [8013]~E(x80132,f104(f912(x80131)))+E(f318(f180(f912(f912(x80131))),f170(x80131,x80132)),f2(a911))+~P13(a911,f318(f159(a911),f318(f318(f145(f912(x80131),a911),f180(f912(x80131))),x80132)))
% 109.14/108.85 [8262]P1(f318(x82621,x82622))+~P1(f318(x82621,f318(a97,f534(x82621,x82622))))+~P1(f318(f318(f320(f918(f917(a911,a911),a909)),x82622),a89))
% 109.14/108.85 [8280]E(x82801,f104(f912(x82802)))+E(f318(f180(f912(x82802)),f318(f318(f155(f912(x82802)),x82801),f2(a911))),f318(f180(f912(f912(x82802))),f170(x82802,x82801)))+~P13(a911,f318(f159(a911),f318(f318(f145(f912(x82802),a911),f180(f912(x82802))),x82801)))
% 109.14/108.85 [8418]~P40(x84181,x84182)+~P41(x84181,x84182)+P40(x84181,f318(f318(f3(f918(f917(x84181,x84181),a909)),x84182),f298(x84181,f179(f918(f917(x84181,x84181),a909)))))
% 109.14/108.85 [8988]~P1(f318(f55(x89881),f318(f253(x89881),x89882)))+~P1(f318(f55(x89881),f233(f918(x89881,a909))))+P1(f318(f55(x89881),f318(f253(x89881),f318(f318(f10(a909,a909,x89881),a313),x89882))))
% 109.14/108.85 [9055]E(f318(f318(f243(a911,a911),f318(a103,f318(f318(f30(a911),f318(f318(f3(a911),x90551),x90552)),x90552))),f39(a911,f318(f318(f3(a911),x90551),x90552),x90552)),f78(f917(a911,a911),f42(x90551,x90552)))+~P1(f318(f318(f226(a911),f2(a911)),x90552))+~P1(f318(f318(f225(a911),x90552),x90551))
% 109.14/108.85 [9337]~P1(f318(f55(x93371),f318(f253(x93371),x93372)))+P1(f318(f55(x93371),f233(f918(x93371,a909))))+~P1(f318(f55(x93371),f318(f253(x93371),f318(f318(f10(a909,a909,x93371),a313),x93372))))
% 109.14/108.85 [10085]P27(x100851,x100852)+~P39(x100851,f318(f242(f918(f917(x100851,x100851),a909),f918(f917(x100851,x100851),a909)),x100852))+~P1(f318(f318(f225(f918(f917(x100851,x100851),a909)),f318(f318(f280(x100851,x100851,x100851),f318(f242(f918(f917(x100851,x100851),a909),f918(f917(x100851,x100851),a909)),x100852)),f318(f247(f918(f917(x100851,x100851),a909),f918(f917(x100851,x100851),a909)),x100852))),f318(f242(f918(f917(x100851,x100851),a909),f918(f917(x100851,x100851),a909)),x100852)))
% 109.14/108.85 [10163]~E(f288(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x101632,x101631),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x101632),x101631))+P1(f318(f318(f278(a911),x101631),x101632))
% 109.14/108.85 [10164]~E(f291(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x101642,x101641),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x101642),x101641))+P1(f318(f318(f278(a911),x101641),x101642))
% 109.14/108.85 [10165]~E(f288(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x101652,x101651),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x101652),x101651))+P1(f318(f318(f278(a911),x101651),x101652))
% 109.14/108.85 [10166]~E(f291(a911,f278(a911),f318(f318(f20(a911,f918(a911,a909),f918(a911,a909)),f318(f318(f10(f918(a911,f918(a909,a909)),f918(f918(a911,a909),f918(a911,a909)),a911),f20(a911,a909,a909)),f318(f318(f10(f918(a911,a909),f918(a911,f918(a909,a909)),a911),f318(f10(a909,f918(a909,a909),a911),a316)),f278(a911)))),f318(f318(f10(f918(a911,a909),f918(a911,a909),a911),f318(f10(a909,a909,a911),a313)),f318(f9(a911,a911,a909),f278(a911)))),x101662,x101661),f179(f918(a911,a909)))+~P1(f318(f318(f278(a911),x101662),x101661))+P1(f318(f318(f278(a911),x101661),x101662))
% 109.14/108.85 [10336]E(f318(f37(f318(f94(a1),x103361)),f41(f318(f94(a1),x103362),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f94(a1),x103361)))),f41(f318(f94(a1),x103362),f318(f94(a1),x103361)))+~P1(f318(f318(f226(a1),f2(a1)),f318(f94(a1),x103361)))+P1(f318(f318(f226(a1),f318(f94(a1),x103362)),f318(f94(a1),x103361)))
% 109.14/108.85 [10340]E(f318(f37(f318(f94(a1),x103401)),f44(f318(f94(a1),x103402),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f94(a1),x103401)))),f44(f318(f94(a1),x103402),f318(f94(a1),x103401)))+~P1(f318(f318(f226(a1),f2(a1)),f318(f94(a1),x103401)))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),f318(f94(a1),x103402)),f318(f94(a1),x103401))))
% 109.14/108.85 [7390]~P1(f318(f318(f226(a911),f2(a911)),x73902))+P1(f318(f318(f226(a911),x73901),x73902))+E(f318(a103,f318(f318(f30(a911),f318(f318(f3(a911),x73901),x73902)),x73902)),f318(f318(f30(a911),x73901),x73902))
% 109.14/108.85 [7391]~P1(f318(f318(f226(a911),f2(a911)),x73912))+P1(f318(f318(f226(a911),x73911),x73912))+E(f318(a103,f318(f318(f30(a911),f318(f318(f3(a911),x73911),x73912)),x73912)),f318(f318(f30(a911),x73911),x73912))
% 109.14/108.85 [7519]~P1(f318(f318(f226(a911),f2(a911)),x75192))+~P1(f318(f318(f225(a911),x75192),x75191))+E(f318(a103,f318(f318(f30(a911),f318(f318(f3(a911),x75191),x75192)),x75192)),f318(f318(f30(a911),x75191),x75192))
% 109.14/108.85 [8584]~P99(x85841)+~P98(x85841)+~P30(x85841,f318(f94(x85841),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x85842)),x85842)))
% 109.14/108.85 [9233]E(x92331,f2(a911))+E(f318(f318(f248(a911,a911,f917(a911,a911)),f318(f318(f10(a911,f918(a911,f917(a911,a911)),a911),f243(a911,a911)),a103)),f78(f917(a911,a911),f42(f318(f318(f3(a911),x92332),x92331),x92331))),f78(f917(a911,a911),f42(x92332,x92331)))+P1(f318(f318(f226(a911),x92332),x92331))
% 109.14/108.85 [9423]~P40(x94231,x94232)+~P55(x94231,x94232)+P1(f318(f318(f225(f918(f917(x94231,x94231),a909)),f318(f318(f280(x94231,x94231,x94231),f318(f277(x94231,x94231),x94232)),x94232)),x94232))
% 109.14/108.85 [9689]P1(f318(x96892,f639(x96892,x96891)))+P1(f318(x96891,f639(x96892,x96891)))+E(f318(f253(a1),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),x96891)),f318(f253(a1),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),x96892)))
% 109.14/108.85 [9693]~P1(f318(x96932,f639(x96932,x96931)))+~P1(f318(x96931,f639(x96932,x96931)))+E(f318(f253(a1),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),x96931)),f318(f253(a1),f318(f318(f20(a1,a909,a909),f318(f318(f10(a909,f918(a909,a909),a1),a316),f318(f225(a1),f2(a1)))),x96932)))
% 109.14/108.85 [7969]~P99(x79691)+~P73(x79691)+E(f318(f318(f282(x79691),x79692),f318(f94(x79691),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),x79692)
% 109.14/108.85 [7970]~P99(x79701)+~P73(x79701)+E(f318(f318(f282(x79701),x79702),f318(f94(x79701),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),x79702)
% 109.14/108.85 [9443]~P99(x94431)+~E(f318(f94(x94431),x94432),f71(x94431))+P30(x94431,f318(f94(x94431),f318(f318(f73(a1),x94432),f318(f72(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))))
% 109.14/108.85 [9670]~P99(x96701)+E(f318(f94(x96701),x96702),f71(x96701))+~P30(x96701,f318(f94(x96701),f318(f318(f73(a1),x96702),f318(f72(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))))
% 109.14/108.85 [10119]~P145(x101191)+~E(x101192,f2(x101191))+E(f318(f318(f235(x101191),x101192),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f2(x101191))
% 109.14/108.85 [10120]~P145(x101201)+~E(x101202,f71(x101201))+E(f318(f318(f235(x101201),x101202),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f71(x101201))
% 109.14/108.85 [10123]~P145(x101231)+~E(x101232,f318(f72(x101231),f71(x101231)))+E(f318(f318(f235(x101231),x101232),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f71(x101231))
% 109.14/108.85 [10129]~P100(x101291)+~P88(x101291)+E(f318(f318(f235(x101291),f318(f94(x101291),x101292)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f318(f74(x101291),f318(f94(x101291),x101292)),f318(f94(x101291),x101292)))
% 109.14/108.85 [10183]~P145(x101832)+E(x101831,f2(x101832))+~E(f318(f318(f235(x101832),x101831),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f2(x101832))
% 109.14/108.85 [10263]~P116(x102632)+E(x102631,f2(x102632))+P1(f318(f318(f226(x102632),f2(x102632)),f318(f318(f235(x102632),x102631),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.85 [10309]~P116(x103092)+~E(x103091,f2(x103092))+~P1(f318(f318(f226(x103092),f2(x103092)),f318(f318(f235(x103092),x103091),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.85 [10329]P1(f318(f318(f225(a1),x103291),f2(a1)))+P1(f318(f318(f226(a1),x103292),x103291))+E(f318(f37(x103291),f41(x103292,f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103291))),f41(x103292,x103291))
% 109.14/108.85 [10330]~P1(f318(f318(f226(a1),f2(a1)),x103301))+P1(f318(f318(f226(a1),x103302),x103301))+E(f318(f37(x103301),f41(x103302,f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103301))),f41(x103302,x103301))
% 109.14/108.85 [10331]P1(f318(f318(f225(a1),x103311),f2(a1)))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),x103312),x103311)))+E(f318(f37(x103311),f44(x103312,f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103311))),f44(x103312,x103311))
% 109.14/108.85 [10332]~P1(f318(f318(f226(a1),f2(a1)),x103321))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),x103322),x103321)))+E(f318(f37(x103321),f44(x103322,f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103321))),f44(x103322,x103321))
% 109.14/108.85 [10333]~P114(x103331)+~P1(f318(f318(f225(a1),f2(a1)),x103332))+E(f318(f91(x103331),f318(a95,f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103332))),f318(f318(f73(x103331),f318(f91(x103331),f318(a95,x103332))),f318(f91(x103331),f318(a95,x103332))))
% 109.14/108.85 [5170]~P151(x51701,x51702,x51703)+~E(x51703,f2(a1))+P1(f318(x51701,x51702))
% 109.14/108.85 [5299]~P4(x52991)+~P13(x52991,x52993)+P13(x52991,f161(x52991,x52992,x52993))
% 109.14/108.85 [5300]~P4(x53001)+~P13(x53001,x53003)+P13(x53001,f168(x53001,x53002,x53003))
% 109.14/108.85 [4863]~P66(x48632)+~E(x48633,f318(f72(x48632),x48631))+E(x48631,f318(f72(x48632),x48633))
% 109.14/108.85 [4864]~P66(x48642)+~E(x48643,f318(f72(x48642),x48641))+E(x48641,f318(f72(x48642),x48643))
% 109.14/108.85 [4865]~P66(x48651)+~E(f318(f72(x48651),x48653),x48652)+E(f318(f72(x48651),x48652),x48653)
% 109.14/108.85 [4866]~P66(x48661)+~E(f318(f72(x48661),x48663),x48662)+E(f318(f72(x48661),x48662),x48663)
% 109.14/108.85 [4945]~P4(x49453)+E(x49451,x49452)+~E(f318(f295(x49453),x49451),f318(f295(x49453),x49452))
% 109.14/108.85 [4946]~P4(x49463)+E(x49461,x49462)+~E(f318(f273(x49463),x49461),f318(f273(x49463),x49462))
% 109.14/108.85 [4947]~P4(x49473)+E(x49471,x49472)+~E(f318(f274(x49473),x49471),f318(f274(x49473),x49472))
% 109.14/108.85 [4948]~P4(x49483)+E(x49481,x49482)+~E(f318(f292(x49483),x49481),f318(f292(x49483),x49482))
% 109.14/108.85 [4949]~P96(x49493)+E(x49491,x49492)+~E(f318(f72(x49493),x49491),f318(f72(x49493),x49492))
% 109.14/108.85 [4950]~P66(x49503)+E(x49501,x49502)+~E(f318(f72(x49503),x49501),f318(f72(x49503),x49502))
% 109.14/108.85 [4951]~P110(x49513)+E(x49511,x49512)+~E(f318(f91(x49513),x49511),f318(f91(x49513),x49512))
% 109.14/108.85 [4952]~P98(x49523)+E(x49521,x49522)+~E(f318(f93(x49523),x49521),f318(f93(x49523),x49522))
% 109.14/108.85 [5051]~P71(x50511)+~P1(f318(x50512,x50513))+P1(f318(f50(x50511),x50512))
% 109.14/108.85 [5052]~P71(x50521)+~P1(f318(x50522,x50523))+P1(f318(f50(x50521),x50522))
% 109.14/108.85 [5088]~P71(x50883)+P1(f318(x50881,x50882))+~P1(f318(f51(x50883),x50881))
% 109.14/108.85 [5089]~P71(x50893)+P1(f318(x50891,x50892))+~P1(f318(f51(x50893),x50891))
% 109.14/108.85 [5190]~P152(x51901,x51903,x51902)+~E(x51902,f2(a1))+P1(f318(x51901,f2(a1)))
% 109.14/108.85 [5225]~P119(x52252)+~P1(f318(x52251,x52253))+P1(f318(x52251,f229(x52252,x52251)))
% 109.14/108.85 [5226]~P119(x52262)+~P1(f318(x52261,x52263))+P1(f318(x52261,f229(x52262,x52261)))
% 109.14/108.85 [5233]~E(x52331,f2(a911))+E(f852(x52331,x52332,x52333),f179(f918(x52333,a909)))+~E(f318(f29(x52333),x52332),f318(a103,x52331))
% 109.14/108.85 [5384]~E(x53842,f2(a911))+E(f318(f242(a911,a911),x53841),f2(a911))+~P1(f318(f42(x53843,x53842),x53841))
% 109.14/108.85 [5423]P1(f318(x54231,x54232))+~E(x54233,f318(f91(a1),x54232))+~P1(f318(x54231,f318(a95,x54233)))
% 109.14/108.85 [5906]~E(x59063,f2(a911))+~P1(f318(x59061,x59062))+P1(f318(x59061,f39(a911,x59062,x59063)))
% 109.14/108.85 [5963]~P119(x59631)+~P1(f318(x59632,x59633))+~P1(f318(f318(f226(x59631),x59633),f229(x59631,x59632)))
% 109.14/108.85 [6145]~P111(x61452)+~P111(x61451)+E(f122(x61451,x61452,f123(x61451,x61453),f123(x61452,x61453)),f123(f917(x61451,x61452),x61453))
% 109.14/108.85 [6325]~E(x63253,f2(a911))+P1(f318(x63251,x63252))+~P1(f318(x63251,f39(a911,x63252,x63253)))
% 109.14/108.85 [6337]~P5(x63371)+~P1(f318(f318(f225(x63371),x63372),f318(x63373,x63372)))+P1(f318(f318(f225(x63371),x63372),f87(x63371,x63373)))
% 109.14/108.85 [7005]E(x70051,f2(a911))+~P1(f318(x70052,f375(x70051,x70053,x70052)))+P1(f318(x70052,f39(a911,x70053,x70051)))
% 109.14/108.85 [7117]~P5(x71171)+~P1(f318(f318(f225(x71171),x71172),f339(x71173,x71172,x71171)))+P1(f318(f318(f225(x71171),x71172),f32(x71171,x71173)))
% 109.14/108.85 [7119]~P1(f318(x71191,x71192))+~P1(f318(x71191,f375(x71193,x71192,x71191)))+P1(f318(x71191,f39(a911,x71192,x71193)))
% 109.14/108.85 [7221]E(x72211,f104(x72212))+E(f318(f318(f142(x72212),f685(x72213,x72211,x72212)),f688(x72213,x72211,x72212)),x72211)+~P1(f318(f318(f320(f912(x72212)),x72211),f152(x72212,x72213)))
% 109.14/108.85 [7252]~P144(x72521)+~P1(f318(f318(f320(x72521),x72522),f100(x72521)))+P1(f318(f318(f320(x72521),f318(f318(f235(x72521),x72522),x72523)),f100(x72521)))
% 109.14/108.85 [7564]P39(x75641,x75642)+~P1(f318(f318(f320(x75641),x75643),f594(x75642,x75641)))+P1(f318(f318(f320(x75641),f609(x75642,x75641,x75643)),f594(x75642,x75641)))
% 109.14/108.85 [7831]E(x78311,f104(x78312))+~P1(f318(f318(f320(f912(x78312)),x78311),f152(x78312,x78313)))+P1(f318(f318(f320(f912(x78312)),f688(x78313,x78311,x78312)),f152(x78312,x78313)))
% 109.14/108.85 [7882]E(x78821,f2(a911))+E(f318(f318(f73(a911),f318(f318(f74(a911),x78821),f376(x78821,x78822,x78823))),f375(x78821,x78822,x78823)),x78822)+P1(f318(x78823,f39(a911,x78822,x78821)))
% 109.14/108.85 [7926]~P1(f318(x79263,x79262))+E(f318(f318(f73(a911),f318(f318(f74(a911),x79261),f376(x79261,x79262,x79263))),f375(x79261,x79262,x79263)),x79262)+P1(f318(x79263,f39(a911,x79262,x79261)))
% 109.14/108.85 [8066]P1(f318(f318(f226(a1),x80661),f362(x80662,x80663,x80661)))+P1(f318(f318(x80663,f318(f318(f30(a1),x80662),x80661)),f39(a1,x80662,x80661)))+~P1(f318(f318(f226(a1),x80661),f2(a1)))
% 109.14/108.85 [8335]P1(f318(f318(x83352,f318(f318(f30(a1),x83351),x83353)),f39(a1,x83351,x83353)))+~P1(f318(f318(f226(a1),x83353),f2(a1)))+P1(f318(f318(f225(a1),f362(x83351,x83352,x83353)),f2(a1)))
% 109.14/108.85 [8513]E(f318(f318(f73(a1),f318(f318(f74(a1),x85131),f363(x85132,x85133,x85131))),f362(x85132,x85133,x85131)),x85132)+P1(f318(f318(x85133,f318(f318(f30(a1),x85132),x85131)),f39(a1,x85132,x85131)))+~P1(f318(f318(f226(a1),x85131),f2(a1)))
% 109.14/108.85 [8754]~P1(f318(f318(x87541,f363(x87542,x87541,x87543)),f362(x87542,x87541,x87543)))+P1(f318(f318(x87541,f318(f318(f30(a1),x87542),x87543)),f39(a1,x87542,x87543)))+~P1(f318(f318(f226(a1),x87543),f2(a1)))
% 109.14/108.85 [9002]~P4(x90021)+~P13(x90021,x90023)+P13(x90021,f140(x90021,x90021,f7(x90021),x90022,x90023))
% 109.14/108.85 [9504]~P131(x95042)+E(x95041,f2(x95042))+~P1(f318(f318(f225(x95042),f318(f318(f73(x95042),f318(f318(f74(x95042),x95043),x95043)),f318(f318(f74(x95042),x95041),x95041))),f2(x95042)))
% 109.14/108.85 [9505]~P131(x95052)+E(x95051,f2(x95052))+~P1(f318(f318(f225(x95052),f318(f318(f73(x95052),f318(f318(f74(x95052),x95051),x95051)),f318(f318(f74(x95052),x95053),x95053))),f2(x95052)))
% 109.14/108.85 [10422]~P116(x104221)+~P1(f318(f318(f226(x104221),x104222),f2(x104221)))+P1(f318(f318(f226(x104221),f318(f318(f235(x104221),x104222),f318(a103,f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x104223)))),f2(x104221)))
% 109.14/108.85 [10428]~P116(x104282)+E(x104281,f2(x104282))+~P1(f318(f318(f225(x104282),f318(f318(f73(x104282),f318(f318(f235(x104282),x104283),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x104282),x104281),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))),f2(x104282)))
% 109.14/108.85 [10429]~P116(x104292)+E(x104291,f2(x104292))+~P1(f318(f318(f225(x104292),f318(f318(f73(x104292),f318(f318(f235(x104292),x104291),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x104292),x104293),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))),f2(x104292)))
% 109.14/108.85 [4900]~E(x49002,x49003)+~P66(x49001)+E(f318(f318(f3(x49001),x49002),x49003),f2(x49001))
% 109.14/108.85 [4901]~E(x49012,x49013)+~P67(x49011)+E(f318(f318(f3(x49011),x49012),x49013),f2(x49011))
% 109.14/108.85 [4914]~P149(x49141)+~E(x49143,f2(x49141))+E(f318(f318(f73(x49141),x49142),x49143),x49142)
% 109.14/108.85 [4932]~P147(x49321)+~E(x49323,f2(x49321))+E(f318(f318(f74(x49321),x49322),x49323),f2(x49321))
% 109.14/108.85 [4933]~P147(x49331)+~E(x49332,f2(x49331))+E(f318(f318(f74(x49331),x49332),x49333),f2(x49331))
% 109.14/108.85 [4953]~E(x49533,f104(x49531))+~E(x49532,f104(x49531))+E(f318(f318(f125(x49531),x49532),x49533),f104(x49531))
% 109.14/108.85 [4954]~E(x49543,f104(x49541))+~E(x49542,f104(x49541))+E(f318(f318(f125(x49541),x49542),x49543),f104(x49541))
% 109.14/108.85 [5042]~P149(x50422)+E(x50421,f2(x50422))+~E(f318(f318(f73(x50422),x50423),x50421),x50423)
% 109.14/108.85 [5043]~P66(x50431)+~E(x50432,f318(f72(x50431),x50433))+E(f318(f318(f73(x50431),x50432),x50433),f2(x50431))
% 109.14/108.85 [5050]E(x50501,f104(x50502))+E(x50503,f2(a911))+~E(f318(f318(f166(x50502),x50503),x50501),f104(x50502))
% 109.14/108.85 [5056]~P66(x50563)+E(x50561,x50562)+~E(f318(f318(f3(x50563),x50561),x50562),f2(x50563))
% 109.14/108.85 [5057]~P67(x50573)+E(x50571,x50572)+~E(f318(f318(f3(x50573),x50571),x50572),f2(x50573))
% 109.14/108.85 [5071]~P145(x50712)+E(x50711,f2(x50712))+~E(f318(f318(f235(x50712),x50711),x50713),f2(x50712))
% 109.14/108.85 [5072]~P104(x50722)+E(x50721,f233(x50722))+~E(f318(f318(f92(x50722),x50723),x50721),f233(x50722))
% 109.14/108.85 [5073]~P104(x50732)+E(x50731,f233(x50732))+~E(f318(f318(f92(x50732),x50731),x50733),f233(x50732))
% 109.14/108.85 [5074]~P105(x50742)+E(x50741,f179(x50742))+~E(f318(f318(f101(x50742),x50743),x50741),f179(x50742))
% 109.14/108.85 [5075]~P105(x50752)+E(x50751,f179(x50752))+~E(f318(f318(f101(x50752),x50751),x50753),f179(x50752))
% 109.14/108.85 [5144]~P66(x51442)+E(x51441,f318(f72(x51442),x51443))+~E(f318(f318(f73(x51442),x51441),x51443),f2(x51442))
% 109.14/108.85 [5145]~P66(x51451)+E(f318(f72(x51451),x51452),x51453)+~E(f318(f318(f73(x51451),x51452),x51453),f2(x51451))
% 109.14/108.85 [5146]~E(x51462,x51463)+~P113(x51461)+P1(f318(f318(f225(x51461),x51462),x51463))
% 109.14/108.85 [5147]~E(x51472,x51473)+~P2(x51471)+P1(f318(f318(f225(x51471),x51472),x51473))
% 109.14/108.85 [5148]~E(x51482,x51483)+~P113(x51481)+P1(f318(f318(f225(x51481),x51482),x51483))
% 109.14/108.85 [5149]~E(x51492,x51493)+~P113(x51491)+P1(f318(f318(f225(x51491),x51492),x51493))
% 109.14/108.85 [5250]~P123(x52501)+~E(x52502,f318(f72(x52501),x52503))+E(f318(f318(f74(x52501),x52502),x52502),f318(f318(f74(x52501),x52503),x52503))
% 109.14/108.85 [5258]~P4(x52581)+~P13(x52581,x52583)+P13(x52581,f318(f318(f166(x52581),x52582),x52583))
% 109.14/108.85 [5259]~P4(x52591)+~P13(x52591,x52593)+P13(x52591,f318(f318(f129(x52591),x52592),x52593))
% 109.14/108.85 [5296]E(x52961,x52962)+E(x52963,f2(a911))+~E(f318(f318(f74(a911),x52963),x52961),f318(f318(f74(a911),x52963),x52962))
% 109.14/108.85 [5297]E(x52971,x52972)+E(x52973,f2(a911))+~E(f318(f318(f74(a911),x52973),x52971),f318(f318(f74(a911),x52973),x52972))
% 109.14/108.85 [5298]E(x52981,x52982)+E(x52983,f2(a911))+~E(f318(f318(f74(a911),x52981),x52983),f318(f318(f74(a911),x52982),x52983))
% 109.14/108.85 [5377]~E(x53772,x53773)+~P113(x53771)+E(f294(x53771,x53772,x53773),f318(f318(f300(x53771),x53772),f179(f918(x53771,a909))))
% 109.14/108.85 [5413]~P116(x54131)+~E(f318(f69(x54131),x54132),f318(f69(x54131),x54133))+P1(f318(f318(f278(x54131),x54132),x54133))
% 109.14/108.85 [5416]~E(x54161,x54162)+~P4(x54163)+~P1(f318(f318(f226(x54163),x54161),x54162))
% 109.14/108.85 [5417]~E(x54171,x54172)+~P4(x54173)+~P1(f318(f318(f226(x54173),x54171),x54172))
% 109.14/108.85 [5418]~E(x54181,x54182)+~P113(x54183)+~P1(f318(f318(f226(x54183),x54181),x54182))
% 109.14/108.85 [5419]~E(x54191,x54192)+~P113(x54193)+~P1(f318(f318(f226(x54193),x54191),x54192))
% 109.14/108.85 [5420]~E(x54201,x54202)+~P113(x54203)+~P1(f318(f318(f226(x54203),x54201),x54202))
% 109.14/108.85 [5421]~E(x54211,x54212)+~P4(x54213)+~P1(f318(f318(f226(x54213),x54211),x54212))
% 109.14/108.85 [5422]~E(x54221,x54222)+~P113(x54223)+~P1(f318(f318(f226(x54223),x54221),x54222))
% 109.14/108.85 [5433]~P113(x54331)+E(f318(f293(x54331,x54332),x54333),f179(f918(x54331,a909)))+P1(f318(f318(f226(x54331),x54332),x54333))
% 109.14/108.85 [5434]~P113(x54341)+E(f318(f293(x54341,x54342),x54343),f179(f918(x54341,a909)))+P1(f318(f318(f226(x54341),x54342),x54343))
% 109.14/108.85 [5482]~P113(x54821)+E(f294(x54821,x54822,x54823),f179(f918(x54821,a909)))+P1(f318(f318(f225(x54821),x54822),x54823))
% 109.14/108.85 [5483]~P113(x54831)+E(f296(x54831,x54832,x54833),f179(f918(x54831,a909)))+P1(f318(f318(f226(x54831),x54832),x54833))
% 109.14/108.85 [5484]~P113(x54841)+E(f179(f918(x54841,a909)),f294(x54841,x54842,x54843))+P1(f318(f318(f225(x54841),x54842),x54843))
% 109.14/108.85 [5485]~P113(x54851)+E(f179(f918(x54851,a909)),f296(x54851,x54852,x54853))+P1(f318(f318(f226(x54851),x54852),x54853))
% 109.14/108.85 [5493]~P102(x54931)+~E(f318(f318(f101(x54931),x54932),x54933),x54933)+P1(f318(f318(f225(x54931),x54932),x54933))
% 109.14/108.85 [5494]~P108(x54941)+~E(f318(f318(f92(x54941),x54942),x54943),x54942)+P1(f318(f318(f225(x54941),x54942),x54943))
% 109.14/108.85 [5495]~P4(x54951)+~E(f318(f318(f223(x54951),x54952),x54953),x54952)+P1(f318(f318(f225(x54951),x54952),x54953))
% 109.14/108.85 [5496]~P4(x54961)+~E(f318(f318(f224(x54961),x54962),x54963),x54963)+P1(f318(f318(f225(x54961),x54962),x54963))
% 109.14/108.85 [5514]~P4(x55141)+P13(x55141,x55142)+~P13(x55141,f318(f318(f142(x55141),x55143),x55142))
% 109.14/108.85 [5515]~P4(x55151)+P13(x55151,x55152)+~P13(x55151,f318(f318(f142(x55151),x55153),x55152))
% 109.14/108.85 [5516]~P4(x55161)+P13(x55161,x55162)+~P13(x55161,f318(f318(f125(x55161),x55163),x55162))
% 109.14/108.85 [5517]~P4(x55171)+P13(x55171,x55172)+~P13(x55171,f318(f318(f125(x55171),x55172),x55173))
% 109.14/108.85 [5522]~P69(x55221)+~E(f39(x55221,x55223,x55222),f2(x55221))+P1(f318(f318(f278(x55221),x55222),x55223))
% 109.14/108.85 [5582]~P4(x55821)+P1(f318(f318(f225(x55821),x55823),x55822))+P1(f318(f318(f225(x55821),x55822),x55823))
% 109.14/108.85 [5583]~P4(x55831)+P1(f318(f318(f225(x55831),x55833),x55832))+P1(f318(f318(f225(x55831),x55832),x55833))
% 109.14/108.85 [5584]~P4(x55841)+P1(f318(f318(f226(x55841),x55843),x55842))+P1(f318(f318(f225(x55841),x55842),x55843))
% 109.14/108.85 [5585]~P4(x55851)+P1(f318(f318(f226(x55851),x55853),x55852))+P1(f318(f318(f225(x55851),x55852),x55853))
% 109.14/108.85 [5586]~P4(x55861)+P1(f318(f318(f226(x55861),x55863),x55862))+P1(f318(f318(f225(x55861),x55862),x55863))
% 109.14/108.85 [5587]~P4(x55871)+P1(f318(f318(f226(x55871),x55873),x55872))+P1(f318(f318(f225(x55871),x55872),x55873))
% 109.14/108.85 [5588]~P4(x55881)+P1(f318(f318(f226(x55881),x55883),x55882))+P1(f318(f318(f225(x55881),x55882),x55883))
% 109.14/108.85 [5624]~P102(x56241)+E(f318(f318(f101(x56241),x56242),x56243),x56242)+~P1(f318(f318(f225(x56241),x56243),x56242))
% 109.14/108.85 [5625]~P102(x56251)+E(f318(f318(f101(x56251),x56252),x56253),x56253)+~P1(f318(f318(f225(x56251),x56252),x56253))
% 109.14/108.85 [5626]~P102(x56261)+E(f318(f318(f101(x56261),x56262),x56263),x56263)+~P1(f318(f318(f225(x56261),x56262),x56263))
% 109.14/108.85 [5627]~P108(x56271)+E(f318(f318(f92(x56271),x56272),x56273),x56273)+~P1(f318(f318(f225(x56271),x56273),x56272))
% 109.14/108.85 [5628]~P108(x56281)+E(f318(f318(f92(x56281),x56282),x56283),x56282)+~P1(f318(f318(f225(x56281),x56282),x56283))
% 109.14/108.85 [5629]~P108(x56291)+E(f318(f318(f92(x56291),x56292),x56293),x56292)+~P1(f318(f318(f225(x56291),x56292),x56293))
% 109.14/108.85 [5630]~P4(x56301)+E(f318(f318(f223(x56301),x56302),x56303),x56303)+~P1(f318(f318(f225(x56301),x56303),x56302))
% 109.14/108.85 [5631]~P4(x56311)+E(f318(f318(f223(x56311),x56312),x56313),x56312)+~P1(f318(f318(f225(x56311),x56312),x56313))
% 109.14/108.85 [5632]~P4(x56321)+E(f318(f318(f223(x56321),x56322),x56323),x56322)+~P1(f318(f318(f225(x56321),x56322),x56323))
% 109.14/108.85 [5633]~P4(x56331)+E(f318(f318(f224(x56331),x56332),x56333),x56332)+~P1(f318(f318(f225(x56331),x56333),x56332))
% 109.14/108.85 [5634]~P4(x56341)+E(f318(f318(f224(x56341),x56342),x56343),x56343)+~P1(f318(f318(f225(x56341),x56342),x56343))
% 109.14/108.85 [5635]~P4(x56351)+E(f318(f318(f224(x56351),x56352),x56353),x56353)+~P1(f318(f318(f225(x56351),x56352),x56353))
% 109.14/108.85 [5642]~P125(x56422)+E(x56421,f2(x56422))+E(f318(f318(f282(x56422),f318(f72(x56422),x56423)),f318(f72(x56422),x56421)),f318(f318(f282(x56422),x56423),x56421))
% 109.14/108.85 [5648]~P69(x56481)+E(f39(x56481,x56482,x56483),f2(x56481))+~P1(f318(f318(f278(x56481),x56483),x56482))
% 109.14/108.85 [5649]~P69(x56491)+E(f39(x56491,x56492,x56493),f2(x56491))+~P1(f318(f318(f278(x56491),x56493),x56492))
% 109.14/108.85 [5695]~P113(x56951)+E(f318(f293(x56951,x56952),x56953),f179(f918(x56951,a909)))+~P1(f318(f318(f225(x56951),x56953),x56952))
% 109.14/108.85 [5730]~P113(x57301)+E(f294(x57301,x57302,x57303),f179(f918(x57301,a909)))+~P1(f318(f318(f226(x57301),x57303),x57302))
% 109.14/108.85 [5731]~P113(x57311)+E(f296(x57311,x57312,x57313),f179(f918(x57311,a909)))+~P1(f318(f318(f225(x57311),x57313),x57312))
% 109.14/108.85 [5732]~P113(x57321)+E(f297(x57321,x57322,x57323),f179(f918(x57321,a909)))+~P1(f318(f318(f225(x57321),x57323),x57322))
% 109.14/108.85 [5775]~P119(x57751)+~P1(f318(x57752,x57753))+P1(f318(f318(f225(x57751),f229(x57751,x57752)),x57753))
% 109.14/108.85 [5785]~E(f318(f318(f3(a911),x57851),x57853),x57852)+E(x57851,f318(f318(f73(a911),x57852),x57853))+~P1(f318(f318(f225(a911),x57853),x57851))
% 109.14/108.85 [5786]~E(x57861,f318(f318(f73(a911),x57863),x57862))+E(f318(f318(f3(a911),x57861),x57862),x57863)+~P1(f318(f318(f225(a911),x57862),x57861))
% 109.14/108.85 [5831]~P1(f318(x58311,x58313))+P1(f318(x58311,f435(x58311,x58312)))+~P1(f318(f318(f225(a911),x58313),x58312))
% 109.14/108.85 [5832]~P1(f318(x58321,x58323))+P1(f318(x58321,f595(x58321,x58322)))+~P1(f318(f318(f226(a911),x58323),x58322))
% 109.14/108.85 [5839]~P113(x58391)+~E(f318(f293(x58391,x58392),x58393),f179(f918(x58391,a909)))+~P1(f318(f318(f226(x58391),x58392),x58393))
% 109.14/108.85 [5840]~P113(x58401)+~E(f318(f293(x58401,x58402),x58403),f179(f918(x58401,a909)))+~P1(f318(f318(f226(x58401),x58402),x58403))
% 109.14/108.85 [5844]~P2(x58441)+~P1(f318(f318(f226(x58441),x58442),x58443))+P1(f318(f318(f225(x58441),x58442),x58443))
% 109.14/108.85 [5845]~P2(x58451)+~P1(f318(f318(f226(x58451),x58452),x58453))+P1(f318(f318(f225(x58451),x58452),x58453))
% 109.14/108.85 [5846]~P113(x58461)+~P1(f318(f318(f226(x58461),x58462),x58463))+P1(f318(f318(f225(x58461),x58462),x58463))
% 109.14/108.85 [5847]~P113(x58471)+~P1(f318(f318(f226(x58471),x58472),x58473))+P1(f318(f318(f225(x58471),x58472),x58473))
% 109.14/108.85 [5956]~P113(x59561)+~E(f294(x59561,x59562,x59563),f179(f918(x59561,a909)))+~P1(f318(f318(f225(x59561),x59562),x59563))
% 109.14/108.85 [5957]~P113(x59571)+~E(f296(x59571,x59572,x59573),f179(f918(x59571,a909)))+~P1(f318(f318(f226(x59571),x59572),x59573))
% 109.14/108.85 [5958]~P113(x59581)+~E(f179(f918(x59581,a909)),f294(x59581,x59582,x59583))+~P1(f318(f318(f225(x59581),x59582),x59583))
% 109.14/108.85 [5959]~P113(x59591)+~E(f179(f918(x59591,a909)),f296(x59591,x59592,x59593))+~P1(f318(f318(f226(x59591),x59592),x59593))
% 109.14/108.85 [5970]P1(f318(x59701,x59702))+~P1(f318(x59701,f458(x59701,x59703)))+~P1(f318(f318(f225(a911),x59702),x59703))
% 109.14/108.85 [5971]P1(f318(x59711,x59712))+~P1(f318(x59711,f615(x59711,x59713)))+~P1(f318(f318(f226(a911),x59712),x59713))
% 109.14/108.85 [5979]~E(x59791,f318(a103,x59793))+P1(f318(f318(f226(a911),x59791),f318(a103,x59792)))+~P1(f318(f318(f226(a911),x59793),x59792))
% 109.14/108.85 [5999]E(x59991,x59992)+~E(f318(f318(f74(a911),x59993),x59991),f318(f318(f74(a911),x59993),x59992))+~P1(f318(f318(f226(a911),f2(a911)),x59993))
% 109.14/108.85 [6059]E(f318(x60591,f888(x60591,x60592,x60593)),f71(a911))+~E(f318(f318(f8(x60593,a911),x60591),x60592),f71(a911))+~P1(f318(f55(x60593),x60592))
% 109.14/108.85 [6075]~P5(x60751)+P1(f318(f318(f225(x60751),x60752),f31(x60751,x60753)))+~P1(f318(f318(f320(x60751),x60752),x60753))
% 109.14/108.85 [6098]~P2(x60981)+~P1(f318(f318(f226(x60981),x60983),x60982))+~P1(f318(f318(f225(x60981),x60982),x60983))
% 109.14/108.85 [6099]~P2(x60991)+~P1(f318(f318(f226(x60991),x60993),x60992))+~P1(f318(f318(f226(x60991),x60992),x60993))
% 109.14/108.85 [6100]~P2(x61001)+~P1(f318(f318(f226(x61001),x61003),x61002))+~P1(f318(f318(f226(x61001),x61002),x61003))
% 109.14/108.85 [6101]~P2(x61011)+~P1(f318(f318(f226(x61011),x61013),x61012))+~P1(f318(f318(f226(x61011),x61012),x61013))
% 109.14/108.85 [6102]~P2(x61021)+~P1(f318(f318(f226(x61021),x61023),x61022))+~P1(f318(f318(f226(x61021),x61022),x61023))
% 109.14/108.85 [6103]~P4(x61031)+~P1(f318(f318(f226(x61031),x61033),x61032))+~P1(f318(f318(f225(x61031),x61032),x61033))
% 109.14/108.85 [6104]~P4(x61041)+~P1(f318(f318(f226(x61041),x61043),x61042))+~P1(f318(f318(f225(x61041),x61042),x61043))
% 109.14/108.85 [6105]~P4(x61051)+~P1(f318(f318(f226(x61051),x61053),x61052))+~P1(f318(f318(f225(x61051),x61052),x61053))
% 109.14/108.85 [6106]~P4(x61061)+~P1(f318(f318(f226(x61061),x61063),x61062))+~P1(f318(f318(f226(x61061),x61062),x61063))
% 109.14/108.85 [6107]~P113(x61071)+~P1(f318(f318(f226(x61071),x61073),x61072))+~P1(f318(f318(f226(x61071),x61072),x61073))
% 109.14/108.85 [6129]~E(x61292,x61293)+~E(x61291,x61292)+E(f281(a911,f278(a911),x61291,x61292),f318(f318(f300(a911),x61293),f179(f918(a911,a909))))
% 109.14/108.85 [6137]~E(f318(x61372,f816(x61372,x61373,x61371)),f2(a911))+E(f318(f318(f8(x61371,a911),x61372),x61373),f2(a911))+~P1(f318(f55(x61371),x61373))
% 109.14/108.85 [6138]~E(f318(x61382,f393(x61382,x61383,x61381)),f71(a911))+E(f318(f318(f11(x61381,a911),x61382),x61383),f71(a911))+~P1(f318(f55(x61381),x61383))
% 109.14/108.85 [6152]~P3(x61521)+~P1(f318(f318(f226(x61521),x61523),x61522))+P1(f318(f318(f320(x61521),x61522),f318(f295(x61521),x61523)))
% 109.14/108.85 [6153]~P3(x61531)+~P1(f318(f318(f225(x61531),x61533),x61532))+P1(f318(f318(f320(x61531),x61532),f318(f274(x61531),x61533)))
% 109.14/108.85 [6154]~P3(x61541)+~P1(f318(f318(f226(x61541),x61542),x61543))+P1(f318(f318(f320(x61541),x61542),f318(f273(x61541),x61543)))
% 109.14/108.85 [6155]~P3(x61551)+~P1(f318(f318(f225(x61551),x61552),x61553))+P1(f318(f318(f320(x61551),x61552),f318(f292(x61551),x61553)))
% 109.14/108.85 [6156]~P116(x61561)+~P1(f318(f318(f278(x61561),x61562),x61563))+P1(f318(f318(f278(x61561),x61562),f318(f69(x61561),x61563)))
% 109.14/108.85 [6168]E(f318(x61681,f853(x61681,x61682,x61683)),f318(a103,f2(a911)))+~E(f318(f318(f8(x61683,a911),x61681),x61682),f318(a103,f2(a911)))+~P1(f318(f55(x61683),x61682))
% 109.14/108.85 [6252]~P5(x62521)+~P1(f318(f318(f320(x62521),x62523),x62522))+P1(f318(f318(f225(x62521),f32(x62521,x62522)),x62523))
% 109.14/108.85 [6272]~P1(f318(f318(f225(a911),x62721),x62723))+P1(f318(f318(f225(a911),x62721),x62722))+~P1(f318(f318(f225(a911),x62723),x62722))
% 109.14/108.85 [6273]~P1(f318(f318(f225(a1),x62731),x62733))+P1(f318(f318(f225(a1),x62731),x62732))+~P1(f318(f318(f225(a1),x62733),x62732))
% 109.14/108.85 [6295]~P3(x62951)+~P1(f318(f318(f320(x62951),x62953),f318(f274(x62951),x62952)))+P1(f318(f318(f225(x62951),x62952),x62953))
% 109.14/108.85 [6296]~P3(x62961)+~P1(f318(f318(f320(x62961),x62962),f318(f292(x62961),x62963)))+P1(f318(f318(f225(x62961),x62962),x62963))
% 109.14/108.85 [6297]~P3(x62971)+~P1(f318(f318(f320(x62971),x62973),f318(f295(x62971),x62972)))+P1(f318(f318(f226(x62971),x62972),x62973))
% 109.14/108.85 [6298]~P3(x62981)+~P1(f318(f318(f320(x62981),x62982),f318(f273(x62981),x62983)))+P1(f318(f318(f226(x62981),x62982),x62983))
% 109.14/108.85 [6299]~P116(x62991)+~P1(f318(f318(f278(x62991),x62992),f318(f69(x62991),x62993)))+P1(f318(f318(f278(x62991),x62992),x62993))
% 109.14/108.85 [6369]~P1(f318(x63691,x63692))+P1(f318(x63691,f780(x63691)))+~P1(f318(f318(f320(x63693),x63692),f233(f918(x63693,a909))))
% 109.14/108.85 [6475]~P113(x64751)+~P42(a911,x64751,x64752)+P1(f318(f318(f225(x64751),f318(x64752,x64753)),f318(x64752,f318(a103,x64753))))
% 109.14/108.85 [6509]~P74(x65091)+P1(f318(f318(f226(x65091),f2(x65091)),f394(x65093,x65092,x65091)))+P1(f318(f318(f225(x65091),x65092),x65093))
% 109.14/108.85 [6510]~P75(x65101)+P1(f318(f318(f226(x65101),f2(x65101)),f459(x65103,x65102,x65101)))+P1(f318(f318(f225(x65101),x65102),x65103))
% 109.14/108.85 [6579]~P65(x65791)+~P1(f318(f318(f225(x65791),x65793),f318(f72(x65791),x65792)))+P1(f318(f318(f225(x65791),x65792),f318(f72(x65791),x65793)))
% 109.14/108.85 [6580]~P65(x65801)+~P1(f318(f318(f225(x65801),x65803),f318(f72(x65801),x65802)))+P1(f318(f318(f225(x65801),x65802),f318(f72(x65801),x65803)))
% 109.14/108.85 [6581]~P65(x65811)+~P1(f318(f318(f226(x65811),x65813),f318(f72(x65811),x65812)))+P1(f318(f318(f226(x65811),x65812),f318(f72(x65811),x65813)))
% 109.14/108.85 [6582]~P65(x65821)+~P1(f318(f318(f226(x65821),x65823),f318(f72(x65821),x65822)))+P1(f318(f318(f226(x65821),x65822),f318(f72(x65821),x65823)))
% 109.14/108.85 [6594]~P1(f318(f318(f226(a911),x65941),x65943))+~P1(f318(f318(f226(a911),x65943),x65942))+P1(f318(f318(f226(a911),f318(a103,x65941)),x65942))
% 109.14/108.85 [6621]~P130(x66211)+P1(f318(f318(f225(x66211),f318(f91(x66211),x66212)),f318(f91(x66211),x66213)))+~P1(f318(f318(f225(a911),x66212),x66213))
% 109.14/108.85 [6622]~P116(x66221)+P1(f318(f318(f225(x66221),f318(f93(x66221),x66222)),f318(f93(x66221),x66223)))+~P1(f318(f318(f225(a1),x66222),x66223))
% 109.14/108.85 [6623]~P130(x66231)+P1(f318(f318(f226(x66231),f318(f91(x66231),x66232)),f318(f91(x66231),x66233)))+~P1(f318(f318(f226(a911),x66232),x66233))
% 109.14/108.85 [6624]~P116(x66241)+P1(f318(f318(f226(x66241),f318(f93(x66241),x66242)),f318(f93(x66241),x66243)))+~P1(f318(f318(f226(a1),x66242),x66243))
% 109.14/108.85 [6625]~P130(x66251)+P1(f318(f318(f226(x66251),f318(f91(x66251),x66252)),f318(f91(x66251),x66253)))+~P1(f318(f318(f226(a911),x66252),x66253))
% 109.14/108.85 [6631]~P4(x66311)+E(f318(f318(f101(f918(x66311,a909)),f318(f273(x66311),x66312)),f318(f293(x66311,x66312),x66313)),f318(f273(x66311),x66313))+~P1(f318(f318(f225(x66311),x66312),x66313))
% 109.14/108.85 [6656]~P65(x66561)+~P1(f318(f318(f225(x66561),x66563),x66562))+P1(f318(f318(f225(x66561),f318(f72(x66561),x66562)),f318(f72(x66561),x66563)))
% 109.14/108.85 [6657]~P65(x66571)+~P1(f318(f318(f225(x66571),x66573),x66572))+P1(f318(f318(f225(x66571),f318(f72(x66571),x66572)),f318(f72(x66571),x66573)))
% 109.14/108.85 [6658]~P96(x66581)+~P1(f318(f318(f225(x66581),x66583),x66582))+P1(f318(f318(f225(x66581),f318(f72(x66581),x66582)),f318(f72(x66581),x66583)))
% 109.14/108.85 [6659]~P96(x66591)+~P1(f318(f318(f225(x66591),x66593),x66592))+P1(f318(f318(f225(x66591),f318(f72(x66591),x66592)),f318(f72(x66591),x66593)))
% 109.14/108.85 [6660]~P65(x66601)+~P1(f318(f318(f226(x66601),x66603),x66602))+P1(f318(f318(f226(x66601),f318(f72(x66601),x66602)),f318(f72(x66601),x66603)))
% 109.14/108.85 [6697]~P4(x66971)+E(f318(f318(f101(f918(x66971,a909)),f318(f273(x66971),x66972)),f294(x66971,x66972,x66973)),f318(f292(x66971),x66973))+~P1(f318(f318(f225(x66971),x66972),x66973))
% 109.14/108.85 [6698]~P4(x66981)+E(f318(f318(f101(f918(x66981,a909)),f318(f292(x66981),x66982)),f296(x66981,x66982,x66983)),f318(f292(x66981),x66983))+~P1(f318(f318(f225(x66981),x66982),x66983))
% 109.14/108.85 [6699]~P4(x66991)+E(f318(f318(f101(f918(x66991,a909)),f318(f292(x66991),x66992)),f297(x66991,x66992,x66993)),f318(f273(x66991),x66993))+~P1(f318(f318(f226(x66991),x66992),x66993))
% 109.14/108.85 [6736]~P4(x67361)+E(f318(f318(f101(f918(x67361,a909)),f318(f293(x67361,x67362),x67363)),f318(f274(x67361),x67363)),f318(f274(x67361),x67362))+~P1(f318(f318(f225(x67361),x67362),x67363))
% 109.14/108.85 [6804]~P5(x68041)+~P1(f318(f318(f225(x68041),f318(x68042,x68043)),x68043))+P1(f318(f318(f225(x68041),f86(x68041,x68042)),x68043))
% 109.14/108.85 [6894]~P4(x68941)+E(f318(f318(f101(f918(x68941,a909)),f294(x68941,x68942,x68943)),f318(f295(x68941),x68943)),f318(f274(x68941),x68942))+~P1(f318(f318(f225(x68941),x68942),x68943))
% 109.14/108.85 [6895]~P4(x68951)+E(f318(f318(f101(f918(x68951,a909)),f296(x68951,x68952,x68953)),f318(f295(x68951),x68953)),f318(f295(x68951),x68952))+~P1(f318(f318(f225(x68951),x68952),x68953))
% 109.14/108.85 [6896]~P4(x68961)+E(f318(f318(f101(f918(x68961,a909)),f297(x68961,x68962,x68963)),f318(f274(x68961),x68963)),f318(f295(x68961),x68962))+~P1(f318(f318(f226(x68961),x68962),x68963))
% 109.14/108.85 [6910]P1(f318(x69101,x69102))+~P1(f318(f318(f225(a911),x69102),x69103))+P1(f318(f318(f320(a911),f458(x69101,x69103)),f294(a911,f2(a911),x69103)))
% 109.14/108.85 [6944]E(x69441,x69442)+~E(f318(f318(f155(x69443),x69441),f635(x69443,x69442,x69441)),f318(f318(f155(x69443),x69442),f635(x69443,x69442,x69441)))+~E(f318(f180(f912(x69443)),x69441),f318(f180(f912(x69443)),x69442))
% 109.14/108.85 [6949]~E(x69493,f318(f318(f30(a911),x69491),x69492))+~P1(f318(f318(f226(a911),f2(a911)),x69492))+P1(f318(f318(f226(a911),x69491),f318(f318(f74(a911),x69492),f318(a103,x69493))))
% 109.14/108.85 [6963]~P1(f318(x69631,x69633))+~P1(f318(f318(f225(a911),x69633),x69632))+P1(f318(f318(f320(a911),f435(x69631,x69632)),f294(a911,f2(a911),x69632)))
% 109.14/108.85 [7003]~P1(f318(x70031,x70033))+P1(f318(x70031,f501(x70031,x70032)))+~P1(f318(f318(f320(a911),x70033),f294(a911,f2(a911),x70032)))
% 109.14/108.85 [7022]~P130(x70223)+~P1(f318(f318(f225(x70223),f318(f91(x70223),x70221)),f318(f91(x70223),x70222)))+P1(f318(f318(f225(a911),x70221),x70222))
% 109.14/108.85 [7023]~P116(x70233)+~P1(f318(f318(f225(x70233),f318(f93(x70233),x70231)),f318(f93(x70233),x70232)))+P1(f318(f318(f225(a1),x70231),x70232))
% 109.14/108.85 [7024]~P130(x70243)+~P1(f318(f318(f226(x70243),f318(f91(x70243),x70241)),f318(f91(x70243),x70242)))+P1(f318(f318(f226(a911),x70241),x70242))
% 109.14/108.85 [7025]~P130(x70253)+~P1(f318(f318(f226(x70253),f318(f91(x70253),x70251)),f318(f91(x70253),x70252)))+P1(f318(f318(f226(a911),x70251),x70252))
% 109.14/108.85 [7026]~P116(x70263)+~P1(f318(f318(f226(x70263),f318(f93(x70263),x70261)),f318(f93(x70263),x70262)))+P1(f318(f318(f226(a1),x70261),x70262))
% 109.14/108.85 [7043]~P130(x70431)+~P1(f318(f318(f226(x70431),f71(x70431)),x70432))+P1(f318(f318(f226(x70431),f71(x70431)),f318(f318(f235(x70431),x70432),f318(a103,x70433))))
% 109.14/108.85 [7046]~P65(x70461)+~P1(f318(f318(f225(x70461),f318(f72(x70461),x70463)),f318(f72(x70461),x70462)))+P1(f318(f318(f225(x70461),x70462),x70463))
% 109.14/108.85 [7047]~P96(x70471)+~P1(f318(f318(f225(x70471),f318(f72(x70471),x70473)),f318(f72(x70471),x70472)))+P1(f318(f318(f225(x70471),x70472),x70473))
% 109.14/108.85 [7048]~P65(x70481)+~P1(f318(f318(f226(x70481),f318(f72(x70481),x70483)),f318(f72(x70481),x70482)))+P1(f318(f318(f226(x70481),x70482),x70483))
% 109.14/108.85 [7072]P1(f318(x70721,x70722))+~P1(f318(x70721,f466(x70721,x70723)))+~P1(f318(f318(f320(a911),x70722),f294(a911,f2(a911),x70723)))
% 109.14/108.85 [7092]~P74(x70921)+P1(f318(f318(f226(x70921),f394(x70923,x70922,x70921)),f71(x70921)))+P1(f318(f318(f225(x70921),x70922),x70923))
% 109.14/108.85 [7114]~E(f39(a911,x71143,x71142),f39(a911,x71141,x71142))+E(f318(f318(f73(a911),x71141),f318(f318(f74(a911),x71142),f412(x71141,x71142,x71143))),x71143)+~P1(f318(f318(f225(a911),x71141),x71143))
% 109.14/108.85 [7169]E(f318(f318(f8(x71691,a911),x71692),x71693),f2(a911))+~P1(f318(f55(x71691),x71693))+P1(f318(f318(f320(x71691),f816(x71692,x71693,x71691)),x71693))
% 109.14/108.85 [7170]E(f318(f318(f11(x71701,a911),x71702),x71703),f71(a911))+~P1(f318(f55(x71701),x71703))+P1(f318(f318(f320(x71701),f393(x71702,x71703,x71701)),x71703))
% 109.14/108.85 [7192]~P4(x71921)+~P1(f318(f318(f225(x71921),x71923),x71922))+P1(f318(f318(f225(f918(x71921,a909)),f318(f295(x71921),x71922)),f318(f295(x71921),x71923)))
% 109.14/108.85 [7193]~P4(x71931)+~P1(f318(f318(f225(x71931),x71932),x71933))+P1(f318(f318(f225(f918(x71931,a909)),f318(f273(x71931),x71932)),f318(f273(x71931),x71933)))
% 109.14/108.85 [7194]~P113(x71941)+~P1(f318(f318(f225(x71941),x71943),x71942))+P1(f318(f318(f225(f918(x71941,a909)),f318(f274(x71941),x71942)),f318(f274(x71941),x71943)))
% 109.14/108.85 [7195]~P113(x71951)+~P1(f318(f318(f225(x71951),x71952),x71953))+P1(f318(f318(f225(f918(x71951,a909)),f318(f292(x71951),x71952)),f318(f292(x71951),x71953)))
% 109.14/108.85 [7196]~P4(x71961)+~P1(f318(f318(f226(x71961),x71962),x71963))+P1(f318(f318(f226(f918(x71961,a909)),f318(f273(x71961),x71962)),f318(f273(x71961),x71963)))
% 109.14/108.85 [7207]~P5(x72071)+P1(f318(f318(f225(x72071),x72072),f32(x72071,x72073)))+P1(f318(f318(f320(x72071),f339(x72073,x72072,x72071)),x72073))
% 109.14/108.85 [7213]~P65(x72131)+P1(f318(f318(f225(x72131),f318(f318(f3(x72131),x72132),x72133)),f2(x72131)))+~P1(f318(f318(f225(x72131),x72132),x72133))
% 109.14/108.85 [7214]~P65(x72141)+P1(f318(f318(f226(x72141),f318(f318(f3(x72141),x72142),x72143)),f2(x72141)))+~P1(f318(f318(f226(x72141),x72142),x72143))
% 109.14/108.85 [7255]P1(f318(x72551,x72552))+P1(f318(f318(f225(a911),f466(x72551,x72553)),x72553))+~P1(f318(f318(f320(a911),x72552),f294(a911,f2(a911),x72553)))
% 109.14/108.85 [7297]~E(f318(f318(f8(x72971,a911),x72972),x72973),f71(a911))+~P1(f318(f55(x72971),x72973))+P1(f318(f318(f320(x72971),f888(x72972,x72973,x72971)),x72973))
% 109.14/108.85 [7298]~P1(f318(x72981,x72983))+P1(f318(f318(f225(a911),f501(x72981,x72982)),x72982))+~P1(f318(f318(f320(a911),x72983),f294(a911,f2(a911),x72982)))
% 109.14/108.85 [7338]~P5(x73381)+P1(f318(f318(f320(x73381),f467(x73383,x73382,x73381)),x73382))+P1(f318(f318(f225(x73381),f31(x73381,x73382)),x73383))
% 109.14/108.85 [7372]~E(f318(f318(f8(x73721,a911),x73722),x73723),f318(a103,f2(a911)))+~P1(f318(f55(x73721),x73723))+P1(f318(f318(f320(x73721),f853(x73722,x73723,x73721)),x73723))
% 109.14/108.85 [7383]E(x73831,f2(a911))+P1(f318(x73832,f39(a911,x73833,x73831)))+P1(f318(f318(f226(a911),f375(x73831,x73833,x73832)),x73831))
% 109.14/108.85 [7485]~P1(f318(x74851,x74852))+P1(f318(x74851,f39(a911,x74852,x74853)))+P1(f318(f318(f226(a911),f375(x74853,x74852,x74851)),x74853))
% 109.14/108.85 [7596]E(x75961,f104(x75962))+~P1(f318(f318(f320(f912(x75962)),x75961),f152(x75962,x75963)))+P1(f318(f318(f320(x75962),f685(x75963,x75961,x75962)),x75963))
% 109.14/108.85 [7618]~P4(x76181)+E(f318(f318(f101(f918(x76181,a909)),f318(f318(f300(x76181),x76182),f179(f918(x76181,a909)))),f297(x76181,x76182,x76183)),f318(f293(x76181,x76182),x76183))+~P1(f318(f318(f226(x76181),x76182),x76183))
% 109.14/108.85 [7640]~P4(x76401)+E(f318(f318(f101(f918(x76401,a909)),f318(f318(f300(x76401),x76402),f179(f918(x76401,a909)))),f296(x76401,x76402,x76403)),f294(x76401,x76402,x76403))+~P1(f318(f318(f225(x76401),x76402),x76403))
% 109.14/108.85 [7747]~P4(x77471)+P1(f318(f318(f225(x77471),x77472),x77473))+~P1(f318(f318(f225(f918(x77471,a909)),f318(f295(x77471),x77473)),f318(f295(x77471),x77472)))
% 109.14/108.85 [7748]~P113(x77481)+P1(f318(f318(f225(x77481),x77482),x77483))+~P1(f318(f318(f225(f918(x77481,a909)),f318(f274(x77481),x77483)),f318(f274(x77481),x77482)))
% 109.14/108.85 [7749]~P4(x77491)+P1(f318(f318(f225(x77491),x77492),x77493))+~P1(f318(f318(f225(f918(x77491,a909)),f318(f273(x77491),x77492)),f318(f273(x77491),x77493)))
% 109.14/108.85 [7750]~P113(x77501)+P1(f318(f318(f225(x77501),x77502),x77503))+~P1(f318(f318(f225(f918(x77501,a909)),f318(f292(x77501),x77502)),f318(f292(x77501),x77503)))
% 109.14/108.85 [7751]~P4(x77511)+P1(f318(f318(f226(x77511),x77512),x77513))+~P1(f318(f318(f226(f918(x77511,a909)),f318(f273(x77511),x77512)),f318(f273(x77511),x77513)))
% 109.14/108.85 [7774]~P65(x77741)+~P1(f318(f318(f225(x77741),f318(f318(f3(x77741),x77742),x77743)),f2(x77741)))+P1(f318(f318(f225(x77741),x77742),x77743))
% 109.14/108.85 [7775]~P65(x77751)+~P1(f318(f318(f226(x77751),f318(f318(f3(x77751),x77752),x77753)),f2(x77751)))+P1(f318(f318(f226(x77751),x77752),x77753))
% 109.14/108.85 [7933]E(x79331,f2(a911))+~E(f318(f133(a911,a911,f73(a911),x79332),x79333),f2(a911))+~P1(f318(f318(f320(a911),x79331),f318(f163(a911),x79333)))
% 109.14/108.85 [7937]~P5(x79371)+~P1(f318(f318(f225(x79371),f467(x79373,x79372,x79371)),x79373))+P1(f318(f318(f225(x79371),f31(x79371,x79372)),x79373))
% 109.14/108.85 [8087]P1(f318(f318(f225(a1),f2(a1)),f364(x80871,x80872,x80873)))+P1(f318(f318(x80872,f318(f318(f30(a1),x80871),x80873)),f39(a1,x80871,x80873)))+~P1(f318(f318(f226(a1),f2(a1)),x80873))
% 109.14/108.85 [8173]E(x81731,x81732)+~E(f318(f180(f912(x81733)),x81731),f318(f180(f912(x81733)),x81732))+~P1(f318(f318(f248(x81733,x81733,a909),a315),f659(x81733,x81731,x81732)))
% 109.14/108.85 [8249]~P39(x82492,x82493)+E(x82491,f179(f918(x82492,a909)))+~P1(f318(f318(f225(f918(x82492,a909)),x82491),f318(f276(x82492,x82492,x82493),x82491)))
% 109.14/108.85 [8282]~P75(x82821)+~P1(f318(f318(f225(x82821),x82822),f318(f318(f73(x82821),x82823),f459(x82823,x82822,x82821))))+P1(f318(f318(f225(x82821),x82822),x82823))
% 109.14/108.85 [8317]P56(x83171,x83172,x83173)+P1(f318(f318(f320(x83171),f524(x83173,x83172,x83171)),x83172))+P1(f318(f318(f320(f917(x83171,x83171)),f525(x83173,x83172,x83171)),x83173))
% 109.14/108.85 [8338]P1(f318(f318(x83382,f318(f318(f30(a1),x83381),x83383)),f39(a1,x83381,x83383)))+~P1(f318(f318(f226(a1),f2(a1)),x83383))+P1(f318(f318(f226(a1),f364(x83381,x83382,x83383)),x83383))
% 109.14/108.85 [8361]E(f318(f301(a911,a911,f318(f318(f9(a911,a911,a911),f3(a911)),x83611)),f318(f293(a911,x83612),x83613)),f179(f918(a911,a909)))+P1(f318(f318(f226(a911),x83611),x83613))+P1(f318(f318(f226(a911),x83612),x83613))
% 109.14/108.85 [8471]E(f318(f301(a911,a911,f318(f318(f9(a911,a911,a911),f3(a911)),x84711)),f318(f293(a911,x84712),x84713)),f318(f318(f300(a911),f2(a911)),f179(f918(a911,a909))))+P1(f318(f318(f226(a911),x84711),x84713))+~P1(f318(f318(f226(a911),x84712),x84713))
% 109.14/108.85 [8482]~P4(x84821)+E(f140(x84821,x84821,f7(x84821),x84822,x84823),x84823)+~P1(f318(f318(f320(x84821),x84822),f318(f163(x84821),x84823)))
% 109.14/108.85 [8495]P25(x84951,x84951,x84952,x84953)+~P1(f318(f55(x84951),x84953))+~P1(f318(f318(f225(f918(x84951,a909)),x84953),f318(f301(x84951,x84951,x84952),x84953)))
% 109.14/108.85 [8521]E(f318(f318(f73(a1),f318(f318(f74(a1),x85211),f365(x85212,x85213,x85211))),f364(x85212,x85213,x85211)),x85212)+P1(f318(f318(x85213,f318(f318(f30(a1),x85212),x85211)),f39(a1,x85212,x85211)))+~P1(f318(f318(f226(a1),f2(a1)),x85211))
% 109.14/108.85 [8761]~P1(f318(f318(x87611,f365(x87612,x87611,x87613)),f364(x87612,x87611,x87613)))+P1(f318(f318(x87611,f318(f318(f30(a1),x87612),x87613)),f39(a1,x87612,x87613)))+~P1(f318(f318(f226(a1),f2(a1)),x87613))
% 109.14/108.85 [8837]P26(x88371,x88372,x88373,f233(f918(x88371,a909)),f233(f918(x88372,a909)))+~P25(x88371,x88372,x88373,f233(f918(x88371,a909)))+~E(f318(f301(x88371,x88372,x88373),f233(f918(x88371,a909))),f233(f918(x88372,a909)))
% 109.14/108.85 [8838]P26(x88381,x88382,x88383,f233(f918(x88381,a909)),f233(f918(x88382,a909)))+~P25(x88381,x88382,x88383,f233(f918(x88381,a909)))+~E(f318(f301(x88381,x88382,x88383),f233(f918(x88381,a909))),f233(f918(x88382,a909)))
% 109.14/108.85 [9645]~P1(f318(f55(x96451),x96452))+~P1(f318(f318(f320(x96451),x96453),x96452))+P1(f318(f318(f226(a911),f318(f29(x96451),f318(f318(f3(f918(x96451,a909)),x96452),f318(f318(f300(x96451),x96453),f179(f918(x96451,a909)))))),f318(f29(x96451),x96452)))
% 109.14/108.85 [10258]P56(x102581,x102582,x102583)+~P1(f318(f318(f248(x102581,x102581,a909),f318(f318(f9(x102581,f918(x102581,a909),f918(x102581,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x102581,a909),f918(x102581,a909)),x102581),f10(a909,a909,x102581)),f318(f318(f10(a909,f918(a909,a909),x102581),a316),f318(f318(f9(x102581,f918(x102581,a909),a909),f320(x102581)),x102582)))),f318(f318(f9(x102581,f918(x102581,a909),a909),f320(x102581)),x102582))),f525(x102583,x102582,x102581)))+P1(f318(f318(f320(x102581),f524(x102583,x102582,x102581)),x102582))
% 109.14/108.85 [5605]~P125(x56052)+E(x56051,f2(x56052))+E(f318(f318(f282(x56052),x56053),f318(f72(x56052),x56051)),f318(f72(x56052),f318(f318(f282(x56052),x56053),x56051)))
% 109.14/108.85 [5746]~E(x57463,f179(f918(x57461,a909)))+~E(x57462,f179(f918(x57461,a909)))+E(f318(f318(f101(f918(x57461,a909)),x57462),x57463),f179(f918(x57461,a909)))
% 109.14/108.85 [5804]~E(x58043,f2(a911))+~P1(f318(x58041,f2(a911)))+P1(f318(x58041,f318(f318(f30(a911),x58042),x58043)))
% 109.14/108.85 [5805]~E(x58053,f2(a911))+~P1(f318(x58051,f2(a911)))+P1(f318(x58051,f318(f318(f30(a911),x58052),x58053)))
% 109.14/108.85 [5948]~P75(x59482)+E(x59481,f2(x59482))+E(f318(f318(f282(x59482),f318(f69(x59482),x59483)),f318(f69(x59482),x59481)),f318(f69(x59482),f318(f318(f282(x59482),x59483),x59481)))
% 109.14/108.85 [6068]~P69(x60681)+E(f318(f318(f74(x60681),x60682),f318(f318(f30(x60681),x60683),x60682)),x60683)+~P1(f318(f318(f278(x60681),x60682),x60683))
% 109.14/108.85 [6122]~P1(f318(f55(x61221),x61223))+E(f318(f29(x61221),f318(f318(f300(x61221),x61222),x61223)),f318(a103,f318(f29(x61221),x61223)))+P1(f318(f318(f320(x61221),x61222),x61223))
% 109.14/108.85 [6123]~P1(f318(f55(x61231),x61233))+E(f318(f29(x61231),f318(f318(f300(x61231),x61232),x61233)),f318(a103,f318(f29(x61231),x61233)))+P1(f318(f318(f320(x61231),x61232),x61233))
% 109.14/108.85 [6200]~E(x62002,f2(a911))+P1(f318(x62001,f2(a911)))+~P1(f318(x62001,f318(f318(f30(a911),x62003),x62002)))
% 109.14/108.85 [6217]~P1(f318(f55(x62171),x62173))+E(f318(f29(x62171),f318(f318(f300(x62171),x62172),x62173)),f318(f29(x62171),x62173))+~P1(f318(f318(f320(x62171),x62172),x62173))
% 109.14/108.85 [6254]~P1(f318(f55(x62541),x62543))+E(f318(f29(x62541),f318(f318(f300(x62541),x62542),x62543)),f318(f318(f73(a911),f71(a911)),f318(f29(x62541),x62543)))+P1(f318(f318(f320(x62541),x62542),x62543))
% 109.14/108.85 [6370]E(f318(f318(f73(a911),x63701),f825(x63701,x63702,x63703)),x63702)+~P1(f318(x63703,f2(a911)))+P1(f318(x63703,f318(f318(f3(a911),x63702),x63701)))
% 109.14/108.85 [6371]E(f318(f318(f73(a911),x63711),f833(x63711,x63712,x63713)),x63712)+~P1(f318(x63713,f2(a911)))+P1(f318(x63713,f318(f318(f3(a911),x63712),x63711)))
% 109.14/108.85 [6417]~P5(x64171)+~P1(f318(f55(x64171),x64173))+E(f318(f318(f58(x64171,x64171,f101(x64171)),x64172),x64173),f318(f318(f101(x64171),x64172),f31(x64171,x64173)))
% 109.14/108.85 [6418]~P5(x64181)+~P1(f318(f55(x64181),x64183))+E(f318(f318(f58(x64181,x64181,f92(x64181)),x64182),x64183),f318(f318(f92(x64181),x64182),f32(x64181,x64183)))
% 109.14/108.85 [6424]~P99(x64241)+~E(f318(f94(x64241),x64242),f318(f94(x64241),x64243))+P30(x64241,f318(f94(x64241),f318(f318(f73(a1),x64242),f318(f72(a1),x64243))))
% 109.14/108.85 [6432]~P144(x64321)+E(f318(f318(f3(x64321),f318(f91(x64321),x64322)),f318(f91(x64321),x64323)),f318(f91(x64321),f318(f318(f3(a911),x64322),x64323)))+~P1(f318(f318(f225(a911),x64323),x64322))
% 109.14/108.85 [6439]~P116(x64391)+~P1(f318(f318(f278(x64391),x64392),x64393))+P1(f318(f318(f278(x64391),f318(f69(x64391),x64392)),x64393))
% 109.14/108.85 [6520]E(f318(f318(f73(a911),x65201),f825(x65201,x65202,x65203)),x65202)+P1(f318(f318(f226(a911),x65202),x65201))+P1(f318(x65203,f318(f318(f3(a911),x65202),x65201)))
% 109.14/108.85 [6521]E(f318(f318(f73(a911),x65211),f833(x65211,x65212,x65213)),x65212)+P1(f318(f318(f226(a911),x65212),x65211))+P1(f318(x65213,f318(f318(f3(a911),x65212),x65211)))
% 109.14/108.85 [6538]~P116(x65381)+E(f318(f318(f74(x65381),f318(f69(x65381),x65382)),x65383),f318(f69(x65381),f318(f318(f74(x65381),x65382),x65383)))+~P1(f318(f318(f225(x65381),f2(x65381)),x65383))
% 109.14/108.85 [6539]~P74(x65391)+E(f318(f318(f282(x65391),f318(f69(x65391),x65392)),x65393),f318(f69(x65391),f318(f318(f282(x65391),x65392),x65393)))+~P1(f318(f318(f226(x65391),f2(x65391)),x65393))
% 109.14/108.85 [6547]~P103(x65471)+~P1(f318(f55(x65471),x65473))+E(f318(f318(f58(x65471,x65471,f92(x65471)),x65472),x65473),f12(x65471,f318(f318(f300(x65471),x65472),x65473)))
% 109.14/108.85 [6548]~P103(x65481)+~P1(f318(f55(x65481),x65483))+E(f318(f318(f58(x65481,x65481,f101(x65481)),x65482),x65483),f15(x65481,f318(f318(f300(x65481),x65482),x65483)))
% 109.14/108.85 [6549]~P4(x65491)+~P1(f318(f55(x65491),x65493))+E(f318(f318(f58(x65491,x65491,f223(x65491)),x65492),x65493),f16(x65491,f318(f318(f300(x65491),x65492),x65493)))
% 109.14/108.85 [6550]~P4(x65501)+~P1(f318(f55(x65501),x65503))+E(f318(f318(f58(x65501,x65501,f224(x65501)),x65502),x65503),f17(x65501,f318(f318(f300(x65501),x65502),x65503)))
% 109.14/108.85 [6596]E(x65961,f104(x65962))+~E(f170(x65962,x65963),f104(f912(x65962)))+~P1(f318(f318(f320(f912(x65962)),x65961),f318(f163(f912(x65962)),x65963)))
% 109.14/108.85 [6639]~P1(f318(f128(x66391),x66393))+P1(f318(f318(f320(x66391),x66392),f318(f163(x66391),x66393)))+P1(f318(f128(x66391),f318(f318(f142(x66391),x66392),x66393)))
% 109.14/108.85 [6650]~P101(x66501)+~P1(f318(f55(x66501),x66503))+E(f318(f57(x66501,f74(x66501)),f318(f318(f300(x66501),x66502),x66503)),f318(f318(f58(x66501,x66501,f74(x66501)),x66502),x66503))
% 109.14/108.85 [6670]~P4(x66701)+~P1(f318(f55(x66701),x66703))+E(f13(x66701,f223(x66701),f318(f318(f300(x66701),x66702),x66703)),f318(f318(f58(x66701,x66701,f223(x66701)),x66702),x66703))
% 109.14/108.85 [6671]~P4(x66711)+~P1(f318(f55(x66711),x66713))+E(f14(x66711,f224(x66711),f318(f318(f300(x66711),x66712),x66713)),f318(f318(f58(x66711,x66711,f224(x66711)),x66712),x66713))
% 109.14/108.85 [6672]P1(f318(x66721,f2(a911)))+~P1(f318(f318(f226(a911),x66722),x66723))+~P1(f318(x66721,f318(f318(f3(a911),x66722),x66723)))
% 109.14/108.85 [6673]P1(f318(x66731,f2(a911)))+~P1(f318(f318(f226(a911),x66732),x66733))+~P1(f318(x66731,f318(f318(f3(a911),x66732),x66733)))
% 109.14/108.85 [6693]~P91(x66931)+P1(f318(f318(f225(x66931),x66932),x66933))+~P1(f318(f318(f225(x66931),f318(f69(x66931),x66932)),x66933))
% 109.14/108.85 [6694]~P91(x66941)+P1(f318(f318(f225(x66941),x66942),x66943))+~P1(f318(f318(f225(x66941),f318(f69(x66941),x66942)),x66943))
% 109.14/108.85 [6695]~P116(x66951)+P1(f318(f318(f226(x66951),x66952),x66953))+~P1(f318(f318(f226(x66951),f318(f69(x66951),x66952)),x66953))
% 109.14/108.85 [6696]~P116(x66961)+P1(f318(f318(f278(x66961),x66962),x66963))+~P1(f318(f318(f278(x66961),f318(f69(x66961),x66962)),x66963))
% 109.14/108.85 [6713]E(x67131,f104(x67132))+E(f318(f132(x67132),f318(f318(f129(x67132),x67133),x67131)),f318(f318(f155(x67132),x67131),x67133))+~P1(f318(f318(f226(a911),x67133),f318(f180(f912(x67132)),x67131)))
% 109.14/108.85 [6769]~P1(f318(x67691,x67693))+P1(f318(x67691,f608(x67691,x67692)))+~P1(f318(f318(f320(a911),x67693),f318(f293(a911,f2(a911)),x67692)))
% 109.14/108.85 [6789]P1(f318(x67891,x67892))+~P1(f318(f318(f226(a911),x67892),x67893))+P1(f318(f318(f320(a911),f615(x67891,x67893)),f318(f293(a911,f2(a911)),x67893)))
% 109.14/108.85 [6806]~P130(x68061)+~P1(f318(f318(f225(x68061),f2(x68061)),x68062))+P1(f318(f318(f225(x68061),f2(x68061)),f318(f318(f235(x68061),x68062),x68063)))
% 109.14/108.85 [6807]~P130(x68071)+~P1(f318(f318(f225(x68071),f71(x68071)),x68072))+P1(f318(f318(f225(x68071),f71(x68071)),f318(f318(f235(x68071),x68072),x68073)))
% 109.14/108.85 [6809]~P130(x68091)+~P1(f318(f318(f226(x68091),f2(x68091)),x68092))+P1(f318(f318(f226(x68091),f2(x68091)),f318(f318(f235(x68091),x68092),x68093)))
% 109.14/108.85 [6833]~P1(f318(x68331,x68333))+~P1(f318(f318(f226(a911),x68333),x68332))+P1(f318(f318(f320(a911),f595(x68331,x68332)),f318(f293(a911,f2(a911)),x68332)))
% 109.14/108.85 [6842]P1(f318(f55(x68421),x68422))+~P1(f318(f55(x68421),x68423))+~P1(f318(f318(f225(f918(x68421,a909)),x68422),x68423))
% 109.14/108.85 [6843]P1(f318(f55(x68431),x68432))+~P1(f318(f55(x68431),x68433))+~P1(f318(f318(f225(f918(x68431,a909)),x68432),x68433))
% 109.14/108.85 [6850]P1(f318(x68501,x68502))+~P1(f318(x68501,f616(x68501,x68503)))+~P1(f318(f318(f320(a911),x68502),f318(f293(a911,f2(a911)),x68503)))
% 109.14/108.85 [6863]E(x68631,f2(a911))+P1(f318(x68632,f374(x68631,x68633,x68632)))+~P1(f318(x68632,f318(f318(f30(a911),x68633),x68631)))
% 109.14/108.85 [6870]~P131(x68702)+E(x68701,f2(x68702))+~E(f318(f318(f73(x68702),f318(f318(f74(x68702),x68703),x68703)),f318(f318(f74(x68702),x68701),x68701)),f2(x68702))
% 109.14/108.85 [6871]~P131(x68712)+E(x68711,f2(x68712))+~E(f318(f318(f73(x68712),f318(f318(f74(x68712),x68711),x68711)),f318(f318(f74(x68712),x68713),x68713)),f2(x68712))
% 109.14/108.85 [6911]E(x69111,f2(a911))+~P1(f318(x69112,f372(x69111,x69113,x69112)))+P1(f318(x69112,f318(f318(f30(a911),x69113),x69111)))
% 109.14/108.85 [6916]~P4(x69161)+~P13(x69161,x69163)+P13(x69161,f318(f318(f139(x69161,x69161,f7(x69161)),x69162),x69163))
% 109.14/108.85 [6957]P1(f318(x69571,f374(x69572,x69573,x69571)))+P1(f318(x69571,f2(a911)))+~P1(f318(x69571,f318(f318(f30(a911),x69573),x69572)))
% 109.14/108.85 [6962]~P99(x69621)+E(f318(f94(x69621),x69622),f318(f94(x69621),x69623))+~P30(x69621,f318(f94(x69621),f318(f318(f73(a1),x69622),f318(f72(a1),x69623))))
% 109.14/108.85 [7029]E(x70291,f2(a1))+E(x70292,f2(a1))+~P1(f318(f43(x70292,x70292),f318(f318(f243(a1,a1),x70293),x70291)))
% 109.14/108.85 [7030]E(x70301,f71(a1))+E(x70302,f2(a1))+~P1(f318(f43(x70302,x70302),f318(f318(f243(a1,a1),x70301),x70303)))
% 109.14/108.85 [7045]P1(f318(x70451,x70452))+P1(f318(f318(f226(a911),f616(x70451,x70453)),x70453))+~P1(f318(f318(f320(a911),x70452),f318(f293(a911,f2(a911)),x70453)))
% 109.14/108.85 [7068]~P1(f318(x70681,f825(x70683,x70682,x70681)))+~P1(f318(x70681,f2(a911)))+P1(f318(x70681,f318(f318(f3(a911),x70682),x70683)))
% 109.14/108.85 [7069]~P1(f318(x70691,f833(x70693,x70692,x70691)))+~P1(f318(x70691,f2(a911)))+P1(f318(x70691,f318(f318(f3(a911),x70692),x70693)))
% 109.14/108.85 [7070]~P1(f318(x70701,f372(x70703,x70702,x70701)))+~P1(f318(x70701,f2(a911)))+P1(f318(x70701,f318(f318(f30(a911),x70702),x70703)))
% 109.14/108.85 [7088]~P1(f318(x70881,x70883))+P1(f318(f318(f226(a911),f608(x70881,x70882)),x70882))+~P1(f318(f318(f320(a911),x70883),f318(f293(a911,f2(a911)),x70882)))
% 109.14/108.85 [7089]E(f318(f318(f3(a911),f318(f318(f3(a911),x70891),x70892)),f318(f318(f3(a911),x70893),x70892)),f318(f318(f3(a911),x70891),x70893))+~P1(f318(f318(f225(a911),x70892),x70891))+~P1(f318(f318(f225(a911),x70892),x70893))
% 109.14/108.85 [7126]~P65(x71261)+~P1(f318(f318(f225(x71261),f318(f72(x71261),x71263)),x71262))+P1(f318(f318(f225(x71261),f318(f72(x71261),x71262)),x71263))
% 109.14/108.85 [7127]~P65(x71271)+~P1(f318(f318(f225(x71271),f318(f72(x71271),x71273)),x71272))+P1(f318(f318(f225(x71271),f318(f72(x71271),x71272)),x71273))
% 109.14/108.85 [7128]~P91(x71281)+~P1(f318(f318(f225(x71281),f318(f69(x71281),x71282)),x71283))+P1(f318(f318(f225(x71281),f318(f72(x71281),x71282)),x71283))
% 109.14/108.85 [7129]~P91(x71291)+~P1(f318(f318(f225(x71291),f318(f69(x71291),x71292)),x71293))+P1(f318(f318(f225(x71291),f318(f72(x71291),x71292)),x71293))
% 109.14/108.85 [7130]~P65(x71301)+~P1(f318(f318(f226(x71301),f318(f72(x71301),x71303)),x71302))+P1(f318(f318(f226(x71301),f318(f72(x71301),x71302)),x71303))
% 109.14/108.85 [7131]~P65(x71311)+~P1(f318(f318(f226(x71311),f318(f72(x71311),x71313)),x71312))+P1(f318(f318(f226(x71311),f318(f72(x71311),x71312)),x71313))
% 109.14/108.85 [7132]~P116(x71321)+~P1(f318(f318(f226(x71321),f318(f69(x71321),x71322)),x71323))+P1(f318(f318(f226(x71321),f318(f72(x71321),x71322)),x71323))
% 109.14/108.85 [7164]~P1(f318(x71643,f825(x71642,x71641,x71643)))+P1(f318(f318(f226(a911),x71641),x71642))+P1(f318(x71643,f318(f318(f3(a911),x71641),x71642)))
% 109.14/108.85 [7165]~P1(f318(x71653,f833(x71652,x71651,x71653)))+P1(f318(f318(f226(a911),x71651),x71652))+P1(f318(x71653,f318(f318(f3(a911),x71651),x71652)))
% 109.14/108.85 [7217]~E(f875(x72173,x72172,x72171),f876(x72173,x72172,x72171))+E(f318(f318(f92(f918(x72171,a909)),x72172),f31(f918(x72171,a909),x72173)),f179(f918(x72171,a909)))+P1(f318(f318(f320(f918(x72171,a909)),x72172),x72173))
% 109.14/108.85 [7224]~P1(f318(f55(x72241),x72243))+P1(f318(f55(x72241),f32(f918(x72241,a909),x72242)))+~P1(f318(f318(f320(f918(x72241,a909)),x72243),x72242))
% 109.14/108.85 [7284]~P4(x72841)+E(f318(f318(f101(f918(x72841,a909)),f318(f293(x72841,x72842),x72843)),f318(f318(f300(x72841),x72843),f179(f918(x72841,a909)))),f294(x72841,x72842,x72843))+~P1(f318(f318(f225(x72841),x72842),x72843))
% 109.14/108.85 [7287]E(x72871,f2(a911))+P1(f318(f318(f226(a911),f373(x72871,x72873,x72872)),x72871))+P1(f318(x72872,f318(f318(f30(a911),x72873),x72871)))
% 109.14/108.85 [7316]P1(f318(f318(f226(a911),f318(f180(f912(x73161)),x73162)),f782(x73163,x73161)))+~P1(f318(f55(f912(x73161)),x73163))+~P1(f318(f318(f320(f912(x73161)),x73162),x73163))
% 109.14/108.85 [7321]E(x73211,x73212)+~P1(f318(f318(f225(f918(x73213,a909)),x73211),x73212))+P1(f318(f318(f226(f918(x73213,a909)),x73211),x73212))
% 109.14/108.85 [7322]E(x73221,x73222)+~P1(f318(f318(f225(f918(x73223,a909)),x73221),x73222))+P1(f318(f318(f226(f918(x73223,a909)),x73221),x73222))
% 109.14/108.85 [7335]E(x73351,x73352)+~E(f318(f180(f912(x73353)),x73351),f318(f180(f912(x73353)),x73352))+P1(f318(f318(f226(a911),f635(x73353,x73351,x73352)),f318(f180(f912(x73353)),x73352)))
% 109.14/108.85 [7384]P8(x73841,x73842,x73843)+~E(f318(f255(x73841,x73841),x73843),x73842)+~E(f318(f318(f280(x73841,x73841,x73841),f318(f277(x73841,x73841),x73843)),x73843),x73843)
% 109.14/108.85 [7461]~P1(f318(x74611,f2(a911)))+P1(f318(f318(f226(a911),f373(x74613,x74612,x74611)),x74613))+P1(f318(x74611,f318(f318(f30(a911),x74612),x74613)))
% 109.14/108.85 [7470]~P4(x74701)+E(f318(f318(f101(f918(x74701,a909)),f297(x74701,x74702,x74703)),f318(f318(f300(x74701),x74703),f179(f918(x74701,a909)))),f296(x74701,x74702,x74703))+~P1(f318(f318(f226(x74701),x74702),x74703))
% 109.14/108.85 [7553]~P1(f318(f55(x75531),x75533))+P1(f318(f318(f225(a911),f318(f29(x75531),x75532)),f318(f29(x75531),x75533)))+~P1(f318(f318(f225(f918(x75531,a909)),x75532),x75533))
% 109.14/108.85 [7554]~P1(f318(f55(x75541),x75543))+P1(f318(f318(f226(a911),f318(f29(x75541),x75542)),f318(f29(x75541),x75543)))+~P1(f318(f318(f226(f918(x75541,a909)),x75542),x75543))
% 109.14/108.85 [7684]E(x76841,x76842)+~P1(f318(f318(f225(f918(x76843,a909)),x76842),x76841))+~P1(f318(f318(f225(f918(x76843,a909)),x76841),x76842))
% 109.14/108.85 [7685]E(x76851,x76852)+~P1(f318(f318(f225(f918(x76853,a909)),x76852),x76851))+~P1(f318(f318(f225(f918(x76853,a909)),x76851),x76852))
% 109.14/108.85 [7688]~P4(x76881)+P13(x76881,x76882)+~P13(x76881,f318(f318(f139(x76881,x76881,f7(x76881)),x76883),x76882))
% 109.14/108.85 [7756]~P1(f318(f318(f226(a911),x77563),x77562))+~P1(f318(f318(f226(a911),x77563),x77561))+P1(f318(f318(f226(a911),f318(f318(f3(a911),x77561),x77562)),f318(f318(f3(a911),x77561),x77563)))
% 109.14/108.85 [7757]~P1(f318(f318(f225(a911),x77572),x77571))+~P1(f318(f318(f226(a911),x77571),x77573))+P1(f318(f318(f226(a911),f318(f318(f3(a911),x77571),x77572)),f318(f318(f3(a911),x77573),x77572)))
% 109.14/108.85 [7772]~P1(f318(f318(f226(a1),x77722),f2(a1)))+~P1(f318(f318(f225(a1),x77723),x77721))+P1(f318(f318(f225(a1),f318(f318(f30(a1),x77721),x77722)),f318(f318(f30(a1),x77723),x77722)))
% 109.14/108.85 [7788]~P1(f318(f318(f226(a911),f2(a911)),x77881))+~P1(f318(f318(f225(a911),x77882),x77883))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x77881),x77882)),f318(f318(f74(a911),x77881),x77883)))
% 109.14/108.85 [7789]~P1(f318(f318(f226(a911),f2(a911)),x77893))+~P1(f318(f318(f225(a911),x77893),x77892))+P1(f318(f318(f225(a911),f318(f318(f30(a911),x77891),x77892)),f318(f318(f30(a911),x77891),x77893)))
% 109.14/108.85 [7790]~P1(f318(f318(f226(a1),f2(a1)),x77902))+~P1(f318(f318(f225(a1),x77901),x77903))+P1(f318(f318(f225(a1),f318(f318(f30(a1),x77901),x77902)),f318(f318(f30(a1),x77903),x77902)))
% 109.14/108.85 [7791]~P1(f318(f318(f226(a911),f2(a911)),x77911))+~P1(f318(f318(f226(a911),x77912),x77913))+P1(f318(f318(f226(a911),f318(f318(f74(a911),x77911),x77912)),f318(f318(f74(a911),x77911),x77913)))
% 109.14/108.85 [7792]~P1(f318(f318(f226(a911),f2(a911)),x77921))+~P1(f318(f318(f226(a911),x77922),x77923))+P1(f318(f318(f226(a911),f318(f318(f74(a911),x77921),x77922)),f318(f318(f74(a911),x77921),x77923)))
% 109.14/108.85 [7793]~P1(f318(f318(f226(a911),f2(a911)),x77932))+~P1(f318(f318(f226(a911),x77931),x77933))+P1(f318(f318(f226(a911),f318(f318(f74(a911),x77931),x77932)),f318(f318(f74(a911),x77933),x77932)))
% 109.14/108.85 [7794]~P1(f318(f318(f226(a911),f2(a911)),x77942))+~P1(f318(f318(f226(a911),x77941),x77943))+P1(f318(f318(f226(a911),f318(f318(f74(a911),x77941),x77942)),f318(f318(f74(a911),x77943),x77942)))
% 109.14/108.85 [7795]~P1(f318(f318(f226(a911),f2(a911)),x77951))+~P1(f318(f318(f226(a911),x77952),x77953))+P1(f318(f318(f226(a911),f318(f318(f74(a911),x77951),x77952)),f318(f318(f74(a911),x77951),x77953)))
% 109.14/108.85 [7796]~P1(f318(f318(f226(a1),f2(a1)),x77961))+~P1(f318(f318(f226(a1),x77962),x77963))+P1(f318(f318(f226(a1),f318(f318(f74(a1),x77961),x77962)),f318(f318(f74(a1),x77961),x77963)))
% 109.14/108.85 [7797]~P1(f318(f318(f226(a911),f2(a911)),x77971))+~P1(f318(f318(f278(a911),x77972),x77973))+P1(f318(f318(f278(a911),f318(f318(f74(a911),x77971),x77972)),f318(f318(f74(a911),x77971),x77973)))
% 109.14/108.85 [7845]E(x78451,f2(a911))+E(f318(f318(f73(a911),f318(f318(f74(a911),x78451),f372(x78451,x78452,x78453))),f373(x78451,x78452,x78453)),x78452)+P1(f318(x78453,f318(f318(f30(a911),x78452),x78451)))
% 109.14/108.85 [7905]E(f318(f318(f73(a911),f318(f318(f74(a911),x79051),f372(x79051,x79052,x79053))),f373(x79051,x79052,x79053)),x79052)+~P1(f318(x79053,f2(a911)))+P1(f318(x79053,f318(f318(f30(a911),x79052),x79051)))
% 109.14/108.85 [7924]~P1(f318(f55(x79241),x79243))+P1(f318(f318(f320(x79241),f413(x79242,x79243,x79241)),x79243))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f11(x79241,a911),x79242),x79243)))
% 109.14/108.85 [7925]~P1(f318(f55(x79251),x79253))+P1(f318(f318(f320(x79251),f414(x79252,x79253,x79251)),x79253))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f11(x79251,a911),x79252),x79253)))
% 109.14/108.85 [8024]E(x80241,f2(a911))+P1(f318(f318(f278(a911),x80242),x80243))+~P1(f318(f318(f278(a911),f318(f318(f74(a911),x80241),x80242)),f318(f318(f74(a911),x80241),x80243)))
% 109.14/108.85 [8214]E(x82141,f179(f918(x82142,a909)))+E(x82141,f318(f318(f300(x82142),x82143),f179(f918(x82142,a909))))+~P1(f318(f318(f225(f918(x82142,a909)),x82141),f318(f318(f300(x82142),x82143),f179(f918(x82142,a909)))))
% 109.14/108.85 [8238]~P4(x82381)+~P13(x82381,x82383)+P13(x82381,f318(f318(f129(x82381),f318(f180(f912(x82381)),f168(x82381,x82382,x82383))),x82383))
% 109.14/108.85 [8250]~P1(f318(f318(f226(a911),f2(a911)),x82503))+P1(f318(f318(f225(a911),x82501),x82502))+~P1(f318(f318(f225(a911),f318(f318(f74(a911),x82503),x82501)),f318(f318(f74(a911),x82503),x82502)))
% 109.14/108.85 [8251]~P1(f318(f318(f226(a911),f2(a911)),x82513))+P1(f318(f318(f225(a911),x82511),x82512))+~P1(f318(f318(f225(a911),f318(f318(f74(a911),x82513),x82511)),f318(f318(f74(a911),x82513),x82512)))
% 109.14/108.85 [8252]~P1(f318(f318(f226(a911),f71(a911)),x82523))+P1(f318(f318(f225(a911),x82521),x82522))+~P1(f318(f318(f278(a911),f318(f318(f235(a911),x82523),x82521)),f318(f318(f235(a911),x82523),x82522)))
% 109.14/108.85 [8253]~P1(f318(f318(f226(a911),f2(a911)),x82533))+P1(f318(f318(f225(a911),x82531),x82532))+~P1(f318(f318(f225(a911),f318(f318(f74(a911),x82531),x82533)),f318(f318(f74(a911),x82532),x82533)))
% 109.14/108.85 [8254]~P1(f318(f318(f226(a911),f2(a911)),x82543))+P1(f318(f318(f226(a911),x82541),x82542))+~P1(f318(f318(f226(a911),f318(f318(f235(a911),x82543),x82541)),f318(f318(f235(a911),x82543),x82542)))
% 109.14/108.85 [8255]~P1(f318(f318(f226(a911),f2(a911)),x82553))+P1(f318(f318(f226(a911),x82551),x82552))+~P1(f318(f318(f226(a911),f318(f318(f74(a911),x82553),x82551)),f318(f318(f74(a911),x82553),x82552)))
% 109.14/108.85 [8256]~P1(f318(f318(f226(a911),f2(a911)),x82563))+P1(f318(f318(f278(a911),x82561),x82562))+~P1(f318(f318(f278(a911),f318(f318(f74(a911),x82563),x82561)),f318(f318(f74(a911),x82563),x82562)))
% 109.14/108.85 [8257]~P1(f318(f318(f226(a911),f2(a911)),x82573))+P1(f318(f318(f278(a911),x82571),x82572))+~P1(f318(f318(f278(a911),f318(f318(f74(a911),x82573),x82571)),f318(f318(f74(a911),x82573),x82572)))
% 109.14/108.85 [8298]~E(f318(f318(f92(f918(x82981,a909)),f876(x82983,x82982,x82981)),f875(x82983,x82982,x82981)),f179(f918(x82981,a909)))+E(f318(f318(f92(f918(x82981,a909)),x82982),f31(f918(x82981,a909),x82983)),f179(f918(x82981,a909)))+P1(f318(f318(f320(f918(x82981,a909)),x82982),x82983))
% 109.14/108.85 [8311]E(x83111,f104(x83112))+~E(f318(f133(f912(x83112),f912(x83112),f125(x83112),f104(x83112)),x83113),f104(x83112))+~P1(f318(f318(f320(f912(x83112)),x83111),f318(f163(f912(x83112)),x83113)))
% 109.14/108.85 [8312]E(x83121,f104(x83122))+~E(f318(f133(f912(x83122),f912(x83122),f125(x83122),f104(x83122)),x83123),f104(x83122))+~P1(f318(f318(f320(f912(x83122)),x83121),f318(f163(f912(x83122)),x83123)))
% 109.14/108.85 [8366]E(x83661,f179(f918(f918(x83662,a909),a909)))+P1(f318(f318(f320(f918(x83662,a909)),f735(x83663,x83661,x83662)),x83661))+P1(f318(f318(f225(f918(x83662,a909)),f32(f918(x83662,a909),x83661)),x83663))
% 109.14/108.85 [8371]~P76(x83711)+~P82(x83711)+E(f318(f318(f8(a1,x83711),f318(f318(f10(a911,x83711,a1),x83712),a95)),f318(f301(a911,a1,f91(a1)),x83713)),f318(f318(f8(a911,x83711),x83712),x83713))
% 109.14/108.85 [8372]~P76(x83721)+~P82(x83721)+E(f318(f318(f11(a1,x83721),f318(f318(f10(a911,x83721,a1),x83722),a95)),f318(f301(a911,a1,f91(a1)),x83723)),f318(f318(f11(a911,x83721),x83722),x83723))
% 109.14/108.85 [8414]~P1(f318(f55(x84141),x84143))+~P1(f318(f318(f226(a911),f2(a911)),f318(x84142,f413(x84142,x84143,x84141))))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f11(x84141,a911),x84142),x84143)))
% 109.14/108.85 [8415]~P1(f318(f55(x84151),x84153))+~P1(f318(f318(f226(a911),f2(a911)),f318(x84152,f414(x84152,x84153,x84151))))+P1(f318(f318(f226(a911),f2(a911)),f318(f318(f11(x84151,a911),x84152),x84153)))
% 109.14/108.85 [8452]~P73(x84522)+E(x84521,f71(x84522))+E(f318(f318(f282(x84522),f318(f318(f3(x84522),f318(f318(f235(x84522),x84521),x84523)),f71(x84522))),f318(f318(f3(x84522),x84521),f71(x84522))),f318(f318(f8(a911,x84522),f318(f235(x84522),x84521)),f318(f293(a911,f2(a911)),x84523)))
% 109.14/108.85 [8506]E(x85061,f2(a911))+~P1(f318(x85063,f318(f318(f30(a911),x85062),x85061)))+P1(f318(f318(f226(a911),x85062),f318(f318(f74(a911),x85061),f318(a103,f374(x85061,x85062,x85063)))))
% 109.14/108.85 [8525]P1(f318(x85251,f2(a911)))+~P1(f318(x85251,f318(f318(f30(a911),x85252),x85253)))+P1(f318(f318(f226(a911),x85252),f318(f318(f74(a911),x85253),f318(a103,f374(x85253,x85252,x85251)))))
% 109.14/108.85 [8561]E(x85611,f2(a911))+~P1(f318(x85613,f318(f318(f30(a911),x85612),x85611)))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x85611),f374(x85611,x85612,x85613))),x85612))
% 109.14/108.85 [8595]P1(f318(x85951,f2(a911)))+~P1(f318(x85951,f318(f318(f30(a911),x85953),x85952)))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x85952),f374(x85952,x85953,x85951))),x85953))
% 109.14/108.85 [8603]~P4(x86031)+E(f318(f318(f139(x86031,x86031,f7(x86031)),x86032),x86033),f140(x86031,x86031,f7(x86031),x86032,x86033))+P1(f318(f318(f320(x86031),x86032),f318(f163(x86031),x86033)))
% 109.14/108.85 [8638]~E(f318(x86383,f583(x86382,x86383,x86381)),f318(x86383,f585(x86382,x86383,x86381)))+~P63(x86381,f318(x86383,f584(x86382,x86383,x86381)))+P63(x86381,f318(f318(f33(x86382,f918(x86381,f918(x86381,a909))),f233(f918(x86382,a909))),x86383))
% 109.14/108.85 [8647]E(x86471,f179(f918(f918(x86472,a909),a909)))+~P1(f318(f318(f225(f918(x86472,a909)),f735(x86473,x86471,x86472)),x86473))+P1(f318(f318(f225(f918(x86472,a909)),f32(f918(x86472,a909),x86471)),x86473))
% 109.14/108.85 [8711]~P75(x87111)+~P1(f318(f318(f226(x87111),x87112),x87113))+P1(f318(f318(f226(x87111),x87112),f318(f318(f282(x87111),f318(f318(f73(x87111),x87112),x87113)),f318(f318(f73(x87111),f71(x87111)),f71(x87111)))))
% 109.14/108.85 [8769]~P1(f318(f318(x87691,f485(x87691,x87693,x87692)),f489(x87691,x87693,x87692)))+P1(f318(f318(x87691,x87692),x87693))+~P1(f318(f306(f917(a1,a1),a46),f318(f318(f243(a1,a1),x87692),x87693)))
% 109.14/108.85 [8770]~P1(f318(f318(x87701,f490(x87701,x87703,x87702)),f492(x87701,x87703,x87702)))+P1(f318(f318(x87701,x87702),x87703))+~P1(f318(f306(f917(a1,a1),a52),f318(f318(f243(a1,a1),x87702),x87703)))
% 109.14/108.85 [8771]~P1(f318(f318(x87711,f495(x87711,x87713,x87712)),f497(x87711,x87713,x87712)))+P1(f318(f318(x87711,x87712),x87713))+~P1(f318(f306(f917(a1,a1),a212),f318(f318(f243(a1,a1),x87712),x87713)))
% 109.14/108.85 [8772]~P1(f318(f318(x87721,f498(x87721,x87723,x87722)),f500(x87721,x87723,x87722)))+P1(f318(f318(x87721,x87722),x87723))+~P1(f318(f306(f917(a911,a911),a210),f318(f318(f243(a911,a911),x87722),x87723)))
% 109.14/108.85 [8773]~P1(f318(f318(x87731,f669(x87731,x87733,x87732)),f671(x87731,x87733,x87732)))+P1(f318(f318(x87731,x87732),x87733))+~P1(f318(f306(f917(a1,a1),a173),f318(f318(f243(a1,a1),x87732),x87733)))
% 109.14/108.85 [8774]~P1(f318(f318(x87741,f766(x87741,x87743,x87742)),f767(x87741,x87743,x87742)))+P1(f318(f318(x87741,x87742),x87743))+~P1(f318(f306(f917(a1,a1),a124),f318(f318(f243(a1,a1),x87742),x87743)))
% 109.14/108.85 [9045]P1(f318(f318(x90451,x90452),x90453))+P1(f318(f306(f917(a911,a911),a210),f318(f318(f243(a911,a911),f498(x90451,x90453,x90452)),f500(x90451,x90453,x90452))))+~P1(f318(f306(f917(a911,a911),a210),f318(f318(f243(a911,a911),x90452),x90453)))
% 109.14/108.85 [9046]P1(f318(f318(x90461,x90462),x90463))+P1(f318(f306(f917(a1,a1),a46),f318(f318(f243(a1,a1),f485(x90461,x90463,x90462)),f489(x90461,x90463,x90462))))+~P1(f318(f306(f917(a1,a1),a46),f318(f318(f243(a1,a1),x90462),x90463)))
% 109.14/108.85 [9047]P1(f318(f318(x90471,x90472),x90473))+P1(f318(f306(f917(a1,a1),a52),f318(f318(f243(a1,a1),f490(x90471,x90473,x90472)),f492(x90471,x90473,x90472))))+~P1(f318(f306(f917(a1,a1),a52),f318(f318(f243(a1,a1),x90472),x90473)))
% 109.14/108.85 [9048]P1(f318(f318(x90481,x90482),x90483))+P1(f318(f306(f917(a1,a1),a212),f318(f318(f243(a1,a1),f495(x90481,x90483,x90482)),f497(x90481,x90483,x90482))))+~P1(f318(f306(f917(a1,a1),a212),f318(f318(f243(a1,a1),x90482),x90483)))
% 109.14/108.85 [9049]P1(f318(f318(x90491,x90492),x90493))+P1(f318(f306(f917(a1,a1),a173),f318(f318(f243(a1,a1),f669(x90491,x90493,x90492)),f671(x90491,x90493,x90492))))+~P1(f318(f306(f917(a1,a1),a173),f318(f318(f243(a1,a1),x90492),x90493)))
% 109.14/108.85 [9050]P1(f318(f318(x90501,x90502),x90503))+P1(f318(f306(f917(a1,a1),a124),f318(f318(f243(a1,a1),f766(x90501,x90503,x90502)),f767(x90501,x90503,x90502))))+~P1(f318(f306(f917(a1,a1),a124),f318(f318(f243(a1,a1),x90502),x90503)))
% 109.14/108.85 [9382]~P1(f318(f55(x93821),x93823))+P1(f318(f318(f320(f917(f918(x93821,a909),f918(x93821,a909))),f318(f318(f243(f918(x93821,a909),f918(x93821,a909)),x93822),x93823)),f305(x93821)))+~P1(f318(f318(f226(f918(x93821,a909)),x93822),x93823))
% 109.14/108.85 [9464]~P63(x94641,f318(x94643,f584(x94642,x94643,x94641)))+P63(x94641,f318(f318(f33(x94642,f918(x94641,f918(x94641,a909))),f233(f918(x94642,a909))),x94643))+~E(f318(f318(f92(f918(x94641,a909)),f240(x94641,x94641,f318(x94643,f583(x94642,x94643,x94641)))),f241(x94641,x94641,f318(x94643,f585(x94642,x94643,x94641)))),f179(f918(x94641,a909)))
% 109.14/108.85 [9661]P56(x96611,x96612,x96613)+P1(f318(f318(f320(f917(x96611,x96611)),f525(x96613,x96612,x96611)),x96613))+~P1(f318(f318(f320(f917(x96611,x96611)),f318(f318(f243(x96611,x96611),f524(x96613,x96612,x96611)),f524(x96613,x96612,x96611))),x96613))
% 109.14/108.85 [10270]P56(x102701,x102702,x102703)+~P1(f318(f318(f248(x102701,x102701,a909),f318(f318(f9(x102701,f918(x102701,a909),f918(x102701,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x102701,a909),f918(x102701,a909)),x102701),f10(a909,a909,x102701)),f318(f318(f10(a909,f918(a909,a909),x102701),a316),f318(f318(f9(x102701,f918(x102701,a909),a909),f320(x102701)),x102702)))),f318(f318(f9(x102701,f918(x102701,a909),a909),f320(x102701)),x102702))),f525(x102703,x102702,x102701)))+~P1(f318(f318(f320(f917(x102701,x102701)),f318(f318(f243(x102701,x102701),f524(x102703,x102702,x102701)),f524(x102703,x102702,x102701))),x102703))
% 109.14/108.85 [5787]~P69(x57872)+E(x57871,f2(x57872))+E(f318(f318(f30(x57872),f318(f318(f74(x57872),x57873),x57871)),x57871),x57873)
% 109.14/108.85 [5788]~P69(x57882)+E(x57881,f2(x57882))+E(f318(f318(f30(x57882),f318(f318(f74(x57882),x57881),x57883)),x57881),x57883)
% 109.14/108.85 [6433]~P69(x64331)+E(f318(f318(f74(x64331),f318(f318(f30(x64331),x64332),x64333)),x64333),x64332)+~P1(f318(f318(f278(x64331),x64333),x64332))
% 109.14/108.85 [6595]~P76(x65951)+~E(f318(x65952,f2(a911)),f2(x65951))+E(f318(f318(f8(a911,x65951),x65952),f318(f293(a911,f318(a103,f2(a911))),x65953)),f318(f318(f8(a911,x65951),x65952),f318(f293(a911,f2(a911)),x65953)))
% 109.14/108.85 [6729]~P69(x67292)+E(x67291,f2(x67292))+E(f318(f318(f30(x67292),f318(f318(f73(x67292),x67293),x67291)),x67291),f318(f318(f73(x67292),f318(f318(f30(x67292),x67293),x67291)),f71(x67292)))
% 109.14/108.85 [6730]~P69(x67302)+E(x67301,f2(x67302))+E(f318(f318(f30(x67302),f318(f318(f73(x67302),x67301),x67303)),x67301),f318(f318(f73(x67302),f318(f318(f30(x67302),x67303),x67301)),f71(x67302)))
% 109.14/108.85 [6947]~P1(f318(x69473,f2(a1)))+P1(f318(f318(f225(a911),x69471),x69472))+P1(f318(x69473,f318(f91(a1),f318(f318(f3(a911),x69472),x69471))))
% 109.14/108.85 [7051]P1(f318(f318(f226(a911),x70512),x70511))+P1(f318(f318(f225(a911),x70511),x70512))+P1(f318(x70513,f318(f91(a1),f318(f318(f3(a911),x70512),x70511))))
% 109.14/108.85 [7125]E(f318(f318(f73(a911),f318(f94(a911),x71251)),f318(f318(f73(a911),f318(f94(a911),x71252)),x71253)),f318(f318(f73(a911),f318(f94(a911),x71251)),x71253))+P1(f318(a184,f318(f94(a1),x71251)))+~P1(f318(a184,f318(f94(a1),x71252)))
% 109.14/108.85 [7204]~E(x72042,f318(f318(f30(a911),x72043),x72041))+~P1(f318(f318(f226(a911),f2(a911)),x72041))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x72041),x72042)),x72043))
% 109.14/108.85 [7318]~P1(f318(f55(x73181),x73183))+~P1(f318(f55(x73181),x73182))+P1(f318(f55(x73181),f318(f318(f101(f918(x73181,a909)),x73182),x73183)))
% 109.14/108.85 [7319]~P1(f318(f55(x73191),x73193))+~P1(f318(f55(x73191),x73192))+P1(f318(f55(x73191),f318(f318(f101(f918(x73191,a909)),x73192),x73193)))
% 109.14/108.85 [7320]~P1(f318(f55(x73201),x73203))+~P1(f318(f55(x73201),x73202))+P1(f318(f55(x73201),f318(f318(f3(f918(x73201,a909)),x73202),x73203)))
% 109.14/108.85 [7369]~P40(x73691,x73693)+~P40(x73691,x73692)+P40(x73691,f318(f318(f92(f918(f917(x73691,x73691),a909)),x73692),x73693))
% 109.14/108.85 [7370]~P55(x73701,x73703)+~P55(x73701,x73702)+P55(x73701,f318(f318(f101(f918(f917(x73701,x73701),a909)),x73702),x73703))
% 109.14/108.85 [7371]~P55(x73711,x73713)+~P55(x73711,x73712)+P55(x73711,f318(f318(f92(f918(f917(x73711,x73711),a909)),x73712),x73713))
% 109.14/108.85 [7602]~P4(x76021)+~P1(f318(f55(x76021),x76022))+E(f130(x76021,f318(f318(f3(f918(x76021,a909)),x76022),f318(f318(f300(x76021),x76023),f179(f918(x76021,a909))))),f161(x76021,x76023,f130(x76021,x76022)))
% 109.14/108.85 [7664]P1(f318(x76641,f2(a1)))+~P1(f318(f318(f226(a911),x76642),x76643))+~P1(f318(x76641,f318(f91(a1),f318(f318(f3(a911),x76642),x76643))))
% 109.14/108.85 [7682]~P1(f318(f55(x76821),x76822))+E(f318(f29(x76821),f318(f318(f3(f918(x76821,a909)),x76822),f318(f318(f300(x76821),x76823),f179(f918(x76821,a909))))),f318(f29(x76821),x76822))+P1(f318(f318(f320(x76821),x76823),x76822))
% 109.14/108.85 [7813]~P130(x78131)+~P1(f318(f318(f226(x78131),f71(x78131)),x78132))+P1(f318(f318(f226(x78131),f71(x78131)),f318(f318(f74(x78131),x78132),f318(f318(f235(x78131),x78132),x78133))))
% 109.14/108.85 [7855]~P1(f318(f55(x78551),x78553))+E(f318(f318(f3(a911),f318(f29(x78551),x78552)),f318(f29(x78551),x78553)),f318(f29(x78551),f318(f318(f3(f918(x78551,a909)),x78552),x78553)))+~P1(f318(f318(f225(f918(x78551,a909)),x78553),x78552))
% 109.14/108.85 [7913]~P1(f318(f318(f225(a911),x79132),x79133))+~P1(f318(f318(f225(a911),x79131),f318(f318(f3(a911),x79133),x79132)))+P1(f318(f318(f225(a911),f318(f318(f73(a911),x79131),x79132)),x79133))
% 109.14/108.85 [7971]P1(f318(f55(x79711),x79712))+~P1(f318(f55(x79711),x79713))+~P1(f318(f55(x79711),f318(f318(f3(f918(x79711,a909)),x79712),x79713)))
% 109.14/108.85 [7976]~P1(f318(f55(x79761),x79762))+E(f318(f29(x79761),f318(f318(f3(f918(x79761,a909)),x79762),f318(f318(f300(x79761),x79763),f179(f918(x79761,a909))))),f318(f318(f3(a911),f318(f29(x79761),x79762)),f71(a911)))+~P1(f318(f318(f320(x79761),x79763),x79762))
% 109.14/108.85 [7977]~P1(f318(f55(x79771),x79772))+E(f318(f29(x79771),f318(f318(f3(f918(x79771,a909)),x79772),f318(f318(f300(x79771),x79773),f179(f918(x79771,a909))))),f318(f318(f3(a911),f318(f29(x79771),x79772)),f71(a911)))+~P1(f318(f318(f320(x79771),x79773),x79772))
% 109.14/108.85 [8049]P63(x80491,x80492)+~P63(x80491,x80493)+~P1(f318(f318(f225(f918(x80491,f918(x80491,a909))),x80492),x80493))
% 109.14/108.85 [8086]~P1(f318(f318(f225(a911),x80863),x80862))+P1(f318(f318(f225(a911),x80861),f318(f318(f3(a911),x80862),x80863)))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),x80861),x80863)),x80862))
% 109.14/108.85 [8104]P39(x81041,x81042)+~P39(x81041,x81043)+~P1(f318(f318(f225(f918(f917(x81041,x81041),a909)),x81042),x81043))
% 109.14/108.85 [8105]P61(x81051,x81052)+~P61(x81051,x81053)+~P1(f318(f318(f225(f918(f917(x81051,x81051),a909)),x81052),x81053))
% 109.14/108.85 [8106]P41(x81061,x81062)+~P41(x81061,x81063)+~P1(f318(f318(f225(f918(f917(x81061,x81061),a909)),x81062),x81063))
% 109.14/108.85 [8346]~P130(x83461)+~P1(f318(f318(f226(x83461),f71(x83461)),x83462))+P1(f318(f318(f226(x83461),f318(f318(f235(x83461),x83462),x83463)),f318(f318(f74(x83461),x83462),f318(f318(f235(x83461),x83462),x83463))))
% 109.14/108.85 [8433]~P1(f318(x84331,f2(a1)))+~P1(f318(x84331,f318(f318(f3(a1),f318(f91(a1),x84332)),f318(f91(a1),x84333))))+P1(f318(x84331,f318(f91(a1),f318(f318(f3(a911),x84332),x84333))))
% 109.14/108.85 [8448]~P1(f318(f318(f225(a911),x84483),x84482))+P1(f318(x84481,f318(f318(f3(a1),f318(f91(a1),x84482)),f318(f91(a1),x84483))))+~P1(f318(x84481,f318(f91(a1),f318(f318(f3(a911),x84482),x84483))))
% 109.14/108.85 [8468]P1(f318(f318(f226(a911),x84681),x84682))+~P1(f318(x84683,f318(f318(f3(a1),f318(f91(a1),x84681)),f318(f91(a1),x84682))))+P1(f318(x84683,f318(f91(a1),f318(f318(f3(a911),x84681),x84682))))
% 109.14/108.85 [8518]~P131(x85182)+E(x85181,f2(x85182))+P1(f318(f318(f226(x85182),f2(x85182)),f318(f318(f73(x85182),f318(f318(f74(x85182),x85183),x85183)),f318(f318(f74(x85182),x85181),x85181))))
% 109.14/108.85 [8519]~P131(x85192)+E(x85191,f2(x85192))+P1(f318(f318(f226(x85192),f2(x85192)),f318(f318(f73(x85192),f318(f318(f74(x85192),x85191),x85191)),f318(f318(f74(x85192),x85193),x85193))))
% 109.14/108.85 [8622]~P1(f318(f318(f226(a911),f2(a911)),x86221))+~P1(f318(f318(f226(a1),x86222),x86223))+P1(f318(f318(f226(a1),f318(f318(f74(a1),f318(f91(a1),x86221)),x86222)),f318(f318(f74(a1),f318(f91(a1),x86221)),x86223)))
% 109.14/108.85 [8679]E(f318(f318(f92(f918(x86791,a909)),x86792),f31(f918(x86791,a909),x86793)),f179(f918(x86791,a909)))+P1(f318(f318(f320(f918(x86791,a909)),x86792),x86793))+P1(f318(f318(f320(f918(x86791,a909)),f876(x86793,x86792,x86791)),f318(f318(f300(f918(x86791,a909)),x86792),x86793)))
% 109.14/108.85 [8680]E(f318(f318(f92(f918(x86801,a909)),x86802),f31(f918(x86801,a909),x86803)),f179(f918(x86801,a909)))+P1(f318(f318(f320(f918(x86801,a909)),x86802),x86803))+P1(f318(f318(f320(f918(x86801,a909)),f875(x86803,x86802,x86801)),f318(f318(f300(f918(x86801,a909)),x86802),x86803)))
% 109.14/108.85 [8710]E(x87101,x87102)+~E(f318(f180(f912(x87103)),x87101),f318(f180(f912(x87103)),x87102))+P1(f318(f318(f320(f917(x87103,x87103)),f659(x87103,x87101,x87102)),f318(f163(f917(x87103,x87103)),f318(f318(f172(x87103,x87103),x87102),x87101))))
% 109.14/108.85 [8952]E(f298(x89521,x89522),f298(x89521,x89523))+~P1(f318(f318(f225(f918(f917(x89521,x89521),a909)),x89523),f298(x89521,x89522)))+~P1(f318(f318(f225(f918(f917(x89521,x89521),a909)),x89522),x89523))
% 109.14/108.85 [9024]~P56(x90241,f233(f918(x90241,a909)),x90243)+P1(f318(f318(f225(f918(f917(f912(x90241),f912(x90241)),a909)),f148(x90241,x90242)),f149(x90241,x90243)))+~P1(f318(f318(f225(f918(f917(x90241,x90241),a909)),x90242),x90243))
% 109.14/108.85 [9215]P39(x92151,x92152)+~P1(f318(f318(f320(x92151),x92153),f594(x92152,x92151)))+P1(f318(f318(f320(f917(x92151,x92151)),f318(f318(f243(x92151,x92151),f609(x92152,x92151,x92153)),x92153)),x92152))
% 109.14/108.85 [9244]~P1(f318(f55(x92441),x92442))+P1(f318(f55(f918(x92441,a909)),f318(f318(f54(x92441),x92442),x92443)))+~P1(f318(f318(f225(f918(f917(x92441,x92441),a909)),x92443),f318(f318(f245(x92441,x92441),x92442),f318(f18(f918(x92441,a909),x92441),x92442))))
% 109.14/108.85 [9287]P56(x92871,x92872,x92873)+P1(f318(f318(f320(x92871),f538(x92873,x92872,x92871)),x92872))+~P1(f318(f318(f225(f918(f917(x92871,x92871),a909)),x92873),f318(f318(f245(x92871,x92871),x92872),f318(f18(f918(x92871,a909),x92871),x92872))))
% 109.14/108.85 [9288]P56(x92881,x92882,x92883)+P1(f318(f318(f320(x92881),f541(x92882,x92883,x92881)),x92882))+~P1(f318(f318(f225(f918(f917(x92881,x92881),a909)),x92883),f318(f318(f245(x92881,x92881),x92882),f318(f18(f918(x92881,a909),x92881),x92882))))
% 109.14/108.85 [9327]~P75(x93271)+~P1(f318(f318(f226(x93271),x93272),x93273))+P1(f318(f318(f226(x93271),f318(f318(f282(x93271),f318(f318(f73(x93271),x93272),x93273)),f318(f318(f73(x93271),f71(x93271)),f71(x93271)))),x93273))
% 109.14/108.85 [9356]~P74(x93561)+P1(f318(f318(f225(x93561),x93562),x93563))+~P1(f318(f318(f225(x93561),f318(f318(f74(x93561),f394(x93563,x93562,x93561)),x93562)),x93563))
% 109.14/108.85 [9495]E(f318(f180(f912(f912(x94951))),f318(f127(f912(x94951),f318(f318(f10(a911,a909,f912(x94951)),f318(f226(a911),x94952)),f180(f912(x94951)))),f170(x94951,x94953))),f318(f180(f912(x94951)),f318(f318(f155(f912(x94951)),x94953),x94952)))+~P13(a911,f318(f159(a911),f318(f318(f145(f912(x94951),a911),f180(f912(x94951))),x94953)))+~P1(f318(f318(f226(a911),x94952),f318(f180(f912(f912(x94951))),x94953)))
% 109.14/108.85 [9608]~P39(x96081,x96082)+P27(x96081,f318(f318(f243(f918(f917(x96081,x96081),a909),f918(f917(x96081,x96081),a909)),x96082),x96083))+~P1(f318(f318(f225(f918(f917(x96081,x96081),a909)),f318(f318(f280(x96081,x96081,x96081),x96082),x96083)),x96082))
% 109.14/108.85 [9613]E(f318(f318(f145(f912(x96131),x96131),f318(f318(f9(f912(x96131),a911,x96131),f155(x96131)),x96132)),f318(f127(f912(x96131),f318(f318(f10(a911,a909,f912(x96131)),f318(f226(a911),x96132)),f180(f912(x96131)))),f170(x96131,x96133))),f318(f318(f155(f912(x96131)),x96133),x96132))+~P13(a911,f318(f159(a911),f318(f318(f145(f912(x96131),a911),f180(f912(x96131))),x96133)))+~P1(f318(f318(f226(a911),x96132),f318(f180(f912(f912(x96131))),x96133)))
% 109.14/108.85 [9758]P56(x97581,x97582,x97583)+~P1(f318(f318(f320(f917(x97581,x97581)),f318(f318(f243(x97581,x97581),f538(x97583,x97582,x97581)),f538(x97583,x97582,x97581))),x97583))+~P1(f318(f318(f225(f918(f917(x97581,x97581),a909)),x97583),f318(f318(f245(x97581,x97581),x97582),f318(f18(f918(x97581,a909),x97581),x97582))))
% 109.14/108.85 [9759]P56(x97591,x97592,x97593)+~P1(f318(f318(f320(f917(x97591,x97591)),f318(f318(f243(x97591,x97591),f541(x97592,x97593,x97591)),f541(x97592,x97593,x97591))),x97593))+~P1(f318(f318(f225(f918(f917(x97591,x97591),a909)),x97593),f318(f318(f245(x97591,x97591),x97592),f318(f18(f918(x97591,a909),x97591),x97592))))
% 109.14/108.85 [9957]~P144(x99571)+~P128(x99571)+E(f318(f318(f282(x99571),f318(f93(x99571),f318(f318(f66(f917(a1,a1),a1,x99572,f242(a1,a1)),f203(x99572)),x99573))),f318(f93(x99571),f318(f318(f66(f917(a1,a1),a1,x99572,f247(a1,a1)),f203(x99572)),x99573))),f213(x99572,x99571,x99573))
% 109.14/108.85 [10139]~E(x101393,f2(a911))+~E(f318(f180(f912(x101391)),f318(f318(f155(f912(x101391)),x101392),f707(x101393,x101391,x101392))),x101393)+E(f318(f318(f145(a911,f912(x101391)),f318(f318(f9(a911,f912(a911),f912(x101391)),f318(f318(f10(f918(a911,x101391),f918(f912(a911),f912(x101391)),a911),f145(a911,x101391)),f318(f9(a911,a911,x101391),f318(f318(f10(f912(x101391),f918(a911,x101391),a911),f155(x101391)),f318(f155(f912(x101391)),x101392))))),f130(a911,f318(f293(a911,f2(a911)),f318(f180(f912(f912(x101391))),x101392))))),f130(a911,f318(f293(a911,f2(a911)),x101393))),f170(x101391,x101392))
% 109.14/108.85 [10140]E(x101401,f104(f912(x101402)))+~E(f318(f180(f912(x101402)),f318(f318(f155(f912(x101402)),x101401),f707(x101403,x101402,x101401))),x101403)+E(f318(f318(f145(a911,f912(x101402)),f318(f318(f9(a911,f912(a911),f912(x101402)),f318(f318(f10(f918(a911,x101402),f918(f912(a911),f912(x101402)),a911),f145(a911,x101402)),f318(f9(a911,a911,x101402),f318(f318(f10(f912(x101402),f918(a911,x101402),a911),f155(x101402)),f318(f155(f912(x101402)),x101401))))),f130(a911,f318(f293(a911,f2(a911)),f318(f180(f912(f912(x101402))),x101401))))),f130(a911,f318(f293(a911,f2(a911)),x101403))),f170(x101402,x101401))
% 109.14/108.85 [10141]~E(x101413,f2(a911))+E(f318(f318(f145(a911,f912(x101411)),f318(f318(f9(a911,f912(a911),f912(x101411)),f318(f318(f10(f918(a911,x101411),f918(f912(a911),f912(x101411)),a911),f145(a911,x101411)),f318(f9(a911,a911,x101411),f318(f318(f10(f912(x101411),f918(a911,x101411),a911),f155(x101411)),f318(f155(f912(x101411)),x101412))))),f130(a911,f318(f293(a911,f2(a911)),f318(f180(f912(f912(x101411))),x101412))))),f130(a911,f318(f293(a911,f2(a911)),x101413))),f170(x101411,x101412))+P1(f318(f318(f226(a911),f707(x101413,x101411,x101412)),f318(f180(f912(f912(x101411))),x101412)))
% 109.14/108.85 [10142]E(x101421,f104(f912(x101422)))+E(f318(f318(f145(a911,f912(x101422)),f318(f318(f9(a911,f912(a911),f912(x101422)),f318(f318(f10(f918(a911,x101422),f918(f912(a911),f912(x101422)),a911),f145(a911,x101422)),f318(f9(a911,a911,x101422),f318(f318(f10(f912(x101422),f918(a911,x101422),a911),f155(x101422)),f318(f155(f912(x101422)),x101421))))),f130(a911,f318(f293(a911,f2(a911)),f318(f180(f912(f912(x101422))),x101421))))),f130(a911,f318(f293(a911,f2(a911)),x101423))),f170(x101422,x101421))+P1(f318(f318(f226(a911),f707(x101423,x101422,x101421)),f318(f180(f912(f912(x101422))),x101421)))
% 109.14/108.85 [7852]E(f318(f318(f73(a911),f318(f94(a911),x78521)),f318(f318(f73(a911),f318(f94(a911),x78522)),x78523)),f318(f318(f73(a911),f318(f94(a911),f318(f318(f73(a1),x78521),x78522))),x78523))+P1(f318(a184,f318(f94(a1),x78521)))+P1(f318(a184,f318(f94(a1),x78522)))
% 109.14/108.85 [8614]~P1(f318(f55(x86141),x86142))+~P1(f318(f318(f320(x86141),x86143),x86142))+E(f318(a103,f318(f29(x86141),f318(f318(f3(f918(x86141,a909)),x86142),f318(f318(f300(x86141),x86143),f179(f918(x86141,a909)))))),f318(f29(x86141),x86142))
% 109.14/108.85 [8628]~P1(f318(f55(x86281),x86282))+~P1(f318(f318(f320(x86281),x86283),x86282))+E(f318(f318(f73(a911),f71(a911)),f318(f29(x86281),f318(f318(f3(f918(x86281,a909)),x86282),f318(f318(f300(x86281),x86283),f179(f918(x86281,a909)))))),f318(f29(x86281),x86282))
% 109.14/108.85 [8718]~P4(x87181)+~P1(f318(f55(x87181),x87183))+E(f318(f318(f139(x87181,x87181,f7(x87181)),x87182),f130(x87181,f318(f318(f3(f918(x87181,a909)),x87183),f318(f318(f300(x87181),x87182),f179(f918(x87181,a909)))))),f130(x87181,f318(f318(f300(x87181),x87182),x87183)))
% 109.14/108.85 [8876]~P1(f318(f55(x88761),x88763))+~P1(f318(f55(x88761),x88762))+E(f318(f318(f73(a911),f318(f29(x88761),f318(f318(f101(f918(x88761,a909)),x88762),x88763))),f318(f29(x88761),f318(f318(f92(f918(x88761,a909)),x88762),x88763))),f318(f318(f73(a911),f318(f29(x88761),x88762)),f318(f29(x88761),x88763)))
% 109.14/108.85 [8877]~P1(f318(f55(x88771),x88773))+~P1(f318(f55(x88771),x88772))+E(f318(f318(f73(a911),f318(f29(x88771),f318(f318(f101(f918(x88771,a909)),x88772),x88773))),f318(f29(x88771),f318(f318(f92(f918(x88771,a909)),x88772),x88773))),f318(f318(f73(a911),f318(f29(x88771),x88772)),f318(f29(x88771),x88773)))
% 109.14/108.85 [10100]~P25(x101001,f918(f918(x101001,a909),a909),f318(f318(f9(x101001,f918(f917(x101001,x101001),a909),f918(f918(x101001,a909),a909)),f318(f318(f10(f918(x101001,a909),f918(f918(f917(x101001,x101001),a909),f918(f918(x101001,a909),a909)),x101001),f54(x101001)),f318(f318(f9(x101001,f918(x101001,a909),f918(x101001,a909)),f300(x101001)),f179(f918(x101001,a909))))),x101003),x101002)+~P1(f318(f55(x101001),x101002))+E(f318(f29(f918(x101001,a909)),f318(f318(f54(x101001),x101002),x101003)),f318(f29(x101001),x101002))
% 109.14/108.85 [10417]~P42(f918(x104171,a909),f918(x104171,a909),x104172)+~P1(f318(f318(f225(f918(x104171,a909)),x104173),f318(x104172,f86(f918(x104171,a909),f318(f318(f9(f918(x104171,a909),f918(x104171,a909),f918(x104171,a909)),f318(f318(f10(f918(x104171,a909),f918(f918(x104171,a909),f918(x104171,a909)),f918(x104171,a909)),f101(f918(x104171,a909))),f318(f318(f9(f918(x104171,a909),f918(x104171,a909),f918(x104171,a909)),f318(f318(f10(f918(x104171,a909),f918(f918(x104171,a909),f918(x104171,a909)),f918(x104171,a909)),f101(f918(x104171,a909))),x104172)),x104173))),f87(f918(x104171,a909),x104172))))))+P1(f318(f318(f225(f918(x104171,a909)),f86(f918(x104171,a909),f318(f318(f9(f918(x104171,a909),f918(x104171,a909),f918(x104171,a909)),f318(f318(f10(f918(x104171,a909),f918(f918(x104171,a909),f918(x104171,a909)),f918(x104171,a909)),f101(f918(x104171,a909))),f318(f318(f9(f918(x104171,a909),f918(x104171,a909),f918(x104171,a909)),f318(f318(f10(f918(x104171,a909),f918(f918(x104171,a909),f918(x104171,a909)),f918(x104171,a909)),f101(f918(x104171,a909))),x104172)),x104173))),f87(f918(x104171,a909),x104172)))),f318(x104172,f86(f918(x104171,a909),f318(f318(f9(f918(x104171,a909),f918(x104171,a909),f918(x104171,a909)),f318(f318(f10(f918(x104171,a909),f918(f918(x104171,a909),f918(x104171,a909)),f918(x104171,a909)),f101(f918(x104171,a909))),f318(f318(f9(f918(x104171,a909),f918(x104171,a909),f918(x104171,a909)),f318(f318(f10(f918(x104171,a909),f918(f918(x104171,a909),f918(x104171,a909)),f918(x104171,a909)),f101(f918(x104171,a909))),x104172)),x104173))),f87(f918(x104171,a909),x104172))))))
% 109.14/108.85 [8265]~P99(x82651)+P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x82653)))+E(f318(f318(f235(x82651),x82652),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x82653)),x82653))),f71(x82651))
% 109.14/108.85 [8340]~P99(x83401)+P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x83403)))+E(f318(f318(f235(x83401),f318(f94(x83401),x83402)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x83403)),x83403))),f71(x83401))
% 109.14/108.85 [9601]~P99(x96011)+~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x96013)))+E(f318(f318(f235(x96011),x96012),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96013)),x96013))),f318(f318(f81(x96011,x96011),f318(f318(f235(x96011),x96012),f318(f94(a911),x96013))),f318(f318(f20(x96011,x96011,x96011),f318(f318(f10(x96011,f918(x96011,x96011),x96011),f74(x96011)),f318(f74(x96011),x96012))),f7(x96011))))
% 109.14/108.85 [9666]~P99(x96661)+~P1(f318(f318(f225(a1),f2(a1)),f318(f94(a1),x96663)))+E(f318(f318(f235(x96661),f318(f94(x96661),x96662)),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96663)),x96663))),f318(f318(f81(x96661,x96661),f318(f318(f235(x96661),f318(f94(x96661),x96662)),f318(f94(a911),x96663))),f318(f318(f20(x96661,x96661,x96661),f318(f318(f10(x96661,f918(x96661,x96661),x96661),f74(x96661)),f318(f74(x96661),f318(f94(x96661),x96662)))),f7(x96661))))
% 109.14/108.85 [10020]~P1(f318(f128(x100201),x100203))+~P1(f318(f318(f320(x100201),x100202),f318(f163(x100201),x100203)))+E(f318(f318(f129(x100201),f318(f180(f912(x100201)),f168(x100201,f318(f318(f10(a909,a909,x100201),a313),f318(f318(f9(x100201,x100201,a909),a315),x100202)),f318(f159(x100201),x100203)))),f318(f159(x100201),x100203)),f318(f318(f142(x100201),x100202),f318(f159(x100201),f168(x100201,f318(f318(f10(a909,a909,x100201),a313),f318(f318(f9(x100201,x100201,a909),a315),x100202)),x100203))))
% 109.14/108.85 [10074]P1(f318(f318(f225(f918(f917(x100741,x100741),a909)),f298(x100741,x100742)),x100743))+~P1(f318(f318(f225(f918(f917(x100741,x100741),a909)),f298(x100741,f179(f918(f917(x100741,x100741),a909)))),x100743))+~P1(f318(f318(f225(f918(f917(x100741,x100741),a909)),f318(f318(f280(x100741,x100741,x100741),f318(f318(f92(f918(f917(x100741,x100741),a909)),f298(x100741,x100742)),x100743)),x100742)),x100743))
% 109.14/108.85 [9928]~P1(f318(f55(x99281),f318(f253(x99281),x99283)))+~P1(f318(f55(x99281),f318(f253(x99281),x99282)))+P1(f318(f55(x99281),f318(f253(x99281),f318(f318(f20(x99281,a909,a909),f318(f318(f10(a909,f918(a909,a909),x99281),a317),x99282)),x99283))))
% 109.14/108.85 [10202]P1(f318(f318(f225(f918(f917(x102021,x102021),a909)),f318(f318(f280(x102021,x102021,x102021),x102022),f298(x102021,x102022))),x102023))+~P1(f318(f318(f225(f918(f917(x102021,x102021),a909)),x102022),x102023))+~P1(f318(f318(f225(f918(f917(x102021,x102021),a909)),f318(f318(f280(x102021,x102021,x102021),f318(f318(f92(f918(f917(x102021,x102021),a909)),f318(f318(f280(x102021,x102021,x102021),x102022),f298(x102021,x102022))),x102023)),x102022)),x102023))
% 109.14/108.85 [10159]~P1(f318(f128(x101591),x101593))+~P1(f318(f318(f320(x101591),x101592),f318(f163(x101591),x101593)))+E(f318(f159(x101591),f318(f162(x101591),f318(f318(f129(x101591),f318(f180(f912(x101591)),f168(x101591,f318(f318(f10(a909,a909,x101591),a313),f318(f318(f9(x101591,x101591,a909),a315),x101592)),x101593))),x101593))),f168(x101591,f318(f318(f10(a909,a909,x101591),a313),f318(f318(f9(x101591,x101591,a909),a315),x101592)),f318(f159(x101591),x101593)))
% 109.14/108.85 [10352]~P116(x103522)+E(x103521,f2(x103522))+~E(f318(f318(f73(x103522),f318(f318(f235(x103522),x103523),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x103522),x103521),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f2(x103522))
% 109.14/108.85 [10353]~P116(x103532)+E(x103531,f2(x103532))+~E(f318(f318(f73(x103532),f318(f318(f235(x103532),x103531),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x103532),x103533),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f2(x103532))
% 109.14/108.85 [10387]~P116(x103872)+E(x103871,f2(x103872))+P1(f318(f318(f226(x103872),f2(x103872)),f318(f318(f73(x103872),f318(f318(f235(x103872),x103873),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x103872),x103871),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))))
% 109.14/108.85 [10388]~P116(x103882)+E(x103881,f2(x103882))+P1(f318(f318(f226(x103882),f2(x103882)),f318(f318(f73(x103882),f318(f318(f235(x103882),x103881),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x103882),x103883),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))))
% 109.14/108.85 [10413]~P116(x104131)+P1(f318(f318(f225(x104131),f2(x104131)),x104132))+~P1(f318(f318(f225(x104131),f2(x104131)),f318(f318(f235(x104131),x104132),f318(a103,f318(f318(f74(a911),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x104133)))))
% 109.14/108.85 [5616]~P24(x56161,x56164,x56163)+P24(x56161,x56162,x56163)+~P24(x56161,x56162,x56164)
% 109.14/108.85 [5081]~E(x50812,f83(x50813,x50811))+P1(f318(x50811,x50812))+~P1(f318(x50811,x50814))
% 109.14/108.85 [5332]E(f62(x53323,x53322,x53324),x53322)+E(x53321,f733(x53322,x53323,x53324))+~P1(f318(x53324,x53321))
% 109.14/108.85 [6651]E(f62(x66511,x66512,x66513),f78(x66511,x66513))+~E(f771(x66512,x66511,x66513,x66514),x66514)+~P1(f318(x66513,x66514))
% 109.14/108.85 [6864]~P39(x68642,x68644)+~P39(x68641,x68643)+P39(f917(x68641,x68642),f311(x68641,x68642,x68643,x68644))
% 109.14/108.85 [6865]~P40(x68652,x68654)+~P40(x68651,x68653)+P40(f917(x68651,x68652),f311(x68651,x68652,x68653,x68654))
% 109.14/108.85 [5271]~P7(x52714,x52711)+~E(f318(x52711,x52712),f318(x52711,x52713))+P1(f318(f318(x52711,x52712),x52713))
% 109.14/108.85 [5431]~P7(x54314,x54311)+E(f318(x54311,x54312),f318(x54311,x54313))+~P1(f318(f318(x54311,x54312),x54313))
% 109.14/108.85 [5432]~P15(x54324,x54321)+E(f318(x54321,x54322),f318(x54321,x54323))+~P1(f318(f318(x54321,x54322),x54323))
% 109.14/108.85 [5525]~P18(x55253,x55254,x55251)+E(f318(x55251,x55252),f318(f57(x55253,x55254),x55252))+~P1(f318(f55(x55253),x55252))
% 109.14/108.85 [5526]~P9(x55263,x55264,x55261)+E(f318(x55261,x55262),f318(f57(x55263,x55264),x55262))+~P1(f318(f55(x55263),x55262))
% 109.14/108.85 [5651]~P7(x56514,x56511)+~P1(f318(f318(x56511,x56513),x56512))+P1(f318(f318(x56511,x56512),x56513))
% 109.14/108.85 [5652]~P54(x56524,x56521)+~P1(f318(f318(x56521,x56523),x56522))+P1(f318(f318(x56521,x56522),x56523))
% 109.14/108.85 [5653]~P15(x56534,x56531)+~P1(f318(f318(x56531,x56533),x56532))+P1(f318(f318(x56531,x56532),x56533))
% 109.14/108.85 [5654]~P15(x56543,x56541)+P1(f318(f318(x56541,x56542),x56542))+~P1(f318(f318(x56541,x56544),x56542))
% 109.14/108.85 [5655]~P15(x56553,x56551)+P1(f318(f318(x56551,x56552),x56552))+~P1(f318(f318(x56551,x56552),x56554))
% 109.14/108.85 [5727]E(x57271,x57272)+~E(f318(f242(x57273,x57274),x57271),f318(f242(x57273,x57274),x57272))+~E(f318(f247(x57273,x57274),x57271),f318(f247(x57273,x57274),x57272))
% 109.14/108.85 [5728]E(x57281,x57282)+~E(f318(f242(x57283,x57284),x57281),f318(f242(x57283,x57284),x57282))+~E(f318(f247(x57283,x57284),x57281),f318(f247(x57283,x57284),x57282))
% 109.14/108.85 [5755]E(x57551,x57552)+~P1(f318(f42(x57553,x57554),x57552))+~P1(f318(f42(x57553,x57554),x57551))
% 109.14/108.85 [5947]~P76(x59472)+E(f222(x59471,x59472,x59473,x59474),f2(x59472))+P1(f318(f55(x59471),x59474))
% 109.14/108.85 [5997]~P7(x59973,x59972)+~P1(f318(x59971,x59974))+P1(f318(x59971,f815(x59971,x59972,x59973)))
% 109.14/108.85 [6091]~P1(f318(f306(x60911,x60912),x60914))+P1(f318(f306(x60911,x60912),x60913))+~P1(f318(f318(x60912,x60913),x60914))
% 109.14/108.85 [6092]~P1(f318(f306(x60921,x60922),x60924))+P1(f318(f306(x60921,x60922),x60923))+~P1(f318(f318(x60922,x60923),x60924))
% 109.14/108.85 [6093]~P1(f318(f306(x60931,x60932),x60934))+P1(f318(f306(x60931,x60932),x60933))+~P1(f318(f318(x60932,x60933),x60934))
% 109.14/108.85 [6899]~P31(x68991,x68993,x68994)+P1(f318(x68991,x68992))+~P1(f318(f318(f320(a1),x68992),f294(a1,x68993,x68994)))
% 109.14/108.85 [7085]~P7(x70851,x70853)+~P1(f318(x70852,x70854))+P1(f318(f318(f320(x70851),f815(x70852,x70853,x70851)),f261(x70851,x70853)))
% 109.14/108.85 [7965]E(x79651,f2(a911))+~P1(f318(x79652,x79653))+P1(f318(x79652,f764(x79652,x79653,x79651,x79654)))
% 109.14/108.85 [8044]~P4(x80442)+~P1(f318(f128(x80441),x80444))+P1(f318(f128(x80441),f141(x80441,x80442,x80443,x80444)))
% 109.14/108.85 [8085]E(f62(x80851,x80852,x80853),f78(x80851,x80853))+~P1(f318(x80853,x80854))+P1(f318(x80853,f771(x80852,x80851,x80853,x80854)))
% 109.14/108.85 [8270]~P1(f318(f55(x82702),x82704))+~P1(f318(f55(x82701),x82703))+P1(f318(f55(f919(x82701,x82702)),f304(x82701,x82702,x82703,x82704)))
% 109.14/108.85 [8271]~P1(f318(f55(x82712),x82714))+~P1(f318(f55(x82711),x82713))+P1(f318(f55(f919(x82711,x82712)),f304(x82711,x82712,x82713,x82714)))
% 109.14/108.85 [8272]~P1(f318(f128(x82722),x82724))+~P1(f318(f128(x82721),x82723))+P1(f318(f128(f917(x82721,x82722)),f53(x82721,x82722,x82723,x82724)))
% 109.14/108.85 [8275]P1(f318(f318(f320(f912(x82751)),f318(f318(f125(x82751),x82752),x82753)),f152(x82751,x82754)))+~P1(f318(f318(f320(f912(x82751)),x82753),f152(x82751,x82754)))+~P1(f318(f318(f320(f912(x82751)),x82752),f152(x82751,x82754)))
% 109.14/108.85 [8549]E(x85491,f2(a911))+P1(f318(x85492,x85493))+~P1(f318(x85492,f765(x85492,x85493,x85491,x85494)))
% 109.14/108.85 [8587]~P4(x85873)+~P1(f318(f128(x85871),f141(x85871,x85873,x85874,x85872)))+P1(f318(f128(x85871),x85872))
% 109.14/108.85 [8865]~P1(f318(f318(f320(f917(x88651,x88651)),f318(f318(f243(x88651,x88651),x88652),x88654)),f298(x88651,x88653)))+P1(f318(f318(f320(x88651),x88652),f307(x88651,x88653)))+~P1(f318(f318(f320(x88651),x88654),f307(x88651,x88653)))
% 109.14/108.85 [8866]~P1(f318(f318(f320(f917(x88661,x88661)),f318(f318(f243(x88661,x88661),x88662),x88664)),f298(x88661,x88663)))+P1(f318(f318(f320(x88661),x88662),f307(x88661,x88663)))+~P1(f318(f318(f320(x88661),x88664),f307(x88661,x88663)))
% 109.14/108.85 [5251]~P76(x52512)+E(f318(f318(f8(x52511,x52512),x52513),x52514),f2(x52512))+P1(f318(f55(x52511),x52514))
% 109.14/108.85 [5252]~P76(x52522)+E(f318(f318(f8(x52521,x52522),x52523),x52524),f2(x52522))+P1(f318(f55(x52521),x52524))
% 109.14/108.85 [5253]~P76(x52532)+E(f318(f318(f8(x52531,x52532),x52533),x52534),f2(x52532))+P1(f318(f55(x52531),x52534))
% 109.14/108.85 [5254]~P82(x52542)+E(f318(f318(f11(x52541,x52542),x52543),x52544),f71(x52542))+P1(f318(f55(x52541),x52544))
% 109.14/108.85 [5255]~P82(x52552)+E(f318(f318(f11(x52551,x52552),x52553),x52554),f71(x52552))+P1(f318(f55(x52551),x52554))
% 109.14/108.85 [5256]~P82(x52562)+E(f318(f318(f11(x52561,x52562),x52563),x52564),f71(x52562))+P1(f318(f55(x52561),x52564))
% 109.14/108.85 [5393]~P78(x53933)+E(x53931,x53932)+~E(f318(f318(f73(x53933),x53934),x53931),f318(f318(f73(x53933),x53934),x53932))
% 109.14/108.85 [5394]~P78(x53943)+E(x53941,x53942)+~E(f318(f318(f73(x53943),x53944),x53941),f318(f318(f73(x53943),x53944),x53942))
% 109.14/108.85 [5395]~P79(x53953)+E(x53951,x53952)+~E(f318(f318(f73(x53953),x53954),x53951),f318(f318(f73(x53953),x53954),x53952))
% 109.14/108.85 [5396]~P78(x53963)+E(x53961,x53962)+~E(f318(f318(f73(x53963),x53961),x53964),f318(f318(f73(x53963),x53962),x53964))
% 109.14/108.85 [5397]~P78(x53973)+E(x53971,x53972)+~E(f318(f318(f73(x53973),x53971),x53974),f318(f318(f73(x53973),x53972),x53974))
% 109.14/108.85 [5492]~P124(x54921)+~E(x54923,f318(f318(f74(x54921),x54922),x54924))+P1(f318(f318(f278(x54921),x54922),x54923))
% 109.14/108.85 [5520]~P5(x55203)+E(x55201,f179(f918(x55202,a909)))+E(f318(f318(f33(x55202,x55203),x55201),f318(f18(x55203,x55202),x55204)),x55204)
% 109.14/108.85 [5521]~P5(x55213)+E(x55211,f179(f918(x55212,a909)))+E(f318(f318(f34(x55212,x55213),x55211),f318(f18(x55213,x55212),x55214)),x55214)
% 109.14/108.85 [5741]~P113(x57413)+E(x57411,x57412)+~E(f294(x57413,x57414,x57411),f318(f318(f300(x57413),x57412),f179(f918(x57413,a909))))
% 109.14/108.85 [5742]~P113(x57423)+E(x57421,x57422)+~E(f294(x57423,x57421,x57422),f318(f318(f300(x57423),x57424),f179(f918(x57423,a909))))
% 109.14/108.85 [5803]~P37(x58033,x58031,x58034)+P37(x58033,x58031,f318(f318(f142(x58033),x58032),x58034))+P1(f318(x58031,x58032))
% 109.14/108.85 [5905]~P33(x59051,x59052,x59054)+~P1(f318(x59052,x59053))+P33(x59051,x59052,f318(f318(f142(x59051),x59053),x59054))
% 109.14/108.85 [6049]P1(f318(x60491,x60492))+~P1(f318(f239(x60493,x60491),x60494))+~P1(f318(f318(f320(x60493),x60492),x60494))
% 109.14/108.85 [6058]~P33(x60581,x60582,x60584)+~P33(x60581,x60582,x60583)+P33(x60581,x60582,f318(f318(f125(x60581),x60583),x60584))
% 109.14/108.85 [6072]P35(x60721,x60722,x60723)+~P35(x60721,x60722,f318(f318(f142(x60721),x60724),x60723))+P1(f318(x60722,x60724))
% 109.14/108.85 [6073]P37(x60731,x60732,x60733)+~P37(x60731,x60732,f318(f318(f142(x60731),x60734),x60733))+P1(f318(x60732,x60734))
% 109.14/108.85 [6149]P35(x61491,x61492,x61493)+P35(x61491,x61492,x61494)+~P35(x61491,x61492,f318(f318(f125(x61491),x61494),x61493))
% 109.14/108.85 [6169]~P76(x61691)+E(f318(f318(f8(a911,x61691),x61692),f318(f293(a911,x61693),f318(a103,x61694))),f2(x61691))+~P1(f318(f318(f226(a911),x61694),x61693))
% 109.14/108.85 [6174]~P70(x61741)+~E(f39(x61741,x61742,x61743),f39(x61741,x61744,x61743))+E(f39(x61741,f318(f72(x61741),x61742),x61743),f39(x61741,f318(f72(x61741),x61744),x61743))
% 109.14/108.85 [6243]P1(f318(x62431,x62432))+~E(f318(f127(x62433,x62431),x62434),x62434)+~P1(f318(f318(f320(x62433),x62432),f318(f163(x62433),x62434)))
% 109.14/108.85 [6262]~E(f318(f318(f73(a911),x62623),x62622),f318(f318(f73(a911),x62621),x62624))+~P1(f318(f318(f226(a911),x62623),x62624))+P1(f318(f318(f226(a911),x62621),x62622))
% 109.14/108.85 [6266]P35(x62661,x62662,x62663)+~P1(f318(x62662,x62664))+~P1(f318(f318(f320(x62661),x62664),f318(f163(x62661),x62663)))
% 109.14/108.85 [6267]P35(x62671,x62672,x62673)+~P1(f318(x62672,x62674))+~P1(f318(f318(f320(x62671),x62674),f318(f163(x62671),x62673)))
% 109.14/108.85 [6268]P35(x62681,x62682,x62683)+~P1(f318(x62682,x62684))+~P1(f318(f318(f320(x62681),x62684),f318(f163(x62681),x62683)))
% 109.14/108.85 [6271]~P69(x62711)+E(f39(x62711,f39(x62711,x62712,x62713),x62714),f39(x62711,x62712,x62714))+~P1(f318(f318(f278(x62711),x62714),x62713))
% 109.14/108.85 [6309]~P33(x63093,x63091,x63094)+P1(f318(x63091,x63092))+~P1(f318(f318(f320(x63093),x63092),f318(f163(x63093),x63094)))
% 109.14/108.85 [6310]~P33(x63103,x63101,x63104)+P1(f318(x63101,x63102))+~P1(f318(f318(f320(x63103),x63102),f318(f163(x63103),x63104)))
% 109.14/108.85 [6311]~P33(x63113,x63111,x63114)+P1(f318(x63111,x63112))+~P1(f318(f318(f320(x63113),x63112),f318(f163(x63113),x63114)))
% 109.14/108.85 [6313]~E(f318(f127(x63131,x63132),x63133),f104(x63131))+~P1(f318(x63132,x63134))+~P1(f318(f318(f320(x63131),x63134),f318(f163(x63131),x63133)))
% 109.14/108.85 [6314]~E(f168(x63143,x63141,x63144),x63144)+P1(f318(x63141,x63142))+~P1(f318(f318(f320(x63143),x63142),f318(f163(x63143),x63144)))
% 109.14/108.85 [6336]~E(x63364,f179(f918(x63362,a909)))+~E(x63363,f179(f918(x63361,a909)))+E(f304(x63361,x63362,x63363,x63364),f179(f918(f919(x63361,x63362),a909)))
% 109.14/108.85 [6482]P1(f318(x64821,x64822))+~P1(f318(f151(x64823,x64821),x64824))+~P1(f318(f318(f320(x64823),x64822),f318(f163(x64823),x64824)))
% 109.14/108.85 [6620]~P32(x66201,x66203,x66204)+P1(f318(x66201,x66202))+~P1(f318(f318(f320(a911),x66202),f318(f293(a911,x66203),x66204)))
% 109.14/108.85 [6759]~P76(x67591)+E(f318(f318(f8(a911,x67591),x67592),f294(a911,x67593,f318(a103,x67594))),f2(x67591))+~P1(f318(f318(f226(a911),f318(a103,x67594)),x67593))
% 109.14/108.85 [6902]~P4(x69021)+E(f318(f318(f3(f918(x69021,a909)),f318(f293(x69021,x69022),x69023)),f318(f293(x69021,x69022),x69024)),f318(f293(x69021,x69024),x69023))+~P1(f318(f318(f225(x69021),x69022),x69024))
% 109.14/108.85 [6966]~E(x69663,x69664)+E(x69661,f2(a911))+P1(f318(f318(f320(x69662),x69663),f318(f163(x69662),f160(x69662,x69661,x69664))))
% 109.14/108.85 [7249]~P1(f318(f318(f320(f912(x72491)),x72494),f152(x72491,x72493)))+P1(f318(f318(f320(x72491),x72492),x72493))+~P1(f318(f318(f320(x72491),x72492),f318(f163(x72491),x72494)))
% 109.14/108.85 [7256]~P39(x72561,x72562)+P1(f318(f318(f320(x72561),f604(x72562,x72561,x72563)),x72563))+~P1(f318(f318(f320(x72561),x72564),x72563))
% 109.14/108.85 [7289]~P25(x72892,x72891,x72893,x72894)+E(f318(f29(x72891),f318(f301(x72892,x72891,x72893),x72894)),f318(f29(x72892),x72894))+~P1(f318(f55(x72892),x72894))
% 109.14/108.85 [7312]~P76(x73121)+E(f318(f318(f318(f59(x73121,x73122,f73(x73121)),x73123),f2(x73121)),x73124),f318(f318(f8(x73122,x73121),x73123),x73124))+~P1(f318(f55(x73122),x73124))
% 109.14/108.85 [7313]~P76(x73131)+E(f318(f318(f318(f59(x73131,x73132,f73(x73131)),x73133),f2(x73131)),x73134),f318(f318(f8(x73132,x73131),x73133),x73134))+~P1(f318(f55(x73132),x73134))
% 109.14/108.85 [7314]~P82(x73141)+E(f318(f318(f318(f59(x73141,x73142,f74(x73141)),x73143),f71(x73141)),x73144),f318(f318(f11(x73142,x73141),x73143),x73144))+~P1(f318(f55(x73142),x73144))
% 109.14/108.85 [7315]~P82(x73151)+E(f318(f318(f318(f59(x73151,x73152,f74(x73151)),x73153),f71(x73151)),x73154),f318(f318(f11(x73152,x73151),x73153),x73154))+~P1(f318(f55(x73152),x73154))
% 109.14/108.85 [7343]P25(x73431,x73432,x73433,x73434)+~E(f318(f29(x73432),f318(f301(x73431,x73432,x73433),x73434)),f318(f29(x73431),x73434))+~P1(f318(f55(x73431),x73434))
% 109.14/108.85 [7344]P25(x73441,x73442,x73443,x73444)+~E(f318(f29(x73442),f318(f301(x73441,x73442,x73443),x73444)),f318(f29(x73441),x73444))+~P1(f318(f55(x73441),x73444))
% 109.14/108.85 [7525]~P76(x75251)+E(f318(f318(f73(x75251),f318(x75252,x75253)),f318(f318(f8(a911,x75251),x75252),f296(a911,x75253,x75254))),f318(f318(f8(a911,x75251),x75252),f294(a911,x75253,x75254)))+~P1(f318(f318(f225(a911),x75253),x75254))
% 109.14/108.85 [7534]~P76(x75341)+~P25(x75342,x75341,x75343,x75344)+E(f318(f318(f8(x75341,x75341),f25(x75341)),f318(f301(x75342,x75341,x75343),x75344)),f318(f318(f8(x75342,x75341),x75343),x75344))
% 109.14/108.85 [7535]~P82(x75351)+~P25(x75352,x75351,x75353,x75354)+E(f318(f318(f11(x75351,x75351),f25(x75351)),f318(f301(x75352,x75351,x75353),x75354)),f318(f318(f11(x75352,x75351),x75353),x75354))
% 109.14/108.85 [7583]E(f318(f29(f919(x75831,x75832)),f304(x75831,x75832,x75833,x75834)),f318(f318(f73(a911),f318(f29(x75831),x75833)),f318(f29(x75832),x75834)))+~P1(f318(f55(x75832),x75834))+~P1(f318(f55(x75831),x75833))
% 109.14/108.85 [7584]E(f318(f29(f919(x75841,x75842)),f304(x75841,x75842,x75843,x75844)),f318(f318(f73(a911),f318(f29(x75841),x75843)),f318(f29(x75842),x75844)))+~P1(f318(f55(x75842),x75844))+~P1(f318(f55(x75841),x75843))
% 109.14/108.85 [7665]E(x76651,x76652)+P1(f318(f318(f320(x76653),x76651),f318(f163(x76653),f161(x76653,x76652,x76654))))+~P1(f318(f318(f320(x76653),x76651),f318(f163(x76653),x76654)))
% 109.14/108.85 [7806]~P1(f318(f318(f225(f918(x78061,a909)),x78064),f318(x78063,x78064)))+~P1(f318(f318(f320(x78061),x78062),x78064))+P1(f318(f318(f320(x78061),x78062),f87(f918(x78061,a909),x78063)))
% 109.14/108.85 [7891]~P76(x78911)+E(f318(f318(f73(x78911),f318(f318(f8(a911,x78911),x78912),f318(f293(a911,x78913),x78914))),f318(x78912,x78914)),f318(f318(f8(a911,x78911),x78912),f318(f293(a911,x78913),f318(a103,x78914))))+P1(f318(f318(f226(a911),x78914),x78913))
% 109.14/108.85 [7943]~P25(x79431,x79432,x79433,f233(f918(x79431,a909)))+~P1(f318(f55(x79432),x79434))+P1(f318(f55(x79431),f318(f302(x79431,x79432,x79433),x79434)))
% 109.14/108.85 [8059]P1(f318(f318(f320(f912(x80591)),f318(f318(f142(x80591),x80592),x80593)),f152(x80591,x80594)))+~P1(f318(f318(f320(f912(x80591)),x80593),f152(x80591,x80594)))+~P1(f318(f318(f320(x80591),x80592),x80594))
% 109.14/108.85 [8103]E(x81031,x81032)+~P1(f318(f318(f320(x81033),x81031),f318(f163(x81033),f161(x81033,x81032,x81034))))+P1(f318(f318(f320(x81033),x81031),f318(f163(x81033),x81034)))
% 109.14/108.85 [8140]~E(f318(f301(x81403,x81401,x81404),f233(f918(x81403,a909))),f233(f918(x81401,a909)))+P1(f318(f55(x81401),x81402))+~P1(f318(f55(x81403),f318(f302(x81403,x81401,x81404),x81402)))
% 109.14/108.85 [8240]~P25(x82401,x82403,x82404,x82402)+P1(f318(f55(x82401),x82402))+~P1(f318(f55(x82403),f318(f301(x82401,x82403,x82404),x82402)))
% 109.14/108.85 [8263]~E(x82632,x82633)+P1(f318(f318(f320(f917(x82631,x82631)),f318(f318(f243(x82631,x82631),x82632),x82633)),f254(x82631,x82634)))+~P1(f318(f318(f320(x82631),x82632),x82634))
% 109.14/108.85 [8264]~E(x82642,x82643)+P1(f318(f318(f320(f917(x82641,x82641)),f318(f318(f243(x82641,x82641),x82642),x82643)),f254(x82641,x82644)))+~P1(f318(f318(f320(x82641),x82642),x82644))
% 109.14/108.85 [8299]~P76(x82991)+E(f318(f318(f73(x82991),f318(f318(f8(a911,x82991),x82992),f294(a911,x82993,x82994))),f318(x82992,f318(a103,x82994))),f318(f318(f8(a911,x82991),x82992),f294(a911,x82993,f318(a103,x82994))))+P1(f318(f318(f226(a911),f318(a103,x82994)),x82993))
% 109.14/108.85 [8356]~E(x83562,x83564)+P1(f318(f318(f320(f917(x83561,x83561)),f318(f318(f243(x83561,x83561),x83562),x83564)),f298(x83561,x83563)))+P1(f318(f318(f320(x83561),x83562),f318(f255(x83561,x83561),x83563)))
% 109.14/108.85 [8358]P1(f318(x83581,x83582))+~P1(f318(x83581,f318(f318(f155(x83583),x83584),f658(x83581,x83584,x83583))))+~P1(f318(f318(f320(x83583),x83582),f318(f163(x83583),x83584)))
% 109.14/108.85 [8494]~P1(f318(f318(f320(x84941),x84942),f307(x84941,x84944)))+P1(f318(f318(f320(f912(x84941)),f318(f318(f142(x84941),x84942),x84943)),f307(f912(x84941),f148(x84941,x84944))))+~P1(f318(f318(f320(f912(x84941)),x84943),f307(f912(x84941),f148(x84941,x84944))))
% 109.14/108.85 [8509]~P25(x85092,x85093,x85094,f723(x85094,x85093,x85092,x85091))+P25(x85092,x85093,x85094,f32(f918(x85092,a909),x85091))+E(x85091,f179(f918(f918(x85092,a909),a909)))
% 109.14/108.85 [8782]E(x87821,x87822)+~P1(f318(f318(f320(f917(x87823,x87823)),f318(f318(f243(x87823,x87823),x87821),x87822)),f298(x87823,x87824)))+P1(f318(f318(f320(x87823),x87821),f318(f255(x87823,x87823),x87824)))
% 109.14/108.85 [9060]E(x90601,f2(a911))+P1(f318(x90602,x90603))+P1(f318(f318(f320(x90604),f765(x90602,x90603,x90601,x90604)),f318(f163(x90604),f160(x90604,x90601,x90603))))
% 109.14/108.85 [9072]E(x90721,f2(a911))+~P1(f318(x90723,x90724))+P1(f318(f318(f320(x90722),f764(x90723,x90724,x90721,x90722)),f318(f163(x90722),f160(x90722,x90721,x90724))))
% 109.14/108.85 [9074]~P26(x90741,x90742,x90743,f233(f918(x90741,a909)),f233(f918(x90742,a909)))+~P1(f318(f55(x90742),x90744))+P1(f318(f55(x90741),f318(f302(x90741,x90742,x90743),x90744)))
% 109.14/108.85 [9076]P25(x90762,x90763,x90764,f32(f918(x90762,a909),x90761))+E(x90761,f179(f918(f918(x90762,a909),a909)))+P1(f318(f318(f320(f918(x90762,a909)),f723(x90764,x90763,x90762,x90761)),x90761))
% 109.14/108.85 [9192]~P26(x91923,x91921,x91924,f233(f918(x91923,a909)),f233(f918(x91921,a909)))+P1(f318(f55(x91921),x91922))+~P1(f318(f55(x91923),f318(f302(x91923,x91921,x91924),x91922)))
% 109.14/108.85 [9205]P1(f318(f55(x92051),x92052))+~P1(f318(f55(x92054),f318(f301(x92051,x92054,x92053),x92052)))+P1(f318(f318(f320(x92051),f574(x92053,x92054,x92052,x92051)),x92052))
% 109.14/108.85 [9299]~P5(x92992)+E(f318(f318(f58(x92991,x92992,f318(f318(f10(x92992,f918(x92992,x92992),x92991),f101(x92992)),x92993)),f179(x92992)),x92994),f318(f318(f33(x92991,x92992),x92994),x92993))+~P1(f318(f55(x92991),x92994))
% 109.14/108.85 [9300]~P5(x93002)+E(f318(f318(f58(x93001,x93002,f318(f318(f10(x93002,f918(x93002,x93002),x93001),f92(x93002)),x93003)),f233(x93002)),x93004),f318(f318(f34(x93001,x93002),x93004),x93003))+~P1(f318(f55(x93001),x93004))
% 109.14/108.85 [9385]P1(f318(x93851,x93852))+~P1(f318(x93851,f318(f318(f155(x93853),x93854),f693(x93852,x93851,x93854,x93853))))+~P1(f318(f318(f320(x93853),x93852),f318(f163(x93853),x93854)))
% 109.14/108.85 [9406]E(x94061,x94062)+~P1(f318(f318(f320(f917(x94063,x94063)),f318(f318(f243(x94063,x94063),x94061),x94062)),f298(x94063,x94064)))+P1(f318(f318(f320(f917(x94063,x94063)),f318(f318(f243(x94063,x94063),x94061),x94062)),f318(f318(f280(x94063,x94063,x94063),x94064),f298(x94063,x94064))))
% 109.14/108.85 [9407]E(x94071,x94072)+~P1(f318(f318(f320(f917(x94073,x94073)),f318(f318(f243(x94073,x94073),x94071),x94072)),f298(x94073,x94074)))+P1(f318(f318(f320(f917(x94073,x94073)),f318(f318(f243(x94073,x94073),x94071),x94072)),f318(f318(f280(x94073,x94073,x94073),x94074),f298(x94073,x94074))))
% 109.14/108.85 [9465]~E(f318(f180(f912(x94651)),x94652),f318(f180(f912(x94651)),x94653))+~P1(f318(f318(f320(f917(f912(x94651),f912(x94651))),f318(f318(f243(f912(x94651),f912(x94651)),x94652),x94653)),f138(x94651,x94654)))+P1(f318(f318(f320(f917(f912(x94651),f912(x94651))),f318(f318(f243(f912(x94651),f912(x94651)),x94652),x94653)),f136(x94651,x94654)))
% 109.14/108.85 [9483]E(x94831,x94832)+P1(f318(f318(f320(f917(x94833,x94833)),f318(f318(f243(x94833,x94833),x94831),x94832)),f298(x94833,x94834)))+~P1(f318(f318(f320(f917(x94833,x94833)),f318(f318(f243(x94833,x94833),x94831),x94832)),f318(f318(f280(x94833,x94833,x94833),x94834),f298(x94833,x94834))))
% 109.14/108.85 [9707]P33(x97071,f318(f318(f20(x97071,a909,a909),f318(f318(f10(a909,f918(a909,a909),x97071),a317),f318(f318(f10(a909,a909,x97071),a313),x97072))),f318(a315,x97073)),x97074)+~P1(f318(x97072,x97073))+~P37(x97071,x97072,f318(f318(f142(x97071),x97073),x97074))
% 109.14/108.85 [9886]~P33(x98861,f318(f318(f20(x98861,a909,a909),f318(f318(f10(a909,f918(a909,a909),x98861),a317),f318(f318(f10(a909,a909,x98861),a313),x98862))),f318(a315,x98863)),x98864)+~P1(f318(x98862,x98863))+P37(x98861,x98862,f318(f318(f142(x98861),x98863),x98864))
% 109.14/108.85 [9890]~P37(x98901,x98902,x98904)+~P33(x98901,f318(f318(f20(x98901,a909,a909),f318(f318(f10(a909,f918(a909,a909),x98901),a317),f318(f318(f10(a909,a909,x98901),a313),x98902))),f318(a315,x98903)),x98904)+P37(x98901,x98902,f318(f318(f142(x98901),x98903),x98904))
% 109.14/108.85 [9929]~P67(x99291)+E(f318(f318(f8(a911,x99291),f318(f318(f20(a911,x99291,x99291),f318(f318(f10(x99291,f918(x99291,x99291),a911),f3(x99291)),x99292)),f318(f318(f10(a911,x99291,a911),x99292),f318(f318(f9(a911,a911,a911),f73(a911)),f71(a911))))),f294(a911,x99293,x99294)),f2(x99291))+P1(f318(f318(f225(a911),x99293),x99294))
% 109.14/108.85 [10154]~P39(x101542,x101544)+~P25(x101542,x101541,x101543,f233(f918(x101542,a909)))+P39(x101541,f318(f301(f917(x101542,x101542),f917(x101541,x101541),f249(x101542,x101541,x101542,x101541,x101543,x101543)),x101544))
% 109.14/108.85 [10365]~E(f318(f180(f912(x103651)),x103653),f318(f180(f912(x103651)),x103652))+P1(f318(f318(f320(f917(f912(x103651),f912(x103651))),f318(f318(f243(f912(x103651),f912(x103651)),x103652),x103653)),f149(x103651,x103654)))+~P1(f318(f318(f248(x103651,x103651,a909),f318(f318(f9(x103651,f918(f917(x103651,x103651),a909),f918(x103651,a909)),f318(f318(f10(f918(x103651,f918(f918(f917(x103651,x103651),a909),a909)),f918(f918(f917(x103651,x103651),a909),f918(x103651,a909)),x103651),f9(x103651,f918(f917(x103651,x103651),a909),a909)),f318(f318(f10(f918(x103651,f917(x103651,x103651)),f918(x103651,f918(f918(f917(x103651,x103651),a909),a909)),x103651),f318(f10(f917(x103651,x103651),f918(f918(f917(x103651,x103651),a909),a909),x103651),f320(f917(x103651,x103651)))),f243(x103651,x103651)))),x103654)),f660(x103654,x103653,x103652,x103651)))
% 109.14/108.85 [6224]~P69(x62241)+~E(x62242,f2(x62241))+E(f318(f318(f30(x62241),f318(f318(f74(x62241),x62242),x62243)),f318(f318(f74(x62241),x62242),x62244)),f2(x62241))
% 109.14/108.85 [6265]E(x62651,f104(x62652))+E(x62653,f318(f318(f3(a911),f318(f180(f912(x62652)),x62651)),f71(a911)))+E(f135(x62652,f318(f318(f150(x62652,x62651),x62653),x62654)),f135(x62652,x62651))
% 109.14/108.85 [6302]E(x63021,x63022)+P1(f318(x63023,x63022))+~P1(f318(f318(f318(f300(x63024),x63021),x63023),x63022))
% 109.14/108.85 [6318]~P76(x63181)+~P1(f318(f128(x63182),x63184))+E(f318(f156(x63181),f318(f318(f145(x63182,x63181),x63183),x63184)),f318(f318(f8(x63182,x63181),x63183),f318(f163(x63182),x63184)))
% 109.14/108.85 [6329]~P82(x63292)+~P1(f318(f55(x63291),x63294))+E(f318(f318(f11(x63291,x63292),f318(f18(x63292,x63291),x63293)),x63294),f318(f318(f235(x63292),x63293),f318(f29(x63291),x63294)))
% 109.14/108.85 [6383]~P69(x63832)+E(x63831,f2(x63832))+E(f318(f318(f30(x63832),f318(f318(f74(x63832),x63833),x63831)),f318(f318(f74(x63832),x63834),x63831)),f318(f318(f30(x63832),x63833),x63834))
% 109.14/108.85 [6384]~P69(x63842)+E(x63841,f2(x63842))+E(f318(f318(f30(x63842),f318(f318(f74(x63842),x63841),x63843)),f318(f318(f74(x63842),x63841),x63844)),f318(f318(f30(x63842),x63843),x63844))
% 109.14/108.85 [6385]~P72(x63852)+E(x63851,f2(x63852))+E(f318(f318(f282(x63852),f318(f318(f74(x63852),x63853),x63851)),f318(f318(f74(x63852),x63854),x63851)),f318(f318(f282(x63852),x63853),x63854))
% 109.14/108.85 [6386]~P72(x63862)+E(x63861,f2(x63862))+E(f318(f318(f282(x63862),f318(f318(f74(x63862),x63861),x63863)),f318(f318(f74(x63862),x63861),x63864)),f318(f318(f282(x63862),x63863),x63864))
% 109.14/108.85 [6387]~P69(x63872)+E(x63871,f2(x63872))+E(f318(f318(f30(x63872),f318(f318(f74(x63872),x63871),x63873)),f318(f318(f74(x63872),x63871),x63874)),f318(f318(f30(x63872),x63873),x63874))
% 109.14/108.85 [6451]P1(f318(x64511,x64512))+~E(x64513,f318(f318(f73(a911),x64514),x64512))+~P1(f318(x64511,f318(f318(f3(a911),x64513),x64514)))
% 109.14/108.85 [6452]P1(f318(x64521,x64522))+~E(x64523,f318(f318(f73(a911),x64524),x64522))+~P1(f318(x64521,f318(f318(f3(a911),x64523),x64524)))
% 109.14/108.85 [6535]P29(x65351,x65352,x65353)+P28(x65351,f634(x65353,x65352,x65351),x65354)+~P1(f318(f318(f320(f910(x65351)),x65354),x65352))
% 109.14/108.85 [6537]~P1(f318(x65372,x65373))+~P1(f318(f151(x65371,x65372),x65374))+P1(f318(f151(x65371,x65372),f318(f318(f142(x65371),x65373),x65374)))
% 109.14/108.85 [6578]E(x65781,f104(x65782))+~E(x65783,f318(f318(f3(a911),f318(f180(f912(x65782)),x65781)),f71(a911)))+E(f135(x65782,f318(f318(f150(x65782,x65781),x65783),x65784)),x65784)
% 109.14/108.85 [6600]~P102(x66001)+~P1(f318(f318(f225(x66001),x66002),x66004))+P1(f318(f318(f225(x66001),x66002),f318(f318(f101(x66001),x66003),x66004)))
% 109.14/108.85 [6601]~P102(x66011)+~P1(f318(f318(f225(x66011),x66012),x66013))+P1(f318(f318(f225(x66011),x66012),f318(f318(f101(x66011),x66013),x66014)))
% 109.14/108.85 [6602]~P4(x66021)+~P1(f318(f318(f225(x66021),x66022),x66024))+P1(f318(f318(f225(x66021),x66022),f318(f318(f224(x66021),x66023),x66024)))
% 109.14/108.85 [6603]~P4(x66031)+~P1(f318(f318(f225(x66031),x66032),x66034))+P1(f318(f318(f225(x66031),x66032),f318(f318(f224(x66031),x66033),x66034)))
% 109.14/108.85 [6604]~P4(x66041)+~P1(f318(f318(f225(x66041),x66042),x66043))+P1(f318(f318(f225(x66041),x66042),f318(f318(f224(x66041),x66043),x66044)))
% 109.14/108.85 [6605]~P4(x66051)+~P1(f318(f318(f225(x66051),x66052),x66053))+P1(f318(f318(f225(x66051),x66052),f318(f318(f224(x66051),x66053),x66054)))
% 109.14/108.85 [6606]~P102(x66061)+~P1(f318(f318(f226(x66061),x66062),x66064))+P1(f318(f318(f226(x66061),x66062),f318(f318(f101(x66061),x66063),x66064)))
% 109.14/108.85 [6607]~P102(x66071)+~P1(f318(f318(f226(x66071),x66072),x66073))+P1(f318(f318(f226(x66071),x66072),f318(f318(f101(x66071),x66073),x66074)))
% 109.14/108.85 [6608]~P4(x66081)+~P1(f318(f318(f226(x66081),x66082),x66084))+P1(f318(f318(f226(x66081),x66082),f318(f318(f224(x66081),x66083),x66084)))
% 109.14/108.85 [6609]~P4(x66091)+~P1(f318(f318(f226(x66091),x66092),x66094))+P1(f318(f318(f226(x66091),x66092),f318(f318(f224(x66091),x66093),x66094)))
% 109.14/108.85 [6610]~P4(x66101)+~P1(f318(f318(f226(x66101),x66102),x66103))+P1(f318(f318(f226(x66101),x66102),f318(f318(f224(x66101),x66103),x66104)))
% 109.14/108.85 [6611]~P4(x66111)+~P1(f318(f318(f226(x66111),x66112),x66113))+P1(f318(f318(f226(x66111),x66112),f318(f318(f224(x66111),x66113),x66114)))
% 109.14/108.85 [6612]~P121(x66121)+~P1(f318(f318(f278(x66121),x66122),x66124))+P1(f318(f318(f278(x66121),x66122),f318(f318(f74(x66121),x66123),x66124)))
% 109.14/108.85 [6613]~P121(x66131)+~P1(f318(f318(f278(x66131),x66132),x66133))+P1(f318(f318(f278(x66131),x66132),f318(f318(f74(x66131),x66133),x66134)))
% 109.14/108.85 [6700]~E(f318(f318(f155(x67001),x67002),x67003),x67004)+E(f318(f318(f150(x67001,x67002),x67003),x67004),x67002)+~P1(f318(f318(f226(a911),x67003),f318(f180(f912(x67001)),x67002)))
% 109.14/108.85 [6742]P1(f318(x67421,x67422))+~P1(f318(x67423,x67422))+~P1(f318(f318(f225(f918(x67424,a909)),x67423),x67421))
% 109.14/108.85 [6743]P1(f318(x67431,x67432))+~P1(f318(x67433,x67432))+~P1(f318(f318(f225(f918(x67434,a909)),x67433),x67431))
% 109.14/108.85 [6776]~E(f318(f318(f150(x67761,x67762),x67763),x67764),x67762)+E(f318(f318(f155(x67761),x67762),x67763),x67764)+~P1(f318(f318(f226(a911),x67763),f318(f180(f912(x67761)),x67762)))
% 109.14/108.85 [6790]~P1(f318(f151(x67901,x67902),x67904))+~P1(f318(f151(x67901,x67902),x67903))+P1(f318(f151(x67901,x67902),f318(f318(f125(x67901),x67903),x67904)))
% 109.14/108.85 [6891]P28(x68911,x68912,x68913)+~P28(x68911,f318(a103,x68912),f874(x68912,x68914,x68911))+~P1(f318(f318(f320(f910(x68911)),x68913),x68914))
% 109.14/108.85 [6898]E(x68981,f179(f918(x68982,a909)))+E(x68983,f179(f918(x68984,a909)))+~E(f318(f318(f245(x68984,x68982),x68983),f318(f18(f918(x68982,a909),x68984),x68981)),f179(f918(f917(x68984,x68982),a909)))
% 109.14/108.85 [6912]E(x69121,x69122)+P1(f318(f318(f320(x69123),x69121),x69124))+~P1(f318(f318(f320(x69123),x69121),f318(f318(f300(x69123),x69122),x69124)))
% 109.14/108.85 [6913]E(x69131,x69132)+P1(f318(f318(f320(x69133),x69131),x69134))+~P1(f318(f318(f320(x69133),x69131),f318(f318(f300(x69133),x69132),x69134)))
% 109.14/108.85 [6929]~P4(x69291)+P1(f318(f318(f225(x69291),x69292),x69293))+~P1(f318(f318(f225(x69291),x69292),f318(f318(f223(x69291),x69294),x69293)))
% 109.14/108.85 [6930]~P4(x69301)+P1(f318(f318(f225(x69301),x69302),x69303))+~P1(f318(f318(f225(x69301),x69302),f318(f318(f223(x69301),x69304),x69303)))
% 109.14/108.85 [6931]~P4(x69311)+P1(f318(f318(f225(x69311),x69312),x69313))+~P1(f318(f318(f225(x69311),x69312),f318(f318(f223(x69311),x69313),x69314)))
% 109.14/108.85 [6932]~P4(x69321)+P1(f318(f318(f225(x69321),x69322),x69323))+~P1(f318(f318(f225(x69321),x69322),f318(f318(f223(x69321),x69323),x69324)))
% 109.14/108.85 [6933]~P108(x69331)+P1(f318(f318(f225(x69331),x69332),x69333))+~P1(f318(f318(f225(x69331),x69332),f318(f318(f92(x69331),x69334),x69333)))
% 109.14/108.85 [6934]~P108(x69341)+P1(f318(f318(f225(x69341),x69342),x69343))+~P1(f318(f318(f225(x69341),x69342),f318(f318(f92(x69341),x69344),x69343)))
% 109.14/108.85 [6935]~P108(x69351)+P1(f318(f318(f225(x69351),x69352),x69353))+~P1(f318(f318(f225(x69351),x69352),f318(f318(f92(x69351),x69353),x69354)))
% 109.14/108.85 [6936]~P108(x69361)+P1(f318(f318(f225(x69361),x69362),x69363))+~P1(f318(f318(f225(x69361),x69362),f318(f318(f92(x69361),x69363),x69364)))
% 109.14/108.85 [6937]~P4(x69371)+P1(f318(f318(f226(x69371),x69372),x69373))+~P1(f318(f318(f226(x69371),x69372),f318(f318(f223(x69371),x69374),x69373)))
% 109.14/108.85 [6938]~P4(x69381)+P1(f318(f318(f226(x69381),x69382),x69383))+~P1(f318(f318(f226(x69381),x69382),f318(f318(f223(x69381),x69383),x69384)))
% 109.14/108.85 [6958]~E(f318(f318(f155(x69581),x69583),x69584),x69582)+P1(f318(f318(f320(x69581),x69582),f318(f163(x69581),x69583)))+~P1(f318(f318(f226(a911),x69584),f318(f180(f912(x69581)),x69583)))
% 109.14/108.85 [6967]~P4(x69671)+~P13(x69671,f318(f318(f142(x69671),x69672),f318(f318(f142(x69671),x69673),x69674)))+P1(f318(f318(f225(x69671),x69672),x69673))
% 109.14/108.85 [7021]~P4(x70211)+P13(x70211,f318(f318(f142(x70211),x70212),x70213))+~P13(x70211,f318(f318(f142(x70211),x70214),f318(f318(f142(x70211),x70212),x70213)))
% 109.14/108.85 [7115]~P33(x71152,x71151,x71153)+P1(f318(x71151,f318(f318(f155(x71152),x71153),x71154)))+~P1(f318(f318(f226(a911),x71154),f318(f180(f912(x71152)),x71153)))
% 109.14/108.85 [7133]E(x71331,f2(a1))+E(f318(f318(f30(a1),x71332),x71331),x71333)+~P1(f318(f43(x71332,x71331),f318(f318(f243(a1,a1),x71333),x71334)))
% 109.14/108.85 [7154]E(f39(a1,x71542,x71541),x71543)+E(x71541,f2(a1))+~P1(f318(f43(x71542,x71541),f318(f318(f243(a1,a1),x71544),x71543)))
% 109.14/108.85 [7270]P1(f318(f318(f320(x72701),x72702),x72703))+~P1(f318(f318(f320(x72701),x72702),x72704))+~P1(f318(f318(f225(f918(x72701,a909)),x72704),x72703))
% 109.14/108.85 [7271]P1(f318(f318(f320(x72711),x72712),x72713))+~P1(f318(f318(f320(x72711),x72712),x72714))+~P1(f318(f318(f225(f918(x72711,a909)),x72714),x72713))
% 109.14/108.85 [7272]P1(f318(f318(f320(x72721),x72722),x72723))+~P1(f318(f318(f320(x72721),x72722),x72724))+~P1(f318(f318(f225(f918(x72721,a909)),x72724),x72723))
% 109.14/108.85 [7273]P1(f318(f318(f320(x72731),x72732),x72733))+~P1(f318(f318(f320(x72731),x72732),x72734))+~P1(f318(f318(f226(f918(x72731,a909)),x72734),x72733))
% 109.14/108.85 [7274]P1(f318(f318(f320(x72741),x72742),x72743))+~P1(f318(f318(f320(x72741),x72742),x72744))+~P1(f318(f318(f225(f918(x72741,a909)),x72744),x72743))
% 109.14/108.85 [7285]~P123(x72851)+~E(x72853,f2(x72851))+P1(f318(f318(f278(x72851),f318(f318(f74(x72851),x72852),x72853)),f318(f318(f74(x72851),x72854),x72853)))
% 109.14/108.85 [7286]~P123(x72861)+~E(x72862,f2(x72861))+P1(f318(f318(f278(x72861),f318(f318(f74(x72861),x72862),x72863)),f318(f318(f74(x72861),x72862),x72864)))
% 109.14/108.85 [7388]P35(x73881,x73882,x73883)+~P1(f318(x73882,f318(f318(f155(x73881),x73883),x73884)))+~P1(f318(f318(f226(a911),x73884),f318(f180(f912(x73881)),x73883)))
% 109.14/108.85 [7493]~P3(x74932)+~P1(f318(f318(f226(f918(x74931,x74932)),x74933),x74934))+P1(f318(f318(f225(f918(x74931,x74932)),x74933),x74934))
% 109.14/108.85 [7573]~P24(x75731,x75732,x75734)+P24(x75731,x75732,f318(f318(f300(f910(x75731)),x75733),x75734))+~P24(x75731,x75732,f318(f318(f300(f910(x75731)),x75733),f179(f918(f910(x75731),a909))))
% 109.14/108.85 [7615]~P1(f318(f318(f320(x76151),x76152),x76154))+P1(f318(f318(f320(x76151),x76152),f31(f918(x76151,a909),x76153)))+~P1(f318(f318(f320(f918(x76151,a909)),x76154),x76153))
% 109.14/108.85 [7625]P28(x76251,x76252,x76253)+P1(f318(f318(f320(f910(x76251)),f874(x76252,x76254,x76251)),x76254))+~P1(f318(f318(f320(f910(x76251)),x76253),x76254))
% 109.14/108.85 [7643]~P89(x76431)+~P1(f318(f318(f225(x76431),x76433),x76434))+P1(f318(f318(f225(x76431),f318(f318(f73(x76431),x76432),x76433)),f318(f318(f73(x76431),x76432),x76434)))
% 109.14/108.85 [7644]~P90(x76441)+~P1(f318(f318(f225(x76441),x76443),x76444))+P1(f318(f318(f225(x76441),f318(f318(f73(x76441),x76442),x76443)),f318(f318(f73(x76441),x76442),x76444)))
% 109.14/108.85 [7645]~P89(x76451)+~P1(f318(f318(f225(x76451),x76452),x76454))+P1(f318(f318(f225(x76451),f318(f318(f73(x76451),x76452),x76453)),f318(f318(f73(x76451),x76454),x76453)))
% 109.14/108.85 [7646]~P90(x76461)+~P1(f318(f318(f225(x76461),x76462),x76464))+P1(f318(f318(f225(x76461),f318(f318(f73(x76461),x76462),x76463)),f318(f318(f73(x76461),x76464),x76463)))
% 109.14/108.85 [7647]~P89(x76471)+~P1(f318(f318(f226(x76471),x76473),x76474))+P1(f318(f318(f226(x76471),f318(f318(f73(x76471),x76472),x76473)),f318(f318(f73(x76471),x76472),x76474)))
% 109.14/108.85 [7648]~P92(x76481)+~P1(f318(f318(f226(x76481),x76483),x76484))+P1(f318(f318(f226(x76481),f318(f318(f73(x76481),x76482),x76483)),f318(f318(f73(x76481),x76482),x76484)))
% 109.14/108.85 [7649]~P89(x76491)+~P1(f318(f318(f226(x76491),x76492),x76494))+P1(f318(f318(f226(x76491),f318(f318(f73(x76491),x76492),x76493)),f318(f318(f73(x76491),x76494),x76493)))
% 109.14/108.85 [7650]~P92(x76501)+~P1(f318(f318(f226(x76501),x76502),x76504))+P1(f318(f318(f226(x76501),f318(f318(f73(x76501),x76502),x76503)),f318(f318(f73(x76501),x76504),x76503)))
% 109.14/108.85 [7651]~P123(x76511)+~P1(f318(f318(f278(x76511),x76513),x76514))+P1(f318(f318(f278(x76511),f318(f318(f74(x76511),x76512),x76513)),f318(f318(f74(x76511),x76512),x76514)))
% 109.14/108.85 [7652]~P123(x76521)+~P1(f318(f318(f278(x76521),x76522),x76524))+P1(f318(f318(f278(x76521),f318(f318(f74(x76521),x76522),x76523)),f318(f318(f74(x76521),x76524),x76523)))
% 109.14/108.85 [7659]~P129(x76591)+~P100(x76591)+E(f318(f318(f3(x76591),f318(f318(f74(x76591),x76592),f318(f94(x76591),x76593))),f318(f318(f74(x76591),x76594),f318(f94(x76591),x76593))),f318(f318(f74(x76591),f318(f318(f3(x76591),x76592),x76594)),f318(f94(x76591),x76593)))
% 109.14/108.85 [7660]~P100(x76601)+~P148(x76601)+E(f318(f318(f73(x76601),f318(f318(f74(x76601),x76602),f318(f94(x76601),x76603))),f318(f318(f74(x76601),x76604),f318(f94(x76601),x76603))),f318(f318(f74(x76601),f318(f318(f73(x76601),x76602),x76604)),f318(f94(x76601),x76603)))
% 109.14/108.85 [7696]~P76(x76961)+E(f318(f318(f73(x76961),f318(x76962,x76963)),f318(f318(f8(a911,x76961),x76962),f294(a911,f318(a103,x76963),x76964))),f318(f318(f8(a911,x76961),x76962),f294(a911,x76963,x76964)))+~P1(f318(f318(f225(a911),x76963),x76964))
% 109.14/108.85 [7707]~P25(x77072,x77071,x77073,f318(f163(x77072),x77074))+~P1(f318(f128(x77072),x77074))+P1(f318(f128(x77071),f318(f318(f145(x77072,x77071),x77073),x77074)))
% 109.14/108.85 [7754]~P1(f318(f318(f225(a911),x77542),x77544))+~P1(f318(f318(f225(a911),x77541),x77543))+P1(f318(f318(f225(a911),f318(f318(f73(a911),x77541),x77542)),f318(f318(f73(a911),x77543),x77544)))
% 109.14/108.85 [7755]~P1(f318(f318(f225(a911),x77552),x77554))+~P1(f318(f318(f225(a911),x77551),x77553))+P1(f318(f318(f225(a911),f318(f318(f74(a911),x77551),x77552)),f318(f318(f74(a911),x77553),x77554)))
% 109.14/108.85 [7758]~P1(f318(f318(f226(a911),x77582),x77584))+~P1(f318(f318(f226(a911),x77581),x77583))+P1(f318(f318(f226(a911),f318(f318(f73(a911),x77581),x77582)),f318(f318(f73(a911),x77583),x77584)))
% 109.14/108.85 [7759]~P1(f318(f318(f225(a1),x77592),x77594))+~P1(f318(f318(f226(a1),x77591),x77593))+P1(f318(f318(f226(a1),f318(f318(f73(a1),x77591),x77592)),f318(f318(f73(a1),x77593),x77594)))
% 109.14/108.85 [7807]P1(f318(f318(f320(x78071),x78072),x78073))+~P1(f318(f318(f320(x78071),x78072),f32(f918(x78071,a909),x78074)))+~P1(f318(f318(f320(f918(x78071,a909)),x78073),x78074))
% 109.14/108.85 [7808]P1(f318(f318(f320(x78081),x78082),x78083))+~P1(f318(f318(f320(x78081),x78082),f32(f918(x78081,a909),x78084)))+~P1(f318(f318(f320(f918(x78081,a909)),x78083),x78084))
% 109.14/108.85 [7825]~P1(f318(x78251,f655(x78251,x78253,x78252)))+P1(f318(x78251,f318(f318(f155(x78252),x78253),x78254)))+~P1(f318(f318(f226(a911),x78254),f318(f180(f912(x78252)),x78253)))
% 109.14/108.85 [7830]P1(f318(x78301,x78302))+~P1(f318(f318(f320(x78304),x78302),f318(f163(x78304),x78303)))+P1(f318(f318(f226(a911),f658(x78301,x78303,x78304)),f318(f180(f912(x78304)),x78303)))
% 109.14/108.85 [7876]~P3(x78761)+~P1(f318(f318(f226(f918(x78762,x78761)),x78764),x78763))+~P1(f318(f318(f225(f918(x78762,x78761)),x78763),x78764))
% 109.14/108.85 [7922]~P1(f318(x79224,x79222))+~P1(f318(f318(f320(x79221),x79222),x79223))+P1(f318(f318(f320(x79221),x79222),f318(f318(f92(f918(x79221,a909)),x79223),f318(f253(x79221),x79224))))
% 109.14/108.85 [7935]P1(f318(f318(f320(x79351),x79352),x79353))+~P1(f318(f318(f225(f918(x79351,a909)),x79353),x79354))+P1(f318(f318(f225(f918(x79351,a909)),x79353),f318(f318(f300(x79351),x79352),x79354)))
% 109.14/108.85 [7936]P1(f318(f318(f320(x79361),x79362),x79363))+~P1(f318(f318(f225(f918(x79361,a909)),x79363),x79364))+P1(f318(f318(f225(f918(x79361,a909)),x79363),f318(f318(f300(x79361),x79362),x79364)))
% 109.14/108.85 [8067]~P1(f318(f318(f320(x80671),x80673),x80674))+~P1(f318(f318(f226(f918(x80671,a909)),x80672),x80674))+P1(f318(f318(f226(f918(x80671,a909)),x80672),f318(f318(f300(x80671),x80673),x80674)))
% 109.14/108.85 [8069]E(f318(f318(f92(f918(x80691,a909)),x80692),x80693),f179(f918(x80691,a909)))+~E(f318(f318(f92(f918(x80691,a909)),f31(f918(x80691,a909),x80694)),x80693),f179(f918(x80691,a909)))+~P1(f318(f318(f320(f918(x80691,a909)),x80692),x80694))
% 109.14/108.85 [8135]P1(f318(f318(f320(x81351),x81352),x81353))+~P1(f318(f318(f225(f918(x81351,a909)),x81353),f318(f318(f300(x81351),x81352),x81354)))+P1(f318(f318(f225(f918(x81351,a909)),x81353),x81354))
% 109.14/108.85 [8136]P1(f318(f318(f320(x81361),x81362),x81363))+~P1(f318(f318(f225(f918(x81361,a909)),x81363),f318(f318(f300(x81361),x81362),x81364)))+P1(f318(f318(f225(f918(x81361,a909)),x81363),x81364))
% 109.14/108.85 [8153]P1(f318(f318(f320(x81532),f655(x81531,x81533,x81532)),f318(f163(x81532),x81533)))+P1(f318(x81531,f318(f318(f155(x81532),x81533),x81534)))+~P1(f318(f318(f226(a911),x81534),f318(f180(f912(x81532)),x81533)))
% 109.14/108.85 [8161]~P1(f318(f318(f225(f918(x81611,a909)),x81612),x81614))+P1(f318(f318(f225(f918(x81611,a909)),x81612),x81613))+~P1(f318(f318(f225(f918(x81611,a909)),x81614),x81613))
% 109.14/108.85 [8162]~P1(f318(f318(f226(f918(x81621,a909)),x81622),x81624))+~P1(f318(f318(f225(f918(x81621,a909)),x81624),x81623))+P1(f318(f318(f226(f918(x81621,a909)),x81622),x81623))
% 109.14/108.85 [8163]~P1(f318(f318(f225(f918(x81631,a909)),x81632),x81634))+~P1(f318(f318(f226(f918(x81631,a909)),x81634),x81633))+P1(f318(f318(f226(f918(x81631,a909)),x81632),x81633))
% 109.14/108.85 [8164]~P1(f318(f318(f226(f918(x81641,a909)),x81642),x81644))+P1(f318(f318(f226(f918(x81641,a909)),x81642),x81643))+~P1(f318(f318(f226(f918(x81641,a909)),x81644),x81643))
% 109.14/108.85 [8213]~P1(f318(f318(f320(x82131),x82134),x82133))+~P1(f318(f318(f226(f918(x82131,a909)),x82132),f318(f318(f300(x82131),x82134),x82133)))+P1(f318(f318(f226(f918(x82131,a909)),x82132),x82133))
% 109.14/108.85 [8221]~P89(x82211)+P1(f318(f318(f225(x82211),x82212),x82213))+~P1(f318(f318(f225(x82211),f318(f318(f73(x82211),x82214),x82212)),f318(f318(f73(x82211),x82214),x82213)))
% 109.14/108.85 [8222]~P89(x82221)+P1(f318(f318(f225(x82221),x82222),x82223))+~P1(f318(f318(f225(x82221),f318(f318(f73(x82221),x82224),x82222)),f318(f318(f73(x82221),x82224),x82223)))
% 109.14/108.85 [8223]~P89(x82231)+P1(f318(f318(f225(x82231),x82232),x82233))+~P1(f318(f318(f225(x82231),f318(f318(f73(x82231),x82232),x82234)),f318(f318(f73(x82231),x82233),x82234)))
% 109.14/108.85 [8224]~P89(x82241)+P1(f318(f318(f225(x82241),x82242),x82243))+~P1(f318(f318(f225(x82241),f318(f318(f73(x82241),x82242),x82244)),f318(f318(f73(x82241),x82243),x82244)))
% 109.14/108.85 [8225]~P89(x82251)+P1(f318(f318(f226(x82251),x82252),x82253))+~P1(f318(f318(f226(x82251),f318(f318(f73(x82251),x82254),x82252)),f318(f318(f73(x82251),x82254),x82253)))
% 109.14/108.85 [8226]~P89(x82261)+P1(f318(f318(f226(x82261),x82262),x82263))+~P1(f318(f318(f226(x82261),f318(f318(f73(x82261),x82264),x82262)),f318(f318(f73(x82261),x82264),x82263)))
% 109.14/108.85 [8227]~P89(x82271)+P1(f318(f318(f226(x82271),x82272),x82273))+~P1(f318(f318(f226(x82271),f318(f318(f73(x82271),x82272),x82274)),f318(f318(f73(x82271),x82273),x82274)))
% 109.14/108.85 [8228]~P89(x82281)+P1(f318(f318(f226(x82281),x82282),x82283))+~P1(f318(f318(f226(x82281),f318(f318(f73(x82281),x82282),x82284)),f318(f318(f73(x82281),x82283),x82284)))
% 109.14/108.85 [8283]P1(f318(x82831,x82832))+~E(f318(f318(f129(x82833),f318(f180(f912(x82833)),f168(x82833,x82831,x82834))),x82834),f104(x82833))+~P1(f318(f318(f320(x82833),x82832),f318(f163(x82833),x82834)))
% 109.14/108.85 [8399]P1(f318(x83991,x83992))+~P1(f318(f318(f320(x83993),x83992),f318(f163(x83993),x83994)))+P1(f318(f318(f226(a911),f318(f180(f912(x83993)),f318(f127(x83993,x83991),x83994))),f318(f180(f912(x83993)),x83994)))
% 109.14/108.85 [8882]~P1(f318(x88821,f748(x88821,x88823,x88822,x88824)))+P1(f318(x88821,f318(f318(f155(x88822),x88823),x88824)))+~P1(f318(f318(f226(a911),x88824),f318(f180(f912(x88822)),x88823)))
% 109.14/108.85 [8901]~P25(x89014,x89013,x89011,f233(f918(x89014,a909)))+E(f318(x89011,f700(x89012,x89011,x89013,x89014)),x89012)+~P1(f318(f318(f320(x89013),x89012),f318(f301(x89014,x89013,x89011),f233(f918(x89014,a909)))))
% 109.14/108.85 [8976]E(f168(x89761,x89762,x89763),f318(f318(f166(x89761),x89764),x89763))+P1(f318(f318(f226(a911),f718(x89762,x89763,x89761,x89764)),x89764))+P1(f318(f318(f226(a911),x89764),f318(f180(f912(x89761)),x89763)))
% 109.14/108.85 [8979]E(f168(x89791,x89792,x89793),f318(f318(f166(x89791),x89794),x89793))+P1(f318(f318(f226(a911),f718(x89792,x89793,x89791,x89794)),x89794))+P1(f318(x89792,f318(f318(f155(x89791),x89793),x89794)))
% 109.14/108.85 [9017]P1(f318(x90171,x90172))+~P1(f318(f318(f320(x90174),x90172),f318(f163(x90174),x90173)))+P1(f318(f318(f226(a911),f693(x90172,x90171,x90173,x90174)),f318(f180(f912(x90174)),x90173)))
% 109.14/108.85 [9020]E(f168(x90201,x90202,x90203),f318(f318(f166(x90201),x90204),x90203))+P1(f318(f318(f226(a911),x90204),f318(f180(f912(x90201)),x90203)))+P1(f318(f318(f226(a911),f718(x90202,x90203,x90201,x90204)),f318(f180(f912(x90201)),x90203)))
% 109.14/108.85 [9026]E(f168(x90261,x90262,x90263),f318(f318(f166(x90261),x90264),x90263))+P1(f318(x90262,f318(f318(f155(x90261),x90263),x90264)))+P1(f318(f318(f226(a911),f718(x90262,x90263,x90261,x90264)),f318(f180(f912(x90261)),x90263)))
% 109.14/108.85 [9052]~P130(x90524)+P1(f318(f318(f320(x90521),f431(x90522,x90523,x90521,x90524)),x90523))+P1(f318(f318(f226(x90524),f2(x90524)),f318(f318(f11(x90521,x90524),x90522),x90523)))
% 109.14/108.85 [9053]~P130(x90534)+P1(f318(f318(f320(x90531),f432(x90532,x90533,x90531,x90534)),x90533))+P1(f318(f318(f225(x90534),f2(x90534)),f318(f318(f11(x90531,x90534),x90532),x90533)))
% 109.14/108.85 [9078]~P1(f318(f55(x90781),x90784))+P1(f318(f318(f320(x90781),f545(x90782,x90783,x90784,x90781)),x90784))+P1(f318(f55(f917(x90781,x90783)),f318(f318(f245(x90781,x90783),x90784),x90782)))
% 109.14/108.85 [9111]P1(f318(f318(f320(x91112),f748(x91111,x91113,x91112,x91114)),f318(f163(x91112),x91113)))+P1(f318(x91111,f318(f318(f155(x91112),x91113),x91114)))+~P1(f318(f318(f226(a911),x91114),f318(f180(f912(x91112)),x91113)))
% 109.14/108.85 [9229]P1(f318(f318(f225(a911),x92294),f318(f180(f912(x92292)),f168(x92292,x92293,x92291))))+P1(f318(f318(f226(a911),f719(x92291,x92292,x92293,x92294)),x92294))+~P1(f318(f318(f225(a911),x92294),f318(f180(f912(x92292)),x92291)))
% 109.14/108.85 [9389]E(f168(x93891,x93892,x93893),f318(f318(f166(x93891),x93894),x93893))+~P1(f318(x93892,f318(f318(f155(x93891),x93893),f718(x93892,x93893,x93891,x93894))))+P1(f318(f318(f226(a911),x93894),f318(f180(f912(x93891)),x93893)))
% 109.14/108.85 [9397]E(f168(x93971,x93972,x93973),f318(f318(f166(x93971),x93974),x93973))+~P1(f318(x93972,f318(f318(f155(x93971),x93973),f718(x93972,x93973,x93971,x93974))))+P1(f318(x93972,f318(f318(f155(x93971),x93973),x93974)))
% 109.14/108.85 [9401]~P1(f318(f55(x94011),x94013))+~P1(f318(f55(x94012),f318(x94014,f545(x94014,x94012,x94013,x94011))))+P1(f318(f55(f917(x94011,x94012)),f318(f318(f245(x94011,x94012),x94013),x94014)))
% 109.14/108.85 [9409]~P130(x94091)+~P1(f318(f318(f225(x94091),f2(x94091)),f318(x94093,f432(x94093,x94094,x94092,x94091))))+P1(f318(f318(f225(x94091),f2(x94091)),f318(f318(f11(x94092,x94091),x94093),x94094)))
% 109.14/108.85 [9410]~P130(x94101)+~P1(f318(f318(f226(x94101),f2(x94101)),f318(x94103,f431(x94103,x94104,x94102,x94101))))+P1(f318(f318(f226(x94101),f2(x94101)),f318(f318(f11(x94102,x94101),x94103),x94104)))
% 109.14/108.85 [9418]~E(f318(f180(f912(x94184)),x94182),f318(f180(f912(x94184)),x94183))+P1(f318(f318(f320(f917(f912(x94184),f912(x94184))),f318(f318(f243(f912(x94184),f912(x94184)),x94183),x94182)),f149(x94184,x94181)))+P1(f318(f318(f226(a911),f647(x94181,x94182,x94183,x94184)),f318(f180(f912(x94184)),x94183)))
% 109.14/108.85 [9474]~P1(f318(x94743,f318(f318(f155(x94742),x94744),f719(x94744,x94742,x94743,x94741))))+P1(f318(f318(f225(a911),x94741),f318(f180(f912(x94742)),f168(x94742,x94743,x94744))))+~P1(f318(f318(f225(a911),x94741),f318(f180(f912(x94742)),x94744)))
% 109.14/108.85 [9560]E(f318(f318(f166(x95601),f656(x95602,x95603,x95604,x95601)),x95603),f318(f318(f166(x95601),f656(x95602,x95603,x95604,x95601)),x95604))+~P1(f318(f318(f320(f917(f912(x95601),f912(x95601))),f318(f318(f243(f912(x95601),f912(x95601)),x95604),x95603)),f138(x95601,x95602)))+P1(f318(f318(f226(a911),f318(f180(f912(x95601)),x95604)),f318(f180(f912(x95601)),x95603)))
% 109.14/108.85 [9610]~P1(f318(f318(f226(a911),f2(a911)),x96103))+~P1(f318(f318(f226(a911),x96104),x96101))+P1(f318(f318(f226(a911),f318(f318(f73(a911),f318(f318(f74(a911),x96101),f39(a911,x96102,x96103))),x96104)),f318(f318(f74(a911),x96101),x96103)))
% 109.14/108.85 [9826]~P3(x98262)+~P1(f318(f318(f225(x98262),f318(x98263,f867(x98264,x98263,x98261,x98262))),f318(x98264,f867(x98264,x98263,x98261,x98262))))+P1(f318(f318(f225(f918(x98261,x98262)),x98263),x98264))
% 109.14/108.85 [9827]~P3(x98272)+~P1(f318(f318(f225(x98272),f318(x98273,f886(x98271,x98274,x98273,x98272))),f318(x98274,f886(x98271,x98274,x98273,x98272))))+P1(f318(f318(f225(f918(x98271,x98272)),x98273),x98274))
% 109.14/108.85 [9934]~P67(x99341)+E(f318(f318(f8(a911,x99341),f318(f318(f20(a911,x99341,x99341),f318(f318(f10(x99341,f918(x99341,x99341),a911),f3(x99341)),x99342)),f318(f318(f10(a911,x99341,a911),x99342),f318(f318(f9(a911,a911,a911),f73(a911)),f71(a911))))),f294(a911,x99343,x99344)),f318(f318(f3(x99341),f318(x99342,x99343)),f318(x99342,f318(f318(f73(a911),x99344),f71(a911)))))+~P1(f318(f318(f225(a911),x99343),x99344))
% 109.14/108.85 [10019]~P39(x100193,f318(f318(f280(x100193,x100193,x100193),x100192),f298(x100193,x100192)))+~P1(f318(f318(f320(f917(x100193,x100193)),f318(f318(f243(x100193,x100193),f318(x100191,f318(a103,f828(x100192,x100191,x100193)))),f318(x100191,f828(x100192,x100191,x100193)))),f298(x100193,x100192)))+E(f318(x100191,f318(f318(f73(a911),f827(x100192,x100191,x100193)),x100194)),f318(x100191,f827(x100192,x100191,x100193)))
% 109.14/108.85 [6882]~P69(x68821)+E(f318(f318(f30(x68821),f318(f318(f74(x68821),x68822),x68823)),x68824),f318(f318(f74(x68821),x68822),f318(f318(f30(x68821),x68823),x68824)))+~P1(f318(f318(f278(x68821),x68824),x68823))
% 109.14/108.85 [6961]E(f318(f318(f125(x69611),x69612),x69613),x69614)+~E(x69613,f318(f318(f129(x69611),f318(f180(f912(x69611)),x69612)),x69614))+~E(f318(f318(f166(x69611),f318(f180(f912(x69611)),x69612)),x69614),x69612)
% 109.14/108.85 [7018]~P73(x70182)+E(x70181,f2(x70182))+E(f318(f318(f282(x70182),f318(f318(f235(x70182),x70183),x70184)),f318(f318(f235(x70182),x70181),x70184)),f318(f318(f235(x70182),f318(f318(f282(x70182),x70183),x70181)),x70184))
% 109.14/108.85 [7163]~P69(x71631)+E(f318(f318(f30(x71631),f318(f318(f74(x71631),x71632),x71633)),x71634),f318(f318(f74(x71631),f318(f318(f30(x71631),x71632),x71634)),x71633))+~P1(f318(f318(f278(x71631),x71634),x71632))
% 109.14/108.85 [7171]~P108(x71711)+~P1(f318(f318(f225(x71711),x71713),x71714))+P1(f318(f318(f225(x71711),f318(f318(f92(x71711),x71712),x71713)),x71714))
% 109.14/108.85 [7172]~P108(x71721)+~P1(f318(f318(f225(x71721),x71722),x71724))+P1(f318(f318(f225(x71721),f318(f318(f92(x71721),x71722),x71723)),x71724))
% 109.14/108.85 [7173]~P4(x71731)+~P1(f318(f318(f225(x71731),x71733),x71734))+P1(f318(f318(f225(x71731),f318(f318(f223(x71731),x71732),x71733)),x71734))
% 109.14/108.85 [7174]~P4(x71741)+~P1(f318(f318(f225(x71741),x71743),x71744))+P1(f318(f318(f225(x71741),f318(f318(f223(x71741),x71742),x71743)),x71744))
% 109.14/108.85 [7175]~P4(x71751)+~P1(f318(f318(f225(x71751),x71752),x71754))+P1(f318(f318(f225(x71751),f318(f318(f223(x71751),x71752),x71753)),x71754))
% 109.14/108.85 [7176]~P4(x71761)+~P1(f318(f318(f225(x71761),x71762),x71764))+P1(f318(f318(f225(x71761),f318(f318(f223(x71761),x71762),x71763)),x71764))
% 109.14/108.85 [7177]~P108(x71771)+~P1(f318(f318(f226(x71771),x71773),x71774))+P1(f318(f318(f226(x71771),f318(f318(f92(x71771),x71772),x71773)),x71774))
% 109.14/108.85 [7178]~P108(x71781)+~P1(f318(f318(f226(x71781),x71782),x71784))+P1(f318(f318(f226(x71781),f318(f318(f92(x71781),x71782),x71783)),x71784))
% 109.14/108.85 [7179]~P4(x71791)+~P1(f318(f318(f226(x71791),x71793),x71794))+P1(f318(f318(f226(x71791),f318(f318(f223(x71791),x71792),x71793)),x71794))
% 109.14/108.85 [7180]~P4(x71801)+~P1(f318(f318(f226(x71801),x71803),x71804))+P1(f318(f318(f226(x71801),f318(f318(f223(x71801),x71802),x71803)),x71804))
% 109.14/108.85 [7181]~P4(x71811)+~P1(f318(f318(f226(x71811),x71812),x71814))+P1(f318(f318(f226(x71811),f318(f318(f223(x71811),x71812),x71813)),x71814))
% 109.14/108.85 [7182]~P4(x71821)+~P1(f318(f318(f226(x71821),x71822),x71824))+P1(f318(f318(f226(x71821),f318(f318(f223(x71821),x71822),x71823)),x71824))
% 109.14/108.85 [7205]~P1(f318(x72053,x72054))+~P1(f318(x72052,x72054))+P1(f318(f318(f318(f92(f918(x72051,a909)),x72052),x72053),x72054))
% 109.14/108.85 [7330]P24(x73301,x73302,x73303)+~P24(x73301,x73304,x73303)+~P1(f318(f318(f225(f918(f910(x73301),a909)),x73304),x73302))
% 109.14/108.85 [7331]P24(x73311,x73312,x73313)+~P24(x73311,x73312,x73314)+~P1(f318(f318(f225(f918(f910(x73311),a909)),x73313),x73314))
% 109.14/108.85 [7686]~P76(x76861)+E(f318(f318(f73(x76861),f318(x76862,x76863)),f318(f318(f8(a911,x76861),x76862),f318(f293(a911,f318(a103,x76863)),x76864))),f318(f318(f8(a911,x76861),x76862),f318(f293(a911,x76863),x76864)))+~P1(f318(f318(f226(a911),x76863),x76864))
% 109.14/108.85 [7704]E(x77041,x77042)+P1(f318(f318(f163(x77043),x77044),x77042))+~P1(f318(f318(f163(x77043),f318(f318(f142(x77043),x77041),x77044)),x77042))
% 109.14/108.85 [7714]~P4(x77141)+P1(f318(f318(f225(x77141),x77142),x77143))+~P1(f318(f318(f225(x77141),f318(f318(f224(x77141),x77144),x77142)),x77143))
% 109.14/108.85 [7715]~P4(x77151)+P1(f318(f318(f225(x77151),x77152),x77153))+~P1(f318(f318(f225(x77151),f318(f318(f224(x77151),x77154),x77152)),x77153))
% 109.14/108.85 [7716]~P4(x77161)+P1(f318(f318(f225(x77161),x77162),x77163))+~P1(f318(f318(f225(x77161),f318(f318(f224(x77161),x77162),x77164)),x77163))
% 109.14/108.85 [7717]~P4(x77171)+P1(f318(f318(f225(x77171),x77172),x77173))+~P1(f318(f318(f225(x77171),f318(f318(f224(x77171),x77172),x77174)),x77173))
% 109.14/108.85 [7718]~P102(x77181)+P1(f318(f318(f225(x77181),x77182),x77183))+~P1(f318(f318(f225(x77181),f318(f318(f101(x77181),x77184),x77182)),x77183))
% 109.14/108.85 [7719]~P102(x77191)+P1(f318(f318(f225(x77191),x77192),x77193))+~P1(f318(f318(f225(x77191),f318(f318(f101(x77191),x77194),x77192)),x77193))
% 109.14/108.85 [7720]~P102(x77201)+P1(f318(f318(f225(x77201),x77202),x77203))+~P1(f318(f318(f225(x77201),f318(f318(f101(x77201),x77202),x77204)),x77203))
% 109.14/108.85 [7721]~P102(x77211)+P1(f318(f318(f225(x77211),x77212),x77213))+~P1(f318(f318(f225(x77211),f318(f318(f101(x77211),x77212),x77214)),x77213))
% 109.14/108.85 [7722]~P4(x77221)+P1(f318(f318(f226(x77221),x77222),x77223))+~P1(f318(f318(f226(x77221),f318(f318(f224(x77221),x77224),x77222)),x77223))
% 109.14/108.85 [7723]~P4(x77231)+P1(f318(f318(f226(x77231),x77232),x77233))+~P1(f318(f318(f226(x77231),f318(f318(f224(x77231),x77232),x77234)),x77233))
% 109.14/108.85 [7724]~P121(x77241)+P1(f318(f318(f278(x77241),x77242),x77243))+~P1(f318(f318(f278(x77241),f318(f318(f74(x77241),x77244),x77242)),x77243))
% 109.14/108.85 [7725]~P121(x77251)+P1(f318(f318(f278(x77251),x77252),x77253))+~P1(f318(f318(f278(x77251),f318(f318(f74(x77251),x77252),x77254)),x77253))
% 109.14/108.85 [7798]~P1(f318(f318(f320(x77981),x77982),x77984))+P1(f318(f318(f320(x77981),x77982),x77983))+P1(f318(f318(f320(x77981),x77982),f318(f318(f3(f918(x77981,a909)),x77984),x77983)))
% 109.14/108.85 [7799]~P1(f318(f318(f320(x77991),x77992),x77994))+P1(f318(f318(f320(x77991),x77992),x77993))+P1(f318(f318(f320(x77991),x77992),f318(f318(f3(f918(x77991,a909)),x77994),x77993)))
% 109.14/108.85 [7883]P1(f318(x78831,x78832))+P1(f318(x78833,x78832))+~P1(f318(f318(f318(f101(f918(x78834,a909)),x78833),x78831),x78832))
% 109.14/108.85 [7893]~P1(f318(f318(f320(x78931),x78932),x78934))+~P1(f318(f318(f320(x78931),x78932),x78933))+P1(f318(f318(f320(x78931),x78932),f318(f318(f92(f918(x78931,a909)),x78933),x78934)))
% 109.14/108.85 [7894]~P1(f318(f318(f320(x78941),x78942),x78944))+~P1(f318(f318(f320(x78941),x78942),x78943))+P1(f318(f318(f320(x78941),x78942),f318(f318(f92(f918(x78941,a909)),x78943),x78944)))
% 109.14/108.85 [7944]~P102(x79441)+~P1(f318(f55(x79441),x79444))+E(f318(f318(f58(x79441,x79441,f101(x79441)),x79442),f318(f318(f300(x79441),x79443),x79444)),f318(f318(f101(x79441),x79443),f318(f318(f58(x79441,x79441,f101(x79441)),x79442),x79444)))
% 109.14/108.85 [7945]~P108(x79451)+~P1(f318(f55(x79451),x79454))+E(f318(f318(f58(x79451,x79451,f92(x79451)),x79452),f318(f318(f300(x79451),x79453),x79454)),f318(f318(f92(x79451),x79453),f318(f318(f58(x79451,x79451,f92(x79451)),x79452),x79454)))
% 109.14/108.85 [7946]~P4(x79461)+~P1(f318(f55(x79461),x79464))+E(f318(f318(f58(x79461,x79461,f223(x79461)),x79462),f318(f318(f300(x79461),x79463),x79464)),f318(f318(f223(x79461),x79463),f318(f318(f58(x79461,x79461,f223(x79461)),x79462),x79464)))
% 109.14/108.85 [7947]~P4(x79471)+~P1(f318(f55(x79471),x79474))+E(f318(f318(f58(x79471,x79471,f224(x79471)),x79472),f318(f318(f300(x79471),x79473),x79474)),f318(f318(f224(x79471),x79473),f318(f318(f58(x79471,x79471,f224(x79471)),x79472),x79474)))
% 109.14/108.85 [7949]~P129(x79491)+~P100(x79491)+E(f318(f318(f3(x79491),f318(f318(f74(x79491),f318(f94(x79491),x79492)),x79493)),f318(f318(f74(x79491),f318(f94(x79491),x79492)),x79494)),f318(f318(f74(x79491),f318(f94(x79491),x79492)),f318(f318(f3(x79491),x79493),x79494)))
% 109.14/108.85 [7950]~P100(x79501)+~P148(x79501)+E(f318(f318(f73(x79501),f318(f318(f74(x79501),f318(f94(x79501),x79502)),x79503)),f318(f318(f74(x79501),f318(f94(x79501),x79502)),x79504)),f318(f318(f74(x79501),f318(f94(x79501),x79502)),f318(f318(f73(x79501),x79503),x79504)))
% 109.14/108.85 [8064]E(x80641,x80642)+P1(f318(f318(f320(x80643),x80641),f318(f163(x80643),x80644)))+~P1(f318(f318(f320(x80643),x80641),f318(f163(x80643),f318(f318(f142(x80643),x80642),x80644))))
% 109.14/108.85 [8234]P58(x82341,x82342,x82343)+~P58(x82341,x82342,x82344)+~P1(f318(f318(f225(f918(f917(x82341,x82342),a909)),x82343),x82344))
% 109.14/108.85 [8284]P1(f318(f318(f320(x82841),x82842),x82843))+P1(f318(f318(f320(x82841),x82842),x82844))+~P1(f318(f318(f320(x82841),x82842),f318(f318(f101(f918(x82841,a909)),x82844),x82843)))
% 109.14/108.85 [8285]P1(f318(f318(f320(x82851),x82852),x82853))+P1(f318(f318(f320(x82851),x82852),x82854))+~P1(f318(f318(f320(x82851),x82852),f318(f318(f101(f918(x82851,a909)),x82854),x82853)))
% 109.14/108.85 [8293]~P56(x82931,x82934,x82933)+~P1(f318(f318(f320(x82931),x82932),x82934))+P1(f318(f318(f320(f917(x82931,x82931)),f318(f318(f243(x82931,x82931),x82932),x82932)),x82933))
% 109.14/108.85 [8294]~P56(x82941,x82944,x82943)+~P1(f318(f318(f320(x82941),x82942),x82944))+P1(f318(f318(f320(f917(x82941,x82941)),f318(f318(f243(x82941,x82941),x82942),x82942)),x82943))
% 109.14/108.85 [8295]~P56(x82951,x82954,x82953)+~P1(f318(f318(f320(x82951),x82952),x82954))+P1(f318(f318(f320(f917(x82951,x82951)),f318(f318(f243(x82951,x82951),x82952),x82952)),x82953))
% 109.14/108.85 [8307]~P1(f318(f55(x83072),x83074))+~P1(f318(f55(x83071),x83073))+P1(f318(f55(f917(x83071,x83072)),f318(f318(f245(x83071,x83072),x83073),f318(f18(f918(x83072,a909),x83071),x83074))))
% 109.14/108.85 [8308]~P1(f318(f318(f320(x83081),x83082),x83084))+~P1(f318(f318(f225(f918(x83081,a909)),x83083),x83084))+P1(f318(f318(f225(f918(x83081,a909)),f318(f318(f300(x83081),x83082),x83083)),x83084))
% 109.14/108.85 [8315]~P114(x83152)+~P82(x83152)+E(f318(f318(f11(x83151,x83152),f318(f318(f10(a911,x83152,x83151),f91(x83152)),x83153)),x83154),f318(f91(x83152),f318(f318(f11(x83151,a911),x83153),x83154)))
% 109.14/108.85 [8316]~P144(x83162)+~P82(x83162)+E(f318(f318(f11(x83161,x83162),f318(f318(f10(a1,x83162,x83161),f93(x83162)),x83163)),x83164),f318(f93(x83162),f318(f318(f11(x83161,a1),x83163),x83164)))
% 109.14/108.85 [8341]E(f318(f318(f3(f918(x83411,a909)),x83412),f318(f318(f3(f918(x83411,a909)),x83413),x83414)),x83414)+~P1(f318(f318(f225(f918(x83411,a909)),x83412),x83413))+~P1(f318(f318(f225(f918(x83411,a909)),x83414),x83412))
% 109.14/108.85 [8434]~P1(f318(f55(x84341),x84344))+E(f318(f318(f3(a911),f318(f318(f8(x84341,a911),x84342),x84343)),f318(f318(f8(x84341,a911),x84342),x84344)),f318(f318(f8(x84341,a911),x84342),f318(f318(f3(f918(x84341,a909)),x84343),x84344)))+~P1(f318(f318(f225(f918(x84341,a909)),x84344),x84343))
% 109.14/108.85 [8583]~P8(x85831,x85834,x85833)+~P1(f318(f318(f320(x85831),x85832),x85834))+P1(f318(f318(f320(x85831),x85832),f318(f276(x85831,x85831,x85833),f318(f318(f300(x85831),x85832),f179(f918(x85831,a909))))))
% 109.14/108.85 [8645]~P1(f318(f318(f225(f918(x86451,a909)),x86452),x86453))+~P1(f318(f318(f225(f918(x86451,a909)),x86452),x86454))+P1(f318(f318(f225(f918(x86451,a909)),x86452),f318(f318(f92(f918(x86451,a909)),x86453),x86454)))
% 109.14/108.85 [8749]E(x87491,f179(f918(x87492,a909)))+P1(f318(f55(x87493),x87494))+~P1(f318(f55(f917(x87493,x87492)),f318(f318(f245(x87493,x87492),x87494),f318(f18(f918(x87492,a909),x87493),x87491))))
% 109.14/108.85 [8750]E(x87501,f179(f918(x87502,a909)))+P1(f318(f55(x87503),x87504))+~P1(f318(f55(f917(x87502,x87503)),f318(f318(f245(x87502,x87503),x87501),f318(f18(f918(x87503,a909),x87502),x87504))))
% 109.14/108.85 [8818]P1(f318(f318(f320(x88181),x88182),f307(x88181,x88183)))+~P1(f318(f318(f320(x88181),x88184),f307(x88181,x88183)))+~P1(f318(f318(f320(f917(x88181,x88181)),f318(f318(f243(x88181,x88181),x88182),x88184)),x88183))
% 109.14/108.85 [8819]P1(f318(f318(f320(x88191),x88192),f307(x88191,x88193)))+~P1(f318(f318(f320(x88191),x88194),f307(x88191,x88193)))+~P1(f318(f318(f320(f917(x88191,x88191)),f318(f318(f243(x88191,x88191),x88192),x88194)),x88193))
% 109.14/108.85 [8874]~P39(x88741,x88744)+P1(f318(f318(f320(f917(x88741,x88741)),f318(f318(f243(x88741,x88741),x88743),x88742)),f298(x88741,x88744)))+P39(x88741,f318(f318(f300(f917(x88741,x88741)),f318(f318(f243(x88741,x88741),x88742),x88743)),x88744))
% 109.14/108.85 [8875]~P61(x88751,x88754)+P1(f318(f318(f320(f917(x88751,x88751)),f318(f318(f243(x88751,x88751),x88753),x88752)),f298(x88751,x88754)))+P61(x88751,f318(f318(f300(f917(x88751,x88751)),f318(f318(f243(x88751,x88751),x88752),x88753)),x88754))
% 109.14/108.85 [8957]~E(x89572,x89573)+~P1(f318(f318(f320(x89571),x89572),f318(f163(x89571),x89574)))+P1(f318(f318(f320(f917(x89571,x89571)),f318(f318(f243(x89571,x89571),x89572),x89573)),f318(f163(f917(x89571,x89571)),f318(f318(f172(x89571,x89571),x89574),x89574))))
% 109.14/108.85 [8986]~P42(f918(x89861,a909),f918(x89861,a909),x89863)+~P1(f318(f318(f320(x89861),x89862),f87(f918(x89861,a909),x89863)))+P1(f318(f318(f320(x89861),x89862),f318(x89863,f318(f318(f101(f918(x89861,a909)),x89864),f87(f918(x89861,a909),x89863)))))
% 109.14/108.85 [9051]~E(x90513,x90514)+P1(f318(f318(f248(x90511,x90511,a909),a315),x90512))+~P1(f318(f318(f320(f917(x90511,x90511)),x90512),f318(f163(f917(x90511,x90511)),f318(f318(f172(x90511,x90511),x90513),x90514))))
% 109.14/108.85 [9095]P1(f318(f318(f320(f917(f912(x90951),f912(x90951))),f318(f318(f243(f912(x90951),f912(x90951)),x90952),x90953)),f138(x90951,x90954)))+~E(f318(f318(f166(x90951),f318(f180(f912(x90951)),x90952)),x90953),x90952)+~P1(f318(f318(f226(a911),f318(f180(f912(x90951)),x90952)),f318(f180(f912(x90951)),x90953)))
% 109.14/108.85 [9097]~P55(x90971,x90974)+~P1(f318(f318(f320(f917(x90971,x90971)),f318(f318(f243(x90971,x90971),x90973),x90972)),x90974))+P1(f318(f318(f320(f917(x90971,x90971)),f318(f318(f243(x90971,x90971),x90972),x90973)),x90974))
% 109.14/108.85 [9098]~P55(x90981,x90984)+~P1(f318(f318(f320(f917(x90981,x90981)),f318(f318(f243(x90981,x90981),x90983),x90982)),x90984))+P1(f318(f318(f320(f917(x90981,x90981)),f318(f318(f243(x90981,x90981),x90982),x90983)),x90984))
% 109.14/108.85 [9190]~P1(f318(f55(x91901),x91904))+P1(f318(f318(f320(x91901),f865(x91902,x91903,x91904,x91901)),x91904))+P1(f318(f55(x91903),f318(f318(f33(x91901,f918(x91903,a909)),x91904),x91902)))
% 109.14/108.85 [9191]~P1(f318(f55(x91911),x91914))+P1(f318(f318(f320(x91911),f582(x91912,x91913,x91914,x91911)),x91914))+P1(f318(f55(x91913),f318(f318(f33(x91911,f918(x91913,a909)),x91914),x91912)))
% 109.14/108.85 [9270]P1(f318(f318(f320(f917(x92701,x92701)),x92702),f318(f318(f280(x92701,x92701,x92701),x92703),f298(x92701,x92703))))+~P1(f318(f318(f226(a911),f2(a911)),x92704))+~P1(f318(f318(f320(f917(x92701,x92701)),x92702),f318(f318(f174(f917(x92701,x92701),a909),x92704),x92703)))
% 109.14/108.85 [9278]~P39(x92781,x92782)+~P1(f318(f318(f320(f917(x92781,x92781)),f318(f318(f243(x92781,x92781),x92784),x92783)),x92782))+~P1(f318(f318(f320(f917(x92781,x92781)),f318(f318(f243(x92781,x92781),x92783),x92784)),x92782))
% 109.14/108.85 [9279]~P39(x92791,x92792)+~P1(f318(f318(f320(f917(x92791,x92791)),f318(f318(f243(x92791,x92791),x92794),x92793)),x92792))+~P1(f318(f318(f320(f917(x92791,x92791)),f318(f318(f243(x92791,x92791),x92793),x92794)),x92792))
% 109.14/108.85 [9408]~P1(f318(f55(x94081),x94084))+E(f318(f318(f8(x94081,a911),f318(f318(f10(f918(x94082,a909),a911,x94081),f29(x94082)),x94083)),x94084),f318(f29(f917(x94081,x94082)),f318(f318(f245(x94081,x94082),x94084),x94083)))+P1(f318(f318(f320(x94081),f546(x94083,x94082,x94084,x94081)),x94084))
% 109.14/108.85 [9412]~P1(f318(f128(x94121),x94122))+P1(f318(f128(x94121),f318(f318(f150(x94121,x94122),x94123),x94124)))+P1(f318(f318(f320(x94121),x94124),f318(f318(f3(f918(x94121,a909)),f318(f163(x94121),x94122)),f318(f318(f300(x94121),f318(f318(f155(x94121),x94122),x94123)),f179(f918(x94121,a909))))))
% 109.14/108.85 [9430]~P1(f318(f55(x94302),x94303))+~P1(f318(f55(x94301),f318(x94304,f865(x94304,x94301,x94303,x94302))))+P1(f318(f55(x94301),f318(f318(f33(x94302,f918(x94301,a909)),x94303),x94304)))
% 109.14/108.85 [9431]~P1(f318(f55(x94312),x94313))+~P1(f318(f55(x94311),f318(x94314,f582(x94314,x94311,x94313,x94312))))+P1(f318(f55(x94311),f318(f318(f33(x94312,f918(x94311,a909)),x94313),x94314)))
% 109.14/108.85 [9512]~P1(f318(f318(f320(f917(x95121,x95121)),x95122),f318(f318(f280(x95121,x95121,x95121),x95124),f298(x95121,x95124))))+P1(f318(f318(f320(f917(x95121,x95121)),x95122),f318(f318(f280(x95121,x95121,x95121),x95123),f298(x95121,x95123))))+~P1(f318(f318(f225(f918(f917(x95121,x95121),a909)),x95124),x95123))
% 109.14/108.85 [9522]E(f318(f318(f166(x95221),f656(x95224,x95223,x95222,x95221)),x95223),f318(f318(f166(x95221),f656(x95224,x95223,x95222,x95221)),x95222))+~P1(f318(f318(f320(f917(f912(x95221),f912(x95221))),f318(f318(f243(f912(x95221),f912(x95221)),x95222),x95223)),f138(x95221,x95224)))+E(f318(f318(f166(x95221),f318(f180(f912(x95221)),x95222)),x95223),x95222)
% 109.14/108.85 [9542]~P1(f318(f55(x95421),x95424))+E(f318(f318(f8(x95421,a911),f318(f318(f10(f918(x95422,a909),a911,x95421),f29(x95422)),x95423)),x95424),f318(f29(f917(x95421,x95422)),f318(f318(f245(x95421,x95422),x95424),x95423)))+~P1(f318(f55(x95422),f318(x95423,f546(x95423,x95422,x95424,x95421))))
% 109.14/108.85 [9547]~E(f318(f180(f912(x95471)),x95473),f318(f180(f912(x95471)),x95472))+P1(f318(f318(f320(f917(f912(x95471),f912(x95471))),f318(f318(f243(f912(x95471),f912(x95471)),x95472),x95473)),f149(x95471,x95474)))+P1(f318(f318(f320(f917(x95471,x95471)),f660(x95474,x95473,x95472,x95471)),f318(f163(f917(x95471,x95471)),f318(f318(f172(x95471,x95471),x95472),x95473))))
% 109.14/108.85 [9619]~P1(f318(f318(f320(f917(f912(x96191),f912(x96191))),f318(f318(f243(f912(x96191),f912(x96191)),x96192),x96193)),f138(x96191,x96194)))+E(f318(f318(f166(x96191),f318(f180(f912(x96191)),x96192)),x96193),x96192)+P1(f318(f318(f226(a911),f656(x96194,x96193,x96192,x96191)),f318(f318(f223(a911),f318(f180(f912(x96191)),x96192)),f318(f180(f912(x96191)),x96193))))
% 109.14/108.85 [9643]~P1(f318(f318(f320(f917(f912(x96431),f912(x96431))),f318(f318(f243(f912(x96431),f912(x96431)),x96432),x96433)),f138(x96431,x96434)))+P1(f318(f318(f226(a911),f318(f180(f912(x96431)),x96432)),f318(f180(f912(x96431)),x96433)))+P1(f318(f318(f226(a911),f656(x96434,x96433,x96432,x96431)),f318(f318(f223(a911),f318(f180(f912(x96431)),x96432)),f318(f180(f912(x96431)),x96433))))
% 109.14/108.85 [10079]~P1(f318(f318(f320(f917(f912(x100791),f912(x100791))),f318(f318(f243(f912(x100791),f912(x100791)),x100792),x100793)),f138(x100791,x100794)))+E(f318(f318(f166(x100791),f318(f180(f912(x100791)),x100792)),x100793),x100792)+P1(f318(f318(f320(f917(x100791,x100791)),f318(f318(f243(x100791,x100791),f318(f318(f155(x100791),x100792),f656(x100794,x100793,x100792,x100791))),f318(f318(f155(x100791),x100793),f656(x100794,x100793,x100792,x100791)))),x100794))
% 109.14/108.85 [10080]~P1(f318(f318(f320(f917(f912(x100801),f912(x100801))),f318(f318(f243(f912(x100801),f912(x100801)),x100802),x100803)),f138(x100801,x100804)))+P1(f318(f318(f226(a911),f318(f180(f912(x100801)),x100802)),f318(f180(f912(x100801)),x100803)))+P1(f318(f318(f320(f917(x100801,x100801)),f318(f318(f243(x100801,x100801),f318(f318(f155(x100801),x100802),f656(x100804,x100803,x100802,x100801))),f318(f318(f155(x100801),x100803),f656(x100804,x100803,x100802,x100801)))),x100804))
% 109.14/108.85 [10134]~E(f318(f180(f912(x101341)),x101342),f318(f180(f912(x101341)),x101343))+P1(f318(f318(f320(f917(f912(x101341),f912(x101341))),f318(f318(f243(f912(x101341),f912(x101341)),x101342),x101343)),f149(x101341,x101344)))+~P1(f318(f318(f320(f917(x101341,x101341)),f318(f318(f243(x101341,x101341),f318(f318(f155(x101341),x101342),f647(x101344,x101343,x101342,x101341))),f318(f318(f155(x101341),x101343),f647(x101344,x101343,x101342,x101341)))),x101344))
% 109.14/108.85 [10280]~P76(x102801)+~P1(f318(f55(x102802),x102804))+E(f318(f156(x102801),f318(f318(f145(x102802,x102801),x102803),f83(f912(x102802),f318(f318(f20(f912(x102802),a909,a909),f318(f318(f10(a909,f918(a909,a909),f912(x102802)),a316),f318(f318(f9(f912(x102802),f918(x102802,a909),a909),f318(f318(f10(f918(x102802,a909),f918(f918(x102802,a909),a909),f912(x102802)),a315),f163(x102802))),x102804))),f128(x102802))))),f222(x102802,x102801,x102803,x102804))
% 109.14/108.85 [7536]~P72(x75362)+E(x75361,f2(x75362))+E(f318(f318(f282(x75362),f318(f318(f73(x75362),x75363),f318(f318(f74(x75362),x75364),x75361))),x75361),f318(f318(f73(x75362),x75364),f318(f318(f282(x75362),x75363),x75361)))
% 109.14/108.85 [7537]~P69(x75372)+E(x75371,f2(x75372))+E(f318(f318(f30(x75372),f318(f318(f73(x75372),x75373),f318(f318(f74(x75372),x75374),x75371))),x75371),f318(f318(f73(x75372),x75374),f318(f318(f30(x75372),x75373),x75371)))
% 109.14/108.85 [7538]~P69(x75382)+E(x75381,f2(x75382))+E(f318(f318(f30(x75382),f318(f318(f73(x75382),x75383),f318(f318(f74(x75382),x75381),x75384))),x75381),f318(f318(f73(x75382),x75384),f318(f318(f30(x75382),x75383),x75381)))
% 109.14/108.85 [7762]~P73(x77622)+E(x77621,f2(x77622))+E(f318(f318(f282(x77622),f318(f318(f3(x77622),x77623),f318(f318(f74(x77622),x77621),x77624))),x77621),f318(f318(f3(x77622),f318(f318(f282(x77622),x77623),x77621)),x77624))
% 109.14/108.85 [7763]~P72(x77632)+E(x77631,f2(x77632))+E(f318(f318(f282(x77632),f318(f318(f73(x77632),x77633),f318(f318(f74(x77632),x77634),x77631))),x77631),f318(f318(f73(x77632),f318(f318(f282(x77632),x77633),x77631)),x77634))
% 109.14/108.85 [7764]~P73(x77642)+E(x77641,f2(x77642))+E(f318(f318(f282(x77642),f318(f318(f73(x77642),x77643),f318(f318(f74(x77642),x77641),x77644))),x77641),f318(f318(f73(x77642),f318(f318(f282(x77642),x77643),x77641)),x77644))
% 109.14/108.85 [8466]~P1(f318(f151(x84661,x84663),x84664))+~P1(f318(f151(x84661,x84662),x84664))+P1(f318(f151(x84661,f318(f318(f92(f918(x84661,a909)),x84662),x84663)),x84664))
% 109.14/108.85 [8832]~E(f318(f318(f280(x88321,x88321,x88321),x88322),x88324),f179(f918(f917(x88321,x88321),a909)))+~E(f318(f318(f280(x88321,x88321,x88321),x88322),x88323),f179(f918(f917(x88321,x88321),a909)))+E(f318(f318(f280(x88321,x88321,x88321),x88322),f318(f318(f101(f918(f917(x88321,x88321),a909)),x88323),x88324)),f179(f918(f917(x88321,x88321),a909)))
% 109.14/108.85 [8958]~P1(f318(f318(f225(f918(x89581,a909)),x89583),x89584))+~P1(f318(f318(f225(f918(x89581,a909)),x89582),x89584))+P1(f318(f318(f225(f918(x89581,a909)),f318(f318(f101(f918(x89581,a909)),x89582),x89583)),x89584))
% 109.14/108.85 [9338]~P1(f318(f55(x93381),x93384))+~P1(f318(f55(x93381),x93383))+E(f318(f318(f3(a911),f318(f318(f73(a911),f318(f318(f8(x93381,a911),x93382),x93383)),f318(f318(f8(x93381,a911),x93382),x93384))),f318(f318(f8(x93381,a911),x93382),f318(f318(f92(f918(x93381,a909)),x93383),x93384))),f318(f318(f8(x93381,a911),x93382),f318(f318(f101(f918(x93381,a909)),x93383),x93384)))
% 109.14/108.85 [9426]~P1(f318(f318(f320(x94261),x94263),x94262))+~P1(f318(f318(f225(f918(x94261,a909)),x94262),f318(f318(f300(x94261),x94263),x94264)))+P1(f318(f318(f225(f918(x94261,a909)),f318(f318(f3(f918(x94261,a909)),x94262),f318(f318(f300(x94261),x94263),f179(f918(x94261,a909))))),x94264))
% 109.14/108.85 [9594]~P1(f318(f318(f320(x95941),x95943),x95942))+P1(f318(f318(f225(f918(x95941,a909)),x95942),f318(f318(f300(x95941),x95943),x95944)))+~P1(f318(f318(f225(f918(x95941,a909)),f318(f318(f3(f918(x95941,a909)),x95942),f318(f318(f300(x95941),x95943),f179(f918(x95941,a909))))),x95944))
% 109.14/108.85 [9595]~P1(f318(f318(f320(x95951),x95953),x95952))+P1(f318(f318(f225(f918(x95951,a909)),x95952),f318(f318(f300(x95951),x95953),x95954)))+~P1(f318(f318(f225(f918(x95951,a909)),f318(f318(f3(f918(x95951,a909)),x95952),f318(f318(f300(x95951),x95953),f179(f918(x95951,a909))))),x95954))
% 109.14/108.85 [9618]~P1(f318(f318(f225(f918(x96181,a909)),x96182),x96184))+P1(f318(f318(f225(f918(x96181,a909)),x96182),f318(f318(f300(x96181),x96183),x96184)))+~P1(f318(f318(f225(f918(x96181,a909)),f318(f318(f3(f918(x96181,a909)),x96182),f318(f318(f300(x96181),x96183),f179(f918(x96181,a909))))),x96184))
% 109.14/108.85 [9696]~P1(f318(f318(f225(a911),x96961),x96963))+~P1(f318(f318(f226(a911),x96962),x96964))+P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),f318(f318(f243(a911,a911),x96961),x96962)),f318(f318(f243(a911,a911),x96963),x96964))),a26))
% 109.14/108.85 [9697]~P1(f318(f318(f225(a911),x96972),x96974))+~P1(f318(f318(f225(a911),x96971),x96973))+P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),f318(f318(f243(a911,a911),x96971),x96972)),f318(f318(f243(a911,a911),x96973),x96974))),a64))
% 109.14/108.85 [10017]~P1(f318(f318(f320(f912(x100171)),x100174),f152(x100171,x100173)))+~P1(f318(f318(f320(f912(x100171)),x100174),f152(x100171,x100172)))+P1(f318(f151(x100171,f318(f318(f92(f918(x100171,a909)),f318(f318(f9(x100171,f918(x100171,a909),a909),f320(x100171)),x100172)),f318(f318(f9(x100171,f918(x100171,a909),a909),f320(x100171)),x100173))),x100174))
% 109.14/108.85 [10109]~P25(x101091,f918(f918(x101091,a909),a909),f318(f318(f9(x101091,f918(f917(x101091,x101091),a909),f918(f918(x101091,a909),a909)),f318(f318(f10(f918(x101091,a909),f918(f918(f917(x101091,x101091),a909),f918(f918(x101091,a909),a909)),x101091),f54(x101091)),f318(f318(f9(x101091,f918(x101091,a909),f918(x101091,a909)),f300(x101091)),f179(f918(x101091,a909))))),x101093),x101092)+~P1(f318(f318(f320(x101091),x101094),x101092))+E(f318(f318(f3(f918(f918(x101091,a909),a909)),f318(f318(f54(x101091),x101092),x101093)),f318(f318(f54(x101091),f318(f318(f300(x101091),x101094),f179(f918(x101091,a909)))),x101093)),f318(f318(f54(x101091),f318(f318(f3(f918(x101091,a909)),x101092),f318(f318(f300(x101091),x101094),f179(f918(x101091,a909))))),x101093))
% 109.14/108.85 [10228]~P56(x102281,x102282,x102284)+~P1(f318(f318(f320(f917(x102281,x102281)),x102283),x102284))+P1(f318(f318(f248(x102281,x102281,a909),f318(f318(f9(x102281,f918(x102281,a909),f918(x102281,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x102281,a909),f918(x102281,a909)),x102281),f10(a909,a909,x102281)),f318(f318(f10(a909,f918(a909,a909),x102281),a316),f318(f318(f9(x102281,f918(x102281,a909),a909),f320(x102281)),x102282)))),f318(f318(f9(x102281,f918(x102281,a909),a909),f320(x102281)),x102282))),x102283))
% 109.14/108.85 [10241]P1(f318(f55(x102411),x102412))+~P1(f318(f55(x102413),f318(f301(x102411,x102413,x102414),x102412)))+~P1(f318(f55(x102411),f318(f253(x102411),f318(f318(f20(x102411,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102411),a316),f318(f318(f9(x102411,f918(x102411,a909),a909),f320(x102411)),x102412))),f318(f318(f9(x102411,x102413,a909),f318(f318(f10(x102413,f918(x102413,a909),x102411),a315),x102414)),f318(x102414,f574(x102414,x102413,x102412,x102411)))))))
% 109.14/108.85 [8217]~P73(x82172)+E(x82171,f2(x82172))+E(f318(f318(f282(x82172),f318(f318(f3(x82172),f318(f318(f74(x82172),x82171),x82173)),x82174)),x82171),f318(f318(f3(x82172),x82173),f318(f318(f282(x82172),x82174),x82171)))
% 109.14/108.85 [8218]~P73(x82182)+E(x82181,f2(x82182))+E(f318(f318(f282(x82182),f318(f318(f73(x82182),f318(f318(f74(x82182),x82181),x82183)),x82184)),x82181),f318(f318(f73(x82182),x82183),f318(f318(f282(x82182),x82184),x82181)))
% 109.14/108.85 [9125]~E(f318(f318(f280(x91251,x91251,x91251),x91253),x91254),f179(f918(f917(x91251,x91251),a909)))+~E(f318(f318(f280(x91251,x91251,x91251),x91252),x91254),f179(f918(f917(x91251,x91251),a909)))+E(f318(f318(f280(x91251,x91251,x91251),f318(f318(f101(f918(f917(x91251,x91251),a909)),x91252),x91253)),x91254),f179(f918(f917(x91251,x91251),a909)))
% 109.14/108.85 [9919]~P1(f318(f151(x99191,x99193),x99194))+~P1(f318(f151(x99191,x99192),x99194))+P1(f318(f151(x99191,f318(f318(f20(x99191,a909,a909),f318(f318(f10(a909,f918(a909,a909),x99191),a316),x99192)),x99193)),x99194))
% 109.14/108.85 [10168]P1(f318(x101681,f560(x101682,x101683,x101681,x101684)))+~P1(f318(f55(x101684),f318(f253(x101684),x101681)))+P1(f318(f55(x101683),f318(f253(x101683),f318(f318(f10(f918(x101684,a909),a909,x101683),f79(x101684)),f318(f318(f10(f918(x101684,a909),f918(x101684,a909),x101683),f318(f20(x101684,a909,a909),f318(f318(f10(a909,f918(a909,a909),x101684),a316),x101681))),x101682)))))
% 109.14/108.85 [10187]~P1(f318(f55(x101872),f318(f253(x101872),x101873)))+~P1(f318(f55(x101871),f318(f253(x101871),f318(f318(f9(x101871,x101872,a909),x101874),f560(x101874,x101871,x101873,x101872)))))+P1(f318(f55(x101871),f318(f253(x101871),f318(f318(f10(f918(x101872,a909),a909,x101871),f79(x101872)),f318(f318(f10(f918(x101872,a909),f918(x101872,a909),x101871),f318(f20(x101872,a909,a909),f318(f318(f10(a909,f918(a909,a909),x101872),a316),x101873))),x101874)))))
% 109.14/108.85 [10251]~P1(f318(f55(x102511),x102514))+P1(f318(f318(f320(x102511),f788(x102512,x102513,x102514,x102511)),x102514))+P1(f318(f55(x102513),f318(f253(x102513),f318(f318(f10(f918(x102511,a909),a909,x102513),f79(x102511)),f318(f318(f10(f918(x102511,a909),f918(x102511,a909),x102513),f318(f20(x102511,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102511),a316),f318(f318(f9(x102511,f918(x102511,a909),a909),f320(x102511)),x102514)))),x102512)))))
% 109.14/108.85 [10257]~P1(f318(f55(x102572),x102573))+~P1(f318(f55(x102571),f318(f253(x102571),f318(f318(f9(x102571,x102572,a909),x102574),f788(x102574,x102571,x102573,x102572)))))+P1(f318(f55(x102571),f318(f253(x102571),f318(f318(f10(f918(x102572,a909),a909,x102571),f79(x102572)),f318(f318(f10(f918(x102572,a909),f918(x102572,a909),x102571),f318(f20(x102572,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102572),a316),f318(f318(f9(x102572,f918(x102572,a909),a909),f320(x102572)),x102573)))),x102574)))))
% 109.14/108.85 [5158]~E(x51582,x51584)+E(f160(x51581,x51582,x51583),f160(x51581,x51584,x51585))+~E(x51582,f2(a911))
% 109.14/108.85 [5412]E(x54121,x54122)+~E(f160(x54124,x54123,x54121),f160(x54124,x54125,x54122))+E(x54123,f2(a911))
% 109.14/108.85 [6678]E(x66781,x66782)+~E(f318(x66783,x66781),f318(x66783,x66782))+~P25(x66784,x66785,x66783,f233(f918(x66784,a909)))
% 109.14/108.85 [6679]E(x66791,x66792)+~E(f318(x66793,x66791),f318(x66793,x66792))+~P25(x66794,x66795,x66793,f233(f918(x66794,a909)))
% 109.14/108.85 [7568]E(x75681,x75682)+~P25(x75683,x75684,x75685,f233(f918(x75683,a909)))+~E(f318(f301(x75683,x75684,x75685),x75681),f318(f301(x75683,x75684,x75685),x75682))
% 109.14/108.85 [7818]P25(x78182,x78183,f654(x78184,x78183,x78182,x78181),x78181)+~E(f318(f301(x78183,x78182,x78185),x78184),x78181)+E(x78181,f179(f918(x78182,a909)))
% 109.14/108.85 [8352]~P1(f318(f318(x83523,x83522),x83525))+~P1(f318(f318(x83523,x83524),x83522))+P1(f318(f318(f320(x83521),x83522),f281(x83521,x83523,x83524,x83525)))
% 109.14/108.85 [8353]~P1(f318(f318(x83533,x83532),x83535))+~P1(f318(f318(x83533,x83534),x83532))+P1(f318(f318(f320(x83531),x83532),f290(x83531,x83533,x83534,x83535)))
% 109.14/108.85 [8652]~P25(x86521,x86522,x86523,x86524)+P26(x86521,x86522,x86523,x86524,x86525)+~E(f318(f301(x86521,x86522,x86523),x86524),x86525)
% 109.14/108.85 [8789]~P26(x87891,x87893,x87894,x87892,x87895)+~P1(f318(f55(x87893),x87895))+P1(f318(f55(x87891),x87892))
% 109.14/108.85 [8790]~P26(x87903,x87901,x87904,x87905,x87902)+~P1(f318(f55(x87903),x87905))+P1(f318(f55(x87901),x87902))
% 109.14/108.85 [8915]~P25(x89151,x89153,x89155,f233(f918(x89151,a909)))+~P25(x89153,x89152,x89154,f233(f918(x89153,a909)))+P25(x89151,x89152,f318(f66(x89153,x89152,x89151,x89154),x89155),f233(f918(x89151,a909)))
% 109.14/108.85 [9489]P1(f318(f318(f320(f917(x94891,x94891)),f318(f318(f243(x94891,x94891),x94892),x94893)),f298(x94891,x94894)))+~P1(f318(f318(f320(f917(x94891,x94891)),f318(f318(f243(x94891,x94891),x94892),x94895)),f298(x94891,x94894)))+~P1(f318(f318(f320(f917(x94891,x94891)),f318(f318(f243(x94891,x94891),x94895),x94893)),f298(x94891,x94894)))
% 109.14/108.85 [9529]~P4(x95292)+~P1(f318(f128(x95291),x95295))+P1(f318(f128(x95291),f140(x95291,x95292,x95293,x95294,x95295)))
% 109.14/108.85 [9658]~P26(x96583,x96582,x96584,f233(f918(x96583,a909)),f233(f918(x96582,a909)))+~P26(x96581,x96583,x96585,f233(f918(x96581,a909)),f233(f918(x96583,a909)))+P26(x96581,x96582,f318(f66(x96583,x96582,x96581,x96584),x96585),f233(f918(x96581,a909)),f233(f918(x96582,a909)))
% 109.14/108.85 [5487]~E(x54872,f104(x54871))+E(f318(f318(f125(x54871),x54872),x54873),f318(f318(f142(x54871),x54874),x54875))+~E(x54873,f318(f318(f142(x54871),x54874),x54875))
% 109.14/108.85 [5488]~E(x54882,f104(x54881))+E(f318(f318(f125(x54881),x54882),x54883),f318(f318(f142(x54881),x54884),x54885))+~E(f318(f318(f142(x54881),x54884),x54885),x54883)
% 109.14/108.85 [6637]~E(f318(f180(f912(x66371)),x66375),f318(f180(f912(x66372)),x66374))+E(f318(f318(f145(f917(x66371,x66372),x66372),f247(x66371,x66372)),x66373),x66374)+~E(f318(f318(f172(x66371,x66372),x66375),x66374),x66373)
% 109.14/108.85 [6638]~E(f318(f180(f912(x66381)),x66384),f318(f180(f912(x66382)),x66385))+E(f318(f318(f145(f917(x66381,x66382),x66381),f242(x66381,x66382)),x66383),x66384)+~E(f318(f318(f172(x66381,x66382),x66384),x66385),x66383)
% 109.14/108.85 [7116]~P4(x71161)+~P13(x71161,f318(f318(f145(x71162,x71161),x71163),x71165))+P13(x71161,f318(f318(f145(x71162,x71161),x71163),f318(f127(x71162,x71164),x71165)))
% 109.14/108.85 [7257]~P4(x72571)+P13(x72571,f318(f318(f145(x72572,x72571),x72573),f161(x72572,x72574,x72575)))+~P13(x72571,f318(f318(f145(x72572,x72571),x72573),x72575))
% 109.14/108.85 [7280]~P58(x72803,x72802,x72805)+~P58(x72801,x72803,x72804)+P58(x72801,x72802,f318(f318(f280(x72801,x72803,x72802),x72804),x72805))
% 109.14/108.85 [7376]E(x73761,x73762)+~P25(x73763,x73764,x73765,f233(f918(x73763,a909)))+~E(f318(f318(f145(x73763,x73764),x73765),x73761),f318(f318(f145(x73763,x73764),x73765),x73762))
% 109.14/108.85 [7377]E(x73771,x73772)+~P25(x73773,x73774,x73775,f233(f918(x73773,a909)))+~E(f318(f318(f145(x73773,x73774),x73775),x73771),f318(f318(f145(x73773,x73774),x73775),x73772))
% 109.14/108.85 [7523]~P1(f318(f318(f225(a911),x75231),f318(x75233,x75235)))+P1(f318(f318(f225(a911),x75231),f146(x75232,x75233,x75234)))+~P1(f318(f318(f320(x75232),x75235),f318(f163(x75232),x75234)))
% 109.14/108.85 [7524]~P1(f318(f318(f226(a911),x75241),f318(x75243,x75245)))+P1(f318(f318(f226(a911),x75241),f146(x75242,x75243,x75244)))+~P1(f318(f318(f320(x75242),x75245),f318(f163(x75242),x75244)))
% 109.14/108.85 [7877]~E(x78773,f2(a911))+P1(f318(x78771,x78772))+~P1(f318(f318(f320(x78774),x78772),f318(f163(x78774),f160(x78774,x78773,x78775))))
% 109.14/108.85 [7892]~E(x78921,f2(a911))+~P1(f318(x78922,x78923))+~P1(f318(f318(f320(x78924),x78923),f318(f163(x78924),f160(x78924,x78921,x78925))))
% 109.14/108.85 [7914]P1(f318(x79141,x79142))+~P1(f318(x79141,x79143))+~P1(f318(f318(f320(x79144),x79142),f318(f163(x79144),f160(x79144,x79145,x79143))))
% 109.14/108.85 [7915]P1(f318(x79151,x79152))+~P1(f318(x79151,x79153))+~P1(f318(f318(f320(x79154),x79153),f318(f163(x79154),f160(x79154,x79155,x79152))))
% 109.14/108.85 [7919]~P113(x79191)+P1(f318(f318(f225(f918(x79191,a909)),f294(x79191,x79192,x79193)),f294(x79191,x79194,x79195)))+P1(f318(f318(f225(x79191),x79192),x79193))
% 109.14/108.85 [7942]~P5(x79421)+P1(f318(f318(f225(x79421),f318(f318(f34(x79422,x79421),x79423),x79424)),f318(x79424,x79425)))+~P1(f318(f318(f320(x79422),x79425),x79423))
% 109.14/108.85 [8014]~P25(x80141,x80142,x80144,x80143)+E(f318(f70(x80141,x80142,x80143,x80144),f318(x80144,x80145)),x80145)+~P1(f318(f318(f320(x80141),x80145),x80143))
% 109.14/108.85 [8015]~P25(x80151,x80152,x80154,x80153)+E(f318(f84(x80151,x80152,x80153,x80154),f318(x80154,x80155)),x80155)+~P1(f318(f318(f320(x80151),x80155),x80153))
% 109.14/108.85 [8208]~P1(f318(x82081,x82085))+P1(f318(x82081,f415(x82081,x82082,x82083,x82084)))+~P1(f318(f318(f320(x82084),x82085),x82083))
% 109.14/108.85 [8209]~P1(f318(x82091,x82095))+P1(f318(x82091,f415(x82091,x82092,x82093,x82094)))+~P1(f318(f318(f320(x82094),x82095),x82092))
% 109.14/108.85 [8305]P1(f318(f55(x83051),x83052))+~P1(f318(f55(x83053),x83054))+~P1(f318(f318(f225(f918(x83051,a909)),x83052),f318(f301(x83053,x83051,x83055),x83054)))
% 109.14/108.85 [8314]~P25(x83144,x83141,x83142,f233(f918(x83144,a909)))+~P1(f318(f318(f320(x83144),x83143),x83145))+P1(f318(f318(f320(x83141),f318(x83142,x83143)),f318(f301(x83144,x83141,x83142),x83145)))
% 109.14/108.85 [8469]E(x84691,x84692)+~P25(x84693,x84694,x84695,f318(f318(f101(f918(x84693,a909)),f318(f163(x84693),x84691)),f318(f163(x84693),x84692)))+~E(f318(f318(f145(x84693,x84694),x84695),x84691),f318(f318(f145(x84693,x84694),x84695),x84692))
% 109.14/108.85 [8470]E(x84701,x84702)+~P25(x84703,x84704,x84705,f318(f318(f101(f918(x84703,a909)),f318(f163(x84703),x84701)),f318(f163(x84703),x84702)))+~E(f318(f318(f145(x84703,x84704),x84705),x84701),f318(f318(f145(x84703,x84704),x84705),x84702))
% 109.14/108.85 [8520]~P113(x85201)+~P1(f318(f318(f226(f918(x85201,a909)),f294(x85201,x85204,x85205)),f294(x85201,x85202,x85203)))+P1(f318(f318(f225(x85201),x85202),x85203))
% 109.14/108.85 [8582]~P25(x85821,x85824,x85825,f233(f918(x85821,a909)))+~P1(f318(f318(f320(x85824),f318(x85825,x85822)),f318(f301(x85821,x85824,x85825),x85823)))+P1(f318(f318(f320(x85821),x85822),x85823))
% 109.14/108.85 [8658]P1(f318(x86581,x86582))+~P1(f318(x86581,f360(x86581,x86583,x86584,x86585)))+~P1(f318(f318(f320(x86585),x86582),x86584))
% 109.14/108.85 [8659]P1(f318(x86591,x86592))+~P1(f318(x86591,f360(x86591,x86593,x86594,x86595)))+~P1(f318(f318(f320(x86595),x86592),x86593))
% 109.14/108.85 [8955]~P25(x89552,x89553,x89551,x89554)+E(f318(x89551,f318(f70(x89552,x89553,x89554,x89551),x89555)),x89555)+~P1(f318(f318(f320(x89553),x89555),f318(f301(x89552,x89553,x89551),x89554)))
% 109.14/108.85 [9065]E(x90651,f104(x90652))+E(f318(f318(f142(x90652),x90653),f672(x90654,x90653,x90655,x90651,x90652)),x90651)+~E(f318(f318(f125(x90652),x90651),x90655),f318(f318(f142(x90652),x90653),x90654))
% 109.14/108.85 [9066]E(x90661,f104(x90662))+E(f318(f318(f142(x90662),x90663),f673(x90664,x90661,x90665,x90663,x90662)),x90661)+~E(f318(f318(f125(x90662),x90661),x90664),f318(f318(f142(x90662),x90663),x90665))
% 109.14/108.85 [9083]E(f318(f318(f142(x90832),x90833),f672(x90834,x90833,x90831,x90835,x90832)),x90835)+~E(f318(f318(f125(x90832),x90835),x90831),f318(f318(f142(x90832),x90833),x90834))+E(x90831,f318(f318(f142(x90832),x90833),x90834))
% 109.14/108.85 [9084]E(f318(f318(f142(x90841),x90842),f673(x90844,x90845,x90843,x90842,x90841)),x90845)+~E(f318(f318(f125(x90841),x90845),x90844),f318(f318(f142(x90841),x90842),x90843))+E(f318(f318(f142(x90841),x90842),x90843),x90844)
% 109.14/108.85 [9161]~E(f318(f301(x91613,x91612,x91614),f233(f918(x91613,a909))),f233(f918(x91612,a909)))+~E(f318(f301(x91611,x91613,x91615),f233(f918(x91611,a909))),f233(f918(x91613,a909)))+E(f318(f301(x91611,x91612,f318(f66(x91613,x91612,x91611,x91614),x91615)),f233(f918(x91611,a909))),f233(f918(x91612,a909)))
% 109.14/108.85 [9539]E(x95391,f104(x95392))+~E(f318(f318(f125(x95392),x95391),x95393),f318(f318(f142(x95392),x95395),x95394))+E(f318(f318(f125(x95392),f673(x95393,x95391,x95394,x95395,x95392)),x95393),x95394)
% 109.14/108.85 [9540]E(x95401,f104(x95402))+~E(f318(f318(f125(x95402),x95401),x95405),f318(f318(f142(x95402),x95404),x95403))+E(f318(f318(f125(x95402),f672(x95403,x95404,x95405,x95401,x95402)),x95405),x95403)
% 109.14/108.85 [9548]E(f318(f318(f125(x95482),f672(x95484,x95483,x95481,x95485,x95482)),x95481),x95484)+~E(f318(f318(f125(x95482),x95485),x95481),f318(f318(f142(x95482),x95483),x95484))+E(x95481,f318(f318(f142(x95482),x95483),x95484))
% 109.14/108.85 [9549]~E(f318(f318(f125(x95491),x95495),x95494),f318(f318(f142(x95491),x95492),x95493))+E(f318(f318(f125(x95491),f673(x95494,x95495,x95493,x95492,x95491)),x95494),x95493)+E(f318(f318(f142(x95491),x95492),x95493),x95494)
% 109.14/108.85 [9550]E(f318(f318(f125(x95501),x95505),f675(x95503,x95502,x95504,x95505,x95501)),x95502)+E(f318(f318(f125(x95501),x95502),f674(x95503,x95502,x95504,x95505,x95501)),x95505)+~E(f318(f318(f125(x95501),x95505),x95504),f318(f318(f125(x95501),x95502),x95503))
% 109.14/108.85 [9580]~P4(x95801)+P13(x95801,f318(f318(f145(x95802,x95801),x95803),f140(x95802,x95801,x95803,x95804,x95805)))+~P13(x95801,f318(f318(f145(x95802,x95801),x95803),x95805))
% 109.14/108.85 [9592]~P62(x95925,x95921,x95924,x95923)+P1(f318(f318(x95921,x95922),f536(x95923,x95924,x95921,x95925,x95922)))+~P1(f318(f318(f320(x95925),x95922),x95924))
% 109.14/108.85 [9593]~P62(x95935,x95931,x95934,x95933)+P1(f318(f318(x95931,x95932),f794(x95933,x95934,x95931,x95935,x95932)))+~P1(f318(f318(f320(x95935),x95932),x95934))
% 109.14/108.85 [9708]~P1(f318(f318(f320(f917(x97081,x97081)),f318(f318(f243(x97081,x97081),x97085),x97083)),f298(x97081,x97084)))+P1(f318(f318(f320(f917(x97081,x97081)),f318(f318(f243(x97081,x97081),x97082),x97083)),f318(f318(f280(x97081,x97081,x97081),x97084),f298(x97081,x97084))))+~P1(f318(f318(f320(f917(x97081,x97081)),f318(f318(f243(x97081,x97081),x97082),x97085)),f318(f318(f280(x97081,x97081,x97081),x97084),f298(x97081,x97084))))
% 109.14/108.85 [9709]~P1(f318(f318(f320(f917(x97091,x97091)),f318(f318(f243(x97091,x97091),x97092),x97095)),f298(x97091,x97094)))+P1(f318(f318(f320(f917(x97091,x97091)),f318(f318(f243(x97091,x97091),x97092),x97093)),f318(f318(f280(x97091,x97091,x97091),x97094),f298(x97091,x97094))))+~P1(f318(f318(f320(f917(x97091,x97091)),f318(f318(f243(x97091,x97091),x97095),x97093)),f318(f318(f280(x97091,x97091,x97091),x97094),f298(x97091,x97094))))
% 109.14/108.85 [9711]P1(f318(f318(f320(f917(f912(x97111),f912(x97111))),f318(f318(f243(f912(x97111),f912(x97111)),x97112),x97113)),f149(x97111,f298(x97111,x97114))))+~P1(f318(f318(f320(f917(f912(x97111),f912(x97111))),f318(f318(f243(f912(x97111),f912(x97111)),x97112),x97115)),f149(x97111,f298(x97111,x97114))))+~P1(f318(f318(f320(f917(f912(x97111),f912(x97111))),f318(f318(f243(f912(x97111),f912(x97111)),x97115),x97113)),f149(x97111,f298(x97111,x97114))))
% 109.14/108.85 [9715]E(f318(f318(f125(x97151),x97152),f674(x97153,x97152,x97154,x97155,x97151)),x97155)+E(f318(f318(f125(x97151),f675(x97153,x97152,x97154,x97155,x97151)),x97153),x97154)+~E(f318(f318(f125(x97151),x97152),x97153),f318(f318(f125(x97151),x97155),x97154))
% 109.14/108.85 [9716]E(f318(f318(f125(x97161),x97162),f675(x97163,x97164,x97165,x97162,x97161)),x97164)+E(f318(f318(f125(x97161),f674(x97163,x97164,x97165,x97162,x97161)),x97165),x97163)+~E(f318(f318(f125(x97161),x97162),x97165),f318(f318(f125(x97161),x97164),x97163))
% 109.14/108.85 [9776]P1(f318(f318(f320(f917(x97761,x97761)),f318(f318(f243(x97761,x97761),x97762),x97763)),f318(f318(f280(x97761,x97761,x97761),x97764),f298(x97761,x97764))))+~P1(f318(f318(f320(f917(x97761,x97761)),f318(f318(f243(x97761,x97761),x97762),x97765)),f318(f318(f280(x97761,x97761,x97761),x97764),f298(x97761,x97764))))+~P1(f318(f318(f320(f917(x97761,x97761)),f318(f318(f243(x97761,x97761),x97765),x97763)),f318(f318(f280(x97761,x97761,x97761),x97764),f298(x97761,x97764))))
% 109.14/108.85 [9807]P36(x98071,x98072,x98073,x98074,x98075)+~E(f318(f180(f912(x98071)),x98074),f318(f180(f912(x98072)),x98075))+~P1(f318(f318(f248(x98071,x98072,a909),x98073),f694(x98075,x98074,x98073,x98072,x98071)))
% 109.14/108.85 [9808]P36(x98081,x98082,x98083,x98084,x98085)+~E(f318(f180(f912(x98081)),x98084),f318(f180(f912(x98082)),x98085))+~P1(f318(f318(f248(x98081,x98082,a909),x98083),f695(x98083,x98085,x98084,x98082,x98081)))
% 109.14/108.85 [9813]E(f318(f318(f125(x98131),f674(x98132,x98133,x98134,x98135,x98131)),x98134),x98132)+~E(f318(f318(f125(x98131),x98133),x98132),f318(f318(f125(x98131),x98135),x98134))+E(f318(f318(f125(x98131),f675(x98132,x98133,x98134,x98135,x98131)),x98132),x98134)
% 109.14/108.85 [9833]~P4(x98332)+E(f318(f318(f139(x98331,x98332,x98333),x98334),x98335),f318(f318(f142(x98331),x98334),x98335))+P1(f318(f318(f320(x98331),f739(x98334,x98333,x98335,x98331,x98332)),f318(f163(x98331),x98335)))
% 109.14/108.85 [9837]~P62(x98371,x98374,x98373,x98372)+~P1(f318(f318(f320(x98371),x98375),x98373))+P1(f318(f318(f320(x98371),f536(x98372,x98373,x98374,x98371,x98375)),x98372))
% 109.14/108.85 [9838]~P62(x98381,x98384,x98383,x98382)+~P1(f318(f318(f320(x98381),x98385),x98383))+P1(f318(f318(f320(x98381),f794(x98382,x98383,x98384,x98381,x98385)),x98382))
% 109.14/108.85 [9970]~P1(f318(f318(f320(f917(f918(x99701,a909),f918(x99701,a909))),f318(f318(f243(f918(x99701,a909),f918(x99701,a909)),x99704),x99703)),f310(x99701,x99702)))+~P1(f318(f318(f320(x99701),x99705),x99704))+P1(f318(f318(f320(x99701),f601(x99702,x99703,x99704,x99701,x99705)),x99703))
% 109.14/108.85 [9979]~P4(x99792)+E(f318(f318(f139(x99791,x99792,x99793),x99794),x99795),f318(f318(f142(x99791),x99794),x99795))+~P1(f318(f318(f225(x99792),f318(x99793,x99794)),f318(x99793,f739(x99794,x99793,x99795,x99791,x99792))))
% 109.14/108.85 [10026]~P25(x100263,x100264,x100265,f233(f918(x100263,a909)))+P1(f318(x100261,x100262))+~P1(f318(x100261,f318(f84(x100263,x100264,f233(f918(x100263,a909)),x100265),f806(x100262,x100261,x100265,x100264,x100263))))
% 109.14/108.85 [10149]P36(x101491,x101492,x101493,x101494,x101495)+~E(f318(f180(f912(x101491)),x101494),f318(f180(f912(x101492)),x101495))+~P1(f318(f318(x101493,f318(f318(f155(x101491),x101494),f696(x101495,x101494,x101493,x101492,x101491))),f318(f318(f155(x101492),x101495),f696(x101495,x101494,x101493,x101492,x101491))))
% 109.14/108.85 [10150]P36(x101501,x101502,x101503,x101504,x101505)+~E(f318(f180(f912(x101501)),x101504),f318(f180(f912(x101502)),x101505))+~P1(f318(f318(x101503,f318(f318(f155(x101501),x101504),f731(x101503,x101505,x101502,x101504,x101501))),f318(f318(f155(x101502),x101505),f731(x101503,x101505,x101502,x101504,x101501))))
% 109.14/108.85 [6709]~P17(x67092,x67095,x67091)+~P1(f318(f55(x67092),x67094))+E(f318(x67091,f318(f318(f300(x67092),x67093),x67094)),f318(f318(f58(x67092,x67092,x67095),x67093),x67094))
% 109.14/108.85 [6710]~E(x67103,x67104)+~E(x67102,x67105)+E(f318(f318(f300(x67101),x67102),f318(f318(f300(x67101),x67103),f179(f918(x67101,a909)))),f318(f318(f300(x67101),x67104),f318(f318(f300(x67101),x67105),f179(f918(x67101,a909)))))
% 109.14/108.85 [6720]P1(f318(x67202,x67205))+E(f168(x67201,x67202,f318(f318(f125(x67201),x67203),x67204)),f168(x67201,x67202,x67203))+~P1(f318(f318(f320(x67201),x67205),f318(f163(x67201),x67203)))
% 109.14/108.85 [6760]E(f318(x67601,x67602),f233(f918(x67603,a909)))+~E(f318(f318(f34(x67604,f918(x67603,a909)),x67605),x67601),f233(f918(x67603,a909)))+~P1(f318(f318(f320(x67604),x67602),x67605))
% 109.14/108.85 [6761]E(f318(x67611,x67612),f179(f918(x67613,a909)))+~E(f318(f318(f33(x67614,f918(x67613,a909)),x67615),x67611),f179(f918(x67613,a909)))+~P1(f318(f318(f320(x67614),x67612),x67615))
% 109.14/108.85 [6762]E(f318(x67621,x67622),f233(f918(x67623,a909)))+~E(f318(f318(f34(x67624,f918(x67623,a909)),x67625),x67621),f233(f918(x67623,a909)))+~P1(f318(f318(f320(x67624),x67622),x67625))
% 109.14/108.85 [6763]E(f318(x67631,x67632),f179(f918(x67633,a909)))+~E(f318(f318(f33(x67634,f918(x67633,a909)),x67635),x67631),f179(f918(x67633,a909)))+~P1(f318(f318(f320(x67634),x67632),x67635))
% 109.14/108.85 [6954]~E(x69544,f318(f318(f125(x69541),x69545),f318(f318(f142(x69541),x69542),x69543)))+P1(f318(f318(f320(x69541),x69542),f318(f163(x69541),x69543)))+P1(f318(f318(f320(x69541),x69542),f318(f163(x69541),x69544)))
% 109.14/108.85 [6955]~E(x69554,f318(f318(f125(x69551),x69553),f318(f318(f142(x69551),x69552),x69555)))+P1(f318(f318(f320(x69551),x69552),f318(f163(x69551),x69553)))+P1(f318(f318(f320(x69551),x69552),f318(f163(x69551),x69554)))
% 109.14/108.85 [7266]~E(x72662,x72664)+~P149(x72661)+E(f318(f318(f73(x72661),f318(f318(f74(x72661),x72662),x72663)),f318(f318(f74(x72661),x72664),x72665)),f318(f318(f73(x72661),f318(f318(f74(x72661),x72662),x72665)),f318(f318(f74(x72661),x72664),x72663)))
% 109.14/108.85 [7267]~E(x72672,x72674)+~P149(x72671)+E(f318(f318(f73(x72671),f318(f318(f74(x72671),x72672),x72673)),f318(f318(f74(x72671),x72674),x72675)),f318(f318(f73(x72671),f318(f318(f74(x72671),x72672),x72675)),f318(f318(f74(x72671),x72674),x72673)))
% 109.14/108.85 [7329]~P5(x73291)+~P1(f318(f318(f320(x73294),x73293),x73295))+P1(f318(f318(f225(x73291),f318(x73292,x73293)),f318(f318(f33(x73294,x73291),x73295),x73292)))
% 109.14/108.85 [7380]~P3(x73801)+P1(f318(f318(f225(x73801),f318(x73802,x73803)),f318(x73804,x73803)))+~P1(f318(f318(f225(f918(x73805,x73801)),x73802),x73804))
% 109.14/108.85 [7381]~P3(x73811)+P1(f318(f318(f225(x73811),f318(x73812,x73813)),f318(x73814,x73813)))+~P1(f318(f318(f225(f918(x73815,x73811)),x73812),x73814))
% 109.14/108.85 [7382]~P3(x73821)+P1(f318(f318(f225(x73821),f318(x73822,x73823)),f318(x73824,x73823)))+~P1(f318(f318(f225(f918(x73825,x73821)),x73822),x73824))
% 109.14/108.85 [7495]E(x74951,x74952)+E(x74953,x74951)+~E(f318(f318(f300(x74954),x74951),f318(f318(f300(x74954),x74955),f179(f918(x74954,a909)))),f318(f318(f300(x74954),x74952),f318(f318(f300(x74954),x74953),f179(f918(x74954,a909)))))
% 109.14/108.85 [7496]E(x74961,x74962)+E(x74963,x74961)+~E(f318(f318(f300(x74964),x74963),f318(f318(f300(x74964),x74962),f179(f918(x74964,a909)))),f318(f318(f300(x74964),x74965),f318(f318(f300(x74964),x74961),f179(f918(x74964,a909)))))
% 109.14/108.85 [7497]E(x74971,x74972)+E(x74971,x74973)+~E(f318(f318(f300(x74974),x74973),f318(f318(f300(x74974),x74972),f179(f918(x74974,a909)))),f318(f318(f300(x74974),x74975),f318(f318(f300(x74974),x74971),f179(f918(x74974,a909)))))
% 109.14/108.85 [7498]E(x74981,x74982)+E(x74981,x74983)+~E(f318(f318(f300(x74984),x74981),f318(f318(f300(x74984),x74985),f179(f918(x74984,a909)))),f318(f318(f300(x74984),x74982),f318(f318(f300(x74984),x74983),f179(f918(x74984,a909)))))
% 109.14/108.85 [8020]P25(x80201,x80202,x80203,x80204)+~P25(x80201,x80202,x80203,x80205)+~P1(f318(f318(f225(f918(x80201,a909)),x80204),x80205))
% 109.14/108.85 [8050]~E(f318(x80503,x80505),x80504)+~P25(x80501,x80502,x80503,f233(f918(x80501,a909)))+E(f318(f84(x80501,x80502,f233(f918(x80501,a909)),x80503),x80504),x80505)
% 109.14/108.85 [8192]E(x81921,x81922)+~E(f318(f301(x81923,x81924,x81925),x81921),f318(f301(x81923,x81924,x81925),x81922))+~P25(x81923,x81924,x81925,f318(f318(f101(f918(x81923,a909)),x81921),x81922))
% 109.14/108.85 [8274]P1(f318(x82742,x82744))+E(f318(f318(f129(x82741),f318(f180(f912(x82741)),f168(x82741,x82742,x82743))),x82743),f318(f318(f142(x82741),x82744),x82745))+~E(f318(f318(f125(x82741),f168(x82741,x82742,x82743)),f318(f318(f142(x82741),x82744),x82745)),x82743)
% 109.14/108.85 [8303]~P25(x83031,x83032,x83033,x83035)+~P25(x83031,x83032,x83033,x83034)+P25(x83031,x83032,x83033,f318(f318(f92(f918(x83031,a909)),x83034),x83035))
% 109.14/108.85 [8408]~P76(x84081)+E(f318(f318(f73(x84081),f318(x84082,x84083)),f318(f156(x84081),f318(f318(f145(x84084,x84081),x84082),f161(x84084,x84083,x84085)))),f318(f156(x84081),f318(f318(f145(x84084,x84081),x84082),x84085)))+~P1(f318(f318(f320(x84084),x84083),f318(f163(x84084),x84085)))
% 109.14/108.85 [8493]~P4(x84931)+~P13(x84931,f318(f318(f145(x84932,x84931),x84933),x84935))+P13(x84931,f318(f318(f145(x84932,x84931),x84933),f318(f318(f139(x84932,x84931,x84933),x84934),x84935)))
% 109.14/108.85 [8578]~P5(x85781)+P1(f318(f318(f225(x85781),f318(f318(f33(x85782,x85781),x85783),x85784)),f318(f318(f33(x85782,x85781),x85785),x85784)))+~P1(f318(f318(f225(f918(x85782,a909)),x85783),x85785))
% 109.14/108.85 [8579]~P5(x85791)+P1(f318(f318(f225(x85791),f318(f318(f34(x85792,x85791),x85793),x85794)),f318(f318(f34(x85792,x85791),x85795),x85794)))+~P1(f318(f318(f225(f918(x85792,a909)),x85795),x85793))
% 109.14/108.85 [8615]~P4(x86153)+P1(f318(f128(x86151),x86152))+~P1(f318(f128(x86151),f318(f318(f139(x86151,x86153,x86154),x86155),x86152)))
% 109.14/108.85 [8760]~P4(x87601)+~P1(f318(f318(f320(x87602),x87603),f318(f163(x87602),x87604)))+~P1(f318(f128(x87602),f318(f318(f139(x87602,x87601,x87605),x87603),x87604)))
% 109.14/108.85 [8844]~P4(x88441)+P13(x88441,f318(f318(f145(x88442,x88441),x88443),x88444))+~P13(x88441,f318(f318(f145(x88442,x88441),x88443),f318(f318(f139(x88442,x88441,x88443),x88445),x88444)))
% 109.14/108.85 [8892]~P25(x88922,x88921,x88924,x88923)+E(f318(f301(x88921,x88922,f84(x88922,x88921,x88923,x88924)),f318(f301(x88922,x88921,x88924),x88925)),x88925)+~P1(f318(f318(f225(f918(x88922,a909)),x88925),x88923))
% 109.14/108.85 [8943]~P4(x89432)+E(f318(f318(f139(x89431,x89432,x89433),x89434),x89435),f140(x89431,x89432,x89433,x89434,x89435))+P1(f318(f318(f320(x89432),f318(x89433,x89434)),f318(f301(x89431,x89432,x89433),f318(f163(x89431),x89435))))
% 109.14/108.85 [9029]~P4(x90292)+E(f140(x90291,x90292,x90293,x90294,x90295),x90295)+~P1(f318(f318(f320(x90292),f318(x90293,x90294)),f318(f301(x90291,x90292,x90293),f318(f163(x90291),x90295))))
% 109.14/108.85 [9044]~P25(x90442,x90441,x90443,x90445)+P1(f318(f318(f226(f918(x90441,a909)),f318(f301(x90442,x90441,x90443),x90444)),f318(f301(x90442,x90441,x90443),x90445)))+~P1(f318(f318(f226(f918(x90442,a909)),x90444),x90445))
% 109.14/108.85 [9075]~P25(x90752,x90751,x90753,f233(f918(x90752,a909)))+P1(f318(f318(f225(f918(x90751,a909)),f318(f301(x90752,x90751,x90753),x90754)),f318(f301(x90752,x90751,x90753),x90755)))+~P1(f318(f318(f225(f918(x90752,a909)),x90754),x90755))
% 109.14/108.85 [9198]~P25(x91981,x91982,x91983,f233(f918(x91981,a909)))+~P1(f318(f318(f225(f918(x91982,a909)),x91984),f318(f301(x91981,x91982,x91983),x91985)))+P1(f318(f318(f225(f918(x91981,a909)),f318(f302(x91981,x91982,x91983),x91984)),x91985))
% 109.14/108.85 [9219]~E(f318(f301(x92193,x92191,x92194),f233(f918(x92193,a909))),f233(f918(x92191,a909)))+P1(f318(f318(f225(f918(x92191,a909)),x92192),f318(f301(x92193,x92191,x92194),x92195)))+~P1(f318(f318(f225(f918(x92193,a909)),f318(f302(x92193,x92191,x92194),x92192)),x92195))
% 109.14/108.85 [9331]~P25(x93311,x93314,x93315,f233(f918(x93311,a909)))+~P1(f318(f318(f225(f918(x93314,a909)),f318(f301(x93311,x93314,x93315),x93312)),f318(f301(x93311,x93314,x93315),x93313)))+P1(f318(f318(f225(f918(x93311,a909)),x93312),x93313))
% 109.14/108.85 [9457]~P86(x94571)+~E(f318(x94573,f715(x94573,x94574,x94575,x94572,x94571)),f2(x94571))+E(f318(f156(x94571),f318(f318(f145(x94572,x94571),x94573),f318(f127(x94572,x94574),x94575))),f318(f156(x94571),f318(f318(f145(x94572,x94571),x94573),x94575)))
% 109.14/108.85 [9484]~P26(x94841,x94842,x94843,f233(f918(x94841,a909)),f233(f918(x94842,a909)))+~P1(f318(f318(f225(f918(x94842,a909)),x94844),f318(f301(x94841,x94842,x94843),x94845)))+P1(f318(f318(f225(f918(x94841,a909)),f318(f302(x94841,x94842,x94843),x94844)),x94845))
% 109.14/108.85 [9513]~P26(x95133,x95131,x95134,f233(f918(x95133,a909)),f233(f918(x95131,a909)))+P1(f318(f318(f225(f918(x95131,a909)),x95132),f318(f301(x95133,x95131,x95134),x95135)))+~P1(f318(f318(f225(f918(x95133,a909)),f318(f302(x95133,x95131,x95134),x95132)),x95135))
% 109.14/108.85 [9636]~P16(x96361,x96362,x96363)+~P1(f318(f55(x96361),x96365))+P1(f318(f60(x96361,x96362,x96363,x96364,x96365),f318(f318(f58(x96361,x96362,x96363),x96364),x96365)))
% 109.14/108.85 [9728]~P26(x97282,x97281,x97284,f233(f918(x97282,a909)),f233(f918(x97281,a909)))+~P26(x97281,x97283,x97285,f233(f918(x97281,a909)),f233(f918(x97283,a909)))+E(f318(f66(x97281,x97282,x97283,f84(x97282,x97281,f233(f918(x97282,a909)),x97284)),f84(x97281,x97283,f233(f918(x97281,a909)),x97285)),f84(x97282,x97283,f233(f918(x97282,a909)),f318(f66(x97281,x97283,x97282,x97285),x97284)))
% 109.14/108.85 [9729]P1(f318(x97291,f640(x97292,x97291,x97293,x97294,x97295)))+~P1(f318(f318(f225(f918(x97295,a909)),x97294),x97293))+P1(f318(f318(f225(f918(x97295,a909)),f318(f318(f92(f918(x97295,a909)),x97294),f318(f253(x97295),x97291))),f318(f318(f92(f918(x97295,a909)),x97293),f318(f253(x97295),x97292))))
% 109.14/108.85 [9744]~P86(x97441)+~P1(f318(x97444,f715(x97443,x97444,x97445,x97442,x97441)))+E(f318(f156(x97441),f318(f318(f145(x97442,x97441),x97443),f318(f127(x97442,x97444),x97445))),f318(f156(x97441),f318(f318(f145(x97442,x97441),x97443),x97445)))
% 109.14/108.85 [9835]~P5(x98355)+P1(f318(f318(f320(x98351),f473(x98352,x98353,x98351,x98354,x98355)),x98353))+P1(f318(f318(f225(x98355),x98354),f318(f318(f34(x98351,x98355),x98353),x98352)))
% 109.14/108.85 [9839]~P86(x98391)+E(f318(f156(x98391),f318(f318(f145(x98392,x98391),x98393),f318(f127(x98392,x98394),x98395))),f318(f156(x98391),f318(f318(f145(x98392,x98391),x98393),x98395)))+P1(f318(f318(f320(x98392),f715(x98393,x98394,x98395,x98392,x98391)),f318(f163(x98392),x98395)))
% 109.14/108.85 [9846]~P1(f318(x98465,f640(x98465,x98463,x98464,x98462,x98461)))+~P1(f318(f318(f225(f918(x98461,a909)),x98462),x98464))+P1(f318(f318(f225(f918(x98461,a909)),f318(f318(f92(f918(x98461,a909)),x98462),f318(f253(x98461),x98463))),f318(f318(f92(f918(x98461,a909)),x98464),f318(f253(x98461),x98465))))
% 109.14/108.85 [9863]~P25(x98635,x98633,x98634,f233(f918(x98635,a909)))+P1(f318(x98631,x98632))+P1(f318(f318(f320(x98633),f806(x98632,x98631,x98634,x98633,x98635)),f318(f301(x98635,x98633,x98634),f233(f918(x98635,a909)))))
% 109.14/108.85 [9887]P36(x98871,x98872,x98873,x98874,x98875)+~E(f318(f180(f912(x98872)),x98875),f318(f180(f912(x98871)),x98874))+P1(f318(f318(f226(a911),f696(x98875,x98874,x98873,x98872,x98871)),f318(f180(f912(x98871)),x98874)))
% 109.14/108.85 [9888]P36(x98881,x98882,x98883,x98884,x98885)+~E(f318(f180(f912(x98882)),x98885),f318(f180(f912(x98881)),x98884))+P1(f318(f318(f226(a911),f731(x98883,x98885,x98882,x98884,x98881)),f318(f180(f912(x98881)),x98884)))
% 109.14/108.85 [9921]P1(f318(f318(f320(x99211),f640(x99212,x99213,x99214,x99215,x99211)),x99215))+~P1(f318(f318(f225(f918(x99211,a909)),x99215),x99214))+P1(f318(f318(f225(f918(x99211,a909)),f318(f318(f92(f918(x99211,a909)),x99215),f318(f253(x99211),x99213))),f318(f318(f92(f918(x99211,a909)),x99214),f318(f253(x99211),x99212))))
% 109.14/108.85 [9980]~P5(x99801)+~P1(f318(f318(f225(x99801),x99802),f318(x99805,f473(x99805,x99804,x99803,x99802,x99801))))+P1(f318(f318(f225(x99801),x99802),f318(f318(f34(x99803,x99801),x99804),x99805)))
% 109.14/108.85 [10015]~P82(x100151)+~P1(f318(f55(x100152),x100155))+E(f318(f318(f318(f59(x100151,x100152,f74(x100151)),f318(f318(f20(x100152,x100151,x100151),f318(f318(f10(x100151,f918(x100151,x100151),x100152),f74(x100151)),x100153)),x100154)),f71(x100151)),x100155),f318(f318(f74(x100151),f318(f318(f318(f59(x100151,x100152,f74(x100151)),x100153),f71(x100151)),x100155)),f318(f318(f318(f59(x100151,x100152,f74(x100151)),x100154),f71(x100151)),x100155)))
% 109.14/108.85 [10065]~P1(f318(f318(f320(f917(f918(x100651,a909),f918(x100651,a909))),f318(f318(f243(f918(x100651,a909),f918(x100651,a909)),x100655),x100654)),f310(x100651,x100653)))+~P1(f318(f318(f320(x100651),x100652),x100655))+P1(f318(f318(f320(f917(x100651,x100651)),f318(f318(f243(x100651,x100651),x100652),f601(x100653,x100654,x100655,x100651,x100652))),x100653))
% 109.14/108.85 [10182]~P1(f318(f318(f320(f917(f912(x101821),f912(x101821))),f318(f318(f243(f912(x101821),f912(x101821)),f318(f318(f125(x101821),x101825),x101822)),f318(f318(f125(x101821),x101825),x101823))),f138(x101821,x101824)))+P1(f318(f318(f320(f917(f912(x101821),f912(x101821))),f318(f318(f243(f912(x101821),f912(x101821)),x101822),x101823)),f138(x101821,x101824)))+P1(f318(f318(f320(f917(x101821,x101821)),f318(f318(f243(x101821,x101821),f684(x101824,x101823,x101822,x101825,x101821)),f684(x101824,x101823,x101822,x101825,x101821))),x101824))
% 109.14/108.85 [7385]~E(x73853,x73855)+E(f318(f318(f155(x73851),f318(f318(f150(x73851,x73852),x73853),x73854)),x73855),x73854)+~P1(f318(f318(f226(a911),x73853),f318(f180(f912(x73851)),x73852)))
% 109.14/108.85 [7491]~E(f318(f318(f125(x74911),x74912),x74914),f318(f318(f125(x74911),x74913),x74915))+E(f318(f318(f166(x74911),f318(f180(f912(x74911)),x74912)),x74913),x74912)+P1(f318(f318(f225(a911),f318(f180(f912(x74911)),x74913)),f318(f180(f912(x74911)),x74912)))
% 109.14/108.85 [7492]E(x74921,x74922)+E(f318(f318(f155(x74923),f318(f318(f150(x74923,x74924),x74921),x74925)),x74922),f318(f318(f155(x74923),x74924),x74922))+~P1(f318(f318(f226(a911),x74921),f318(f180(f912(x74923)),x74924)))
% 109.14/108.85 [7985]~E(f318(f318(f125(x79851),x79852),x79854),f318(f318(f125(x79851),x79853),x79855))+E(f318(f318(f166(x79851),f318(f180(f912(x79851)),x79852)),x79853),x79852)+~P1(f318(f318(f225(a911),f318(f180(f912(x79851)),x79852)),f318(f180(f912(x79851)),x79853)))
% 109.14/108.85 [8009]~P1(f318(f55(x80091),f318(x80094,x80095)))+~P1(f318(f318(f320(x80092),x80095),x80093))+P1(f318(f55(x80091),f318(f318(f34(x80092,f918(x80091,a909)),x80093),x80094)))
% 109.14/108.85 [8175]~P56(x81751,x81753,x81755)+~P56(x81751,x81752,x81754)+P56(x81751,f318(f318(f101(f918(x81751,a909)),x81752),x81753),f318(f318(f101(f918(f917(x81751,x81751),a909)),x81754),x81755))
% 109.14/108.85 [8176]~P56(x81761,x81763,x81765)+~P56(x81761,x81762,x81764)+P56(x81761,f318(f318(f92(f918(x81761,a909)),x81762),x81763),f318(f318(f92(f918(f917(x81761,x81761),a909)),x81764),x81765))
% 109.14/108.85 [8533]E(f318(f318(f243(x85331,x85332),f318(f318(f155(x85331),x85333),x85334)),f318(f318(f155(x85332),x85335),x85334)),f318(f318(f155(f917(x85331,x85332)),f318(f318(f172(x85331,x85332),x85333),x85335)),x85334))+~P1(f318(f318(f226(a911),x85334),f318(f180(f912(x85331)),x85333)))+~P1(f318(f318(f226(a911),x85334),f318(f180(f912(x85332)),x85335)))
% 109.14/108.85 [8690]~P56(x86901,x86903,x86904)+P1(f318(f318(f320(x86901),x86902),x86903))+~P1(f318(f318(f320(f917(x86901,x86901)),f318(f318(f243(x86901,x86901),x86905),x86902)),x86904))
% 109.14/108.85 [8691]~P56(x86911,x86913,x86914)+P1(f318(f318(f320(x86911),x86912),x86913))+~P1(f318(f318(f320(f917(x86911,x86911)),f318(f318(f243(x86911,x86911),x86912),x86915)),x86914))
% 109.14/108.85 [8692]~P8(x86921,x86923,x86924)+P1(f318(f318(f320(x86921),x86922),x86923))+~P1(f318(f318(f320(f917(x86921,x86921)),f318(f318(f243(x86921,x86921),x86925),x86922)),x86924))
% 109.14/108.85 [8693]~P8(x86931,x86933,x86934)+P1(f318(f318(f320(x86931),x86932),x86933))+~P1(f318(f318(f320(f917(x86931,x86931)),f318(f318(f243(x86931,x86931),x86932),x86935)),x86934))
% 109.14/108.85 [8968]~P8(x89681,x89685,x89682)+E(f318(f276(x89681,x89681,x89682),f318(f318(f300(x89681),x89683),f179(f918(x89681,a909)))),f318(f276(x89681,x89681,x89682),f318(f318(f300(x89681),x89684),f179(f918(x89681,a909)))))+~P1(f318(f318(f320(f917(x89681,x89681)),f318(f318(f243(x89681,x89681),x89683),x89684)),x89682))
% 109.14/108.85 [8969]~P8(x89691,x89695,x89692)+E(f318(f276(x89691,x89691,x89692),f318(f318(f300(x89691),x89693),f179(f918(x89691,a909)))),f318(f276(x89691,x89691,x89692),f318(f318(f300(x89691),x89694),f179(f918(x89691,a909)))))+~P1(f318(f318(f320(f917(x89691,x89691)),f318(f318(f243(x89691,x89691),x89693),x89694)),x89692))
% 109.14/108.85 [9158]P1(f318(x91581,x91582))+~P1(f318(f318(f320(x91583),x91582),x91585))+P1(f318(f318(f320(x91583),f360(x91581,x91584,x91585,x91583)),f318(f318(f101(f918(x91583,a909)),x91585),x91584)))
% 109.14/108.85 [9159]P1(f318(x91591,x91592))+~P1(f318(f318(f320(x91593),x91592),x91594))+P1(f318(f318(f320(x91593),f360(x91591,x91594,x91595,x91593)),f318(f318(f101(f918(x91593,a909)),x91595),x91594)))
% 109.14/108.85 [9167]~P1(f318(x91672,x91675))+~P1(f318(f318(f320(x91671),x91675),x91674))+P1(f318(f318(f320(x91671),f415(x91672,x91673,x91674,x91671)),f318(f318(f101(f918(x91671,a909)),x91674),x91673)))
% 109.14/108.85 [9168]~P1(f318(x91682,x91685))+~P1(f318(f318(f320(x91681),x91685),x91683))+P1(f318(f318(f320(x91681),f415(x91682,x91683,x91684,x91681)),f318(f318(f101(f918(x91681,a909)),x91684),x91683)))
% 109.14/108.85 [9183]~P1(f318(f318(f225(f918(x91831,a909)),x91833),x91835))+~P1(f318(f318(f225(f918(x91831,a909)),x91832),x91834))+P1(f318(f318(f225(f918(x91831,a909)),f318(f318(f101(f918(x91831,a909)),x91832),x91833)),f318(f318(f101(f918(x91831,a909)),x91834),x91835)))
% 109.14/108.85 [9184]~P1(f318(f318(f225(f918(x91841,a909)),x91843),x91845))+~P1(f318(f318(f225(f918(x91841,a909)),x91842),x91844))+P1(f318(f318(f225(f918(x91841,a909)),f318(f318(f92(f918(x91841,a909)),x91842),x91843)),f318(f318(f92(f918(x91841,a909)),x91844),x91845)))
% 109.14/108.85 [9185]~P1(f318(f318(f225(f918(x91851,a909)),x91855),x91853))+~P1(f318(f318(f225(f918(x91851,a909)),x91852),x91854))+P1(f318(f318(f225(f918(x91851,a909)),f318(f318(f3(f918(x91851,a909)),x91852),x91853)),f318(f318(f3(f918(x91851,a909)),x91854),x91855)))
% 109.14/108.85 [9274]P1(f318(f318(f320(f917(x92741,x92741)),f318(f318(f243(x92741,x92741),x92742),x92743)),f312(x92741,x92744,x92745)))+~P1(f318(f318(f225(a911),f318(x92744,x92742)),f318(x92744,x92743)))+~P1(f318(f318(f320(f917(x92741,x92741)),f318(f318(f243(x92741,x92741),x92742),x92743)),x92745))
% 109.14/108.85 [9471]P1(f318(f318(f320(f917(x94711,x94711)),f318(f318(f243(x94711,x94711),x94712),x94713)),f298(x94711,x94714)))+~P1(f318(f318(f320(f917(x94711,x94711)),f318(f318(f243(x94711,x94711),x94712),x94715)),f298(x94711,x94714)))+~P1(f318(f318(f320(f917(x94711,x94711)),f318(f318(f243(x94711,x94711),x94715),x94713)),x94714))
% 109.14/108.85 [9472]P1(f318(f318(f320(f917(x94721,x94721)),f318(f318(f243(x94721,x94721),x94722),x94723)),f298(x94721,x94724)))+~P1(f318(f318(f320(f917(x94721,x94721)),f318(f318(f243(x94721,x94721),x94725),x94723)),f298(x94721,x94724)))+~P1(f318(f318(f320(f917(x94721,x94721)),f318(f318(f243(x94721,x94721),x94722),x94725)),x94724))
% 109.14/108.85 [9570]E(x95701,x95702)+E(f318(a103,f620(x95703,x95704,x95701,x95702,x95705)),x95704)+~P1(f318(f318(f320(f917(x95705,x95705)),f318(f318(f243(x95705,x95705),x95702),x95701)),f318(f318(f174(f917(x95705,x95705),a909),x95704),x95703)))
% 109.14/108.85 [9571]E(x95711,x95712)+E(f318(a103,f623(x95713,x95714,x95711,x95712,x95715)),x95714)+~P1(f318(f318(f320(f917(x95715,x95715)),f318(f318(f243(x95715,x95715),x95712),x95711)),f318(f318(f174(f917(x95715,x95715),a909),x95714),x95713)))
% 109.14/108.85 [9572]E(x95721,f2(a911))+E(f318(a103,f620(x95722,x95721,x95723,x95724,x95725)),x95721)+~P1(f318(f318(f320(f917(x95725,x95725)),f318(f318(f243(x95725,x95725),x95724),x95723)),f318(f318(f174(f917(x95725,x95725),a909),x95721),x95722)))
% 109.14/108.85 [9573]E(x95731,f2(a911))+E(f318(a103,f623(x95732,x95731,x95733,x95734,x95735)),x95731)+~P1(f318(f318(f320(f917(x95735,x95735)),f318(f318(f243(x95735,x95735),x95734),x95733)),f318(f318(f174(f917(x95735,x95735),a909),x95731),x95732)))
% 109.14/108.85 [9591]P1(f318(f318(f320(f917(x95911,x95911)),f318(f318(f243(x95911,x95911),x95912),x95913)),f318(f318(f280(x95911,x95911,x95911),x95914),f298(x95911,x95914))))+~P1(f318(f318(f320(f917(x95911,x95911)),f318(f318(f243(x95911,x95911),x95912),x95915)),x95914))+~P1(f318(f318(f320(f917(x95911,x95911)),f318(f318(f243(x95911,x95911),x95915),x95913)),x95914))
% 109.14/108.85 [9596]~P1(f318(f318(f320(f917(x95961,x95961)),f318(f318(f243(x95961,x95961),x95962),x95965)),f298(x95961,x95964)))+P1(f318(f318(f320(f917(x95961,x95961)),f318(f318(f243(x95961,x95961),x95962),x95963)),f318(f318(f280(x95961,x95961,x95961),x95964),f298(x95961,x95964))))+~P1(f318(f318(f320(f917(x95961,x95961)),f318(f318(f243(x95961,x95961),x95965),x95963)),x95964))
% 109.14/108.85 [9597]~P1(f318(f318(f320(f917(x95971,x95971)),f318(f318(f243(x95971,x95971),x95975),x95973)),f298(x95971,x95974)))+P1(f318(f318(f320(f917(x95971,x95971)),f318(f318(f243(x95971,x95971),x95972),x95973)),f318(f318(f280(x95971,x95971,x95971),x95974),f298(x95971,x95974))))+~P1(f318(f318(f320(f917(x95971,x95971)),f318(f318(f243(x95971,x95971),x95972),x95975)),x95974))
% 109.14/108.85 [9630]~P8(x96301,x96305,x96302)+~P1(f318(f318(f320(f917(x96301,x96301)),f318(f318(f243(x96301,x96301),x96303),x96304)),x96302))+P1(f318(f318(f225(f918(x96301,a909)),f318(f276(x96301,x96301,x96302),f318(f318(f300(x96301),x96303),f179(f918(x96301,a909))))),f318(f276(x96301,x96301,x96302),f318(f318(f300(x96301),x96304),f179(f918(x96301,a909))))))
% 109.14/108.85 [9701]P1(f318(f318(f320(f917(x97011,x97011)),f318(f318(f243(x97011,x97011),x97012),x97013)),f318(f318(f280(x97011,x97011,x97011),x97014),f298(x97011,x97014))))+~P1(f318(f318(f320(f917(x97011,x97011)),f318(f318(f243(x97011,x97011),x97012),x97015)),f318(f318(f280(x97011,x97011,x97011),x97014),f298(x97011,x97014))))+~P1(f318(f318(f320(f917(x97011,x97011)),f318(f318(f243(x97011,x97011),x97015),x97013)),x97014))
% 109.14/108.85 [9702]P1(f318(f318(f320(f917(x97021,x97021)),f318(f318(f243(x97021,x97021),x97022),x97023)),f318(f318(f280(x97021,x97021,x97021),x97024),f298(x97021,x97024))))+~P1(f318(f318(f320(f917(x97021,x97021)),f318(f318(f243(x97021,x97021),x97025),x97023)),f318(f318(f280(x97021,x97021,x97021),x97024),f298(x97021,x97024))))+~P1(f318(f318(f320(f917(x97021,x97021)),f318(f318(f243(x97021,x97021),x97022),x97025)),x97024))
% 109.14/108.85 [9751]~P1(f318(f60(x97511,x97511,x97514,x97512,x97513),x97515))+P1(f318(f318(f320(x97511),x97512),x97513))+P1(f318(f56(x97511,x97514,f318(f318(f300(x97511),x97512),x97513)),x97515))
% 109.14/108.85 [9796]~E(f318(f301(x97963,x97962,x97965),x97964),x97961)+E(x97961,f179(f918(x97962,a909)))+P1(f318(f318(f225(f918(x97963,a909)),f318(f301(x97962,x97963,f654(x97964,x97963,x97962,x97961)),x97961)),x97964))
% 109.14/108.85 [9849]~P5(x98495)+P1(f318(f318(f320(x98491),f475(x98492,x98493,x98494,x98491,x98495)),x98494))+P1(f318(f318(f225(x98495),f318(f318(f33(x98491,x98495),x98494),x98493)),x98492))
% 109.14/108.85 [9907]P36(x99071,x99072,x99073,x99074,x99075)+~E(f318(f180(f912(x99071)),x99074),f318(f180(f912(x99072)),x99075))+P1(f318(f318(f320(f917(x99071,x99072)),f694(x99075,x99074,x99073,x99072,x99071)),f318(f163(f917(x99071,x99072)),f318(f318(f172(x99071,x99072),x99074),x99075))))
% 109.14/108.85 [9908]P36(x99081,x99082,x99083,x99084,x99085)+~E(f318(f180(f912(x99081)),x99084),f318(f180(f912(x99082)),x99085))+P1(f318(f318(f320(f917(x99081,x99082)),f695(x99083,x99085,x99084,x99082,x99081)),f318(f163(f917(x99081,x99082)),f318(f318(f172(x99081,x99082),x99084),x99085))))
% 109.14/108.85 [10044]E(x100441,x100442)+P1(f318(f318(f320(f917(x100443,x100443)),f318(f318(f243(x100443,x100443),x100441),f622(x100444,x100445,x100442,x100441,x100443))),x100444))+~P1(f318(f318(f320(f917(x100443,x100443)),f318(f318(f243(x100443,x100443),x100441),x100442)),f318(f318(f174(f917(x100443,x100443),a909),x100445),x100444)))
% 109.14/108.85 [10045]E(x100451,f2(a911))+P1(f318(f318(f320(f917(x100452,x100452)),f318(f318(f243(x100452,x100452),x100453),f622(x100454,x100451,x100455,x100453,x100452))),x100454))+~P1(f318(f318(f320(f917(x100452,x100452)),f318(f318(f243(x100452,x100452),x100453),x100455)),f318(f318(f174(f917(x100452,x100452),a909),x100451),x100454)))
% 109.14/108.85 [10081]~P5(x100811)+~P1(f318(f318(f225(x100811),f318(x100814,f475(x100815,x100814,x100813,x100812,x100811))),x100815))+P1(f318(f318(f225(x100811),f318(f318(f33(x100812,x100811),x100813),x100814)),x100815))
% 109.14/108.85 [10116]E(x101161,x101162)+P1(f318(f318(f320(f917(x101163,x101163)),f318(f318(f243(x101163,x101163),f621(x101164,x101165,x101161,x101162,x101163)),x101161)),x101164))+~P1(f318(f318(f320(f917(x101163,x101163)),f318(f318(f243(x101163,x101163),x101162),x101161)),f318(f318(f174(f917(x101163,x101163),a909),x101165),x101164)))
% 109.14/108.85 [10117]E(x101171,f2(a911))+P1(f318(f318(f320(f917(x101172,x101172)),f318(f318(f243(x101172,x101172),f621(x101173,x101171,x101174,x101175,x101172)),x101174)),x101173))+~P1(f318(f318(f320(f917(x101172,x101172)),f318(f318(f243(x101172,x101172),x101175),x101174)),f318(f318(f174(f917(x101172,x101172),a909),x101171),x101173)))
% 109.14/108.85 [10127]E(x101271,x101272)+P1(f318(f318(f320(f917(x101273,x101273)),f318(f318(f243(x101273,x101273),x101271),f621(x101274,x101275,x101272,x101271,x101273))),f318(f318(f174(f917(x101273,x101273),a909),f620(x101274,x101275,x101272,x101271,x101273)),x101274)))+~P1(f318(f318(f320(f917(x101273,x101273)),f318(f318(f243(x101273,x101273),x101271),x101272)),f318(f318(f174(f917(x101273,x101273),a909),x101275),x101274)))
% 109.14/108.85 [10128]E(x101281,f2(a911))+P1(f318(f318(f320(f917(x101282,x101282)),f318(f318(f243(x101282,x101282),x101283),f621(x101284,x101281,x101285,x101283,x101282))),f318(f318(f174(f917(x101282,x101282),a909),f620(x101284,x101281,x101285,x101283,x101282)),x101284)))+~P1(f318(f318(f320(f917(x101282,x101282)),f318(f318(f243(x101282,x101282),x101283),x101285)),f318(f318(f174(f917(x101282,x101282),a909),x101281),x101284)))
% 109.14/108.85 [10174]E(x101741,x101742)+P1(f318(f318(f320(f917(x101743,x101743)),f318(f318(f243(x101743,x101743),f622(x101744,x101745,x101741,x101742,x101743)),x101741)),f318(f318(f174(f917(x101743,x101743),a909),f623(x101744,x101745,x101741,x101742,x101743)),x101744)))+~P1(f318(f318(f320(f917(x101743,x101743)),f318(f318(f243(x101743,x101743),x101742),x101741)),f318(f318(f174(f917(x101743,x101743),a909),x101745),x101744)))
% 109.14/108.85 [10175]E(x101751,f2(a911))+P1(f318(f318(f320(f917(x101752,x101752)),f318(f318(f243(x101752,x101752),f622(x101753,x101751,x101754,x101755,x101752)),x101754)),f318(f318(f174(f917(x101752,x101752),a909),f623(x101753,x101751,x101754,x101755,x101752)),x101753)))+~P1(f318(f318(f320(f917(x101752,x101752)),f318(f318(f243(x101752,x101752),x101755),x101754)),f318(f318(f174(f917(x101752,x101752),a909),x101751),x101753)))
% 109.14/108.85 [10211]~P76(x102112)+~P1(f318(f55(x102111),x102115))+E(f318(f318(f8(x102111,x102112),f318(f318(f9(x102111,x102112,x102112),f318(f318(f20(x102111,x102112,f918(x102112,x102112)),f318(f318(f10(a909,f918(x102112,f918(x102112,x102112)),x102111),f85(x102112)),f318(f318(f9(x102111,f918(x102111,a909),a909),f320(x102111)),x102113))),x102114)),f2(x102112))),x102115),f318(f318(f8(x102111,x102112),x102114),f318(f318(f92(f918(x102111,a909)),x102115),x102113)))
% 109.14/108.85 [8757]~P76(x87571)+~P1(f318(f55(x87574),x87575))+E(f318(f318(f73(x87571),f318(x87572,x87573)),f318(f318(f8(x87574,x87571),x87572),f318(f318(f3(f918(x87574,a909)),x87575),f318(f318(f300(x87574),x87573),f179(f918(x87574,a909)))))),f318(f318(f8(x87574,x87571),x87572),f318(f318(f300(x87574),x87573),x87575)))
% 109.14/108.85 [8758]~P82(x87581)+~P1(f318(f55(x87584),x87585))+E(f318(f318(f74(x87581),f318(x87582,x87583)),f318(f318(f11(x87584,x87581),x87582),f318(f318(f3(f918(x87584,a909)),x87585),f318(f318(f300(x87584),x87583),f179(f918(x87584,a909)))))),f318(f318(f11(x87584,x87581),x87582),f318(f318(f300(x87584),x87583),x87585)))
% 109.14/108.85 [9090]~P4(x90902)+~P13(x90902,f318(f159(x90902),f318(f318(f145(x90901,x90902),x90904),x90905)))+E(f318(f127(x90901,f318(f318(f10(x90902,a909,x90901),f318(f226(x90902),x90903)),x90904)),x90905),f168(x90901,f318(f318(f10(x90902,a909,x90901),f318(f226(x90902),x90903)),x90904),x90905))
% 109.14/108.85 [9115]~P76(x91151)+E(f318(f318(f73(x91151),f318(f318(f8(a911,x91151),x91152),f294(a911,x91153,x91154))),f318(f318(f8(a911,x91151),x91152),f294(a911,f318(f318(f73(a911),x91154),f71(a911)),f318(f318(f73(a911),x91154),x91155)))),f318(f318(f8(a911,x91151),x91152),f294(a911,x91153,f318(f318(f73(a911),x91154),x91155))))+~P1(f318(f318(f225(a911),x91153),f318(f318(f73(a911),x91154),f71(a911))))
% 109.14/108.85 [9116]~P1(f318(f318(f320(x91161),x91164),x91165))+~P1(f318(f318(f225(f918(x91161,a909)),f318(f163(x91161),x91162)),x91165))+P1(f318(f318(f225(f918(x91161,a909)),f318(f163(x91161),f318(f318(f150(x91161,x91162),x91163),x91164))),x91165))
% 109.14/108.85 [9339]~P5(x93392)+~P1(f318(f55(x93391),x93395))+E(f318(f318(f58(x93391,x93392,f318(f318(f10(x93392,f918(x93392,x93392),x93391),f101(x93392)),x93393)),x93394),x93395),f318(f318(f101(x93392),x93394),f318(f318(f33(x93391,x93392),x93395),x93393)))
% 109.14/108.85 [9340]~P5(x93402)+~P1(f318(f55(x93401),x93405))+E(f318(f318(f58(x93401,x93402,f318(f318(f10(x93402,f918(x93402,x93402),x93401),f92(x93402)),x93403)),x93404),x93405),f318(f318(f92(x93402),x93404),f318(f318(f34(x93401,x93402),x93405),x93403)))
% 109.14/108.85 [9387]E(f318(x93871,x93872),f318(x93871,x93873))+P1(f318(f318(f226(a911),f318(x93871,x93872)),f318(x93871,x93873)))+~P1(f318(f318(f320(f917(x93874,x93874)),f318(f318(f243(x93874,x93874),x93872),x93873)),f144(x93874,f318(f318(f142(f918(x93874,a911)),x93871),x93875))))
% 109.14/108.85 [9421]~E(f318(x94214,x94212),f318(x94214,x94213))+~P1(f318(f318(f320(f917(x94211,x94211)),f318(f318(f243(x94211,x94211),x94212),x94213)),f144(x94211,x94215)))+P1(f318(f318(f320(f917(x94211,x94211)),f318(f318(f243(x94211,x94211),x94212),x94213)),f144(x94211,f318(f318(f142(f918(x94211,a911)),x94214),x94215))))
% 109.14/108.85 [9442]~P25(x94421,x94422,x94423,x94425)+P25(x94421,x94422,x94423,f318(f318(f300(x94421),x94424),x94425))+P1(f318(f318(f320(x94422),f318(x94423,x94424)),f318(f301(x94421,x94422,x94423),f318(f318(f3(f918(x94421,a909)),x94425),f318(f318(f300(x94421),x94424),f179(f918(x94421,a909)))))))
% 109.14/108.85 [9447]P1(f318(x94472,x94475))+~P1(f318(f318(f320(x94471),x94475),f318(f163(x94471),x94473)))+E(f318(f318(f129(x94471),f318(f180(f912(x94471)),f168(x94471,x94472,f318(f318(f125(x94471),x94473),x94474)))),f318(f318(f125(x94471),x94473),x94474)),f318(f318(f125(x94471),f318(f318(f129(x94471),f318(f180(f912(x94471)),f168(x94471,x94472,x94473))),x94473)),x94474))
% 109.14/108.85 [9453]~P1(f318(f318(f320(f917(x94531,x94531)),f318(f318(f243(x94531,x94531),x94532),x94533)),f144(x94531,x94535)))+~P1(f318(f318(f225(a911),f318(x94534,x94532)),f318(x94534,x94533)))+P1(f318(f318(f320(f917(x94531,x94531)),f318(f318(f243(x94531,x94531),x94532),x94533)),f144(x94531,f318(f318(f142(f918(x94531,a911)),x94534),x94535))))
% 109.14/108.85 [9520]P1(f318(f318(f320(f917(x95204,x95204)),f318(f318(f243(x95204,x95204),x95202),x95203)),f144(x95204,x95205)))+P1(f318(f318(f226(a911),f318(x95201,x95202)),f318(x95201,x95203)))+~P1(f318(f318(f320(f917(x95204,x95204)),f318(f318(f243(x95204,x95204),x95202),x95203)),f144(x95204,f318(f318(f142(f918(x95204,a911)),x95201),x95205))))
% 109.14/108.85 [9663]~P1(f318(f318(f320(f917(f912(x96631),f912(x96631))),f318(f318(f243(f912(x96631),f912(x96631)),x96632),x96634)),f149(x96631,x96635)))+~P1(f318(f318(f226(a911),x96633),f318(f180(f912(x96631)),x96632)))+P1(f318(f318(f320(f917(x96631,x96631)),f318(f318(f243(x96631,x96631),f318(f318(f155(x96631),x96632),x96633)),f318(f318(f155(x96631),x96634),x96633))),x96635))
% 109.14/108.85 [9935]E(x99351,f2(a1))+~P1(f318(f43(x99353,x99351),f318(f318(f243(a1,a1),x99354),x99355)))+P1(f318(f43(f318(f318(f74(a1),x99352),x99353),x99351),f318(f318(f243(a1,a1),f318(f318(f73(a1),f318(f318(f74(a1),x99352),x99354)),f318(f318(f30(a1),f318(f318(f74(a1),x99352),x99355)),x99351))),f39(a1,f318(f318(f74(a1),x99352),x99355),x99351))))
% 109.14/108.85 [9944]~P1(f318(f318(f226(a911),f2(a911)),x99443))+~P1(f318(f42(x99442,x99443),f318(f318(f243(a911,a911),x99444),x99445)))+P1(f318(f42(f318(f318(f74(a911),x99441),x99442),x99443),f318(f318(f243(a911,a911),f318(f318(f73(a911),f318(f318(f74(a911),x99441),x99444)),f318(f318(f30(a911),f318(f318(f74(a911),x99441),x99445)),x99443))),f39(a911,f318(f318(f74(a911),x99441),x99445),x99443))))
% 109.14/108.85 [10229]~P76(x102292)+~P1(f318(f55(x102291),x102294))+E(f318(f318(f8(x102291,x102292),x102293),f318(f253(x102291),f318(f318(f20(x102291,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102291),a316),f318(f318(f9(x102291,f918(x102291,a909),a909),f320(x102291)),x102294))),f318(f318(f9(x102291,f918(x102291,a909),a909),f320(x102291)),x102295)))),f318(f318(f8(x102291,x102292),f318(f318(f9(x102291,x102292,x102292),f318(f318(f20(x102291,x102292,f918(x102292,x102292)),f318(f318(f10(a909,f918(x102292,f918(x102292,x102292)),x102291),f85(x102292)),f318(f318(f9(x102291,f918(x102291,a909),a909),f320(x102291)),x102295))),x102293)),f2(x102292))),x102294))
% 109.14/108.85 [8387]~E(f318(f318(f125(x83871),x83872),x83875),f318(f318(f125(x83871),x83873),x83874))+E(f318(f318(f125(x83871),f318(f318(f129(x83871),f318(f180(f912(x83871)),x83872)),x83873)),x83874),x83875)+P1(f318(f318(f225(a911),f318(f180(f912(x83871)),x83873)),f318(f180(f912(x83871)),x83872)))
% 109.14/108.85 [8581]~E(f318(f318(f125(x85812),x85813),x85811),f318(f318(f125(x85812),x85814),x85815))+E(x85811,f318(f318(f125(x85812),f318(f318(f129(x85812),f318(f180(f912(x85812)),x85813)),x85814)),x85815))+~P1(f318(f318(f225(a911),f318(f180(f912(x85812)),x85813)),f318(f180(f912(x85812)),x85814)))
% 109.14/108.85 [8673]~E(f318(f318(f73(a911),f318(f318(f74(a911),x86733),x86734)),x86731),f318(f318(f73(a911),f318(f318(f74(a911),x86732),x86734)),x86735))+~P1(f318(f318(f225(a911),x86733),x86732))+E(x86731,f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x86732),x86733)),x86734)),x86735))
% 109.14/108.85 [8674]~E(f318(f318(f73(a911),f318(f318(f74(a911),x86741),x86743)),x86744),f318(f318(f73(a911),f318(f318(f74(a911),x86742),x86743)),x86745))+~P1(f318(f318(f225(a911),x86742),x86741))+E(f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x86741),x86742)),x86743)),x86744),x86745)
% 109.14/108.85 [8835]E(f318(f318(f73(a911),f318(f318(f74(a911),x88351),x88352)),x88353),f318(f318(f73(a911),f318(f318(f74(a911),x88354),x88352)),x88355))+~P1(f318(f318(f225(a911),x88354),x88351))+~E(x88355,f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x88351),x88354)),x88352)),x88353))
% 109.14/108.85 [8836]E(f318(f318(f73(a911),f318(f318(f74(a911),x88361),x88362)),x88363),f318(f318(f73(a911),f318(f318(f74(a911),x88364),x88362)),x88365))+~P1(f318(f318(f225(a911),x88364),x88361))+~E(f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x88361),x88364)),x88362)),x88363),x88365)
% 109.14/108.85 [9725]~P76(x97252)+~P1(f318(f55(x97251),x97255))+E(f318(f318(f8(x97251,x97252),f318(f318(f20(x97251,x97252,x97252),f318(f318(f10(x97252,f918(x97252,x97252),x97251),f73(x97252)),x97253)),x97254)),x97255),f318(f318(f73(x97252),f318(f318(f8(x97251,x97252),x97253),x97255)),f318(f318(f8(x97251,x97252),x97254),x97255)))
% 109.14/108.85 [9726]~P82(x97262)+~P1(f318(f55(x97261),x97265))+E(f318(f318(f11(x97261,x97262),f318(f318(f20(x97261,x97262,x97262),f318(f318(f10(x97262,f918(x97262,x97262),x97261),f74(x97262)),x97263)),x97264)),x97265),f318(f318(f74(x97262),f318(f318(f11(x97261,x97262),x97263),x97265)),f318(f318(f11(x97261,x97262),x97264),x97265)))
% 109.14/108.85 [9727]~P72(x97272)+~P1(f318(f55(x97271),x97275))+E(f318(f318(f11(x97271,x97272),f318(f318(f20(x97271,x97272,x97272),f318(f318(f10(x97272,f918(x97272,x97272),x97271),f282(x97272)),x97273)),x97274)),x97275),f318(f318(f282(x97272),f318(f318(f11(x97271,x97272),x97273),x97275)),f318(f318(f11(x97271,x97272),x97274),x97275)))
% 109.14/108.85 [9869]~E(f626(x98695,x98694,x98693,x98692,x98691),f627(x98695,x98694,x98693,x98692,x98691))+P1(f318(f318(f320(f917(x98691,x98691)),f318(f318(f243(x98691,x98691),x98692),x98693)),f298(x98691,x98694)))+~P1(f318(f318(f320(f917(x98691,x98691)),f318(f318(f243(x98691,x98691),x98692),x98693)),f298(x98691,f318(f318(f101(f918(f917(x98691,x98691),a909)),x98694),x98695))))
% 109.14/108.85 [9870]~E(f628(x98705,x98704,x98703,x98702,x98701),f629(x98705,x98704,x98703,x98702,x98701))+P1(f318(f318(f320(f917(x98701,x98701)),f318(f318(f243(x98701,x98701),x98702),x98703)),f298(x98701,x98704)))+~P1(f318(f318(f320(f917(x98701,x98701)),f318(f318(f243(x98701,x98701),x98702),x98703)),f298(x98701,f318(f318(f101(f918(f917(x98701,x98701),a909)),x98704),x98705))))
% 109.14/108.85 [10073]P1(f318(f318(f320(f917(x100731,x100731)),f318(f318(f243(x100731,x100731),x100732),f629(x100735,x100734,x100733,x100732,x100731))),f298(x100731,x100734)))+P1(f318(f318(f320(f917(x100731,x100731)),f318(f318(f243(x100731,x100731),x100732),x100733)),f298(x100731,x100734)))+~P1(f318(f318(f320(f917(x100731,x100731)),f318(f318(f243(x100731,x100731),x100732),x100733)),f298(x100731,f318(f318(f101(f918(f917(x100731,x100731),a909)),x100734),x100735))))
% 109.14/108.85 [10146]P1(f318(f318(f320(f917(x101461,x101461)),f318(f318(f243(x101461,x101461),f627(x101465,x101464,x101463,x101462,x101461)),x101463)),f298(x101461,x101464)))+P1(f318(f318(f320(f917(x101461,x101461)),f318(f318(f243(x101461,x101461),x101462),x101463)),f298(x101461,x101464)))+~P1(f318(f318(f320(f917(x101461,x101461)),f318(f318(f243(x101461,x101461),x101462),x101463)),f298(x101461,f318(f318(f101(f918(f917(x101461,x101461),a909)),x101464),x101465))))
% 109.14/108.85 [10180]P1(f318(f318(f320(f917(x101801,x101801)),f318(f318(f243(x101801,x101801),x101802),x101803)),f298(x101801,x101804)))+P1(f318(f318(f320(f917(x101801,x101801)),f318(f318(f243(x101801,x101801),f626(x101805,x101804,x101803,x101802,x101801)),f627(x101805,x101804,x101803,x101802,x101801))),x101805))+~P1(f318(f318(f320(f917(x101801,x101801)),f318(f318(f243(x101801,x101801),x101802),x101803)),f298(x101801,f318(f318(f101(f918(f917(x101801,x101801),a909)),x101804),x101805))))
% 109.14/108.85 [10181]P1(f318(f318(f320(f917(x101811,x101811)),f318(f318(f243(x101811,x101811),x101812),x101813)),f298(x101811,x101814)))+P1(f318(f318(f320(f917(x101811,x101811)),f318(f318(f243(x101811,x101811),f629(x101815,x101814,x101813,x101812,x101811)),f628(x101815,x101814,x101813,x101812,x101811))),x101815))+~P1(f318(f318(f320(f917(x101811,x101811)),f318(f318(f243(x101811,x101811),x101812),x101813)),f298(x101811,f318(f318(f101(f918(f917(x101811,x101811),a909)),x101814),x101815))))
% 109.14/108.85 [10351]~P1(f318(f318(f320(f917(f912(x103511),f912(x103511))),f318(f318(f243(f912(x103511),f912(x103511)),x103514),x103515)),f149(x103511,x103512)))+~P1(f318(f318(f320(f917(x103511,x103511)),x103513),f318(f163(f917(x103511,x103511)),f318(f318(f172(x103511,x103511),x103514),x103515))))+P1(f318(f318(f248(x103511,x103511,a909),f318(f318(f9(x103511,f918(f917(x103511,x103511),a909),f918(x103511,a909)),f318(f318(f10(f918(x103511,f918(f918(f917(x103511,x103511),a909),a909)),f918(f918(f917(x103511,x103511),a909),f918(x103511,a909)),x103511),f9(x103511,f918(f917(x103511,x103511),a909),a909)),f318(f318(f10(f918(x103511,f917(x103511,x103511)),f918(x103511,f918(f918(f917(x103511,x103511),a909),a909)),x103511),f318(f10(f917(x103511,x103511),f918(f918(f917(x103511,x103511),a909),a909),x103511),f320(f917(x103511,x103511)))),f243(x103511,x103511)))),x103512)),x103513))
% 109.14/108.85 [9755]~P1(f318(f318(f225(a911),x97553),x97552))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),f318(f318(f74(a911),x97553),x97554)),x97551)),f318(f318(f73(a911),f318(f318(f74(a911),x97552),x97554)),x97555)))+P1(f318(f318(f225(a911),x97551),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x97552),x97553)),x97554)),x97555)))
% 109.14/108.85 [9756]~P1(f318(f318(f225(a911),x97563),x97562))+~P1(f318(f318(f226(a911),f318(f318(f73(a911),f318(f318(f74(a911),x97563),x97564)),x97561)),f318(f318(f73(a911),f318(f318(f74(a911),x97562),x97564)),x97565)))+P1(f318(f318(f226(a911),x97561),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x97562),x97563)),x97564)),x97565)))
% 109.14/108.85 [9780]~P1(f318(f318(f225(a911),x97801),x97804))+P1(f318(f318(f225(a911),f318(f318(f73(a911),f318(f318(f74(a911),x97801),x97802)),x97803)),f318(f318(f73(a911),f318(f318(f74(a911),x97804),x97802)),x97805)))+~P1(f318(f318(f225(a911),x97803),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x97804),x97801)),x97802)),x97805)))
% 109.14/108.85 [9781]~P1(f318(f318(f225(a911),x97811),x97814))+P1(f318(f318(f226(a911),f318(f318(f73(a911),f318(f318(f74(a911),x97811),x97812)),x97813)),f318(f318(f73(a911),f318(f318(f74(a911),x97814),x97812)),x97815)))+~P1(f318(f318(f226(a911),x97813),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x97814),x97811)),x97812)),x97815)))
% 109.14/108.85 [9905]~P1(f318(f318(f225(a911),x99052),x99051))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),f318(f318(f74(a911),x99051),x99053)),x99054)),f318(f318(f73(a911),f318(f318(f74(a911),x99052),x99053)),x99055)))+P1(f318(f318(f225(a911),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x99051),x99052)),x99053)),x99054)),x99055))
% 109.14/108.85 [9906]~P1(f318(f318(f225(a911),x99062),x99061))+~P1(f318(f318(f226(a911),f318(f318(f73(a911),f318(f318(f74(a911),x99061),x99063)),x99064)),f318(f318(f73(a911),f318(f318(f74(a911),x99062),x99063)),x99065)))+P1(f318(f318(f226(a911),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x99061),x99062)),x99063)),x99064)),x99065))
% 109.14/108.85 [9967]~P1(f318(f318(f225(a911),x99674),x99671))+P1(f318(f318(f225(a911),f318(f318(f73(a911),f318(f318(f74(a911),x99671),x99672)),x99673)),f318(f318(f73(a911),f318(f318(f74(a911),x99674),x99672)),x99675)))+~P1(f318(f318(f225(a911),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x99671),x99674)),x99672)),x99673)),x99675))
% 109.14/108.85 [9968]~P1(f318(f318(f225(a911),x99684),x99681))+P1(f318(f318(f226(a911),f318(f318(f73(a911),f318(f318(f74(a911),x99681),x99682)),x99683)),f318(f318(f73(a911),f318(f318(f74(a911),x99684),x99682)),x99685)))+~P1(f318(f318(f226(a911),f318(f318(f73(a911),f318(f318(f74(a911),f318(f318(f3(a911),x99681),x99684)),x99682)),x99683)),x99685))
% 109.14/108.85 [10169]~P11(x101691,x101692,x101695,x101693)+~P1(f318(f318(f320(f917(x101691,x101691)),x101694),x101695))+P1(f318(f318(f248(x101691,x101691,a909),f318(f318(f9(x101691,f918(x101691,x101692),f918(x101691,a909)),f318(f318(f10(f918(x101692,a909),f918(f918(x101691,x101692),f918(x101691,a909)),x101691),f10(x101692,a909,x101691)),f318(f318(f10(x101692,f918(x101692,a909),x101691),a315),x101693))),x101693)),x101694))
% 109.14/108.85 [10191]~P113(x101911)+~P42(x101911,f918(x101912,a909),x101913)+P42(x101911,f918(x101912,a909),f318(f318(f9(x101911,f918(x101912,a909),f918(x101912,a909)),f318(f318(f10(f918(x101912,a909),f918(f918(x101912,a909),f918(x101912,a909)),x101911),f101(f918(x101912,a909))),f318(f318(f9(x101911,f918(x101912,a909),f918(x101912,a909)),f318(f318(f10(f918(x101912,a909),f918(f918(x101912,a909),f918(x101912,a909)),x101911),f101(f918(x101912,a909))),x101913)),x101914))),x101915))
% 109.14/108.85 [8545]~P19(x85456,x85451,x85452,x85454)+E(f318(f66(x85451,x85451,x85451,f318(x85452,x85453)),f318(x85454,x85455)),f318(f66(x85451,x85451,x85451,f318(x85454,x85455)),f318(x85452,x85453)))+~P1(f318(f55(x85456),x85455))
% 109.14/108.85 [8980]~P25(x89801,x89803,x89805,x89806)+~P25(x89803,x89802,x89804,f318(f301(x89801,x89803,x89805),x89806))+P25(x89801,x89802,f318(f66(x89803,x89802,x89801,x89804),x89805),x89806)
% 109.14/108.85 [8981]~P25(x89811,x89813,x89815,x89816)+~P25(x89813,x89812,x89814,f318(f301(x89811,x89813,x89815),x89816))+P25(x89811,x89812,f318(f66(x89813,x89812,x89811,x89814),x89815),x89816)
% 109.14/108.85 [9163]~P25(x91634,x91631,x91635,x91636)+~P25(x91634,x91632,f318(f66(x91631,x91632,x91634,x91633),x91635),x91636)+P25(x91631,x91632,x91633,f318(f301(x91634,x91631,x91635),x91636))
% 109.14/108.85 [9557]~P1(f318(f318(x95574,x95572),x95576))+~P1(f318(f318(x95573,x95575),x95572))+P1(f318(f318(f320(x95571),x95572),f288(x95571,x95573,x95574,x95575,x95576)))
% 109.14/108.85 [9558]~P1(f318(f318(x95583,x95582),x95586))+~P1(f318(f318(x95584,x95585),x95582))+P1(f318(f318(f320(x95581),x95582),f291(x95581,x95583,x95584,x95585,x95586)))
% 109.14/108.85 [9664]E(x96641,x96642)+E(x96643,x96644)+~P1(f318(f318(f320(f917(f912(x96645),f912(x96645))),f318(f318(f243(f912(x96645),f912(x96645)),f318(f318(f142(x96645),x96643),x96641)),f318(f318(f142(x96645),x96644),x96642))),f148(x96645,x96646)))
% 109.14/108.85 [9678]~E(x96782,x96784)+P1(f318(f318(f320(f917(f912(x96781),f912(x96781))),f318(f318(f243(f912(x96781),f912(x96781)),f318(f318(f142(x96781),x96782),x96783)),f318(f318(f142(x96781),x96784),x96785))),f136(x96781,x96786)))+~P1(f318(f318(f320(f917(f912(x96781),f912(x96781))),f318(f318(f243(f912(x96781),f912(x96781)),x96783),x96785)),f136(x96781,x96786)))
% 109.14/108.85 [9679]~E(x96792,x96794)+P1(f318(f318(f320(f917(f912(x96791),f912(x96791))),f318(f318(f243(f912(x96791),f912(x96791)),f318(f318(f142(x96791),x96792),x96793)),f318(f318(f142(x96791),x96794),x96795))),f138(x96791,x96796)))+~P1(f318(f318(f320(f917(f912(x96791),f912(x96791))),f318(f318(f243(f912(x96791),f912(x96791)),x96793),x96795)),f138(x96791,x96796)))
% 109.14/108.85 [9680]~E(x96802,x96804)+P1(f318(f318(f320(f917(f912(x96801),f912(x96801))),f318(f318(f243(f912(x96801),f912(x96801)),f318(f318(f142(x96801),x96802),x96803)),f318(f318(f142(x96801),x96804),x96805))),f148(x96801,x96806)))+~P1(f318(f318(f320(f917(f912(x96801),f912(x96801))),f318(f318(f243(f912(x96801),f912(x96801)),x96803),x96805)),f148(x96801,x96806)))
% 109.14/108.85 [9681]~E(x96812,x96814)+P1(f318(f318(f320(f917(f912(x96811),f912(x96811))),f318(f318(f243(f912(x96811),f912(x96811)),f318(f318(f125(x96811),x96812),x96813)),f318(f318(f125(x96811),x96814),x96815))),f148(x96811,x96816)))+~P1(f318(f318(f320(f917(f912(x96811),f912(x96811))),f318(f318(f243(f912(x96811),f912(x96811)),x96813),x96815)),f148(x96811,x96816)))
% 109.14/108.85 [9682]~E(x96823,x96825)+P1(f318(f318(f320(f917(f912(x96821),f912(x96821))),f318(f318(f243(f912(x96821),f912(x96821)),f318(f318(f125(x96821),x96822),x96823)),f318(f318(f125(x96821),x96824),x96825))),f148(x96821,x96826)))+~P1(f318(f318(f320(f917(f912(x96821),f912(x96821))),f318(f318(f243(f912(x96821),f912(x96821)),x96822),x96824)),f148(x96821,x96826)))
% 109.14/108.85 [9745]E(x97451,x97452)+P1(f318(f318(f320(f917(f912(x97453),f912(x97453))),f318(f318(f243(f912(x97453),f912(x97453)),x97451),x97452)),f148(x97453,x97454)))+~P1(f318(f318(f320(f917(f912(x97453),f912(x97453))),f318(f318(f243(f912(x97453),f912(x97453)),f318(f318(f142(x97453),x97455),x97451)),f318(f318(f142(x97453),x97456),x97452))),f148(x97453,x97454)))
% 109.14/108.85 [9909]~E(x99093,x99095)+P1(f318(f318(f320(f917(f912(x99091),f912(x99091))),f318(f318(f243(f912(x99091),f912(x99091)),f318(f318(f125(x99091),x99092),f318(f318(f142(x99091),x99093),f104(x99091)))),f318(f318(f125(x99091),x99094),f318(f318(f142(x99091),x99095),f104(x99091))))),f148(x99091,x99096)))+~P1(f318(f318(f320(f917(f912(x99091),f912(x99091))),f318(f318(f243(f912(x99091),f912(x99091)),x99092),x99094)),f148(x99091,x99096)))
% 109.14/108.85 [9971]E(x99711,x99712)+E(x99713,x99714)+~P1(f318(f318(f320(f917(f912(x99715),f912(x99715))),f318(f318(f243(f912(x99715),f912(x99715)),f318(f318(f125(x99715),x99713),f318(f318(f142(x99715),x99711),f104(x99715)))),f318(f318(f125(x99715),x99714),f318(f318(f142(x99715),x99712),f104(x99715))))),f148(x99715,x99716)))
% 109.14/108.85 [9994]E(x99941,x99942)+~P1(f318(f318(f320(f917(f912(x99943),f912(x99943))),f318(f318(f243(f912(x99943),f912(x99943)),f318(f318(f125(x99943),x99941),f318(f318(f142(x99943),x99945),f104(x99943)))),f318(f318(f125(x99943),x99942),f318(f318(f142(x99943),x99946),f104(x99943))))),f148(x99943,x99944)))+P1(f318(f318(f320(f917(f912(x99943),f912(x99943))),f318(f318(f243(f912(x99943),f912(x99943)),x99941),x99942)),f148(x99943,x99944)))
% 109.14/108.85 [10036]~P1(f318(f318(f320(f917(f918(x100361,a909),f918(x100361,a909))),f318(f318(f243(f918(x100361,a909),f918(x100361,a909)),x100362),x100364)),f310(x100361,x100366)))+~P1(f318(f318(f320(f917(f918(x100361,a909),f918(x100361,a909))),f318(f318(f243(f918(x100361,a909),f918(x100361,a909)),x100363),x100365)),f310(x100361,x100366)))+P1(f318(f318(f320(f917(f918(x100361,a909),f918(x100361,a909))),f318(f318(f243(f918(x100361,a909),f918(x100361,a909)),f318(f318(f101(f918(x100361,a909)),x100362),x100363)),f318(f318(f101(f918(x100361,a909)),x100364),x100365))),f310(x100361,x100366)))
% 109.14/108.85 [5795]~E(f318(f318(f125(x57951),x57956),x57953),x57955)+E(f318(f318(f125(x57951),x57952),x57953),f318(f318(f142(x57951),x57954),x57955))+~E(x57952,f318(f318(f142(x57951),x57954),x57956))
% 109.14/108.85 [5796]~E(f318(f318(f125(x57961),x57966),x57963),x57965)+E(f318(f318(f125(x57961),x57962),x57963),f318(f318(f125(x57961),x57964),x57965))+~E(x57962,f318(f318(f125(x57961),x57964),x57966))
% 109.14/108.85 [5797]E(f318(f318(f125(x57971),x57972),x57973),f318(f318(f142(x57971),x57974),x57975))+~E(f318(f318(f142(x57971),x57974),x57976),x57972)+~E(x57975,f318(f318(f125(x57971),x57976),x57973))
% 109.14/108.85 [5798]E(f318(f318(f125(x57981),x57982),x57983),f318(f318(f142(x57981),x57984),x57985))+~E(f318(f318(f142(x57981),x57984),x57986),x57982)+~E(x57985,f318(f318(f125(x57981),x57986),x57983))
% 109.14/108.85 [5799]~E(f318(f318(f125(x57991),x57992),x57996),x57994)+E(f318(f318(f125(x57991),x57992),x57993),f318(f318(f125(x57991),x57994),x57995))+~E(x57993,f318(f318(f125(x57991),x57996),x57995))
% 109.14/108.85 [5800]~E(f318(f318(f125(x58001),x58002),x58006),x58004)+E(f318(f318(f125(x58001),x58002),x58003),f318(f318(f125(x58001),x58004),x58005))+~E(x58003,f318(f318(f125(x58001),x58006),x58005))
% 109.14/108.85 [6945]E(f318(x69451,x69452),f318(x69453,x69452))+~E(f318(f318(f145(x69454,x69455),x69451),x69456),f318(f318(f145(x69454,x69455),x69453),x69456))+~P1(f318(f318(f320(x69454),x69452),f318(f163(x69454),x69456)))
% 109.14/108.85 [7332]~P19(x73324,x73325,x73326,x73321)+E(f318(f318(x73321,x73322),x73323),f318(f318(f58(x73324,x73325,x73326),x73323),x73322))+~P1(f318(f55(x73324),x73322))
% 109.14/108.85 [7401]~E(x74012,f318(x74014,x74016))+~P1(f318(f318(f320(x74013),x74016),x74015))+P1(f318(f318(f320(x74011),x74012),f318(f301(x74013,x74011,x74014),x74015)))
% 109.14/108.85 [7402]~E(x74022,f318(x74024,x74026))+~P1(f318(f318(f320(x74023),x74026),x74025))+P1(f318(f318(f320(x74021),x74022),f318(f301(x74023,x74021,x74024),x74025)))
% 109.14/108.85 [7403]~E(x74032,f318(x74034,x74036))+~P1(f318(f318(f320(x74033),x74036),x74035))+P1(f318(f318(f320(x74031),x74032),f318(f301(x74033,x74031,x74034),x74035)))
% 109.14/108.85 [7404]~E(f318(x74044,x74042),x74046)+~P1(f318(f318(f320(x74043),x74046),x74045))+P1(f318(f318(f320(x74041),x74042),f318(f302(x74041,x74043,x74044),x74045)))
% 109.14/108.85 [7837]~P34(x78371,x78372,x78374,x78376)+P34(x78371,x78372,f318(f318(f142(x78371),x78373),x78374),f318(f318(f142(x78371),x78375),x78376))+~P1(f318(f318(x78372,x78373),x78375))
% 109.14/108.85 [7838]~P34(x78381,x78382,x78384,x78386)+P34(x78381,x78382,f318(f318(f142(x78381),x78383),x78384),f318(f318(f142(x78381),x78385),x78386))+~P1(f318(f318(x78382,x78383),x78385))
% 109.14/108.85 [8845]~P60(x88454,x88455,x88451,x88452,x88456)+E(f318(x88451,f318(x88452,x88453)),x88453)+~P1(f318(f318(f320(x88455),x88453),x88456))
% 109.14/108.85 [9348]~P26(x93482,x93481,x93485,x93484,x93483)+E(f318(f84(x93481,x93482,x93483,f84(x93482,x93481,x93484,x93485)),x93486),f318(x93485,x93486))+~P1(f318(f318(f320(x93482),x93486),x93484))
% 109.14/108.85 [9359]~P25(x93591,x93592,x93593,x93596)+P25(x93591,x93592,f68(x93591,x93592,x93593,x93594,x93595),x93596)+P1(f318(f318(f320(x93592),x93595),f318(f301(x93591,x93592,x93593),x93596)))
% 109.14/108.85 [9667]E(x96671,x96672)+E(f318(f180(f912(x96673)),x96674),f318(f180(f912(x96673)),x96675))+~P1(f318(f318(f320(f917(f912(x96673),f912(x96673))),f318(f318(f243(f912(x96673),f912(x96673)),f318(f318(f142(x96673),x96671),x96674)),f318(f318(f142(x96673),x96672),x96675))),f136(x96673,x96676)))
% 109.14/108.85 [9739]~P16(x97391,x97392,x97393)+E(f318(f318(f58(x97391,x97392,x97393),x97394),x97395),x97396)+~P1(f318(f60(x97391,x97392,x97393,x97394,x97395),x97396))
% 109.14/108.85 [9746]E(f318(f180(f912(x97461)),x97462),f318(f180(f912(x97461)),x97463))+P1(f318(f318(f320(f917(f912(x97461),f912(x97461))),f318(f318(f243(f912(x97461),f912(x97461)),x97462),x97463)),f136(x97461,x97464)))+~P1(f318(f318(f320(f917(f912(x97461),f912(x97461))),f318(f318(f243(f912(x97461),f912(x97461)),f318(f318(f142(x97461),x97465),x97462)),f318(f318(f142(x97461),x97466),x97463))),f136(x97461,x97464)))
% 109.14/108.85 [9774]~P1(f318(f318(f320(f917(x97741,x97741)),f318(f318(f243(x97741,x97741),x97742),x97744)),f298(x97741,x97746)))+P1(f318(f318(f320(f917(f912(x97741),f912(x97741))),f318(f318(f243(f912(x97741),f912(x97741)),f318(f318(f142(x97741),x97742),x97743)),f318(f318(f142(x97741),x97744),x97745))),f298(f912(x97741),f148(x97741,x97746))))+~P1(f318(f318(f320(f917(f912(x97741),f912(x97741))),f318(f318(f243(f912(x97741),f912(x97741)),x97743),x97745)),f298(f912(x97741),f148(x97741,x97746))))
% 109.14/108.85 [9976]~P1(f318(x99762,x99766))+~E(f318(f127(x99761,x99762),x99763),f318(f318(f142(x99761),x99764),x99765))+~P1(f318(f318(f320(x99761),x99766),f318(f163(x99761),f738(x99765,x99764,x99763,x99762,x99761))))
% 109.14/108.85 [9977]~P1(f318(x99774,x99776))+~E(f318(f318(f142(x99771),x99772),x99773),f318(f127(x99771,x99774),x99775))+~P1(f318(f318(f320(x99771),x99776),f318(f163(x99771),f741(x99775,x99774,x99773,x99772,x99771))))
% 109.14/108.85 [10271]~P76(x102712)+E(f318(f318(f8(x102711,x102712),f318(f318(f10(f918(x102713,a909),x102712,x102711),f318(f8(x102713,x102712),x102714)),f318(f318(f10(f918(x102713,a909),f918(x102713,a909),x102711),f253(x102713)),f318(f318(f10(f918(x102713,a909),f918(x102713,a909),x102711),f318(f20(x102713,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102713),a316),f318(f318(f9(x102713,f918(x102713,a909),a909),f320(x102713)),x102715)))),f318(f9(x102713,x102711,a909),f318(f318(f10(x102711,f918(x102711,a909),x102713),a315),x102716)))))),f318(f301(x102713,x102711,x102716),x102715)),f318(f318(f8(x102713,x102712),x102714),x102715))+~P1(f318(f55(x102713),x102715))
% 109.14/108.85 [7002]~P4(x70023)+P1(f318(x70022,x70025))+E(f318(f127(x70021,x70022),f318(f318(f139(x70021,x70023,x70024),x70025),x70026)),f318(f127(x70021,x70022),x70026))
% 109.14/108.85 [7004]P1(f318(x70041,x70042))+~E(f157(x70043,x70041,x70044),f318(f318(f243(f912(x70043),f912(x70043)),x70045),x70046))+~P1(f318(f318(f320(x70043),x70042),f318(f163(x70043),x70045)))
% 109.14/108.85 [7049]~P1(f318(x70492,x70496))+~E(f157(x70491,x70492,x70493),f318(f318(f243(f912(x70491),f912(x70491)),x70494),x70495))+~P1(f318(f318(f320(x70491),x70496),f318(f163(x70491),x70495)))
% 109.14/108.85 [7703]~P14(x77031,x77032,x77033)+~P1(f318(f55(x77031),x77036))+E(f318(f318(f58(x77031,x77032,x77033),x77034),f318(f318(f300(x77031),x77035),x77036)),f318(f318(f58(x77031,x77032,x77033),f318(f318(x77033,x77035),x77034)),x77036))
% 109.14/108.85 [7753]~P4(x77532)+~P1(f318(f318(f225(x77532),f318(x77533,x77534)),f318(x77533,x77535)))+E(f318(f318(f139(x77531,x77532,x77533),x77534),f318(f318(f142(x77531),x77535),x77536)),f318(f318(f142(x77531),x77534),f318(f318(f142(x77531),x77535),x77536)))
% 109.14/108.85 [7866]E(x78661,x78662)+~E(f318(f318(f245(x78663,x78664),x78661),f318(f18(f918(x78664,a909),x78663),x78665)),f318(f318(f245(x78663,x78664),x78662),f318(f18(f918(x78664,a909),x78663),x78665)))+~P1(f318(f318(f320(x78664),x78666),x78665))
% 109.14/108.85 [7934]~P14(x79341,x79342,x79343)+~P1(f318(f55(x79341),x79346))+E(f318(f318(f58(x79341,x79342,x79343),x79344),f318(f318(f300(x79341),x79345),x79346)),f318(f318(x79343,x79345),f318(f318(f58(x79341,x79342,x79343),x79344),x79346)))
% 109.14/108.85 [8051]~P16(x80511,x80512,x80513)+~P1(f318(f55(x80511),x80516))+E(f318(f318(f58(x80511,x80512,x80513),f318(f318(x80513,x80514),x80515)),x80516),f318(f318(x80513,x80514),f318(f318(f58(x80511,x80512,x80513),x80515),x80516)))
% 109.14/108.85 [8115]~P20(x81152,x81155,x81156,x81151)+~P1(f318(f55(x81152),x81154))+E(f318(x81151,f318(f318(f300(x81152),x81153),x81154)),f318(f66(x81155,x81155,x81155,f318(x81151,x81154)),f318(x81156,x81153)))
% 109.14/108.85 [8146]~P4(x81462)+P1(f318(f318(f225(x81462),f318(x81463,x81464)),f318(x81463,x81465)))+E(f318(f318(f139(x81461,x81462,x81463),x81464),f318(f318(f142(x81461),x81465),x81466)),f318(f318(f142(x81461),x81465),f318(f318(f139(x81461,x81462,x81463),x81464),x81466)))
% 109.14/108.85 [8296]~E(f318(f180(f912(x82961)),x82965),f318(f180(f912(x82962)),x82966))+~E(f318(f180(f912(x82961)),x82963),f318(f180(f912(x82962)),x82964))+E(f318(f318(f125(f917(x82961,x82962)),f318(f318(f172(x82961,x82962),x82963),x82964)),f318(f318(f172(x82961,x82962),x82965),x82966)),f318(f318(f172(x82961,x82962),f318(f318(f125(x82961),x82963),x82965)),f318(f318(f125(x82962),x82964),x82966)))
% 109.14/108.85 [8405]~E(x84052,f318(f301(x84053,x84051,x84054),x84056))+P1(f318(f318(f225(f918(x84051,a909)),x84052),f318(f301(x84053,x84051,x84054),x84055)))+~P1(f318(f318(f225(f918(x84053,a909)),x84056),x84055))
% 109.14/108.85 [8504]~P4(x85045)+E(f318(x85041,x85042),f318(x85041,x85043))+E(f318(f318(f139(x85044,x85045,x85041),x85042),f318(f318(f139(x85044,x85045,x85041),x85043),x85046)),f318(f318(f139(x85044,x85045,x85041),x85043),f318(f318(f139(x85044,x85045,x85041),x85042),x85046)))
% 109.14/108.85 [8681]~P1(f318(f318(f320(x86812),x86814),f318(x86816,x86813)))+~P1(f318(f318(f320(x86811),x86813),x86815))+P1(f318(f318(f320(f917(x86811,x86812)),f318(f318(f243(x86811,x86812),x86813),x86814)),f318(f318(f245(x86811,x86812),x86815),x86816)))
% 109.14/108.85 [8682]~P1(f318(f318(f320(x86822),x86824),f318(x86826,x86823)))+~P1(f318(f318(f320(x86821),x86823),x86825))+P1(f318(f318(f320(f917(x86821,x86822)),f318(f318(f243(x86821,x86822),x86823),x86824)),f318(f318(f245(x86821,x86822),x86825),x86826)))
% 109.14/108.85 [9156]~P76(x91562)+~P25(x91564,x91561,x91565,x91566)+E(f318(f318(f8(x91561,x91562),x91563),f318(f301(x91564,x91561,x91565),x91566)),f318(f318(f8(x91564,x91562),f318(f66(x91561,x91562,x91564,x91563),x91565)),x91566))
% 109.14/108.85 [9157]~P82(x91572)+~P25(x91574,x91571,x91575,x91576)+E(f318(f318(f11(x91571,x91572),x91573),f318(f301(x91574,x91571,x91575),x91576)),f318(f318(f11(x91574,x91572),f318(f66(x91571,x91572,x91574,x91573),x91575)),x91576))
% 109.14/108.85 [9199]~P36(x91992,x91995,x91991,x91993,x91996)+P1(f318(f318(x91991,f318(f318(f155(x91992),x91993),x91994)),f318(f318(f155(x91995),x91996),x91994)))+~P1(f318(f318(f226(a911),x91994),f318(f180(f912(x91992)),x91993)))
% 109.14/108.85 [9200]~P36(x92002,x92005,x92001,x92003,x92006)+P1(f318(f318(x92001,f318(f318(f155(x92002),x92003),x92004)),f318(f318(f155(x92005),x92006),x92004)))+~P1(f318(f318(f226(a911),x92004),f318(f180(f912(x92005)),x92006)))
% 109.14/108.85 [9201]~P36(x92012,x92015,x92011,x92013,x92016)+P1(f318(f318(x92011,f318(f318(f155(x92012),x92013),x92014)),f318(f318(f155(x92015),x92016),x92014)))+~P1(f318(f318(f226(a911),x92014),f318(f180(f912(x92012)),x92013)))
% 109.14/108.85 [9210]~E(f318(f301(x92101,x92102,x92103),x92104),x92106)+E(f318(f301(x92101,x92102,x92103),f318(f301(x92102,x92101,f84(x92101,x92102,x92104,x92103)),x92105)),x92105)+~P1(f318(f318(f225(f918(x92102,a909)),x92105),x92106))
% 109.14/108.85 [9416]~P19(x94163,x94161,x94166,x94162)+~P1(f318(f55(x94163),x94164))+E(f318(f66(x94161,x94161,x94161,f318(x94162,f318(f318(f3(f918(x94163,a909)),x94164),f318(f318(f300(x94163),x94165),f179(f918(x94163,a909)))))),f318(x94166,x94165)),f318(x94162,f318(f318(f300(x94163),x94165),x94164)))
% 109.14/108.85 [9429]~P1(f318(f318(f320(x94295),x94293),x94296))+P1(f318(f318(f320(x94291),f318(x94292,x94293)),f87(f918(x94291,a909),x94294)))+~P1(f318(f318(f225(f918(x94291,a909)),f318(f301(x94295,x94291,x94292),x94296)),f318(x94294,f318(f301(x94295,x94291,x94292),x94296))))
% 109.14/108.85 [10056]~E(f318(f301(x100562,x100564,x100566),f233(f918(x100562,a909))),f233(f918(x100564,a909)))+~E(f318(f301(x100561,x100563,x100565),f233(f918(x100561,a909))),f233(f918(x100563,a909)))+E(f318(f301(f917(x100561,x100562),f917(x100563,x100564),f249(x100561,x100563,x100562,x100564,x100565,x100566)),f233(f918(f917(x100561,x100562),a909))),f233(f918(f917(x100563,x100564),a909)))
% 109.14/108.85 [10107]~P25(x101073,x101074,x101075,f318(x101076,f550(x101076,x101075,x101074,x101073,x101072,x101071)))+P25(x101073,x101074,x101075,f318(f318(f34(x101072,f918(x101073,a909)),x101071),x101076))+E(x101071,f179(f918(x101072,a909)))
% 109.14/108.85 [10153]P25(x101536,x101535,x101534,f318(f318(f34(x101532,f918(x101536,a909)),x101531),x101533))+E(x101531,f179(f918(x101532,a909)))+P1(f318(f318(f320(x101532),f550(x101533,x101534,x101535,x101536,x101532,x101531)),x101531))
% 109.14/108.85 [10156]P1(f318(f318(f320(x101561),f597(x101562,x101563,x101564,x101565,x101566,x101561)),x101566))+P1(f318(f318(f225(f918(f917(x101561,x101564),a909)),f318(f318(f245(x101561,x101564),x101566),x101563)),f318(f318(f245(x101561,x101564),x101565),x101562)))+~P1(f318(f318(f225(f918(x101561,a909)),x101566),x101565))
% 109.14/108.85 [10283]~P1(f318(f318(f225(f918(x102832,a909)),f318(x102834,f597(x102836,x102834,x102832,x102835,x102833,x102831))),f318(x102836,f597(x102836,x102834,x102832,x102835,x102833,x102831))))+~P1(f318(f318(f225(f918(x102831,a909)),x102833),x102835))+P1(f318(f318(f225(f918(f917(x102831,x102832),a909)),f318(f318(f245(x102831,x102832),x102833),x102834)),f318(f318(f245(x102831,x102832),x102835),x102836)))
% 109.14/108.85 [7888]~P1(f318(x78881,x78885))+~P1(f318(x78886,x78884))+P1(f318(x78881,f318(f247(x78882,x78883),f318(f318(f243(x78882,x78883),x78884),x78885))))
% 109.14/108.85 [7889]~P1(f318(x78891,x78894))+~P1(f318(x78896,x78895))+P1(f318(x78891,f318(f242(x78892,x78893),f318(f318(f243(x78892,x78893),x78894),x78895))))
% 109.14/108.85 [7938]~P1(f318(f318(x79384,x79386),x79385))+~P1(f318(f318(f320(x79381),x79386),x79383))+P1(f318(f318(f318(f33(x79381,f918(x79382,a909)),x79383),x79384),x79385))
% 109.14/108.85 [7939]~P1(f318(f318(x79394,x79396),x79395))+~P1(f318(f318(f320(x79391),x79396),x79393))+P1(f318(f318(f318(f33(x79391,f918(x79392,a909)),x79393),x79394),x79395))
% 109.14/108.85 [8243]~P1(f318(f318(f320(x82431),x82432),f318(x82435,x82436)))+~P1(f318(f318(f320(x82433),x82436),x82434))+P1(f318(f318(f320(x82431),x82432),f318(f318(f33(x82433,f918(x82431,a909)),x82434),x82435)))
% 109.14/108.85 [8244]~P1(f318(f318(f320(x82441),x82442),f318(x82445,x82446)))+~P1(f318(f318(f320(x82443),x82446),x82444))+P1(f318(f318(f320(x82441),x82442),f318(f318(f33(x82443,f918(x82441,a909)),x82444),x82445)))
% 109.14/108.85 [8289]P1(f318(f318(x82891,x82892),x82893))+~P1(f318(f318(x82894,x82892),x82893))+~P1(f318(f318(f225(f918(x82895,f918(x82896,a909))),x82894),x82891))
% 109.14/108.85 [8290]P1(f318(f318(x82901,x82902),x82903))+~P1(f318(f318(x82904,x82902),x82903))+~P1(f318(f318(f225(f918(x82905,f918(x82906,a909))),x82904),x82901))
% 109.14/108.85 [8426]P1(f318(f318(x84261,x84262),x84263))+~P1(f318(f318(f320(x84264),x84262),x84265))+~P1(f318(f318(f318(f34(x84264,f918(x84266,a909)),x84265),x84261),x84263))
% 109.14/108.85 [8427]P1(f318(f318(x84271,x84272),x84273))+~P1(f318(f318(f320(x84274),x84272),x84275))+~P1(f318(f318(f318(f34(x84274,f918(x84276,a909)),x84275),x84271),x84273))
% 109.14/108.85 [8428]P1(f318(f318(x84281,x84282),x84283))+~P1(f318(f318(f320(x84284),x84282),x84285))+~P1(f318(f318(f318(f34(x84284,f918(x84286,a909)),x84285),x84281),x84283))
% 109.14/108.85 [8556]P1(f318(f318(f320(x85561),x85562),f318(x85563,x85564)))+~P1(f318(f318(f320(x85565),x85564),x85566))+~P1(f318(f318(f320(x85561),x85562),f318(f318(f34(x85565,f918(x85561,a909)),x85566),x85563)))
% 109.14/108.85 [8557]P1(f318(f318(f320(x85571),x85572),f318(x85573,x85574)))+~P1(f318(f318(f320(x85575),x85574),x85576))+~P1(f318(f318(f320(x85571),x85572),f318(f318(f34(x85575,f918(x85571,a909)),x85576),x85573)))
% 109.14/108.85 [8558]P1(f318(f318(f320(x85581),x85582),f318(x85583,x85584)))+~P1(f318(f318(f320(x85585),x85584),x85586))+~P1(f318(f318(f320(x85581),x85582),f318(f318(f34(x85585,f918(x85581,a909)),x85586),x85583)))
% 109.14/108.85 [8825]~P11(x88254,x88255,x88256,x88251)+E(f318(x88251,x88252),f318(x88251,x88253))+~P1(f318(f318(f320(f917(x88254,x88254)),f318(f318(f243(x88254,x88254),x88252),x88253)),x88256))
% 109.14/108.85 [8859]P1(f318(f318(f225(f918(x88591,a909)),x88592),f318(x88593,x88594)))+~P1(f318(f318(f320(x88595),x88594),x88596))+~P1(f318(f318(f225(f918(x88591,a909)),x88592),f318(f318(f34(x88595,f918(x88591,a909)),x88596),x88593)))
% 109.14/108.85 [8894]~P58(x88943,x88944,f318(f277(x88944,x88943),x88945))+E(x88941,f179(f918(x88942,a909)))+E(f318(f318(f34(x88942,f918(x88943,a909)),x88941),f318(f318(f10(f918(x88944,a909),f918(x88943,a909),x88942),f276(x88944,x88943,x88945)),x88946)),f318(f276(x88944,x88943,x88945),f318(f318(f34(x88942,f918(x88944,a909)),x88941),x88946)))
% 109.14/108.85 [8971]P1(f318(f318(f320(x89711),x89712),f318(f276(x89713,x89711,x89714),x89715)))+~P1(f318(f318(f320(x89713),x89716),x89715))+~P1(f318(f318(f320(f917(x89713,x89711)),f318(f318(f243(x89713,x89711),x89716),x89712)),x89714))
% 109.14/108.85 [8972]P1(f318(f318(f320(x89721),x89722),f318(f276(x89723,x89721,x89724),x89725)))+~P1(f318(f318(f320(x89723),x89726),x89725))+~P1(f318(f318(f320(f917(x89723,x89721)),f318(f318(f243(x89723,x89721),x89726),x89722)),x89724))
% 109.14/108.85 [9276]P1(f318(f318(f225(f918(x92761,a909)),f318(f276(x92762,x92761,x92763),x92764)),f318(f276(x92762,x92761,x92765),x92766)))+~P1(f318(f318(f225(f918(x92762,a909)),x92764),x92766))+~P1(f318(f318(f225(f918(f917(x92762,x92761),a909)),x92763),x92765))
% 109.14/108.85 [9473]~P1(f318(f318(f320(x94732),x94736),x94734))+~P1(f318(f318(f225(f918(x94731,a909)),x94733),x94735))+P1(f318(f318(f225(f918(f917(x94731,x94732),a909)),f318(f318(f245(x94731,x94732),x94733),f318(f18(f918(x94732,a909),x94731),x94734))),f318(f318(f245(x94731,x94732),x94735),f318(f18(f918(x94732,a909),x94731),x94734))))
% 109.14/108.85 [9481]~P36(x94811,x94812,x94813,x94815,x94816)+P1(f318(f318(f248(x94811,x94812,a909),x94813),x94814))+~P1(f318(f318(f320(f917(x94811,x94812)),x94814),f318(f163(f917(x94811,x94812)),f318(f318(f172(x94811,x94812),x94815),x94816))))
% 109.14/108.85 [9617]~E(x96173,x96175)+P1(f318(f318(f320(f917(f912(x96171),f912(x96171))),f318(f318(f243(f912(x96171),f912(x96171)),f318(f318(f142(x96171),x96172),x96173)),f318(f318(f142(x96171),x96174),x96175))),f148(x96171,x96176)))+~P1(f318(f318(f320(f917(x96171,x96171)),f318(f318(f243(x96171,x96171),x96172),x96174)),x96176))
% 109.14/108.85 [9623]~E(f318(f180(f912(x96231)),x96233),f318(f180(f912(x96231)),x96235))+P1(f318(f318(f320(f917(f912(x96231),f912(x96231))),f318(f318(f243(f912(x96231),f912(x96231)),f318(f318(f142(x96231),x96232),x96233)),f318(f318(f142(x96231),x96234),x96235))),f136(x96231,x96236)))+~P1(f318(f318(f320(f917(x96231,x96231)),f318(f318(f243(x96231,x96231),x96232),x96234)),x96236))
% 109.14/108.85 [9659]P1(f318(f318(f320(f917(x96591,x96591)),f318(f318(f243(x96591,x96591),x96592),x96593)),f318(f318(f174(f917(x96591,x96591),a909),f318(a103,x96594)),x96595)))+~P1(f318(f318(f320(f917(x96591,x96591)),f318(f318(f243(x96591,x96591),x96596),x96593)),x96595))+~P1(f318(f318(f320(f917(x96591,x96591)),f318(f318(f243(x96591,x96591),x96592),x96596)),f318(f318(f174(f917(x96591,x96591),a909),x96594),x96595)))
% 109.14/108.85 [9660]P1(f318(f318(f320(f917(x96601,x96601)),f318(f318(f243(x96601,x96601),x96602),x96603)),f318(f318(f174(f917(x96601,x96601),a909),f318(a103,x96604)),x96605)))+~P1(f318(f318(f320(f917(x96601,x96601)),f318(f318(f243(x96601,x96601),x96602),x96606)),x96605))+~P1(f318(f318(f320(f917(x96601,x96601)),f318(f318(f243(x96601,x96601),x96606),x96603)),f318(f318(f174(f917(x96601,x96601),a909),x96604),x96605)))
% 109.14/108.85 [9662]~P1(f318(f318(f320(x96624),x96625),x96626))+P1(f318(f318(f225(f918(x96621,a909)),x96622),x96623))+~P1(f318(f318(f225(f918(f917(x96621,x96624),a909)),f318(f318(f245(x96621,x96624),x96622),f318(f18(f918(x96624,a909),x96621),x96626))),f318(f318(f245(x96621,x96624),x96623),f318(f18(f918(x96624,a909),x96621),x96626))))
% 109.14/108.85 [9717]E(x97171,x97172)+~P1(f318(f318(f320(f917(f912(x97173),f912(x97173))),f318(f318(f243(f912(x97173),f912(x97173)),f318(f318(f142(x97173),x97171),x97175)),f318(f318(f142(x97173),x97172),x97176))),f136(x97173,x97174)))+P1(f318(f318(f320(f917(x97173,x97173)),f318(f318(f243(x97173,x97173),x97171),x97172)),x97174))
% 109.14/108.85 [9718]E(x97181,x97182)+~P1(f318(f318(f320(f917(f912(x97183),f912(x97183))),f318(f318(f243(f912(x97183),f912(x97183)),f318(f318(f142(x97183),x97181),x97185)),f318(f318(f142(x97183),x97182),x97186))),f138(x97183,x97184)))+P1(f318(f318(f320(f917(x97183,x97183)),f318(f318(f243(x97183,x97183),x97181),x97182)),x97184))
% 109.14/108.85 [9719]E(x97191,x97192)+~P1(f318(f318(f320(f917(f912(x97193),f912(x97193))),f318(f318(f243(f912(x97193),f912(x97193)),f318(f318(f142(x97193),x97191),x97195)),f318(f318(f142(x97193),x97192),x97196))),f148(x97193,x97194)))+P1(f318(f318(f320(f917(x97193,x97193)),f318(f318(f243(x97193,x97193),x97191),x97192)),x97194))
% 109.14/108.85 [9754]P1(f318(f318(f320(f917(f912(x97541),f912(x97541))),f318(f318(f243(f912(x97541),f912(x97541)),f318(f318(f142(x97541),x97542),x97543)),f318(f318(f142(x97541),x97544),x97545))),f149(x97541,x97546)))+~P1(f318(f318(f320(f917(f912(x97541),f912(x97541))),f318(f318(f243(f912(x97541),f912(x97541)),x97543),x97545)),f149(x97541,x97546)))+~P1(f318(f318(f320(f917(x97541,x97541)),f318(f318(f243(x97541,x97541),x97542),x97544)),x97546))
% 109.14/108.85 [9778]P1(f318(x97781,x97782))+~P1(f318(x97781,f872(x97781,x97783,x97784,x97785,x97786)))+~P1(f318(f318(f320(x97786),x97782),f318(f318(f33(x97785,f918(x97786,a909)),x97784),x97783)))
% 109.14/108.85 [9783]~P1(f318(f318(f320(f917(f912(x97831),f912(x97831))),f318(f318(f243(f912(x97831),f912(x97831)),f318(f318(f142(x97831),x97832),x97835)),f318(f318(f142(x97831),x97833),x97836))),f136(x97831,x97834)))+P1(f318(f318(f320(f917(f912(x97831),f912(x97831))),f318(f318(f243(f912(x97831),f912(x97831)),x97835),x97836)),f136(x97831,x97834)))+P1(f318(f318(f320(f917(x97831,x97831)),f318(f318(f243(x97831,x97831),x97832),x97833)),x97834))
% 109.14/108.85 [9784]~P1(f318(f318(f320(f917(f912(x97841),f912(x97841))),f318(f318(f243(f912(x97841),f912(x97841)),f318(f318(f142(x97841),x97842),x97845)),f318(f318(f142(x97841),x97843),x97846))),f138(x97841,x97844)))+P1(f318(f318(f320(f917(f912(x97841),f912(x97841))),f318(f318(f243(f912(x97841),f912(x97841)),x97845),x97846)),f138(x97841,x97844)))+P1(f318(f318(f320(f917(x97841,x97841)),f318(f318(f243(x97841,x97841),x97842),x97843)),x97844))
% 109.14/108.85 [9785]~P1(f318(f318(f320(f917(f912(x97851),f912(x97851))),f318(f318(f243(f912(x97851),f912(x97851)),f318(f318(f142(x97851),x97852),x97855)),f318(f318(f142(x97851),x97853),x97856))),f148(x97851,x97854)))+P1(f318(f318(f320(f917(f912(x97851),f912(x97851))),f318(f318(f243(f912(x97851),f912(x97851)),x97855),x97856)),f148(x97851,x97854)))+P1(f318(f318(f320(f917(x97851,x97851)),f318(f318(f243(x97851,x97851),x97852),x97853)),x97854))
% 109.14/108.85 [9881]P1(f318(x98811,x98812))+P1(f318(f318(f320(x98813),f873(x98811,x98814,x98815,x98813,x98816)),x98815))+~P1(f318(f318(f320(x98816),x98812),f318(f318(f33(x98813,f918(x98816,a909)),x98815),x98814)))
% 109.14/108.85 [9892]~E(x98922,x98924)+P1(f318(f318(f320(f917(f912(x98921),f912(x98921))),f318(f318(f243(f912(x98921),f912(x98921)),f318(f318(f125(x98921),x98922),f318(f318(f142(x98921),x98923),f104(x98921)))),f318(f318(f125(x98921),x98924),f318(f318(f142(x98921),x98925),f104(x98921))))),f148(x98921,x98926)))+~P1(f318(f318(f320(f917(x98921,x98921)),f318(f318(f243(x98921,x98921),x98923),x98925)),x98926))
% 109.14/108.85 [9984]E(x99841,x99842)+~P1(f318(f318(f320(f917(f912(x99843),f912(x99843))),f318(f318(f243(f912(x99843),f912(x99843)),f318(f318(f125(x99843),x99845),f318(f318(f142(x99843),x99841),f104(x99843)))),f318(f318(f125(x99843),x99846),f318(f318(f142(x99843),x99842),f104(x99843))))),f148(x99843,x99844)))+P1(f318(f318(f320(f917(x99843,x99843)),f318(f318(f243(x99843,x99843),x99841),x99842)),x99844))
% 109.14/108.85 [10013]~P1(f318(f318(f320(f917(f912(x100131),f912(x100131))),f318(f318(f243(f912(x100131),f912(x100131)),f318(f318(f125(x100131),x100135),f318(f318(f142(x100131),x100132),f104(x100131)))),f318(f318(f125(x100131),x100136),f318(f318(f142(x100131),x100133),f104(x100131))))),f148(x100131,x100134)))+P1(f318(f318(f320(f917(f912(x100131),f912(x100131))),f318(f318(f243(f912(x100131),f912(x100131)),x100135),x100136)),f148(x100131,x100134)))+P1(f318(f318(f320(f917(x100131,x100131)),f318(f318(f243(x100131,x100131),x100132),x100133)),x100134))
% 109.14/108.85 [10037]P1(f318(x100371,x100372))+P1(f318(f318(f320(x100373),f872(x100371,x100374,x100375,x100376,x100373)),f318(x100374,f873(x100371,x100374,x100375,x100376,x100373))))+~P1(f318(f318(f320(x100373),x100372),f318(f318(f33(x100376,f918(x100373,a909)),x100375),x100374)))
% 109.14/108.85 [10160]P1(f318(f318(f320(x101601),f831(x101602,x101603,x101604,x101605,x101606,x101601)),x101605))+~P1(f318(f318(f225(f918(x101601,a909)),x101606),x101605))+P1(f318(f318(f225(f918(x101604,a909)),f318(f318(f34(x101601,f918(x101604,a909)),x101605),x101603)),f318(f318(f34(x101601,f918(x101604,a909)),x101605),x101602)))
% 109.14/108.85 [10284]~P1(f318(f318(f225(f918(x102841,a909)),f318(x102844,f831(x102845,x102844,x102841,x102843,x102846,x102842))),f318(x102845,f831(x102845,x102844,x102841,x102843,x102846,x102842))))+~P1(f318(f318(f225(f918(x102842,a909)),x102846),x102843))+P1(f318(f318(f225(f918(x102841,a909)),f318(f318(f34(x102842,f918(x102841,a909)),x102843),x102844)),f318(f318(f34(x102842,f918(x102841,a909)),x102843),x102845)))
% 109.14/108.85 [8994]~P16(x89943,x89944,x89941)+~P1(f318(f55(x89943),x89946))+E(f318(f318(x89941,x89942),f318(f318(f58(x89943,x89944,x89941),x89945),f318(f318(f3(f918(x89943,a909)),x89946),f318(f318(f300(x89943),x89942),f179(f918(x89943,a909)))))),f318(f318(f58(x89943,x89944,x89941),x89945),f318(f318(f300(x89943),x89942),x89946)))
% 109.14/108.85 [9285]~P1(f318(f318(f320(x92855),x92853),x92856))+P1(f318(f318(f225(f918(x92851,a909)),f318(x92852,x92853)),x92854))+~P1(f318(f318(f225(f918(x92851,a909)),f318(f318(f33(x92855,f918(x92851,a909)),x92856),x92852)),x92854))
% 109.14/108.85 [9956]~P8(x99561,x99565,x99564)+P1(f318(f318(f320(f917(x99561,x99561)),f318(f318(f243(x99561,x99561),x99562),x99563)),x99564))+~P1(f318(f318(f320(x99561),x99566),f318(f318(f92(f918(x99561,a909)),f318(f276(x99561,x99561,x99564),f318(f318(f300(x99561),x99562),f179(f918(x99561,a909))))),f318(f276(x99561,x99561,x99564),f318(f318(f300(x99561),x99563),f179(f918(x99561,a909)))))))
% 109.14/108.85 [8719]~P129(x87192)+~E(f318(f318(f73(x87192),f318(f318(f74(x87192),x87194),x87195)),x87191),f318(f318(f73(x87192),f318(f318(f74(x87192),x87193),x87195)),x87196))+E(x87191,f318(f318(f73(x87192),f318(f318(f74(x87192),f318(f318(f3(x87192),x87193),x87194)),x87195)),x87196))
% 109.14/108.85 [8720]~P129(x87201)+~E(f318(f318(f73(x87201),f318(f318(f74(x87201),x87202),x87204)),x87205),f318(f318(f73(x87201),f318(f318(f74(x87201),x87203),x87204)),x87206))+E(f318(f318(f73(x87201),f318(f318(f74(x87201),f318(f318(f3(x87201),x87202),x87203)),x87204)),x87205),x87206)
% 109.14/108.85 [8897]~P129(x88971)+E(f318(f318(f73(x88971),f318(f318(f74(x88971),x88972),x88973)),x88974),f318(f318(f73(x88971),f318(f318(f74(x88971),x88975),x88973)),x88976))+~E(x88976,f318(f318(f73(x88971),f318(f318(f74(x88971),f318(f318(f3(x88971),x88972),x88975)),x88973)),x88974))
% 109.14/108.85 [8898]~P129(x88981)+E(f318(f318(f73(x88981),f318(f318(f74(x88981),x88982),x88983)),x88984),f318(f318(f73(x88981),f318(f318(f74(x88981),x88985),x88983)),x88986))+~E(f318(f318(f73(x88981),f318(f318(f74(x88981),f318(f318(f3(x88981),x88982),x88985)),x88983)),x88984),x88986)
% 109.14/108.85 [9221]~P1(f318(f318(x92214,x92215),x92216))+~P1(f318(f318(x92213,x92215),x92216))+P1(f318(f318(f318(f318(f92(f918(x92211,f918(x92212,a909))),x92213),x92214),x92215),x92216))
% 109.14/108.85 [9490]P1(f318(f318(x94901,x94902),x94903))+P1(f318(f318(x94904,x94902),x94903))+~P1(f318(f318(f318(f318(f101(f918(x94905,f918(x94906,a909))),x94904),x94901),x94902),x94903))
% 109.14/108.85 [9798]~P140(x97981)+~P1(f318(f318(f225(x97981),f318(f318(f73(x97981),f318(f318(f74(x97981),x97984),x97985)),x97982)),f318(f318(f73(x97981),f318(f318(f74(x97981),x97983),x97985)),x97986)))+P1(f318(f318(f225(x97981),x97982),f318(f318(f73(x97981),f318(f318(f74(x97981),f318(f318(f3(x97981),x97983),x97984)),x97985)),x97986)))
% 109.14/108.85 [9799]~P140(x97991)+~P1(f318(f318(f226(x97991),f318(f318(f73(x97991),f318(f318(f74(x97991),x97994),x97995)),x97992)),f318(f318(f73(x97991),f318(f318(f74(x97991),x97993),x97995)),x97996)))+P1(f318(f318(f226(x97991),x97992),f318(f318(f73(x97991),f318(f318(f74(x97991),f318(f318(f3(x97991),x97993),x97994)),x97995)),x97996)))
% 109.14/108.85 [9831]~P140(x98311)+P1(f318(f318(f225(x98311),f318(f318(f73(x98311),f318(f318(f74(x98311),x98312),x98313)),x98314)),f318(f318(f73(x98311),f318(f318(f74(x98311),x98315),x98313)),x98316)))+~P1(f318(f318(f225(x98311),x98314),f318(f318(f73(x98311),f318(f318(f74(x98311),f318(f318(f3(x98311),x98315),x98312)),x98313)),x98316)))
% 109.14/108.85 [9832]~P140(x98321)+P1(f318(f318(f226(x98321),f318(f318(f73(x98321),f318(f318(f74(x98321),x98322),x98323)),x98324)),f318(f318(f73(x98321),f318(f318(f74(x98321),x98325),x98323)),x98326)))+~P1(f318(f318(f226(x98321),x98324),f318(f318(f73(x98321),f318(f318(f74(x98321),f318(f318(f3(x98321),x98325),x98322)),x98323)),x98326)))
% 109.14/108.85 [9948]~P140(x99481)+~P1(f318(f318(f225(x99481),f318(f318(f73(x99481),f318(f318(f74(x99481),x99482),x99484)),x99485)),f318(f318(f73(x99481),f318(f318(f74(x99481),x99483),x99484)),x99486)))+P1(f318(f318(f225(x99481),f318(f318(f73(x99481),f318(f318(f74(x99481),f318(f318(f3(x99481),x99482),x99483)),x99484)),x99485)),x99486))
% 109.14/108.85 [9949]~P140(x99491)+~P1(f318(f318(f226(x99491),f318(f318(f73(x99491),f318(f318(f74(x99491),x99492),x99494)),x99495)),f318(f318(f73(x99491),f318(f318(f74(x99491),x99493),x99494)),x99496)))+P1(f318(f318(f226(x99491),f318(f318(f73(x99491),f318(f318(f74(x99491),f318(f318(f3(x99491),x99492),x99493)),x99494)),x99495)),x99496))
% 109.14/108.85 [9996]~P140(x99961)+P1(f318(f318(f225(x99961),f318(f318(f73(x99961),f318(f318(f74(x99961),x99962),x99963)),x99964)),f318(f318(f73(x99961),f318(f318(f74(x99961),x99965),x99963)),x99966)))+~P1(f318(f318(f225(x99961),f318(f318(f73(x99961),f318(f318(f74(x99961),f318(f318(f3(x99961),x99962),x99965)),x99963)),x99964)),x99966))
% 109.14/108.85 [9997]~P140(x99971)+P1(f318(f318(f226(x99971),f318(f318(f73(x99971),f318(f318(f74(x99971),x99972),x99973)),x99974)),f318(f318(f73(x99971),f318(f318(f74(x99971),x99975),x99973)),x99976)))+~P1(f318(f318(f226(x99971),f318(f318(f73(x99971),f318(f318(f74(x99971),f318(f318(f3(x99971),x99972),x99975)),x99973)),x99974)),x99976))
% 109.14/108.85 [10147]~P76(x101472)+~P1(f318(f55(x101471),x101476))+E(f318(f318(f8(x101471,x101472),f318(f318(f20(x101471,x101472,x101472),f318(f318(f20(x101471,x101472,f918(x101472,x101472)),f318(f318(f10(a909,f918(x101472,f918(x101472,x101472)),x101471),f85(x101472)),x101473)),x101474)),x101475)),x101476),f318(f318(f73(x101472),f318(f318(f8(x101471,x101472),x101474),f318(f318(f92(f918(x101471,a909)),x101476),f318(f253(x101471),x101473)))),f318(f318(f8(x101471,x101472),x101475),f318(f318(f92(f918(x101471,a909)),x101476),f318(f72(f918(x101471,a909)),f318(f253(x101471),x101473))))))
% 109.14/108.85 [10207]P1(f318(f318(f320(x102072),x102074),x102076))+P1(f318(f318(f320(x102072),x102075),x102076))+E(f318(f302(x102071,x102072,f318(f318(f9(x102071,x102072,x102072),f318(f318(f9(x102071,x102072,f918(x102072,x102072)),f318(f318(f10(a909,f918(x102072,f918(x102072,x102072)),x102071),f85(x102072)),f318(f318(f9(x102071,f918(x102071,a909),a909),f320(x102071)),x102073))),x102074)),x102075)),x102076),f179(f918(x102071,a909)))
% 109.14/108.85 [10208]P1(f318(f318(f320(x102082),x102085),x102086))+~P1(f318(f318(f320(x102082),x102084),x102086))+E(f318(f302(x102081,x102082,f318(f318(f9(x102081,x102082,x102082),f318(f318(f9(x102081,x102082,f918(x102082,x102082)),f318(f318(f10(a909,f918(x102082,f918(x102082,x102082)),x102081),f85(x102082)),f318(f318(f9(x102081,f918(x102081,a909),a909),f320(x102081)),x102083))),x102084)),x102085)),x102086),x102083)
% 109.14/108.85 [10209]P1(f318(f318(f320(x102092),x102094),x102096))+~P1(f318(f318(f320(x102092),x102095),x102096))+E(f318(f302(x102091,x102092,f318(f318(f9(x102091,x102092,x102092),f318(f318(f9(x102091,x102092,f918(x102092,x102092)),f318(f318(f10(a909,f918(x102092,f918(x102092,x102092)),x102091),f85(x102092)),f318(f318(f9(x102091,f918(x102091,a909),a909),f320(x102091)),x102093))),x102094)),x102095)),x102096),f318(f72(f918(x102091,a909)),x102093))
% 109.14/108.85 [10210]~P1(f318(f318(f320(x102102),x102104),x102106))+~P1(f318(f318(f320(x102102),x102105),x102106))+E(f318(f302(x102101,x102102,f318(f318(f9(x102101,x102102,x102102),f318(f318(f9(x102101,x102102,f918(x102102,x102102)),f318(f318(f10(a909,f918(x102102,f918(x102102,x102102)),x102101),f85(x102102)),f318(f318(f9(x102101,f918(x102101,a909),a909),f320(x102101)),x102103))),x102104)),x102105)),x102106),f233(f918(x102101,a909)))
% 109.14/108.85 [8751]E(x87511,x87512)+~P60(x87514,x87515,x87513,x87516,x87517)+~E(f318(x87513,x87511),f318(x87513,x87512))
% 109.14/108.85 [8780]~P10(x87806,x87805,x87807,x87804,x87801)+E(f318(f318(x87801,x87802),x87803),x87804)+P1(f318(f55(x87805),x87803))
% 109.14/108.85 [8781]~P10(x87816,x87815,x87817,x87814,x87811)+E(f318(f318(x87811,x87812),x87813),x87814)+P1(f318(f55(x87815),x87813))
% 109.14/108.85 [9646]P45(x96461,x96462,x96463,x96464,x96465,f318(f318(x96463,x96466),x96467))+~E(f318(f318(x96463,x96466),x96467),x96464)+~E(x96465,f179(f918(x96461,a909)))
% 109.14/108.85 [9851]~P1(f318(x98516,x98513))+~P1(f318(f318(f320(f917(x98512,x98512)),f318(f318(f243(x98512,x98512),x98514),x98515)),f318(x98517,x98513)))+P1(f318(f318(f320(f917(f917(x98511,x98512),f917(x98511,x98512))),f318(f318(f243(f917(x98511,x98512),f917(x98511,x98512)),f318(f318(f243(x98511,x98512),x98513),x98514)),f318(f318(f243(x98511,x98512),x98513),x98515))),f271(x98511,x98512,x98516,x98517)))
% 109.14/108.85 [10274]~P45(x102742,x102747,x102743,x102746,x102741,f318(f318(x102743,x102745),x102744))+E(f318(f318(x102743,f443(x102744,x102745,x102741,x102746,x102743,x102747,x102742)),f444(x102744,x102745,x102741,x102746,x102743,x102747,x102742)),f318(f318(x102743,x102745),x102744))+E(x102741,f179(f918(x102742,a909)))
% 109.14/108.85 [10275]~P45(x102757,x102756,x102751,x102754,x102755,f318(f318(x102751,x102752),x102753))+E(f318(f318(x102751,f443(x102753,x102752,x102755,x102754,x102751,x102756,x102757)),f444(x102753,x102752,x102755,x102754,x102751,x102756,x102757)),f318(f318(x102751,x102752),x102753))+E(f318(f318(x102751,x102752),x102753),x102754)
% 109.14/108.85 [9323]~P36(x93231,x93232,x93233,x93235,x93237)+P36(x93231,x93232,x93233,f318(f318(f142(x93231),x93234),x93235),f318(f318(f142(x93232),x93236),x93237))+~P1(f318(f318(x93233,x93234),x93236))
% 109.14/108.85 [9341]P36(x93411,x93412,x93413,x93414,x93415)+~P36(x93411,x93412,x93413,f318(f318(f125(x93411),x93416),x93414),f318(f318(f125(x93412),x93417),x93415))+~E(f318(f180(f912(x93411)),x93416),f318(f180(f912(x93412)),x93417))
% 109.14/108.85 [9342]P36(x93421,x93422,x93423,x93424,x93425)+~P36(x93421,x93422,x93423,f318(f318(f125(x93421),x93424),x93426),f318(f318(f125(x93422),x93425),x93427))+~E(f318(f180(f912(x93421)),x93424),f318(f180(f912(x93422)),x93425))
% 109.14/108.85 [9561]~P36(x95611,x95612,x95613,x95615,x95617)+~P36(x95611,x95612,x95613,x95614,x95616)+P36(x95611,x95612,x95613,f318(f318(f125(x95611),x95614),x95615),f318(f318(f125(x95612),x95616),x95617))
% 109.14/108.85 [9932]~P1(f318(f60(x99321,x99324,x99325,x99326,x99323),x99327))+P1(f318(f60(x99321,x99324,x99325,x99326,f318(f318(f300(x99321),x99322),x99323)),f318(f318(x99325,x99322),x99327)))+P1(f318(f318(f320(x99321),x99322),x99323))
% 109.14/108.85 [10301]~P45(x103012,x103017,x103016,x103015,x103011,f318(f318(x103016,x103014),x103013))+E(x103011,f179(f918(x103012,a909)))+P1(f318(f318(f320(x103012),f443(x103013,x103014,x103011,x103015,x103016,x103017,x103012)),x103011))
% 109.14/108.85 [10302]~P45(x103025,x103027,x103021,x103024,x103026,f318(f318(x103021,x103022),x103023))+E(f318(f318(x103021,x103022),x103023),x103024)+P1(f318(f318(f320(x103025),f443(x103023,x103022,x103026,x103024,x103021,x103027,x103025)),x103026))
% 109.14/108.85 [10435]E(f318(f318(f243(x104351,x104352),x104353),x104354),f318(f318(f243(x104351,x104352),x104355),x104356))+P1(f318(f318(f320(f917(f917(x104351,x104352),f917(x104351,x104352))),f318(f318(f243(f917(x104351,x104352),f917(x104351,x104352)),f318(f318(f243(x104351,x104352),f832(x104357,x104354,x104353,x104356,x104355,x104352,x104351)),f837(x104357,x104354,x104353,x104356,x104355,x104352,x104351))),f318(f318(f243(x104351,x104352),x104353),x104354))),f298(f917(x104351,x104352),x104357)))+~P1(f318(f318(f320(f917(f917(x104351,x104352),f917(x104351,x104352))),f318(f318(f243(f917(x104351,x104352),f917(x104351,x104352)),f318(f318(f243(x104351,x104352),x104355),x104356)),f318(f318(f243(x104351,x104352),x104353),x104354))),f298(f917(x104351,x104352),x104357)))
% 109.14/108.85 [9021]~P21(x90214,x90215,x90216,x90217,x90211)+~P1(f318(f55(x90215),x90213))+E(f318(f318(x90211,x90212),x90213),f318(f318(f318(f59(x90214,x90215,x90216),x90212),x90217),x90213))
% 109.14/108.85 [9022]~P10(x90224,x90225,x90226,x90227,x90221)+~P1(f318(f55(x90225),x90223))+E(f318(f318(x90221,x90222),x90223),f318(f318(f318(f59(x90224,x90225,x90226),x90222),x90227),x90223))
% 109.14/108.85 [9825]~P23(x98253,x98254,x98255,x98257,x98256,x98251)+~P1(f318(f55(x98254),x98252))+E(f318(x98251,x98252),f318(f318(f318(f59(x98253,x98254,x98255),x98256),x98257),x98252))
% 109.14/108.85 [9992]P45(x99921,x99922,x99923,x99924,x99925,f318(f318(x99923,x99926),x99927))+~P45(x99921,x99922,x99923,x99924,f318(f318(f3(f918(x99921,a909)),x99925),f318(f318(f300(x99921),x99926),f179(f918(x99921,a909)))),x99927)+~P1(f318(f318(f320(x99921),x99926),x99925))
% 109.14/108.85 [10347]P1(f318(f318(x103477,f784(x103474,x103475,x103471,x103476,x103473,x103472,x103477)),f785(x103474,x103475,x103471,x103476,x103473,x103472,x103477)))+~P1(f318(f318(x103477,f318(f247(x103472,x103473),x103476)),f318(f242(x103472,x103473),x103476)))+P1(f318(x103471,f318(f318(f248(x103472,x103473,x103474),x103475),x103476)))
% 109.14/108.86 [10358]~P45(x103582,x103583,x103584,x103585,x103581,f318(f318(x103584,x103587),x103586))+P45(x103582,x103583,x103584,x103585,f318(f318(f3(f918(x103582,a909)),x103581),f318(f318(f300(x103582),f443(x103586,x103587,x103581,x103585,x103584,x103583,x103582)),f179(f918(x103582,a909)))),f444(x103586,x103587,x103581,x103585,x103584,x103583,x103582))+E(x103581,f179(f918(x103582,a909)))
% 109.14/108.86 [10359]~P45(x103595,x103596,x103591,x103594,x103597,f318(f318(x103591,x103592),x103593))+P45(x103595,x103596,x103591,x103594,f318(f318(f3(f918(x103595,a909)),x103597),f318(f318(f300(x103595),f443(x103593,x103592,x103597,x103594,x103591,x103596,x103595)),f179(f918(x103595,a909)))),f444(x103593,x103592,x103597,x103594,x103591,x103596,x103595))+E(f318(f318(x103591,x103592),x103593),x103594)
% 109.14/108.86 [10392]~P1(f318(x103921,f318(f318(x103925,f785(x103924,x103925,x103921,x103926,x103923,x103922,x103927)),f784(x103924,x103925,x103921,x103926,x103923,x103922,x103927))))+~P1(f318(f318(x103927,f318(f247(x103922,x103923),x103926)),f318(f242(x103922,x103923),x103926)))+P1(f318(x103921,f318(f318(f248(x103922,x103923,x103924),x103925),x103926)))
% 109.14/108.86 [9631]P1(f318(f318(f225(f918(f917(x96311,x96312),a909)),f318(f318(f280(x96311,x96313,x96312),x96314),x96315)),f318(f318(f280(x96311,x96313,x96312),x96316),x96317)))+~P1(f318(f318(f225(f918(f917(x96313,x96312),a909)),x96315),x96317))+~P1(f318(f318(f225(f918(f917(x96311,x96313),a909)),x96314),x96316))
% 109.14/108.86 [10426]E(f318(f318(f243(x104261,x104262),x104263),x104264),f318(f318(f243(x104261,x104262),x104265),x104266))+~P1(f318(f318(f320(f917(f917(x104261,x104262),f917(x104261,x104262))),f318(f318(f243(f917(x104261,x104262),f917(x104261,x104262)),f318(f318(f243(x104261,x104262),x104263),x104264)),f318(f318(f243(x104261,x104262),x104265),x104266))),f298(f917(x104261,x104262),x104267)))+P1(f318(f318(f320(f917(f917(x104261,x104262),f917(x104261,x104262))),f318(f318(f243(f917(x104261,x104262),f917(x104261,x104262)),f318(f318(f243(x104261,x104262),x104263),x104264)),f318(f318(f243(x104261,x104262),f832(x104267,x104266,x104265,x104264,x104263,x104262,x104261)),f837(x104267,x104266,x104265,x104264,x104263,x104262,x104261)))),x104267))
% 109.14/108.86 [10002]~P1(f318(f318(f320(x100021),x100026),x100025))+P1(f318(f60(x100021,x100022,x100023,x100024,x100025),f318(f318(x100023,x100026),x100027)))+~P1(f318(f60(x100021,x100022,x100023,x100024,f318(f318(f3(f918(x100021,a909)),x100025),f318(f318(f300(x100021),x100026),f179(f918(x100021,a909))))),x100027))
% 109.14/108.86 [10442]~P146(x104421)+~P25(f917(x104422,x104423),x104421,f318(f248(x104422,x104423,x104421),f318(f318(f9(x104422,f918(x104423,x104421),f918(x104423,x104421)),f318(f318(f10(f918(x104421,x104421),f918(f918(x104423,x104421),f918(x104423,x104421)),x104422),f10(x104421,x104421,x104423)),f318(f318(f10(x104421,f918(x104421,x104421),x104422),f74(x104421)),x104424))),x104425)),f318(f318(f245(x104422,x104423),x104426),f318(f18(f918(x104423,a909),x104422),x104427)))+E(f318(f318(f8(x104421,x104421),f25(x104421)),f318(f253(x104421),f318(f318(f10(f918(x104422,a909),a909,x104421),f79(x104422)),f318(f318(f10(f918(x104422,f918(x104423,a909)),f918(x104422,a909),x104421),f318(f10(f918(x104423,a909),a909,x104422),f79(x104423))),f318(f318(f9(x104421,f918(x104422,f918(x104423,a909)),f918(x104422,f918(x104423,a909))),f318(f318(f10(f918(x104422,f918(f918(x104423,a909),f918(x104423,a909))),f918(f918(x104422,f918(x104423,a909)),f918(x104422,f918(x104423,a909))),x104421),f20(x104422,f918(x104423,a909),f918(x104423,a909))),f318(f318(f10(f918(x104422,f918(x104423,f918(a909,a909))),f918(x104422,f918(f918(x104423,a909),f918(x104423,a909))),x104421),f318(f10(f918(x104423,f918(a909,a909)),f918(f918(x104423,a909),f918(x104423,a909)),x104422),f20(x104423,a909,a909))),f318(f318(f10(f918(x104422,f918(x104423,a909)),f918(x104422,f918(x104423,f918(a909,a909))),x104421),f318(f10(f918(x104423,a909),f918(x104423,f918(a909,a909)),x104422),f318(f10(a909,f918(a909,a909),x104423),a316))),f318(f318(f9(x104421,f918(x104422,f918(x104423,x104421)),f918(x104422,f918(x104423,a909))),f318(f318(f10(f918(f918(x104423,x104421),f918(x104423,a909)),f918(f918(x104422,f918(x104423,x104421)),f918(x104422,f918(x104423,a909))),x104421),f10(f918(x104423,x104421),f918(x104423,a909),x104422)),f318(f318(f10(f918(x104421,a909),f918(f918(x104423,x104421),f918(x104423,a909)),x104421),f10(x104421,a909,x104423)),a315))),f318(f318(f9(x104422,f918(x104423,x104421),f918(x104423,x104421)),f318(f318(f10(f918(x104421,x104421),f918(f918(x104423,x104421),f918(x104423,x104421)),x104422),f10(x104421,x104421,x104423)),f318(f318(f10(x104421,f918(x104421,x104421),x104422),f74(x104421)),x104424))),x104425)))))),f318(f318(f9(x104422,f918(x104423,a909),f918(x104423,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x104423,a909),f918(x104423,a909)),x104422),f10(a909,a909,x104423)),f318(f318(f10(a909,f918(a909,a909),x104422),a316),f318(f318(f9(x104422,f918(x104422,a909),a909),f320(x104422)),x104426)))),f318(f318(f9(x104423,f918(x104423,a909),a909),f320(x104423)),x104427))))))),f318(f318(f74(x104421),f318(f318(f8(x104422,x104421),x104424),x104426)),f318(f318(f8(x104423,x104421),x104425),x104427)))
% 109.14/108.86 [9634]~P26(x96343,x96342,x96344,x96348,x96347)+~P26(x96341,x96343,x96345,x96346,x96348)+P26(x96341,x96342,f318(f66(x96343,x96342,x96341,x96344),x96345),x96346,x96347)
% 109.14/108.86 [9635]~P26(x96351,x96353,x96355,x96356,x96358)+~P26(x96353,x96352,x96354,x96358,x96357)+P26(x96351,x96352,f318(f66(x96353,x96352,x96351,x96354),x96355),x96356,x96357)
% 109.14/108.86 [9668]P26(x96681,x96682,x96683,x96684,x96685)+~P26(x96686,x96681,x96687,x96688,x96684)+~P26(x96686,x96682,f318(f66(x96681,x96682,x96686,x96683),x96687),x96688,x96685)
% 109.14/108.86 [9822]~P1(f318(f318(x98224,x98226),x98228))+~P1(f318(f318(x98225,x98228),x98227))+P1(f318(f318(f244(x98221,x98222,x98223,x98224,x98225),x98226),x98227))
% 109.14/108.86 [9823]~P1(f318(f318(x98234,x98236),x98238))+~P1(f318(f318(x98235,x98238),x98237))+P1(f318(f318(f244(x98231,x98232,x98233,x98234,x98235),x98236),x98237))
% 109.14/108.86 [9392]~P19(x93928,x93921,x93923,x93925)+~P1(f318(f55(x93928),x93926))+E(f318(f66(x93921,x93921,x93922,f318(x93923,x93924)),f318(f66(x93921,x93921,x93922,f318(x93925,x93926)),x93927)),f318(f66(x93921,x93921,x93922,f318(x93925,x93926)),f318(f66(x93921,x93921,x93922,f318(x93923,x93924)),x93927)))
% 109.14/108.86 [9809]~P22(x98097,x98092,x98095,x98098,x98096,x98091)+~P1(f318(f55(x98092),x98094))+E(f318(x98091,f318(f318(f300(x98092),x98093),x98094)),f318(f318(x98095,f318(x98096,x98093)),f318(x98091,x98094)))
% 109.14/108.86 [9945]~P25(x99452,x99454,x99456,x99458)+~P25(x99451,x99453,x99455,x99457)+P25(f917(x99451,x99452),f917(x99453,x99454),f249(x99451,x99453,x99452,x99454,x99455,x99456),f318(f318(f245(x99451,x99452),x99457),f318(f18(f918(x99452,a909),x99451),x99458)))
% 109.14/108.86 [9581]P1(f318(f318(f320(f917(x95811,x95812)),f318(f318(f243(x95811,x95812),x95813),x95814)),f318(f318(f280(x95811,x95815,x95812),x95816),x95817)))+~P1(f318(f318(f320(f917(x95811,x95815)),f318(f318(f243(x95811,x95815),x95813),x95818)),x95816))+~P1(f318(f318(f320(f917(x95815,x95812)),f318(f318(f243(x95815,x95812),x95818),x95814)),x95817))
% 109.14/108.86 [9786]~P1(f318(f318(f225(f918(f917(x97863,x97862),a909)),x97865),f318(f318(f245(x97863,x97862),x97868),f318(f18(f918(x97862,a909),x97863),x97867))))+~P1(f318(f318(f225(f918(f917(x97861,x97863),a909)),x97864),f318(f318(f245(x97861,x97863),x97866),f318(f18(f918(x97863,a909),x97861),x97868))))+P1(f318(f318(f225(f918(f917(x97861,x97862),a909)),f318(f318(f280(x97861,x97863,x97862),x97864),x97865)),f318(f318(f245(x97861,x97862),x97866),f318(f18(f918(x97862,a909),x97861),x97867))))
% 109.14/108.86 [9845]~E(x98453,x98455)+P1(f318(f318(f320(f917(f917(x98451,x98452),f917(x98451,x98452))),f318(f318(f243(f917(x98451,x98452),f917(x98451,x98452)),f318(f318(f243(x98451,x98452),x98453),x98454)),f318(f318(f243(x98451,x98452),x98455),x98456))),f311(x98451,x98452,x98457,x98458)))+~P1(f318(f318(f320(f917(x98452,x98452)),f318(f318(f243(x98452,x98452),x98454),x98456)),x98458))
% 109.14/108.86 [9969]E(x99691,x99692)+~P1(f318(f318(f320(f917(f917(x99693,x99695),f917(x99693,x99695))),f318(f318(f243(f917(x99693,x99695),f917(x99693,x99695)),f318(f318(f243(x99693,x99695),x99691),x99696)),f318(f318(f243(x99693,x99695),x99692),x99697))),f311(x99693,x99695,x99694,x99698)))+P1(f318(f318(f320(f917(x99693,x99693)),f318(f318(f243(x99693,x99693),x99691),x99692)),x99694))
% 109.14/108.86 [9983]~P1(f318(f318(f320(f917(f917(x99831,x99835),f917(x99831,x99835))),f318(f318(f243(f917(x99831,x99835),f917(x99831,x99835)),f318(f318(f243(x99831,x99835),x99832),x99836)),f318(f318(f243(x99831,x99835),x99833),x99837))),f311(x99831,x99835,x99834,x99838)))+P1(f318(f318(f320(f917(x99831,x99831)),f318(f318(f243(x99831,x99831),x99832),x99833)),x99834))+P1(f318(f318(f320(f917(x99835,x99835)),f318(f318(f243(x99835,x99835),x99836),x99837)),x99838))
% 109.14/108.86 [9882]~P23(x98827,x98825,x98821,x98828,x98822,x98824)+~P1(f318(f55(x98825),x98826))+E(f318(f318(x98821,f318(x98822,x98823)),f318(x98824,f318(f318(f3(f918(x98825,a909)),x98826),f318(f318(f300(x98825),x98823),f179(f918(x98825,a909)))))),f318(x98824,f318(f318(f300(x98825),x98823),x98826)))
% 109.14/108.86 [9346]~P1(f318(f318(f318(x93465,x93468),x93466),x93467))+~P1(f318(f318(f320(x93461),x93468),x93464))+P1(f318(f318(f318(f318(f33(x93461,f918(x93462,f918(x93463,a909))),x93464),x93465),x93466),x93467))
% 109.14/108.86 [9347]~P1(f318(f318(f318(x93475,x93478),x93476),x93477))+~P1(f318(f318(f320(x93471),x93478),x93474))+P1(f318(f318(f318(f318(f33(x93471,f918(x93472,f918(x93473,a909))),x93474),x93475),x93476),x93477))
% 109.14/108.86 [9567]P1(f318(f318(f318(x95671,x95672),x95673),x95674))+~P1(f318(f318(f320(x95675),x95672),x95676))+~P1(f318(f318(f318(f318(f34(x95675,f918(x95677,f918(x95678,a909))),x95676),x95671),x95673),x95674))
% 109.14/108.86 [9568]P1(f318(f318(f318(x95681,x95682),x95683),x95684))+~P1(f318(f318(f320(x95685),x95682),x95686))+~P1(f318(f318(f318(f318(f34(x95685,f918(x95687,f918(x95688,a909))),x95686),x95681),x95683),x95684))
% 109.14/108.86 [9569]P1(f318(f318(f318(x95691,x95692),x95693),x95694))+~P1(f318(f318(f320(x95695),x95692),x95696))+~P1(f318(f318(f318(f318(f34(x95695,f918(x95697,f918(x95698,a909))),x95696),x95691),x95693),x95694))
% 109.14/108.86 [9779]~P21(x97793,x97792,x97794,x97798,x97791)+~P1(f318(f55(x97792),x97797))+E(f318(f318(x97791,f318(f318(f20(x97792,x97793,x97793),f318(f318(f10(x97793,f918(x97793,x97793),x97792),x97794),x97795)),x97796)),x97797),f318(f318(x97794,f318(f318(x97791,x97795),x97797)),f318(f318(x97791,x97796),x97797)))
% 109.14/108.86 [10062]~E(f318(f301(x100622,x100624,x100626),x100628),x1006210)+~E(f318(f301(x100621,x100623,x100625),x100627),x100629)+E(f318(f301(f917(x100621,x100622),f917(x100623,x100624),f249(x100621,x100623,x100622,x100624,x100625,x100626)),f318(f318(f245(x100621,x100622),x100627),f318(f18(f918(x100622,a909),x100621),x100628))),f318(f318(f245(x100623,x100624),x100629),f318(f18(f918(x100624,a909),x100623),x1006210)))
% 109.14/108.86 [5001]~P51(x50011,x50012)+~P53(x50011,x50012)+~P54(x50011,x50012)+P7(x50011,x50012)
% 109.14/108.86 [5002]~P51(x50021,x50022)+~P53(x50021,x50022)+~P54(x50021,x50022)+P7(x50021,x50022)
% 109.14/108.86 [4958]~P4(x49582)+~P13(x49582,x49581)+P13(x49582,f105(x49582,x49581))+E(x49581,f104(x49582))
% 109.14/108.86 [4959]~P4(x49592)+~P13(x49592,x49591)+P13(x49592,f703(x49591,x49592))+E(x49591,f104(x49592))
% 109.14/108.86 [5202]~P5(x52022)+E(f12(x52022,x52021),f32(x52022,x52021))+E(x52021,f179(f918(x52022,a909)))+~P1(f318(f55(x52022),x52021))
% 109.14/108.86 [5203]~P5(x52032)+E(f15(x52032,x52031),f31(x52032,x52031))+E(x52031,f179(f918(x52032,a909)))+~P1(f318(f55(x52032),x52031))
% 109.14/108.86 [5366]~P4(x53662)+~P13(x53662,x53661)+E(x53661,f104(x53662))+E(f318(f318(f142(x53662),f722(x53661,x53662)),f703(x53661,x53662)),x53661)
% 109.14/108.86 [6180]~P103(x61802)+E(x61801,f179(f918(x61802,a909)))+P1(f318(f318(f225(x61802),f12(x61802,x61801)),f15(x61802,x61801)))+~P1(f318(f55(x61802),x61801))
% 109.14/108.86 [6191]~P43(x61912)+~P43(x61911)+E(x61911,x61912)+~E(f318(f301(a1,a911,a95),x61911),f318(f301(a1,a911,a95),x61912))
% 109.14/108.86 [9202]~P116(x92021)+~P1(f318(f318(f320(x92021),x92022),f100(x92021)))+P1(f318(f318(f226(x92021),f318(f318(f73(x92021),f318(f318(f73(x92021),f71(x92021)),x92022)),x92022)),f2(x92021)))+~P1(f318(f318(f226(x92021),x92022),f2(x92021)))
% 109.14/108.86 [9450]~P116(x94501)+~P1(f318(f318(f320(x94501),x94502),f100(x94501)))+~P1(f318(f318(f226(x94501),f318(f318(f73(x94501),f318(f318(f73(x94501),f71(x94501)),x94502)),x94502)),f2(x94501)))+P1(f318(f318(f226(x94501),x94502),f2(x94501)))
% 109.14/108.86 [5017]~P118(x50172)+~P146(x50172)+E(x50171,f2(a911))+E(f318(f318(f235(x50172),f2(x50172)),x50171),f2(x50172))
% 109.14/108.86 [5020]~P118(x50201)+~P146(x50201)+~E(x50202,f2(a911))+E(f318(f318(f235(x50201),f2(x50201)),x50202),f71(x50201))
% 109.14/108.86 [5188]~P145(x51882)+E(x51881,f71(x51882))+E(x51881,f318(f72(x51882),f71(x51882)))+~E(f318(f318(f74(x51882),x51881),x51881),f71(x51882))
% 109.14/108.86 [5442]~P94(x54422)+E(x54421,f2(x54422))+E(f75(x54422,x54421),f318(f72(x54422),f71(x54422)))+P1(f318(f318(f226(x54422),f2(x54422)),x54421))
% 109.14/108.86 [5636]~E(x56362,f71(a1))+~E(x56361,f71(a1))+E(f318(f318(f74(a1),x56361),x56362),f71(a1))+~P1(f318(f318(f226(a1),f2(a1)),x56361))
% 109.14/108.86 [5682]~P94(x56822)+E(f75(x56822,x56821),f71(x56822))+E(x56821,f2(x56822))+~P1(f318(f318(f226(x56822),f2(x56822)),x56821))
% 109.14/108.86 [5691]E(x56911,x56912)+~E(f318(f94(a911),x56911),f318(f94(a911),x56912))+P1(f318(a184,f318(f94(a1),x56912)))+P1(f318(a184,f318(f94(a1),x56911)))
% 109.14/108.86 [5744]~P98(x57441)+~E(x57442,f2(x57441))+E(f318(f318(f73(x57441),x57442),x57442),f2(x57441))+~P1(f318(f318(f320(x57441),x57442),f100(x57441)))
% 109.14/108.86 [5784]E(x57841,f2(a1))+~E(f318(f318(f30(a1),x57842),x57841),f2(a1))+P1(f318(f318(f226(a1),x57841),x57842))+P1(f318(f318(f226(a1),x57842),x57841))
% 109.14/108.86 [5814]E(x58141,f2(a1))+~E(f318(f318(f30(a1),x58142),x58141),f2(a1))+P1(f318(f318(f225(a1),x58142),f2(a1)))+P1(f318(f318(f226(a1),x58142),x58141))
% 109.14/108.86 [5848]E(x58481,f2(a1))+~E(f318(f318(f30(a1),x58482),x58481),f2(a1))+P1(f318(f318(f225(a1),f2(a1)),x58482))+P1(f318(f318(f226(a1),x58481),x58482))
% 109.14/108.86 [5881]E(x58811,f2(a1))+~E(f318(f318(f30(a1),x58812),x58811),f2(a1))+P1(f318(f318(f225(a1),x58812),f2(a1)))+P1(f318(f318(f225(a1),f2(a1)),x58812))
% 109.14/108.86 [5883]~P98(x58832)+E(x58831,f2(x58832))+~E(f318(f318(f73(x58832),x58831),x58831),f2(x58832))+~P1(f318(f318(f320(x58832),x58831),f100(x58832)))
% 109.14/108.86 [5945]E(f318(f94(a911),x59451),f318(f94(a911),x59452))+~E(f318(f94(a1),x59452),f2(a1))+P1(f318(a184,f318(f94(a1),x59452)))+~P1(f318(a184,f318(f94(a1),x59451)))
% 109.14/108.86 [5975]~E(f318(f94(a911),x59752),f318(f94(a911),x59751))+E(f318(f94(a1),x59751),f2(a1))+P1(f318(a184,f318(f94(a1),x59751)))+~P1(f318(a184,f318(f94(a1),x59752)))
% 109.14/108.86 [5986]~P4(x59862)+E(x59861,f179(f918(x59862,a909)))+~P1(f318(f55(x59862),x59861))+P1(f318(f318(f320(x59862),f16(x59862,x59861)),x59861))
% 109.14/108.86 [5987]~P4(x59872)+E(x59871,f179(f918(x59872,a909)))+~P1(f318(f55(x59872),x59871))+P1(f318(f318(f320(x59872),f17(x59872,x59871)),x59871))
% 109.14/108.86 [6157]~P116(x61571)+~P99(x61571)+P1(f318(f318(f225(x61571),f2(x61571)),f318(f94(x61571),x61572)))+~P1(f318(f318(f225(a1),a76),x61572))
% 109.14/108.86 [6158]~P116(x61581)+~P99(x61581)+P1(f318(f318(f226(x61581),f2(x61581)),f318(f94(x61581),x61582)))+~P1(f318(f318(f226(a1),a76),x61582))
% 109.14/108.86 [6179]~P116(x61791)+~P99(x61791)+E(f318(f69(x61791),f318(f94(x61791),x61792)),f318(f94(x61791),x61792))+P1(f318(f318(f226(x61791),f318(f94(x61791),x61792)),f2(x61791)))
% 109.14/108.86 [6214]E(x62141,x62142)+~E(f318(a95,x62141),f318(a95,x62142))+~P1(f318(f318(f225(a1),f2(a1)),x62142))+~P1(f318(f318(f225(a1),f2(a1)),x62141))
% 109.14/108.86 [6215]E(x62151,x62152)+~E(f318(a95,x62151),f318(a95,x62152))+~P1(f318(f318(f225(a1),f2(a1)),x62152))+~P1(f318(f318(f225(a1),f2(a1)),x62151))
% 109.14/108.86 [6246]~E(x62461,f2(a1))+E(f40(x62461,x62462),f318(f318(f243(a1,a1),f2(a1)),f2(a1)))+P1(f318(f318(f225(a1),f2(a1)),x62462))+~P1(f318(f318(f225(a1),f2(a1)),x62461))
% 109.14/108.86 [6409]~P99(x64092)+~P116(x64092)+~P1(f318(f318(f225(x64092),f2(x64092)),f318(f94(x64092),x64091)))+P1(f318(f318(f225(a1),a76),x64091))
% 109.14/108.86 [6410]~P99(x64102)+~P116(x64102)+~P1(f318(f318(f226(x64102),f2(x64102)),f318(f94(x64102),x64101)))+P1(f318(f318(f226(a1),a76),x64101))
% 109.14/108.86 [6415]~P116(x64151)+~P99(x64151)+P1(f318(f318(f225(x64151),f318(f94(x64151),x64152)),f2(x64151)))+~P1(f318(f318(f225(a1),x64152),a76))
% 109.14/108.86 [6416]~P116(x64161)+~P99(x64161)+P1(f318(f318(f226(x64161),f318(f94(x64161),x64162)),f2(x64161)))+~P1(f318(f318(f226(a1),x64162),a76))
% 109.14/108.86 [6734]~P99(x67342)+~P116(x67342)+~P1(f318(f318(f225(x67342),f318(f94(x67342),x67341)),f2(x67342)))+P1(f318(f318(f225(a1),x67341),a76))
% 109.14/108.86 [6735]~P99(x67352)+~P116(x67352)+~P1(f318(f318(f226(x67352),f318(f94(x67352),x67351)),f2(x67352)))+P1(f318(f318(f226(a1),x67351),a76))
% 109.14/108.86 [6827]~P116(x68271)+~P99(x68271)+E(f318(f69(x68271),f318(f94(x68271),x68272)),f318(f72(x68271),f318(f94(x68271),x68272)))+~P1(f318(f318(f226(x68271),f318(f94(x68271),x68272)),f2(x68271)))
% 109.14/108.86 [6847]E(f318(f94(a911),x68471),f318(f94(a911),x68472))+~E(f318(f94(a1),x68472),f2(a1))+~P1(f318(f318(f225(a1),f318(f94(a1),x68471)),f2(a1)))+~P1(f318(a184,f318(f94(a1),x68471)))
% 109.14/108.86 [7010]E(x70101,x70102)+~E(f318(a5,x70101),f318(a5,x70102))+~P1(f318(f318(f320(a911),x70102),f233(f918(a911,a909))))+~P1(f318(f318(f320(a911),x70101),f233(f918(a911,a909))))
% 109.14/108.86 [7237]P1(f318(f318(f225(a911),f318(a95,x72371)),f318(a95,x72372)))+~P1(f318(f318(f225(a1),f2(a1)),x72372))+~P1(f318(f318(f225(a1),f2(a1)),x72371))+~P1(f318(f318(f225(a1),x72371),x72372))
% 109.14/108.86 [7238]P1(f318(f318(f226(a911),f318(a95,x72381)),f318(a95,x72382)))+~P1(f318(f318(f225(a1),f2(a1)),x72382))+~P1(f318(f318(f225(a1),f2(a1)),x72381))+~P1(f318(f318(f226(a1),x72381),x72382))
% 109.14/108.86 [7468]~P43(x74682)+~P6(x74681)+~P1(f318(f318(f320(a1),x74681),x74682))+P1(f318(f318(f320(a911),f318(a95,x74681)),f318(f301(a1,a911,a95),x74682)))
% 109.14/108.86 [7473]~P1(f318(f318(f225(a911),f318(a95,x74731)),f318(a95,x74732)))+~P1(f318(f318(f225(a1),f2(a1)),x74732))+~P1(f318(f318(f225(a1),f2(a1)),x74731))+P1(f318(f318(f225(a1),x74731),x74732))
% 109.14/108.86 [7474]~P1(f318(f318(f226(a911),f318(a95,x74741)),f318(a95,x74742)))+~P1(f318(f318(f225(a1),f2(a1)),x74742))+~P1(f318(f318(f225(a1),f2(a1)),x74741))+P1(f318(f318(f226(a1),x74741),x74742))
% 109.14/108.86 [7709]~P4(x77092)+E(x77091,f179(f918(x77092,a909)))+~P1(f318(f55(x77092),x77091))+P1(f318(f318(f225(x77092),f13(x77092,f223(x77092),x77091)),f14(x77092,f224(x77092),x77091)))
% 109.14/108.86 [8027]~P43(x80272)+~P6(x80271)+P1(f318(f318(f320(a1),x80271),x80272))+~P1(f318(f318(f320(a911),f318(a95,x80271)),f318(f301(a1,a911,a95),x80272)))
% 109.14/108.86 [5981]~P144(x59812)+E(x59811,f2(a1))+E(f318(f72(x59812),f318(f93(x59812),f318(f72(a1),x59811))),f318(f93(x59812),x59811))+~P1(f318(f318(f226(a1),x59811),f2(a1)))
% 109.14/108.86 [6398]~P83(x63982)+E(x63981,f179(f918(x63982,a909)))+E(f17(x63982,f318(f301(x63982,x63982,f72(x63982)),x63981)),f318(f72(x63982),f16(x63982,x63981)))+~P1(f318(f55(x63982),x63981))
% 109.14/108.86 [6399]~P83(x63992)+E(x63991,f179(f918(x63992,a909)))+E(f16(x63992,f318(f301(x63992,x63992,f72(x63992)),x63991)),f318(f72(x63992),f17(x63992,x63991)))+~P1(f318(f55(x63992),x63991))
% 109.14/108.86 [6522]E(x65221,f2(a1))+E(f318(a45,f44(f318(f72(a1),x65221),f318(f72(a1),x65222))),f40(x65221,x65222))+P1(f318(f318(f225(a1),f2(a1)),x65222))+~P1(f318(f318(f225(a1),f2(a1)),x65221))
% 109.14/108.86 [7389]~P1(f318(f318(f225(a1),f2(a1)),x73891))+~P1(f318(f318(f226(a1),f2(a1)),x73892))+~P1(f318(f318(f225(a1),x73892),x73891))+P1(f318(f318(f226(a1),f2(a1)),f318(f318(f30(a1),x73891),x73892)))
% 109.14/108.86 [7782]~E(x77822,f2(a1))+E(f206(x77821,x77822),f318(f318(f243(a1,a1),f2(a1)),f71(a1)))+P1(f318(f318(f226(a1),x77822),f2(a1)))+~P1(f318(f306(f917(a1,a1),a212),f318(f318(f243(a1,a1),x77821),x77822)))
% 109.14/108.86 [7783]~E(x77831,f2(a1))+E(f206(x77831,x77832),f318(f318(f243(a1,a1),f2(a1)),f71(a1)))+P1(f318(f318(f226(a1),x77832),f2(a1)))+~P1(f318(f306(f917(a1,a1),a212),f318(f318(f243(a1,a1),x77831),x77832)))
% 109.14/108.86 [8803]~P43(x88032)+~P43(x88031)+P1(f318(f318(f225(f918(a911,a909)),f318(f301(a1,a911,a95),x88031)),f318(f301(a1,a911,a95),x88032)))+~P1(f318(f318(f225(f918(a1,a909)),x88031),x88032))
% 109.14/108.86 [8804]~P43(x88042)+~P43(x88041)+P1(f318(f318(f226(f918(a911,a909)),f318(f301(a1,a911,a95),x88041)),f318(f301(a1,a911,a95),x88042)))+~P1(f318(f318(f226(f918(a1,a909)),x88041),x88042))
% 109.14/108.86 [9039]~E(f725(x90392,x90391),f726(x90392,x90391))+~P1(f318(f128(x90391),f727(x90392,x90391)))+~P1(f318(f128(f912(x90391)),x90392))+P1(f318(f128(x90391),f318(f133(f912(x90391),f912(x90391),f125(x90391),f104(x90391)),x90392)))
% 109.14/108.86 [9126]~P43(x91262)+~P43(x91261)+~P1(f318(f318(f225(f918(a911,a909)),f318(f301(a1,a911,a95),x91261)),f318(f301(a1,a911,a95),x91262)))+P1(f318(f318(f225(f918(a1,a909)),x91261),x91262))
% 109.14/108.86 [9127]~P43(x91272)+~P43(x91271)+~P1(f318(f318(f226(f918(a911,a909)),f318(f301(a1,a911,a95),x91271)),f318(f301(a1,a911,a95),x91272)))+P1(f318(f318(f226(f918(a1,a909)),x91271),x91272))
% 109.14/108.86 [9133]~E(f725(x91332,x91331),f726(x91332,x91331))+~P1(f318(f128(f912(x91331)),x91332))+P1(f318(f128(x91331),f318(f133(f912(x91331),f912(x91331),f125(x91331),f104(x91331)),x91332)))+P1(f318(f318(f320(f912(x91331)),f727(x91332,x91331)),f318(f163(f912(x91331)),x91332)))
% 109.14/108.86 [9174]~P1(f318(f128(x91741),f727(x91742,x91741)))+~P1(f318(f128(f912(x91741)),x91742))+P1(f318(f128(x91741),f318(f133(f912(x91741),f912(x91741),f125(x91741),f104(x91741)),x91742)))+P1(f318(f318(f320(f912(x91741)),f726(x91742,x91741)),f318(f163(f912(x91741)),x91742)))
% 109.14/108.86 [9175]~P1(f318(f128(x91751),f727(x91752,x91751)))+~P1(f318(f128(f912(x91751)),x91752))+P1(f318(f128(x91751),f318(f133(f912(x91751),f912(x91751),f125(x91751),f104(x91751)),x91752)))+P1(f318(f318(f320(f912(x91751)),f725(x91752,x91751)),f318(f163(f912(x91751)),x91752)))
% 109.14/108.86 [9240]~P1(f318(f128(f912(x92401)),x92402))+P1(f318(f128(x92401),f318(f133(f912(x92401),f912(x92401),f125(x92401),f104(x92401)),x92402)))+P1(f318(f318(f320(f912(x92401)),f726(x92402,x92401)),f318(f163(f912(x92401)),x92402)))+P1(f318(f318(f320(f912(x92401)),f727(x92402,x92401)),f318(f163(f912(x92401)),x92402)))
% 109.14/108.86 [9241]~P1(f318(f128(f912(x92411)),x92412))+P1(f318(f128(x92411),f318(f133(f912(x92411),f912(x92411),f125(x92411),f104(x92411)),x92412)))+P1(f318(f318(f320(f912(x92411)),f725(x92412,x92411)),f318(f163(f912(x92411)),x92412)))+P1(f318(f318(f320(f912(x92411)),f727(x92412,x92411)),f318(f163(f912(x92411)),x92412)))
% 109.14/108.86 [9255]~E(f318(f318(f92(f918(x92551,a909)),f318(f163(x92551),f726(x92552,x92551))),f318(f163(x92551),f725(x92552,x92551))),f179(f918(x92551,a909)))+~P1(f318(f128(x92551),f727(x92552,x92551)))+~P1(f318(f128(f912(x92551)),x92552))+P1(f318(f128(x92551),f318(f133(f912(x92551),f912(x92551),f125(x92551),f104(x92551)),x92552)))
% 109.14/108.86 [9329]~E(f318(f318(f92(f918(x93291,a909)),f318(f163(x93291),f726(x93292,x93291))),f318(f163(x93291),f725(x93292,x93291))),f179(f918(x93291,a909)))+~P1(f318(f128(f912(x93291)),x93292))+P1(f318(f128(x93291),f318(f133(f912(x93291),f912(x93291),f125(x93291),f104(x93291)),x93292)))+P1(f318(f318(f320(f912(x93291)),f727(x93292,x93291)),f318(f163(f912(x93291)),x93292)))
% 109.14/108.86 [9606]E(x96061,f2(a1))+E(x96062,f2(a1))+E(f318(f318(f81(a1,f917(a1,a1)),f318(f318(a208,x96062),x96061)),f318(f318(f20(a1,a1,f917(a1,a1)),f318(f318(f10(a1,f918(a1,f917(a1,a1)),a1),f243(a1,a1)),f318(f30(a1),x96062))),f318(f30(a1),x96061))),f206(x96062,x96061))+P1(f318(f318(f226(a1),x96061),f2(a1)))
% 109.14/108.86 [8478]~P99(x84782)+~P116(x84782)+~P1(f318(f318(f225(x84782),f318(f94(x84782),x84781)),f71(x84782)))+P1(f318(f318(f225(a1),x84781),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))
% 109.14/108.86 [8479]~P99(x84792)+~P116(x84792)+~P1(f318(f318(f226(x84792),f318(f94(x84792),x84791)),f71(x84792)))+P1(f318(f318(f226(a1),x84791),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))
% 109.14/108.86 [8762]~P116(x87621)+~P99(x87621)+P1(f318(f318(f225(x87621),f318(f94(x87621),x87622)),f71(x87621)))+~P1(f318(f318(f225(a1),x87622),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))
% 109.14/108.86 [8763]~P116(x87631)+~P99(x87631)+P1(f318(f318(f226(x87631),f318(f94(x87631),x87632)),f71(x87631)))+~P1(f318(f318(f226(a1),x87632),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)))
% 109.14/108.86 [8966]~P99(x89662)+~P116(x89662)+~P1(f318(f318(f225(x89662),f71(x89662)),f318(f94(x89662),x89661)))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),x89661))
% 109.14/108.86 [8967]~P99(x89672)+~P116(x89672)+~P1(f318(f318(f226(x89672),f71(x89672)),f318(f94(x89672),x89671)))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),x89671))
% 109.14/108.86 [9316]~P116(x93161)+~P99(x93161)+P1(f318(f318(f225(x93161),f71(x93161)),f318(f94(x93161),x93162)))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),x93162))
% 109.14/108.86 [9317]~P116(x93171)+~P99(x93171)+P1(f318(f318(f226(x93171),f71(x93171)),f318(f94(x93171),x93172)))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76)),x93172))
% 109.14/108.86 [9448]~P98(x94481)+~P99(x94481)+~P30(x94481,f318(f94(x94481),x94482))+P30(x94481,f318(f94(x94481),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x94482)),x94482)),a88)))
% 109.14/108.86 [9671]~P98(x96711)+~P99(x96711)+P30(x96711,f318(f94(x96711),x96712))+~P30(x96711,f318(f94(x96711),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),x96712)),x96712)),a88)))
% 109.14/108.86 [10184]~P145(x101842)+E(x101841,f71(x101842))+E(x101841,f318(f72(x101842),f71(x101842)))+~E(f318(f318(f235(x101842),x101841),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f71(x101842))
% 109.14/108.86 [10266]~P99(x102661)+~P74(x102661)+~P1(f318(f318(f226(x102661),f2(x102661)),x102662))+P1(f318(f318(f226(x102661),f2(x102661)),f318(f318(f282(x102661),x102662),f318(f94(x102661),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.86 [10267]~P99(x102671)+~P74(x102671)+~P1(f318(f318(f226(x102671),f2(x102671)),x102672))+P1(f318(f318(f226(x102671),f2(x102671)),f318(f318(f282(x102671),x102672),f318(f94(x102671),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.86 [10310]~P99(x103101)+~P74(x103101)+P1(f318(f318(f226(x103101),f2(x103101)),x103102))+~P1(f318(f318(f226(x103101),f2(x103101)),f318(f318(f282(x103101),x103102),f318(f94(x103101),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.86 [10399]~P144(x103992)+E(x103991,f2(a1))+P1(f318(f318(f226(a1),x103991),f2(a1)))+E(f318(f318(f248(a1,a1,x103992),f318(f318(f9(a1,f918(a1,f918(x103992,x103992)),f918(a1,x103992)),f318(f318(f10(f918(f918(x103992,x103992),x103992),f918(f918(a1,f918(x103992,x103992)),f918(a1,x103992)),a1),f10(f918(x103992,x103992),x103992,a1)),f318(f318(f10(x103992,f918(f918(x103992,x103992),x103992),a1),f81(x103992,x103992)),f93(x103992)))),f318(f318(f9(a1,f918(x103992,x103992),f918(x103992,x103992)),f318(f318(f10(f918(x103992,f918(x103992,x103992)),f918(f918(x103992,x103992),f918(x103992,x103992)),a1),f20(x103992,x103992,x103992)),f318(f318(f9(a1,f918(x103992,x103992),f918(x103992,f918(x103992,x103992))),f318(f318(f10(f918(x103992,f918(x103992,x103992)),f918(f918(x103992,x103992),f918(x103992,f918(x103992,x103992))),a1),f10(x103992,f918(x103992,x103992),x103992)),f318(f318(f10(a909,f918(x103992,f918(x103992,x103992)),a1),f85(x103992)),f318(f318(f9(a1,a1,a909),a315),f2(a1))))),f318(f318(f20(x103992,x103992,x103992),f73(x103992)),f7(x103992))))),f318(f318(f9(x103992,x103992,x103992),f318(f318(f10(x103992,f918(x103992,x103992),x103992),f73(x103992)),f318(f318(f20(x103992,x103992,x103992),f73(x103992)),f7(x103992)))),f71(x103992))))),f40(x103991,f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f93(x103992),x103991))
% 109.14/108.86 [10337]P1(f318(f318(f225(a1),x103371),f2(a1)))+P1(f318(f318(f226(a1),x103372),x103371))+~P1(f318(f306(f917(a1,a1),a52),f318(f318(f243(a1,a1),x103372),x103371)))+E(f318(f37(x103371),f41(x103372,f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103371))),f41(x103372,x103371))
% 109.14/108.86 [10339]P1(f318(f318(f225(a1),x103391),f2(a1)))+~P1(f318(f306(f917(a1,a1),a46),f318(f318(f243(a1,a1),x103392),x103391)))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),x103392),x103391)))+E(f318(f37(x103391),f44(x103392,f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),x103391))),f44(x103392,x103391))
% 109.14/108.86 [5320]~P113(x53201)+~P113(x53202)+~P52(x53201,x53202,x53203)+P42(x53201,x53202,x53203)
% 109.14/108.86 [5450]~P40(x54501,x54503)+~P55(x54501,x54503)+~P56(x54501,x54502,x54503)+P8(x54501,x54502,x54503)
% 109.14/108.86 [5451]~P40(x54511,x54513)+~P55(x54511,x54513)+~P56(x54511,x54512,x54513)+P8(x54511,x54512,x54513)
% 109.14/108.86 [5213]~P5(x52133)+~P42(x52133,x52133,x52131)+E(f318(x52131,x52132),x52132)+~E(x52132,f87(x52133,x52131))
% 109.14/108.86 [5214]~P5(x52143)+~P42(x52143,x52143,x52141)+E(f318(x52141,x52142),x52142)+~E(x52142,f86(x52143,x52141))
% 109.14/108.86 [4986]~P98(x49863)+~P99(x49863)+E(x49861,x49862)+~E(f318(f94(x49863),x49861),f318(f94(x49863),x49862))
% 109.14/108.86 [5460]~P53(x54601,x54602)+~P54(x54601,x54602)+P15(x54601,x54602)+~P1(f318(f318(x54602,x54603),x54603))
% 109.14/108.86 [5461]~P53(x54611,x54612)+~P54(x54611,x54612)+P15(x54611,x54612)+~P1(f318(f318(x54612,x54613),x54613))
% 109.14/108.86 [5960]P15(x59602,x59601)+E(f318(x59601,f801(x59601)),f318(x59601,f802(x59601)))+P1(f318(f318(x59601,f801(x59601)),f802(x59601)))+~P1(f318(f318(x59601,x59603),x59603))
% 109.14/108.86 [6167]~P1(f318(x61671,x61672))+~P1(f318(x61671,x61673))+~P1(f318(f318(f225(a911),x61673),f887(x61672,x61671)))+P1(f318(x61671,f2(a911)))
% 109.14/108.86 [6235]P15(x62351,x62352)+P1(f318(f318(x62352,f801(x62352)),f801(x62352)))+P1(f318(f318(x62352,f801(x62352)),f802(x62352)))+~P1(f318(f318(x62352,x62353),x62353))
% 109.14/108.86 [6236]P15(x62361,x62362)+P1(f318(f318(x62362,f801(x62362)),f802(x62362)))+P1(f318(f318(x62362,f802(x62362)),f802(x62362)))+~P1(f318(f318(x62362,x62363),x62363))
% 109.14/108.86 [6588]P152(x65882,x65883,x65881)+E(x65881,f2(a1))+P1(f318(f318(f225(a1),f2(a1)),f856(x65881,x65883,x65882)))+P1(f318(f318(f226(a1),x65881),f2(a1)))
% 109.14/108.86 [6589]P151(x65892,x65893,x65891)+E(x65891,f2(a1))+P1(f318(f318(f225(a1),f2(a1)),f860(x65891,x65893,x65892)))+P1(f318(f318(f226(a1),x65891),f2(a1)))
% 109.14/108.86 [6711]P151(x67111,x67112,x67113)+~P1(f318(x67111,x67112))+P1(f318(f318(f225(a1),f2(a1)),f860(x67113,x67112,x67111)))+P1(f318(f318(f226(a1),x67113),f2(a1)))
% 109.14/108.86 [6740]P152(x67401,x67402,x67403)+P1(f318(f318(f225(a1),f2(a1)),f856(x67403,x67402,x67401)))+~P1(f318(x67401,f2(a1)))+P1(f318(f318(f226(a1),x67403),f2(a1)))
% 109.14/108.86 [6770]P152(x67702,x67703,x67701)+E(x67701,f2(a1))+~P1(f318(x67702,f857(x67701,x67703,x67702)))+P1(f318(f318(f226(a1),x67701),f2(a1)))
% 109.14/108.86 [6771]P151(x67712,x67713,x67711)+E(x67711,f2(a1))+~P1(f318(x67712,f860(x67711,x67713,x67712)))+P1(f318(f318(f226(a1),x67711),f2(a1)))
% 109.14/108.86 [6873]~P4(x68731)+~P5(x68731)+~P1(f318(f318(f226(x68731),x68732),f31(x68731,x68733)))+P1(f318(f318(f226(x68731),x68732),f557(x68733,x68732,x68731)))
% 109.14/108.86 [6883]P151(x68831,x68832,x68833)+~P1(f318(x68831,x68832))+~P1(f318(x68831,f860(x68833,x68832,x68831)))+P1(f318(f318(f226(a1),x68833),f2(a1)))
% 109.14/108.86 [6909]P152(x69091,x69092,x69093)+~P1(f318(x69091,f857(x69093,x69092,x69091)))+~P1(f318(x69091,f2(a1)))+P1(f318(f318(f226(a1),x69093),f2(a1)))
% 109.14/108.86 [7159]P152(x71592,x71593,x71591)+E(x71591,f2(a1))+P1(f318(f318(f225(a1),f2(a1)),f856(x71591,x71593,x71592)))+P1(f318(f318(f226(a1),x71591),f855(x71591,x71593,x71592)))
% 109.14/108.86 [7160]P151(x71602,x71603,x71601)+E(x71601,f2(a1))+P1(f318(f318(f225(a1),f2(a1)),f860(x71601,x71603,x71602)))+P1(f318(f318(f226(a1),x71601),f859(x71601,x71603,x71602)))
% 109.14/108.86 [7279]P151(x72791,x72792,x72793)+~P1(f318(x72791,x72792))+P1(f318(f318(f225(a1),f2(a1)),f860(x72793,x72792,x72791)))+P1(f318(f318(f226(a1),x72793),f859(x72793,x72792,x72791)))
% 109.14/108.86 [7300]P152(x73001,x73002,x73003)+P1(f318(f318(f225(a1),f2(a1)),f856(x73003,x73002,x73001)))+P1(f318(f318(f226(a1),x73003),f855(x73003,x73002,x73001)))+~P1(f318(x73001,f2(a1)))
% 109.14/108.86 [7333]P152(x73332,x73333,x73331)+E(x73331,f2(a1))+~P1(f318(x73332,f857(x73331,x73333,x73332)))+P1(f318(f318(f226(a1),x73331),f855(x73331,x73333,x73332)))
% 109.14/108.86 [7334]P151(x73342,x73343,x73341)+E(x73341,f2(a1))+~P1(f318(x73342,f860(x73341,x73343,x73342)))+P1(f318(f318(f226(a1),x73341),f859(x73341,x73343,x73342)))
% 109.14/108.86 [7378]P152(x73782,x73783,x73781)+E(x73781,f2(a1))+P1(f318(f318(f225(a1),f2(a1)),f856(x73781,x73783,x73782)))+~P1(f318(x73782,f858(x73781,x73783,x73782)))
% 109.14/108.86 [7379]P151(x73792,x73793,x73791)+E(x73791,f2(a1))+P1(f318(f318(f225(a1),f2(a1)),f860(x73791,x73793,x73792)))+~P1(f318(x73792,f859(x73791,x73793,x73792)))
% 109.14/108.86 [7472]P151(x74721,x74722,x74723)+~P1(f318(x74721,x74722))+~P1(f318(x74721,f860(x74723,x74722,x74721)))+P1(f318(f318(f226(a1),x74723),f859(x74723,x74722,x74721)))
% 109.14/108.86 [7481]P152(x74811,x74812,x74813)+~P1(f318(x74811,f857(x74813,x74812,x74811)))+P1(f318(f318(f226(a1),x74813),f855(x74813,x74812,x74811)))+~P1(f318(x74811,f2(a1)))
% 109.14/108.86 [7484]P151(x74841,x74842,x74843)+~P1(f318(x74841,x74842))+P1(f318(f318(f225(a1),f2(a1)),f860(x74843,x74842,x74841)))+~P1(f318(x74841,f859(x74843,x74842,x74841)))
% 109.14/108.86 [7501]P152(x75011,x75012,x75013)+P1(f318(f318(f225(a1),f2(a1)),f856(x75013,x75012,x75011)))+~P1(f318(x75011,f858(x75013,x75012,x75011)))+~P1(f318(x75011,f2(a1)))
% 109.14/108.86 [7521]P152(x75212,x75213,x75211)+E(x75211,f2(a1))+~P1(f318(x75212,f857(x75211,x75213,x75212)))+~P1(f318(x75212,f858(x75211,x75213,x75212)))
% 109.14/108.86 [7522]P151(x75222,x75223,x75221)+E(x75221,f2(a1))+~P1(f318(x75222,f860(x75221,x75223,x75222)))+~P1(f318(x75222,f859(x75221,x75223,x75222)))
% 109.14/108.86 [7607]P151(x76071,x76072,x76073)+~P1(f318(x76071,x76072))+~P1(f318(x76071,f860(x76073,x76072,x76071)))+~P1(f318(x76071,f859(x76073,x76072,x76071)))
% 109.14/108.86 [7624]P152(x76241,x76242,x76243)+~P1(f318(x76241,f857(x76243,x76242,x76241)))+~P1(f318(x76241,f858(x76243,x76242,x76241)))+~P1(f318(x76241,f2(a1)))
% 109.14/108.86 [7669]P152(x76692,x76693,x76691)+E(x76691,f2(a1))+P1(f318(f318(f225(a1),f2(a1)),f856(x76691,x76693,x76692)))+P1(f318(f318(f225(a1),f855(x76691,x76693,x76692)),f2(a1)))
% 109.14/108.86 [7670]P151(x76702,x76703,x76701)+E(x76701,f2(a1))+P1(f318(f318(f225(a1),f2(a1)),f860(x76701,x76703,x76702)))+P1(f318(f318(f225(a1),f859(x76701,x76703,x76702)),f2(a1)))
% 109.14/108.86 [7671]~P93(x76711)+~P1(f318(f318(f225(x76711),x76713),f2(x76711)))+~P1(f318(f318(f225(x76711),x76712),f2(x76711)))+P1(f318(f318(f225(x76711),f318(f318(f73(x76711),x76712),x76713)),f2(x76711)))
% 109.14/108.86 [7672]~P144(x76721)+~P1(f318(f318(f320(x76721),x76723),f100(x76721)))+~P1(f318(f318(f320(x76721),x76722),f100(x76721)))+P1(f318(f318(f320(x76721),f318(f318(f3(x76721),x76722),x76723)),f100(x76721)))
% 109.14/108.86 [7673]~P144(x76731)+~P1(f318(f318(f320(x76731),x76733),f100(x76731)))+~P1(f318(f318(f320(x76731),x76732),f100(x76731)))+P1(f318(f318(f320(x76731),f318(f318(f73(x76731),x76732),x76733)),f100(x76731)))
% 109.14/108.86 [7674]~P114(x76741)+~P1(f318(f318(f320(x76741),x76743),f177(x76741)))+~P1(f318(f318(f320(x76741),x76742),f177(x76741)))+P1(f318(f318(f320(x76741),f318(f318(f73(x76741),x76742),x76743)),f177(x76741)))
% 109.14/108.86 [7675]~P144(x76751)+~P1(f318(f318(f320(x76751),x76753),f100(x76751)))+~P1(f318(f318(f320(x76751),x76752),f100(x76751)))+P1(f318(f318(f320(x76751),f318(f318(f74(x76751),x76752),x76753)),f100(x76751)))
% 109.14/108.86 [7676]~P114(x76761)+~P1(f318(f318(f320(x76761),x76763),f177(x76761)))+~P1(f318(f318(f320(x76761),x76762),f177(x76761)))+P1(f318(f318(f320(x76761),f318(f318(f74(x76761),x76762),x76763)),f177(x76761)))
% 109.14/108.86 [7677]~P93(x76771)+~P1(f318(f318(f225(x76771),x76773),f2(x76771)))+~P1(f318(f318(f226(x76771),x76772),f2(x76771)))+P1(f318(f318(f226(x76771),f318(f318(f73(x76771),x76772),x76773)),f2(x76771)))
% 109.14/108.86 [7678]~P93(x76781)+~P1(f318(f318(f225(x76781),x76782),f2(x76781)))+~P1(f318(f318(f226(x76781),x76783),f2(x76781)))+P1(f318(f318(f226(x76781),f318(f318(f73(x76781),x76782),x76783)),f2(x76781)))
% 109.14/108.86 [7679]~P93(x76791)+~P1(f318(f318(f226(x76791),x76793),f2(x76791)))+~P1(f318(f318(f226(x76791),x76792),f2(x76791)))+P1(f318(f318(f226(x76791),f318(f318(f73(x76791),x76792),x76793)),f2(x76791)))
% 109.14/108.86 [7705]P152(x77053,x77052,x77051)+E(x77051,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x77051),f857(x77051,x77052,x77053))),f856(x77051,x77052,x77053)),x77052)+P1(f318(f318(f226(a1),x77051),f2(a1)))
% 109.14/108.86 [7706]P151(x77063,x77062,x77061)+E(x77061,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x77061),f861(x77061,x77062,x77063))),f860(x77061,x77062,x77063)),x77062)+P1(f318(f318(f226(a1),x77061),f2(a1)))
% 109.14/108.86 [7787]P151(x77871,x77872,x77873)+~P1(f318(x77871,x77872))+P1(f318(f318(f225(a1),f2(a1)),f860(x77873,x77872,x77871)))+P1(f318(f318(f225(a1),f859(x77873,x77872,x77871)),f2(a1)))
% 109.14/108.86 [7819]P152(x78191,x78192,x78193)+P1(f318(f318(f225(a1),f2(a1)),f856(x78193,x78192,x78191)))+~P1(f318(x78191,f2(a1)))+P1(f318(f318(f225(a1),f855(x78193,x78192,x78191)),f2(a1)))
% 109.14/108.86 [7828]P151(x78283,x78282,x78281)+~P1(f318(x78283,x78282))+E(f318(f318(f73(a1),f318(f318(f74(a1),x78281),f861(x78281,x78282,x78283))),f860(x78281,x78282,x78283)),x78282)+P1(f318(f318(f226(a1),x78281),f2(a1)))
% 109.14/108.86 [7834]P152(x78342,x78343,x78341)+E(x78341,f2(a1))+~P1(f318(x78342,f857(x78341,x78343,x78342)))+P1(f318(f318(f225(a1),f855(x78341,x78343,x78342)),f2(a1)))
% 109.14/108.86 [7835]P151(x78352,x78353,x78351)+E(x78351,f2(a1))+~P1(f318(x78352,f860(x78351,x78353,x78352)))+P1(f318(f318(f225(a1),f859(x78351,x78353,x78352)),f2(a1)))
% 109.14/108.86 [7839]P152(x78393,x78392,x78391)+E(f318(f318(f73(a1),f318(f318(f74(a1),x78391),f857(x78391,x78392,x78393))),f856(x78391,x78392,x78393)),x78392)+~P1(f318(x78393,f2(a1)))+P1(f318(f318(f226(a1),x78391),f2(a1)))
% 109.14/108.86 [7895]P151(x78951,x78952,x78953)+~P1(f318(x78951,x78952))+~P1(f318(x78951,f860(x78953,x78952,x78951)))+P1(f318(f318(f225(a1),f859(x78953,x78952,x78951)),f2(a1)))
% 109.14/108.86 [7900]P152(x79001,x79002,x79003)+~P1(f318(x79001,f857(x79003,x79002,x79001)))+~P1(f318(x79001,f2(a1)))+P1(f318(f318(f225(a1),f855(x79003,x79002,x79001)),f2(a1)))
% 109.14/108.86 [7972]~P131(x79721)+~P1(f318(f318(f225(x79721),f318(f318(f74(x79721),x79723),x79722)),f2(x79721)))+P1(f318(f318(f225(x79721),x79722),f2(x79721)))+P1(f318(f318(f225(x79721),x79723),f2(x79721)))
% 109.14/108.86 [7973]~P74(x79731)+~P1(f318(f318(f225(x79731),f318(f318(f282(x79731),x79733),x79732)),f2(x79731)))+P1(f318(f318(f225(x79731),x79732),f2(x79731)))+P1(f318(f318(f225(x79731),x79733),f2(x79731)))
% 109.14/108.86 [7974]~P74(x79741)+~P1(f318(f318(f226(x79741),f318(f318(f282(x79741),x79743),x79742)),f2(x79741)))+P1(f318(f318(f226(x79741),x79742),f2(x79741)))+P1(f318(f318(f226(x79741),x79743),f2(x79741)))
% 109.14/108.86 [8080]P152(x80803,x80802,x80801)+E(x80801,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x80801),f857(x80801,x80802,x80803))),f856(x80801,x80802,x80803)),x80802)+P1(f318(f318(f226(a1),x80801),f855(x80801,x80802,x80803)))
% 109.14/108.86 [8081]P151(x80813,x80812,x80811)+E(x80811,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x80811),f861(x80811,x80812,x80813))),f860(x80811,x80812,x80813)),x80812)+P1(f318(f318(f226(a1),x80811),f859(x80811,x80812,x80813)))
% 109.14/108.86 [8093]P152(x80933,x80932,x80931)+E(x80931,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x80931),f858(x80931,x80932,x80933))),f855(x80931,x80932,x80933)),x80932)+P1(f318(f318(f225(a1),f2(a1)),f856(x80931,x80932,x80933)))
% 109.14/108.86 [8094]P151(x80943,x80942,x80941)+E(x80941,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x80941),f862(x80941,x80942,x80943))),f859(x80941,x80942,x80943)),x80942)+P1(f318(f318(f225(a1),f2(a1)),f860(x80941,x80942,x80943)))
% 109.14/108.86 [8134]P151(x81343,x81342,x81341)+~P1(f318(x81343,x81342))+E(f318(f318(f73(a1),f318(f318(f74(a1),x81341),f861(x81341,x81342,x81343))),f860(x81341,x81342,x81343)),x81342)+P1(f318(f318(f226(a1),x81341),f859(x81341,x81342,x81343)))
% 109.14/108.86 [8143]P152(x81433,x81432,x81431)+E(f318(f318(f73(a1),f318(f318(f74(a1),x81431),f857(x81431,x81432,x81433))),f856(x81431,x81432,x81433)),x81432)+P1(f318(f318(f226(a1),x81431),f855(x81431,x81432,x81433)))+~P1(f318(x81433,f2(a1)))
% 109.14/108.86 [8149]P151(x81493,x81492,x81491)+~P1(f318(x81493,x81492))+E(f318(f318(f73(a1),f318(f318(f74(a1),x81491),f862(x81491,x81492,x81493))),f859(x81491,x81492,x81493)),x81492)+P1(f318(f318(f225(a1),f2(a1)),f860(x81491,x81492,x81493)))
% 109.14/108.86 [8155]P152(x81553,x81552,x81551)+E(f318(f318(f73(a1),f318(f318(f74(a1),x81551),f858(x81551,x81552,x81553))),f855(x81551,x81552,x81553)),x81552)+P1(f318(f318(f225(a1),f2(a1)),f856(x81551,x81552,x81553)))+~P1(f318(x81553,f2(a1)))
% 109.14/108.86 [8166]P152(x81663,x81662,x81661)+E(x81661,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x81661),f857(x81661,x81662,x81663))),f856(x81661,x81662,x81663)),x81662)+~P1(f318(x81663,f858(x81661,x81662,x81663)))
% 109.14/108.86 [8167]P151(x81673,x81672,x81671)+E(x81671,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x81671),f861(x81671,x81672,x81673))),f860(x81671,x81672,x81673)),x81672)+~P1(f318(x81673,f859(x81671,x81672,x81673)))
% 109.14/108.86 [8168]P152(x81683,x81682,x81681)+E(x81681,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x81681),f858(x81681,x81682,x81683))),f855(x81681,x81682,x81683)),x81682)+~P1(f318(x81683,f857(x81681,x81682,x81683)))
% 109.14/108.86 [8169]P151(x81693,x81692,x81691)+E(x81691,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x81691),f862(x81691,x81692,x81693))),f859(x81691,x81692,x81693)),x81692)+~P1(f318(x81693,f860(x81691,x81692,x81693)))
% 109.14/108.86 [8232]P151(x82323,x82322,x82321)+~P1(f318(x82323,x82322))+E(f318(f318(f73(a1),f318(f318(f74(a1),x82321),f861(x82321,x82322,x82323))),f860(x82321,x82322,x82323)),x82322)+~P1(f318(x82323,f859(x82321,x82322,x82323)))
% 109.14/108.86 [8233]P151(x82333,x82332,x82331)+~P1(f318(x82333,x82332))+E(f318(f318(f73(a1),f318(f318(f74(a1),x82331),f862(x82331,x82332,x82333))),f859(x82331,x82332,x82333)),x82332)+~P1(f318(x82333,f860(x82331,x82332,x82333)))
% 109.14/108.86 [8247]P152(x82473,x82472,x82471)+E(f318(f318(f73(a1),f318(f318(f74(a1),x82471),f857(x82471,x82472,x82473))),f856(x82471,x82472,x82473)),x82472)+~P1(f318(x82473,f858(x82471,x82472,x82473)))+~P1(f318(x82473,f2(a1)))
% 109.14/108.86 [8248]P152(x82483,x82482,x82481)+E(f318(f318(f73(a1),f318(f318(f74(a1),x82481),f858(x82481,x82482,x82483))),f855(x82481,x82482,x82483)),x82482)+~P1(f318(x82483,f857(x82481,x82482,x82483)))+~P1(f318(x82483,f2(a1)))
% 109.14/108.86 [8349]P152(x83493,x83492,x83491)+E(x83491,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x83491),f857(x83491,x83492,x83493))),f856(x83491,x83492,x83493)),x83492)+P1(f318(f318(f225(a1),f855(x83491,x83492,x83493)),f2(a1)))
% 109.14/108.86 [8350]P151(x83503,x83502,x83501)+E(x83501,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x83501),f861(x83501,x83502,x83503))),f860(x83501,x83502,x83503)),x83502)+P1(f318(f318(f225(a1),f859(x83501,x83502,x83503)),f2(a1)))
% 109.14/108.86 [8386]P151(x83863,x83862,x83861)+~P1(f318(x83863,x83862))+E(f318(f318(f73(a1),f318(f318(f74(a1),x83861),f861(x83861,x83862,x83863))),f860(x83861,x83862,x83863)),x83862)+P1(f318(f318(f225(a1),f859(x83861,x83862,x83863)),f2(a1)))
% 109.14/108.86 [8391]P152(x83913,x83912,x83911)+E(f318(f318(f73(a1),f318(f318(f74(a1),x83911),f857(x83911,x83912,x83913))),f856(x83911,x83912,x83913)),x83912)+~P1(f318(x83913,f2(a1)))+P1(f318(f318(f225(a1),f855(x83911,x83912,x83913)),f2(a1)))
% 109.14/108.86 [8523]P152(x85233,x85232,x85231)+E(x85231,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x85231),f858(x85231,x85232,x85233))),f855(x85231,x85232,x85233)),x85232)+E(f318(f318(f73(a1),f318(f318(f74(a1),x85231),f857(x85231,x85232,x85233))),f856(x85231,x85232,x85233)),x85232)
% 109.14/108.86 [8524]P151(x85243,x85242,x85241)+E(x85241,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x85241),f862(x85241,x85242,x85243))),f859(x85241,x85242,x85243)),x85242)+E(f318(f318(f73(a1),f318(f318(f74(a1),x85241),f861(x85241,x85242,x85243))),f860(x85241,x85242,x85243)),x85242)
% 109.14/108.86 [8544]P151(x85443,x85442,x85441)+~P1(f318(x85443,x85442))+E(f318(f318(f73(a1),f318(f318(f74(a1),x85441),f862(x85441,x85442,x85443))),f859(x85441,x85442,x85443)),x85442)+E(f318(f318(f73(a1),f318(f318(f74(a1),x85441),f861(x85441,x85442,x85443))),f860(x85441,x85442,x85443)),x85442)
% 109.14/108.86 [8551]P152(x85513,x85512,x85511)+E(f318(f318(f73(a1),f318(f318(f74(a1),x85511),f858(x85511,x85512,x85513))),f855(x85511,x85512,x85513)),x85512)+E(f318(f318(f73(a1),f318(f318(f74(a1),x85511),f857(x85511,x85512,x85513))),f856(x85511,x85512,x85513)),x85512)+~P1(f318(x85513,f2(a1)))
% 109.14/108.86 [9214]~P131(x92141)+~E(x92143,f2(x92141))+~E(x92142,f2(x92141))+P1(f318(f318(f225(x92141),f318(f318(f73(x92141),f318(f318(f74(x92141),x92142),x92142)),f318(f318(f74(x92141),x92143),x92143))),f2(x92141)))
% 109.14/108.86 [10412]~P116(x104121)+~E(x104123,f2(x104121))+~E(x104122,f2(x104121))+P1(f318(f318(f225(x104121),f318(f318(f73(x104121),f318(f318(f235(x104121),x104122),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x104121),x104123),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))),f2(x104121)))
% 109.14/108.86 [4936]~E(x49363,x49361)+~P125(x49362)+E(x49361,f2(x49362))+E(f318(f318(f282(x49362),x49363),x49361),f71(x49362))
% 109.14/108.86 [4987]~P105(x49871)+~E(x49873,f179(x49871))+~E(x49872,f179(x49871))+E(f318(f318(f101(x49871),x49872),x49873),f179(x49871))
% 109.14/108.86 [4988]~P104(x49881)+~E(x49883,f233(x49881))+~E(x49882,f233(x49881))+E(f318(f318(f92(x49881),x49882),x49883),f233(x49881))
% 109.14/108.86 [5082]~P125(x50823)+E(x50821,x50822)+E(x50822,f2(x50823))+~E(f318(f318(f282(x50823),x50821),x50822),f71(x50823))
% 109.14/108.86 [5099]~P138(x50992)+E(x50991,f2(x50992))+E(x50993,f2(x50992))+~E(f318(f318(f74(x50992),x50993),x50991),f2(x50992))
% 109.14/108.86 [5100]~P138(x51002)+E(x51001,f2(x51002))+E(x51003,f2(x51002))+~E(f318(f318(f74(x51002),x51003),x51001),f2(x51002))
% 109.14/108.86 [5101]~P147(x51012)+E(x51011,f2(x51012))+E(x51013,f2(x51012))+~E(f318(f318(f74(x51012),x51013),x51011),f2(x51012))
% 109.14/108.86 [5480]~P123(x54803)+E(x54801,x54802)+E(x54801,f318(f72(x54803),x54802))+~E(f318(f318(f74(x54803),x54801),x54801),f318(f318(f74(x54803),x54802),x54802))
% 109.14/108.86 [5519]~P96(x55191)+E(f318(f72(x55191),x55192),x55193)+~E(f318(f318(f101(x55191),x55192),x55193),f233(x55191))+~E(f318(f318(f92(x55191),x55192),x55193),f179(x55191))
% 109.14/108.86 [5594]~P4(x55943)+E(x55941,x55942)+P1(f318(f318(f226(x55943),x55942),x55941))+P1(f318(f318(f226(x55943),x55941),x55942))
% 109.14/108.86 [5595]~P4(x55953)+E(x55951,x55952)+P1(f318(f318(f226(x55953),x55952),x55951))+P1(f318(f318(f226(x55953),x55951),x55952))
% 109.14/108.86 [5596]~P4(x55963)+E(x55961,x55962)+P1(f318(f318(f226(x55963),x55962),x55961))+P1(f318(f318(f226(x55963),x55961),x55962))
% 109.14/108.86 [5597]~P4(x55973)+E(x55971,x55972)+P1(f318(f318(f226(x55973),x55972),x55971))+P1(f318(f318(f226(x55973),x55971),x55972))
% 109.14/108.86 [5598]~P4(x55983)+E(x55981,x55982)+P1(f318(f318(f226(x55983),x55982),x55981))+P1(f318(f318(f226(x55983),x55981),x55982))
% 109.14/108.86 [5599]~P116(x55993)+E(x55991,x55992)+P1(f318(f318(f226(x55993),x55992),x55991))+P1(f318(f318(f226(x55993),x55991),x55992))
% 109.14/108.86 [5600]~P4(x56003)+E(x56001,x56002)+P1(f318(f318(f226(x56003),x56002),x56001))+P1(f318(f318(f226(x56003),x56001),x56002))
% 109.14/108.86 [5601]~E(x56012,x56013)+~P4(x56011)+P1(f318(f318(f226(x56011),x56012),x56013))+P1(f318(f318(f225(x56011),x56012),x56013))
% 109.14/108.86 [5776]P152(x57762,x57763,x57761)+E(x57761,f2(a1))+P1(f318(f318(f226(a1),x57761),f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x57761))
% 109.14/108.86 [5777]P151(x57772,x57773,x57771)+E(x57771,f2(a1))+P1(f318(f318(f226(a1),x57771),f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x57771))
% 109.14/108.86 [5802]E(x58021,x58022)+P1(f318(f318(x58023,x58021),x58022))+P1(f318(f318(f226(a911),x58022),x58021))+P1(f318(f318(f226(a911),x58021),x58022))
% 109.14/108.86 [5864]~P113(x58643)+E(x58641,x58642)+~P1(f318(f318(f225(x58643),x58642),x58641))+P1(f318(f318(f226(x58643),x58642),x58641))
% 109.14/108.86 [5865]~P4(x58653)+E(x58651,x58652)+~P1(f318(f318(f225(x58653),x58651),x58652))+P1(f318(f318(f226(x58653),x58651),x58652))
% 109.14/108.86 [5866]~P4(x58663)+E(x58661,x58662)+~P1(f318(f318(f225(x58663),x58661),x58662))+P1(f318(f318(f226(x58663),x58661),x58662))
% 109.14/108.86 [5867]~P113(x58673)+E(x58671,x58672)+~P1(f318(f318(f225(x58673),x58671),x58672))+P1(f318(f318(f226(x58673),x58671),x58672))
% 109.14/108.86 [5868]~P113(x58683)+E(x58681,x58682)+~P1(f318(f318(f225(x58683),x58681),x58682))+P1(f318(f318(f226(x58683),x58681),x58682))
% 109.14/108.86 [5869]~P113(x58693)+E(x58691,x58692)+~P1(f318(f318(f225(x58693),x58691),x58692))+P1(f318(f318(f226(x58693),x58691),x58692))
% 109.14/108.86 [5870]~P113(x58703)+E(x58701,x58702)+~P1(f318(f318(f225(x58703),x58701),x58702))+P1(f318(f318(f226(x58703),x58701),x58702))
% 109.14/108.86 [5871]~P113(x58713)+E(x58711,x58712)+~P1(f318(f318(f225(x58713),x58711),x58712))+P1(f318(f318(f226(x58713),x58711),x58712))
% 109.14/108.86 [5872]~P113(x58723)+E(x58721,x58722)+~P1(f318(f318(f225(x58723),x58721),x58722))+P1(f318(f318(f226(x58723),x58721),x58722))
% 109.14/108.86 [5978]P151(x59781,x59782,x59783)+~P1(f318(x59781,x59782))+P1(f318(f318(f226(a1),x59783),f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x59783))
% 109.14/108.86 [6033]P152(x60331,x60332,x60333)+~P1(f318(x60331,f2(a1)))+P1(f318(f318(f226(a1),x60333),f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x60333))
% 109.14/108.86 [6038]~P103(x60381)+E(f318(f318(f101(x60381),x60382),f12(x60381,x60383)),x60382)+~P1(f318(f55(x60381),x60383))+~P1(f318(f318(f320(x60381),x60382),x60383))
% 109.14/108.86 [6039]~P103(x60391)+E(f318(f318(f92(x60391),x60392),f15(x60391,x60393)),x60392)+~P1(f318(f55(x60391),x60393))+~P1(f318(f318(f320(x60391),x60392),x60393))
% 109.14/108.86 [6076]~P103(x60761)+E(f318(f318(f101(x60761),x60762),f15(x60761,x60763)),f15(x60761,x60763))+~P1(f318(f55(x60761),x60763))+~P1(f318(f318(f320(x60761),x60762),x60763))
% 109.14/108.86 [6077]~P103(x60771)+E(f318(f318(f92(x60771),x60772),f12(x60771,x60773)),f12(x60771,x60773))+~P1(f318(f55(x60771),x60773))+~P1(f318(f318(f320(x60771),x60772),x60773))
% 109.14/108.86 [6078]~P4(x60781)+E(f318(f318(f223(x60781),x60782),f16(x60781,x60783)),f16(x60781,x60783))+~P1(f318(f55(x60781),x60783))+~P1(f318(f318(f320(x60781),x60782),x60783))
% 109.14/108.86 [6079]~P4(x60791)+E(f318(f318(f224(x60791),x60792),f17(x60791,x60793)),f17(x60791,x60793))+~P1(f318(f55(x60791),x60793))+~P1(f318(f318(f320(x60791),x60792),x60793))
% 109.14/108.86 [6115]E(x61151,x61152)+~P113(x61153)+~P1(f318(f318(f225(x61153),x61152),x61151))+~P1(f318(f318(f225(x61153),x61151),x61152))
% 109.14/108.86 [6116]E(x61161,x61162)+~P113(x61163)+~P1(f318(f318(f225(x61163),x61162),x61161))+~P1(f318(f318(f225(x61163),x61161),x61162))
% 109.14/108.86 [6117]E(x61171,x61172)+~P113(x61173)+~P1(f318(f318(f225(x61173),x61172),x61171))+~P1(f318(f318(f225(x61173),x61171),x61172))
% 109.14/108.86 [6118]E(x61181,x61182)+~P113(x61183)+~P1(f318(f318(f225(x61183),x61182),x61181))+~P1(f318(f318(f225(x61183),x61181),x61182))
% 109.14/108.86 [6120]~E(x61201,x61202)+~P4(x61203)+~P1(f318(f318(f225(x61203),x61201),x61202))+~P1(f318(f318(f226(x61203),x61201),x61202))
% 109.14/108.86 [6263]~P2(x62631)+P1(f318(f318(f226(x62631),x62633),x62632))+~P1(f318(f318(f225(x62631),x62633),x62632))+P1(f318(f318(f225(x62631),x62632),x62633))
% 109.14/108.86 [6292]~P4(x62921)+~P1(f318(f55(x62921),x62923))+P1(f318(f318(f225(x62921),x62922),f17(x62921,x62923)))+~P1(f318(f318(f320(x62921),x62922),x62923))
% 109.14/108.86 [6334]~P4(x63341)+E(f318(f318(f223(x63341),x63342),f14(x63341,f224(x63341),x63343)),x63342)+~P1(f318(f55(x63341),x63343))+~P1(f318(f318(f320(x63341),x63342),x63343))
% 109.14/108.86 [6335]~P4(x63351)+E(f318(f318(f224(x63351),x63352),f13(x63351,f223(x63351),x63353)),x63352)+~P1(f318(f55(x63351),x63353))+~P1(f318(f318(f320(x63351),x63352),x63353))
% 109.14/108.86 [6474]E(x64741,x64742)+~E(f318(f318(f3(a911),x64741),x64743),f318(f318(f3(a911),x64742),x64743))+~P1(f318(f318(f225(a911),x64743),x64741))+~P1(f318(f318(f225(a911),x64743),x64742))
% 109.14/108.86 [6501]~P4(x65011)+~P1(f318(f55(x65011),x65012))+~P1(f318(f318(f320(x65011),x65013),x65012))+P1(f318(f318(f225(x65011),f16(x65011,x65012)),x65013))
% 109.14/108.86 [6542]E(x65421,f2(a911))+~P1(f318(f42(x65423,x65421),x65422))+P1(f318(f318(f226(a911),f2(a911)),x65421))+P1(f318(f318(f226(a911),x65421),f318(f247(a911,a911),x65422)))
% 109.14/108.86 [6566]P152(x65662,x65663,x65661)+E(x65661,f2(a1))+P1(f318(f318(f226(a1),x65661),f855(x65661,x65663,x65662)))+P1(f318(f318(f226(a1),f2(a1)),x65661))
% 109.14/108.86 [6567]P151(x65672,x65673,x65671)+E(x65671,f2(a1))+P1(f318(f318(f226(a1),x65671),f859(x65671,x65673,x65672)))+P1(f318(f318(f226(a1),f2(a1)),x65671))
% 109.14/108.86 [6568]~P4(x65681)+E(f318(f318(f223(x65681),x65682),f13(x65681,f223(x65681),x65683)),f13(x65681,f223(x65681),x65683))+~P1(f318(f55(x65681),x65683))+~P1(f318(f318(f320(x65681),x65682),x65683))
% 109.14/108.86 [6569]~P4(x65691)+E(f318(f318(f224(x65691),x65692),f14(x65691,f224(x65691),x65693)),f14(x65691,f224(x65691),x65693))+~P1(f318(f55(x65691),x65693))+~P1(f318(f318(f320(x65691),x65692),x65693))
% 109.14/108.86 [6575]~P1(f318(x65751,x65752))+P1(f318(x65751,f411(x65752,x65751,x65753)))+P1(f318(x65751,f2(a911)))+~P1(f318(f318(f226(a911),x65752),x65753))
% 109.14/108.86 [6632]~P1(f318(x66321,x66322))+~P1(f318(f55(x66323),x66322))+P1(f318(x66321,f896(x66321,x66322,x66323)))+P1(f318(x66321,f179(f918(x66323,a909))))
% 109.14/108.86 [6645]~P116(x66451)+~P99(x66451)+P1(f318(f318(f225(x66451),f318(f94(x66451),x66452)),f318(f94(x66451),x66453)))+~P1(f318(f318(f225(a1),x66452),x66453))
% 109.14/108.86 [6646]~P116(x66461)+~P99(x66461)+P1(f318(f318(f226(x66461),f318(f94(x66461),x66462)),f318(f94(x66461),x66463)))+~P1(f318(f318(f226(a1),x66462),x66463))
% 109.14/108.86 [6649]~P1(f318(x66491,x66493))+~P1(f318(f55(x66492),x66493))+P1(f318(f55(x66492),f896(x66491,x66493,x66492)))+P1(f318(x66491,f179(f918(x66492,a909))))
% 109.14/108.86 [6681]P151(x66811,x66812,x66813)+~P1(f318(x66811,x66812))+P1(f318(f318(f226(a1),x66813),f859(x66813,x66812,x66811)))+P1(f318(f318(f226(a1),f2(a1)),x66813))
% 109.14/108.86 [6717]P152(x67171,x67172,x67173)+P1(f318(f318(f226(a1),x67173),f855(x67173,x67172,x67171)))+~P1(f318(x67171,f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x67173))
% 109.14/108.86 [6751]~P3(x67511)+~P100(x67511)+E(f318(f318(f223(x67511),f318(f94(x67511),x67512)),f318(f94(x67511),x67513)),f318(f94(x67511),x67513))+P1(f318(f318(f225(x67511),f318(f94(x67511),x67512)),f318(f94(x67511),x67513)))
% 109.14/108.86 [6752]~P3(x67521)+~P100(x67521)+E(f318(f318(f224(x67521),f318(f94(x67521),x67522)),f318(f94(x67521),x67523)),f318(f94(x67521),x67522))+P1(f318(f318(f225(x67521),f318(f94(x67521),x67522)),f318(f94(x67521),x67523)))
% 109.14/108.86 [6758]E(x67581,f2(a911))+~P1(f318(f42(x67583,x67581),x67582))+~P1(f318(f318(f226(a911),f2(a911)),x67581))+P1(f318(f318(f225(a911),f2(a911)),f318(f247(a911,a911),x67582)))
% 109.14/108.86 [6811]P152(x68112,x68113,x68111)+E(x68111,f2(a1))+~P1(f318(x68112,f858(x68111,x68113,x68112)))+P1(f318(f318(f226(a1),f2(a1)),x68111))
% 109.14/108.86 [6812]P151(x68122,x68123,x68121)+E(x68121,f2(a1))+~P1(f318(x68122,f859(x68121,x68123,x68122)))+P1(f318(f318(f226(a1),f2(a1)),x68121))
% 109.14/108.86 [6816]P1(f318(x68161,x68162))+~P1(f318(f55(x68163),x68162))+P1(f318(x68161,f423(x68161,x68162,x68163)))+~P1(f318(x68161,f179(f918(x68163,a909))))
% 109.14/108.86 [6838]P1(f318(x68381,x68382))+P1(f318(f55(x68383),f423(x68381,x68382,x68383)))+~P1(f318(f55(x68383),x68382))+~P1(f318(x68381,f179(f918(x68383,a909))))
% 109.14/108.86 [6903]P151(x69031,x69032,x69033)+~P1(f318(x69031,x69032))+~P1(f318(x69031,f859(x69033,x69032,x69031)))+P1(f318(f318(f226(a1),f2(a1)),x69033))
% 109.14/108.86 [6928]P152(x69281,x69282,x69283)+~P1(f318(x69281,f858(x69283,x69282,x69281)))+~P1(f318(x69281,f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x69283))
% 109.14/108.86 [6939]E(x69391,f2(a911))+~P1(f318(f42(x69393,x69391),x69392))+P1(f318(f318(f225(a911),f318(f247(a911,a911),x69392)),f2(a911)))+P1(f318(f318(f226(a911),f2(a911)),x69391))
% 109.14/108.86 [7034]~P99(x70343)+~P116(x70343)+~P1(f318(f318(f225(x70343),f318(f94(x70343),x70341)),f318(f94(x70343),x70342)))+P1(f318(f318(f225(a1),x70341),x70342))
% 109.14/108.86 [7035]~P99(x70353)+~P116(x70353)+~P1(f318(f318(f226(x70353),f318(f94(x70353),x70351)),f318(f94(x70353),x70352)))+P1(f318(f318(f226(a1),x70351),x70352))
% 109.14/108.86 [7064]~P4(x70641)+~P13(x70641,x70643)+P13(x70641,f318(f318(f142(x70641),x70642),x70643))+~P1(f318(f318(f225(x70641),x70642),f706(x70643,x70642,x70641)))
% 109.14/108.86 [7065]~P4(x70651)+~P13(x70651,x70653)+P13(x70651,f318(f318(f142(x70651),x70652),x70653))+~P1(f318(f318(f225(x70651),x70652),f708(x70653,x70652,x70651)))
% 109.14/108.86 [7066]~P4(x70661)+~P13(x70661,x70663)+P13(x70661,f318(f318(f142(x70661),x70662),x70663))+~P1(f318(f318(f225(x70661),x70662),f747(x70662,x70663,x70661)))
% 109.14/108.86 [7152]P152(x71522,x71523,x71521)+E(x71521,f2(a1))+P1(f318(f318(f226(a1),x71521),f2(a1)))+P1(f318(f318(f226(a1),f856(x71521,x71523,x71522)),x71521))
% 109.14/108.86 [7153]P151(x71532,x71533,x71531)+E(x71531,f2(a1))+P1(f318(f318(f226(a1),x71531),f2(a1)))+P1(f318(f318(f226(a1),f860(x71531,x71533,x71532)),x71531))
% 109.14/108.86 [7158]~P4(x71581)+~P100(x71581)+P1(f318(f318(f225(x71581),f318(f94(x71581),x71582)),f318(f94(x71581),x71583)))+P1(f318(f318(f226(x71581),f318(f94(x71581),x71583)),f318(f94(x71581),x71582)))
% 109.14/108.86 [7190]P152(x71902,x71903,x71901)+E(x71901,f2(a1))+P1(f318(f318(f225(a1),f855(x71901,x71903,x71902)),f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x71901))
% 109.14/108.86 [7191]P151(x71912,x71913,x71911)+E(x71911,f2(a1))+P1(f318(f318(f225(a1),f859(x71911,x71913,x71912)),f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x71911))
% 109.14/108.86 [7216]~P4(x72161)+~P13(x72161,x72163)+E(f318(f318(f139(x72161,x72161,f7(x72161)),x72162),f161(x72161,x72162,x72163)),x72163)+~P1(f318(f318(f320(x72161),x72162),f318(f163(x72161),x72163)))
% 109.14/108.86 [7262]P151(x72621,x72622,x72623)+~P1(f318(x72621,x72622))+P1(f318(f318(f226(a1),x72623),f2(a1)))+P1(f318(f318(f226(a1),f860(x72623,x72622,x72621)),x72623))
% 109.14/108.86 [7268]~P3(x72681)+~P100(x72681)+E(f318(f318(f223(x72681),f318(f94(x72681),x72682)),f318(f94(x72681),x72683)),f318(f94(x72681),x72682))+~P1(f318(f318(f225(x72681),f318(f94(x72681),x72682)),f318(f94(x72681),x72683)))
% 109.14/108.86 [7269]~P3(x72691)+~P100(x72691)+E(f318(f318(f224(x72691),f318(f94(x72691),x72692)),f318(f94(x72691),x72693)),f318(f94(x72691),x72693))+~P1(f318(f318(f225(x72691),f318(f94(x72691),x72692)),f318(f94(x72691),x72693)))
% 109.14/108.86 [7283]P152(x72831,x72832,x72833)+~P1(f318(x72831,f2(a1)))+P1(f318(f318(f226(a1),x72833),f2(a1)))+P1(f318(f318(f226(a1),f856(x72833,x72832,x72831)),x72833))
% 109.14/108.86 [7293]P151(x72931,x72932,x72933)+~P1(f318(x72931,x72932))+P1(f318(f318(f225(a1),f859(x72933,x72932,x72931)),f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x72933))
% 109.14/108.86 [7317]P152(x73171,x73172,x73173)+~P1(f318(x73171,f2(a1)))+P1(f318(f318(f225(a1),f855(x73173,x73172,x73171)),f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x73173))
% 109.14/108.86 [7345]~P1(f318(x73451,x73452))+P1(f318(x73451,f2(a911)))+~P1(f318(f318(f226(a911),x73452),x73453))+P1(f318(f318(f226(a911),f411(x73452,x73451,x73453)),x73453))
% 109.14/108.86 [7362]~P4(x73621)+~P13(x73621,x73623)+P13(x73621,f318(f318(f142(x73621),x73622),x73623))+P1(f318(f318(f320(x73621),f706(x73623,x73622,x73621)),f318(f163(x73621),x73623)))
% 109.14/108.86 [7363]~P4(x73631)+~P13(x73631,x73633)+P13(x73631,f318(f318(f142(x73631),x73632),x73633))+P1(f318(f318(f320(x73631),f708(x73633,x73632,x73631)),f318(f163(x73631),x73633)))
% 109.14/108.86 [7364]~P4(x73641)+~P13(x73641,x73643)+P13(x73641,f318(f318(f142(x73641),x73642),x73643))+P1(f318(f318(f320(x73641),f747(x73642,x73643,x73641)),f318(f163(x73641),x73643)))
% 109.14/108.86 [7476]~P4(x74761)+~P5(x74761)+~P1(f318(f318(f226(x74761),x74763),f31(x74761,x74762)))+P1(f318(f318(f320(x74761),f557(x74762,x74763,x74761)),x74762))
% 109.14/108.86 [7622]~P4(x76221)+~P5(x76221)+~P1(f318(f318(f226(x76221),f32(x76221,x76223)),x76222))+P1(f318(f318(f320(x76221),f567(x76222,x76223,x76221)),x76223))
% 109.14/108.86 [7623]~P4(x76231)+~P5(x76231)+~P1(f318(f318(f226(x76231),f32(x76231,x76233)),x76232))+P1(f318(f318(f226(x76231),f567(x76232,x76233,x76231)),x76232))
% 109.14/108.86 [7635]P152(x76352,x76353,x76351)+E(x76351,f2(a1))+P1(f318(f318(f226(a1),x76351),f855(x76351,x76353,x76352)))+P1(f318(f318(f226(a1),f856(x76351,x76353,x76352)),x76351))
% 109.14/108.86 [7636]P151(x76362,x76363,x76361)+E(x76361,f2(a1))+P1(f318(f318(f226(a1),x76361),f859(x76361,x76363,x76362)))+P1(f318(f318(f226(a1),f860(x76361,x76363,x76362)),x76361))
% 109.14/108.86 [7726]P152(x77263,x77262,x77261)+E(x77261,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x77261),f858(x77261,x77262,x77263))),f855(x77261,x77262,x77263)),x77262)+P1(f318(f318(f226(a1),f2(a1)),x77261))
% 109.14/108.86 [7727]P151(x77273,x77272,x77271)+E(x77271,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x77271),f862(x77271,x77272,x77273))),f859(x77271,x77272,x77273)),x77272)+P1(f318(f318(f226(a1),f2(a1)),x77271))
% 109.14/108.86 [7728]~P139(x77281)+~P1(f318(f318(f225(x77281),x77282),f2(x77281)))+P1(f318(f318(f225(x77281),f318(f318(f74(x77281),x77282),x77283)),f2(x77281)))+~P1(f318(f318(f225(x77281),f2(x77281)),x77283))
% 109.14/108.86 [7729]~P139(x77291)+~P1(f318(f318(f225(x77291),x77293),f2(x77291)))+P1(f318(f318(f225(x77291),f318(f318(f74(x77291),x77292),x77293)),f2(x77291)))+~P1(f318(f318(f225(x77291),f2(x77291)),x77292))
% 109.14/108.86 [7730]~P139(x77301)+~P1(f318(f318(f225(x77301),x77303),f2(x77301)))+P1(f318(f318(f225(x77301),f318(f318(f74(x77301),x77302),x77303)),f2(x77301)))+~P1(f318(f318(f225(x77301),f2(x77301)),x77302))
% 109.14/108.86 [7731]~P139(x77311)+~P1(f318(f318(f225(x77311),x77312),f2(x77311)))+P1(f318(f318(f225(x77311),f318(f318(f74(x77311),x77312),x77313)),f2(x77311)))+~P1(f318(f318(f225(x77311),f2(x77311)),x77313))
% 109.14/108.86 [7732]~P139(x77321)+~P1(f318(f318(f225(x77321),x77322),f2(x77321)))+P1(f318(f318(f225(x77321),f318(f318(f74(x77321),x77322),x77323)),f2(x77321)))+~P1(f318(f318(f225(x77321),f2(x77321)),x77323))
% 109.14/108.86 [7733]~P131(x77331)+~P1(f318(f318(f225(x77331),x77333),f2(x77331)))+P1(f318(f318(f225(x77331),f318(f318(f74(x77331),x77332),x77333)),f2(x77331)))+~P1(f318(f318(f225(x77331),f2(x77331)),x77332))
% 109.14/108.86 [7734]~P131(x77341)+~P1(f318(f318(f225(x77341),x77342),f2(x77341)))+P1(f318(f318(f225(x77341),f318(f318(f74(x77341),x77342),x77343)),f2(x77341)))+~P1(f318(f318(f225(x77341),f2(x77341)),x77343))
% 109.14/108.86 [7735]~P74(x77351)+~P1(f318(f318(f225(x77351),x77353),f2(x77351)))+P1(f318(f318(f225(x77351),f318(f318(f282(x77351),x77352),x77353)),f2(x77351)))+~P1(f318(f318(f225(x77351),f2(x77351)),x77352))
% 109.14/108.86 [7736]~P74(x77361)+~P1(f318(f318(f225(x77361),x77362),f2(x77361)))+P1(f318(f318(f225(x77361),f318(f318(f282(x77361),x77362),x77363)),f2(x77361)))+~P1(f318(f318(f225(x77361),f2(x77361)),x77363))
% 109.14/108.86 [7737]~P75(x77371)+~P1(f318(f318(f225(x77371),x77372),f2(x77371)))+P1(f318(f318(f225(x77371),f318(f318(f282(x77371),x77372),x77373)),f2(x77371)))+~P1(f318(f318(f226(x77371),f2(x77371)),x77373))
% 109.14/108.86 [7738]~P75(x77381)+~P1(f318(f318(f226(x77381),x77383),f2(x77381)))+P1(f318(f318(f225(x77381),f318(f318(f282(x77381),x77382),x77383)),f2(x77381)))+~P1(f318(f318(f225(x77381),f2(x77381)),x77382))
% 109.14/108.86 [7739]~P134(x77391)+~P1(f318(f318(f226(x77391),x77392),f2(x77391)))+P1(f318(f318(f226(x77391),f318(f318(f74(x77391),x77392),x77393)),f2(x77391)))+~P1(f318(f318(f226(x77391),f2(x77391)),x77393))
% 109.14/108.86 [7740]~P134(x77401)+~P1(f318(f318(f226(x77401),x77403),f2(x77401)))+P1(f318(f318(f226(x77401),f318(f318(f74(x77401),x77402),x77403)),f2(x77401)))+~P1(f318(f318(f226(x77401),f2(x77401)),x77402))
% 109.14/108.86 [7741]~P134(x77411)+~P1(f318(f318(f226(x77411),x77412),f2(x77411)))+P1(f318(f318(f226(x77411),f318(f318(f74(x77411),x77412),x77413)),f2(x77411)))+~P1(f318(f318(f226(x77411),f2(x77411)),x77413))
% 109.14/108.86 [7742]~P74(x77421)+~P1(f318(f318(f226(x77421),x77423),f2(x77421)))+P1(f318(f318(f226(x77421),f318(f318(f282(x77421),x77422),x77423)),f2(x77421)))+~P1(f318(f318(f226(x77421),f2(x77421)),x77422))
% 109.14/108.86 [7743]~P74(x77431)+~P1(f318(f318(f226(x77431),x77432),f2(x77431)))+P1(f318(f318(f226(x77431),f318(f318(f282(x77431),x77432),x77433)),f2(x77431)))+~P1(f318(f318(f226(x77431),f2(x77431)),x77433))
% 109.14/108.86 [7744]~P75(x77441)+~P1(f318(f318(f226(x77441),x77443),f2(x77441)))+P1(f318(f318(f226(x77441),f318(f318(f282(x77441),x77442),x77443)),f2(x77441)))+~P1(f318(f318(f226(x77441),f2(x77441)),x77442))
% 109.14/108.86 [7745]~P75(x77451)+~P1(f318(f318(f226(x77451),x77452),f2(x77451)))+P1(f318(f318(f226(x77451),f318(f318(f282(x77451),x77452),x77453)),f2(x77451)))+~P1(f318(f318(f226(x77451),f2(x77451)),x77453))
% 109.14/108.86 [7760]P151(x77601,x77602,x77603)+~P1(f318(x77601,x77602))+P1(f318(f318(f226(a1),x77603),f859(x77603,x77602,x77601)))+P1(f318(f318(f226(a1),f860(x77603,x77602,x77601)),x77603))
% 109.14/108.86 [7773]P152(x77731,x77732,x77733)+P1(f318(f318(f226(a1),x77733),f855(x77733,x77732,x77731)))+~P1(f318(x77731,f2(a1)))+P1(f318(f318(f226(a1),f856(x77733,x77732,x77731)),x77733))
% 109.14/108.86 [7826]P152(x78262,x78263,x78261)+E(x78261,f2(a1))+~P1(f318(x78262,f858(x78261,x78263,x78262)))+P1(f318(f318(f226(a1),f856(x78261,x78263,x78262)),x78261))
% 109.14/108.86 [7827]P151(x78272,x78273,x78271)+E(x78271,f2(a1))+~P1(f318(x78272,f859(x78271,x78273,x78272)))+P1(f318(f318(f226(a1),f860(x78271,x78273,x78272)),x78271))
% 109.14/108.86 [7836]P151(x78363,x78362,x78361)+~P1(f318(x78363,x78362))+E(f318(f318(f73(a1),f318(f318(f74(a1),x78361),f862(x78361,x78362,x78363))),f859(x78361,x78362,x78363)),x78362)+P1(f318(f318(f226(a1),f2(a1)),x78361))
% 109.14/108.86 [7851]P152(x78513,x78512,x78511)+E(f318(f318(f73(a1),f318(f318(f74(a1),x78511),f858(x78511,x78512,x78513))),f855(x78511,x78512,x78513)),x78512)+~P1(f318(x78513,f2(a1)))+P1(f318(f318(f226(a1),f2(a1)),x78511))
% 109.14/108.86 [7879]~P1(f318(x78791,x78793))+~P1(f318(f55(x78792),x78793))+P1(f318(f318(f320(x78792),f897(x78791,x78793,x78792)),f896(x78791,x78793,x78792)))+P1(f318(x78791,f179(f918(x78792,a909))))
% 109.14/108.86 [7890]P151(x78901,x78902,x78903)+~P1(f318(x78901,x78902))+~P1(f318(x78901,f859(x78903,x78902,x78901)))+P1(f318(f318(f226(a1),f860(x78903,x78902,x78901)),x78903))
% 109.14/108.86 [7896]P152(x78961,x78962,x78963)+~P1(f318(x78961,f858(x78963,x78962,x78961)))+~P1(f318(x78961,f2(a1)))+P1(f318(f318(f226(a1),f856(x78963,x78962,x78961)),x78963))
% 109.14/108.86 [7966]~P100(x79661)+~P4(x79661)+~P1(f318(f318(f225(x79661),f318(f94(x79661),x79662)),f318(f94(x79661),x79663)))+~P1(f318(f318(f226(x79661),f318(f94(x79661),x79663)),f318(f94(x79661),x79662)))
% 109.14/108.86 [8003]~P131(x80031)+~P1(f318(f318(f225(x80031),f318(f318(f74(x80031),x80033),x80032)),f2(x80031)))+P1(f318(f318(f225(x80031),x80032),f2(x80031)))+P1(f318(f318(f225(x80031),f2(x80031)),x80032))
% 109.14/108.86 [8004]~P131(x80041)+~P1(f318(f318(f225(x80041),f318(f318(f74(x80041),x80042),x80043)),f2(x80041)))+P1(f318(f318(f225(x80041),x80042),f2(x80041)))+P1(f318(f318(f225(x80041),f2(x80041)),x80042))
% 109.14/108.86 [8005]~P74(x80051)+~P1(f318(f318(f225(x80051),f318(f318(f282(x80051),x80053),x80052)),f2(x80051)))+P1(f318(f318(f225(x80051),x80052),f2(x80051)))+P1(f318(f318(f225(x80051),f2(x80051)),x80052))
% 109.14/108.86 [8006]~P74(x80061)+~P1(f318(f318(f225(x80061),f318(f318(f282(x80061),x80062),x80063)),f2(x80061)))+P1(f318(f318(f225(x80061),x80062),f2(x80061)))+P1(f318(f318(f225(x80061),f2(x80061)),x80062))
% 109.14/108.86 [8007]~P74(x80071)+~P1(f318(f318(f226(x80071),f318(f318(f282(x80071),x80073),x80072)),f2(x80071)))+P1(f318(f318(f226(x80071),x80072),f2(x80071)))+P1(f318(f318(f226(x80071),f2(x80071)),x80072))
% 109.14/108.86 [8008]~P74(x80081)+~P1(f318(f318(f226(x80081),f318(f318(f282(x80081),x80082),x80083)),f2(x80081)))+P1(f318(f318(f226(x80081),x80082),f2(x80081)))+P1(f318(f318(f226(x80081),f2(x80081)),x80082))
% 109.14/108.86 [8028]~P131(x80281)+~P1(f318(f318(f225(x80281),f318(f318(f74(x80281),x80282),x80283)),f2(x80281)))+P1(f318(f318(f225(x80281),f2(x80281)),x80282))+P1(f318(f318(f225(x80281),f2(x80281)),x80283))
% 109.14/108.86 [8029]~P74(x80291)+~P1(f318(f318(f225(x80291),f318(f318(f282(x80291),x80292),x80293)),f2(x80291)))+P1(f318(f318(f225(x80291),f2(x80291)),x80292))+P1(f318(f318(f225(x80291),f2(x80291)),x80293))
% 109.14/108.86 [8030]~P74(x80301)+~P1(f318(f318(f226(x80301),f318(f318(f282(x80301),x80302),x80303)),f2(x80301)))+P1(f318(f318(f226(x80301),f2(x80301)),x80302))+P1(f318(f318(f226(x80301),f2(x80301)),x80303))
% 109.14/108.86 [8052]P152(x80522,x80523,x80521)+E(x80521,f2(a1))+P1(f318(f318(f225(a1),f855(x80521,x80523,x80522)),f2(a1)))+P1(f318(f318(f226(a1),f856(x80521,x80523,x80522)),x80521))
% 109.14/108.86 [8053]P151(x80532,x80533,x80531)+E(x80531,f2(a1))+P1(f318(f318(f225(a1),f859(x80531,x80533,x80532)),f2(a1)))+P1(f318(f318(f226(a1),f860(x80531,x80533,x80532)),x80531))
% 109.14/108.86 [8060]~P130(x80601)+~P1(f318(f318(f226(x80601),x80602),f71(x80601)))+P1(f318(f318(f226(x80601),f318(f318(f235(x80601),x80602),f318(a103,x80603))),f71(x80601)))+~P1(f318(f318(f226(x80601),f2(x80601)),x80602))
% 109.14/108.86 [8109]~P4(x81091)+~E(x81093,f104(x81091))+~P13(x81091,f318(f159(x81091),x81093))+E(f318(f133(x81091,x81091,f318(f9(x81091,x81091,x81091),f224(x81091)),x81092),f318(f159(x81091),x81093)),x81092)
% 109.14/108.86 [8112]P151(x81121,x81122,x81123)+~P1(f318(x81121,x81122))+P1(f318(f318(f225(a1),f859(x81123,x81122,x81121)),f2(a1)))+P1(f318(f318(f226(a1),f860(x81123,x81122,x81121)),x81123))
% 109.14/108.86 [8118]P152(x81181,x81182,x81183)+~P1(f318(x81181,f2(a1)))+P1(f318(f318(f225(a1),f855(x81183,x81182,x81181)),f2(a1)))+P1(f318(f318(f226(a1),f856(x81183,x81182,x81181)),x81183))
% 109.14/108.86 [8344]P152(x83443,x83442,x83441)+E(x83441,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x83441),f858(x83441,x83442,x83443))),f855(x83441,x83442,x83443)),x83442)+P1(f318(f318(f226(a1),f856(x83441,x83442,x83443)),x83441))
% 109.14/108.86 [8345]P151(x83453,x83452,x83451)+E(x83451,f2(a1))+E(f318(f318(f73(a1),f318(f318(f74(a1),x83451),f862(x83451,x83452,x83453))),f859(x83451,x83452,x83453)),x83452)+P1(f318(f318(f226(a1),f860(x83451,x83452,x83453)),x83451))
% 109.14/108.86 [8377]P151(x83773,x83772,x83771)+~P1(f318(x83773,x83772))+E(f318(f318(f73(a1),f318(f318(f74(a1),x83771),f862(x83771,x83772,x83773))),f859(x83771,x83772,x83773)),x83772)+P1(f318(f318(f226(a1),f860(x83771,x83772,x83773)),x83771))
% 109.14/108.86 [8378]~P76(x83781)+~P82(x83781)+~P43(x83783)+E(f318(f318(f8(a911,x83781),f318(f318(f10(a1,x83781,a911),x83782),f91(a1))),f318(f301(a1,a911,a95),x83783)),f318(f318(f8(a1,x83781),x83782),x83783))
% 109.14/108.86 [8379]~P76(x83791)+~P82(x83791)+~P43(x83793)+E(f318(f318(f11(a911,x83791),f318(f318(f10(a1,x83791,a911),x83792),f91(a1))),f318(f301(a1,a911,a95),x83793)),f318(f318(f11(a1,x83791),x83792),x83793))
% 109.14/108.86 [8388]P152(x83883,x83882,x83881)+E(f318(f318(f73(a1),f318(f318(f74(a1),x83881),f858(x83881,x83882,x83883))),f855(x83881,x83882,x83883)),x83882)+~P1(f318(x83883,f2(a1)))+P1(f318(f318(f226(a1),f856(x83881,x83882,x83883)),x83881))
% 109.14/108.86 [8410]~E(x84102,f2(a911))+~E(f318(f242(a911,a911),x84103),f2(a911))+~E(x84101,f318(f318(f73(a911),f318(f318(f74(a911),f318(f242(a911,a911),x84103)),x84102)),f318(f247(a911,a911),x84103)))+P1(f318(f42(x84101,x84102),x84103))
% 109.14/108.86 [8467]P1(f318(x84671,x84672))+~P1(f318(f318(f320(x84673),f424(x84671,x84672,x84673)),f423(x84671,x84672,x84673)))+~P1(f318(f55(x84673),x84672))+~P1(f318(x84671,f179(f918(x84673,a909))))
% 109.14/108.86 [9091]P1(f318(x90911,x90912))+~P1(f318(f55(x90913),x90912))+~P1(f318(x90911,f318(f318(f300(x90913),f424(x90911,x90912,x90913)),f423(x90911,x90912,x90913))))+~P1(f318(x90911,f179(f918(x90913,a909))))
% 109.14/108.86 [9322]P1(f318(f318(f225(a1),x93221),f2(a1)))+~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f74(a1),x93223),x93221)),x93222)),f2(a1)))+~P1(f318(f318(f225(a1),f2(a1)),x93222))+~P1(f318(f318(f226(a1),f2(a1)),x93223))
% 109.14/108.86 [5934]~P103(x59342)+E(x59341,f179(f918(x59342,a909)))+~P1(f318(f55(x59342),x59341))+E(f12(x59342,f318(f318(f300(x59342),x59343),x59341)),f318(f318(f92(x59342),x59343),f12(x59342,x59341)))
% 109.14/108.86 [5935]~P103(x59352)+E(x59351,f179(f918(x59352,a909)))+~P1(f318(f55(x59352),x59351))+E(f15(x59352,f318(f318(f300(x59352),x59353),x59351)),f318(f318(f101(x59352),x59353),f15(x59352,x59351)))
% 109.14/108.86 [5936]~P4(x59362)+E(x59361,f179(f918(x59362,a909)))+~P1(f318(f55(x59362),x59361))+E(f16(x59362,f318(f318(f300(x59362),x59363),x59361)),f318(f318(f223(x59362),x59363),f16(x59362,x59361)))
% 109.14/108.86 [5937]~P4(x59372)+E(x59371,f179(f918(x59372,a909)))+~P1(f318(f55(x59372),x59371))+E(f17(x59372,f318(f318(f300(x59372),x59373),x59371)),f318(f318(f224(x59372),x59373),f17(x59372,x59371)))
% 109.14/108.86 [6260]~P131(x62601)+~E(x62603,f2(x62601))+~E(x62602,f2(x62601))+E(f318(f318(f73(x62601),f318(f318(f74(x62601),x62602),x62602)),f318(f318(f74(x62601),x62603),x62603)),f2(x62601))
% 109.14/108.86 [6327]~P101(x63272)+E(x63271,f179(f918(x63272,a909)))+~P1(f318(f55(x63272),x63271))+E(f318(f57(x63272,f74(x63272)),f318(f318(f300(x63272),x63273),x63271)),f318(f318(f74(x63272),x63273),f318(f57(x63272,f74(x63272)),x63271)))
% 109.14/108.86 [6453]~P4(x64532)+E(x64531,f179(f918(x64532,a909)))+~P1(f318(f55(x64532),x64531))+E(f13(x64532,f223(x64532),f318(f318(f300(x64532),x64533),x64531)),f318(f318(f223(x64532),x64533),f13(x64532,f223(x64532),x64531)))
% 109.14/108.86 [6454]~P4(x64542)+E(x64541,f179(f918(x64542,a909)))+~P1(f318(f55(x64542),x64541))+E(f14(x64542,f224(x64542),f318(f318(f300(x64542),x64543),x64541)),f318(f318(f224(x64542),x64543),f14(x64542,f224(x64542),x64541)))
% 109.14/108.86 [6855]~P103(x68551)+~P1(f318(f55(x68551),x68553))+E(f318(f318(f58(x68551,x68551,f92(x68551)),x68552),x68553),f12(x68551,f318(f318(f300(x68551),x68552),x68553)))+P1(f318(f318(f320(x68551),x68552),x68553))
% 109.14/108.86 [6856]~P103(x68561)+~P1(f318(f55(x68561),x68563))+E(f318(f318(f58(x68561,x68561,f101(x68561)),x68562),x68563),f15(x68561,f318(f318(f300(x68561),x68562),x68563)))+P1(f318(f318(f320(x68561),x68562),x68563))
% 109.14/108.86 [6857]~P4(x68571)+~P1(f318(f55(x68571),x68573))+E(f318(f318(f58(x68571,x68571,f223(x68571)),x68572),x68573),f16(x68571,f318(f318(f300(x68571),x68572),x68573)))+P1(f318(f318(f320(x68571),x68572),x68573))
% 109.14/108.86 [6858]~P4(x68581)+~P1(f318(f55(x68581),x68583))+E(f318(f318(f58(x68581,x68581,f224(x68581)),x68582),x68583),f17(x68581,f318(f318(f300(x68581),x68582),x68583)))+P1(f318(f318(f320(x68581),x68582),x68583))
% 109.14/108.86 [6960]~P80(x69601)+~P1(f318(f55(x69601),x69603))+E(f318(f57(x69601,f74(x69601)),f318(f318(f300(x69601),x69602),x69603)),f318(f318(f58(x69601,x69601,f74(x69601)),x69602),x69603))+P1(f318(f318(f320(x69601),x69602),x69603))
% 109.14/108.86 [6976]~P4(x69761)+~P1(f318(f55(x69761),x69763))+E(f13(x69761,f223(x69761),f318(f318(f300(x69761),x69762),x69763)),f318(f318(f58(x69761,x69761,f223(x69761)),x69762),x69763))+P1(f318(f318(f320(x69761),x69762),x69763))
% 109.14/108.86 [6977]~P4(x69771)+~P1(f318(f55(x69771),x69773))+E(f14(x69771,f224(x69771),f318(f318(f300(x69771),x69772),x69773)),f318(f318(f58(x69771,x69771,f224(x69771)),x69772),x69773))+P1(f318(f318(f320(x69771),x69772),x69773))
% 109.14/108.86 [7042]~E(f318(f318(f73(a1),x70422),f318(f318(f74(a1),x70423),x70421)),x70423)+~P1(f318(f318(f226(a1),f2(a1)),x70423))+P1(f318(f318(f225(a1),f71(a1)),x70421))+~P1(f318(f318(f226(a1),x70422),x70423))
% 109.14/108.86 [7071]~E(f318(f318(f73(a1),x70712),f318(f318(f74(a1),x70713),x70711)),x70713)+P1(f318(f318(f225(a1),x70711),f71(a1)))+~P1(f318(f318(f225(a1),f2(a1)),x70712))+~P1(f318(f318(f226(a1),f2(a1)),x70713))
% 109.14/108.86 [7087]E(x70871,f2(a911))+~P1(f318(f42(x70873,x70871),x70872))+~P1(f318(f318(f226(a911),f2(a911)),x70871))+P1(f318(f318(f226(a911),f318(f247(a911,a911),x70872)),x70871))
% 109.14/108.86 [7120]~P143(x71201)+~P1(f318(f318(f225(x71201),x71202),f2(x71201)))+~P1(f318(f318(f225(x71201),x71203),f2(x71201)))+E(f318(f318(f74(x71201),f318(f69(x71201),x71202)),f318(f69(x71201),x71203)),f318(f69(x71201),f318(f318(f74(x71201),x71202),x71203)))
% 109.14/108.86 [7167]~P143(x71671)+~P1(f318(f318(f225(x71671),x71672),f2(x71671)))+E(f318(f318(f74(x71671),f318(f69(x71671),x71672)),f318(f69(x71671),x71673)),f318(f69(x71671),f318(f318(f74(x71671),x71672),x71673)))+~P1(f318(f318(f225(x71671),f2(x71671)),x71673))
% 109.14/108.86 [7168]~P143(x71681)+~P1(f318(f318(f225(x71681),x71683),f2(x71681)))+E(f318(f318(f74(x71681),f318(f69(x71681),x71682)),f318(f69(x71681),x71683)),f318(f69(x71681),f318(f318(f74(x71681),x71682),x71683)))+~P1(f318(f318(f225(x71681),f2(x71681)),x71682))
% 109.14/108.86 [7223]~P143(x72231)+E(f318(f318(f74(x72231),f318(f69(x72231),x72232)),f318(f69(x72231),x72233)),f318(f69(x72231),f318(f318(f74(x72231),x72232),x72233)))+~P1(f318(f318(f225(x72231),f2(x72231)),x72232))+~P1(f318(f318(f225(x72231),f2(x72231)),x72233))
% 109.14/108.86 [7239]~P140(x72391)+~P1(f318(f318(f225(x72391),x72393),f2(x72391)))+~P1(f318(f318(f225(x72391),x72392),f2(x72391)))+P1(f318(f318(f225(x72391),f2(x72391)),f318(f318(f74(x72391),x72392),x72393)))
% 109.14/108.86 [7240]~P140(x72401)+~P1(f318(f318(f225(x72401),x72403),f2(x72401)))+~P1(f318(f318(f225(x72401),x72402),f2(x72401)))+P1(f318(f318(f225(x72401),f2(x72401)),f318(f318(f74(x72401),x72402),x72403)))
% 109.14/108.86 [7241]~P131(x72411)+~P1(f318(f318(f225(x72411),x72413),f2(x72411)))+~P1(f318(f318(f225(x72411),x72412),f2(x72411)))+P1(f318(f318(f225(x72411),f2(x72411)),f318(f318(f74(x72411),x72412),x72413)))
% 109.14/108.86 [7242]~P74(x72421)+~P1(f318(f318(f225(x72421),x72423),f2(x72421)))+~P1(f318(f318(f225(x72421),x72422),f2(x72421)))+P1(f318(f318(f225(x72421),f2(x72421)),f318(f318(f282(x72421),x72422),x72423)))
% 109.14/108.86 [7243]~P75(x72431)+~P1(f318(f318(f226(x72431),x72433),f2(x72431)))+~P1(f318(f318(f225(x72431),x72432),f2(x72431)))+P1(f318(f318(f225(x72431),f2(x72431)),f318(f318(f282(x72431),x72432),x72433)))
% 109.14/108.86 [7244]~P131(x72441)+~P1(f318(f318(f226(x72441),x72443),f2(x72441)))+~P1(f318(f318(f226(x72441),x72442),f2(x72441)))+P1(f318(f318(f226(x72441),f2(x72441)),f318(f318(f74(x72441),x72442),x72443)))
% 109.14/108.86 [7245]~P74(x72451)+~P1(f318(f318(f226(x72451),x72453),f2(x72451)))+~P1(f318(f318(f226(x72451),x72452),f2(x72451)))+P1(f318(f318(f226(x72451),f2(x72451)),f318(f318(f282(x72451),x72452),x72453)))
% 109.14/108.86 [7246]~P75(x72461)+~P1(f318(f318(f226(x72461),x72463),f2(x72461)))+~P1(f318(f318(f226(x72461),x72462),f2(x72461)))+P1(f318(f318(f226(x72461),f2(x72461)),f318(f318(f282(x72461),x72462),x72463)))
% 109.14/108.86 [7247]~P130(x72471)+~P1(f318(f318(f226(a911),f2(a911)),x72473))+~P1(f318(f318(f226(x72471),f71(x72471)),x72472))+P1(f318(f318(f226(x72471),f71(x72471)),f318(f318(f235(x72471),x72472),x72473)))
% 109.14/108.86 [7346]~P93(x73461)+~P1(f318(f318(f225(x73461),f2(x73461)),x73463))+~P1(f318(f318(f225(x73461),f2(x73461)),x73462))+P1(f318(f318(f225(x73461),f2(x73461)),f318(f318(f73(x73461),x73462),x73463)))
% 109.14/108.86 [7347]~P139(x73471)+~P1(f318(f318(f225(x73471),f2(x73471)),x73473))+~P1(f318(f318(f225(x73471),f2(x73471)),x73472))+P1(f318(f318(f225(x73471),f2(x73471)),f318(f318(f74(x73471),x73472),x73473)))
% 109.14/108.86 [7348]~P140(x73481)+~P1(f318(f318(f225(x73481),f2(x73481)),x73483))+~P1(f318(f318(f225(x73481),f2(x73481)),x73482))+P1(f318(f318(f225(x73481),f2(x73481)),f318(f318(f74(x73481),x73482),x73483)))
% 109.14/108.86 [7349]~P131(x73491)+~P1(f318(f318(f225(x73491),f2(x73491)),x73493))+~P1(f318(f318(f225(x73491),f2(x73491)),x73492))+P1(f318(f318(f225(x73491),f2(x73491)),f318(f318(f74(x73491),x73492),x73493)))
% 109.14/108.86 [7350]~P74(x73501)+~P1(f318(f318(f225(x73501),f2(x73501)),x73503))+~P1(f318(f318(f225(x73501),f2(x73501)),x73502))+P1(f318(f318(f225(x73501),f2(x73501)),f318(f318(f282(x73501),x73502),x73503)))
% 109.14/108.86 [7351]~P75(x73511)+~P1(f318(f318(f226(x73511),f2(x73511)),x73513))+~P1(f318(f318(f225(x73511),f2(x73511)),x73512))+P1(f318(f318(f225(x73511),f2(x73511)),f318(f318(f282(x73511),x73512),x73513)))
% 109.14/108.86 [7352]~P93(x73521)+~P1(f318(f318(f225(x73521),f2(x73521)),x73523))+~P1(f318(f318(f226(x73521),f2(x73521)),x73522))+P1(f318(f318(f226(x73521),f2(x73521)),f318(f318(f73(x73521),x73522),x73523)))
% 109.14/108.86 [7353]~P93(x73531)+~P1(f318(f318(f225(x73531),f2(x73531)),x73532))+~P1(f318(f318(f226(x73531),f2(x73531)),x73533))+P1(f318(f318(f226(x73531),f2(x73531)),f318(f318(f73(x73531),x73532),x73533)))
% 109.14/108.86 [7354]~P93(x73541)+~P1(f318(f318(f226(x73541),f2(x73541)),x73543))+~P1(f318(f318(f226(x73541),f2(x73541)),x73542))+P1(f318(f318(f226(x73541),f2(x73541)),f318(f318(f73(x73541),x73542),x73543)))
% 109.14/108.86 [7355]~P134(x73551)+~P1(f318(f318(f226(x73551),f2(x73551)),x73553))+~P1(f318(f318(f226(x73551),f2(x73551)),x73552))+P1(f318(f318(f226(x73551),f2(x73551)),f318(f318(f74(x73551),x73552),x73553)))
% 109.14/108.86 [7356]~P74(x73561)+~P1(f318(f318(f226(x73561),f2(x73561)),x73563))+~P1(f318(f318(f226(x73561),f2(x73561)),x73562))+P1(f318(f318(f226(x73561),f2(x73561)),f318(f318(f282(x73561),x73562),x73563)))
% 109.14/108.86 [7357]~P75(x73571)+~P1(f318(f318(f226(x73571),f2(x73571)),x73573))+~P1(f318(f318(f226(x73571),f2(x73571)),x73572))+P1(f318(f318(f226(x73571),f2(x73571)),f318(f318(f282(x73571),x73572),x73573)))
% 109.14/108.86 [7358]~P130(x73581)+~P1(f318(f318(f226(x73581),f71(x73581)),x73583))+~P1(f318(f318(f226(x73581),f71(x73581)),x73582))+P1(f318(f318(f226(x73581),f71(x73581)),f318(f318(f74(x73581),x73582),x73583)))
% 109.14/108.86 [7433]~P103(x74331)+~P1(f318(f55(x74331),x74333))+E(f12(x74331,f318(f318(f300(x74331),x74332),x74333)),x74332)+~E(f318(f318(f3(f918(x74331,a909)),x74333),f318(f318(f300(x74331),x74332),f179(f918(x74331,a909)))),f179(f918(x74331,a909)))
% 109.14/108.86 [7434]~P103(x74341)+~P1(f318(f55(x74341),x74343))+E(f15(x74341,f318(f318(f300(x74341),x74342),x74343)),x74342)+~E(f318(f318(f3(f918(x74341,a909)),x74343),f318(f318(f300(x74341),x74342),f179(f918(x74341,a909)))),f179(f918(x74341,a909)))
% 109.14/108.86 [7435]~P4(x74351)+~P1(f318(f55(x74351),x74353))+E(f16(x74351,f318(f318(f300(x74351),x74352),x74353)),x74352)+~E(f318(f318(f3(f918(x74351,a909)),x74353),f318(f318(f300(x74351),x74352),f179(f918(x74351,a909)))),f179(f918(x74351,a909)))
% 109.14/108.86 [7436]~P4(x74361)+~P1(f318(f55(x74361),x74363))+E(f17(x74361,f318(f318(f300(x74361),x74362),x74363)),x74362)+~E(f318(f318(f3(f918(x74361,a909)),x74363),f318(f318(f300(x74361),x74362),f179(f918(x74361,a909)))),f179(f918(x74361,a909)))
% 109.14/108.86 [7438]~P131(x74381)+P1(f318(f318(f225(x74381),x74382),f2(x74381)))+P1(f318(f318(f225(x74381),f2(x74381)),x74383))+~P1(f318(f318(f225(x74381),f2(x74381)),f318(f318(f74(x74381),x74383),x74382)))
% 109.14/108.86 [7439]~P131(x74391)+P1(f318(f318(f225(x74391),x74392),f2(x74391)))+P1(f318(f318(f225(x74391),f2(x74391)),x74393))+~P1(f318(f318(f225(x74391),f2(x74391)),f318(f318(f74(x74391),x74392),x74393)))
% 109.14/108.86 [7440]~P74(x74401)+P1(f318(f318(f225(x74401),x74402),f2(x74401)))+P1(f318(f318(f225(x74401),f2(x74401)),x74403))+~P1(f318(f318(f225(x74401),f2(x74401)),f318(f318(f282(x74401),x74403),x74402)))
% 109.14/108.86 [7441]~P74(x74411)+P1(f318(f318(f225(x74411),x74412),f2(x74411)))+P1(f318(f318(f225(x74411),f2(x74411)),x74413))+~P1(f318(f318(f225(x74411),f2(x74411)),f318(f318(f282(x74411),x74412),x74413)))
% 109.14/108.86 [7442]~P131(x74421)+P1(f318(f318(f225(x74421),x74422),f2(x74421)))+P1(f318(f318(f225(x74421),f2(x74421)),x74422))+~P1(f318(f318(f225(x74421),f2(x74421)),f318(f318(f74(x74421),x74423),x74422)))
% 109.14/108.86 [7443]~P131(x74431)+P1(f318(f318(f225(x74431),x74432),f2(x74431)))+P1(f318(f318(f225(x74431),f2(x74431)),x74432))+~P1(f318(f318(f225(x74431),f2(x74431)),f318(f318(f74(x74431),x74432),x74433)))
% 109.14/108.86 [7444]~P74(x74441)+P1(f318(f318(f225(x74441),x74442),f2(x74441)))+P1(f318(f318(f225(x74441),f2(x74441)),x74442))+~P1(f318(f318(f225(x74441),f2(x74441)),f318(f318(f282(x74441),x74443),x74442)))
% 109.14/108.86 [7445]~P74(x74451)+P1(f318(f318(f225(x74451),x74452),f2(x74451)))+P1(f318(f318(f225(x74451),f2(x74451)),x74452))+~P1(f318(f318(f225(x74451),f2(x74451)),f318(f318(f282(x74451),x74452),x74453)))
% 109.14/108.86 [7446]~P74(x74461)+P1(f318(f318(f226(x74461),x74462),f2(x74461)))+P1(f318(f318(f226(x74461),f2(x74461)),x74463))+~P1(f318(f318(f226(x74461),f2(x74461)),f318(f318(f282(x74461),x74463),x74462)))
% 109.14/108.86 [7447]~P74(x74471)+P1(f318(f318(f226(x74471),x74472),f2(x74471)))+P1(f318(f318(f226(x74471),f2(x74471)),x74473))+~P1(f318(f318(f226(x74471),f2(x74471)),f318(f318(f282(x74471),x74472),x74473)))
% 109.14/108.86 [7448]~P74(x74481)+P1(f318(f318(f226(x74481),x74482),f2(x74481)))+P1(f318(f318(f226(x74481),f2(x74481)),x74482))+~P1(f318(f318(f226(x74481),f2(x74481)),f318(f318(f282(x74481),x74483),x74482)))
% 109.14/108.86 [7449]~P74(x74491)+P1(f318(f318(f226(x74491),x74492),f2(x74491)))+P1(f318(f318(f226(x74491),f2(x74491)),x74492))+~P1(f318(f318(f226(x74491),f2(x74491)),f318(f318(f282(x74491),x74492),x74493)))
% 109.14/108.86 [7529]~E(f318(f318(f92(f918(x75291,a909)),f318(f163(x75291),x75292)),f318(f163(x75291),x75293)),f179(f918(x75291,a909)))+~P1(f318(f128(x75291),x75293))+~P1(f318(f128(x75291),x75292))+P1(f318(f128(x75291),f318(f318(f125(x75291),x75292),x75293)))
% 109.14/108.86 [7530]~P4(x75301)+~P1(f318(f55(x75301),x75303))+E(f13(x75301,f223(x75301),f318(f318(f300(x75301),x75302),x75303)),x75302)+~E(f318(f318(f3(f918(x75301,a909)),x75303),f318(f318(f300(x75301),x75302),f179(f918(x75301,a909)))),f179(f918(x75301,a909)))
% 109.14/108.86 [7531]~P4(x75311)+~P1(f318(f55(x75311),x75313))+E(f14(x75311,f224(x75311),f318(f318(f300(x75311),x75312),x75313)),x75312)+~E(f318(f318(f3(f918(x75311,a909)),x75313),f318(f318(f300(x75311),x75312),f179(f918(x75311,a909)))),f179(f918(x75311,a909)))
% 109.14/108.86 [7543]~P91(x75431)+~P1(f318(f318(f225(x75431),x75432),x75433))+~P1(f318(f318(f225(x75431),f318(f72(x75431),x75432)),x75433))+P1(f318(f318(f225(x75431),f318(f69(x75431),x75432)),x75433))
% 109.14/108.86 [7544]~P91(x75441)+~P1(f318(f318(f225(x75441),x75442),x75443))+~P1(f318(f318(f225(x75441),f318(f72(x75441),x75442)),x75443))+P1(f318(f318(f225(x75441),f318(f69(x75441),x75442)),x75443))
% 109.14/108.86 [7545]~P116(x75451)+~P1(f318(f318(f226(x75451),x75452),x75453))+~P1(f318(f318(f226(x75451),f318(f72(x75451),x75452)),x75453))+P1(f318(f318(f226(x75451),f318(f69(x75451),x75452)),x75453))
% 109.14/108.86 [7612]~P134(x76121)+P1(f318(f318(f226(x76121),f2(x76121)),x76122))+~P1(f318(f318(f226(x76121),f2(x76121)),x76123))+~P1(f318(f318(f226(x76121),f2(x76121)),f318(f318(f74(x76121),x76123),x76122)))
% 109.14/108.86 [7613]~P134(x76131)+P1(f318(f318(f226(x76131),f2(x76131)),x76132))+~P1(f318(f318(f226(x76131),f2(x76131)),x76133))+~P1(f318(f318(f226(x76131),f2(x76131)),f318(f318(f74(x76131),x76132),x76133)))
% 109.14/108.86 [7911]E(x79111,x79112)+~P1(f318(f55(x79113),x79111))+~P1(f318(f318(f225(a911),f318(f29(x79113),x79111)),f318(f29(x79113),x79112)))+~P1(f318(f318(f225(f918(x79113,a909)),x79112),x79111))
% 109.14/108.86 [7983]~P1(f318(f318(f225(a911),x79832),x79831))+~P1(f318(f318(f225(a911),x79832),x79833))+~P1(f318(f318(f225(a911),x79831),x79833))+P1(f318(f318(f225(a911),f318(f318(f3(a911),x79831),x79832)),f318(f318(f3(a911),x79833),x79832)))
% 109.14/108.86 [7984]~P1(f318(f318(f225(a911),x79842),x79841))+~P1(f318(f318(f225(a911),x79842),x79843))+~P1(f318(f318(f226(a911),x79841),x79843))+P1(f318(f318(f226(a911),f318(f318(f3(a911),x79841),x79842)),f318(f318(f3(a911),x79843),x79842)))
% 109.14/108.86 [8057]~P1(f318(f318(f226(a1),x80571),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x80572))+~P1(f318(f318(f225(a1),x80572),x80573))+P1(f318(f318(f225(a1),f318(f318(f30(a1),x80571),x80572)),f318(f318(f30(a1),x80571),x80573)))
% 109.14/108.86 [8068]~P1(f318(f318(f225(a1),f2(a1)),x80681))+~P1(f318(f318(f226(a1),f2(a1)),x80683))+~P1(f318(f318(f225(a1),x80683),x80682))+P1(f318(f318(f225(a1),f318(f318(f30(a1),x80681),x80682)),f318(f318(f30(a1),x80681),x80683)))
% 109.14/108.86 [8197]E(f318(x81971,f407(x81972,x81971,x81973)),x81972)+~P1(f318(f318(f225(a1),x81972),f318(x81971,x81973)))+P1(f318(f318(f226(a911),f408(x81972,x81971,x81973)),x81973))+~P1(f318(f318(f225(a1),f318(x81971,f2(a911))),x81972))
% 109.14/108.86 [8198]E(f318(x81981,f409(x81982,x81981,x81983)),x81982)+~P1(f318(f318(f225(a1),x81982),f318(x81981,x81983)))+P1(f318(f318(f226(a911),f410(x81982,x81981,x81983)),x81983))+~P1(f318(f318(f225(a1),f318(x81981,f2(a911))),x81982))
% 109.14/108.86 [8306]~P1(f318(f55(x83061),x83063))+~P1(f318(f318(f226(a911),f318(f29(x83061),x83062)),f318(f29(x83061),x83063)))+~P1(f318(f318(f225(f918(x83061,a909)),x83062),x83063))+P1(f318(f318(f226(f918(x83061,a909)),x83062),x83063))
% 109.14/108.86 [8333]E(f318(f318(f73(a1),f340(x83333,x83331,x83332)),f341(x83333,x83331,x83332)),x83331)+E(f318(f318(f3(a1),x83331),x83332),x83331)+~P1(f318(f318(f226(a1),f2(a1)),x83332))+~P1(f318(f318(f320(a1),f318(f318(f3(a1),x83331),f71(a1))),x83333))
% 109.14/108.86 [8334]E(f318(f318(f3(a1),f348(x83343,x83341,x83342)),f349(x83343,x83341,x83342)),x83341)+E(f318(f318(f73(a1),x83341),x83342),x83341)+~P1(f318(f318(f226(a1),f2(a1)),x83342))+~P1(f318(f318(f320(a1),f318(f318(f73(a1),x83341),f71(a1))),x83343))
% 109.14/108.86 [8383]~P1(f318(f318(f225(a911),x83833),x83831))+P1(f318(f318(f225(a911),x83831),x83832))+~P1(f318(f318(f225(a911),x83833),x83832))+~P1(f318(f318(f225(a911),f318(f318(f3(a911),x83831),x83833)),f318(f318(f3(a911),x83832),x83833)))
% 109.14/108.86 [8384]~P1(f318(f318(f225(a911),x83843),x83841))+P1(f318(f318(f226(a911),x83841),x83842))+~P1(f318(f318(f225(a911),x83843),x83842))+~P1(f318(f318(f226(a911),f318(f318(f3(a911),x83841),x83843)),f318(f318(f3(a911),x83842),x83843)))
% 109.14/108.86 [8403]~P4(x84032)+E(x84031,f104(x84032))+~P13(x84032,f318(f159(x84032),x84031))+E(f318(f133(x84032,x84032,f318(f9(x84032,x84032,x84032),f224(x84032)),x84033),f318(f159(x84032),x84031)),f318(f318(f224(x84032),f318(f318(f155(x84032),x84031),f2(a911))),x84033))
% 109.14/108.86 [8450]~P5(x84501)+~P42(x84501,x84501,x84503)+P1(f318(f318(f225(x84501),x84502),f87(x84501,x84503)))+~P1(f318(f318(f225(x84501),x84502),f318(x84503,f318(f318(f101(x84501),x84502),f87(x84501,x84503)))))
% 109.14/108.86 [8472]E(f318(f318(f3(a1),x84721),x84722),x84721)+~P1(f318(f318(f226(a1),f2(a1)),x84722))+P1(f318(f318(f320(a1),f340(x84723,x84721,x84722)),x84723))+~P1(f318(f318(f320(a1),f318(f318(f3(a1),x84721),f71(a1))),x84723))
% 109.14/108.86 [8473]E(f318(f318(f73(a1),x84731),x84732),x84731)+~P1(f318(f318(f226(a1),f2(a1)),x84732))+P1(f318(f318(f320(a1),f348(x84733,x84731,x84732)),x84733))+~P1(f318(f318(f320(a1),f318(f318(f73(a1),x84731),f71(a1))),x84733))
% 109.14/108.86 [8542]~P1(f318(f318(f225(a1),x85421),f318(x85422,x85423)))+P1(f318(f318(f226(a911),f408(x85421,x85422,x85423)),x85423))+P1(f318(f318(f225(a911),f407(x85421,x85422,x85423)),x85423))+~P1(f318(f318(f225(a1),f318(x85422,f2(a911))),x85421))
% 109.14/108.86 [8543]~P1(f318(f318(f225(a1),x85431),f318(x85432,x85433)))+P1(f318(f318(f226(a911),f410(x85431,x85432,x85433)),x85433))+P1(f318(f318(f225(a911),f409(x85431,x85432,x85433)),x85433))+~P1(f318(f318(f225(a1),f318(x85432,f2(a911))),x85431))
% 109.14/108.86 [8618]E(f318(f318(f3(a1),x86181),x86182),x86181)+~P1(f318(f318(f226(a1),f2(a1)),x86182))+P1(f318(f318(f320(a1),f341(x86183,x86181,x86182)),f294(a1,f71(a1),x86182)))+~P1(f318(f318(f320(a1),f318(f318(f3(a1),x86181),f71(a1))),x86183))
% 109.14/108.86 [8619]E(f318(f318(f73(a1),x86191),x86192),x86191)+~P1(f318(f318(f226(a1),f2(a1)),x86192))+P1(f318(f318(f320(a1),f349(x86193,x86191,x86192)),f294(a1,f71(a1),x86192)))+~P1(f318(f318(f320(a1),f318(f318(f73(a1),x86191),f71(a1))),x86193))
% 109.14/108.86 [8752]~P130(x87521)+~P1(f318(f318(f226(x87521),x87522),f71(x87521)))+~P1(f318(f318(f226(x87521),f2(x87521)),x87522))+P1(f318(f318(f226(x87521),f318(f318(f74(x87521),x87522),f318(f318(f235(x87521),x87522),x87523))),f318(f318(f235(x87521),x87522),x87523)))
% 109.14/108.86 [8839]~P1(f318(x88391,x88392))+P1(f318(x88391,f2(a911)))+~P1(f318(f318(f226(a911),x88392),x88393))+~P1(f318(x88391,f39(a911,f318(a103,f411(x88392,x88391,x88393)),x88393)))
% 109.14/108.86 [8995]E(f500(x89951,x89952,x89953),f2(a911))+P1(f318(f318(x89951,x89953),x89952))+P1(f318(f318(x89951,f500(x89951,x89952,x89953)),f39(a911,f498(x89951,x89952,x89953),f500(x89951,x89952,x89953))))+~P1(f318(f306(f917(a911,a911),a210),f318(f318(f243(a911,a911),x89953),x89952)))
% 109.14/108.86 [9032]~P25(x90321,x90321,x90322,x90323)+E(f318(f301(x90321,x90321,x90322),x90323),x90323)+~P1(f318(f55(x90321),x90323))+~P1(f318(f318(f225(f918(x90321,a909)),f318(f301(x90321,x90321,x90322),x90323)),x90323))
% 109.14/108.86 [9104]~P5(x91041)+~P42(x91041,x91041,x91043)+P1(f318(f318(f225(x91041),f318(f318(f101(x91041),x91042),f87(x91041,x91043))),f318(x91043,f318(f318(f101(x91041),x91042),f87(x91041,x91043)))))+~P1(f318(f318(f225(x91041),x91042),f318(x91043,f318(f318(f101(x91041),x91042),f87(x91041,x91043)))))
% 109.14/108.86 [9237]P1(f318(f318(x92371,x92372),x92373))+P1(f318(f318(f226(a1),f766(x92371,x92373,x92372)),f767(x92371,x92373,x92372)))+P1(f318(f318(x92371,f766(x92371,x92373,x92372)),f318(f318(f73(a1),f767(x92371,x92373,x92372)),f71(a1))))+~P1(f318(f306(f917(a1,a1),a124),f318(f318(f243(a1,a1),x92372),x92373)))
% 109.14/108.86 [9254]P1(f318(f318(x92541,x92542),x92543))+~P1(f318(f318(f226(a1),f497(x92541,x92543,x92542)),f2(a1)))+P1(f318(f318(x92541,f318(f72(a1),f495(x92541,x92543,x92542))),f318(f72(a1),f497(x92541,x92543,x92542))))+~P1(f318(f306(f917(a1,a1),a212),f318(f318(f243(a1,a1),x92542),x92543)))
% 109.14/108.86 [9456]P1(f318(f318(x94561,x94562),x94563))+P1(f318(f318(x94561,f318(f318(f73(a1),f669(x94561,x94563,x94562)),f71(a1))),f671(x94561,x94563,x94562)))+~P1(f318(f318(f225(a1),f669(x94561,x94563,x94562)),f671(x94561,x94563,x94562)))+~P1(f318(f306(f917(a1,a1),a173),f318(f318(f243(a1,a1),x94562),x94563)))
% 109.14/108.86 [9914]~P71(x99142)+~P71(x99141)+~P1(f318(f50(f917(x99141,x99142)),x99143))+P1(f318(f50(x99141),f318(f318(f10(f918(x99142,a909),a909,x99141),f50(x99142)),f318(f318(f10(f918(x99142,f917(x99141,x99142)),f918(x99142,a909),x99141),f318(f10(f917(x99141,x99142),a909,x99142),x99143)),f243(x99141,x99142)))))
% 109.14/108.86 [9915]~P71(x99152)+~P71(x99151)+~P1(f318(f51(f917(x99151,x99152)),x99153))+P1(f318(f51(x99151),f318(f318(f10(f918(x99152,a909),a909,x99151),f51(x99152)),f318(f318(f10(f918(x99152,f917(x99151,x99152)),f918(x99152,a909),x99151),f318(f10(f917(x99151,x99152),a909,x99152),x99153)),f243(x99151,x99152)))))
% 109.14/108.86 [10024]~P71(x100242)+~P71(x100241)+P1(f318(f50(f917(x100241,x100242)),x100243))+~P1(f318(f50(x100241),f318(f318(f10(f918(x100242,a909),a909,x100241),f50(x100242)),f318(f318(f10(f918(x100242,f917(x100241,x100242)),f918(x100242,a909),x100241),f318(f10(f917(x100241,x100242),a909,x100242),x100243)),f243(x100241,x100242)))))
% 109.14/108.86 [10025]~P71(x100252)+~P71(x100251)+P1(f318(f51(f917(x100251,x100252)),x100253))+~P1(f318(f51(x100251),f318(f318(f10(f918(x100252,a909),a909,x100251),f51(x100252)),f318(f318(f10(f918(x100252,f917(x100251,x100252)),f918(x100252,a909),x100251),f318(f10(f917(x100251,x100252),a909,x100252),x100253)),f243(x100251,x100252)))))
% 109.14/108.86 [10172]E(f318(x101721,f407(x101722,x101721,x101723)),x101722)+~P1(f318(f318(f225(a1),x101722),f318(x101721,x101723)))+~P1(f318(f318(f225(a1),f318(f69(a1),f318(f318(f3(a1),f318(x101721,f318(f318(f73(a911),f408(x101722,x101721,x101723)),f71(a911)))),f318(x101721,f408(x101722,x101721,x101723))))),f71(a1)))+~P1(f318(f318(f225(a1),f318(x101721,f2(a911))),x101722))
% 109.14/108.86 [10173]E(f318(x101731,f409(x101732,x101731,x101733)),x101732)+~P1(f318(f318(f225(a1),x101732),f318(x101731,x101733)))+~P1(f318(f318(f225(a1),f318(f69(a1),f318(f318(f3(a1),f318(x101731,f318(f318(f73(a911),f410(x101732,x101731,x101733)),f71(a911)))),f318(x101731,f410(x101732,x101731,x101733))))),f71(a1)))+~P1(f318(f318(f225(a1),f318(x101731,f2(a911))),x101732))
% 109.14/108.86 [10176]~P1(f318(f318(f225(a1),x101761),f318(x101762,x101763)))+~P1(f318(f318(f225(a1),f318(f69(a1),f318(f318(f3(a1),f318(x101762,f318(f318(f73(a911),f408(x101761,x101762,x101763)),f71(a911)))),f318(x101762,f408(x101761,x101762,x101763))))),f71(a1)))+P1(f318(f318(f225(a911),f407(x101761,x101762,x101763)),x101763))+~P1(f318(f318(f225(a1),f318(x101762,f2(a911))),x101761))
% 109.14/108.86 [10177]~P1(f318(f318(f225(a1),x101771),f318(x101772,x101773)))+~P1(f318(f318(f225(a1),f318(f69(a1),f318(f318(f3(a1),f318(x101772,f318(f318(f73(a911),f410(x101771,x101772,x101773)),f71(a911)))),f318(x101772,f410(x101771,x101772,x101773))))),f71(a1)))+P1(f318(f318(f225(a911),f409(x101771,x101772,x101773)),x101773))+~P1(f318(f318(f225(a1),f318(x101772,f2(a911))),x101771))
% 109.14/108.86 [10232]E(x102321,x102322)+~E(f318(f133(f912(x102323),f912(x102323),f125(x102323),f104(x102323)),x102321),f318(f133(f912(x102323),f912(x102323),f125(x102323),f104(x102323)),x102322))+~E(f318(f180(f912(f912(x102323))),x102321),f318(f180(f912(f912(x102323))),x102322))+~P1(f318(f318(f248(f912(x102323),f912(x102323),a909),f318(f318(f9(f912(x102323),f918(f912(x102323),a911),f918(f912(x102323),a909)),f318(f318(f10(f918(a911,a909),f918(f918(f912(x102323),a911),f918(f912(x102323),a909)),f912(x102323)),f10(a911,a909,f912(x102323))),f318(f318(f10(a911,f918(a911,a909),f912(x102323)),a315),f180(f912(x102323))))),f180(f912(x102323)))),f698(x102322,x102321,x102323)))
% 109.14/108.86 [10233]E(x102331,x102332)+~E(f318(f133(f912(x102333),f912(x102333),f125(x102333),f104(x102333)),x102331),f318(f133(f912(x102333),f912(x102333),f125(x102333),f104(x102333)),x102332))+~E(f318(f180(f912(f912(x102333))),x102331),f318(f180(f912(f912(x102333))),x102332))+~P1(f318(f318(f248(f912(x102333),f912(x102333),a909),f318(f318(f9(f912(x102333),f918(f912(x102333),a911),f918(f912(x102333),a909)),f318(f318(f10(f918(a911,a909),f918(f918(f912(x102333),a911),f918(f912(x102333),a909)),f912(x102333)),f10(a911,a909,f912(x102333))),f318(f318(f10(a911,f918(a911,a909),f912(x102333)),a315),f180(f912(x102333))))),f180(f912(x102333)))),f699(x102331,x102332,x102333)))
% 109.14/108.86 [6950]~E(f71(a911),f2(a911))+~P1(f318(f55(x69501),x69503))+~P1(f318(f55(x69501),x69502))+E(f318(f318(f73(a911),f318(f29(x69501),x69502)),f318(f29(x69501),x69503)),f318(f29(x69501),f318(f318(f101(f918(x69501,a909)),x69502),x69503)))
% 109.14/108.86 [7365]~P108(x73651)+~P1(f318(f55(x73651),x73652))+~P1(f318(f318(f320(x73651),x73653),x73652))+P1(f318(f318(f225(x73651),f318(f57(x73651,f92(x73651)),x73652)),x73653))
% 109.14/108.86 [7366]~P4(x73661)+~P1(f318(f55(x73661),x73662))+~P1(f318(f318(f320(x73661),x73663),x73662))+P1(f318(f318(f225(x73661),f318(f57(x73661,f223(x73661)),x73662)),x73663))
% 109.14/108.86 [7606]~P1(f318(f55(x76061),x76063))+~P1(f318(f55(x76061),x76062))+~E(f318(f318(f92(f918(x76061,a909)),x76062),x76063),f179(f918(x76061,a909)))+E(f318(f318(f73(a911),f318(f29(x76061),x76062)),f318(f29(x76061),x76063)),f318(f29(x76061),f318(f318(f101(f918(x76061,a909)),x76062),x76063)))
% 109.14/108.86 [8389]~P39(x83891,x83893)+~P39(x83891,x83892)+~E(f318(f318(f92(f918(x83891,a909)),f318(f255(x83891,x83891),x83892)),f318(f275(x83891,x83891),x83893)),f179(f918(x83891,a909)))+P39(x83891,f318(f318(f101(f918(f917(x83891,x83891),a909)),x83892),x83893))
% 109.14/108.86 [8481]E(x84811,f318(f318(f30(a911),x84812),x84813))+~P1(f318(f318(f226(a911),f2(a911)),x84813))+~P1(f318(f318(f226(a911),x84812),f318(f318(f74(a911),x84813),f318(a103,x84811))))+~P1(f318(f318(f225(a911),f318(f318(f74(a911),x84813),x84811)),x84812))
% 109.14/108.86 [8616]~P1(f318(f55(x86161),x86162))+~P1(f318(f55(x86161),x86163))+E(f318(f318(f73(a911),f318(f29(x86161),x86162)),f318(f29(x86161),x86163)),f318(f29(x86161),f318(f318(f101(f918(x86161,a909)),x86162),x86163)))+P1(f318(f318(f320(x86161),f890(x86163,x86162,x86161)),f318(f318(f92(f918(x86161,a909)),x86162),x86163)))
% 109.14/108.86 [9008]~P131(x90082)+~E(x90081,f2(x90082))+~E(x90083,f2(x90082))+~P1(f318(f318(f226(x90082),f2(x90082)),f318(f318(f73(x90082),f318(f318(f74(x90082),x90083),x90083)),f318(f318(f74(x90082),x90081),x90081))))
% 109.14/108.86 [9541]~P39(x95411,x95413)+~P39(x95411,x95412)+P39(x95411,f318(f318(f101(f918(f917(x95411,x95411),a909)),x95412),x95413))+~P1(f318(f318(f225(f918(f917(x95411,x95411),a909)),f318(f318(f280(x95411,x95411,x95411),x95412),x95413)),x95412))
% 109.14/108.86 [9665]~P1(f318(x96651,x96653))+~P1(f318(f55(x96652),x96653))+P1(f318(x96651,f179(f918(x96652,a909))))+~P1(f318(x96651,f318(f318(f3(f918(x96652,a909)),f896(x96651,x96653,x96652)),f318(f318(f300(x96652),f897(x96651,x96653,x96652)),f179(f918(x96652,a909))))))
% 109.14/108.86 [8793]~P1(f318(f318(f226(a1),f2(a1)),x87933))+P1(f318(f318(f225(a1),f2(a1)),x87931))+~P1(f318(f318(f226(a1),x87932),x87933))+~P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),f318(f318(f74(a1),x87933),x87931)),x87932)))
% 109.14/108.86 [8812]~P103(x88121)+~P1(f318(f55(x88121),x88122))+E(f318(f318(f3(f918(x88121,a909)),x88122),f318(f318(f300(x88121),x88123),f179(f918(x88121,a909)))),f179(f918(x88121,a909)))+E(f318(f318(f92(x88121),x88123),f12(x88121,f318(f318(f3(f918(x88121,a909)),x88122),f318(f318(f300(x88121),x88123),f179(f918(x88121,a909)))))),f12(x88121,f318(f318(f300(x88121),x88123),x88122)))
% 109.14/108.86 [8813]~P103(x88131)+~P1(f318(f55(x88131),x88132))+E(f318(f318(f3(f918(x88131,a909)),x88132),f318(f318(f300(x88131),x88133),f179(f918(x88131,a909)))),f179(f918(x88131,a909)))+E(f318(f318(f101(x88131),x88133),f15(x88131,f318(f318(f3(f918(x88131,a909)),x88132),f318(f318(f300(x88131),x88133),f179(f918(x88131,a909)))))),f15(x88131,f318(f318(f300(x88131),x88133),x88132)))
% 109.14/108.86 [8814]~P4(x88141)+~P1(f318(f55(x88141),x88142))+E(f318(f318(f3(f918(x88141,a909)),x88142),f318(f318(f300(x88141),x88143),f179(f918(x88141,a909)))),f179(f918(x88141,a909)))+E(f318(f318(f223(x88141),x88143),f16(x88141,f318(f318(f3(f918(x88141,a909)),x88142),f318(f318(f300(x88141),x88143),f179(f918(x88141,a909)))))),f16(x88141,f318(f318(f300(x88141),x88143),x88142)))
% 109.14/108.86 [8815]~P4(x88151)+~P1(f318(f55(x88151),x88152))+E(f318(f318(f3(f918(x88151,a909)),x88152),f318(f318(f300(x88151),x88153),f179(f918(x88151,a909)))),f179(f918(x88151,a909)))+E(f318(f318(f224(x88151),x88153),f17(x88151,f318(f318(f3(f918(x88151,a909)),x88152),f318(f318(f300(x88151),x88153),f179(f918(x88151,a909)))))),f17(x88151,f318(f318(f300(x88151),x88153),x88152)))
% 109.14/108.86 [8886]~P4(x88861)+~P1(f318(f55(x88861),x88862))+E(f318(f318(f3(f918(x88861,a909)),x88862),f318(f318(f300(x88861),x88863),f179(f918(x88861,a909)))),f179(f918(x88861,a909)))+E(f318(f318(f223(x88861),x88863),f13(x88861,f223(x88861),f318(f318(f3(f918(x88861,a909)),x88862),f318(f318(f300(x88861),x88863),f179(f918(x88861,a909)))))),f13(x88861,f223(x88861),f318(f318(f300(x88861),x88863),x88862)))
% 109.14/108.86 [8887]~P4(x88871)+~P1(f318(f55(x88871),x88872))+E(f318(f318(f3(f918(x88871,a909)),x88872),f318(f318(f300(x88871),x88873),f179(f918(x88871,a909)))),f179(f918(x88871,a909)))+E(f318(f318(f224(x88871),x88873),f14(x88871,f224(x88871),f318(f318(f3(f918(x88871,a909)),x88872),f318(f318(f300(x88871),x88873),f179(f918(x88871,a909)))))),f14(x88871,f224(x88871),f318(f318(f300(x88871),x88873),x88872)))
% 109.14/108.86 [9259]~P5(x92591)+~P42(x92591,x92591,x92592)+P1(f318(f318(f225(x92591),f86(x92591,x92592)),x92593))+~P1(f318(f318(f225(x92591),f318(x92592,f318(f318(f92(x92591),f86(x92591,x92592)),x92593))),x92593))
% 109.14/108.86 [9475]E(x94751,x94752)+~E(f318(f133(f912(x94753),f912(x94753),f125(x94753),f104(x94753)),x94751),f318(f133(f912(x94753),f912(x94753),f125(x94753),f104(x94753)),x94752))+~E(f318(f180(f912(f912(x94753))),x94751),f318(f180(f912(f912(x94753))),x94752))+P1(f318(f318(f320(f917(f912(x94753),f912(x94753))),f698(x94752,x94751,x94753)),f318(f163(f917(f912(x94753),f912(x94753))),f318(f318(f172(f912(x94753),f912(x94753)),x94751),x94752))))
% 109.14/108.86 [9476]E(x94761,x94762)+~E(f318(f133(f912(x94763),f912(x94763),f125(x94763),f104(x94763)),x94761),f318(f133(f912(x94763),f912(x94763),f125(x94763),f104(x94763)),x94762))+~E(f318(f180(f912(f912(x94763))),x94761),f318(f180(f912(f912(x94763))),x94762))+P1(f318(f318(f320(f917(f912(x94763),f912(x94763))),f699(x94761,x94762,x94763)),f318(f163(f917(f912(x94763),f912(x94763))),f318(f318(f172(f912(x94763),f912(x94763)),x94762),x94761))))
% 109.14/108.86 [10368]~P107(x103682)+E(x103681,f179(f918(x103682,a909)))+~P1(f318(f55(x103682),x103681))+E(f12(x103682,f318(f253(x103682),f318(f318(f10(f918(x103682,a909),a909,x103682),f79(x103682)),f318(f318(f9(x103682,f918(x103682,a909),f918(x103682,a909)),f318(f318(f10(f918(x103682,f918(a909,a909)),f918(f918(x103682,a909),f918(x103682,a909)),x103682),f20(x103682,a909,a909)),f318(f318(f10(f918(x103682,a909),f918(x103682,f918(a909,a909)),x103682),f318(f10(a909,f918(a909,a909),x103682),a316)),f318(f318(f9(x103682,f918(x103682,x103682),f918(x103682,a909)),f318(f318(f10(f918(x103682,a909),f918(f918(x103682,x103682),f918(x103682,a909)),x103682),f10(x103682,a909,x103682)),a315)),f318(f101(x103682),x103683))))),f318(f318(f9(x103682,f918(x103682,a909),a909),f320(x103682)),x103681))))),f318(f318(f101(x103682),x103683),f12(x103682,x103681)))
% 109.14/108.86 [10369]~P107(x103692)+E(x103691,f179(f918(x103692,a909)))+~P1(f318(f55(x103692),x103691))+E(f15(x103692,f318(f253(x103692),f318(f318(f10(f918(x103692,a909),a909,x103692),f79(x103692)),f318(f318(f9(x103692,f918(x103692,a909),f918(x103692,a909)),f318(f318(f10(f918(x103692,f918(a909,a909)),f918(f918(x103692,a909),f918(x103692,a909)),x103692),f20(x103692,a909,a909)),f318(f318(f10(f918(x103692,a909),f918(x103692,f918(a909,a909)),x103692),f318(f10(a909,f918(a909,a909),x103692),a316)),f318(f318(f9(x103692,f918(x103692,x103692),f918(x103692,a909)),f318(f318(f10(f918(x103692,a909),f918(f918(x103692,x103692),f918(x103692,a909)),x103692),f10(x103692,a909,x103692)),a315)),f318(f92(x103692),x103693))))),f318(f318(f9(x103692,f918(x103692,a909),a909),f320(x103692)),x103691))))),f318(f318(f92(x103692),x103693),f15(x103692,x103691)))
% 109.14/108.86 [10370]~P85(x103702)+E(x103701,f179(f918(x103702,a909)))+~P1(f318(f55(x103702),x103701))+E(f16(x103702,f318(f253(x103702),f318(f318(f10(f918(x103702,a909),a909,x103702),f79(x103702)),f318(f318(f9(x103702,f918(x103702,a909),f918(x103702,a909)),f318(f318(f10(f918(x103702,f918(a909,a909)),f918(f918(x103702,a909),f918(x103702,a909)),x103702),f20(x103702,a909,a909)),f318(f318(f10(f918(x103702,a909),f918(x103702,f918(a909,a909)),x103702),f318(f10(a909,f918(a909,a909),x103702),a316)),f318(f318(f9(x103702,f918(x103702,x103702),f918(x103702,a909)),f318(f318(f10(f918(x103702,a909),f918(f918(x103702,x103702),f918(x103702,a909)),x103702),f10(x103702,a909,x103702)),a315)),f318(f73(x103702),x103703))))),f318(f318(f9(x103702,f918(x103702,a909),a909),f320(x103702)),x103701))))),f318(f318(f73(x103702),x103703),f16(x103702,x103701)))
% 109.14/108.86 [10371]~P85(x103712)+E(x103711,f179(f918(x103712,a909)))+~P1(f318(f55(x103712),x103711))+E(f17(x103712,f318(f253(x103712),f318(f318(f10(f918(x103712,a909),a909,x103712),f79(x103712)),f318(f318(f9(x103712,f918(x103712,a909),f918(x103712,a909)),f318(f318(f10(f918(x103712,f918(a909,a909)),f918(f918(x103712,a909),f918(x103712,a909)),x103712),f20(x103712,a909,a909)),f318(f318(f10(f918(x103712,a909),f918(x103712,f918(a909,a909)),x103712),f318(f10(a909,f918(a909,a909),x103712),a316)),f318(f318(f9(x103712,f918(x103712,x103712),f918(x103712,a909)),f318(f318(f10(f918(x103712,a909),f918(f918(x103712,x103712),f918(x103712,a909)),x103712),f10(x103712,a909,x103712)),a315)),f318(f73(x103712),x103713))))),f318(f318(f9(x103712,f918(x103712,a909),a909),f320(x103712)),x103711))))),f318(f318(f73(x103712),x103713),f17(x103712,x103711)))
% 109.14/108.86 [10372]~P4(x103722)+E(x103721,f179(f918(x103722,a909)))+~P1(f318(f55(x103722),x103721))+E(f14(x103722,f224(x103722),f318(f253(x103722),f318(f318(f10(f918(x103722,a909),a909,x103722),f79(x103722)),f318(f318(f9(x103722,f918(x103722,a909),f918(x103722,a909)),f318(f318(f10(f918(x103722,f918(a909,a909)),f918(f918(x103722,a909),f918(x103722,a909)),x103722),f20(x103722,a909,a909)),f318(f318(f10(f918(x103722,a909),f918(x103722,f918(a909,a909)),x103722),f318(f10(a909,f918(a909,a909),x103722),a316)),f318(f318(f9(x103722,f918(x103722,x103722),f918(x103722,a909)),f318(f318(f10(f918(x103722,a909),f918(f918(x103722,x103722),f918(x103722,a909)),x103722),f10(x103722,a909,x103722)),a315)),f318(f223(x103722),x103723))))),f318(f318(f9(x103722,f918(x103722,a909),a909),f320(x103722)),x103721))))),f318(f318(f223(x103722),x103723),f14(x103722,f224(x103722),x103721)))
% 109.14/108.86 [10373]~P4(x103732)+E(x103731,f179(f918(x103732,a909)))+~P1(f318(f55(x103732),x103731))+E(f13(x103732,f223(x103732),f318(f253(x103732),f318(f318(f10(f918(x103732,a909),a909,x103732),f79(x103732)),f318(f318(f9(x103732,f918(x103732,a909),f918(x103732,a909)),f318(f318(f10(f918(x103732,f918(a909,a909)),f918(f918(x103732,a909),f918(x103732,a909)),x103732),f20(x103732,a909,a909)),f318(f318(f10(f918(x103732,a909),f918(x103732,f918(a909,a909)),x103732),f318(f10(a909,f918(a909,a909),x103732),a316)),f318(f318(f9(x103732,f918(x103732,x103732),f918(x103732,a909)),f318(f318(f10(f918(x103732,a909),f918(f918(x103732,x103732),f918(x103732,a909)),x103732),f10(x103732,a909,x103732)),a315)),f318(f224(x103732),x103733))))),f318(f318(f9(x103732,f918(x103732,a909),a909),f320(x103732)),x103731))))),f318(f318(f224(x103732),x103733),f13(x103732,f223(x103732),x103731)))
% 109.14/108.86 [10306]~P116(x103061)+~E(x103063,f2(x103061))+~E(x103062,f2(x103061))+E(f318(f318(f73(x103061),f318(f318(f235(x103061),x103062),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x103061),x103063),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f2(x103061))
% 109.14/108.86 [10378]~P130(x103781)+~P1(f318(f318(f225(x103781),f2(x103781)),x103783))+P1(f318(f318(f225(x103781),x103782),x103783))+~P1(f318(f318(f225(x103781),f318(f318(f235(x103781),x103782),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x103781),x103783),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.86 [10379]~P130(x103791)+~P1(f318(f318(f225(x103791),f2(x103791)),x103793))+P1(f318(f318(f226(x103791),x103792),x103793))+~P1(f318(f318(f226(x103791),f318(f318(f235(x103791),x103792),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x103791),x103793),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))))
% 109.14/108.86 [10406]~P116(x104062)+~E(x104061,f2(x104062))+~E(x104063,f2(x104062))+~P1(f318(f318(f226(x104062),f2(x104062)),f318(f318(f73(x104062),f318(f318(f235(x104062),x104063),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88)))),f318(f318(f235(x104062),x104061),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))))
% 109.14/108.86 [6134]~P4(x61341)+~P113(x61342)+~P52(x61341,x61342,x61343)+P25(x61341,x61342,x61343,x61344)
% 109.14/108.86 [6836]~P7(x68363,x68362)+~P1(f318(x68361,x68364))+~P1(f318(f318(f320(x68363),x68364),f261(x68363,x68362)))+P1(f318(x68361,f823(x68361,x68362,x68363)))
% 109.14/108.86 [8728]P26(x87281,x87282,f820(x87283,x87282,x87284,x87281),x87284,x87283)+~E(f318(f29(x87281),x87284),f318(f29(x87282),x87283))+~P1(f318(f55(x87282),x87283))+~P1(f318(f55(x87281),x87284))
% 109.14/108.86 [9435]E(x94351,x94352)+~E(f652(x94351,x94352,x94354,x94353),f653(x94351,x94352,x94354,x94353))+P1(f318(f318(f320(f917(f912(x94353),f912(x94353))),f318(f318(f243(f912(x94353),f912(x94353)),x94352),x94351)),f138(x94353,x94354)))+P1(f318(f318(f320(f917(f912(x94353),f912(x94353))),f318(f318(f243(f912(x94353),f912(x94353)),x94351),x94352)),f138(x94353,x94354)))
% 109.14/108.86 [4972]~P72(x49722)+~E(x49724,f2(x49722))+~E(x49721,f2(x49722))+E(x49721,f318(f318(f282(x49722),x49723),x49724))
% 109.14/108.86 [4973]~P72(x49731)+~E(x49733,f2(x49731))+~E(x49734,f2(x49731))+E(f318(f318(f282(x49731),x49732),x49733),x49734)
% 109.14/108.86 [5090]~P72(x50902)+E(x50901,f2(x50902))+~E(x50903,f2(x50902))+~E(x50901,f318(f318(f282(x50902),x50904),x50903))
% 109.14/108.86 [5091]~P72(x50912)+E(x50911,f2(x50912))+~E(x50913,f2(x50912))+~E(f318(f318(f282(x50912),x50914),x50913),x50911)
% 109.14/108.86 [5278]~P125(x52782)+E(x52781,f2(x52782))+~E(f318(f318(f282(x52782),x52783),x52781),x52784)+E(x52783,f318(f318(f74(x52782),x52784),x52781))
% 109.14/108.86 [5279]~P125(x52792)+E(x52791,f2(x52792))+~E(f318(f318(f74(x52792),x52793),x52791),x52794)+E(x52793,f318(f318(f282(x52792),x52794),x52791))
% 109.14/108.86 [5280]~P125(x52802)+E(x52801,f2(x52802))+~E(f318(f318(f74(x52802),x52803),x52801),x52804)+E(x52803,f318(f318(f282(x52802),x52804),x52801))
% 109.14/108.86 [5281]~P72(x52812)+E(x52811,f2(x52812))+~E(f318(f318(f282(x52812),x52813),x52811),x52814)+E(x52813,f318(f318(f74(x52812),x52814),x52811))
% 109.14/108.86 [5282]~P72(x52822)+E(x52821,f2(x52822))+~E(f318(f318(f74(x52822),x52823),x52821),x52824)+E(x52823,f318(f318(f282(x52822),x52824),x52821))
% 109.14/108.86 [5283]~P125(x52832)+E(x52831,f2(x52832))+~E(x52833,f318(f318(f282(x52832),x52834),x52831))+E(f318(f318(f74(x52832),x52833),x52831),x52834)
% 109.14/108.86 [5284]~P125(x52842)+E(x52841,f2(x52842))+~E(x52843,f318(f318(f74(x52842),x52844),x52841))+E(f318(f318(f282(x52842),x52843),x52841),x52844)
% 109.14/108.86 [5285]~P125(x52852)+E(x52851,f2(x52852))+~E(x52853,f318(f318(f74(x52852),x52854),x52851))+E(f318(f318(f282(x52852),x52853),x52851),x52854)
% 109.14/108.86 [5286]~P72(x52862)+E(x52861,f2(x52862))+~E(x52863,f318(f318(f282(x52862),x52864),x52861))+E(f318(f318(f74(x52862),x52863),x52861),x52864)
% 109.14/108.86 [5287]~P72(x52872)+E(x52871,f2(x52872))+~E(x52873,f318(f318(f74(x52872),x52874),x52871))+E(f318(f318(f282(x52872),x52873),x52871),x52874)
% 109.14/108.86 [5311]~P72(x53112)+~E(x53111,f2(x53112))+~E(f318(f318(f74(x53112),x53111),x53114),x53113)+E(x53111,f318(f318(f282(x53112),x53113),x53114))
% 109.14/108.86 [5312]~P72(x53121)+~E(x53124,f2(x53121))+~E(x53122,f318(f318(f74(x53121),x53124),x53123))+E(f318(f318(f282(x53121),x53122),x53123),x53124)
% 109.14/108.86 [5387]~E(x53873,x53874)+~E(x53872,x53873)+~P113(x53871)+E(f294(x53871,x53872,x53873),f318(f318(f300(x53871),x53874),f179(f918(x53871,a909))))
% 109.14/108.86 [5589]~E(f105(x55892,x55891),x55893)+~E(f135(x55892,x55891),x55894)+E(x55891,f104(x55892))+E(f318(f318(f125(x55892),x55893),f318(f318(f142(x55892),x55894),f104(x55892))),x55891)
% 109.14/108.86 [6226]~P130(x62263)+E(x62261,x62262)+~E(f318(f318(f235(x62263),x62264),x62261),f318(f318(f235(x62263),x62264),x62262))+~P1(f318(f318(f226(x62263),f71(x62263)),x62264))
% 109.14/108.86 [6227]E(x62271,x62272)+~E(f318(f318(f300(x62273),x62274),x62271),f318(f318(f300(x62273),x62274),x62272))+P1(f318(f318(f320(x62273),x62274),x62272))+P1(f318(f318(f320(x62273),x62274),x62271))
% 109.14/108.86 [6269]E(f318(x62691,x62692),f2(a911))+~E(f318(f318(f8(x62693,a911),x62691),x62694),f2(a911))+~P1(f318(f55(x62693),x62694))+~P1(f318(f318(f320(x62693),x62692),x62694))
% 109.14/108.86 [6270]E(f318(x62701,x62702),f71(a911))+~E(f318(f318(f11(x62703,a911),x62701),x62704),f71(a911))+~P1(f318(f55(x62703),x62704))+~P1(f318(f318(f320(x62703),x62702),x62704))
% 109.14/108.86 [6486]~P113(x64861)+~P1(f318(f318(f225(x64861),x64864),x64863))+P1(f318(f318(f225(x64861),x64862),x64863))+~P1(f318(f318(f225(x64861),x64862),x64864))
% 109.14/108.86 [6487]~P2(x64871)+~P1(f318(f318(f225(x64871),x64872),x64874))+P1(f318(f318(f225(x64871),x64872),x64873))+~P1(f318(f318(f225(x64871),x64874),x64873))
% 109.14/108.86 [6488]~P113(x64881)+~P1(f318(f318(f226(x64881),x64884),x64883))+P1(f318(f318(f226(x64881),x64882),x64883))+~P1(f318(f318(f225(x64881),x64882),x64884))
% 109.14/108.86 [6489]~P113(x64891)+~P1(f318(f318(f226(x64891),x64892),x64894))+P1(f318(f318(f226(x64891),x64892),x64893))+~P1(f318(f318(f225(x64891),x64894),x64893))
% 109.14/108.86 [6490]~P113(x64901)+~P1(f318(f318(f226(x64901),x64904),x64903))+P1(f318(f318(f226(x64901),x64902),x64903))+~P1(f318(f318(f226(x64901),x64902),x64904))
% 109.14/108.86 [6491]~P2(x64911)+~P1(f318(f318(f226(x64911),x64912),x64914))+P1(f318(f318(f226(x64911),x64912),x64913))+~P1(f318(f318(f225(x64911),x64914),x64913))
% 109.14/108.86 [6492]~P2(x64921)+~P1(f318(f318(f226(x64921),x64924),x64923))+P1(f318(f318(f226(x64921),x64922),x64923))+~P1(f318(f318(f225(x64921),x64922),x64924))
% 109.14/108.86 [6493]~P2(x64931)+~P1(f318(f318(f226(x64931),x64932),x64934))+P1(f318(f318(f226(x64931),x64932),x64933))+~P1(f318(f318(f226(x64931),x64934),x64933))
% 109.14/108.86 [6576]~P37(x65764,x65763,x65762)+E(x65761,f759(x65762,x65763,x65764))+~P1(f318(x65763,x65761))+~P1(f318(f318(f320(x65764),x65761),f318(f163(x65764),x65762)))
% 109.14/108.86 [6577]~P37(x65774,x65773,x65772)+E(x65771,f769(x65772,x65773,x65774))+~P1(f318(x65773,x65771))+~P1(f318(f318(f320(x65774),x65771),f318(f163(x65774),x65772)))
% 109.14/108.86 [6727]~P5(x67271)+~P1(f318(f318(f225(x67271),x67272),f32(x67271,x67274)))+P1(f318(f318(f225(x67271),x67272),x67273))+~P1(f318(f318(f320(x67271),x67273),x67274))
% 109.14/108.86 [6875]~P4(x68751)+~P13(x68751,f318(f318(f142(x68751),x68752),x68754))+~P1(f318(f318(f320(x68751),x68753),f318(f163(x68751),x68754)))+P1(f318(f318(f225(x68751),x68752),x68753))
% 109.14/108.86 [6876]~P4(x68761)+~P13(x68761,f318(f318(f142(x68761),x68762),x68764))+~P1(f318(f318(f320(x68761),x68763),f318(f163(x68761),x68764)))+P1(f318(f318(f225(x68761),x68762),x68763))
% 109.14/108.86 [6959]~P5(x69591)+~P1(f318(f318(f225(x69591),f31(x69591,x69594)),x69593))+P1(f318(f318(f225(x69591),x69592),x69593))+~P1(f318(f318(f320(x69591),x69592),x69594))
% 109.14/108.86 [7101]~P69(x71011)+P1(f318(f318(f278(x71011),x71012),f39(x71011,x71013,x71014)))+~P1(f318(f318(f278(x71011),x71012),x71014))+~P1(f318(f318(f278(x71011),x71012),x71013))
% 109.14/108.86 [7102]~P69(x71021)+P1(f318(f318(f278(x71021),x71022),f39(x71021,x71023,x71024)))+~P1(f318(f318(f278(x71021),x71022),x71024))+~P1(f318(f318(f278(x71021),x71022),x71023))
% 109.14/108.86 [7368]~P4(x73681)+E(f318(f318(f101(f918(x73681,a909)),f318(f293(x73681,x73682),x73683)),f318(f293(x73681,x73683),x73684)),f318(f293(x73681,x73682),x73684))+~P1(f318(f318(f225(x73681),x73683),x73684))+~P1(f318(f318(f225(x73681),x73682),x73683))
% 109.14/108.86 [7412]P37(x74121,x74122,x74123)+~E(f763(x74123,x74122,x74121,x74124),x74124)+~P1(f318(x74122,x74124))+~P1(f318(f318(f320(x74121),x74124),f318(f163(x74121),x74123)))
% 109.14/108.86 [7413]P37(x74131,x74132,x74133)+~E(f772(x74133,x74132,x74131,x74134),x74134)+~P1(f318(x74132,x74134))+~P1(f318(f318(f320(x74131),x74134),f318(f163(x74131),x74133)))
% 109.14/108.86 [7451]~P69(x74511)+~P1(f318(f318(f278(x74511),x74512),f39(x74511,x74513,x74514)))+P1(f318(f318(f278(x74511),x74512),x74513))+~P1(f318(f318(f278(x74511),x74512),x74514))
% 109.14/108.86 [7452]~P69(x74521)+~P1(f318(f318(f278(x74521),x74522),f39(x74521,x74523,x74524)))+P1(f318(f318(f278(x74521),x74522),x74523))+~P1(f318(f318(f278(x74521),x74522),x74524))
% 109.14/108.86 [7480]~P4(x74801)+E(f318(f318(f101(f918(x74801,a909)),f318(f293(x74801,x74802),x74803)),f294(x74801,x74803,x74804)),f294(x74801,x74802,x74804))+~P1(f318(f318(f225(x74801),x74803),x74804))+~P1(f318(f318(f225(x74801),x74802),x74803))
% 109.14/108.86 [7539]~P4(x75391)+E(f318(f318(f101(f918(x75391,a909)),f297(x75391,x75392,x75393)),f318(f293(x75391,x75393),x75394)),f297(x75391,x75392,x75394))+~P1(f318(f318(f225(x75391),x75393),x75394))+~P1(f318(f318(f226(x75391),x75392),x75393))
% 109.14/108.86 [7556]~P4(x75561)+E(f318(f318(f101(f918(x75561,a909)),f294(x75561,x75562,x75563)),f297(x75561,x75563,x75564)),f318(f293(x75561,x75562),x75564))+~P1(f318(f318(f225(x75561),x75562),x75563))+~P1(f318(f318(f226(x75561),x75563),x75564))
% 109.14/108.86 [7587]~P4(x75871)+E(f318(f318(f101(f918(x75871,a909)),f294(x75871,x75872,x75873)),f296(x75871,x75873,x75874)),f294(x75871,x75872,x75874))+~P1(f318(f318(f225(x75871),x75873),x75874))+~P1(f318(f318(f225(x75871),x75872),x75873))
% 109.14/108.86 [7588]~P4(x75881)+E(f318(f318(f101(f918(x75881,a909)),f296(x75881,x75882,x75883)),f296(x75881,x75883,x75884)),f296(x75881,x75882,x75884))+~P1(f318(f318(f225(x75881),x75883),x75884))+~P1(f318(f318(f225(x75881),x75882),x75883))
% 109.14/108.86 [7589]~P4(x75891)+E(f318(f318(f101(f918(x75891,a909)),f296(x75891,x75892,x75893)),f297(x75891,x75893,x75894)),f297(x75891,x75892,x75894))+~P1(f318(f318(f225(x75891),x75892),x75893))+~P1(f318(f318(f226(x75891),x75893),x75894))
% 109.14/108.86 [7590]~P4(x75901)+E(f318(f318(f101(f918(x75901,a909)),f297(x75901,x75902,x75903)),f294(x75901,x75903,x75904)),f296(x75901,x75902,x75904))+~P1(f318(f318(f225(x75901),x75903),x75904))+~P1(f318(f318(f226(x75901),x75902),x75903))
% 109.14/108.86 [8373]P25(x83731,x83732,f877(x83733,x83732,x83734,x83731),x83734)+~P1(f318(f55(x83732),x83733))+~P1(f318(f55(x83731),x83734))+~P1(f318(f318(f225(a911),f318(f29(x83731),x83734)),f318(f29(x83732),x83733)))
% 109.14/108.86 [8394]P37(x83941,x83942,x83943)+~P1(f318(x83942,x83944))+P1(f318(x83942,f763(x83943,x83942,x83941,x83944)))+~P1(f318(f318(f320(x83941),x83944),f318(f163(x83941),x83943)))
% 109.14/108.86 [8395]P37(x83951,x83952,x83953)+~P1(f318(x83952,x83954))+P1(f318(x83952,f772(x83953,x83952,x83951,x83954)))+~P1(f318(f318(f320(x83951),x83954),f318(f163(x83951),x83953)))
% 109.14/108.86 [8449]~P82(x84491)+~E(f318(x84493,f422(x84493,x84494,x84492,x84491)),f71(x84491))+E(f318(f318(f318(f59(x84491,x84492,f74(x84491)),x84493),f71(x84491)),x84494),f71(x84491))+~P1(f318(f55(x84492),x84494))
% 109.14/108.86 [8717]~P130(x87171)+~P1(f318(f318(f225(x87171),f2(x87171)),x87173))+P1(f318(f318(f225(x87171),x87172),x87173))+~P1(f318(f318(f225(x87171),f318(f318(f235(x87171),x87172),f318(a103,x87174))),f318(f318(f235(x87171),x87173),f318(a103,x87174))))
% 109.14/108.86 [8885]~P42(f918(x88854,a909),f918(x88854,a909),x88853)+P1(f318(x88851,x88852))+~P1(f318(x88851,f599(x88851,x88853,x88852,x88854)))+~P1(f318(f318(f320(x88854),x88852),f86(f918(x88854,a909),x88853)))
% 109.14/108.86 [9033]P37(x90331,x90332,x90333)+~P1(f318(x90332,x90334))+~P1(f318(f318(f320(x90331),x90334),f318(f163(x90331),x90333)))+P1(f318(f318(f320(x90331),f763(x90333,x90332,x90331,x90334)),f318(f163(x90331),x90333)))
% 109.14/108.86 [9034]P37(x90341,x90342,x90343)+~P1(f318(x90342,x90344))+~P1(f318(f318(f320(x90341),x90344),f318(f163(x90341),x90343)))+P1(f318(f318(f320(x90341),f772(x90343,x90342,x90341,x90344)),f318(f163(x90341),x90343)))
% 109.14/108.86 [9112]~P82(x91121)+E(f318(f318(f318(f59(x91121,x91122,f74(x91121)),x91123),f71(x91121)),x91124),f71(x91121))+~P1(f318(f55(x91122),x91124))+P1(f318(f318(f320(x91122),f422(x91123,x91124,x91122,x91121)),x91124))
% 109.14/108.86 [9607]~P1(f318(f318(f225(a1),x96074),f2(a1)))+P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f74(a1),x96071),f39(a1,x96072,x96073))),x96074)),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x96073))+~P1(f318(f318(f226(a1),x96071),x96074))
% 109.14/108.86 [10075]~P1(f318(f55(x100751),x100752))+~P1(f318(f318(f320(x100751),x100754),x100752))+~P1(f318(f318(f320(x100751),x100753),x100752))+P1(f318(f318(f226(a911),f318(f29(x100751),f318(f318(f3(f918(x100751,a909)),f318(f318(f3(f918(x100751,a909)),x100752),f318(f318(f300(x100751),x100753),f179(f918(x100751,a909))))),f318(f318(f300(x100751),x100754),f179(f918(x100751,a909)))))),f318(f29(x100751),x100752)))
% 109.14/108.86 [7017]~P146(x70173)+~P124(x70173)+P1(f318(x70171,f844(x70172,x70171,x70173)))+~P1(f318(x70171,f318(f318(f74(x70173),x70172),x70174)))
% 109.14/108.86 [7073]~P108(x70731)+~P1(f318(f318(f225(x70731),x70732),x70734))+~P1(f318(f318(f225(x70731),x70732),x70733))+P1(f318(f318(f225(x70731),x70732),f318(f318(f92(x70731),x70733),x70734)))
% 109.14/108.86 [7074]~P108(x70741)+~P1(f318(f318(f225(x70741),x70742),x70744))+~P1(f318(f318(f225(x70741),x70742),x70743))+P1(f318(f318(f225(x70741),x70742),f318(f318(f92(x70741),x70743),x70744)))
% 109.14/108.86 [7075]~P108(x70751)+~P1(f318(f318(f225(x70751),x70752),x70754))+~P1(f318(f318(f225(x70751),x70752),x70753))+P1(f318(f318(f225(x70751),x70752),f318(f318(f92(x70751),x70753),x70754)))
% 109.14/108.86 [7076]~P4(x70761)+~P1(f318(f318(f225(x70761),x70762),x70764))+~P1(f318(f318(f225(x70761),x70762),x70763))+P1(f318(f318(f225(x70761),x70762),f318(f318(f223(x70761),x70763),x70764)))
% 109.14/108.86 [7077]~P4(x70771)+~P1(f318(f318(f225(x70771),x70772),x70774))+~P1(f318(f318(f225(x70771),x70772),x70773))+P1(f318(f318(f225(x70771),x70772),f318(f318(f223(x70771),x70773),x70774)))
% 109.14/108.86 [7078]~P4(x70781)+~P1(f318(f318(f225(x70781),x70782),x70784))+~P1(f318(f318(f225(x70781),x70782),x70783))+P1(f318(f318(f225(x70781),x70782),f318(f318(f223(x70781),x70783),x70784)))
% 109.14/108.86 [7079]~P4(x70791)+~P1(f318(f318(f226(x70791),x70792),x70794))+~P1(f318(f318(f226(x70791),x70792),x70793))+P1(f318(f318(f226(x70791),x70792),f318(f318(f223(x70791),x70793),x70794)))
% 109.14/108.86 [7099]~P73(x70992)+E(x70991,f2(x70992))+E(f318(f318(f282(x70992),f318(f318(f235(x70992),x70991),x70993)),f318(f318(f235(x70992),x70991),x70994)),f318(f318(f235(x70992),x70991),f318(f318(f3(a911),x70993),x70994)))+~P1(f318(f318(f225(a911),x70994),x70993))
% 109.14/108.86 [7145]~P4(x71451)+~P13(x71451,f318(f318(f142(x71451),x71453),x71454))+P13(x71451,f318(f318(f142(x71451),x71452),f318(f318(f142(x71451),x71453),x71454)))+~P1(f318(f318(f225(x71451),x71452),x71453))
% 109.14/108.86 [7146]~P4(x71461)+~P13(x71461,f318(f318(f142(x71461),x71463),x71464))+P13(x71461,f318(f318(f142(x71461),x71462),f318(f318(f142(x71461),x71463),x71464)))+~P1(f318(f318(f225(x71461),x71462),x71463))
% 109.14/108.86 [7183]~P93(x71831)+~P1(f318(f318(f225(x71831),f2(x71831)),x71834))+~P1(f318(f318(f225(x71831),x71832),x71833))+P1(f318(f318(f225(x71831),x71832),f318(f318(f73(x71831),x71833),x71834)))
% 109.14/108.86 [7184]~P93(x71841)+~P1(f318(f318(f225(x71841),f2(x71841)),x71843))+~P1(f318(f318(f225(x71841),x71842),x71844))+P1(f318(f318(f225(x71841),x71842),f318(f318(f73(x71841),x71843),x71844)))
% 109.14/108.86 [7185]~P93(x71851)+~P1(f318(f318(f225(x71851),x71852),x71854))+~P1(f318(f318(f226(x71851),f2(x71851)),x71853))+P1(f318(f318(f226(x71851),x71852),f318(f318(f73(x71851),x71853),x71854)))
% 109.14/108.86 [7186]~P93(x71861)+~P1(f318(f318(f225(x71861),f2(x71861)),x71863))+~P1(f318(f318(f226(x71861),x71862),x71864))+P1(f318(f318(f226(x71861),x71862),f318(f318(f73(x71861),x71863),x71864)))
% 109.14/108.86 [7187]~P130(x71871)+~P1(f318(f318(f226(x71871),f2(x71871)),x71873))+~P1(f318(f318(f226(x71871),x71872),x71874))+P1(f318(f318(f226(x71871),x71872),f318(f318(f73(x71871),x71873),x71874)))
% 109.14/108.86 [7227]~P4(x72271)+P1(f318(f318(f225(x72271),x72272),x72273))+P1(f318(f318(f225(x72271),x72272),x72274))+~P1(f318(f318(f225(x72271),x72272),f318(f318(f224(x72271),x72274),x72273)))
% 109.14/108.86 [7228]~P4(x72281)+P1(f318(f318(f226(x72281),x72282),x72283))+P1(f318(f318(f226(x72281),x72282),x72284))+~P1(f318(f318(f226(x72281),x72282),f318(f318(f224(x72281),x72284),x72283)))
% 109.14/108.86 [7514]~P113(x75142)+~P71(x75141)+~P1(f318(f318(f226(f918(x75141,x75142)),x75143),x75144))+P1(f318(f318(f225(f918(x75141,x75142)),x75143),x75144))
% 109.14/108.86 [7872]~P75(x78721)+~P1(f318(f318(f226(x78721),x78724),f2(x78721)))+~P1(f318(f318(f225(x78721),x78723),f318(f318(f282(x78721),x78722),x78724)))+P1(f318(f318(f225(x78721),x78722),f318(f318(f74(x78721),x78723),x78724)))
% 109.14/108.86 [7873]~P75(x78731)+~P1(f318(f318(f226(x78731),x78734),f2(x78731)))+~P1(f318(f318(f225(x78731),x78733),f318(f318(f74(x78731),x78732),x78734)))+P1(f318(f318(f225(x78731),x78732),f318(f318(f282(x78731),x78733),x78734)))
% 109.14/108.86 [7874]~P75(x78741)+~P1(f318(f318(f226(x78741),x78744),f2(x78741)))+~P1(f318(f318(f226(x78741),x78743),f318(f318(f282(x78741),x78742),x78744)))+P1(f318(f318(f226(x78741),x78742),f318(f318(f74(x78741),x78743),x78744)))
% 109.14/108.86 [7875]~P75(x78751)+~P1(f318(f318(f226(x78751),x78754),f2(x78751)))+~P1(f318(f318(f226(x78751),x78753),f318(f318(f74(x78751),x78752),x78754)))+P1(f318(f318(f226(x78751),x78752),f318(f318(f282(x78751),x78753),x78754)))
% 109.14/108.86 [7986]~P140(x79861)+~P1(f318(f318(f225(x79861),x79862),f2(x79861)))+~P1(f318(f318(f225(x79861),x79864),x79863))+P1(f318(f318(f225(x79861),f318(f318(f74(x79861),x79862),x79863)),f318(f318(f74(x79861),x79862),x79864)))
% 109.14/108.86 [7987]~P131(x79871)+~P1(f318(f318(f226(x79871),x79872),f2(x79871)))+~P1(f318(f318(f225(x79871),x79874),x79873))+P1(f318(f318(f225(x79871),f318(f318(f74(x79871),x79872),x79873)),f318(f318(f74(x79871),x79872),x79874)))
% 109.14/108.86 [7988]~P140(x79881)+~P1(f318(f318(f225(x79881),x79883),f2(x79881)))+~P1(f318(f318(f225(x79881),x79884),x79882))+P1(f318(f318(f225(x79881),f318(f318(f74(x79881),x79882),x79883)),f318(f318(f74(x79881),x79884),x79883)))
% 109.14/108.86 [7989]~P74(x79891)+~P1(f318(f318(f225(x79891),x79893),f2(x79891)))+~P1(f318(f318(f225(x79891),x79894),x79892))+P1(f318(f318(f225(x79891),f318(f318(f282(x79891),x79892),x79893)),f318(f318(f282(x79891),x79894),x79893)))
% 109.14/108.86 [7990]~P131(x79901)+~P1(f318(f318(f226(x79901),x79902),f2(x79901)))+~P1(f318(f318(f226(x79901),x79904),x79903))+P1(f318(f318(f226(x79901),f318(f318(f74(x79901),x79902),x79903)),f318(f318(f74(x79901),x79902),x79904)))
% 109.14/108.86 [7991]~P131(x79911)+~P1(f318(f318(f226(x79911),x79912),f2(x79911)))+~P1(f318(f318(f226(x79911),x79914),x79913))+P1(f318(f318(f226(x79911),f318(f318(f74(x79911),x79912),x79913)),f318(f318(f74(x79911),x79912),x79914)))
% 109.14/108.86 [7992]~P131(x79921)+~P1(f318(f318(f226(x79921),x79923),f2(x79921)))+~P1(f318(f318(f226(x79921),x79924),x79922))+P1(f318(f318(f226(x79921),f318(f318(f74(x79921),x79922),x79923)),f318(f318(f74(x79921),x79924),x79923)))
% 109.14/108.86 [7993]~P131(x79931)+~P1(f318(f318(f226(x79931),x79933),f2(x79931)))+~P1(f318(f318(f226(x79931),x79934),x79932))+P1(f318(f318(f226(x79931),f318(f318(f74(x79931),x79932),x79933)),f318(f318(f74(x79931),x79934),x79933)))
% 109.14/108.86 [7994]~P131(x79941)+~P1(f318(f318(f226(x79941),x79942),f2(x79941)))+~P1(f318(f318(f226(x79941),x79944),x79943))+P1(f318(f318(f226(x79941),f318(f318(f74(x79941),x79942),x79943)),f318(f318(f74(x79941),x79942),x79944)))
% 109.14/108.86 [7995]~P75(x79951)+~P1(f318(f318(f226(x79951),x79953),f2(x79951)))+~P1(f318(f318(f226(x79951),x79954),x79952))+P1(f318(f318(f226(x79951),f318(f318(f282(x79951),x79952),x79953)),f318(f318(f282(x79951),x79954),x79953)))
% 109.14/108.86 [7996]~P130(x79961)+~P1(f318(f318(f226(x79961),f71(x79961)),x79962))+~P1(f318(f318(f225(a911),x79963),x79964))+P1(f318(f318(f225(x79961),f318(f318(f235(x79961),x79962),x79963)),f318(f318(f235(x79961),x79962),x79964)))
% 109.14/108.86 [7997]~P130(x79971)+~P1(f318(f318(f225(x79971),f71(x79971)),x79972))+~P1(f318(f318(f225(a911),x79973),x79974))+P1(f318(f318(f225(x79971),f318(f318(f235(x79971),x79972),x79973)),f318(f318(f235(x79971),x79972),x79974)))
% 109.14/108.86 [7998]~P130(x79981)+~P1(f318(f318(f226(x79981),f71(x79981)),x79982))+~P1(f318(f318(f226(a911),x79983),x79984))+P1(f318(f318(f226(x79981),f318(f318(f235(x79981),x79982),x79983)),f318(f318(f235(x79981),x79982),x79984)))
% 109.14/108.86 [7999]~P130(x79991)+~P1(f318(f318(f226(x79991),f71(x79991)),x79992))+~P1(f318(f318(f226(a911),x79993),x79994))+P1(f318(f318(f226(x79991),f318(f318(f235(x79991),x79992),x79993)),f318(f318(f235(x79991),x79992),x79994)))
% 109.14/108.86 [8022]P1(f318(f318(f226(a911),f2(a911)),f318(x80221,x80222)))+~P1(f318(f55(x80223),x80224))+~P1(f318(f318(f320(x80223),x80222),x80224))+~P1(f318(f318(f226(a911),f2(a911)),f318(f318(f11(x80223,a911),x80221),x80224)))
% 109.14/108.86 [8031]~P130(x80311)+~P1(f318(f318(f225(x80311),x80312),x80314))+~P1(f318(f318(f225(x80311),f2(x80311)),x80312))+P1(f318(f318(f225(x80311),f318(f318(f235(x80311),x80312),x80313)),f318(f318(f235(x80311),x80314),x80313)))
% 109.14/108.86 [8032]~P142(x80321)+~P1(f318(f318(f225(x80321),x80323),x80324))+~P1(f318(f318(f225(x80321),f2(x80321)),x80322))+P1(f318(f318(f225(x80321),f318(f318(f74(x80321),x80322),x80323)),f318(f318(f74(x80321),x80322),x80324)))
% 109.14/108.86 [8033]~P141(x80331)+~P1(f318(f318(f225(x80331),x80333),x80334))+~P1(f318(f318(f225(x80331),f2(x80331)),x80332))+P1(f318(f318(f225(x80331),f318(f318(f74(x80331),x80332),x80333)),f318(f318(f74(x80331),x80332),x80334)))
% 109.14/108.86 [8034]~P131(x80341)+~P1(f318(f318(f226(x80341),f2(x80341)),x80342))+~P1(f318(f318(f225(x80341),x80343),x80344))+P1(f318(f318(f225(x80341),f318(f318(f74(x80341),x80342),x80343)),f318(f318(f74(x80341),x80342),x80344)))
% 109.14/108.86 [8035]~P142(x80351)+~P1(f318(f318(f225(x80351),x80352),x80354))+~P1(f318(f318(f225(x80351),f2(x80351)),x80353))+P1(f318(f318(f225(x80351),f318(f318(f74(x80351),x80352),x80353)),f318(f318(f74(x80351),x80354),x80353)))
% 109.14/108.86 [8036]~P74(x80361)+~P1(f318(f318(f225(x80361),x80362),x80364))+~P1(f318(f318(f225(x80361),f2(x80361)),x80363))+P1(f318(f318(f225(x80361),f318(f318(f282(x80361),x80362),x80363)),f318(f318(f282(x80361),x80364),x80363)))
% 109.14/108.86 [8037]~P131(x80371)+~P1(f318(f318(f226(x80371),x80373),x80374))+~P1(f318(f318(f226(x80371),f2(x80371)),x80372))+P1(f318(f318(f226(x80371),f318(f318(f74(x80371),x80372),x80373)),f318(f318(f74(x80371),x80372),x80374)))
% 109.14/108.86 [8038]~P134(x80381)+~P1(f318(f318(f226(x80381),x80383),x80384))+~P1(f318(f318(f226(x80381),f2(x80381)),x80382))+P1(f318(f318(f226(x80381),f318(f318(f74(x80381),x80382),x80383)),f318(f318(f74(x80381),x80382),x80384)))
% 109.14/108.86 [8039]~P127(x80391)+~P1(f318(f318(f226(x80391),x80393),x80394))+~P1(f318(f318(f226(x80391),f2(x80391)),x80392))+P1(f318(f318(f226(x80391),f318(f318(f74(x80391),x80392),x80393)),f318(f318(f74(x80391),x80392),x80394)))
% 109.14/108.86 [8040]~P131(x80401)+~P1(f318(f318(f226(x80401),x80402),x80404))+~P1(f318(f318(f226(x80401),f2(x80401)),x80403))+P1(f318(f318(f226(x80401),f318(f318(f74(x80401),x80402),x80403)),f318(f318(f74(x80401),x80404),x80403)))
% 109.14/108.86 [8041]~P134(x80411)+~P1(f318(f318(f226(x80411),x80412),x80414))+~P1(f318(f318(f226(x80411),f2(x80411)),x80413))+P1(f318(f318(f226(x80411),f318(f318(f74(x80411),x80412),x80413)),f318(f318(f74(x80411),x80414),x80413)))
% 109.14/108.86 [8042]~P131(x80421)+~P1(f318(f318(f226(x80421),x80423),x80424))+~P1(f318(f318(f226(x80421),f2(x80421)),x80422))+P1(f318(f318(f226(x80421),f318(f318(f74(x80421),x80422),x80423)),f318(f318(f74(x80421),x80422),x80424)))
% 109.14/108.86 [8043]~P75(x80431)+~P1(f318(f318(f226(x80431),x80432),x80434))+~P1(f318(f318(f226(x80431),f2(x80431)),x80433))+P1(f318(f318(f226(x80431),f318(f318(f282(x80431),x80432),x80433)),f318(f318(f282(x80431),x80434),x80433)))
% 109.14/108.86 [8082]~P3(x80822)+P1(f318(f318(f226(f918(x80821,x80822)),x80824),x80823))+~P1(f318(f318(f225(f918(x80821,x80822)),x80824),x80823))+P1(f318(f318(f225(f918(x80821,x80822)),x80823),x80824))
% 109.14/108.86 [8120]P1(f318(f318(f320(x81201),x81202),x81203))+P1(f318(f318(f320(x81201),x81202),x81204))+~P1(f318(f318(f225(f918(x81201,a909)),x81204),x81203))+P1(f318(f318(f226(f918(x81201,a909)),x81204),f318(f318(f300(x81201),x81202),x81203)))
% 109.14/108.86 [8236]~P123(x82362)+E(x82361,f2(x82362))+P1(f318(f318(f278(x82362),x82363),x82364))+~P1(f318(f318(f278(x82362),f318(f318(f74(x82362),x82363),x82361)),f318(f318(f74(x82362),x82364),x82361)))
% 109.14/108.86 [8237]~P123(x82372)+E(x82371,f2(x82372))+P1(f318(f318(f278(x82372),x82373),x82374))+~P1(f318(f318(f278(x82372),f318(f318(f74(x82372),x82371),x82373)),f318(f318(f74(x82372),x82371),x82374)))
% 109.14/108.86 [8288]P1(f318(f318(f320(x82881),x82882),x82883))+P1(f318(f318(f320(x82881),x82882),x82884))+~P1(f318(f318(f226(f918(x82881,a909)),x82884),f318(f318(f300(x82881),x82882),x82883)))+P1(f318(f318(f225(f918(x82881,a909)),x82884),x82883))
% 109.14/108.86 [8354]~P131(x83541)+P1(f318(f318(f226(x83541),x83543),x83542))+P1(f318(f318(f226(x83541),x83542),x83543))+~P1(f318(f318(f226(x83541),f318(f318(f74(x83541),x83544),x83542)),f318(f318(f74(x83541),x83544),x83543)))
% 109.14/108.86 [8355]~P131(x83551)+P1(f318(f318(f226(x83551),x83553),x83552))+P1(f318(f318(f226(x83551),x83552),x83553))+~P1(f318(f318(f226(x83551),f318(f318(f74(x83551),x83552),x83554)),f318(f318(f74(x83551),x83553),x83554)))
% 109.14/108.86 [8364]~P131(x83641)+P1(f318(f318(f226(x83641),x83644),f2(x83641)))+P1(f318(f318(f226(x83641),x83642),x83643))+~P1(f318(f318(f226(x83641),f318(f318(f74(x83641),x83642),x83644)),f318(f318(f74(x83641),x83643),x83644)))
% 109.14/108.86 [8365]~P131(x83651)+P1(f318(f318(f226(x83651),x83654),f2(x83651)))+P1(f318(f318(f226(x83651),x83652),x83653))+~P1(f318(f318(f226(x83651),f318(f318(f74(x83651),x83654),x83652)),f318(f318(f74(x83651),x83654),x83653)))
% 109.14/108.86 [8368]~P131(x83681)+P1(f318(f318(f226(x83681),x83682),x83683))+P1(f318(f318(f226(x83681),f2(x83681)),x83684))+~P1(f318(f318(f226(x83681),f318(f318(f74(x83681),x83684),x83683)),f318(f318(f74(x83681),x83684),x83682)))
% 109.14/108.86 [8369]~P131(x83691)+P1(f318(f318(f226(x83691),x83692),x83693))+P1(f318(f318(f226(x83691),f2(x83691)),x83694))+~P1(f318(f318(f226(x83691),f318(f318(f74(x83691),x83693),x83694)),f318(f318(f74(x83691),x83692),x83694)))
% 109.14/108.86 [8381]~P131(x83811)+P1(f318(f318(f226(x83811),x83812),f2(x83811)))+P1(f318(f318(f226(x83811),f2(x83811)),x83812))+~P1(f318(f318(f226(x83811),f318(f318(f74(x83811),x83813),x83812)),f318(f318(f74(x83811),x83814),x83812)))
% 109.14/108.86 [8382]~P131(x83821)+P1(f318(f318(f226(x83821),x83822),f2(x83821)))+P1(f318(f318(f226(x83821),f2(x83821)),x83822))+~P1(f318(f318(f226(x83821),f318(f318(f74(x83821),x83822),x83823)),f318(f318(f74(x83821),x83822),x83824)))
% 109.14/108.86 [8411]~P131(x84111)+~P1(f318(f318(f226(x84111),x84114),f2(x84111)))+P1(f318(f318(f225(x84111),x84112),x84113))+~P1(f318(f318(f225(x84111),f318(f318(f74(x84111),x84114),x84113)),f318(f318(f74(x84111),x84114),x84112)))
% 109.14/108.86 [8412]~P131(x84121)+~P1(f318(f318(f226(x84121),x84124),f2(x84121)))+P1(f318(f318(f226(x84121),x84122),x84123))+~P1(f318(f318(f226(x84121),f318(f318(f74(x84121),x84124),x84123)),f318(f318(f74(x84121),x84124),x84122)))
% 109.14/108.86 [8422]~P130(x84223)+~P1(f318(f318(f226(x84223),f71(x84223)),x84224))+P1(f318(f318(f225(a911),x84221),x84222))+~P1(f318(f318(f225(x84223),f318(f318(f235(x84223),x84224),x84221)),f318(f318(f235(x84223),x84224),x84222)))
% 109.14/108.86 [8423]~P130(x84233)+~P1(f318(f318(f226(x84233),f71(x84233)),x84234))+P1(f318(f318(f225(a911),x84231),x84232))+~P1(f318(f318(f225(x84233),f318(f318(f235(x84233),x84234),x84231)),f318(f318(f235(x84233),x84234),x84232)))
% 109.14/108.86 [8424]~P130(x84243)+~P1(f318(f318(f226(x84243),f71(x84243)),x84244))+P1(f318(f318(f226(a911),x84241),x84242))+~P1(f318(f318(f226(x84243),f318(f318(f235(x84243),x84244),x84241)),f318(f318(f235(x84243),x84244),x84242)))
% 109.14/108.86 [8425]~P130(x84253)+~P1(f318(f318(f226(x84253),f71(x84253)),x84254))+P1(f318(f318(f226(a911),x84251),x84252))+~P1(f318(f318(f226(x84253),f318(f318(f235(x84253),x84254),x84251)),f318(f318(f235(x84253),x84254),x84252)))
% 109.14/108.86 [8435]~P131(x84351)+P1(f318(f318(f225(x84351),x84352),x84353))+~P1(f318(f318(f226(x84351),f2(x84351)),x84354))+~P1(f318(f318(f225(x84351),f318(f318(f74(x84351),x84354),x84352)),f318(f318(f74(x84351),x84354),x84353)))
% 109.14/108.86 [8436]~P134(x84361)+P1(f318(f318(f225(x84361),x84362),x84363))+~P1(f318(f318(f226(x84361),f2(x84361)),x84364))+~P1(f318(f318(f225(x84361),f318(f318(f74(x84361),x84364),x84362)),f318(f318(f74(x84361),x84364),x84363)))
% 109.14/108.86 [8437]~P134(x84371)+P1(f318(f318(f225(x84371),x84372),x84373))+~P1(f318(f318(f226(x84371),f2(x84371)),x84374))+~P1(f318(f318(f225(x84371),f318(f318(f74(x84371),x84372),x84374)),f318(f318(f74(x84371),x84373),x84374)))
% 109.14/108.86 [8438]~P131(x84381)+P1(f318(f318(f226(x84381),x84382),x84383))+~P1(f318(f318(f226(x84381),f2(x84381)),x84384))+~P1(f318(f318(f226(x84381),f318(f318(f74(x84381),x84384),x84382)),f318(f318(f74(x84381),x84384),x84383)))
% 109.14/108.86 [8439]~P134(x84391)+P1(f318(f318(f226(x84391),x84392),x84393))+~P1(f318(f318(f225(x84391),f2(x84391)),x84394))+~P1(f318(f318(f226(x84391),f318(f318(f74(x84391),x84394),x84392)),f318(f318(f74(x84391),x84394),x84393)))
% 109.14/108.86 [8440]~P135(x84401)+P1(f318(f318(f226(x84401),x84402),x84403))+~P1(f318(f318(f225(x84401),f2(x84401)),x84404))+~P1(f318(f318(f226(x84401),f318(f318(f74(x84401),x84404),x84402)),f318(f318(f74(x84401),x84404),x84403)))
% 109.14/108.86 [8441]~P130(x84411)+~P1(f318(f318(f225(x84411),f2(x84411)),x84413))+P1(f318(f318(f226(x84411),x84412),x84413))+~P1(f318(f318(f226(x84411),f318(f318(f235(x84411),x84412),x84414)),f318(f318(f235(x84411),x84413),x84414)))
% 109.14/108.86 [8442]~P134(x84421)+P1(f318(f318(f226(x84421),x84422),x84423))+~P1(f318(f318(f225(x84421),f2(x84421)),x84424))+~P1(f318(f318(f226(x84421),f318(f318(f74(x84421),x84422),x84424)),f318(f318(f74(x84421),x84423),x84424)))
% 109.14/108.86 [8443]~P135(x84431)+P1(f318(f318(f226(x84431),x84432),x84433))+~P1(f318(f318(f225(x84431),f2(x84431)),x84434))+~P1(f318(f318(f226(x84431),f318(f318(f74(x84431),x84432),x84434)),f318(f318(f74(x84431),x84433),x84434)))
% 109.14/108.86 [8484]P1(f318(f318(f320(x84841),x84842),x84843))+~P1(f318(f318(f225(f918(x84841,a909)),x84843),x84844))+~P1(f318(f318(f226(f918(x84841,a909)),x84843),x84844))+P1(f318(f318(f226(f918(x84841,a909)),x84843),f318(f318(f300(x84841),x84842),x84844)))
% 109.14/108.86 [8516]~P146(x85161)+~P124(x85161)+P1(f318(f318(f278(x85161),x85162),f318(f318(f73(x85161),f844(x85162,x85163,x85161)),f2(x85161))))+~P1(f318(x85163,f318(f318(f74(x85161),x85162),x85164)))
% 109.14/108.86 [8860]E(f318(f318(f3(a1),f331(x88601,x88602,x88603,x88604)),f332(x88601,x88602,x88603,x88604)),x88604)+~P1(f318(f318(f226(a1),f2(a1)),x88603))+~P1(f318(f318(f225(a1),x88601),x88604))+P1(f318(f318(f225(a1),x88601),f318(f318(f73(a1),x88604),x88603)))
% 109.14/108.86 [8861]E(f318(f318(f3(a1),f350(x88611,x88612,x88613,x88614)),f351(x88611,x88612,x88613,x88614)),x88614)+~P1(f318(f318(f226(a1),f2(a1)),x88613))+~P1(f318(f318(f226(a1),x88611),x88614))+P1(f318(f318(f226(a1),x88611),f318(f318(f73(a1),x88614),x88613)))
% 109.14/108.86 [9016]~E(f318(f318(f155(x90161),x90163),f670(x90164,x90163,x90161,x90162)),f318(f318(f155(x90161),x90164),f670(x90164,x90163,x90161,x90162)))+E(f318(f318(f166(x90161),x90162),x90163),f318(f318(f166(x90161),x90162),x90164))+~P1(f318(f318(f225(a911),x90162),f318(f180(f912(x90161)),x90163)))+~P1(f318(f318(f225(a911),x90162),f318(f180(f912(x90161)),x90164)))
% 109.14/108.86 [9079]~P1(f318(f318(f226(a1),f2(a1)),x90793))+~P1(f318(f318(f225(a1),x90791),x90794))+P1(f318(f318(f320(a1),f331(x90791,x90792,x90793,x90794)),x90792))+P1(f318(f318(f225(a1),x90791),f318(f318(f73(a1),x90794),x90793)))
% 109.14/108.86 [9080]~P1(f318(f318(f226(a1),f2(a1)),x90803))+~P1(f318(f318(f226(a1),x90801),x90804))+P1(f318(f318(f320(a1),f350(x90801,x90802,x90803,x90804)),x90802))+P1(f318(f318(f226(a1),x90801),f318(f318(f73(a1),x90804),x90803)))
% 109.14/108.86 [9121]~P108(x91211)+~P1(f318(f55(x91211),x91213))+~P1(f318(f318(f320(x91211),x91214),x91213))+P1(f318(f318(f225(x91211),f318(f318(f58(x91211,x91211,f92(x91211)),x91212),x91213)),f318(f318(f92(x91211),x91214),x91212)))
% 109.14/108.86 [9122]~P4(x91221)+~P1(f318(f55(x91221),x91223))+~P1(f318(f318(f320(x91221),x91224),x91223))+P1(f318(f318(f225(x91221),f318(f318(f58(x91221,x91221,f223(x91221)),x91222),x91223)),f318(f318(f223(x91221),x91224),x91222)))
% 109.14/108.86 [9166]E(f318(f318(f166(x91661),x91662),x91663),f318(f318(f166(x91661),x91662),x91664))+P1(f318(f318(f226(a911),f670(x91663,x91664,x91661,x91662)),x91662))+~P1(f318(f318(f225(a911),x91662),f318(f180(f912(x91661)),x91663)))+~P1(f318(f318(f225(a911),x91662),f318(f180(f912(x91661)),x91664)))
% 109.14/108.86 [9171]~P1(f318(f318(f226(a1),f2(a1)),x91713))+~P1(f318(f318(f225(a1),x91711),x91712))+P1(f318(f318(f320(a1),f332(x91711,x91714,x91713,x91712)),f294(a1,f71(a1),x91713)))+P1(f318(f318(f225(a1),x91711),f318(f318(f73(a1),x91712),x91713)))
% 109.14/108.86 [9172]~P1(f318(f318(f226(a1),f2(a1)),x91723))+~P1(f318(f318(f226(a1),x91721),x91722))+P1(f318(f318(f320(a1),f351(x91721,x91724,x91723,x91722)),f294(a1,f71(a1),x91723)))+P1(f318(f318(f226(a1),x91721),f318(f318(f73(a1),x91722),x91723)))
% 109.14/108.86 [9496]~P102(x94961)+~P1(f318(f55(x94961),x94964))+P1(f318(f318(f320(x94961),f430(x94962,x94963,x94964,x94961)),x94964))+P1(f318(f318(f225(x94961),f318(f318(f58(x94961,x94961,f101(x94961)),x94962),x94964)),f318(f318(f101(x94961),x94963),x94962)))
% 109.14/108.86 [9497]~P4(x94971)+~P1(f318(f55(x94971),x94974))+P1(f318(f318(f320(x94971),f464(x94972,x94973,x94974,x94971)),x94974))+P1(f318(f318(f225(x94971),f318(f318(f58(x94971,x94971,f224(x94971)),x94972),x94974)),f318(f318(f224(x94971),x94973),x94972)))
% 109.14/108.86 [9621]~P102(x96211)+~P1(f318(f55(x96211),x96213))+~P1(f318(f318(f225(x96211),f430(x96212,x96214,x96213,x96211)),x96214))+P1(f318(f318(f225(x96211),f318(f318(f58(x96211,x96211,f101(x96211)),x96212),x96213)),f318(f318(f101(x96211),x96214),x96212)))
% 109.14/108.86 [9622]~P4(x96221)+~P1(f318(f55(x96221),x96223))+~P1(f318(f318(f225(x96221),f464(x96222,x96224,x96223,x96221)),x96224))+P1(f318(f318(f225(x96221),f318(f318(f58(x96221,x96221,f224(x96221)),x96222),x96223)),f318(f318(f224(x96221),x96224),x96222)))
% 109.14/108.86 [9624]~P1(f318(f318(f225(a1),f2(a1)),x96244))+~P1(f318(f318(f226(a1),f2(a1)),x96243))+~P1(f318(f318(f226(a1),x96244),x96241))+P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f74(a1),x96241),f39(a1,x96242,x96243))),x96244)),f318(f318(f74(a1),x96241),x96243)))
% 109.14/108.86 [9943]~P113(x99431)+P1(f318(f318(f225(x99431),f318(x99432,x99433)),f318(x99432,x99434)))+~P1(f318(f318(f225(a911),x99433),x99434))+~P1(f318(f318(f225(x99431),f318(x99432,f898(x99434,x99433,x99432,x99431))),f318(x99432,f318(a103,f898(x99434,x99433,x99432,x99431)))))
% 109.14/108.86 [10048]E(x100481,x100482)+P1(f318(f318(f320(f917(f912(x100483),f912(x100483))),f318(f318(f243(f912(x100483),f912(x100483)),x100482),x100481)),f138(x100483,x100484)))+P1(f318(f318(f320(f917(f912(x100483),f912(x100483))),f318(f318(f243(f912(x100483),f912(x100483)),x100481),x100482)),f138(x100483,x100484)))+~P1(f318(f318(f320(f917(x100483,x100483)),f318(f318(f243(x100483,x100483),f652(x100481,x100482,x100484,x100483)),f653(x100481,x100482,x100484,x100483))),x100484))
% 109.14/108.86 [10049]E(x100491,x100492)+P1(f318(f318(f320(f917(f912(x100493),f912(x100493))),f318(f318(f243(f912(x100493),f912(x100493)),x100492),x100491)),f138(x100493,x100494)))+P1(f318(f318(f320(f917(f912(x100493),f912(x100493))),f318(f318(f243(f912(x100493),f912(x100493)),x100491),x100492)),f138(x100493,x100494)))+~P1(f318(f318(f320(f917(x100493,x100493)),f318(f318(f243(x100493,x100493),f653(x100491,x100492,x100494,x100493)),f652(x100491,x100492,x100494,x100493))),x100494))
% 109.14/108.86 [7576]~P102(x75761)+~P1(f318(f318(f225(x75761),x75763),x75764))+~P1(f318(f318(f225(x75761),x75762),x75764))+P1(f318(f318(f225(x75761),f318(f318(f101(x75761),x75762),x75763)),x75764))
% 109.14/108.86 [7577]~P102(x75771)+~P1(f318(f318(f225(x75771),x75773),x75774))+~P1(f318(f318(f225(x75771),x75772),x75774))+P1(f318(f318(f225(x75771),f318(f318(f101(x75771),x75772),x75773)),x75774))
% 109.14/108.86 [7578]~P102(x75781)+~P1(f318(f318(f225(x75781),x75783),x75784))+~P1(f318(f318(f225(x75781),x75782),x75784))+P1(f318(f318(f225(x75781),f318(f318(f101(x75781),x75782),x75783)),x75784))
% 109.14/108.86 [7579]~P4(x75791)+~P1(f318(f318(f225(x75791),x75793),x75794))+~P1(f318(f318(f225(x75791),x75792),x75794))+P1(f318(f318(f225(x75791),f318(f318(f224(x75791),x75792),x75793)),x75794))
% 109.14/108.86 [7580]~P4(x75801)+~P1(f318(f318(f225(x75801),x75803),x75804))+~P1(f318(f318(f225(x75801),x75802),x75804))+P1(f318(f318(f225(x75801),f318(f318(f224(x75801),x75802),x75803)),x75804))
% 109.14/108.86 [7581]~P4(x75811)+~P1(f318(f318(f225(x75811),x75813),x75814))+~P1(f318(f318(f225(x75811),x75812),x75814))+P1(f318(f318(f225(x75811),f318(f318(f224(x75811),x75812),x75813)),x75814))
% 109.14/108.86 [7582]~P4(x75821)+~P1(f318(f318(f226(x75821),x75823),x75824))+~P1(f318(f318(f226(x75821),x75822),x75824))+P1(f318(f318(f226(x75821),f318(f318(f224(x75821),x75822),x75823)),x75824))
% 109.14/108.86 [7816]~P69(x78161)+E(f318(f318(f73(x78161),f318(f318(f30(x78161),x78162),x78163)),f318(f318(f30(x78161),x78164),x78163)),f318(f318(f30(x78161),f318(f318(f73(x78161),x78162),x78164)),x78163))+~P1(f318(f318(f278(x78161),x78163),x78164))+~P1(f318(f318(f278(x78161),x78163),x78162))
% 109.14/108.86 [7897]~E(x78971,x78973)+E(f130(a911,f318(f293(a911,x78971),x78972)),f318(f318(f142(a911),x78973),x78974))+~E(f130(a911,f318(f293(a911,f318(f318(f73(a911),x78971),f71(a911))),x78972)),x78974)+~P1(f318(f318(f226(a911),x78971),x78972))
% 109.14/108.86 [7906]~P4(x79061)+P1(f318(f318(f225(x79061),x79062),x79063))+P1(f318(f318(f225(x79061),x79064),x79063))+~P1(f318(f318(f225(x79061),f318(f318(f223(x79061),x79064),x79062)),x79063))
% 109.14/108.86 [7907]~P4(x79071)+P1(f318(f318(f226(x79071),x79072),x79073))+P1(f318(f318(f226(x79071),x79074),x79073))+~P1(f318(f318(f226(x79071),f318(f318(f223(x79071),x79074),x79072)),x79073))
% 109.14/108.86 [8178]~P74(x81781)+~P1(f318(f318(f226(x81781),f2(x81781)),x81783))+~P1(f318(f318(f225(x81781),x81782),f318(f318(f282(x81781),x81784),x81783)))+P1(f318(f318(f225(x81781),f318(f318(f74(x81781),x81782),x81783)),x81784))
% 109.14/108.86 [8179]~P75(x81791)+~P1(f318(f318(f226(x81791),f2(x81791)),x81793))+~P1(f318(f318(f225(x81791),x81792),f318(f318(f282(x81791),x81794),x81793)))+P1(f318(f318(f225(x81791),f318(f318(f74(x81791),x81792),x81793)),x81794))
% 109.14/108.86 [8180]~P74(x81801)+~P1(f318(f318(f226(x81801),f2(x81801)),x81803))+~P1(f318(f318(f225(x81801),x81802),f318(f318(f74(x81801),x81804),x81803)))+P1(f318(f318(f225(x81801),f318(f318(f282(x81801),x81802),x81803)),x81804))
% 109.14/108.86 [8181]~P75(x81811)+~P1(f318(f318(f226(x81811),f2(x81811)),x81813))+~P1(f318(f318(f225(x81811),x81812),f318(f318(f74(x81811),x81814),x81813)))+P1(f318(f318(f225(x81811),f318(f318(f282(x81811),x81812),x81813)),x81814))
% 109.14/108.86 [8182]~P75(x81821)+~P1(f318(f318(f226(x81821),f2(x81821)),x81823))+~P1(f318(f318(f225(x81821),x81822),f318(f318(f74(x81821),x81824),x81823)))+P1(f318(f318(f225(x81821),f318(f318(f282(x81821),x81822),x81823)),x81824))
% 109.14/108.86 [8183]~P74(x81831)+~P1(f318(f318(f226(x81831),f2(x81831)),x81833))+~P1(f318(f318(f226(x81831),x81832),f318(f318(f282(x81831),x81834),x81833)))+P1(f318(f318(f226(x81831),f318(f318(f74(x81831),x81832),x81833)),x81834))
% 109.14/108.86 [8184]~P75(x81841)+~P1(f318(f318(f226(x81841),f2(x81841)),x81843))+~P1(f318(f318(f226(x81841),x81842),f318(f318(f282(x81841),x81844),x81843)))+P1(f318(f318(f226(x81841),f318(f318(f74(x81841),x81842),x81843)),x81844))
% 109.14/108.86 [8185]~P74(x81851)+~P1(f318(f318(f226(x81851),f2(x81851)),x81853))+~P1(f318(f318(f226(x81851),x81852),f318(f318(f74(x81851),x81854),x81853)))+P1(f318(f318(f226(x81851),f318(f318(f282(x81851),x81852),x81853)),x81854))
% 109.14/108.86 [8186]~P75(x81861)+~P1(f318(f318(f226(x81861),f2(x81861)),x81863))+~P1(f318(f318(f226(x81861),x81862),f318(f318(f74(x81861),x81864),x81863)))+P1(f318(f318(f226(x81861),f318(f318(f282(x81861),x81862),x81863)),x81864))
% 109.14/108.86 [8187]~P75(x81871)+~P1(f318(f318(f226(x81871),f2(x81871)),x81873))+~P1(f318(f318(f226(x81871),x81872),f318(f318(f74(x81871),x81874),x81873)))+P1(f318(f318(f226(x81871),f318(f318(f282(x81871),x81872),x81873)),x81874))
% 109.14/108.86 [8323]~P74(x83231)+~P1(f318(f318(f226(x83231),f2(x83231)),x83234))+P1(f318(f318(f225(x83231),x83232),f318(f318(f74(x83231),x83233),x83234)))+~P1(f318(f318(f225(x83231),f318(f318(f282(x83231),x83232),x83234)),x83233))
% 109.14/108.86 [8324]~P74(x83241)+~P1(f318(f318(f226(x83241),f2(x83241)),x83244))+P1(f318(f318(f225(x83241),x83242),f318(f318(f282(x83241),x83243),x83244)))+~P1(f318(f318(f225(x83241),f318(f318(f74(x83241),x83242),x83244)),x83243))
% 109.14/108.86 [8325]~P75(x83251)+~P1(f318(f318(f226(x83251),f2(x83251)),x83254))+P1(f318(f318(f225(x83251),x83252),f318(f318(f282(x83251),x83253),x83254)))+~P1(f318(f318(f225(x83251),f318(f318(f74(x83251),x83252),x83254)),x83253))
% 109.14/108.86 [8326]~P75(x83261)+~P1(f318(f318(f226(x83261),f2(x83261)),x83264))+P1(f318(f318(f225(x83261),x83262),f318(f318(f74(x83261),x83263),x83264)))+~P1(f318(f318(f225(x83261),f318(f318(f282(x83261),x83262),x83264)),x83263))
% 109.14/108.86 [8327]~P75(x83271)+~P1(f318(f318(f226(x83271),f2(x83271)),x83274))+P1(f318(f318(f225(x83271),x83272),f318(f318(f282(x83271),x83273),x83274)))+~P1(f318(f318(f225(x83271),f318(f318(f74(x83271),x83272),x83274)),x83273))
% 109.14/108.86 [8328]~P74(x83281)+~P1(f318(f318(f226(x83281),f2(x83281)),x83284))+P1(f318(f318(f226(x83281),x83282),f318(f318(f74(x83281),x83283),x83284)))+~P1(f318(f318(f226(x83281),f318(f318(f282(x83281),x83282),x83284)),x83283))
% 109.14/108.86 [8329]~P74(x83291)+~P1(f318(f318(f226(x83291),f2(x83291)),x83294))+P1(f318(f318(f226(x83291),x83292),f318(f318(f282(x83291),x83293),x83294)))+~P1(f318(f318(f226(x83291),f318(f318(f74(x83291),x83292),x83294)),x83293))
% 109.14/108.86 [8330]~P75(x83301)+~P1(f318(f318(f226(x83301),f2(x83301)),x83304))+P1(f318(f318(f226(x83301),x83302),f318(f318(f282(x83301),x83303),x83304)))+~P1(f318(f318(f226(x83301),f318(f318(f74(x83301),x83302),x83304)),x83303))
% 109.14/108.86 [8331]~P75(x83311)+~P1(f318(f318(f226(x83311),f2(x83311)),x83314))+P1(f318(f318(f226(x83311),x83312),f318(f318(f74(x83311),x83313),x83314)))+~P1(f318(f318(f226(x83311),f318(f318(f282(x83311),x83312),x83314)),x83313))
% 109.14/108.86 [8332]~P75(x83321)+~P1(f318(f318(f226(x83321),f2(x83321)),x83324))+P1(f318(f318(f226(x83321),x83322),f318(f318(f282(x83321),x83323),x83324)))+~P1(f318(f318(f226(x83321),f318(f318(f74(x83321),x83322),x83324)),x83323))
% 109.14/108.86 [8487]~P75(x84871)+~P1(f318(f318(f226(x84871),x84873),f2(x84871)))+~P1(f318(f318(f225(x84871),f318(f318(f282(x84871),x84874),x84873)),x84872))+P1(f318(f318(f225(x84871),f318(f318(f74(x84871),x84872),x84873)),x84874))
% 109.14/108.86 [8488]~P75(x84881)+~P1(f318(f318(f226(x84881),x84883),f2(x84881)))+~P1(f318(f318(f225(x84881),f318(f318(f74(x84881),x84884),x84883)),x84882))+P1(f318(f318(f225(x84881),f318(f318(f282(x84881),x84882),x84883)),x84884))
% 109.14/108.86 [8489]~P75(x84891)+~P1(f318(f318(f226(x84891),x84893),f2(x84891)))+~P1(f318(f318(f226(x84891),f318(f318(f282(x84891),x84894),x84893)),x84892))+P1(f318(f318(f226(x84891),f318(f318(f74(x84891),x84892),x84893)),x84894))
% 109.14/108.86 [8490]~P75(x84901)+~P1(f318(f318(f226(x84901),x84903),f2(x84901)))+~P1(f318(f318(f226(x84901),f318(f318(f74(x84901),x84904),x84903)),x84902))+P1(f318(f318(f226(x84901),f318(f318(f282(x84901),x84902),x84903)),x84904))
% 109.14/108.86 [8502]~P1(f318(x85021,x85024))+~P1(f318(f318(f226(a911),x85022),f318(f318(f74(a911),x85023),f318(a103,x85024))))+P1(f318(x85021,f318(f318(f30(a911),x85022),x85023)))+~P1(f318(f318(f225(a911),f318(f318(f74(a911),x85023),x85024)),x85022))
% 109.14/108.86 [8715]~P102(x87151)+~P1(f318(f55(x87151),x87154))+~P1(f318(f318(f320(x87151),x87152),x87154))+P1(f318(f318(f225(x87151),f318(f318(f101(x87151),x87152),x87153)),f318(f318(f58(x87151,x87151,f101(x87151)),x87153),x87154)))
% 109.14/108.86 [8716]~P4(x87161)+~P1(f318(f55(x87161),x87164))+~P1(f318(f318(f320(x87161),x87162),x87164))+P1(f318(f318(f225(x87161),f318(f318(f224(x87161),x87162),x87163)),f318(f318(f58(x87161,x87161,f224(x87161)),x87163),x87164)))
% 109.14/108.86 [8862]~P1(f318(f55(x88621),x88622))+E(f318(f29(x88621),f318(f318(f3(f918(x88621,a909)),x88622),f318(f318(f300(x88621),x88623),x88624))),f318(f318(f3(a911),f318(f29(x88621),f318(f318(f3(f918(x88621,a909)),x88622),x88624))),f71(a911)))+P1(f318(f318(f320(x88621),x88623),x88624))+~P1(f318(f318(f320(x88621),x88623),x88622))
% 109.14/108.86 [8939]E(f318(f318(f73(a1),f337(x89391,x89392,x89393,x89394)),f338(x89391,x89392,x89393,x89394)),x89394)+~P1(f318(f318(f226(a1),f2(a1)),x89393))+~P1(f318(f318(f225(a1),x89394),x89391))+P1(f318(f318(f225(a1),f318(f318(f3(a1),x89394),x89393)),x89391))
% 109.14/108.86 [8940]E(f318(f318(f73(a1),f354(x89401,x89402,x89403,x89404)),f355(x89401,x89402,x89403,x89404)),x89404)+~P1(f318(f318(f226(a1),f2(a1)),x89403))+~P1(f318(f318(f226(a1),x89404),x89401))+P1(f318(f318(f226(a1),f318(f318(f3(a1),x89404),x89403)),x89401))
% 109.14/108.86 [9151]~P1(f318(f318(f226(a1),f2(a1)),x91513))+~P1(f318(f318(f225(a1),x91514),x91511))+P1(f318(f318(f320(a1),f337(x91511,x91512,x91513,x91514)),x91512))+P1(f318(f318(f225(a1),f318(f318(f3(a1),x91514),x91513)),x91511))
% 109.14/108.86 [9152]~P1(f318(f318(f226(a1),f2(a1)),x91523))+~P1(f318(f318(f226(a1),x91524),x91521))+P1(f318(f318(f320(a1),f354(x91521,x91522,x91523,x91524)),x91522))+P1(f318(f318(f226(a1),f318(f318(f3(a1),x91524),x91523)),x91521))
% 109.14/108.86 [9227]~P1(f318(f318(f226(a1),f2(a1)),x92272))+~P1(f318(f318(f225(a1),x92271),x92273))+P1(f318(f318(f320(a1),f338(x92273,x92274,x92272,x92271)),f294(a1,f71(a1),x92272)))+P1(f318(f318(f225(a1),f318(f318(f3(a1),x92271),x92272)),x92273))
% 109.14/108.86 [9228]~P1(f318(f318(f226(a1),f2(a1)),x92282))+~P1(f318(f318(f226(a1),x92281),x92283))+P1(f318(f318(f320(a1),f355(x92283,x92284,x92282,x92281)),f294(a1,f71(a1),x92282)))+P1(f318(f318(f226(a1),f318(f318(f3(a1),x92281),x92282)),x92283))
% 109.14/108.86 [9245]~P1(f318(f318(f225(a1),f2(a1)),x92454))+~P1(f318(f318(f226(a1),f2(a1)),x92453))+~P1(f318(f318(f226(a1),x92454),x92451))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),f318(f318(f74(a1),x92451),f39(a1,x92452,x92453))),x92454)))
% 109.14/108.86 [9280]E(x92801,x92802)+~P41(x92803,x92804)+~P1(f318(f318(f320(f917(x92803,x92803)),f318(f318(f243(x92803,x92803),x92802),x92801)),x92804))+~P1(f318(f318(f320(f917(x92803,x92803)),f318(f318(f243(x92803,x92803),x92801),x92802)),x92804))
% 109.14/108.86 [9281]E(x92811,x92812)+~P41(x92813,x92814)+~P1(f318(f318(f320(f917(x92813,x92813)),f318(f318(f243(x92813,x92813),x92812),x92811)),x92814))+~P1(f318(f318(f320(f917(x92813,x92813)),f318(f318(f243(x92813,x92813),x92811),x92812)),x92814))
% 109.14/108.86 [9318]~P108(x93181)+~P1(f318(f55(x93181),x93184))+~P1(f318(f318(f225(x93181),x93182),f427(x93183,x93182,x93184,x93181)))+P1(f318(f318(f225(x93181),f318(f318(f92(x93181),x93182),x93183)),f318(f318(f58(x93181,x93181,f92(x93181)),x93183),x93184)))
% 109.14/108.86 [9319]~P4(x93191)+~P1(f318(f55(x93191),x93194))+~P1(f318(f318(f225(x93191),x93192),f452(x93193,x93192,x93194,x93191)))+P1(f318(f318(f225(x93191),f318(f318(f223(x93191),x93192),x93193)),f318(f318(f58(x93191,x93191,f223(x93191)),x93193),x93194)))
% 109.14/108.86 [9335]~P1(f318(f318(f225(a1),x93354),f2(a1)))+~P1(f318(f318(f226(a1),f2(a1)),x93352))+~P1(f318(f318(f226(a1),x93351),x93354))+P1(f318(f318(f226(a1),f318(f318(f74(a1),x93351),x93352)),f318(f318(f73(a1),f318(f318(f74(a1),x93351),f39(a1,x93353,x93352))),x93354)))
% 109.14/108.86 [9360]P1(f318(f55(x93601),x93602))+~P1(f318(f55(x93601),x93603))+~P1(f318(f318(f320(f918(x93601,a909)),x93602),f318(f318(f54(x93601),x93603),x93604)))+~P1(f318(f318(f225(f918(f917(x93601,x93601),a909)),x93604),f318(f318(f245(x93601,x93601),x93603),f318(f18(f918(x93601,a909),x93601),x93603))))
% 109.14/108.86 [9383]~P108(x93831)+~P1(f318(f55(x93831),x93834))+P1(f318(f318(f320(x93831),f427(x93832,x93833,x93834,x93831)),x93834))+P1(f318(f318(f225(x93831),f318(f318(f92(x93831),x93833),x93832)),f318(f318(f58(x93831,x93831,f92(x93831)),x93832),x93834)))
% 109.14/108.86 [9384]~P4(x93841)+~P1(f318(f55(x93841),x93844))+P1(f318(f318(f320(x93841),f452(x93842,x93843,x93844,x93841)),x93844))+P1(f318(f318(f225(x93841),f318(f318(f223(x93841),x93843),x93842)),f318(f318(f58(x93841,x93841,f223(x93841)),x93842),x93844)))
% 109.14/108.86 [9396]~P42(f918(x93961,a909),f918(x93961,a909),x93963)+~P1(f318(f318(f320(x93961),x93962),x93964))+P1(f318(f318(f320(x93961),x93962),f87(f918(x93961,a909),x93963)))+~P1(f318(f318(f225(f918(x93961,a909)),x93964),f318(x93963,f318(f318(f101(f918(x93961,a909)),x93964),f87(f918(x93961,a909),x93963)))))
% 109.14/108.86 [9579]~P42(f918(x95793,a909),f918(x95793,a909),x95794)+P1(f318(x95791,x95792))+~P1(f318(f318(f320(x95793),x95792),f86(f918(x95793,a909),x95794)))+P1(f318(f318(f320(x95793),f599(x95791,x95794,x95792,x95793)),f318(x95794,f318(f318(f92(f918(x95793,a909)),f86(f918(x95793,a909),x95794)),f318(f253(x95793),x95791)))))
% 109.14/108.86 [9811]~P1(f318(f55(x98112),x98114))+~P1(f318(f55(x98111),x98113))+~P1(f318(f318(f225(a911),f318(f29(x98112),x98114)),f318(f29(x98111),x98113)))+P1(f318(f318(f225(f918(x98111,a909)),f318(f301(x98112,x98111,f877(x98113,x98111,x98114,x98112)),x98114)),x98113))
% 109.14/108.86 [9434]~P1(f318(f318(f320(x94341),x94342),x94344))+P1(f318(f318(f320(x94341),x94342),x94343))+~P1(f318(f318(f226(f918(x94341,a909)),x94344),f318(f318(f300(x94341),x94342),x94343)))+P1(f318(f318(f226(f918(x94341,a909)),f318(f318(f3(f918(x94341,a909)),x94344),f318(f318(f300(x94341),x94342),f179(f918(x94341,a909))))),x94343))
% 109.14/108.86 [9604]~P1(f318(f318(f320(x96041),x96042),x96044))+P1(f318(f318(f320(x96041),x96042),x96043))+P1(f318(f318(f226(f918(x96041,a909)),x96044),f318(f318(f300(x96041),x96042),x96043)))+~P1(f318(f318(f226(f918(x96041,a909)),f318(f318(f3(f918(x96041,a909)),x96044),f318(f318(f300(x96041),x96042),f179(f918(x96041,a909))))),x96043))
% 109.14/108.86 [9627]P1(f318(f318(f320(x96271),x96272),x96273))+~P1(f318(f318(f225(f918(x96271,a909)),x96274),x96273))+P1(f318(f318(f226(f918(x96271,a909)),x96274),f318(f318(f300(x96271),x96272),x96273)))+~P1(f318(f318(f226(f918(x96271,a909)),f318(f318(f3(f918(x96271,a909)),x96274),f318(f318(f300(x96271),x96272),f179(f918(x96271,a909))))),x96273))
% 109.14/108.86 [9632]~P1(f318(f318(f320(x96321),x96323),x96322))+~P1(f318(f318(f226(f918(x96321,a909)),x96322),x96324))+P1(f318(f318(f226(f918(x96321,a909)),x96322),f318(f318(f300(x96321),x96323),x96324)))+~P1(f318(f318(f226(f918(x96321,a909)),f318(f318(f3(f918(x96321,a909)),x96322),f318(f318(f300(x96321),x96323),f179(f918(x96321,a909))))),x96324))
% 109.14/108.86 [9648]~P1(f318(f318(f225(f918(x96481,a909)),x96482),x96484))+~P1(f318(f318(f226(f918(x96481,a909)),x96482),x96484))+P1(f318(f318(f226(f918(x96481,a909)),x96482),f318(f318(f300(x96481),x96483),x96484)))+~P1(f318(f318(f226(f918(x96481,a909)),f318(f318(f3(f918(x96481,a909)),x96482),f318(f318(f300(x96481),x96483),f179(f918(x96481,a909))))),x96484))
% 109.14/108.86 [9706]~P113(x97062)+~P71(x97061)+~P1(f318(f318(f225(f918(x97061,x97062)),x97063),x97064))+P1(f318(f51(x97061),f318(f318(f20(x97061,x97062,a909),f318(f318(f10(x97062,f918(x97062,a909),x97061),f225(x97062)),x97063)),x97064)))
% 109.14/108.86 [9862]~P113(x98622)+~P71(x98621)+P1(f318(f318(f225(f918(x98621,x98622)),x98623),x98624))+~P1(f318(f51(x98621),f318(f318(f20(x98621,x98622,a909),f318(f318(f10(x98622,f918(x98622,a909),x98621),f225(x98622)),x98623)),x98624)))
% 109.14/108.86 [10390]~P42(f918(x103901,a909),f918(x103901,a909),x103903)+~P1(f318(f318(f320(x103901),x103902),x103904))+P1(f318(f318(f320(x103901),x103902),f87(f918(x103901,a909),x103903)))+~P1(f318(f318(f225(f918(x103901,a909)),x103904),f318(x103903,f86(f918(x103901,a909),f318(f318(f9(f918(x103901,a909),f918(x103901,a909),f918(x103901,a909)),f318(f318(f10(f918(x103901,a909),f918(f918(x103901,a909),f918(x103901,a909)),f918(x103901,a909)),f101(f918(x103901,a909))),f318(f318(f9(f918(x103901,a909),f918(x103901,a909),f918(x103901,a909)),f318(f318(f10(f918(x103901,a909),f918(f918(x103901,a909),f918(x103901,a909)),f918(x103901,a909)),f101(f918(x103901,a909))),x103903)),x103904))),f87(f918(x103901,a909),x103903))))))
% 109.14/108.86 [10039]E(f318(f318(f155(x100391),f318(f318(f155(f912(x100391)),f170(x100391,x100392)),x100393)),x100394),f318(f318(f155(x100391),f318(f318(f155(f912(x100391)),x100392),x100394)),x100393))+~P1(f318(f318(f226(a911),x100393),f318(f180(f912(f912(x100391))),f170(x100391,x100392))))+~P13(a911,f318(f159(a911),f318(f318(f145(f912(x100391),a911),f180(f912(x100391))),x100392)))+~P1(f318(f318(f226(a911),x100394),f318(f180(f912(f912(x100391))),f318(f127(f912(x100391),f318(f318(f10(a911,a909,f912(x100391)),f318(f226(a911),x100393)),f180(f912(x100391)))),x100392))))
% 109.14/108.86 [10060]~P1(f318(f318(f320(f917(a911,a911)),x100604),x100601))+~P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),x100604),x100602)),a26))+~P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),x100601),x100603)),a27))+P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),x100601),f318(f318(f300(f917(a911,a911)),x100602),x100603))),a27))
% 109.14/108.86 [10061]~P1(f318(f318(f320(f917(a911,a911)),x100614),x100611))+~P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),x100614),x100612)),a64))+~P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),x100611),x100613)),a65))+P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),x100611),f318(f318(f300(f917(a911,a911)),x100612),x100613))),a65))
% 109.14/108.86 [9955]~P113(x99552)+~P71(x99551)+~P1(f318(f318(f226(f918(x99551,x99552)),x99553),x99554))+P1(f318(f50(x99551),f318(f318(f10(a909,a909,x99551),a313),f318(f318(f20(x99551,x99552,a909),f318(f318(f10(x99552,f918(x99552,a909),x99551),a315),x99553)),x99554))))
% 109.14/108.86 [10071]~P1(f318(f318(f320(f917(a911,a911)),x100714),x100713))+~P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),x100711),x100714)),a26))+~P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),x100712),x100713)),a28))+P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),f318(f318(f300(f917(a911,a911)),x100711),x100712)),x100713)),a28))
% 109.14/108.86 [10072]~P1(f318(f318(f320(f917(a911,a911)),x100724),x100723))+~P1(f318(f318(f320(f917(f917(a911,a911),f917(a911,a911))),f318(f318(f243(f917(a911,a911),f917(a911,a911)),x100721),x100724)),a64))+~P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),x100722),x100723)),a63))+P1(f318(f318(f320(f917(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909))),f318(f318(f243(f918(f917(a911,a911),a909),f918(f917(a911,a911),a909)),f318(f318(f300(f917(a911,a911)),x100721),x100722)),x100723)),a63))
% 109.14/108.86 [6176]~P7(x61764,x61761)+~P1(f318(f318(x61761,x61762),x61765))+P1(f318(f318(x61761,x61762),x61763))+~P1(f318(f318(x61761,x61765),x61763))
% 109.14/108.86 [6177]~P53(x61774,x61771)+~P1(f318(f318(x61771,x61772),x61775))+P1(f318(f318(x61771,x61772),x61773))+~P1(f318(f318(x61771,x61775),x61773))
% 109.14/108.86 [6178]~P15(x61784,x61781)+~P1(f318(f318(x61781,x61782),x61785))+P1(f318(f318(x61781,x61782),x61783))+~P1(f318(f318(x61781,x61785),x61783))
% 109.14/108.86 [8827]~P26(x88271,x88273,x88275,x88272,x88274)+E(f318(f29(x88271),x88272),f318(f29(x88273),x88274))+~P1(f318(f55(x88273),x88274))+~P1(f318(f55(x88271),x88272))
% 109.14/108.86 [8847]~P7(x88474,x88473)+~P1(f318(x88471,x88475))+P1(f318(x88472,f829(x88472,x88471,x88473,x88474)))+P1(f318(x88471,f826(x88472,x88471,x88473,x88474)))
% 109.14/108.86 [9087]~P7(x90874,x90873)+~P1(f318(x90872,x90875))+~P1(f318(x90871,f826(x90871,x90872,x90873,x90874)))+P1(f318(x90871,f829(x90871,x90872,x90873,x90874)))
% 109.14/108.86 [9258]~P7(x92584,x92583)+~P1(f318(x92581,x92585))+P1(f318(f318(f320(x92584),f829(x92582,x92581,x92583,x92584)),f261(x92584,x92583)))+P1(f318(x92581,f826(x92582,x92581,x92583,x92584)))
% 109.14/108.86 [9390]~P7(x93901,x93904)+~P1(f318(x93903,x93905))+~P1(f318(x93902,f826(x93902,x93903,x93904,x93901)))+P1(f318(f318(f320(x93901),f829(x93902,x93903,x93904,x93901)),f261(x93901,x93904)))
% 109.14/108.86 [9694]~P40(x96941,x96944)+P1(f318(f318(f320(f917(f912(x96941),f912(x96941))),f318(f318(f243(f912(x96941),f912(x96941)),x96942),x96943)),f138(x96941,x96944)))+~P1(f318(f318(f320(f917(f912(x96941),f912(x96941))),f318(f318(f243(f912(x96941),f912(x96941)),x96942),x96945)),f138(x96941,x96944)))+~P1(f318(f318(f320(f917(f912(x96941),f912(x96941))),f318(f318(f243(f912(x96941),f912(x96941)),x96945),x96943)),f138(x96941,x96944)))
% 109.14/108.86 [5410]~P67(x54105)+E(x54101,x54102)+~E(x54103,x54104)+~E(f318(f318(f3(x54105),x54103),x54104),f318(f318(f3(x54105),x54101),x54102))
% 109.14/108.86 [5411]~P67(x54115)+E(x54111,x54112)+~E(x54113,x54114)+~E(f318(f318(f3(x54115),x54113),x54114),f318(f318(f3(x54115),x54111),x54112))
% 109.14/108.86 [6293]~P17(x62935,x62931,x62933)+E(f318(f318(x62931,x62932),f318(x62933,x62934)),f318(x62933,x62934))+~P1(f318(f55(x62935),x62934))+~P1(f318(f318(f320(x62935),x62932),x62934))
% 109.14/108.86 [6476]~P65(x64761)+~E(f318(f318(f3(x64761),x64764),x64765),f318(f318(f3(x64761),x64762),x64763))+~P1(f318(f318(f225(x64761),x64764),x64765))+P1(f318(f318(f225(x64761),x64762),x64763))
% 109.14/108.86 [6477]~P65(x64771)+~E(f318(f318(f3(x64771),x64774),x64775),f318(f318(f3(x64771),x64772),x64773))+~P1(f318(f318(f225(x64771),x64774),x64775))+P1(f318(f318(f225(x64771),x64772),x64773))
% 109.14/108.86 [6478]~P65(x64781)+~E(f318(f318(f3(x64781),x64784),x64785),f318(f318(f3(x64781),x64782),x64783))+~P1(f318(f318(f226(x64781),x64784),x64785))+P1(f318(f318(f226(x64781),x64782),x64783))
% 109.14/108.86 [6479]~P65(x64791)+~E(f318(f318(f3(x64791),x64794),x64795),f318(f318(f3(x64791),x64792),x64793))+~P1(f318(f318(f226(x64791),x64794),x64795))+P1(f318(f318(f226(x64791),x64792),x64793))
% 109.14/108.86 [7453]~E(x74532,f318(f318(f142(x74531),x74534),x74535))+P1(f318(f318(f320(f912(x74531)),x74532),f152(x74531,x74533)))+~P1(f318(f318(f320(f912(x74531)),x74535),f152(x74531,x74533)))+~P1(f318(f318(f320(x74531),x74534),x74533))
% 109.14/108.86 [7846]~E(f318(f180(f912(x78461)),x78463),f318(f180(f912(x78462)),x78464))+~E(f318(f318(f145(f917(x78461,x78462),x78462),f247(x78461,x78462)),x78465),x78464)+~E(f318(f318(f145(f917(x78461,x78462),x78461),f242(x78461,x78462)),x78465),x78463)+E(f318(f318(f172(x78461,x78462),x78463),x78464),x78465)
% 109.14/108.86 [8174]~P113(x81741)+P1(f318(f318(f226(f918(x81741,a909)),f294(x81741,x81742,x81743)),f294(x81741,x81744,x81745)))+~P1(f318(f318(f225(x81741),x81744),x81745))+P1(f318(f318(f225(x81741),x81742),x81743))
% 109.14/108.86 [8281]~P113(x82811)+P1(f318(f318(f225(f918(x82811,a909)),f294(x82811,x82812,x82813)),f294(x82811,x82814,x82815)))+~P1(f318(f318(f225(x82811),x82813),x82815))+~P1(f318(f318(f225(x82811),x82814),x82812))
% 109.14/108.86 [8397]~P4(x83971)+P1(f318(f318(f225(x83971),x83972),x83973))+P1(f318(f318(f225(x83971),x83974),x83973))+~P1(f318(f318(f225(f918(x83971,a909)),f318(f293(x83971,x83973),x83972)),f318(f293(x83971,x83974),x83975)))
% 109.14/108.86 [8398]~P4(x83981)+P1(f318(f318(f225(x83981),x83982),x83983))+P1(f318(f318(f225(x83981),x83982),x83984))+~P1(f318(f318(f225(f918(x83981,a909)),f318(f293(x83981,x83983),x83982)),f318(f293(x83981,x83985),x83984)))
% 109.14/108.86 [8562]~P108(x85623)+~P108(x85621)+~P42(x85623,x85621,x85622)+P1(f318(f318(f225(x85621),f318(x85622,f318(f318(f92(x85623),x85624),x85625))),f318(f318(f92(x85621),f318(x85622,x85624)),f318(x85622,x85625))))
% 109.14/108.86 [8563]~P4(x85633)+~P108(x85631)+~P42(x85633,x85631,x85632)+P1(f318(f318(f225(x85631),f318(x85632,f318(f318(f223(x85633),x85634),x85635))),f318(f318(f92(x85631),f318(x85632,x85634)),f318(x85632,x85635))))
% 109.14/108.86 [8629]~P113(x86291)+~P1(f318(f318(f225(f918(x86291,a909)),f294(x86291,x86294,x86292)),f294(x86291,x86295,x86293)))+P1(f318(f318(f225(x86291),x86292),x86293))+~P1(f318(f318(f225(x86291),x86294),x86292))
% 109.14/108.86 [8630]~P113(x86301)+~P1(f318(f318(f226(f918(x86301,a909)),f294(x86301,x86304,x86302)),f294(x86301,x86305,x86303)))+P1(f318(f318(f225(x86301),x86302),x86303))+~P1(f318(f318(f225(x86301),x86304),x86302))
% 109.14/108.86 [8631]~P113(x86311)+~P1(f318(f318(f225(f918(x86311,a909)),f294(x86311,x86313,x86314)),f294(x86311,x86312,x86315)))+P1(f318(f318(f225(x86311),x86312),x86313))+~P1(f318(f318(f225(x86311),x86313),x86314))
% 109.14/108.86 [8632]~P113(x86321)+~P1(f318(f318(f226(f918(x86321,a909)),f294(x86321,x86323,x86324)),f294(x86321,x86322,x86325)))+P1(f318(f318(f225(x86321),x86322),x86323))+~P1(f318(f318(f225(x86321),x86323),x86324))
% 109.14/108.86 [6124]~P4(x61245)+~P4(x61241)+~P42(x61245,x61241,x61242)+E(f318(f318(f223(x61241),f318(x61242,x61243)),f318(x61242,x61244)),f318(x61242,f318(f318(f223(x61245),x61243),x61244)))
% 109.14/108.86 [6125]~P4(x61255)+~P4(x61251)+~P42(x61255,x61251,x61252)+E(f318(f318(f224(x61251),f318(x61252,x61253)),f318(x61252,x61254)),f318(x61252,f318(f318(f224(x61255),x61253),x61254)))
% 109.14/108.86 [6175]~P17(x61752,x61755,x61753)+E(x61751,f179(f918(x61752,a909)))+~P1(f318(f55(x61752),x61751))+E(f318(x61753,f318(f318(f300(x61752),x61754),x61751)),f318(f318(x61755,x61754),f318(x61753,x61751)))
% 109.14/108.86 [6948]~E(x69481,x69482)+~E(f318(f318(f92(f918(x69483,a909)),x69484),x69485),f179(f918(x69483,a909)))+~P1(f318(f318(f320(x69483),x69482),x69485))+~P1(f318(f318(f320(x69483),x69481),x69484))
% 109.14/108.86 [7028]~P18(x70282,x70285,x70281)+~P1(f318(f55(x70282),x70284))+E(f318(x70281,f318(f318(f300(x70282),x70283),x70284)),f318(f318(f58(x70282,x70282,x70285),x70283),x70284))+P1(f318(f318(f320(x70282),x70283),x70284))
% 109.14/108.86 [7094]~P76(x70942)+~P1(f318(f55(x70941),x70945))+E(f318(f318(f8(x70941,x70942),x70943),f318(f318(f300(x70941),x70944),x70945)),f318(f318(f73(x70942),f318(x70943,x70944)),f318(f318(f8(x70941,x70942),x70943),x70945)))+P1(f318(f318(f320(x70941),x70944),x70945))
% 109.14/108.86 [7095]~P76(x70952)+~P1(f318(f55(x70951),x70955))+E(f318(f318(f8(x70951,x70952),x70953),f318(f318(f300(x70951),x70954),x70955)),f318(f318(f73(x70952),f318(x70953,x70954)),f318(f318(f8(x70951,x70952),x70953),x70955)))+P1(f318(f318(f320(x70951),x70954),x70955))
% 109.14/108.86 [7096]~P82(x70962)+~P1(f318(f55(x70961),x70965))+E(f318(f318(f11(x70961,x70962),x70963),f318(f318(f300(x70961),x70964),x70965)),f318(f318(f74(x70962),f318(x70963,x70964)),f318(f318(f11(x70961,x70962),x70963),x70965)))+P1(f318(f318(f320(x70961),x70964),x70965))
% 109.14/108.86 [7097]~P82(x70972)+~P1(f318(f55(x70971),x70975))+E(f318(f318(f11(x70971,x70972),x70973),f318(f318(f300(x70971),x70974),x70975)),f318(f318(f74(x70972),f318(x70973,x70974)),f318(f318(f11(x70971,x70972),x70973),x70975)))+P1(f318(f318(f320(x70971),x70974),x70975))
% 109.14/108.86 [7494]~P121(x74941)+~P1(f318(f55(x74944),x74945))+~P1(f318(f318(f320(x74944),x74943),x74945))+P1(f318(f318(f278(x74941),f318(x74942,x74943)),f318(f318(f11(x74944,x74941),x74942),x74945)))
% 109.14/108.86 [7591]~P18(x75912,x75915,x75911)+~P1(f318(f55(x75912),x75914))+E(f318(x75911,f318(f318(f300(x75912),x75913),x75914)),x75913)+~E(f318(f318(f3(f918(x75912,a909)),x75914),f318(f318(f300(x75912),x75913),f179(f918(x75912,a909)))),f179(f918(x75912,a909)))
% 109.14/108.86 [7948]~P69(x79481)+E(f318(f318(f30(x79481),f318(f318(f74(x79481),x79482),x79483)),f318(f318(f74(x79481),x79484),x79485)),f318(f318(f74(x79481),f318(f318(f30(x79481),x79482),x79484)),f318(f318(f30(x79481),x79483),x79485)))+~P1(f318(f318(f278(x79481),x79485),x79483))+~P1(f318(f318(f278(x79481),x79484),x79482))
% 109.14/108.86 [7952]~P102(x79521)+~P1(f318(f318(f225(x79521),x79523),x79525))+~P1(f318(f318(f225(x79521),x79522),x79524))+P1(f318(f318(f225(x79521),f318(f318(f101(x79521),x79522),x79523)),f318(f318(f101(x79521),x79524),x79525)))
% 109.14/108.86 [7953]~P108(x79531)+~P1(f318(f318(f225(x79531),x79533),x79535))+~P1(f318(f318(f225(x79531),x79532),x79534))+P1(f318(f318(f225(x79531),f318(f318(f92(x79531),x79532),x79533)),f318(f318(f92(x79531),x79534),x79535)))
% 109.14/108.86 [7954]~P90(x79541)+~P1(f318(f318(f225(x79541),x79543),x79545))+~P1(f318(f318(f225(x79541),x79542),x79544))+P1(f318(f318(f225(x79541),f318(f318(f73(x79541),x79542),x79543)),f318(f318(f73(x79541),x79544),x79545)))
% 109.14/108.86 [7955]~P4(x79551)+~P1(f318(f318(f225(x79551),x79553),x79555))+~P1(f318(f318(f225(x79551),x79552),x79554))+P1(f318(f318(f225(x79551),f318(f318(f223(x79551),x79552),x79553)),f318(f318(f223(x79551),x79554),x79555)))
% 109.14/108.86 [7956]~P4(x79561)+~P1(f318(f318(f225(x79561),x79563),x79565))+~P1(f318(f318(f225(x79561),x79562),x79564))+P1(f318(f318(f225(x79561),f318(f318(f224(x79561),x79562),x79563)),f318(f318(f224(x79561),x79564),x79565)))
% 109.14/108.86 [7957]~P92(x79571)+~P1(f318(f318(f225(x79571),x79573),x79575))+~P1(f318(f318(f226(x79571),x79572),x79574))+P1(f318(f318(f226(x79571),f318(f318(f73(x79571),x79572),x79573)),f318(f318(f73(x79571),x79574),x79575)))
% 109.14/108.86 [7958]~P92(x79581)+~P1(f318(f318(f225(x79581),x79582),x79584))+~P1(f318(f318(f226(x79581),x79583),x79585))+P1(f318(f318(f226(x79581),f318(f318(f73(x79581),x79582),x79583)),f318(f318(f73(x79581),x79584),x79585)))
% 109.14/108.86 [7959]~P92(x79591)+~P1(f318(f318(f226(x79591),x79593),x79595))+~P1(f318(f318(f226(x79591),x79592),x79594))+P1(f318(f318(f226(x79591),f318(f318(f73(x79591),x79592),x79593)),f318(f318(f73(x79591),x79594),x79595)))
% 109.14/108.86 [7960]~P121(x79601)+~P1(f318(f318(f278(x79601),x79603),x79605))+~P1(f318(f318(f278(x79601),x79602),x79604))+P1(f318(f318(f278(x79601),f318(f318(f74(x79601),x79602),x79603)),f318(f318(f74(x79601),x79604),x79605)))
% 109.14/108.86 [8091]~P149(x80915)+E(x80911,x80912)+E(x80913,x80914)+~E(f318(f318(f73(x80915),f318(f318(f74(x80915),x80913),x80911)),f318(f318(f74(x80915),x80914),x80912)),f318(f318(f73(x80915),f318(f318(f74(x80915),x80913),x80912)),f318(f318(f74(x80915),x80914),x80911)))
% 109.14/108.86 [8092]~P149(x80925)+E(x80921,x80922)+E(x80923,x80924)+~E(f318(f318(f73(x80925),f318(f318(f74(x80925),x80923),x80921)),f318(f318(f74(x80925),x80924),x80922)),f318(f318(f73(x80925),f318(f318(f74(x80925),x80923),x80922)),f318(f318(f74(x80925),x80924),x80921)))
% 109.14/108.86 [8229]P28(x82291,x82292,x82293)+~P29(x82291,x82294,x82295)+~P28(x82291,x82292,f544(x82295,x82294,x82291,x82292))+~P1(f318(f318(f320(f910(x82291)),x82293),x82295))
% 109.14/108.86 [8301]~P4(x83014)+~P1(f318(f128(x83011),x83013))+P1(f318(f318(f320(x83011),x83012),f318(f163(x83011),x83013)))+P1(f318(f128(x83011),f318(f318(f139(x83011,x83014,x83015),x83012),x83013)))
% 109.14/108.86 [8444]~P67(x84441)+E(f318(f318(f3(x84441),f318(f318(f8(a911,x84441),x84442),f318(f293(a911,x84443),x84444))),f318(f318(f8(a911,x84441),x84442),f318(f293(a911,x84443),x84445))),f318(f318(f8(a911,x84441),x84442),f318(f293(a911,x84445),x84444)))+~P1(f318(f318(f225(a911),x84445),x84444))+~P1(f318(f318(f225(a911),x84443),x84445))
% 109.14/108.86 [8445]~P76(x84451)+E(f318(f318(f73(x84451),f318(f318(f8(a911,x84451),x84452),f318(f293(a911,x84453),x84454))),f318(f318(f8(a911,x84451),x84452),f318(f293(a911,x84454),x84455))),f318(f318(f8(a911,x84451),x84452),f318(f293(a911,x84453),x84455)))+~P1(f318(f318(f225(a911),x84454),x84455))+~P1(f318(f318(f225(a911),x84453),x84454))
% 109.14/108.86 [8775]~P73(x87752)+E(x87751,f2(x87752))+E(x87753,f2(x87752))+E(f318(f318(f282(x87752),f318(f318(f3(x87752),f318(f318(f74(x87752),x87754),x87751)),f318(f318(f74(x87752),x87755),x87753))),f318(f318(f74(x87752),x87753),x87751)),f318(f318(f3(x87752),f318(f318(f282(x87752),x87754),x87753)),f318(f318(f282(x87752),x87755),x87751)))
% 109.14/108.86 [8776]~P73(x87762)+E(x87761,f2(x87762))+E(x87763,f2(x87762))+E(f318(f318(f282(x87762),f318(f318(f73(x87762),f318(f318(f74(x87762),x87764),x87761)),f318(f318(f74(x87762),x87765),x87763))),f318(f318(f74(x87762),x87763),x87761)),f318(f318(f73(x87762),f318(f318(f282(x87762),x87764),x87763)),f318(f318(f282(x87762),x87765),x87761)))
% 109.14/108.86 [8785]~E(x87852,f318(x87853,x87851))+E(x87851,f700(x87852,x87853,x87854,x87855))+~P25(x87855,x87854,x87853,f233(f918(x87855,a909)))+~P1(f318(f318(f320(x87854),x87852),f318(f301(x87855,x87854,x87853),f233(f918(x87855,a909)))))
% 109.14/108.86 [8999]~P116(x89991)+~P1(f318(f318(f226(x89991),f318(f69(x89991),x89992)),x89994))+P1(f318(f318(f226(x89991),f318(f318(f74(x89991),f318(f69(x89991),x89992)),f318(f69(x89991),x89993))),f318(f318(f74(x89991),x89994),x89995)))+~P1(f318(f318(f226(x89991),f318(f69(x89991),x89993)),x89995))
% 109.14/108.86 [9018]~P29(x90181,x90185,x90184)+P28(x90181,x90182,x90183)+P1(f318(f318(f320(f910(x90181)),f544(x90184,x90185,x90181,x90182)),x90185))+~P1(f318(f318(f320(f910(x90181)),x90183),x90184))
% 109.14/108.86 [9113]~P25(x91131,x91133,x91135,x91132)+~P1(f318(f55(x91133),x91134))+P1(f318(f318(f225(a911),f318(f29(x91131),x91132)),f318(f29(x91133),x91134)))+~P1(f318(f318(f225(f918(x91133,a909)),f318(f301(x91131,x91133,x91135),x91132)),x91134))
% 109.14/108.86 [9180]~P76(x91802)+~P25(x91801,x91801,x91804,x91805)+~P1(f318(f55(x91801),x91805))+E(f318(f318(f8(x91801,x91802),f318(f66(x91801,x91802,x91801,x91803),x91804)),x91805),f318(f318(f8(x91801,x91802),x91803),f318(f301(x91801,x91801,x91804),x91805)))
% 109.14/108.86 [9181]~P82(x91812)+~P25(x91811,x91811,x91814,x91815)+~P1(f318(f55(x91811),x91815))+E(f318(f318(f11(x91811,x91812),f318(f66(x91811,x91812,x91811,x91813),x91814)),x91815),f318(f318(f11(x91811,x91812),x91813),f318(f301(x91811,x91811,x91814),x91815)))
% 109.14/108.86 [9249]~E(f714(x92492,x92494,x92491,x92493,x92495),x92495)+~E(x92492,f318(x92494,x92495))+~P25(x92493,x92491,x92494,f233(f918(x92493,a909)))+P1(f318(f318(f320(x92491),x92492),f318(f301(x92493,x92491,x92494),f233(f918(x92493,a909)))))
% 109.14/108.86 [9289]~P39(x92891,x92892)+~P1(f318(f318(f320(x92891),x92893),x92894))+~P1(f318(f318(f320(x92891),x92895),x92894))+~P1(f318(f318(f320(f917(x92891,x92891)),f318(f318(f243(x92891,x92891),x92895),f604(x92892,x92891,x92894))),x92892))
% 109.14/108.86 [9334]~P25(x93342,x93343,x93345,x93341)+E(x93341,f179(f918(x93342,a909)))+E(f318(f301(x93343,x93342,f641(x93344,x93343,x93342,x93341)),x93344),x93341)+~P1(f318(f318(f225(f918(x93343,a909)),f318(f301(x93342,x93343,x93345),x93341)),x93344))
% 109.14/108.86 [9372]~E(x93722,f318(x93721,x93725))+~P25(x93724,x93723,x93721,f233(f918(x93724,a909)))+E(f318(x93721,f714(x93722,x93721,x93723,x93724,x93725)),x93722)+P1(f318(f318(f320(x93723),x93722),f318(f301(x93724,x93723,x93721),f233(f918(x93724,a909)))))
% 109.14/108.86 [9842]~P4(x98425)+~P5(x98425)+P1(f318(f318(f320(x98421),f478(x98422,x98423,x98421,x98424,x98425)),x98423))+~P1(f318(f318(f226(x98425),x98424),f318(f318(f33(x98421,x98425),x98423),x98422)))
% 109.14/108.86 [9847]~P4(x98471)+~P5(x98471)+P1(f318(f318(f226(x98471),x98472),f318(x98473,f478(x98473,x98474,x98475,x98472,x98471))))+~P1(f318(f318(f226(x98471),x98472),f318(f318(f33(x98475,x98471),x98474),x98473)))
% 109.14/108.86 [9933]~P80(x99331)+~P1(f318(f60(x99331,x99331,f74(x99331),x99332,x99333),x99335))+P1(f318(f318(f320(x99331),x99332),x99333))+P1(f318(f60(x99331,x99331,f74(x99331),x99334,f318(f318(f300(x99331),x99332),x99333)),f318(f318(f74(x99331),x99334),x99335)))
% 109.14/108.86 [10135]~P76(x101352)+~P1(f318(f55(x101351),x101355))+E(f318(f318(f8(x101351,x101352),f318(f318(f9(x101351,x101352,x101352),f318(f318(f20(x101351,x101352,f918(x101352,x101352)),f318(f318(f10(a909,f918(x101352,f918(x101352,x101352)),x101351),f85(x101352)),f318(a315,x101353))),x101354)),f2(x101352))),x101355),f2(x101352))+P1(f318(f318(f320(x101351),x101353),x101355))
% 109.14/108.86 [10136]~P82(x101362)+~P1(f318(f55(x101361),x101365))+E(f318(f318(f11(x101361,x101362),f318(f318(f9(x101361,x101362,x101362),f318(f318(f20(x101361,x101362,f918(x101362,x101362)),f318(f318(f10(a909,f918(x101362,f918(x101362,x101362)),x101361),f85(x101362)),f318(a315,x101363))),x101364)),f71(x101362))),x101365),f71(x101362))+P1(f318(f318(f320(x101361),x101363),x101365))
% 109.14/108.86 [10137]~P76(x101372)+~P1(f318(f55(x101371),x101375))+E(f318(f318(f8(x101371,x101372),f318(f318(f9(x101371,x101372,x101372),f318(f318(f20(x101371,x101372,f918(x101372,x101372)),f318(f318(f10(a909,f918(x101372,f918(x101372,x101372)),x101371),f85(x101372)),f318(a315,x101373))),x101374)),f2(x101372))),x101375),f318(x101374,x101373))+~P1(f318(f318(f320(x101371),x101373),x101375))
% 109.14/108.86 [10138]~P82(x101382)+~P1(f318(f55(x101381),x101385))+E(f318(f318(f11(x101381,x101382),f318(f318(f9(x101381,x101382,x101382),f318(f318(f20(x101381,x101382,f918(x101382,x101382)),f318(f318(f10(a909,f918(x101382,f918(x101382,x101382)),x101381),f85(x101382)),f318(a315,x101383))),x101384)),f71(x101382))),x101385),f318(x101384,x101383))+~P1(f318(f318(f320(x101381),x101383),x101385))
% 109.14/108.86 [10192]~P76(x101922)+~P1(f318(f55(x101921),x101925))+E(f318(f318(f8(x101921,x101922),f318(f318(f9(x101921,x101922,x101922),f318(f318(f20(x101921,x101922,f918(x101922,x101922)),f318(f318(f10(a909,f918(x101922,f918(x101922,x101922)),x101921),f85(x101922)),f318(f318(f9(x101921,x101921,a909),a315),x101923))),x101924)),f2(x101922))),x101925),f2(x101922))+P1(f318(f318(f320(x101921),x101923),x101925))
% 109.14/108.86 [10193]~P82(x101932)+~P1(f318(f55(x101931),x101935))+E(f318(f318(f11(x101931,x101932),f318(f318(f9(x101931,x101932,x101932),f318(f318(f20(x101931,x101932,f918(x101932,x101932)),f318(f318(f10(a909,f918(x101932,f918(x101932,x101932)),x101931),f85(x101932)),f318(f318(f9(x101931,x101931,a909),a315),x101933))),x101934)),f71(x101932))),x101935),f71(x101932))+P1(f318(f318(f320(x101931),x101933),x101935))
% 109.14/108.86 [10195]~P76(x101952)+~P1(f318(f55(x101951),x101955))+E(f318(f318(f8(x101951,x101952),f318(f318(f9(x101951,x101952,x101952),f318(f318(f20(x101951,x101952,f918(x101952,x101952)),f318(f318(f10(a909,f918(x101952,f918(x101952,x101952)),x101951),f85(x101952)),f318(f318(f9(x101951,x101951,a909),a315),x101953))),x101954)),f2(x101952))),x101955),f318(x101954,x101953))+~P1(f318(f318(f320(x101951),x101953),x101955))
% 109.14/108.86 [10196]~P82(x101962)+~P1(f318(f55(x101961),x101965))+E(f318(f318(f11(x101961,x101962),f318(f318(f9(x101961,x101962,x101962),f318(f318(f20(x101961,x101962,f918(x101962,x101962)),f318(f318(f10(a909,f918(x101962,f918(x101962,x101962)),x101961),f85(x101962)),f318(f318(f9(x101961,x101961,a909),a315),x101963))),x101964)),f71(x101962))),x101965),f318(x101964,x101963))+~P1(f318(f318(f320(x101961),x101963),x101965))
% 109.14/108.86 [7951]~P67(x79512)+~P1(f318(f55(x79511),x79514))+E(f318(f318(f8(x79511,x79512),x79513),f318(f318(f3(f918(x79511,a909)),x79514),f318(f318(f300(x79511),x79515),f179(f918(x79511,a909))))),f318(f318(f8(x79511,x79512),x79513),x79514))+P1(f318(f318(f320(x79511),x79515),x79514))
% 109.14/108.86 [8453]~P129(x84532)+~P1(f318(f55(x84531),x84534))+E(f318(f318(f8(x84531,x84532),x84533),f318(f318(f3(f918(x84531,a909)),x84534),f318(f318(f300(x84531),x84535),f179(f918(x84531,a909))))),f318(f318(f3(x84532),f318(f318(f8(x84531,x84532),x84533),x84534)),f318(x84533,x84535)))+~P1(f318(f318(f320(x84531),x84535),x84534))
% 109.14/108.86 [8454]~P67(x84542)+~P1(f318(f55(x84541),x84544))+E(f318(f318(f8(x84541,x84542),x84543),f318(f318(f3(f918(x84541,a909)),x84544),f318(f318(f300(x84541),x84545),f179(f918(x84541,a909))))),f318(f318(f3(x84542),f318(f318(f8(x84541,x84542),x84543),x84544)),f318(x84543,x84545)))+~P1(f318(f318(f320(x84541),x84545),x84544))
% 109.14/108.86 [8480]~P67(x84801)+~P1(f318(f55(x84802),x84804))+E(f318(f318(f3(x84801),f318(f318(f8(x84802,x84801),x84803),x84804)),f318(f318(f8(x84802,x84801),x84803),x84805)),f318(f318(f8(x84802,x84801),x84803),f318(f318(f3(f918(x84802,a909)),x84804),x84805)))+~P1(f318(f318(f225(f918(x84802,a909)),x84805),x84804))
% 109.14/108.86 [8499]P1(f318(f55(x84991),f318(x84992,x84993)))+~P1(f318(f55(x84994),x84995))+~P1(f318(f318(f320(x84994),x84993),x84995))+~P1(f318(f55(x84991),f318(f318(f33(x84994,f918(x84991,a909)),x84995),x84992)))
% 109.14/108.86 [8612]~P102(x86125)+~P102(x86121)+~P42(x86125,x86121,x86122)+P1(f318(f318(f225(x86121),f318(f318(f101(x86121),f318(x86122,x86123)),f318(x86122,x86124))),f318(x86122,f318(f318(f101(x86125),x86123),x86124))))
% 109.14/108.86 [8613]~P4(x86135)+~P102(x86131)+~P42(x86135,x86131,x86132)+P1(f318(f318(f225(x86131),f318(f318(f101(x86131),f318(x86132,x86133)),f318(x86132,x86134))),f318(x86132,f318(f318(f224(x86135),x86133),x86134))))
% 109.14/108.86 [8951]~P8(x89511,x89515,x89514)+~E(f318(f276(x89511,x89511,x89514),f318(f318(f300(x89511),x89512),f179(f918(x89511,a909)))),f318(f276(x89511,x89511,x89514),f318(f318(f300(x89511),x89513),f179(f918(x89511,a909)))))+~P1(f318(f318(f320(x89511),x89513),x89515))+P1(f318(f318(f320(f917(x89511,x89511)),f318(f318(f243(x89511,x89511),x89512),x89513)),x89514))
% 109.14/108.86 [9243]~P1(f318(x92431,x92435))+P1(f318(x92431,f401(x92431,x92432,x92433,x92434)))+P1(f318(x92431,f391(x92431,x92432,x92433,x92434)))+~P1(f318(f318(f320(x92434),x92435),f318(f318(f101(f918(x92434,a909)),x92433),x92432)))
% 109.14/108.86 [9439]~P1(f318(x94391,x94395))+P1(f318(x94391,f391(x94391,x94392,x94393,x94394)))+P1(f318(f318(f320(x94394),f401(x94391,x94392,x94393,x94394)),x94392))+~P1(f318(f318(f320(x94394),x94395),f318(f318(f101(f918(x94394,a909)),x94393),x94392)))
% 109.14/108.86 [9440]~P1(f318(x94401,x94405))+P1(f318(x94401,f401(x94401,x94402,x94403,x94404)))+P1(f318(f318(f320(x94404),f391(x94401,x94402,x94403,x94404)),x94403))+~P1(f318(f318(f320(x94404),x94405),f318(f318(f101(f918(x94404,a909)),x94403),x94402)))
% 109.14/108.86 [9446]P1(f318(x94461,x94462))+~P1(f318(x94461,f380(x94461,x94463,x94464,x94465)))+~P1(f318(x94461,f369(x94461,x94463,x94464,x94465)))+~P1(f318(f318(f320(x94465),x94462),f318(f318(f101(f918(x94465,a909)),x94464),x94463)))
% 109.14/108.86 [9451]~P40(x94511,x94514)+~P1(f318(f318(f320(f917(x94511,x94511)),f318(f318(f243(x94511,x94511),x94512),x94515)),x94514))+P1(f318(f318(f320(f917(x94511,x94511)),f318(f318(f243(x94511,x94511),x94512),x94513)),x94514))+~P1(f318(f318(f320(f917(x94511,x94511)),f318(f318(f243(x94511,x94511),x94515),x94513)),x94514))
% 109.14/108.86 [9452]~P40(x94521,x94524)+~P1(f318(f318(f320(f917(x94521,x94521)),f318(f318(f243(x94521,x94521),x94522),x94525)),x94524))+P1(f318(f318(f320(f917(x94521,x94521)),f318(f318(f243(x94521,x94521),x94522),x94523)),x94524))+~P1(f318(f318(f320(f917(x94521,x94521)),f318(f318(f243(x94521,x94521),x94525),x94523)),x94524))
% 109.14/108.86 [9491]E(x94911,x94912)+~P1(f318(f318(f320(f917(x94913,x94913)),f318(f318(f243(x94913,x94913),x94911),x94912)),f298(x94913,x94915)))+P1(f318(f318(f320(x94913),x94911),x94914))+~P1(f318(f318(f225(f918(f917(x94913,x94913),a909)),x94915),f318(f318(f245(x94913,x94913),x94914),f318(f18(f918(x94913,a909),x94913),x94914))))
% 109.14/108.86 [9509]P1(f318(x95091,x95092))+~P1(f318(x95091,f369(x95091,x95094,x95095,x95093)))+P1(f318(f318(f320(x95093),f380(x95091,x95094,x95095,x95093)),x95094))+~P1(f318(f318(f320(x95093),x95092),f318(f318(f101(f918(x95093,a909)),x95095),x95094)))
% 109.14/108.86 [9510]P1(f318(x95101,x95102))+~P1(f318(x95101,f380(x95101,x95104,x95105,x95103)))+P1(f318(f318(f320(x95103),f369(x95101,x95104,x95105,x95103)),x95105))+~P1(f318(f318(f320(x95103),x95102),f318(f318(f101(f918(x95103,a909)),x95105),x95104)))
% 109.14/108.86 [9576]P1(f318(x95761,x95762))+P1(f318(f318(f320(x95763),f380(x95761,x95764,x95765,x95763)),x95764))+P1(f318(f318(f320(x95763),f369(x95761,x95764,x95765,x95763)),x95765))+~P1(f318(f318(f320(x95763),x95762),f318(f318(f101(f918(x95763,a909)),x95765),x95764)))
% 109.14/108.86 [9577]~P1(f318(x95772,x95775))+P1(f318(f318(f320(x95771),f401(x95772,x95773,x95774,x95771)),x95773))+P1(f318(f318(f320(x95771),f391(x95772,x95773,x95774,x95771)),x95774))+~P1(f318(f318(f320(x95771),x95775),f318(f318(f101(f918(x95771,a909)),x95774),x95773)))
% 109.14/108.86 [9737]~P8(x97371,x97375,x97374)+~P1(f318(f318(f320(x97371),x97373),x97375))+P1(f318(f318(f320(f917(x97371,x97371)),f318(f318(f243(x97371,x97371),x97372),x97373)),x97374))+~P1(f318(f318(f225(f918(x97371,a909)),f318(f276(x97371,x97371,x97374),f318(f318(f300(x97371),x97373),f179(f918(x97371,a909))))),f318(f276(x97371,x97371,x97374),f318(f318(f300(x97371),x97372),f179(f918(x97371,a909))))))
% 109.14/108.86 [9878]~P4(x98785)+~P5(x98785)+P1(f318(f318(f320(x98781),f480(x98782,x98783,x98784,x98781,x98785)),x98784))+~P1(f318(f318(f226(x98785),f318(f318(f34(x98781,x98785),x98784),x98783)),x98782))
% 109.14/108.86 [9911]~P90(x99115)+~P86(x99115)+P1(f318(f318(f320(x99111),f691(x99112,x99113,x99114,x99111,x99115)),f318(f163(x99111),x99114)))+P1(f318(f318(f225(x99115),f318(f156(x99115),f318(f318(f145(x99111,x99115),x99113),x99114))),f318(f156(x99115),f318(f318(f145(x99111,x99115),x99112),x99114))))
% 109.14/108.86 [10038]~P4(x100381)+~P5(x100381)+P1(f318(f318(f226(x100381),f318(x100382,f480(x100383,x100382,x100384,x100385,x100381))),x100383))+~P1(f318(f318(f226(x100381),f318(f318(f34(x100385,x100381),x100384),x100382)),x100383))
% 109.14/108.86 [10151]~P90(x101511)+~P86(x101511)+~P1(f318(f318(f225(x101511),f318(x101513,f691(x101515,x101513,x101514,x101512,x101511))),f318(x101515,f691(x101515,x101513,x101514,x101512,x101511))))+P1(f318(f318(f225(x101511),f318(f156(x101511),f318(f318(f145(x101512,x101511),x101513),x101514))),f318(f156(x101511),f318(f318(f145(x101512,x101511),x101515),x101514))))
% 109.14/108.86 [8797]~P76(x87971)+~P1(f318(f55(x87974),x87975))+~P1(f318(f318(f320(x87974),x87973),x87975))+E(f318(f318(f73(x87971),f318(x87972,x87973)),f318(f318(f8(x87974,x87971),x87972),f318(f318(f3(f918(x87974,a909)),x87975),f318(f318(f300(x87974),x87973),f179(f918(x87974,a909)))))),f318(f318(f8(x87974,x87971),x87972),x87975))
% 109.14/108.86 [8798]~P76(x87981)+~P1(f318(f55(x87984),x87985))+~P1(f318(f318(f320(x87984),x87983),x87985))+E(f318(f318(f73(x87981),f318(x87982,x87983)),f318(f318(f8(x87984,x87981),x87982),f318(f318(f3(f918(x87984,a909)),x87985),f318(f318(f300(x87984),x87983),f179(f918(x87984,a909)))))),f318(f318(f8(x87984,x87981),x87982),x87985))
% 109.14/108.86 [8799]~P82(x87991)+~P1(f318(f55(x87994),x87995))+~P1(f318(f318(f320(x87994),x87993),x87995))+E(f318(f318(f74(x87991),f318(x87992,x87993)),f318(f318(f11(x87994,x87991),x87992),f318(f318(f3(f918(x87994,a909)),x87995),f318(f318(f300(x87994),x87993),f179(f918(x87994,a909)))))),f318(f318(f11(x87994,x87991),x87992),x87995))
% 109.14/108.86 [8852]~P18(x88521,x88524,x88525)+~P1(f318(f55(x88521),x88522))+E(f318(f318(f3(f918(x88521,a909)),x88522),f318(f318(f300(x88521),x88523),f179(f918(x88521,a909)))),f179(f918(x88521,a909)))+E(f318(f318(x88524,x88523),f318(x88525,f318(f318(f3(f918(x88521,a909)),x88522),f318(f318(f300(x88521),x88523),f179(f918(x88521,a909)))))),f318(x88525,f318(f318(f300(x88521),x88523),x88522)))
% 109.14/108.86 [9222]~P76(x92221)+~P1(f318(f55(x92222),x92225))+~P1(f318(f55(x92222),x92224))+E(f318(f318(f73(x92221),f318(f318(f8(x92222,x92221),x92223),f318(f318(f101(f918(x92222,a909)),x92224),x92225))),f318(f318(f8(x92222,x92221),x92223),f318(f318(f92(f918(x92222,a909)),x92224),x92225))),f318(f318(f73(x92221),f318(f318(f8(x92222,x92221),x92223),x92224)),f318(f318(f8(x92222,x92221),x92223),x92225)))
% 109.14/108.86 [9223]~P82(x92231)+~P1(f318(f55(x92232),x92235))+~P1(f318(f55(x92232),x92234))+E(f318(f318(f74(x92231),f318(f318(f11(x92232,x92231),x92233),f318(f318(f101(f918(x92232,a909)),x92234),x92235))),f318(f318(f11(x92232,x92231),x92233),f318(f318(f92(f918(x92232,a909)),x92234),x92235))),f318(f318(f74(x92231),f318(f318(f11(x92232,x92231),x92233),x92234)),f318(f318(f11(x92232,x92231),x92233),x92235)))
% 109.14/108.86 [9224]~P82(x92241)+~P1(f318(f55(x92242),x92245))+~P1(f318(f55(x92242),x92244))+E(f318(f318(f74(x92241),f318(f318(f11(x92242,x92241),x92243),f318(f318(f101(f918(x92242,a909)),x92244),x92245))),f318(f318(f11(x92242,x92241),x92243),f318(f318(f92(f918(x92242,a909)),x92244),x92245))),f318(f318(f74(x92241),f318(f318(f11(x92242,x92241),x92243),x92244)),f318(f318(f11(x92242,x92241),x92243),x92245)))
% 109.14/108.86 [9371]~P67(x93711)+~P1(f318(f55(x93712),x93715))+~P1(f318(f55(x93712),x93714))+E(f318(f318(f3(x93711),f318(f318(f73(x93711),f318(f318(f8(x93712,x93711),x93713),x93714)),f318(f318(f8(x93712,x93711),x93713),x93715))),f318(f318(f8(x93712,x93711),x93713),f318(f318(f92(f918(x93712,a909)),x93714),x93715))),f318(f318(f8(x93712,x93711),x93713),f318(f318(f101(f918(x93712,a909)),x93714),x93715)))
% 109.14/108.86 [9588]~P25(x95881,x95882,x95883,x95885)+~P25(x95881,x95882,x95883,x95884)+P25(x95881,x95882,x95883,f318(f318(f101(f918(x95881,a909)),x95884),x95885))+~E(f318(f318(f92(f918(x95882,a909)),f318(f301(x95881,x95882,x95883),f318(f318(f3(f918(x95881,a909)),x95884),x95885))),f318(f301(x95881,x95882,x95883),f318(f318(f3(f918(x95881,a909)),x95885),x95884))),f179(f918(x95882,a909)))
% 109.14/108.86 [9712]E(x97121,f2(a1))+~P1(f318(f318(f226(a1),f2(a1)),x97123))+~P1(f318(f43(x97122,x97121),f318(f318(f243(a1,a1),x97124),x97125)))+P1(f318(f43(x97122,f318(f318(f74(a1),x97121),x97123)),f318(f318(f243(a1,a1),f318(f318(f30(a1),x97124),x97123)),f318(f318(f73(a1),f318(f318(f74(a1),x97121),f39(a1,x97124,x97123))),x97125))))
% 109.14/108.86 [9720]~P1(f318(f318(f226(a911),f2(a911)),x97203))+~P1(f318(f318(f226(a911),f2(a911)),x97202))+~P1(f318(f42(x97201,x97202),f318(f318(f243(a911,a911),x97204),x97205)))+P1(f318(f42(x97201,f318(f318(f74(a911),x97202),x97203)),f318(f318(f243(a911,a911),f318(f318(f30(a911),x97204),x97203)),f318(f318(f73(a911),f318(f318(f74(a911),x97202),f39(a911,x97204,x97203))),x97205))))
% 109.14/108.86 [9775]~P82(x97751)+~P1(f318(f55(x97752),x97755))+~P1(f318(f55(x97752),x97754))+E(f318(f318(f74(x97751),f318(f318(f318(f59(x97751,x97752,f74(x97751)),x97753),f71(x97751)),f318(f318(f101(f918(x97752,a909)),x97754),x97755))),f318(f318(f318(f59(x97751,x97752,f74(x97751)),x97753),f71(x97751)),f318(f318(f92(f918(x97752,a909)),x97754),x97755))),f318(f318(f74(x97751),f318(f318(f318(f59(x97751,x97752,f74(x97751)),x97753),f71(x97751)),x97754)),f318(f318(f318(f59(x97751,x97752,f74(x97751)),x97753),f71(x97751)),x97755)))
% 109.14/108.86 [9777]~E(f318(f318(f166(x97771),x97775),x97772),f318(f318(f166(x97771),x97775),x97773))+P1(f318(f318(f320(f917(f912(x97771),f912(x97771))),f318(f318(f243(f912(x97771),f912(x97771)),x97772),x97773)),f138(x97771,x97774)))+~P1(f318(f318(f226(a911),x97775),f318(f318(f223(a911),f318(f180(f912(x97771)),x97772)),f318(f180(f912(x97771)),x97773))))+~P1(f318(f318(f320(f917(x97771,x97771)),f318(f318(f243(x97771,x97771),f318(f318(f155(x97771),x97772),x97775)),f318(f318(f155(x97771),x97773),x97775))),x97774))
% 109.14/108.86 [9900]~P114(x99005)+~P90(x99005)+P1(f318(f318(f320(x99001),f386(x99002,x99003,x99004,x99001,x99005)),x99004))+P1(f318(f318(f225(x99005),f318(f318(f8(x99001,x99005),x99003),x99004)),f318(f318(f74(x99005),f318(f91(x99005),f318(f29(x99001),x99004))),x99002)))
% 109.14/108.86 [10083]~P114(x100831)+~P90(x100831)+~P1(f318(f318(f225(x100831),f318(x100833,f386(x100835,x100833,x100834,x100832,x100831))),x100835))+P1(f318(f318(f225(x100831),f318(f318(f8(x100832,x100831),x100833),x100834)),f318(f318(f74(x100831),f318(f91(x100831),f318(f29(x100832),x100834))),x100835)))
% 109.14/108.86 [8822]E(f318(f318(f125(x88221),x88222),x88223),f318(f318(f125(x88221),x88224),x88225))+~E(f318(f318(f166(x88221),f318(f180(f912(x88221)),x88222)),x88224),x88222)+~E(f318(f318(f125(x88221),f318(f318(f129(x88221),f318(f180(f912(x88221)),x88222)),x88224)),x88225),x88223)+P1(f318(f318(f225(a911),f318(f180(f912(x88221)),x88224)),f318(f180(f912(x88221)),x88222)))
% 109.14/108.86 [8950]E(f318(f318(f125(x89501),x89502),x89503),f318(f318(f125(x89501),x89504),x89505))+~E(f318(f318(f166(x89501),f318(f180(f912(x89501)),x89502)),x89504),x89502)+~E(x89503,f318(f318(f125(x89501),f318(f318(f129(x89501),f318(f180(f912(x89501)),x89502)),x89504)),x89505))+~P1(f318(f318(f225(a911),f318(f180(f912(x89501)),x89502)),f318(f180(f912(x89501)),x89504)))
% 109.14/108.86 [10214]~P1(f318(x102145,x102144))+~P1(f318(f55(x102142),f318(f253(x102142),x102145)))+P1(f318(f55(x102141),f318(f253(x102141),f318(f318(f9(x102141,x102142,a909),x102143),x102144))))+~P1(f318(f55(x102141),f318(f253(x102141),f318(f318(f10(f918(x102142,a909),a909,x102141),f79(x102142)),f318(f318(f10(f918(x102142,a909),f918(x102142,a909),x102141),f318(f20(x102142,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102142),a316),x102145))),x102143)))))
% 109.14/108.86 [10286]~P1(f318(f55(x102862),x102865))+~P1(f318(f318(f320(x102862),x102864),x102865))+P1(f318(f55(x102861),f318(f253(x102861),f318(f318(f9(x102861,x102862,a909),x102863),x102864))))+~P1(f318(f55(x102861),f318(f253(x102861),f318(f318(f10(f918(x102862,a909),a909,x102861),f79(x102862)),f318(f318(f10(f918(x102862,a909),f918(x102862,a909),x102861),f318(f20(x102862,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102862),a316),f318(f318(f9(x102862,f918(x102862,a909),a909),f320(x102862)),x102865)))),x102863)))))
% 109.14/108.86 [8610]~P19(x86105,x86101,x86106,x86102)+E(f318(f66(x86101,x86101,x86101,f318(x86102,x86103)),f318(x86102,x86104)),f318(f66(x86101,x86101,x86101,f318(x86102,x86104)),f318(x86102,x86103)))+~P1(f318(f55(x86105),x86104))+~P1(f318(f55(x86105),x86103))
% 109.14/108.86 [8010]~P25(x80101,x80102,x80104,x80103)+~E(f318(x80104,x80106),x80105)+E(f318(f70(x80101,x80102,x80103,x80104),x80105),x80106)+~P1(f318(f318(f320(x80101),x80106),x80103))
% 109.14/108.86 [8011]~P25(x80111,x80112,x80114,x80113)+~E(f318(x80114,x80116),x80115)+E(f318(f84(x80111,x80112,x80113,x80114),x80115),x80116)+~P1(f318(f318(f320(x80111),x80116),x80113))
% 109.14/108.86 [8196]~P20(x81966,x81961,x81964,x81962)+E(f318(f66(x81961,x81961,x81961,f318(x81962,x81963)),f318(x81964,x81965)),f318(x81962,x81963))+~P1(f318(f55(x81966),x81963))+~P1(f318(f318(f320(x81966),x81965),x81963))
% 109.14/108.86 [9326]E(x93261,x93262)+~E(f318(f84(x93263,x93264,x93265,x93266),x93261),f318(f84(x93263,x93264,x93265,x93266),x93262))+~P1(f318(f318(f320(x93264),x93262),f318(f301(x93263,x93264,x93266),x93265)))+~P1(f318(f318(f320(x93264),x93261),f318(f301(x93263,x93264,x93266),x93265)))
% 109.14/108.86 [9422]~P19(x94223,x94221,x94226,x94222)+E(f318(f66(x94221,x94221,x94221,f318(x94222,f318(f318(f3(f918(x94223,a909)),x94224),f318(f318(f300(x94223),x94225),f179(f918(x94223,a909)))))),f318(x94226,x94225)),f318(x94222,x94224))+~P1(f318(f55(x94223),x94224))+~P1(f318(f318(f320(x94223),x94225),x94224))
% 109.14/108.86 [7103]~P70(x71031)+~E(f39(x71031,x71033,x71034),f39(x71031,x71036,x71034))+~E(f39(x71031,x71032,x71034),f39(x71031,x71035,x71034))+E(f39(x71031,f318(f318(f3(x71031),x71032),x71033),x71034),f39(x71031,f318(f318(f3(x71031),x71035),x71036),x71034))
% 109.14/108.86 [7104]~P69(x71041)+~E(f39(x71041,x71043,x71044),f39(x71041,x71046,x71044))+~E(f39(x71041,x71042,x71044),f39(x71041,x71045,x71044))+E(f39(x71041,f318(f318(f73(x71041),x71042),x71043),x71044),f39(x71041,f318(f318(f73(x71041),x71045),x71046),x71044))
% 109.14/108.86 [7105]~P69(x71051)+~E(f39(x71051,x71053,x71054),f39(x71051,x71056,x71054))+~E(f39(x71051,x71052,x71054),f39(x71051,x71055,x71054))+E(f39(x71051,f318(f318(f74(x71051),x71052),x71053),x71054),f39(x71051,f318(f318(f74(x71051),x71055),x71056),x71054))
% 109.14/108.86 [7901]~P16(x79011,x79012,x79013)+~P1(f318(f55(x79011),x79016))+E(f318(f318(f58(x79011,x79012,x79013),x79014),f318(f318(f300(x79011),x79015),x79016)),f318(f318(f58(x79011,x79012,x79013),f318(f318(x79013,x79015),x79014)),x79016))+P1(f318(f318(f320(x79011),x79015),x79016))
% 109.14/108.86 [7968]~P5(x79681)+P1(f318(f318(f225(x79681),x79682),f318(x79683,x79684)))+~P1(f318(f318(f320(x79685),x79684),x79686))+~P1(f318(f318(f225(x79681),x79682),f318(f318(f34(x79685,x79681),x79686),x79683)))
% 109.14/108.86 [8117]~P16(x81171,x81172,x81173)+~P1(f318(f55(x81171),x81176))+E(f318(f318(f58(x81171,x81172,x81173),x81174),f318(f318(f300(x81171),x81175),x81176)),f318(f318(x81173,x81175),f318(f318(f58(x81171,x81172,x81173),x81174),x81176)))+P1(f318(f318(f320(x81171),x81175),x81176))
% 109.14/108.86 [8216]~P4(x82163)+~P1(f318(x82162,x82165))+~P13(x82163,f318(f318(f145(x82161,x82163),x82164),x82166))+E(f318(f127(x82161,x82162),f318(f318(f139(x82161,x82163,x82164),x82165),x82166)),f318(f318(f139(x82161,x82163,x82164),x82165),f318(f127(x82161,x82162),x82166)))
% 109.14/108.86 [8241]E(x82411,x82412)+E(x82413,f2(a1))+~P1(f318(f43(x82414,x82413),f318(f318(f243(a1,a1),x82415),x82412)))+~P1(f318(f43(x82414,x82413),f318(f318(f243(a1,a1),x82416),x82411)))
% 109.14/108.86 [8242]E(x82421,x82422)+E(x82423,f2(a1))+~P1(f318(f43(x82424,x82423),f318(f318(f243(a1,a1),x82422),x82425)))+~P1(f318(f43(x82424,x82423),f318(f318(f243(a1,a1),x82421),x82426)))
% 109.14/108.86 [8266]~P19(x82662,x82665,x82666,x82661)+~P1(f318(f55(x82662),x82664))+E(f318(x82661,f318(f318(f300(x82662),x82663),x82664)),f318(f66(x82665,x82665,x82665,f318(x82661,x82664)),f318(x82666,x82663)))+P1(f318(f318(f320(x82662),x82663),x82664))
% 109.14/108.86 [8483]~P20(x84835,x84831,x84836,x84832)+E(f318(f66(x84831,x84831,x84831,f318(x84832,x84833)),f318(x84832,x84834)),f318(x84832,x84833))+~P1(f318(f55(x84835),x84833))+~P1(f318(f318(f225(f918(x84835,a909)),x84834),x84833))
% 109.14/108.86 [9629]~P25(x96291,x96292,x96294,x96293)+~P1(f318(f318(f320(x96292),x96295),f318(f301(x96291,x96292,x96294),x96293)))+P1(f318(f318(f320(x96291),f318(f70(x96291,x96292,x96293,x96294),x96295)),x96296))+~P1(f318(f318(f225(f918(x96291,a909)),x96293),x96296))
% 109.14/108.86 [10040]~P76(x100402)+~E(f507(x100401,x100403,x100405,x100406,x100404,x100402),f508(x100401,x100403,x100405,x100406,x100404,x100402))+~P1(f318(f55(x100404),x100406))+E(f318(f318(f8(x100401,x100402),x100403),f318(f301(x100404,x100401,x100405),x100406)),f318(f318(f8(x100404,x100402),f318(f66(x100401,x100402,x100404,x100403),x100405)),x100406))
% 109.14/108.86 [10067]~P76(x100676)+E(f318(x100671,f507(x100672,x100673,x100671,x100674,x100675,x100676)),f318(x100671,f508(x100672,x100673,x100671,x100674,x100675,x100676)))+E(f318(f318(f8(x100672,x100676),x100673),f318(f301(x100675,x100672,x100671),x100674)),f318(f318(f8(x100675,x100676),f318(f66(x100672,x100676,x100675,x100673),x100671)),x100674))+~P1(f318(f55(x100675),x100674))
% 109.14/108.86 [10111]~P76(x101112)+~E(f318(x101113,f318(x101115,f508(x101111,x101113,x101115,x101116,x101114,x101112))),f2(x101112))+~P1(f318(f55(x101114),x101116))+E(f318(f318(f8(x101111,x101112),x101113),f318(f301(x101114,x101111,x101115),x101116)),f318(f318(f8(x101114,x101112),f318(f66(x101111,x101112,x101114,x101113),x101115)),x101116))
% 109.14/108.86 [10157]~P76(x101572)+~P1(f318(f55(x101574),x101576))+E(f318(f318(f8(x101571,x101572),x101573),f318(f301(x101574,x101571,x101575),x101576)),f318(f318(f8(x101574,x101572),f318(f66(x101571,x101572,x101574,x101573),x101575)),x101576))+P1(f318(f318(f320(x101574),f508(x101571,x101573,x101575,x101576,x101574,x101572)),x101576))
% 109.14/108.86 [10158]~P76(x101582)+~P1(f318(f55(x101584),x101586))+E(f318(f318(f8(x101581,x101582),x101583),f318(f301(x101584,x101581,x101585),x101586)),f318(f318(f8(x101584,x101582),f318(f66(x101581,x101582,x101584,x101583),x101585)),x101586))+P1(f318(f318(f320(x101584),f507(x101581,x101583,x101585,x101586,x101584,x101582)),x101586))
% 109.14/108.86 [10234]~P42(f918(f917(x102344,x102345),a909),f918(f917(x102344,x102345),a909),x102346)+~P1(f318(f318(x102341,f606(x102341,x102346,x102343,x102342,x102345,x102344)),f607(x102341,x102346,x102343,x102342,x102345,x102344)))+P1(f318(f318(x102341,x102342),x102343))+~P1(f318(f318(f320(f917(x102344,x102345)),f318(f318(f243(x102344,x102345),x102342),x102343)),f86(f918(f917(x102344,x102345),a909),x102346)))
% 109.14/108.86 [10285]~P82(x102851)+~P1(f318(f55(x102852),x102856))+E(f318(f318(f318(f59(x102851,x102852,f74(x102851)),f318(f318(f20(x102852,f918(x102853,a909),x102851),f318(f318(f9(x102852,x102851,f918(f918(x102853,a909),x102851)),f318(f318(f10(f918(x102853,x102851),f918(x102851,f918(f918(x102853,a909),x102851)),x102852),f59(x102851,x102853,f74(x102851))),x102854)),f71(x102851))),x102855)),f71(x102851)),x102856),f318(f318(f318(f59(x102851,f917(x102852,x102853),f74(x102851)),f318(f248(x102852,x102853,x102851),x102854)),f71(x102851)),f318(f318(f245(x102852,x102853),x102856),x102855)))+P1(f318(f318(f320(x102852),f543(x102854,x102855,x102853,x102856,x102852,x102851)),x102856))
% 109.14/108.86 [10307]~P82(x103071)+~P1(f318(f55(x103072),x103076))+E(f318(f318(f318(f59(x103071,x103072,f74(x103071)),f318(f318(f20(x103072,f918(x103073,a909),x103071),f318(f318(f9(x103072,x103071,f918(f918(x103073,a909),x103071)),f318(f318(f10(f918(x103073,x103071),f918(x103071,f918(f918(x103073,a909),x103071)),x103072),f59(x103071,x103073,f74(x103071))),x103074)),f71(x103071))),x103075)),f71(x103071)),x103076),f318(f318(f318(f59(x103071,f917(x103072,x103073),f74(x103071)),f318(f248(x103072,x103073,x103071),x103074)),f71(x103071)),f318(f318(f245(x103072,x103073),x103076),x103075)))+~P1(f318(f55(x103073),f318(x103075,f543(x103074,x103075,x103073,x103076,x103072,x103071))))
% 109.14/108.86 [8396]~P20(x83962,x83965,x83966,x83961)+~P1(f318(f55(x83962),x83964))+~P1(f318(f55(x83962),x83963))+E(f318(x83961,f318(f318(f101(f918(x83962,a909)),x83963),x83964)),f318(f66(x83965,x83965,x83965,f318(x83961,x83963)),f318(x83961,x83964)))
% 109.14/108.86 [8611]~P5(x86111)+P1(f318(f318(f225(x86111),f318(x86112,x86113)),x86114))+~P1(f318(f318(f320(x86115),x86113),x86116))+~P1(f318(f318(f225(x86111),f318(f318(f33(x86115,x86111),x86116),x86112)),x86114))
% 109.14/108.86 [9042]~P25(x90422,x90421,x90423,x90426)+E(f318(f318(f92(f918(x90421,a909)),f318(f301(x90422,x90421,x90423),x90424)),f318(f301(x90422,x90421,x90423),x90425)),f318(f301(x90422,x90421,x90423),f318(f318(f92(f918(x90422,a909)),x90424),x90425)))+~P1(f318(f318(f225(f918(x90422,a909)),x90425),x90426))+~P1(f318(f318(f225(f918(x90422,a909)),x90424),x90426))
% 109.14/108.86 [9043]~P25(x90432,x90431,x90433,x90436)+E(f318(f318(f3(f918(x90431,a909)),f318(f301(x90432,x90431,x90433),x90434)),f318(f301(x90432,x90431,x90433),x90435)),f318(f301(x90432,x90431,x90433),f318(f318(f3(f918(x90432,a909)),x90434),x90435)))+~P1(f318(f318(f225(f918(x90432,a909)),x90435),x90436))+~P1(f318(f318(f225(f918(x90432,a909)),x90434),x90436))
% 109.14/108.86 [9290]E(x92901,x92902)+~P58(x92903,x92904,x92905)+~P1(f318(f318(f320(f917(x92903,x92904)),f318(f318(f243(x92903,x92904),x92906),x92902)),x92905))+~P1(f318(f318(f320(f917(x92903,x92904)),f318(f318(f243(x92903,x92904),x92906),x92901)),x92905))
% 109.14/108.86 [9291]E(x92911,x92912)+~P58(x92913,x92914,x92915)+~P1(f318(f318(f320(f917(x92913,x92914)),f318(f318(f243(x92913,x92914),x92916),x92912)),x92915))+~P1(f318(f318(f320(f917(x92913,x92914)),f318(f318(f243(x92913,x92914),x92916),x92911)),x92915))
% 109.14/108.86 [10108]~P80(x101081)+~E(f318(x101083,f429(x101084,x101086,x101083,x101085,x101082,x101081)),f318(x101086,f429(x101084,x101086,x101083,x101085,x101082,x101081)))+~P1(f318(f55(x101082),x101085))+E(f318(f318(f318(f59(x101081,x101082,f74(x101081)),x101083),x101084),x101085),f318(f318(f318(f59(x101081,x101082,f74(x101081)),x101086),x101084),x101085))
% 109.14/108.86 [10155]~P80(x101551)+~P1(f318(f55(x101552),x101555))+E(f318(f318(f318(f59(x101551,x101552,f74(x101551)),x101553),x101554),x101555),f318(f318(f318(f59(x101551,x101552,f74(x101551)),x101556),x101554),x101555))+P1(f318(f318(f320(x101552),f429(x101554,x101553,x101556,x101555,x101552,x101551)),x101555))
% 109.14/108.86 [8834]~P80(x88341)+~P1(f318(f55(x88342),x88346))+P1(f318(f318(f320(x88342),x88345),x88346))+E(f318(f318(f318(f59(x88341,x88342,f74(x88341)),x88343),x88344),f318(f318(f300(x88342),x88345),x88346)),f318(f318(f74(x88341),f318(x88343,x88345)),f318(f318(f318(f59(x88341,x88342,f74(x88341)),x88343),x88344),x88346)))
% 109.14/108.86 [8888]~P8(x88881,x88886,x88883)+~P11(x88881,f918(x88882,a909),x88883,x88885)+~P1(f318(f318(f320(x88881),x88884),x88886))+E(f318(f318(f33(x88881,f918(x88882,a909)),f318(f276(x88881,x88881,x88883),f318(f318(f300(x88881),x88884),f179(f918(x88881,a909))))),x88885),f318(x88885,x88884))
% 109.14/108.86 [9019]~P16(x90193,x90194,x90191)+~P1(f318(f55(x90193),x90196))+~P1(f318(f318(f320(x90193),x90192),x90196))+E(f318(f318(x90191,x90192),f318(f318(f58(x90193,x90194,x90191),x90195),f318(f318(f3(f918(x90193,a909)),x90196),f318(f318(f300(x90193),x90192),f179(f918(x90193,a909)))))),f318(f318(f58(x90193,x90194,x90191),x90195),x90196))
% 109.14/108.86 [9308]~P19(x93083,x93081,x93086,x93082)+~P1(f318(f55(x93083),x93085))+~P1(f318(f55(x93083),x93084))+E(f318(f66(x93081,x93081,x93081,f318(x93082,f318(f318(f101(f918(x93083,a909)),x93084),x93085))),f318(x93082,f318(f318(f92(f918(x93083,a909)),x93084),x93085))),f318(f66(x93081,x93081,x93081,f318(x93082,x93084)),f318(x93082,x93085)))
% 109.14/108.86 [10319]~P42(f918(f917(x103194,x103195),a909),f918(f917(x103194,x103195),a909),x103196)+P1(f318(f318(x103191,x103192),x103193))+~P1(f318(f318(f320(f917(x103194,x103195)),f318(f318(f243(x103194,x103195),x103192),x103193)),f86(f918(f917(x103194,x103195),a909),x103196)))+P1(f318(f318(f320(f917(x103194,x103195)),f318(f318(f243(x103194,x103195),f606(x103191,x103196,x103193,x103192,x103195,x103194)),f607(x103191,x103196,x103193,x103192,x103195,x103194))),f318(x103196,f318(f318(f92(f918(f917(x103194,x103195),a909)),f86(f918(f917(x103194,x103195),a909),x103196)),f318(f253(f917(x103194,x103195)),f318(f248(x103194,x103195,a909),x103191))))))
% 109.14/108.86 [9652]~E(x96523,f318(f318(f150(x96521,x96522),x96525),x96526))+P1(f318(f318(f320(f917(f912(x96521),f912(x96521))),f318(f318(f243(f912(x96521),f912(x96521)),x96522),x96523)),f148(x96521,x96524)))+~P1(f318(f318(f226(a911),x96525),f318(f180(f912(x96521)),x96522)))+~P1(f318(f318(f320(f917(x96521,x96521)),f318(f318(f243(x96521,x96521),f318(f318(f155(x96521),x96522),x96525)),x96526)),x96524))
% 109.14/108.86 [10170]~P76(x101702)+~P1(f318(f55(x101701),x101706))+P1(f318(f318(f320(x101701),f547(x101704,x101705,x101703,x101706,x101701,x101702)),x101706))+E(f318(f318(f8(x101701,x101702),f318(f318(f20(x101701,f918(x101703,a909),x101702),f318(f318(f10(f918(x101703,x101702),f918(f918(x101703,a909),x101702),x101701),f8(x101703,x101702)),x101704)),x101705)),x101706),f318(f318(f8(f917(x101701,x101703),x101702),f318(f248(x101701,x101703,x101702),x101704)),f318(f318(f245(x101701,x101703),x101706),x101705)))
% 109.14/108.86 [10171]~P82(x101712)+~P1(f318(f55(x101711),x101716))+P1(f318(f318(f320(x101711),f542(x101714,x101715,x101713,x101716,x101711,x101712)),x101716))+E(f318(f318(f11(x101711,x101712),f318(f318(f20(x101711,f918(x101713,a909),x101712),f318(f318(f10(f918(x101713,x101712),f918(f918(x101713,a909),x101712),x101711),f11(x101713,x101712)),x101714)),x101715)),x101716),f318(f318(f11(f917(x101711,x101713),x101712),f318(f248(x101711,x101713,x101712),x101714)),f318(f318(f245(x101711,x101713),x101716),x101715)))
% 109.14/108.86 [10212]~P76(x102122)+~P1(f318(f55(x102121),x102126))+~P1(f318(f55(x102123),f318(x102125,f547(x102124,x102125,x102123,x102126,x102121,x102122))))+E(f318(f318(f8(x102121,x102122),f318(f318(f20(x102121,f918(x102123,a909),x102122),f318(f318(f10(f918(x102123,x102122),f918(f918(x102123,a909),x102122),x102121),f8(x102123,x102122)),x102124)),x102125)),x102126),f318(f318(f8(f917(x102121,x102123),x102122),f318(f248(x102121,x102123,x102122),x102124)),f318(f318(f245(x102121,x102123),x102126),x102125)))
% 109.14/108.86 [10213]~P82(x102132)+~P1(f318(f55(x102131),x102136))+~P1(f318(f55(x102133),f318(x102135,f542(x102134,x102135,x102133,x102136,x102131,x102132))))+E(f318(f318(f11(x102131,x102132),f318(f318(f20(x102131,f918(x102133,a909),x102132),f318(f318(f10(f918(x102133,x102132),f918(f918(x102133,a909),x102132),x102131),f11(x102133,x102132)),x102134)),x102135)),x102136),f318(f318(f11(f917(x102131,x102133),x102132),f318(f248(x102131,x102133,x102132),x102134)),f318(f318(f245(x102131,x102133),x102136),x102135)))
% 109.14/108.86 [10194]~P82(x101942)+~P1(f318(f55(x101941),x101946))+P1(f318(f318(f320(x101941),x101943),x101946))+E(f318(f318(f11(x101941,x101942),f318(f318(f9(x101941,x101942,x101942),f318(f318(f20(x101941,x101942,f918(x101942,x101942)),f318(f318(f10(a909,f918(x101942,f918(x101942,x101942)),x101941),f85(x101942)),f318(f318(f9(x101941,x101941,a909),a315),x101943))),x101944)),x101945)),x101946),f318(f318(f235(x101942),x101945),f318(f29(x101941),x101946)))
% 109.14/108.86 [10197]~P82(x101972)+~P1(f318(f55(x101971),x101976))+~P1(f318(f318(f320(x101971),x101973),x101976))+E(f318(f318(f11(x101971,x101972),f318(f318(f9(x101971,x101972,x101972),f318(f318(f20(x101971,x101972,f918(x101972,x101972)),f318(f318(f10(a909,f918(x101972,f918(x101972,x101972)),x101971),f85(x101972)),f318(f318(f9(x101971,x101971,a909),a315),x101973))),x101974)),x101975)),x101976),f318(f318(f74(x101972),f318(x101974,x101973)),f318(f318(f235(x101972),x101975),f318(f318(f3(a911),f318(f29(x101971),x101976)),f71(a911)))))
% 109.14/108.86 [10277]~P1(f318(f55(x102771),x102775))+~P1(f318(f55(x102772),x102773))+P1(f318(f318(f320(x102772),f561(x102776,x102774,x102773,x102772,x102775,x102771)),x102773))+E(f318(f318(f8(x102771,a911),f318(f318(f10(f918(x102772,a909),a911,x102771),f29(x102772)),f318(f318(f10(f918(x102772,a909),f918(x102772,a909),x102771),f253(x102772)),f318(f318(f10(f918(x102772,a909),f918(x102772,a909),x102771),f318(f20(x102772,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102772),a316),f318(f318(f9(x102772,f918(x102772,a909),a909),f320(x102772)),x102773)))),x102774)))),x102775),f318(f318(f74(a911),x102776),f318(f29(x102772),x102773)))
% 109.14/108.86 [10278]~P1(f318(f55(x102781),x102785))+~P1(f318(f55(x102782),x102783))+P1(f318(f318(f320(x102782),f562(x102786,x102784,x102783,x102782,x102785,x102781)),x102783))+E(f318(f318(f8(x102781,a911),f318(f318(f10(f918(x102782,a909),a911,x102781),f29(x102782)),f318(f318(f10(f918(x102782,a909),f918(x102782,a909),x102781),f253(x102782)),f318(f318(f10(f918(x102782,a909),f918(x102782,a909),x102781),f318(f20(x102782,a909,a909),f318(f318(f10(a909,f918(a909,a909),x102782),a316),f318(f318(f9(x102782,f918(x102782,a909),a909),f320(x102782)),x102783)))),x102784)))),x102785),f318(f318(f8(x102782,a911),x102786),x102783))
% 109.14/108.86 [10325]~P1(f318(f55(x103252),x103253))+~P1(f318(f55(x103251),x103255))+~E(f318(f29(x103251),f318(f253(x103251),f318(f318(f20(x103251,a909,a909),f318(f318(f10(a909,f918(a909,a909),x103251),a316),f318(f318(f9(x103251,f918(x103251,a909),a909),f320(x103251)),x103255))),f318(f318(f9(x103251,x103252,a909),x103254),f561(x103256,x103254,x103253,x103252,x103255,x103251))))),x103256)+E(f318(f318(f8(x103251,a911),f318(f318(f10(f918(x103252,a909),a911,x103251),f29(x103252)),f318(f318(f10(f918(x103252,a909),f918(x103252,a909),x103251),f253(x103252)),f318(f318(f10(f918(x103252,a909),f918(x103252,a909),x103251),f318(f20(x103252,a909,a909),f318(f318(f10(a909,f918(a909,a909),x103252),a316),f318(f318(f9(x103252,f918(x103252,a909),a909),f320(x103252)),x103253)))),x103254)))),x103255),f318(f318(f74(a911),x103256),f318(f29(x103252),x103253)))
% 109.14/108.86 [10344]~P1(f318(f55(x103442),x103443))+~P1(f318(f55(x103441),x103445))+~E(f318(f29(x103441),f318(f253(x103441),f318(f318(f20(x103441,a909,a909),f318(f318(f10(a909,f918(a909,a909),x103441),a316),f318(f318(f9(x103441,f918(x103441,a909),a909),f320(x103441)),x103445))),f318(f318(f9(x103441,x103442,a909),x103444),f562(x103446,x103444,x103443,x103442,x103445,x103441))))),f318(x103446,f562(x103446,x103444,x103443,x103442,x103445,x103441)))+E(f318(f318(f8(x103441,a911),f318(f318(f10(f918(x103442,a909),a911,x103441),f29(x103442)),f318(f318(f10(f918(x103442,a909),f918(x103442,a909),x103441),f253(x103442)),f318(f318(f10(f918(x103442,a909),f918(x103442,a909),x103441),f318(f20(x103442,a909,a909),f318(f318(f10(a909,f918(a909,a909),x103442),a316),f318(f318(f9(x103442,f918(x103442,a909),a909),f320(x103442)),x103443)))),x103444)))),x103445),f318(f318(f8(x103442,a911),x103446),x103443))
% 109.14/108.86 [9974]E(x99741,x99742)+~P16(x99743,x99744,x99745)+~P1(f318(f60(x99743,x99744,x99745,x99746,x99747),x99742))+~P1(f318(f60(x99743,x99744,x99745,x99746,x99747),x99741))
% 109.14/108.86 [9578]~P36(x95781,x95782,x95783,x95785,x95787)+~P36(x95781,x95782,x95783,x95784,x95786)+P36(x95781,x95782,x95783,f318(f318(f125(x95781),x95784),x95785),f318(f318(f125(x95782),x95786),x95787))+~E(f318(f180(f912(x95781)),x95784),f318(f180(f912(x95782)),x95786))
% 109.14/108.86 [9742]P1(f318(x97421,x97422))+~P1(f318(f318(f320(x97427),x97422),f318(x97426,x97424)))+~P1(f318(x97421,f870(x97421,x97426,x97425,x97423,x97427)))+~P1(f318(f318(f320(x97423),x97424),x97425))
% 109.14/108.86 [10185]~P16(x101857,x101856,x101851)+E(f318(f318(x101851,x101852),f398(x101852,x101853,x101854,x101855,x101851,x101856,x101857)),x101853)+~P1(f318(f60(x101857,x101856,x101851,x101855,x101854),x101853))+~P1(f318(f318(f320(x101857),x101852),x101854))
% 109.14/108.86 [10245]~P16(x102451,x102452,x102453)+~P1(f318(f60(x102451,x102452,x102453,x102454,x102455),x102457))+P1(f318(f60(x102451,x102452,x102453,x102454,f318(f318(f3(f918(x102451,a909)),x102455),f318(f318(f300(x102451),x102456),f179(f918(x102451,a909))))),f398(x102456,x102457,x102455,x102454,x102453,x102452,x102451)))+~P1(f318(f318(f320(x102451),x102456),x102455))
% 109.14/108.86 [9379]P26(x93791,x93792,x93793,x93794,x93795)+~P26(x93791,x93792,x93793,x93796,x93797)+~E(f318(f301(x93791,x93792,x93793),x93794),x93795)+~P1(f318(f318(f225(f918(x93791,a909)),x93794),x93796))
% 109.14/108.86 [9620]~P26(x96201,x96202,x96203,x96205,x96207)+~P26(x96201,x96202,x96203,x96204,x96206)+P26(x96201,x96202,x96203,f318(f318(f101(f918(x96201,a909)),x96204),x96205),f318(f318(f101(f918(x96202,a909)),x96206),x96207))+~E(f318(f318(f92(f918(x96202,a909)),x96206),x96207),f179(f918(x96202,a909)))
% 109.14/108.86 [9625]~P80(x96251)+~P25(x96255,x96252,x96256,x96257)+~P1(f318(f55(x96255),x96257))+E(f318(f318(f318(f59(x96251,x96252,f74(x96251)),x96253),x96254),f318(f301(x96255,x96252,x96256),x96257)),f318(f318(f318(f59(x96251,x96255,f74(x96251)),f318(f66(x96252,x96251,x96255,x96253),x96256)),x96254),x96257))
% 109.14/108.86 [9763]~E(f318(f318(f300(x97631),x97635),x97636),f318(f318(f300(x97631),x97632),x97633))+~P1(f318(f60(x97631,x97631,x97634,x97632,x97633),x97637))+P1(f318(f318(f320(x97631),x97632),x97633))+P1(f318(f56(x97631,x97634,f318(f318(f300(x97631),x97635),x97636)),x97637))
% 109.14/108.86 [9861]P1(f318(x98611,x98612))+~P1(f318(f318(f320(x98613),x98612),f318(x98614,x98617)))+~P1(f318(f318(f320(x98616),x98617),x98615))+P1(f318(f318(f320(x98613),f870(x98611,x98614,x98615,x98616,x98613)),f318(f318(f33(x98616,f918(x98613,a909)),x98615),x98614)))
% 109.14/108.86 [9879]~P25(x98792,x98791,x98795,x98794)+~P25(x98791,x98793,x98796,f318(f301(x98792,x98791,x98795),x98794))+E(f318(f318(f66(x98791,x98792,x98793,f70(x98792,x98791,x98794,x98795)),f70(x98791,x98793,f318(f301(x98792,x98791,x98795),x98794),x98796)),x98797),f318(f70(x98792,x98793,x98794,f318(f66(x98791,x98793,x98792,x98796),x98795)),x98797))+~P1(f318(f318(f320(x98793),x98797),f318(f301(x98791,x98793,x98796),f318(f301(x98792,x98791,x98795),x98794))))
% 109.14/108.86 [9880]~P25(x98802,x98801,x98805,x98804)+~P25(x98801,x98803,x98806,f318(f301(x98802,x98801,x98805),x98804))+E(f318(f318(f66(x98801,x98802,x98803,f84(x98802,x98801,x98804,x98805)),f84(x98801,x98803,f318(f301(x98802,x98801,x98805),x98804),x98806)),x98807),f318(f84(x98802,x98803,x98804,f318(f66(x98801,x98803,x98802,x98806),x98805)),x98807))+~P1(f318(f318(f320(x98803),x98807),f318(f301(x98801,x98803,x98806),f318(f301(x98802,x98801,x98805),x98804))))
% 109.14/108.86 [10186]~P16(x101867,x101866,x101861)+E(f318(f318(x101861,x101862),f421(x101863,x101864,x101862,x101865,x101861,x101866,x101867)),x101863)+P1(f318(f318(f320(x101867),x101862),x101864))+~P1(f318(f60(x101867,x101866,x101861,x101865,f318(f318(f300(x101867),x101862),x101864)),x101863))
% 109.14/108.86 [10244]~P16(x102441,x102444,x102445)+P1(f318(f60(x102441,x102444,x102445,x102446,x102443),f421(x102447,x102443,x102442,x102446,x102445,x102444,x102441)))+P1(f318(f318(f320(x102441),x102442),x102443))+~P1(f318(f60(x102441,x102444,x102445,x102446,f318(f318(f300(x102441),x102442),x102443)),x102447))
% 109.14/108.86 [9952]E(x99521,f2(a1))+~P1(f318(f43(x99523,x99521),f318(f318(f243(a1,a1),x99525),x99527)))+~P1(f318(f43(x99522,x99521),f318(f318(f243(a1,a1),x99524),x99526)))+P1(f318(f43(f318(f318(f73(a1),x99522),x99523),x99521),f318(f318(f243(a1,a1),f318(f318(f73(a1),f318(f318(f73(a1),x99524),x99525)),f318(f318(f30(a1),f318(f318(f73(a1),x99526),x99527)),x99521))),f39(a1,f318(f318(f73(a1),x99526),x99527),x99521))))
% 109.14/108.86 [9954]~P1(f318(f318(f226(a911),f2(a911)),x99543))+~P1(f318(f42(x99542,x99543),f318(f318(f243(a911,a911),x99545),x99547)))+~P1(f318(f42(x99541,x99543),f318(f318(f243(a911,a911),x99544),x99546)))+P1(f318(f42(f318(f318(f73(a911),x99541),x99542),x99543),f318(f318(f243(a911,a911),f318(f318(f73(a911),f318(f318(f73(a911),x99544),x99545)),f318(f318(f30(a911),f318(f318(f73(a911),x99546),x99547)),x99543))),f39(a911,f318(f318(f73(a911),x99546),x99547),x99543))))
% 109.14/108.86 [10324]~P76(x103242)+~P1(f318(f55(x103243),x103245))+~P1(f318(f55(x103241),x103247))+E(f318(f318(f8(x103241,x103242),f318(f318(f20(x103241,f918(x103243,a909),x103242),f318(f318(f10(f918(x103243,x103242),f918(f918(x103243,a909),x103242),x103241),f8(x103243,x103242)),x103244)),f318(f318(f10(f918(x103243,a909),f918(x103243,a909),x103241),f253(x103243)),f318(f318(f10(f918(x103243,a909),f918(x103243,a909),x103241),f318(f20(x103243,a909,a909),f318(f318(f10(a909,f918(a909,a909),x103243),a316),f318(f318(f9(x103243,f918(x103243,a909),a909),f320(x103243)),x103245)))),x103246)))),x103247),f318(f318(f8(x103243,x103242),f318(f318(f20(x103243,f918(x103241,a909),x103242),f318(f318(f10(f918(x103241,x103242),f918(f918(x103241,a909),x103242),x103243),f8(x103241,x103242)),f318(f9(x103241,x103243,x103242),x103244))),f318(f318(f10(f918(x103241,a909),f918(x103241,a909),x103243),f253(x103241)),f318(f318(f10(f918(x103241,a909),f918(x103241,a909),x103243),f318(f20(x103241,a909,a909),f318(f318(f10(a909,f918(a909,a909),x103241),a316),f318(f318(f9(x103241,f918(x103241,a909),a909),f320(x103241)),x103247)))),f318(f9(x103241,x103243,a909),x103246))))),x103245))
% 109.14/108.86 [10276]~P21(x102768,x102767,x102766,x102765,x102761)+~E(f318(x102762,f850(x102764,x102762,x102763,x102761,x102765,x102766,x102767)),f318(x102764,f850(x102764,x102762,x102763,x102761,x102765,x102766,x102767)))+E(f318(f318(x102761,x102762),x102763),f318(f318(x102761,x102764),x102763))+~P1(f318(f55(x102767),x102763))
% 109.14/108.86 [9810]~P22(x98107,x98106,x98101,x98108,x98102,x98104)+E(f318(f318(x98101,f318(x98102,x98103)),f318(x98104,x98105)),f318(x98104,x98105))+~P1(f318(f55(x98106),x98105))+~P1(f318(f318(f320(x98106),x98103),x98105))
% 109.14/108.86 [9814]~P12(x98146,x98141,x98142,x98148,x98143,x98144)+~P8(x98146,x98147,x98148)+P11(x98141,x98142,x98143,f318(x98144,x98145))+~P1(f318(f318(f320(x98146),x98145),x98147))
% 109.14/108.86 [10293]~P21(x102938,x102935,x102937,x102936,x102931)+E(f318(f318(x102931,x102932),x102933),f318(f318(x102931,x102934),x102933))+~P1(f318(f55(x102935),x102933))+P1(f318(f318(f320(x102935),f850(x102932,x102934,x102933,x102931,x102936,x102937,x102935)),x102933))
% 109.14/108.86 [10409]~P1(f318(f318(x104091,x104096),x104095))+P1(f318(f318(x104091,f835(x104091,x104094,x104095,x104096,x104093,x104092,x104097,x104098)),f839(x104091,x104094,x104095,x104096,x104093,x104092,x104097,x104098)))+P1(f318(f318(x104091,x104092),x104093))+~P1(f318(f318(f320(f917(f917(x104098,x104097),f917(x104098,x104097))),f318(f318(f243(f917(x104098,x104097),f917(x104098,x104097)),f318(f318(f243(x104098,x104097),x104092),x104093)),f318(f318(f243(x104098,x104097),x104096),x104095))),f298(f917(x104098,x104097),x104094)))
% 109.14/108.86 [10410]~P1(f318(f318(x104101,x104106),x104105))+P1(f318(f318(x104101,f840(x104101,x104104,x104103,x104102,x104105,x104106,x104107,x104108)),f841(x104101,x104104,x104103,x104102,x104105,x104106,x104107,x104108)))+P1(f318(f318(x104101,x104102),x104103))+~P1(f318(f318(f320(f917(f917(x104108,x104107),f917(x104108,x104107))),f318(f318(f243(f917(x104108,x104107),f917(x104108,x104107)),f318(f318(f243(x104108,x104107),x104106),x104105)),f318(f318(f243(x104108,x104107),x104102),x104103))),f298(f917(x104108,x104107),x104104)))
% 109.14/108.86 [10424]~P1(f318(f318(x104241,f836(x104241,x104246,x104245,x104244,x104243,x104242,x104247,x104248)),f838(x104241,x104246,x104245,x104244,x104243,x104242,x104247,x104248)))+P1(f318(f318(x104241,x104242),x104243))+~P1(f318(f318(x104241,x104244),x104245))+~P1(f318(f318(f320(f917(f917(x104248,x104247),f917(x104248,x104247))),f318(f318(f243(f917(x104248,x104247),f917(x104248,x104247)),f318(f318(f243(x104248,x104247),x104242),x104243)),f318(f318(f243(x104248,x104247),x104244),x104245))),f298(f917(x104248,x104247),x104246)))
% 109.14/108.86 [10425]~P1(f318(f318(x104251,f842(x104251,x104256,x104253,x104252,x104255,x104254,x104257,x104258)),f843(x104251,x104256,x104253,x104252,x104255,x104254,x104257,x104258)))+P1(f318(f318(x104251,x104252),x104253))+~P1(f318(f318(x104251,x104254),x104255))+~P1(f318(f318(f320(f917(f917(x104258,x104257),f917(x104258,x104257))),f318(f318(f243(f917(x104258,x104257),f917(x104258,x104257)),f318(f318(f243(x104258,x104257),x104254),x104255)),f318(f318(f243(x104258,x104257),x104252),x104253))),f298(f917(x104258,x104257),x104256)))
% 109.14/108.86 [10441]~P1(f318(f318(x104411,x104416),x104417))+P1(f318(f318(x104411,x104412),x104413))+P1(f318(f318(f320(f917(f917(x104414,x104415),f917(x104414,x104415))),f318(f318(f243(f917(x104414,x104415),f917(x104414,x104415)),f318(f318(f243(x104414,x104415),x104416),x104417)),f318(f318(f243(x104414,x104415),f840(x104411,x104418,x104413,x104412,x104417,x104416,x104415,x104414)),f841(x104411,x104418,x104413,x104412,x104417,x104416,x104415,x104414)))),f298(f917(x104414,x104415),x104418)))+~P1(f318(f318(f320(f917(f917(x104414,x104415),f917(x104414,x104415))),f318(f318(f243(f917(x104414,x104415),f917(x104414,x104415)),f318(f318(f243(x104414,x104415),x104416),x104417)),f318(f318(f243(x104414,x104415),x104412),x104413))),f298(f917(x104414,x104415),x104418)))
% 109.14/108.86 [10443]~P1(f318(f318(x104431,x104438),x104437))+P1(f318(f318(x104431,x104432),x104433))+P1(f318(f318(f320(f917(f917(x104434,x104435),f917(x104434,x104435))),f318(f318(f243(f917(x104434,x104435),f917(x104434,x104435)),f318(f318(f243(x104434,x104435),f835(x104431,x104436,x104437,x104438,x104433,x104432,x104435,x104434)),f839(x104431,x104436,x104437,x104438,x104433,x104432,x104435,x104434))),f318(f318(f243(x104434,x104435),x104438),x104437))),f298(f917(x104434,x104435),x104436)))+~P1(f318(f318(f320(f917(f917(x104434,x104435),f917(x104434,x104435))),f318(f318(f243(f917(x104434,x104435),f917(x104434,x104435)),f318(f318(f243(x104434,x104435),x104432),x104433)),f318(f318(f243(x104434,x104435),x104438),x104437))),f298(f917(x104434,x104435),x104436)))
% 109.14/108.86 [9405]~P19(x94057,x94051,x94058,x94053)+~P1(f318(f55(x94057),x94055))+~P1(f318(f55(x94057),x94054))+E(f318(f66(x94051,x94051,x94052,f318(x94053,x94054)),f318(f66(x94051,x94051,x94052,f318(x94053,x94055)),x94056)),f318(f66(x94051,x94051,x94052,f318(x94053,x94055)),f318(f66(x94051,x94051,x94052,f318(x94053,x94054)),x94056)))
% 109.14/108.86 [9414]~P36(x94141,x94142,x94143,x94144,x94147)+P36(x94141,x94142,x94143,f318(f318(f150(x94141,x94144),x94145),x94146),f318(f318(f150(x94142,x94147),x94145),x94148))+~P1(f318(f318(x94143,x94146),x94148))+~P1(f318(f318(f226(a911),x94145),f318(f180(f912(x94141)),x94144)))
% 109.14/108.86 [9415]~P36(x94151,x94152,x94153,x94154,x94157)+P36(x94151,x94152,x94153,f318(f318(f150(x94151,x94154),x94155),x94156),f318(f318(f150(x94152,x94157),x94155),x94158))+~P1(f318(f318(x94153,x94156),x94158))+~P1(f318(f318(f226(a911),x94155),f318(f180(f912(x94152)),x94157)))
% 109.14/108.86 [9498]~P25(x94982,x94982,x94985,x94986)+~P21(x94983,x94982,x94987,x94988,x94981)+~P1(f318(f55(x94982),x94986))+E(f318(f318(x94981,f318(f66(x94982,x94983,x94982,x94984),x94985)),x94986),f318(f318(x94981,x94984),f318(f301(x94982,x94982,x94985),x94986)))
% 109.14/108.86 [9740]~P26(x97401,x97403,x97405,x97406,x97408)+~P26(x97403,x97402,x97404,x97408,x97407)+P26(x97401,x97402,f318(f66(x97403,x97402,x97401,x97404),x97405),x97406,x97407)+~P1(f318(f318(f225(f918(x97403,a909)),f318(f301(x97401,x97403,x97405),x97406)),x97408))
% 109.14/108.86 [9764]P26(x97641,x97642,x97643,x97644,x97645)+~P26(x97642,x97646,x97647,x97645,x97648)+~P26(x97641,x97646,f318(f66(x97642,x97646,x97641,x97647),x97643),x97644,x97648)+~P1(f318(f318(f225(f918(x97642,a909)),f318(f301(x97641,x97642,x97643),x97644)),x97645))
% 109.14/108.86 [9812]~P23(x98127,x98122,x98125,x98128,x98126,x98121)+~P1(f318(f55(x98122),x98124))+E(f318(x98121,f318(f318(f300(x98122),x98123),x98124)),f318(f318(x98125,f318(x98126,x98123)),f318(x98121,x98124)))+P1(f318(f318(f320(x98122),x98123),x98124))
% 109.14/108.86 [9828]~P22(x98286,x98285,x98281,x98287,x98288,x98282)+E(f318(f318(x98281,f318(x98282,x98283)),f318(x98282,x98284)),f318(x98282,x98284))+~P1(f318(f55(x98285),x98284))+~P1(f318(f318(f225(f918(x98285,a909)),x98283),x98284))
% 109.14/108.86 [9391]P1(f318(f318(f320(f917(f912(x93911),f912(x93911))),f318(f318(f243(f912(x93911),f912(x93911)),x93912),x93913)),f148(x93911,x93914)))+~E(x93913,f318(f318(f125(x93911),x93915),f318(f318(f142(x93911),x93916),x93917)))+~E(x93912,f318(f318(f125(x93911),x93915),f318(f318(f142(x93911),x93918),x93917)))+~P1(f318(f318(f320(f917(x93911,x93911)),f318(f318(f243(x93911,x93911),x93918),x93916)),x93914))
% 109.14/108.86 [9821]~P22(x98216,x98212,x98215,x98217,x98218,x98211)+~P1(f318(f55(x98212),x98214))+~P1(f318(f55(x98212),x98213))+E(f318(x98211,f318(f318(f101(f918(x98212,a909)),x98213),x98214)),f318(f318(x98215,f318(x98211,x98213)),f318(x98211,x98214)))
% 109.14/108.86 [10396]~P25(x103964,x103962,x103965,x103968)+E(f318(f318(f34(x103961,f918(x103962,a909)),x103963),f318(f318(f10(f918(x103964,a909),f918(x103962,a909),x103961),f301(x103964,x103962,x103965)),x103966)),f318(f301(x103964,x103962,x103965),f318(f318(f34(x103961,f918(x103964,a909)),x103963),x103966)))+~P1(f318(f318(f320(x103961),x103967),x103963))+P1(f318(f318(f320(x103961),f510(x103967,x103966,x103963,x103961,x103968,x103965,x103962,x103964)),x103963))
% 109.14/108.86 [10432]~P25(x104324,x104322,x104325,x104327)+E(f318(f318(f34(x104321,f918(x104322,a909)),x104323),f318(f318(f10(f918(x104324,a909),f918(x104322,a909),x104321),f301(x104324,x104322,x104325)),x104326)),f318(f301(x104324,x104322,x104325),f318(f318(f34(x104321,f918(x104324,a909)),x104323),x104326)))+~P1(f318(f318(f320(x104321),x104328),x104323))+~P1(f318(f318(f225(f918(x104324,a909)),f318(x104326,f510(x104328,x104326,x104323,x104321,x104327,x104325,x104322,x104324))),x104327))
% 109.14/108.86 [10444]~P1(f318(f318(x104441,x104448),x104447))+P1(f318(f318(x104441,x104442),x104443))+~P1(f318(f318(f320(f917(f917(x104444,x104445),f917(x104444,x104445))),f318(f318(f243(f917(x104444,x104445),f917(x104444,x104445)),f318(f318(f243(x104444,x104445),x104442),x104443)),f318(f318(f243(x104444,x104445),x104448),x104447))),f298(f917(x104444,x104445),x104446)))+P1(f318(f318(f320(f917(f917(x104444,x104445),f917(x104444,x104445))),f318(f318(f243(f917(x104444,x104445),f917(x104444,x104445)),f318(f318(f243(x104444,x104445),f836(x104441,x104446,x104447,x104448,x104443,x104442,x104445,x104444)),f838(x104441,x104446,x104447,x104448,x104443,x104442,x104445,x104444))),f318(f318(f243(x104444,x104445),f835(x104441,x104446,x104447,x104448,x104443,x104442,x104445,x104444)),f839(x104441,x104446,x104447,x104448,x104443,x104442,x104445,x104444)))),x104446))
% 109.14/108.86 [10445]~P1(f318(f318(x104451,x104458),x104457))+P1(f318(f318(x104451,x104452),x104453))+~P1(f318(f318(f320(f917(f917(x104454,x104455),f917(x104454,x104455))),f318(f318(f243(f917(x104454,x104455),f917(x104454,x104455)),f318(f318(f243(x104454,x104455),x104458),x104457)),f318(f318(f243(x104454,x104455),x104452),x104453))),f298(f917(x104454,x104455),x104456)))+P1(f318(f318(f320(f917(f917(x104454,x104455),f917(x104454,x104455))),f318(f318(f243(f917(x104454,x104455),f917(x104454,x104455)),f318(f318(f243(x104454,x104455),f840(x104451,x104456,x104453,x104452,x104457,x104458,x104455,x104454)),f841(x104451,x104456,x104453,x104452,x104457,x104458,x104455,x104454))),f318(f318(f243(x104454,x104455),f842(x104451,x104456,x104453,x104452,x104457,x104458,x104455,x104454)),f843(x104451,x104456,x104453,x104452,x104457,x104458,x104455,x104454)))),x104456))
% 109.14/108.86 [9889]~P23(x98897,x98895,x98891,x98898,x98892,x98894)+~P1(f318(f55(x98895),x98896))+~P1(f318(f318(f320(x98895),x98893),x98896))+E(f318(f318(x98891,f318(x98892,x98893)),f318(x98894,f318(f318(f3(f918(x98895,a909)),x98896),f318(f318(f300(x98895),x98893),f179(f918(x98895,a909)))))),f318(x98894,x98896))
% 109.14/108.86 [9897]~P23(x98976,x98973,x98971,x98977,x98978,x98972)+~P1(f318(f55(x98973),x98975))+~P1(f318(f55(x98973),x98974))+E(f318(f318(x98971,f318(x98972,f318(f318(f101(f918(x98973,a909)),x98974),x98975))),f318(x98972,f318(f318(f92(f918(x98973,a909)),x98974),x98975))),f318(f318(x98971,f318(x98972,x98974)),f318(x98972,x98975)))
% 109.14/108.86 [9995]P45(x99951,x99952,x99953,x99954,x99955,f318(f318(x99953,x99956),x99957))+~P45(x99951,x99952,x99953,x99954,f318(f318(f3(f918(x99951,a909)),x99955),f318(f318(f300(x99951),x99958),f179(f918(x99951,a909)))),x99959)+~E(f318(f318(x99953,x99956),x99957),f318(f318(x99953,x99958),x99959))+~P1(f318(f318(f320(x99951),x99958),x99955))
% 109.14/108.86 [9923]~P12(x99236,x99237,x99238,x99239,x992310,x99231)+E(f318(f318(x99231,x99232),x99233),f318(f318(x99231,x99234),x99235))+~P1(f318(f318(f320(f917(x99237,x99237)),f318(f318(f243(x99237,x99237),x99233),x99235)),x992310))+~P1(f318(f318(f320(f917(x99236,x99236)),f318(f318(f243(x99236,x99236),x99232),x99234)),x99239))
% 109.14/108.86 [9651]E(x96511,f2(a1))+E(x96512,f2(a1))+E(f318(f318(f81(a1,f917(a1,a1)),f318(f318(a208,x96512),x96511)),f318(f318(f20(a1,a1,f917(a1,a1)),f318(f318(f10(a1,f918(a1,f917(a1,a1)),a1),f243(a1,a1)),f318(f30(a1),x96512))),f318(f30(a1),x96511))),f206(x96512,x96511))+P1(f318(f318(f226(a1),x96511),f2(a1)))+~P1(f318(f306(f917(a1,a1),a212),f318(f318(f243(a1,a1),x96512),x96511)))
% 109.14/108.86 [9500]~P103(x95002)+E(x95001,f179(f918(x95002,a909)))+~P1(f318(f55(x95002),x95001))+P1(f318(f318(f320(x95002),f12(x95002,x95001)),x95001))+~P1(f318(f318(f320(x95002),f318(f318(f92(x95002),f882(x95001,x95002)),f883(x95001,x95002))),f318(f318(f300(x95002),f882(x95001,x95002)),f318(f318(f300(x95002),f883(x95001,x95002)),f179(f918(x95002,a909))))))
% 109.14/108.86 [9501]~P103(x95012)+E(x95011,f179(f918(x95012,a909)))+~P1(f318(f55(x95012),x95011))+P1(f318(f318(f320(x95012),f15(x95012,x95011)),x95011))+~P1(f318(f318(f320(x95012),f318(f318(f101(x95012),f884(x95011,x95012)),f885(x95011,x95012))),f318(f318(f300(x95012),f884(x95011,x95012)),f318(f318(f300(x95012),f885(x95011,x95012)),f179(f918(x95012,a909))))))
% 109.14/108.86 [9502]~P4(x95022)+E(x95021,f179(f918(x95022,a909)))+~P1(f318(f55(x95022),x95021))+P1(f318(f318(f320(x95022),f16(x95022,x95021)),x95021))+~P1(f318(f318(f320(x95022),f318(f318(f223(x95022),f441(x95021,x95022)),f446(x95021,x95022))),f318(f318(f300(x95022),f441(x95021,x95022)),f318(f318(f300(x95022),f446(x95021,x95022)),f179(f918(x95022,a909))))))
% 109.14/108.86 [9503]~P4(x95032)+E(x95031,f179(f918(x95032,a909)))+~P1(f318(f55(x95032),x95031))+P1(f318(f318(f320(x95032),f17(x95032,x95031)),x95031))+~P1(f318(f318(f320(x95032),f318(f318(f224(x95032),f454(x95031,x95032)),f455(x95031,x95032))),f318(f318(f300(x95032),f454(x95031,x95032)),f318(f318(f300(x95032),f455(x95031,x95032)),f179(f918(x95032,a909))))))
% 109.14/108.86 [9538]~P80(x95382)+E(x95381,f179(f918(x95382,a909)))+~P1(f318(f55(x95382),x95381))+P1(f318(f318(f320(x95382),f318(f57(x95382,f74(x95382)),x95381)),x95381))+~P1(f318(f318(f320(x95382),f318(f318(f74(x95382),f397(x95381,x95382)),f399(x95381,x95382))),f318(f318(f300(x95382),f397(x95381,x95382)),f318(f318(f300(x95382),f399(x95381,x95382)),f179(f918(x95382,a909))))))
% 109.14/108.86 [9543]~P4(x95432)+E(x95431,f179(f918(x95432,a909)))+~P1(f318(f55(x95432),x95431))+P1(f318(f318(f320(x95432),f13(x95432,f223(x95432),x95431)),x95431))+~P1(f318(f318(f320(x95432),f318(f318(f223(x95432),f442(x95431,x95432)),f445(x95431,x95432))),f318(f318(f300(x95432),f442(x95431,x95432)),f318(f318(f300(x95432),f445(x95431,x95432)),f179(f918(x95432,a909))))))
% 109.14/108.86 [9544]~P4(x95442)+E(x95441,f179(f918(x95442,a909)))+~P1(f318(f55(x95442),x95441))+P1(f318(f318(f320(x95442),f14(x95442,f224(x95442),x95441)),x95441))+~P1(f318(f318(f320(x95442),f318(f318(f224(x95442),f456(x95441,x95442)),f457(x95441,x95442))),f318(f318(f300(x95442),f456(x95441,x95442)),f318(f318(f300(x95442),f457(x95441,x95442)),f179(f918(x95442,a909))))))
% 109.14/108.86 [6664]~P93(x66642)+E(x66641,f2(x66642))+~E(f318(f318(f73(x66642),x66643),x66641),f2(x66642))+~P1(f318(f318(f225(x66642),f2(x66642)),x66643))+~P1(f318(f318(f225(x66642),f2(x66642)),x66641))
% 109.14/108.86 [6665]~P93(x66652)+E(x66651,f2(x66652))+~E(f318(f318(f73(x66652),x66651),x66653),f2(x66652))+~P1(f318(f318(f225(x66652),f2(x66652)),x66653))+~P1(f318(f318(f225(x66652),f2(x66652)),x66651))
% 109.14/108.86 [7203]~P4(x72032)+~P13(x72032,x72031)+E(x72031,f104(x72032))+~P1(f318(f318(f320(x72032),x72033),f318(f163(x72032),f703(x72031,x72032))))+P1(f318(f318(f225(x72032),f722(x72031,x72032)),x72033))
% 109.14/108.86 [7373]~P4(x73731)+E(f16(x73731,x73732),x73733)+~P1(f318(f55(x73731),x73732))+~P1(f318(f318(f225(x73731),x73733),f460(x73733,x73732,x73731)))+~P1(f318(f318(f320(x73731),x73733),x73732))
% 109.14/108.86 [7406]~P4(x74061)+~P13(x74061,x74062)+~P13(x74061,x74063)+P13(x74061,f318(f318(f125(x74061),x74062),x74063))+P1(f318(f318(f320(x74061),f709(x74063,x74062,x74061)),f318(f163(x74061),x74062)))
% 109.14/108.86 [7407]~P4(x74071)+~P13(x74071,x74072)+~P13(x74071,x74073)+P13(x74071,f318(f318(f125(x74071),x74072),x74073))+P1(f318(f318(f320(x74071),f710(x74073,x74072,x74071)),f318(f163(x74071),x74073)))
% 109.14/108.86 [7466]~P4(x74661)+E(f16(x74661,x74662),x74663)+~P1(f318(f55(x74661),x74662))+P1(f318(f318(f320(x74661),f460(x74663,x74662,x74661)),x74662))+~P1(f318(f318(f320(x74661),x74663),x74662))
% 109.14/108.86 [7467]~P4(x74671)+E(f17(x74671,x74672),x74673)+~P1(f318(f55(x74671),x74672))+P1(f318(f318(f320(x74671),f448(x74673,x74672,x74671)),x74672))+~P1(f318(f318(f320(x74671),x74673),x74672))
% 109.14/108.86 [8026]~P4(x80261)+E(f17(x80261,x80262),x80263)+~P1(f318(f55(x80261),x80262))+~P1(f318(f318(f320(x80261),x80263),x80262))+~P1(f318(f318(f225(x80261),f448(x80263,x80262,x80261)),x80263))
% 109.14/108.86 [8347]~P4(x83471)+~P13(x83471,x83472)+~P13(x83471,x83473)+P13(x83471,f318(f318(f125(x83471),x83472),x83473))+~P1(f318(f318(f225(x83471),f709(x83473,x83472,x83471)),f710(x83473,x83472,x83471)))
% 109.14/108.86 [9136]~P103(x91362)+E(x91361,f179(f918(x91362,a909)))+~E(f318(f318(f92(x91362),f318(x91363,f891(x91361,x91363,x91362))),f318(x91363,f892(x91361,x91363,x91362))),f318(x91363,f318(f318(f92(x91362),f891(x91361,x91363,x91362)),f892(x91361,x91363,x91362))))+E(f12(x91362,f318(f301(x91362,x91362,x91363),x91361)),f318(x91363,f12(x91362,x91361)))+~P1(f318(f55(x91362),x91361))
% 109.14/108.86 [9137]~P103(x91372)+E(x91371,f179(f918(x91372,a909)))+~E(f318(f318(f101(x91372),f318(x91373,f893(x91371,x91373,x91372))),f318(x91373,f894(x91371,x91373,x91372))),f318(x91373,f318(f318(f101(x91372),f893(x91371,x91373,x91372)),f894(x91371,x91373,x91372))))+E(f15(x91372,f318(f301(x91372,x91372,x91373),x91371)),f318(x91373,f15(x91372,x91371)))+~P1(f318(f55(x91372),x91371))
% 109.14/108.86 [9138]~P4(x91382)+E(x91381,f179(f918(x91382,a909)))+~E(f318(f318(f223(x91382),f318(x91383,f449(x91381,x91383,x91382))),f318(x91383,f451(x91381,x91383,x91382))),f318(x91383,f318(f318(f223(x91382),f449(x91381,x91383,x91382)),f451(x91381,x91383,x91382))))+E(f16(x91382,f318(f301(x91382,x91382,x91383),x91381)),f318(x91383,f16(x91382,x91381)))+~P1(f318(f55(x91382),x91381))
% 109.14/108.86 [9139]~P4(x91392)+E(x91391,f179(f918(x91392,a909)))+~E(f318(f318(f224(x91392),f318(x91393,f461(x91391,x91393,x91392))),f318(x91393,f463(x91391,x91393,x91392))),f318(x91393,f318(f318(f224(x91392),f461(x91391,x91393,x91392)),f463(x91391,x91393,x91392))))+E(f17(x91392,f318(f301(x91392,x91392,x91393),x91391)),f318(x91393,f17(x91392,x91391)))+~P1(f318(f55(x91392),x91391))
% 109.14/108.86 [9203]~P4(x92032)+E(x92031,f179(f918(x92032,a909)))+~E(f318(f318(f223(x92032),f318(x92033,f440(x92031,x92033,x92032))),f318(x92033,f450(x92031,x92033,x92032))),f318(x92033,f318(f318(f223(x92032),f440(x92031,x92033,x92032)),f450(x92031,x92033,x92032))))+E(f13(x92032,f223(x92032),f318(f301(x92032,x92032,x92033),x92031)),f318(x92033,f13(x92032,f223(x92032),x92031)))+~P1(f318(f55(x92032),x92031))
% 109.14/108.86 [9204]~P4(x92042)+E(x92041,f179(f918(x92042,a909)))+~E(f318(f318(f224(x92042),f318(x92043,f453(x92041,x92043,x92042))),f318(x92043,f462(x92041,x92043,x92042))),f318(x92043,f318(f318(f224(x92042),f453(x92041,x92043,x92042)),f462(x92041,x92043,x92042))))+E(f14(x92042,f224(x92042),f318(f301(x92042,x92042,x92043),x92041)),f318(x92043,f14(x92042,f224(x92042),x92041)))+~P1(f318(f55(x92042),x92041))
% 109.14/108.86 [6305]~P103(x63052)+E(x63051,f179(f918(x63052,a909)))+~P1(f318(f55(x63052),x63051))+E(f12(x63052,f318(f318(f300(x63052),x63053),x63051)),f318(f318(f92(x63052),x63053),f12(x63052,x63051)))+P1(f318(f318(f320(x63052),x63053),x63051))
% 109.14/108.86 [6306]~P103(x63062)+E(x63061,f179(f918(x63062,a909)))+~P1(f318(f55(x63062),x63061))+E(f15(x63062,f318(f318(f300(x63062),x63063),x63061)),f318(f318(f101(x63062),x63063),f15(x63062,x63061)))+P1(f318(f318(f320(x63062),x63063),x63061))
% 109.14/108.86 [6307]~P4(x63072)+E(x63071,f179(f918(x63072,a909)))+~P1(f318(f55(x63072),x63071))+E(f16(x63072,f318(f318(f300(x63072),x63073),x63071)),f318(f318(f223(x63072),x63073),f16(x63072,x63071)))+P1(f318(f318(f320(x63072),x63073),x63071))
% 109.14/108.86 [6308]~P4(x63082)+E(x63081,f179(f918(x63082,a909)))+~P1(f318(f55(x63082),x63081))+E(f17(x63082,f318(f318(f300(x63082),x63083),x63081)),f318(f318(f224(x63082),x63083),f17(x63082,x63081)))+P1(f318(f318(f320(x63082),x63083),x63081))
% 109.14/108.86 [6683]~P80(x66832)+E(x66831,f179(f918(x66832,a909)))+~P1(f318(f55(x66832),x66831))+E(f318(f57(x66832,f74(x66832)),f318(f318(f300(x66832),x66833),x66831)),f318(f318(f74(x66832),x66833),f318(f57(x66832,f74(x66832)),x66831)))+P1(f318(f318(f320(x66832),x66833),x66831))
% 109.14/108.86 [6772]~P4(x67722)+E(x67721,f179(f918(x67722,a909)))+~P1(f318(f55(x67722),x67721))+E(f13(x67722,f223(x67722),f318(f318(f300(x67722),x67723),x67721)),f318(f318(f223(x67722),x67723),f13(x67722,f223(x67722),x67721)))+P1(f318(f318(f320(x67722),x67723),x67721))
% 109.14/108.86 [6773]~P4(x67732)+E(x67731,f179(f918(x67732,a909)))+~P1(f318(f55(x67732),x67731))+E(f14(x67732,f224(x67732),f318(f318(f300(x67732),x67733),x67731)),f318(f318(f224(x67732),x67733),f14(x67732,f224(x67732),x67731)))+P1(f318(f318(f320(x67732),x67733),x67731))
% 109.14/108.86 [7209]~P103(x72092)+E(f318(f318(f101(x72092),f15(x72092,x72091)),f15(x72092,x72093)),f15(x72092,x72093))+E(x72091,f179(f918(x72092,a909)))+~P1(f318(f55(x72092),x72093))+~P1(f318(f318(f225(f918(x72092,a909)),x72091),x72093))
% 109.14/108.86 [7210]~P103(x72102)+E(f318(f318(f92(x72102),f12(x72102,x72101)),f12(x72102,x72103)),f12(x72102,x72103))+E(x72101,f179(f918(x72102,a909)))+~P1(f318(f55(x72102),x72103))+~P1(f318(f318(f225(f918(x72102,a909)),x72101),x72103))
% 109.14/108.86 [7211]~P4(x72112)+E(f318(f318(f223(x72112),f16(x72112,x72111)),f16(x72112,x72113)),f16(x72112,x72113))+E(x72111,f179(f918(x72112,a909)))+~P1(f318(f55(x72112),x72113))+~P1(f318(f318(f225(f918(x72112,a909)),x72111),x72113))
% 109.14/108.86 [7212]~P4(x72122)+E(f318(f318(f224(x72122),f17(x72122,x72121)),f17(x72122,x72123)),f17(x72122,x72123))+E(x72121,f179(f918(x72122,a909)))+~P1(f318(f55(x72122),x72123))+~P1(f318(f318(f225(f918(x72122,a909)),x72121),x72123))
% 109.14/108.86 [7508]~P4(x75082)+E(x75081,f179(f918(x75082,a909)))+~P1(f318(f55(x75082),x75083))+P1(f318(f318(f225(x75082),f16(x75082,x75083)),f16(x75082,x75081)))+~P1(f318(f318(f225(f918(x75082,a909)),x75081),x75083))
% 109.14/108.86 [7509]~P4(x75092)+E(x75091,f179(f918(x75092,a909)))+~P1(f318(f55(x75092),x75093))+P1(f318(f318(f225(x75092),f17(x75092,x75091)),f17(x75092,x75093)))+~P1(f318(f318(f225(f918(x75092,a909)),x75091),x75093))
% 109.14/108.86 [7560]~P103(x75601)+E(f12(x75601,x75602),x75603)+~P1(f318(f55(x75601),x75602))+~E(f318(f318(f3(f918(x75601,a909)),x75602),f318(f318(f300(x75601),x75603),f179(f918(x75601,a909)))),f179(f918(x75601,a909)))+~P1(f318(f318(f320(x75601),x75603),x75602))
% 109.14/108.86 [7561]~P103(x75611)+E(f15(x75611,x75612),x75613)+~P1(f318(f55(x75611),x75612))+~E(f318(f318(f3(f918(x75611,a909)),x75612),f318(f318(f300(x75611),x75613),f179(f918(x75611,a909)))),f179(f918(x75611,a909)))+~P1(f318(f318(f320(x75611),x75613),x75612))
% 109.14/108.86 [7562]~P4(x75621)+E(f16(x75621,x75622),x75623)+~P1(f318(f55(x75621),x75622))+~E(f318(f318(f3(f918(x75621,a909)),x75622),f318(f318(f300(x75621),x75623),f179(f918(x75621,a909)))),f179(f918(x75621,a909)))+~P1(f318(f318(f320(x75621),x75623),x75622))
% 109.14/108.86 [7563]~P4(x75631)+E(f17(x75631,x75632),x75633)+~P1(f318(f55(x75631),x75632))+~E(f318(f318(f3(f918(x75631,a909)),x75632),f318(f318(f300(x75631),x75633),f179(f918(x75631,a909)))),f179(f918(x75631,a909)))+~P1(f318(f318(f320(x75631),x75633),x75632))
% 109.14/108.86 [7657]~P4(x76571)+E(f13(x76571,f223(x76571),x76572),x76573)+~P1(f318(f55(x76571),x76572))+~E(f318(f318(f3(f918(x76571,a909)),x76572),f318(f318(f300(x76571),x76573),f179(f918(x76571,a909)))),f179(f918(x76571,a909)))+~P1(f318(f318(f320(x76571),x76573),x76572))
% 109.14/108.86 [7658]~P4(x76581)+E(f14(x76581,f224(x76581),x76582),x76583)+~P1(f318(f55(x76581),x76582))+~E(f318(f318(f3(f918(x76581,a909)),x76582),f318(f318(f300(x76581),x76583),f179(f918(x76581,a909)))),f179(f918(x76581,a909)))+~P1(f318(f318(f320(x76581),x76583),x76582))
% 109.14/108.86 [7693]~P108(x76932)+E(x76931,f179(f918(x76932,a909)))+~P1(f318(f55(x76932),x76931))+~P1(f318(f318(f225(x76932),x76933),f395(x76933,x76931,x76932)))+P1(f318(f318(f225(x76932),x76933),f318(f57(x76932,f92(x76932)),x76931)))
% 109.14/108.86 [7694]~P4(x76942)+E(x76941,f179(f918(x76942,a909)))+~P1(f318(f55(x76942),x76941))+~P1(f318(f318(f225(x76942),x76943),f433(x76943,x76941,x76942)))+P1(f318(f318(f225(x76942),x76943),f318(f57(x76942,f223(x76942)),x76941)))
% 109.14/108.86 [7695]~P4(x76952)+E(x76951,f179(f918(x76952,a909)))+~P1(f318(f55(x76952),x76951))+~P1(f318(f318(f226(x76952),x76953),f437(x76953,x76951,x76952)))+P1(f318(f318(f226(x76952),x76953),f318(f57(x76952,f223(x76952)),x76951)))
% 109.14/108.86 [7779]~P108(x77792)+E(x77791,f179(f918(x77792,a909)))+~P1(f318(f55(x77792),x77791))+P1(f318(f318(f320(x77792),f395(x77793,x77791,x77792)),x77791))+P1(f318(f318(f225(x77792),x77793),f318(f57(x77792,f92(x77792)),x77791)))
% 109.14/108.86 [7780]~P4(x77802)+E(x77801,f179(f918(x77802,a909)))+~P1(f318(f55(x77802),x77801))+P1(f318(f318(f320(x77802),f433(x77803,x77801,x77802)),x77801))+P1(f318(f318(f225(x77802),x77803),f318(f57(x77802,f223(x77802)),x77801)))
% 109.14/108.86 [7781]~P4(x77812)+E(x77811,f179(f918(x77812,a909)))+~P1(f318(f55(x77812),x77811))+P1(f318(f318(f320(x77812),f437(x77813,x77811,x77812)),x77811))+P1(f318(f318(f226(x77812),x77813),f318(f57(x77812,f223(x77812)),x77811)))
% 109.14/108.86 [7903]~P4(x79032)+E(x79031,f179(f918(x79032,a909)))+E(f318(f318(f223(x79032),f13(x79032,f223(x79032),x79031)),f13(x79032,f223(x79032),x79033)),f13(x79032,f223(x79032),x79033))+~P1(f318(f55(x79032),x79033))+~P1(f318(f318(f225(f918(x79032,a909)),x79031),x79033))
% 109.14/108.86 [7904]~P4(x79042)+E(x79041,f179(f918(x79042,a909)))+E(f318(f318(f224(x79042),f14(x79042,f224(x79042),x79041)),f14(x79042,f224(x79042),x79043)),f14(x79042,f224(x79042),x79043))+~P1(f318(f55(x79042),x79043))+~P1(f318(f318(f225(f918(x79042,a909)),x79041),x79043))
% 109.14/108.86 [8100]~E(f387(x81001,x81003,x81002),f388(x81001,x81003,x81002))+~E(f318(f29(x81002),f389(x81001,x81003,x81002)),x81001)+E(f318(f318(f74(a911),x81001),f318(f29(f918(x81002,a909)),x81003)),f318(f29(x81002),f31(f918(x81002,a909),x81003)))+~P1(f318(f55(x81002),f31(f918(x81002,a909),x81003)))+~P1(f318(f55(f918(x81002,a909)),x81003))
% 109.14/108.86 [8286]~P4(x82862)+E(x82861,f179(f918(x82862,a909)))+~P1(f318(f55(x82862),x82863))+P1(f318(f318(f225(x82862),f318(f57(x82862,f223(x82862)),x82863)),f318(f57(x82862,f223(x82862)),x82861)))+~P1(f318(f318(f225(f918(x82862,a909)),x82861),x82863))
% 109.14/108.86 [8580]~E(f387(x85801,x85803,x85802),f388(x85801,x85803,x85802))+E(f318(f318(f74(a911),x85801),f318(f29(f918(x85802,a909)),x85803)),f318(f29(x85802),f31(f918(x85802,a909),x85803)))+P1(f318(f318(f320(f918(x85802,a909)),f389(x85801,x85803,x85802)),x85803))+~P1(f318(f55(x85802),f31(f918(x85802,a909),x85803)))+~P1(f318(f55(f918(x85802,a909)),x85803))
% 109.14/108.86 [8607]~E(f318(f29(x86072),f389(x86071,x86073,x86072)),x86071)+E(f318(f318(f74(a911),x86071),f318(f29(f918(x86072,a909)),x86073)),f318(f29(x86072),f31(f918(x86072,a909),x86073)))+P1(f318(f318(f320(f918(x86072,a909)),f388(x86071,x86073,x86072)),x86073))+~P1(f318(f55(x86072),f31(f918(x86072,a909),x86073)))+~P1(f318(f55(f918(x86072,a909)),x86073))
% 109.14/108.86 [8608]~E(f318(f29(x86082),f389(x86081,x86083,x86082)),x86081)+E(f318(f318(f74(a911),x86081),f318(f29(f918(x86082,a909)),x86083)),f318(f29(x86082),f31(f918(x86082,a909),x86083)))+P1(f318(f318(f320(f918(x86082,a909)),f387(x86081,x86083,x86082)),x86083))+~P1(f318(f55(x86082),f31(f918(x86082,a909),x86083)))+~P1(f318(f55(f918(x86082,a909)),x86083))
% 109.14/108.86 [8633]~E(f318(f29(x86332),f389(x86331,x86333,x86332)),x86331)+~E(f318(f318(f92(f918(x86332,a909)),f388(x86331,x86333,x86332)),f387(x86331,x86333,x86332)),f179(f918(x86332,a909)))+E(f318(f318(f74(a911),x86331),f318(f29(f918(x86332,a909)),x86333)),f318(f29(x86332),f31(f918(x86332,a909),x86333)))+~P1(f318(f55(f918(x86332,a909)),x86333))+~P1(f318(f55(x86332),f31(f918(x86332,a909),x86333)))
% 109.14/108.86 [8895]E(f318(f318(f74(a911),x88951),f318(f29(f918(x88952,a909)),x88953)),f318(f29(x88952),f31(f918(x88952,a909),x88953)))+P1(f318(f318(f320(f918(x88952,a909)),f389(x88951,x88953,x88952)),x88953))+P1(f318(f318(f320(f918(x88952,a909)),f388(x88951,x88953,x88952)),x88953))+~P1(f318(f55(f918(x88952,a909)),x88953))+~P1(f318(f55(x88952),f31(f918(x88952,a909),x88953)))
% 109.14/108.86 [8896]E(f318(f318(f74(a911),x88961),f318(f29(f918(x88962,a909)),x88963)),f318(f29(x88962),f31(f918(x88962,a909),x88963)))+P1(f318(f318(f320(f918(x88962,a909)),f389(x88961,x88963,x88962)),x88963))+P1(f318(f318(f320(f918(x88962,a909)),f387(x88961,x88963,x88962)),x88963))+~P1(f318(f55(f918(x88962,a909)),x88963))+~P1(f318(f55(x88962),f31(f918(x88962,a909),x88963)))
% 109.14/108.86 [8921]~E(f318(f318(f92(f918(x89212,a909)),f388(x89211,x89213,x89212)),f387(x89211,x89213,x89212)),f179(f918(x89212,a909)))+E(f318(f318(f74(a911),x89211),f318(f29(f918(x89212,a909)),x89213)),f318(f29(x89212),f31(f918(x89212,a909),x89213)))+~P1(f318(f55(f918(x89212,a909)),x89213))+P1(f318(f318(f320(f918(x89212,a909)),f389(x89211,x89213,x89212)),x89213))+~P1(f318(f55(x89212),f31(f918(x89212,a909),x89213)))
% 109.14/108.86 [9182]~P101(x91822)+E(x91821,f179(f918(x91822,a909)))+~E(f318(f318(f74(x91822),f318(x91823,f396(x91821,x91823,x91822))),f318(x91823,f400(x91821,x91823,x91822))),f318(x91823,f318(f318(f74(x91822),f396(x91821,x91823,x91822)),f400(x91821,x91823,x91822))))+~P1(f318(f55(x91822),x91821))+E(f318(f57(x91822,f74(x91822)),f318(f301(x91822,x91822,x91823),x91821)),f318(x91823,f318(f57(x91822,f74(x91822)),x91821)))
% 109.14/108.86 [10341]P1(f318(f318(x103411,x103412),x103413))+P1(f318(f318(f226(a1),f490(x103411,x103413,x103412)),f492(x103411,x103413,x103412)))+P1(f318(f318(f225(a1),f492(x103411,x103413,x103412)),f2(a1)))+P1(f318(f318(x103411,f490(x103411,x103413,x103412)),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f492(x103411,x103413,x103412))))+~P1(f318(f306(f917(a1,a1),a52),f318(f318(f243(a1,a1),x103412),x103413)))
% 109.14/108.86 [10342]P1(f318(f318(x103421,x103422),x103423))+P1(f318(f318(f225(a1),f489(x103421,x103423,x103422)),f2(a1)))+P1(f318(f318(x103421,f485(x103421,x103423,x103422)),f318(f318(f74(a1),f318(f94(a1),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f489(x103421,x103423,x103422))))+P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),f485(x103421,x103423,x103422)),f489(x103421,x103423,x103422))))+~P1(f318(f306(f917(a1,a1),a46),f318(f318(f243(a1,a1),x103422),x103423)))
% 109.14/108.86 [8072]~P116(x80721)+~P1(f318(f318(f225(x80721),x80722),f71(x80721)))+~P1(f318(f318(f225(x80721),f2(x80721)),x80722))+~P1(f318(f318(f225(x80721),f2(x80721)),x80723))+P1(f318(f318(f225(x80721),f318(f318(f74(x80721),x80722),x80723)),x80723))
% 109.14/108.86 [8073]~P116(x80731)+~P1(f318(f318(f225(x80731),x80733),f71(x80731)))+~P1(f318(f318(f225(x80731),f2(x80731)),x80733))+~P1(f318(f318(f225(x80731),f2(x80731)),x80732))+P1(f318(f318(f225(x80731),f318(f318(f74(x80731),x80732),x80733)),x80732))
% 109.14/108.86 [8429]~P4(x84292)+E(x84291,f179(f918(x84292,a909)))+~P1(f318(f55(x84292),x84291))+P1(f318(f318(f225(x84292),f438(x84293,x84291,x84292)),x84293))+~P1(f318(f318(f225(x84292),f318(f57(x84292,f223(x84292)),x84291)),x84293))
% 109.14/108.86 [8430]~P4(x84302)+E(x84301,f179(f918(x84302,a909)))+~P1(f318(f55(x84302),x84301))+P1(f318(f318(f320(x84302),f438(x84303,x84301,x84302)),x84301))+~P1(f318(f318(f225(x84302),f318(f57(x84302,f223(x84302)),x84301)),x84303))
% 109.14/108.86 [8431]~P4(x84312)+E(x84311,f179(f918(x84312,a909)))+~P1(f318(f55(x84312),x84311))+P1(f318(f318(f320(x84312),f439(x84313,x84311,x84312)),x84311))+~P1(f318(f318(f226(x84312),f318(f57(x84312,f223(x84312)),x84311)),x84313))
% 109.14/108.86 [8432]~P4(x84322)+E(x84321,f179(f918(x84322,a909)))+~P1(f318(f55(x84322),x84321))+P1(f318(f318(f226(x84322),f439(x84323,x84321,x84322)),x84323))+~P1(f318(f318(f226(x84322),f318(f57(x84322,f223(x84322)),x84321)),x84323))
% 109.14/108.86 [8515]~P1(f318(x85151,x85153))+P1(f318(x85151,f378(x85151,x85152)))+P1(f318(x85151,f377(x85151,x85152)))+~P1(f318(f318(f226(a1),f2(a1)),x85152))+P1(f318(x85151,f318(f318(f3(a1),f377(x85151,x85152)),f318(f318(f74(a1),f379(x85151,x85152)),x85152))))
% 109.14/108.86 [8737]~P1(f318(x87371,x87373))+P1(f318(x87371,f377(x87371,x87372)))+~P1(f318(f318(f226(a1),f2(a1)),x87372))+P1(f318(f318(f320(a1),f378(x87371,x87372)),f294(a1,f71(a1),x87372)))+P1(f318(x87371,f318(f318(f3(a1),f377(x87371,x87372)),f318(f318(f74(a1),f379(x87371,x87372)),x87372))))
% 109.14/108.86 [8942]~P1(f318(x89421,x89423))+~P1(f318(x89421,f377(x89421,x89422)))+P1(f318(x89421,f378(x89421,x89422)))+~P1(f318(f318(f226(a1),f2(a1)),x89422))+~P1(f318(x89421,f318(f318(f3(a1),f377(x89421,x89422)),f318(f318(f74(a1),f379(x89421,x89422)),x89422))))
% 109.14/108.86 [9073]~P1(f318(x90731,x90733))+~P1(f318(x90731,f377(x90731,x90732)))+~P1(f318(f318(f226(a1),f2(a1)),x90732))+P1(f318(f318(f320(a1),f378(x90731,x90732)),f294(a1,f71(a1),x90732)))+~P1(f318(x90731,f318(f318(f3(a1),f377(x90731,x90732)),f318(f318(f74(a1),f379(x90731,x90732)),x90732))))
% 109.14/108.86 [8848]~P103(x88481)+~P1(f318(f55(x88481),x88482))+E(f318(f318(f3(f918(x88481,a909)),x88482),f318(f318(f300(x88481),x88483),f179(f918(x88481,a909)))),f179(f918(x88481,a909)))+~P1(f318(f318(f320(x88481),x88483),x88482))+E(f318(f318(f92(x88481),x88483),f12(x88481,f318(f318(f3(f918(x88481,a909)),x88482),f318(f318(f300(x88481),x88483),f179(f918(x88481,a909)))))),f12(x88481,x88482))
% 109.14/108.86 [8849]~P103(x88491)+~P1(f318(f55(x88491),x88492))+E(f318(f318(f3(f918(x88491,a909)),x88492),f318(f318(f300(x88491),x88493),f179(f918(x88491,a909)))),f179(f918(x88491,a909)))+~P1(f318(f318(f320(x88491),x88493),x88492))+E(f318(f318(f101(x88491),x88493),f15(x88491,f318(f318(f3(f918(x88491,a909)),x88492),f318(f318(f300(x88491),x88493),f179(f918(x88491,a909)))))),f15(x88491,x88492))
% 109.14/108.86 [8850]~P4(x88501)+~P1(f318(f55(x88501),x88502))+E(f318(f318(f3(f918(x88501,a909)),x88502),f318(f318(f300(x88501),x88503),f179(f918(x88501,a909)))),f179(f918(x88501,a909)))+~P1(f318(f318(f320(x88501),x88503),x88502))+E(f318(f318(f223(x88501),x88503),f16(x88501,f318(f318(f3(f918(x88501,a909)),x88502),f318(f318(f300(x88501),x88503),f179(f918(x88501,a909)))))),f16(x88501,x88502))
% 109.14/108.86 [8851]~P4(x88511)+~P1(f318(f55(x88511),x88512))+E(f318(f318(f3(f918(x88511,a909)),x88512),f318(f318(f300(x88511),x88513),f179(f918(x88511,a909)))),f179(f918(x88511,a909)))+~P1(f318(f318(f320(x88511),x88513),x88512))+E(f318(f318(f224(x88511),x88513),f17(x88511,f318(f318(f3(f918(x88511,a909)),x88512),f318(f318(f300(x88511),x88513),f179(f918(x88511,a909)))))),f17(x88511,x88512))
% 109.14/108.86 [8912]~P4(x89121)+~P1(f318(f55(x89121),x89122))+E(f318(f318(f3(f918(x89121,a909)),x89122),f318(f318(f300(x89121),x89123),f179(f918(x89121,a909)))),f179(f918(x89121,a909)))+~P1(f318(f318(f320(x89121),x89123),x89122))+E(f318(f318(f223(x89121),x89123),f13(x89121,f223(x89121),f318(f318(f3(f918(x89121,a909)),x89122),f318(f318(f300(x89121),x89123),f179(f918(x89121,a909)))))),f13(x89121,f223(x89121),x89122))
% 109.14/108.86 [8913]~P4(x89131)+~P1(f318(f55(x89131),x89132))+E(f318(f318(f3(f918(x89131,a909)),x89132),f318(f318(f300(x89131),x89133),f179(f918(x89131,a909)))),f179(f918(x89131,a909)))+~P1(f318(f318(f320(x89131),x89133),x89132))+E(f318(f318(f224(x89131),x89133),f14(x89131,f224(x89131),f318(f318(f3(f918(x89131,a909)),x89132),f318(f318(f300(x89131),x89133),f179(f918(x89131,a909)))))),f14(x89131,f224(x89131),x89132))
% 109.14/108.86 [8929]~P103(x89291)+~P1(f318(f55(x89291),x89293))+~P1(f318(f55(x89291),x89292))+E(f318(f318(f92(f918(x89291,a909)),x89292),x89293),f179(f918(x89291,a909)))+E(f318(f318(f101(x89291),f15(x89291,f318(f318(f101(f918(x89291,a909)),x89292),x89293))),f15(x89291,f318(f318(f92(f918(x89291,a909)),x89292),x89293))),f318(f318(f101(x89291),f15(x89291,x89292)),f15(x89291,x89293)))
% 109.14/108.86 [8930]~P103(x89301)+~P1(f318(f55(x89301),x89303))+~P1(f318(f55(x89301),x89302))+E(f318(f318(f92(f918(x89301,a909)),x89302),x89303),f179(f918(x89301,a909)))+E(f318(f318(f92(x89301),f12(x89301,f318(f318(f101(f918(x89301,a909)),x89302),x89303))),f12(x89301,f318(f318(f92(f918(x89301,a909)),x89302),x89303))),f318(f318(f92(x89301),f12(x89301,x89302)),f12(x89301,x89303)))
% 109.14/108.86 [8931]~P4(x89311)+~P1(f318(f55(x89311),x89313))+~P1(f318(f55(x89311),x89312))+E(f318(f318(f92(f918(x89311,a909)),x89312),x89313),f179(f918(x89311,a909)))+E(f318(f318(f223(x89311),f16(x89311,f318(f318(f101(f918(x89311,a909)),x89312),x89313))),f16(x89311,f318(f318(f92(f918(x89311,a909)),x89312),x89313))),f318(f318(f223(x89311),f16(x89311,x89312)),f16(x89311,x89313)))
% 109.14/108.86 [8932]~P4(x89321)+~P1(f318(f55(x89321),x89323))+~P1(f318(f55(x89321),x89322))+E(f318(f318(f92(f918(x89321,a909)),x89322),x89323),f179(f918(x89321,a909)))+E(f318(f318(f224(x89321),f17(x89321,f318(f318(f101(f918(x89321,a909)),x89322),x89323))),f17(x89321,f318(f318(f92(f918(x89321,a909)),x89322),x89323))),f318(f318(f224(x89321),f17(x89321,x89322)),f17(x89321,x89323)))
% 109.14/108.86 [9154]~P4(x91541)+~P1(f318(f55(x91541),x91543))+~P1(f318(f55(x91541),x91542))+E(f318(f318(f92(f918(x91541,a909)),x91542),x91543),f179(f918(x91541,a909)))+E(f318(f318(f223(x91541),f13(x91541,f223(x91541),f318(f318(f101(f918(x91541,a909)),x91542),x91543))),f13(x91541,f223(x91541),f318(f318(f92(f918(x91541,a909)),x91542),x91543))),f318(f318(f223(x91541),f13(x91541,f223(x91541),x91542)),f13(x91541,f223(x91541),x91543)))
% 109.14/108.86 [9155]~P4(x91551)+~P1(f318(f55(x91551),x91553))+~P1(f318(f55(x91551),x91552))+E(f318(f318(f92(f918(x91551,a909)),x91552),x91553),f179(f918(x91551,a909)))+E(f318(f318(f224(x91551),f14(x91551,f224(x91551),f318(f318(f101(f918(x91551,a909)),x91552),x91553))),f14(x91551,f224(x91551),f318(f318(f92(f918(x91551,a909)),x91552),x91553))),f318(f318(f224(x91551),f14(x91551,f224(x91551),x91552)),f14(x91551,f224(x91551),x91553)))
% 109.14/108.86 [10247]~P130(x102473)+E(x102471,x102472)+~P1(f318(f318(f225(x102473),f2(x102473)),x102472))+~P1(f318(f318(f225(x102473),f2(x102473)),x102471))+~E(f318(f318(f235(x102473),x102471),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))),f318(f318(f235(x102473),x102472),f318(f94(a911),f318(f318(f73(a1),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),f318(f318(f73(a1),f318(f318(f73(a1),f71(a1)),a76)),a76))),a88))))
% 109.14/108.86 [5215]~P100(x52151)+~P72(x52151)+~E(x52154,f2(x52151))+~E(f318(f94(x52151),x52152),f2(x52151))+E(f318(f94(x52151),x52152),f318(f318(f282(x52151),x52153),x52154))
% 109.14/108.86 [5216]~P100(x52161)+~P72(x52161)+~E(x52163,f2(x52161))+~E(f318(f94(x52161),x52164),f2(x52161))+E(f318(f318(f282(x52161),x52162),x52163),f318(f94(x52161),x52164))
% 109.14/108.86 [5308]~P100(x53082)+~P72(x53082)+~E(x53081,f2(x53082))+~E(f318(f94(x53082),x53084),f2(x53082))+E(x53081,f318(f318(f282(x53082),x53083),f318(f94(x53082),x53084)))
% 109.14/108.86 [5309]~P100(x53091)+~P72(x53091)+~E(x53094,f2(x53091))+~E(f318(f94(x53091),x53093),f2(x53091))+E(f318(f318(f282(x53091),x53092),f318(f94(x53091),x53093)),x53094)
% 109.14/108.86 [5341]~P100(x53411)+~P72(x53411)+~E(x53413,f2(x53411))+E(f318(f94(x53411),x53412),f2(x53411))+~E(f318(f94(x53411),x53412),f318(f318(f282(x53411),x53414),x53413))
% 109.14/108.86 [5342]~P100(x53421)+~P72(x53421)+~E(x53423,f2(x53421))+E(f318(f94(x53421),x53422),f2(x53421))+~E(f318(f318(f282(x53421),x53424),x53423),f318(f94(x53421),x53422))
% 109.14/108.86 [5507]~P100(x55072)+~P72(x55072)+E(x55071,f2(x55072))+~E(f318(f94(x55072),x55073),f2(x55072))+~E(x55071,f318(f318(f282(x55072),x55074),f318(f94(x55072),x55073)))
% 109.14/108.86 [5508]~P100(x55082)+~P72(x55082)+E(x55081,f2(x55082))+~E(f318(f94(x55082),x55083),f2(x55082))+~E(f318(f318(f282(x55082),x55084),f318(f94(x55082),x55083)),x55081)
% 109.14/108.86 [5739]~P100(x57392)+~P72(x57392)+~E(x57391,f2(x57392))+E(x57391,f318(f318(f282(x57392),x57393),f318(f94(x57392),x57394)))+~E(f318(f318(f74(x57392),x57391),f318(f94(x57392),x57394)),x57393)
% 109.14/108.86 [5740]~P100(x57401)+~P72(x57401)+~E(x57404,f2(x57401))+~E(x57402,f318(f318(f74(x57401),x57404),f318(f94(x57401),x57403)))+E(f318(f318(f282(x57401),x57402),f318(f94(x57401),x57403)),x57404)
% 109.14/108.86 [5806]~P100(x58061)+~P72(x58061)+E(f318(f94(x58061),x58062),f2(x58061))+~E(f318(f318(f282(x58061),x58063),f318(f94(x58061),x58062)),x58064)+E(x58063,f318(f318(f74(x58061),x58064),f318(f94(x58061),x58062)))
% 109.14/108.86 [5807]~P100(x58071)+~P72(x58071)+E(f318(f94(x58071),x58072),f2(x58071))+~E(f318(f318(f74(x58071),x58073),f318(f94(x58071),x58072)),x58074)+E(x58073,f318(f318(f282(x58071),x58074),f318(f94(x58071),x58072)))
% 109.14/108.86 [5808]~P100(x58081)+~P72(x58081)+E(f318(f94(x58081),x58082),f2(x58081))+~E(x58083,f318(f318(f282(x58081),x58084),f318(f94(x58081),x58082)))+E(f318(f318(f74(x58081),x58083),f318(f94(x58081),x58082)),x58084)
% 109.14/108.86 [5809]~P100(x58091)+~P72(x58091)+E(f318(f94(x58091),x58092),f2(x58091))+~E(x58093,f318(f318(f74(x58091),x58094),f318(f94(x58091),x58092)))+E(f318(f318(f282(x58091),x58093),f318(f94(x58091),x58092)),x58094)
% 109.14/108.86 [6017]~P69(x60172)+E(x60171,f2(x60172))+~E(f318(f318(f30(x60172),x60173),x60171),x60174)+E(x60173,f318(f318(f74(x60172),x60174),x60171))+~P1(f318(f318(f278(x60172),x60171),x60173))
% 109.14/108.86 [6018]~P69(x60182)+E(x60181,f2(x60182))+~E(x60183,f318(f318(f74(x60182),x60184),x60181))+E(f318(f318(f30(x60182),x60183),x60181),x60184)+~P1(f318(f318(f278(x60182),x60181),x60183))
% 109.14/108.86 [6481]E(f888(x64811,x64812,x64813),x64814)+E(f318(x64811,x64814),f2(a911))+~E(f318(f318(f8(x64813,a911),x64811),x64812),f71(a911))+~P1(f318(f55(x64813),x64812))+~P1(f318(f318(f320(x64813),x64814),x64812))
% 109.14/108.86 [6545]E(f853(x65451,x65452,x65453),x65454)+E(f318(x65451,x65454),f2(a911))+~E(f318(f318(f8(x65453,a911),x65451),x65452),f318(a103,f2(a911)))+~P1(f318(f55(x65453),x65452))+~P1(f318(f318(f320(x65453),x65454),x65452))
% 109.14/108.86 [6654]~P4(x66541)+~P5(x66541)+P1(f318(f318(f226(x66541),x66542),f31(x66541,x66543)))+~P1(f318(f318(f226(x66541),x66542),x66544))+~P1(f318(f318(f320(x66541),x66544),x66543))
% 109.14/108.86 [6830]~P4(x68301)+~P5(x68301)+~P1(f318(f318(f226(x68301),x68304),x68303))+P1(f318(f318(f226(x68301),f32(x68301,x68302)),x68303))+~P1(f318(f318(f320(x68301),x68304),x68302))
% 109.14/108.86 [7086]~P130(x70863)+E(x70861,x70862)+~E(f318(f318(f235(x70863),x70861),f318(a103,x70864)),f318(f318(f235(x70863),x70862),f318(a103,x70864)))+~P1(f318(f318(f225(x70863),f2(x70863)),x70862))+~P1(f318(f318(f225(x70863),f2(x70863)),x70861))
% 109.14/108.86 [7299]~E(f889(x72992,x72993,x72991,x72994),x72994)+~E(f318(x72992,x72994),f71(a911))+E(f318(f318(f8(x72991,a911),x72992),x72993),f71(a911))+~P1(f318(f55(x72991),x72993))+~P1(f318(f318(f320(x72991),x72994),x72993))
% 109.14/108.86 [7306]~P121(x73064)+~P138(x73064)+E(f318(x73061,f406(x73061,x73062,x73063,x73064)),f2(x73064))+~E(f318(f318(f11(x73063,x73064),x73061),x73062),f2(x73064))+~P1(f318(f55(x73063),x73062))
% 109.14/108.86 [7396]~E(f864(x73962,x73963,x73961,x73964),x73964)+~E(f318(x73962,x73964),f318(a103,f2(a911)))+E(f318(f318(f8(x73961,a911),x73962),x73963),f318(a103,f2(a911)))+~P1(f318(f55(x73961),x73963))+~P1(f318(f318(f320(x73961),x73964),x73963))
% 109.14/108.86 [8111]~E(f318(x81112,x81114),f71(a911))+~E(f318(x81112,f889(x81112,x81113,x81111,x81114)),f2(a911))+E(f318(f318(f8(x81111,a911),x81112),x81113),f71(a911))+~P1(f318(f55(x81111),x81113))+~P1(f318(f318(f320(x81111),x81114),x81113))
% 109.14/108.86 [8148]~E(f318(x81482,x81484),f318(a103,f2(a911)))+~E(f318(x81482,f864(x81482,x81483,x81481,x81484)),f2(a911))+E(f318(f318(f8(x81481,a911),x81482),x81483),f318(a103,f2(a911)))+~P1(f318(f55(x81481),x81483))+~P1(f318(f318(f320(x81481),x81484),x81483))
% 109.14/108.86 [8239]~P146(x82392)+~P124(x82392)+~P1(f318(x82391,x82394))+~P1(f318(f318(f278(x82392),x82393),f318(f318(f73(x82392),x82394),f2(x82392))))+P1(f318(x82391,f318(f318(f74(x82392),x82393),f851(x82393,x82391,x82392))))
% 109.14/108.86 [8705]~P4(x87051)+~P13(x87051,x87054)+P13(x87051,x87052)+~E(x87052,f318(f318(f142(x87051),x87053),x87054))+~P1(f318(f318(f225(x87051),x87053),f724(x87052,x87051,x87054,x87053)))
% 109.14/108.86 [8741]E(x87411,x87412)+E(f318(f318(f3(a1),f342(x87413,x87412,x87414,x87411)),f343(x87413,x87412,x87414,x87411)),x87411)+~E(f318(f318(f73(a1),x87411),x87414),x87412)+~P1(f318(f318(f226(a1),f2(a1)),x87414))+~P1(f318(f318(f320(a1),x87412),x87413))
% 109.14/108.86 [8742]E(x87421,x87422)+E(f318(f318(f73(a1),f344(x87423,x87422,x87424,x87421)),f345(x87423,x87422,x87424,x87421)),x87421)+~E(f318(f318(f3(a1),x87421),x87424),x87422)+~P1(f318(f318(f226(a1),f2(a1)),x87424))+~P1(f318(f318(f320(a1),x87422),x87423))
% 109.14/108.86 [8927]E(f318(x89271,f425(x89272,x89271,x89273,x89274)),x89272)+P1(f318(f318(f225(a911),x89274),f426(x89272,x89271,x89273,x89274)))+~P1(f318(f318(f225(a1),x89272),f318(x89271,x89273)))+~P1(f318(f318(f226(a911),x89274),x89273))+~P1(f318(f318(f225(a1),f318(x89271,x89274)),x89272))
% 109.14/108.86 [8928]~P4(x89281)+~P13(x89281,x89283)+P13(x89281,x89282)+~E(x89282,f318(f318(f142(x89281),x89284),x89283))+P1(f318(f318(f320(x89281),f724(x89282,x89281,x89283,x89284)),f318(f163(x89281),x89283)))
% 109.14/108.86 [8946]~P121(x89464)+~P138(x89464)+~E(f318(f318(f11(x89461,x89464),x89462),x89463),f2(x89464))+~P1(f318(f55(x89461),x89463))+P1(f318(f318(f320(x89461),f406(x89462,x89463,x89461,x89464)),x89463))
% 109.14/108.86 [8987]~E(f318(x89872,x89874),f71(a911))+E(f318(f318(f8(x89871,a911),x89872),x89873),f71(a911))+~P1(f318(f55(x89871),x89873))+~P1(f318(f318(f320(x89871),x89874),x89873))+P1(f318(f318(f320(x89871),f889(x89872,x89873,x89871,x89874)),x89873))
% 109.14/108.86 [9000]E(x90001,x90002)+~E(f318(f318(f73(a1),x90002),x90004),x90001)+~P1(f318(f318(f226(a1),f2(a1)),x90004))+~P1(f318(f318(f320(a1),x90001),x90003))+P1(f318(f318(f320(a1),f342(x90003,x90001,x90004,x90002)),x90003))
% 109.14/108.86 [9001]E(x90011,x90012)+~E(f318(f318(f3(a1),x90012),x90014),x90011)+~P1(f318(f318(f226(a1),f2(a1)),x90014))+~P1(f318(f318(f320(a1),x90011),x90013))+P1(f318(f318(f320(a1),f344(x90013,x90011,x90014,x90012)),x90013))
% 109.14/108.86 [9003]~E(f318(x90032,x90034),f318(a103,f2(a911)))+E(f318(f318(f8(x90031,a911),x90032),x90033),f318(a103,f2(a911)))+~P1(f318(f55(x90031),x90033))+~P1(f318(f318(f320(x90031),x90034),x90033))+P1(f318(f318(f320(x90031),f864(x90032,x90033,x90031,x90034)),x90033))
% 109.14/108.86 [9009]P62(x90092,x90093,x90094,x90091)+E(x90091,f179(f918(x90092,a909)))+~P1(f318(f55(x90092),x90094))+~P1(f318(f55(x90092),x90091))+P1(f318(f318(f320(x90092),f792(x90093,x90091,x90094,x90092)),x90094))
% 109.14/108.86 [9010]P62(x90102,x90103,x90104,x90101)+E(x90101,f179(f918(x90102,a909)))+~P1(f318(f55(x90102),x90104))+~P1(f318(f55(x90102),x90101))+P1(f318(f318(f320(x90102),f535(x90101,x90104,x90103,x90102)),x90104))
% 109.14/108.86 [9011]P62(x90112,x90113,x90114,x90111)+E(x90111,f179(f918(x90112,a909)))+~P1(f318(f55(x90112),x90114))+~P1(f318(f55(x90112),x90111))+P1(f318(f318(f320(x90112),f793(x90111,x90114,x90113,x90112)),x90114))
% 109.14/108.86 [9085]E(x90851,x90852)+~E(f318(f318(f73(a1),x90852),x90854),x90851)+~P1(f318(f318(f226(a1),f2(a1)),x90854))+~P1(f318(f318(f320(a1),x90851),x90853))+P1(f318(f318(f320(a1),f343(x90853,x90851,x90854,x90852)),f294(a1,f71(a1),x90854)))
% 109.14/108.86 [9086]E(x90861,x90862)+~E(f318(f318(f3(a1),x90862),x90864),x90861)+~P1(f318(f318(f226(a1),f2(a1)),x90864))+~P1(f318(f318(f320(a1),x90861),x90863))+P1(f318(f318(f320(a1),f345(x90863,x90861,x90864,x90862)),f294(a1,f71(a1),x90864)))
% 109.14/108.86 [9160]P1(f318(f318(f225(a911),x91601),f425(x91602,x91603,x91604,x91601)))+~P1(f318(f318(f225(a1),x91602),f318(x91603,x91604)))+P1(f318(f318(f225(a911),x91601),f426(x91602,x91603,x91604,x91601)))+~P1(f318(f318(f226(a911),x91601),x91604))+~P1(f318(f318(f225(a1),f318(x91603,x91601)),x91602))
% 109.14/108.86 [9268]E(f318(x92681,f425(x92682,x92681,x92683,x92684)),x92682)+~P1(f318(f318(f225(a1),x92682),f318(x92681,x92683)))+P1(f318(f318(f226(a911),f426(x92682,x92681,x92683,x92684)),x92683))+~P1(f318(f318(f226(a911),x92684),x92683))+~P1(f318(f318(f225(a1),f318(x92681,x92684)),x92682))
% 109.14/108.86 [9402]~P1(f318(f318(f225(a1),x94022),f318(x94023,x94024)))+P1(f318(f318(f225(a911),x94021),f426(x94022,x94023,x94024,x94021)))+P1(f318(f318(f225(a911),f425(x94022,x94023,x94024,x94021)),x94024))+~P1(f318(f318(f226(a911),x94021),x94024))+~P1(f318(f318(f225(a1),f318(x94023,x94021)),x94022))
% 109.14/108.86 [9403]~P1(f318(f318(f225(a1),x94032),f318(x94033,x94034)))+P1(f318(f318(f225(a911),x94031),f425(x94032,x94033,x94034,x94031)))+P1(f318(f318(f226(a911),f426(x94032,x94033,x94034,x94031)),x94034))+~P1(f318(f318(f226(a911),x94031),x94034))+~P1(f318(f318(f225(a1),f318(x94033,x94031)),x94032))
% 109.14/108.86 [9515]~P1(f318(f318(f225(a1),x95151),f318(x95152,x95153)))+P1(f318(f318(f226(a911),f426(x95151,x95152,x95153,x95154)),x95153))+~P1(f318(f318(f226(a911),x95154),x95153))+~P1(f318(f318(f225(a1),f318(x95152,x95154)),x95151))+P1(f318(f318(f225(a911),f425(x95151,x95152,x95153,x95154)),x95153))
% 109.14/108.86 [9598]E(x95981,f179(f918(x95982,a909)))+~P1(f318(f55(x95982),x95984))+~P1(f318(f55(x95982),x95981))+P1(f318(f318(f320(f917(f918(x95982,a909),f918(x95982,a909))),f318(f318(f243(f918(x95982,a909),f918(x95982,a909)),x95984),x95981)),f310(x95982,x95983)))+P1(f318(f318(f320(x95982),f537(x95983,x95981,x95984,x95982)),x95984))
% 109.14/108.86 [9599]E(x95991,f179(f918(x95992,a909)))+~P1(f318(f55(x95992),x95994))+~P1(f318(f55(x95992),x95991))+P1(f318(f318(f320(f917(f918(x95992,a909),f918(x95992,a909))),f318(f318(f243(f918(x95992,a909),f918(x95992,a909)),x95994),x95991)),f310(x95992,x95993)))+P1(f318(f318(f320(x95992),f600(x95993,x95991,x95994,x95992)),x95994))
% 109.14/108.86 [10287]E(f318(x102871,f425(x102872,x102871,x102873,x102874)),x102872)+~P1(f318(f318(f225(a1),x102872),f318(x102871,x102873)))+~P1(f318(f318(f225(a1),f318(f69(a1),f318(f318(f3(a1),f318(x102871,f318(f318(f73(a911),f426(x102872,x102871,x102873,x102874)),f71(a911)))),f318(x102871,f426(x102872,x102871,x102873,x102874))))),f71(a1)))+~P1(f318(f318(f226(a911),x102874),x102873))+~P1(f318(f318(f225(a1),f318(x102871,x102874)),x102872))
% 109.14/108.86 [10288]~P1(f318(f318(f225(a1),x102882),f318(x102883,x102884)))+P1(f318(f318(f225(a911),x102881),f425(x102882,x102883,x102884,x102881)))+~P1(f318(f318(f225(a1),f318(f69(a1),f318(f318(f3(a1),f318(x102883,f318(f318(f73(a911),f426(x102882,x102883,x102884,x102881)),f71(a911)))),f318(x102883,f426(x102882,x102883,x102884,x102881))))),f71(a1)))+~P1(f318(f318(f226(a911),x102881),x102884))+~P1(f318(f318(f225(a1),f318(x102883,x102881)),x102882))
% 109.14/108.86 [10289]~P1(f318(f318(f225(a1),x102891),f318(x102892,x102893)))+~P1(f318(f318(f225(a1),f318(f69(a1),f318(f318(f3(a1),f318(x102892,f318(f318(f73(a911),f426(x102891,x102892,x102893,x102894)),f71(a911)))),f318(x102892,f426(x102891,x102892,x102893,x102894))))),f71(a1)))+~P1(f318(f318(f226(a911),x102894),x102893))+~P1(f318(f318(f225(a1),f318(x102892,x102894)),x102891))+P1(f318(f318(f225(a911),f425(x102891,x102892,x102893,x102894)),x102893))
% 109.14/108.86 [5763]~P100(x57632)+~P72(x57632)+E(x57631,f2(x57632))+~E(f318(f318(f282(x57632),x57633),x57631),f318(f94(x57632),x57634))+E(x57633,f318(f318(f74(x57632),f318(f94(x57632),x57634)),x57631))
% 109.14/108.86 [5764]~P100(x57642)+~P72(x57642)+E(x57641,f2(x57642))+~E(f318(f94(x57642),x57643),f318(f318(f282(x57642),x57644),x57641))+E(f318(f318(f74(x57642),f318(f94(x57642),x57643)),x57641),x57644)
% 109.14/108.86 [5920]~P100(x59202)+~P72(x59202)+E(x59201,f2(x59202))+E(f318(f94(x59202),x59203),f318(f318(f282(x59202),x59204),x59201))+~E(f318(f318(f74(x59202),f318(f94(x59202),x59203)),x59201),x59204)
% 109.14/108.86 [5921]~P100(x59212)+~P72(x59212)+E(x59211,f2(x59212))+E(f318(f318(f282(x59212),x59213),x59211),f318(f94(x59212),x59214))+~E(x59213,f318(f318(f74(x59212),f318(f94(x59212),x59214)),x59211))
% 109.14/108.86 [6053]~P100(x60531)+~P72(x60531)+~E(f318(f94(x60531),x60532),f2(x60531))+E(f318(f94(x60531),x60532),f318(f318(f282(x60531),x60533),x60534))+~E(f318(f318(f74(x60531),f318(f94(x60531),x60532)),x60534),x60533)
% 109.14/108.86 [6054]~P100(x60541)+~P72(x60541)+~E(f318(f94(x60541),x60544),f2(x60541))+E(f318(f318(f282(x60541),x60542),x60543),f318(f94(x60541),x60544))+~E(x60542,f318(f318(f74(x60541),f318(f94(x60541),x60544)),x60543))
% 109.14/108.86 [7359]~P74(x73591)+P1(f318(f318(f226(x73591),x73592),f2(x73591)))+~P1(f318(f318(f225(x73591),x73593),f2(x73591)))+P1(f318(f318(f226(x73591),f2(x73591)),x73592))+P1(f318(f318(f225(x73591),x73593),f318(f318(f282(x73591),x73594),x73592)))
% 109.14/108.86 [7360]~P74(x73601)+P1(f318(f318(f226(x73601),x73602),f2(x73601)))+~P1(f318(f318(f226(x73601),x73603),f2(x73601)))+P1(f318(f318(f226(x73601),f2(x73601)),x73602))+P1(f318(f318(f226(x73601),x73603),f318(f318(f282(x73601),x73604),x73602)))
% 109.14/108.86 [7597]~P74(x75971)+P1(f318(f318(f225(x75971),x75972),f2(x75971)))+P1(f318(f318(f226(x75971),x75973),f2(x75971)))+P1(f318(f318(f226(x75971),f2(x75971)),x75973))+~P1(f318(f318(f225(x75971),x75972),f318(f318(f282(x75971),x75974),x75973)))
% 109.14/108.86 [7598]~P74(x75981)+P1(f318(f318(f226(x75981),x75982),f2(x75981)))+P1(f318(f318(f226(x75981),x75983),f2(x75981)))+P1(f318(f318(f226(x75981),f2(x75981)),x75983))+~P1(f318(f318(f226(x75981),x75982),f318(f318(f282(x75981),x75984),x75983)))
% 109.14/108.86 [7712]E(x77121,x77122)+~E(f318(f318(f155(x77123),x77124),x77121),f318(f318(f155(x77123),x77124),x77122))+~P1(f318(f128(x77123),x77124))+~P1(f318(f318(f226(a911),x77122),f318(f180(f912(x77123)),x77124)))+~P1(f318(f318(f226(a911),x77121),f318(f180(f912(x77123)),x77124)))
% 109.14/108.86 [7713]E(x77131,x77132)+~E(f318(f318(f155(x77133),x77134),x77131),f318(f318(f155(x77133),x77134),x77132))+~P1(f318(f128(x77133),x77134))+~P1(f318(f318(f226(a911),x77132),f318(f180(f912(x77133)),x77134)))+~P1(f318(f318(f226(a911),x77131),f318(f180(f912(x77133)),x77134)))
% 109.14/108.86 [8074]~P74(x80741)+~P1(f318(f318(f225(x80741),x80743),f2(x80741)))+P1(f318(f318(f226(x80741),f2(x80741)),x80742))+~P1(f318(f318(f225(x80741),x80744),f318(f318(f74(x80741),x80743),x80742)))+P1(f318(f318(f225(x80741),x80743),f318(f318(f282(x80741),x80744),x80742)))
% 109.14/108.86 [8075]~P74(x80751)+~P1(f318(f318(f226(x80751),x80753),f2(x80751)))+P1(f318(f318(f226(x80751),f2(x80751)),x80752))+~P1(f318(f318(f226(x80751),x80754),f318(f318(f74(x80751),x80753),x80752)))+P1(f318(f318(f226(x80751),x80753),f318(f318(f282(x80751),x80754),x80752)))
% 109.14/108.86 [8076]~P74(x80761)+~P1(f318(f318(f226(x80761),x80762),f2(x80761)))+P1(f318(f318(f226(x80761),f2(x80761)),x80762))+~P1(f318(f318(f225(x80761),x80764),f318(f318(f74(x80761),x80763),x80762)))+P1(f318(f318(f225(x80761),x80763),f318(f318(f282(x80761),x80764),x80762)))
% 109.14/108.86 [8077]~P74(x80771)+~P1(f318(f318(f226(x80771),x80772),f2(x80771)))+P1(f318(f318(f226(x80771),f2(x80771)),x80772))+~P1(f318(f318(f225(x80771),x80774),f318(f318(f282(x80771),x80773),x80772)))+P1(f318(f318(f225(x80771),x80773),f318(f318(f74(x80771),x80774),x80772)))
% 109.14/108.86 [8078]~P74(x80781)+~P1(f318(f318(f226(x80781),x80782),f2(x80781)))+P1(f318(f318(f226(x80781),f2(x80781)),x80782))+~P1(f318(f318(f226(x80781),x80784),f318(f318(f74(x80781),x80783),x80782)))+P1(f318(f318(f226(x80781),x80783),f318(f318(f282(x80781),x80784),x80782)))
% 109.14/108.86 [8079]~P74(x80791)+~P1(f318(f318(f226(x80791),x80792),f2(x80791)))+P1(f318(f318(f226(x80791),f2(x80791)),x80792))+~P1(f318(f318(f226(x80791),x80794),f318(f318(f282(x80791),x80793),x80792)))+P1(f318(f318(f226(x80791),x80793),f318(f318(f74(x80791),x80794),x80792)))
% 109.14/108.86 [8207]~P69(x82071)+~P1(f318(f318(f278(x82071),x82073),x82074))+~P1(f318(f318(f278(x82071),x82073),x82072))+~P1(f318(f318(f278(x82071),x82072),x82074))+P1(f318(f318(f278(x82071),f318(f318(f30(x82071),x82072),x82073)),f318(f318(f30(x82071),x82074),x82073)))
% 109.14/108.86 [8219]~P4(x82191)+~P13(x82191,x82192)+~P1(f318(f318(f225(a911),x82193),x82194))+P1(f318(f318(f225(x82191),f318(f318(f155(x82191),x82192),x82193)),f318(f318(f155(x82191),x82192),x82194)))+~P1(f318(f318(f226(a911),x82194),f318(f180(f912(x82191)),x82192)))
% 109.14/108.86 [8220]~P4(x82201)+~P13(x82201,x82202)+~P1(f318(f318(f225(a911),x82203),x82204))+P1(f318(f318(f225(x82201),f318(f318(f155(x82201),x82202),x82203)),f318(f318(f155(x82201),x82202),x82204)))+~P1(f318(f318(f226(a911),x82204),f318(f180(f912(x82201)),x82202)))
% 109.14/108.86 [8277]~P130(x82771)+~P1(f318(f318(f225(x82771),x82772),f71(x82771)))+~P1(f318(f318(f225(x82771),f2(x82771)),x82772))+~P1(f318(f318(f225(a911),x82774),x82773))+P1(f318(f318(f225(x82771),f318(f318(f235(x82771),x82772),x82773)),f318(f318(f235(x82771),x82772),x82774)))
% 109.14/108.86 [8278]~P130(x82781)+~P1(f318(f318(f226(x82781),x82782),f71(x82781)))+~P1(f318(f318(f226(x82781),f2(x82781)),x82782))+~P1(f318(f318(f226(a911),x82784),x82783))+P1(f318(f318(f226(x82781),f318(f318(f235(x82781),x82782),x82783)),f318(f318(f235(x82781),x82782),x82784)))
% 109.14/108.86 [8279]~P130(x82791)+~P1(f318(f318(f225(x82791),f2(x82791)),x82792))+~P1(f318(f318(f226(a911),f2(a911)),x82793))+~P1(f318(f318(f226(x82791),x82792),x82794))+P1(f318(f318(f226(x82791),f318(f318(f235(x82791),x82792),x82793)),f318(f318(f235(x82791),x82794),x82793)))
% 109.14/108.86 [8297]~P4(x82971)+~P13(x82971,f318(f159(x82971),x82972))+~P1(f318(f318(f225(a911),x82974),x82973))+P1(f318(f318(f225(x82971),f318(f318(f155(x82971),x82972),x82973)),f318(f318(f155(x82971),x82972),x82974)))+~P1(f318(f318(f226(a911),x82973),f318(f180(f912(x82971)),x82972)))
% 109.14/108.86 [8522]~P69(x85221)+P1(f318(f318(f278(x85221),x85222),x85223))+~P1(f318(f318(f278(x85221),x85224),x85223))+~P1(f318(f318(f278(x85221),x85224),x85222))+~P1(f318(f318(f278(x85221),f318(f318(f30(x85221),x85222),x85224)),f318(f318(f30(x85221),x85223),x85224)))
% 109.14/108.86 [8537]~P74(x85371)+~P1(f318(f318(f225(x85371),x85372),f2(x85371)))+~P1(f318(f318(f225(x85371),x85373),x85374))+~P1(f318(f318(f226(x85371),f2(x85371)),f318(f318(f74(x85371),x85373),x85374)))+P1(f318(f318(f225(x85371),f318(f318(f282(x85371),x85372),x85373)),f318(f318(f282(x85371),x85372),x85374)))
% 109.14/108.86 [8538]~P75(x85381)+~P1(f318(f318(f226(x85381),x85382),f2(x85381)))+~P1(f318(f318(f226(x85381),x85383),x85384))+~P1(f318(f318(f226(x85381),f2(x85381)),f318(f318(f74(x85381),x85383),x85384)))+P1(f318(f318(f226(x85381),f318(f318(f282(x85381),x85382),x85383)),f318(f318(f282(x85381),x85382),x85384)))
% 109.14/108.86 [8547]~P75(x85471)+~P1(f318(f318(f225(x85471),x85474),x85473))+~P1(f318(f318(f225(x85471),f2(x85471)),x85472))+~P1(f318(f318(f226(x85471),f2(x85471)),f318(f318(f74(x85471),x85473),x85474)))+P1(f318(f318(f225(x85471),f318(f318(f282(x85471),x85472),x85473)),f318(f318(f282(x85471),x85472),x85474)))
% 109.14/108.86 [8548]~P75(x85481)+~P1(f318(f318(f226(x85481),x85484),x85483))+~P1(f318(f318(f226(x85481),f2(x85481)),x85482))+~P1(f318(f318(f226(x85481),f2(x85481)),f318(f318(f74(x85481),x85483),x85484)))+P1(f318(f318(f226(x85481),f318(f318(f282(x85481),x85482),x85483)),f318(f318(f282(x85481),x85482),x85484)))
% 109.14/108.86 [8648]P1(f318(x86481,x86482))+~P1(f318(f55(x86484),x86482))+P1(f318(x86481,f899(x86481,x86483,x86482,x86484)))+~P1(f318(x86481,f179(f918(x86484,a909))))+~P1(f318(f318(f225(f918(x86484,a909)),x86482),x86483))
% 109.14/108.86 [8657]P1(f318(x86571,x86572))+P1(f318(f55(x86573),f899(x86571,x86574,x86572,x86573)))+~P1(f318(f55(x86573),x86572))+~P1(f318(x86571,f179(f918(x86573,a909))))+~P1(f318(f318(f225(f918(x86573,a909)),x86572),x86574))
% 109.14/108.86 [8922]E(f318(f318(f73(a1),f346(x89221,x89222,x89223,x89224)),f347(x89221,x89222,x89223,x89224)),x89224)+~P1(f318(f318(f226(a1),f2(a1)),x89223))+~P1(f318(f318(f226(a1),x89222),x89224))+~P1(f318(f318(f320(a1),x89222),x89221))+P1(f318(f318(f226(a1),x89222),f318(f318(f3(a1),x89224),x89223)))
% 109.14/108.86 [9142]~P1(f318(f318(f226(a1),f2(a1)),x91423))+~P1(f318(f318(f226(a1),x91422),x91424))+~P1(f318(f318(f320(a1),x91422),x91421))+P1(f318(f318(f320(a1),f346(x91421,x91422,x91423,x91424)),x91421))+P1(f318(f318(f226(a1),x91422),f318(f318(f3(a1),x91424),x91423)))
% 109.14/108.86 [9153]P1(f318(x91531,x91532))+~P1(f318(f55(x91533),x91532))+P1(f318(f318(f320(x91533),f900(x91531,x91534,x91532,x91533)),x91534))+~P1(f318(x91531,f179(f918(x91533,a909))))+~P1(f318(f318(f225(f918(x91533,a909)),x91532),x91534))
% 109.14/108.86 [9170]E(f318(f318(f73(a1),f333(x91701,x91702,x91703,x91704)),f334(x91701,x91702,x91703,x91704)),x91704)+~P1(f318(f318(f226(a1),f2(a1)),x91703))+~P1(f318(f318(f225(a1),x91702),x91704))+P1(f318(f318(f225(a1),x91702),f318(f318(f3(a1),x91704),x91703)))+~P1(f318(f318(f320(a1),f318(f318(f3(a1),x91702),f71(a1))),x91701))
% 109.14/108.86 [9218]~P1(f318(f318(f226(a1),f2(a1)),x92183))+~P1(f318(f318(f226(a1),x92181),x92182))+~P1(f318(f318(f320(a1),x92181),x92184))+P1(f318(f318(f320(a1),f347(x92184,x92181,x92183,x92182)),f294(a1,f71(a1),x92183)))+P1(f318(f318(f226(a1),x92181),f318(f318(f3(a1),x92182),x92183)))
% 109.14/108.86 [9238]~P76(x92382)+~E(f773(x92383,x92384,x92381,x92382),f774(x92383,x92384,x92381,x92382))+~P1(f318(f55(x92381),f775(x92383,x92384,x92381,x92382)))+E(f318(f318(f8(f918(x92381,a909),x92382),f318(f8(x92381,x92382),x92383)),x92384),f318(f318(f8(x92381,x92382),x92383),f31(f918(x92381,a909),x92384)))+~P1(f318(f55(f918(x92381,a909)),x92384))
% 109.14/108.86 [9242]~P76(x92422)+~E(f318(x92423,f776(x92423,x92424,x92421,x92422)),f2(x92422))+~P1(f318(f55(x92421),f775(x92423,x92424,x92421,x92422)))+E(f318(f318(f8(f918(x92421,a909),x92422),f318(f8(x92421,x92422),x92423)),x92424),f318(f318(f8(x92421,x92422),x92423),f31(f918(x92421,a909),x92424)))+~P1(f318(f55(f918(x92421,a909)),x92424))
% 109.14/108.86 [9315]~P1(f318(f318(f226(a1),f2(a1)),x93153))+~P1(f318(f318(f225(a1),x93152),x93154))+P1(f318(f318(f320(a1),f333(x93151,x93152,x93153,x93154)),x93151))+P1(f318(f318(f225(a1),x93152),f318(f318(f3(a1),x93154),x93153)))+~P1(f318(f318(f320(a1),f318(f318(f3(a1),x93152),f71(a1))),x93151))
% 109.14/108.86 [9361]~P1(f318(f318(f226(a1),f2(a1)),x93613))+~P1(f318(f318(f225(a1),x93611),x93612))+P1(f318(f318(f320(a1),f334(x93614,x93611,x93613,x93612)),f294(a1,f71(a1),x93613)))+P1(f318(f318(f225(a1),x93611),f318(f318(f3(a1),x93612),x93613)))+~P1(f318(f318(f320(a1),f318(f318(f3(a1),x93611),f71(a1))),x93614))
% 109.14/108.86 [9381]~P76(x93812)+~E(f773(x93813,x93814,x93811,x93812),f774(x93813,x93814,x93811,x93812))+E(f318(f318(f8(f918(x93811,a909),x93812),f318(f8(x93811,x93812),x93813)),x93814),f318(f318(f8(x93811,x93812),x93813),f31(f918(x93811,a909),x93814)))+P1(f318(f318(f320(f918(x93811,a909)),f775(x93813,x93814,x93811,x93812)),x93814))+~P1(f318(f55(f918(x93811,a909)),x93814))
% 109.14/108.86 [9386]~P76(x93862)+~E(f318(x93863,f776(x93863,x93864,x93861,x93862)),f2(x93862))+E(f318(f318(f8(f918(x93861,a909),x93862),f318(f8(x93861,x93862),x93863)),x93864),f318(f318(f8(x93861,x93862),x93863),f31(f918(x93861,a909),x93864)))+P1(f318(f318(f320(f918(x93861,a909)),f775(x93863,x93864,x93861,x93862)),x93864))+~P1(f318(f55(f918(x93861,a909)),x93864))
% 109.14/108.86 [9492]~P76(x94922)+~P1(f318(f55(x94921),f775(x94923,x94924,x94921,x94922)))+E(f318(f318(f8(f918(x94921,a909),x94922),f318(f8(x94921,x94922),x94923)),x94924),f318(f318(f8(x94921,x94922),x94923),f31(f918(x94921,a909),x94924)))+P1(f318(f318(f320(f918(x94921,a909)),f774(x94923,x94924,x94921,x94922)),x94924))+~P1(f318(f55(f918(x94921,a909)),x94924))
% 109.14/108.86 [9493]~P76(x94932)+~P1(f318(f55(x94931),f775(x94933,x94934,x94931,x94932)))+E(f318(f318(f8(f918(x94931,a909),x94932),f318(f8(x94931,x94932),x94933)),x94934),f318(f318(f8(x94931,x94932),x94933),f31(f918(x94931,a909),x94934)))+P1(f318(f318(f320(f918(x94931,a909)),f773(x94933,x94934,x94931,x94932)),x94934))+~P1(f318(f55(f918(x94931,a909)),x94934))
% 109.14/108.86 [9574]~P76(x95742)+E(f318(f318(f8(f918(x95741,a909),x95742),f318(f8(x95741,x95742),x95743)),x95744),f318(f318(f8(x95741,x95742),x95743),f31(f918(x95741,a909),x95744)))+P1(f318(f318(f320(f918(x95741,a909)),f775(x95743,x95744,x95741,x95742)),x95744))+P1(f318(f318(f320(f918(x95741,a909)),f774(x95743,x95744,x95741,x95742)),x95744))+~P1(f318(f55(f918(x95741,a909)),x95744))
% 109.14/108.86 [9575]~P76(x95752)+E(f318(f318(f8(f918(x95751,a909),x95752),f318(f8(x95751,x95752),x95753)),x95754),f318(f318(f8(x95751,x95752),x95753),f31(f918(x95751,a909),x95754)))+P1(f318(f318(f320(f918(x95751,a909)),f775(x95753,x95754,x95751,x95752)),x95754))+P1(f318(f318(f320(f918(x95751,a909)),f773(x95753,x95754,x95751,x95752)),x95754))+~P1(f318(f55(f918(x95751,a909)),x95754))
% 109.14/108.86 [9589]~P76(x95892)+P1(f318(f318(f320(x95891),f776(x95893,x95894,x95891,x95892)),f774(x95893,x95894,x95891,x95892)))+~P1(f318(f55(x95891),f775(x95893,x95894,x95891,x95892)))+E(f318(f318(f8(f918(x95891,a909),x95892),f318(f8(x95891,x95892),x95893)),x95894),f318(f318(f8(x95891,x95892),x95893),f31(f918(x95891,a909),x95894)))+~P1(f318(f55(f918(x95891,a909)),x95894))
% 109.14/108.86 [9590]~P76(x95902)+P1(f318(f318(f320(x95901),f776(x95903,x95904,x95901,x95902)),f773(x95903,x95904,x95901,x95902)))+~P1(f318(f55(x95901),f775(x95903,x95904,x95901,x95902)))+E(f318(f318(f8(f918(x95901,a909),x95902),f318(f8(x95901,x95902),x95903)),x95904),f318(f318(f8(x95901,x95902),x95903),f31(f918(x95901,a909),x95904)))+~P1(f318(f55(f918(x95901,a909)),x95904))
% 109.14/108.86 [9602]P1(f318(x96021,x96022))+~P1(f318(f318(f320(x96023),f900(x96021,x96024,x96022,x96023)),f899(x96021,x96024,x96022,x96023)))+~P1(f318(f55(x96023),x96022))+~P1(f318(x96021,f179(f918(x96023,a909))))+~P1(f318(f318(f225(f918(x96023,a909)),x96022),x96024))
% 109.14/108.86 [9638]~P76(x96382)+P1(f318(f318(f320(x96381),f776(x96383,x96384,x96381,x96382)),f774(x96383,x96384,x96381,x96382)))+E(f318(f318(f8(f918(x96381,a909),x96382),f318(f8(x96381,x96382),x96383)),x96384),f318(f318(f8(x96381,x96382),x96383),f31(f918(x96381,a909),x96384)))+P1(f318(f318(f320(f918(x96381,a909)),f775(x96383,x96384,x96381,x96382)),x96384))+~P1(f318(f55(f918(x96381,a909)),x96384))
% 109.14/108.86 [9639]~P76(x96392)+P1(f318(f318(f320(x96391),f776(x96393,x96394,x96391,x96392)),f773(x96393,x96394,x96391,x96392)))+E(f318(f318(f8(f918(x96391,a909),x96392),f318(f8(x96391,x96392),x96393)),x96394),f318(f318(f8(x96391,x96392),x96393),f31(f918(x96391,a909),x96394)))+P1(f318(f318(f320(f918(x96391,a909)),f775(x96393,x96394,x96391,x96392)),x96394))+~P1(f318(f55(f918(x96391,a909)),x96394))
% 109.14/108.86 [9841]P1(f318(x98411,x98412))+~P1(f318(f55(x98413),x98412))+~P1(f318(x98411,f318(f318(f300(x98413),f900(x98411,x98414,x98412,x98413)),f899(x98411,x98414,x98412,x98413))))+~P1(f318(x98411,f179(f918(x98413,a909))))+~P1(f318(f318(f225(f918(x98413,a909)),x98412),x98414))
% 109.14/108.86 [7847]~P74(x78471)+P1(f318(f318(f226(x78471),x78472),f2(x78471)))+~P1(f318(f318(f225(x78471),f2(x78471)),x78474))+P1(f318(f318(f226(x78471),f2(x78471)),x78472))+P1(f318(f318(f225(x78471),f318(f318(f282(x78471),x78473),x78472)),x78474))
% 109.14/108.86 [7848]~P74(x78481)+P1(f318(f318(f226(x78481),x78482),f2(x78481)))+P1(f318(f318(f226(x78481),f2(x78481)),x78482))+~P1(f318(f318(f226(x78481),f2(x78481)),x78484))+P1(f318(f318(f226(x78481),f318(f318(f282(x78481),x78483),x78482)),x78484))
% 109.14/108.86 [8065]~P5(x80651)+~P42(x80651,x80651,x80654)+~E(x80653,f87(x80651,x80654))+P1(f318(f318(f225(x80651),x80652),x80653))+~P1(f318(f318(f225(x80651),x80652),f318(x80654,f318(f318(f101(x80651),x80652),x80653))))
% 109.14/108.86 [8123]~P1(f318(f318(f225(a1),x81234),f2(a1)))+~E(x81232,f318(f318(f73(a1),f318(f318(f74(a1),x81231),x81233)),x81234))+P1(f318(f318(f226(a1),f2(a1)),x81231))+~P1(f318(f318(f226(a1),x81231),x81234))+P1(f318(f43(x81232,x81231),f318(f318(f243(a1,a1),x81233),x81234)))
% 109.14/108.86 [8157]~P1(f318(x81571,x81574))+P1(f318(x81571,f385(x81572,x81571,x81573)))+~P1(f318(f318(f225(a1),f2(a1)),x81572))+~P1(f318(f318(f226(a1),f2(a1)),x81573))+P1(f318(x81571,f318(f318(f3(a1),x81574),f318(f318(f74(a1),x81572),x81573))))
% 109.14/108.86 [8158]~P1(f318(x81581,x81584))+P1(f318(x81581,f390(x81582,x81581,x81583)))+~P1(f318(f318(f225(a1),f2(a1)),x81582))+~P1(f318(f318(f226(a1),f2(a1)),x81583))+P1(f318(x81581,f318(f318(f73(a1),x81584),f318(f318(f74(a1),x81582),x81583))))
% 109.14/108.86 [8159]~P74(x81591)+P1(f318(f318(f226(x81591),x81592),f2(x81591)))+P1(f318(f318(f226(x81591),f2(x81591)),x81592))+P1(f318(f318(f225(x81591),f2(x81591)),x81593))+~P1(f318(f318(f225(x81591),f318(f318(f282(x81591),x81594),x81592)),x81593))
% 109.14/108.86 [8160]~P74(x81601)+P1(f318(f318(f226(x81601),x81602),f2(x81601)))+P1(f318(f318(f226(x81601),f2(x81601)),x81602))+P1(f318(f318(f226(x81601),f2(x81601)),x81603))+~P1(f318(f318(f226(x81601),f318(f318(f282(x81601),x81604),x81602)),x81603))
% 109.14/108.86 [8215]~E(x82151,f318(f318(f73(a1),f318(f318(f74(a1),x82152),x82153)),x82154))+~P1(f318(f318(f225(a1),f2(a1)),x82154))+~P1(f318(f318(f226(a1),f2(a1)),x82152))+~P1(f318(f318(f226(a1),x82154),x82152))+P1(f318(f43(x82151,x82152),f318(f318(f243(a1,a1),x82153),x82154)))
% 109.14/108.86 [8336]~P74(x83361)+P1(f318(f318(f226(x83361),x83362),f2(x83361)))+~P1(f318(f318(f225(x83361),f2(x83361)),x83364))+~P1(f318(f318(f225(x83361),x83363),f318(f318(f74(x83361),x83364),x83362)))+P1(f318(f318(f225(x83361),f318(f318(f282(x83361),x83363),x83362)),x83364))
% 109.14/108.86 [8337]~P74(x83371)+P1(f318(f318(f226(x83371),x83372),f2(x83371)))+~P1(f318(f318(f226(x83371),f2(x83371)),x83374))+~P1(f318(f318(f226(x83371),x83373),f318(f318(f74(x83371),x83374),x83372)))+P1(f318(f318(f226(x83371),f318(f318(f282(x83371),x83373),x83372)),x83374))
% 109.14/108.86 [8419]~P74(x84191)+P1(f318(f318(f226(x84191),x84192),f2(x84191)))+~P1(f318(f318(f225(x84191),x84193),f2(x84191)))+P1(f318(f318(f225(x84191),x84193),f318(f318(f282(x84191),x84194),x84192)))+~P1(f318(f318(f225(x84191),f318(f318(f74(x84191),x84193),x84192)),x84194))
% 109.14/108.86 [8420]~P74(x84201)+P1(f318(f318(f226(x84201),x84202),f2(x84201)))+~P1(f318(f318(f226(x84201),x84203),f2(x84201)))+P1(f318(f318(f226(x84201),x84203),f318(f318(f282(x84201),x84204),x84202)))+~P1(f318(f318(f226(x84201),f318(f318(f74(x84201),x84203),x84202)),x84204))
% 109.14/108.86 [8569]~P74(x85691)+~P1(f318(f318(f226(x85691),x85692),f2(x85691)))+P1(f318(f318(f226(x85691),f2(x85691)),x85692))+~P1(f318(f318(f225(x85691),f318(f318(f282(x85691),x85694),x85692)),x85693))+P1(f318(f318(f225(x85691),f318(f318(f74(x85691),x85693),x85692)),x85694))
% 109.14/108.86 [8570]~P74(x85701)+~P1(f318(f318(f226(x85701),x85702),f2(x85701)))+P1(f318(f318(f226(x85701),f2(x85701)),x85702))+~P1(f318(f318(f225(x85701),f318(f318(f74(x85701),x85704),x85702)),x85703))+P1(f318(f318(f225(x85701),f318(f318(f282(x85701),x85703),x85702)),x85704))
% 109.14/108.86 [8571]~P74(x85711)+~P1(f318(f318(f226(x85711),x85712),f2(x85711)))+P1(f318(f318(f226(x85711),f2(x85711)),x85712))+~P1(f318(f318(f226(x85711),f318(f318(f282(x85711),x85714),x85712)),x85713))+P1(f318(f318(f226(x85711),f318(f318(f74(x85711),x85713),x85712)),x85714))
% 109.14/108.86 [8572]~P74(x85721)+~P1(f318(f318(f226(x85721),x85722),f2(x85721)))+P1(f318(f318(f226(x85721),f2(x85721)),x85722))+~P1(f318(f318(f226(x85721),f318(f318(f74(x85721),x85724),x85722)),x85723))+P1(f318(f318(f226(x85721),f318(f318(f282(x85721),x85723),x85722)),x85724))
% 109.14/108.86 [8589]~P74(x85891)+~P1(f318(f318(f225(x85891),f2(x85891)),x85894))+P1(f318(f318(f226(x85891),f2(x85891)),x85892))+~P1(f318(f318(f225(x85891),f318(f318(f74(x85891),x85894),x85892)),x85893))+P1(f318(f318(f225(x85891),f318(f318(f282(x85891),x85893),x85892)),x85894))
% 109.14/108.86 [8590]~P74(x85901)+~P1(f318(f318(f226(x85901),f2(x85901)),x85904))+P1(f318(f318(f226(x85901),f2(x85901)),x85902))+~P1(f318(f318(f226(x85901),f318(f318(f74(x85901),x85904),x85902)),x85903))+P1(f318(f318(f226(x85901),f318(f318(f282(x85901),x85903),x85902)),x85904))
% 109.14/108.86 [8643]~P100(x86431)+~P74(x86431)+~P1(f318(f318(f226(x86431),f2(x86431)),x86434))+~P1(f318(f318(f225(x86431),f318(f318(f282(x86431),x86432),x86434)),f318(f94(x86431),x86433)))+P1(f318(f318(f225(x86431),x86432),f318(f318(f74(x86431),f318(f94(x86431),x86433)),x86434)))
% 109.14/108.86 [8644]~P100(x86441)+~P74(x86441)+~P1(f318(f318(f226(x86441),f2(x86441)),x86444))+~P1(f318(f318(f226(x86441),f318(f318(f282(x86441),x86442),x86444)),f318(f94(x86441),x86443)))+P1(f318(f318(f226(x86441),x86442),f318(f318(f74(x86441),f318(f94(x86441),x86443)),x86444)))
% 109.14/108.86 [8649]~P100(x86491)+~P74(x86491)+~P1(f318(f318(f226(x86491),f2(x86491)),x86493))+P1(f318(f318(f225(x86491),f318(f318(f282(x86491),x86492),x86493)),f318(f94(x86491),x86494)))+~P1(f318(f318(f225(x86491),x86492),f318(f318(f74(x86491),f318(f94(x86491),x86494)),x86493)))
% 109.14/108.86 [8650]~P100(x86501)+~P74(x86501)+~P1(f318(f318(f226(x86501),f2(x86501)),x86503))+P1(f318(f318(f226(x86501),f318(f318(f282(x86501),x86502),x86503)),f318(f94(x86501),x86504)))+~P1(f318(f318(f226(x86501),x86502),f318(f318(f74(x86501),f318(f94(x86501),x86504)),x86503)))
% 109.14/108.86 [8669]~P74(x86691)+~P1(f318(f318(f226(x86691),x86694),f2(x86691)))+~P1(f318(f318(f225(x86691),x86693),f318(f318(f74(x86691),x86692),x86694)))+P1(f318(f318(f225(x86691),x86692),f318(f318(f282(x86691),x86693),x86694)))+~P1(f318(f318(f225(x86691),f318(f318(f74(x86691),x86692),x86694)),x86693))
% 109.14/108.86 [8670]~P74(x86701)+~P1(f318(f318(f225(x86701),x86702),f2(x86701)))+~P1(f318(f318(f225(x86701),x86703),f318(f318(f74(x86701),x86702),x86704)))+P1(f318(f318(f225(x86701),x86702),f318(f318(f282(x86701),x86703),x86704)))+~P1(f318(f318(f225(x86701),f318(f318(f74(x86701),x86702),x86704)),x86703))
% 109.14/108.86 [8671]~P74(x86711)+~P1(f318(f318(f226(x86711),x86714),f2(x86711)))+~P1(f318(f318(f226(x86711),x86713),f318(f318(f74(x86711),x86712),x86714)))+P1(f318(f318(f226(x86711),x86712),f318(f318(f282(x86711),x86713),x86714)))+~P1(f318(f318(f226(x86711),f318(f318(f74(x86711),x86712),x86714)),x86713))
% 109.14/108.86 [8672]~P74(x86721)+~P1(f318(f318(f226(x86721),x86722),f2(x86721)))+~P1(f318(f318(f226(x86721),x86723),f318(f318(f74(x86721),x86722),x86724)))+P1(f318(f318(f226(x86721),x86722),f318(f318(f282(x86721),x86723),x86724)))+~P1(f318(f318(f226(x86721),f318(f318(f74(x86721),x86722),x86724)),x86723))
% 109.14/108.86 [8721]~P100(x87211)+~P74(x87211)+~P1(f318(f318(f226(x87211),f2(x87211)),f318(f94(x87211),x87213)))+~P1(f318(f318(f225(x87211),x87212),f318(f318(f282(x87211),x87214),f318(f94(x87211),x87213))))+P1(f318(f318(f225(x87211),f318(f318(f74(x87211),x87212),f318(f94(x87211),x87213))),x87214))
% 109.14/108.86 [8722]~P100(x87221)+~P74(x87221)+~P1(f318(f318(f226(x87221),f2(x87221)),f318(f94(x87221),x87223)))+~P1(f318(f318(f225(x87221),x87222),f318(f318(f74(x87221),x87224),f318(f94(x87221),x87223))))+P1(f318(f318(f225(x87221),f318(f318(f282(x87221),x87222),f318(f94(x87221),x87223))),x87224))
% 109.14/108.86 [8723]~P100(x87231)+~P74(x87231)+~P1(f318(f318(f226(x87231),f2(x87231)),f318(f94(x87231),x87233)))+~P1(f318(f318(f226(x87231),x87232),f318(f318(f282(x87231),x87234),f318(f94(x87231),x87233))))+P1(f318(f318(f226(x87231),f318(f318(f74(x87231),x87232),f318(f94(x87231),x87233))),x87234))
% 109.14/108.86 [8724]~P100(x87241)+~P74(x87241)+~P1(f318(f318(f226(x87241),f2(x87241)),f318(f94(x87241),x87243)))+~P1(f318(f318(f226(x87241),x87242),f318(f318(f74(x87241),x87244),f318(f94(x87241),x87243))))+P1(f318(f318(f226(x87241),f318(f318(f282(x87241),x87242),f318(f94(x87241),x87243))),x87244))
% 109.14/108.86 [8794]~P74(x87941)+~P1(f318(f318(f226(x87941),x87943),f2(x87941)))+~P1(f318(f318(f225(x87941),x87942),f318(f318(f74(x87941),x87944),x87943)))+~P1(f318(f318(f225(x87941),f318(f318(f74(x87941),x87944),x87943)),x87942))+P1(f318(f318(f225(x87941),f318(f318(f282(x87941),x87942),x87943)),x87944))
% 109.14/108.86 [8795]~P74(x87951)+~P1(f318(f318(f226(x87951),x87953),f2(x87951)))+~P1(f318(f318(f226(x87951),x87952),f318(f318(f74(x87951),x87954),x87953)))+~P1(f318(f318(f226(x87951),f318(f318(f74(x87951),x87954),x87953)),x87952))+P1(f318(f318(f226(x87951),f318(f318(f282(x87951),x87952),x87953)),x87954))
% 109.14/108.86 [8807]~P74(x88071)+~P1(f318(f318(f225(x88071),f2(x88071)),x88074))+~P1(f318(f318(f225(x88071),x88072),f318(f318(f74(x88071),x88074),x88073)))+~P1(f318(f318(f225(x88071),f318(f318(f74(x88071),x88074),x88073)),x88072))+P1(f318(f318(f225(x88071),f318(f318(f282(x88071),x88072),x88073)),x88074))
% 109.14/108.86 [8808]~P74(x88081)+~P1(f318(f318(f226(x88081),f2(x88081)),x88084))+~P1(f318(f318(f226(x88081),x88082),f318(f318(f74(x88081),x88084),x88083)))+~P1(f318(f318(f226(x88081),f318(f318(f74(x88081),x88084),x88083)),x88082))+P1(f318(f318(f226(x88081),f318(f318(f282(x88081),x88082),x88083)),x88084))
% 109.14/108.86 [8840]~P100(x88401)+~P74(x88401)+~P1(f318(f318(f226(x88401),f2(x88401)),f318(f94(x88401),x88404)))+P1(f318(f318(f225(x88401),x88402),f318(f318(f74(x88401),x88403),f318(f94(x88401),x88404))))+~P1(f318(f318(f225(x88401),f318(f318(f282(x88401),x88402),f318(f94(x88401),x88404))),x88403))
% 109.14/108.86 [8841]~P100(x88411)+~P74(x88411)+~P1(f318(f318(f226(x88411),f2(x88411)),f318(f94(x88411),x88414)))+P1(f318(f318(f225(x88411),x88412),f318(f318(f282(x88411),x88413),f318(f94(x88411),x88414))))+~P1(f318(f318(f225(x88411),f318(f318(f74(x88411),x88412),f318(f94(x88411),x88414))),x88413))
% 109.14/108.86 [8842]~P100(x88421)+~P74(x88421)+~P1(f318(f318(f226(x88421),f2(x88421)),f318(f94(x88421),x88424)))+P1(f318(f318(f226(x88421),x88422),f318(f318(f74(x88421),x88423),f318(f94(x88421),x88424))))+~P1(f318(f318(f226(x88421),f318(f318(f282(x88421),x88422),f318(f94(x88421),x88424))),x88423))
% 109.14/108.86 [8843]~P100(x88431)+~P74(x88431)+~P1(f318(f318(f226(x88431),f2(x88431)),f318(f94(x88431),x88434)))+P1(f318(f318(f226(x88431),x88432),f318(f318(f282(x88431),x88433),f318(f94(x88431),x88434))))+~P1(f318(f318(f226(x88431),f318(f318(f74(x88431),x88432),f318(f94(x88431),x88434))),x88433))
% 109.14/108.86 [8993]E(f318(f318(f3(a1),f352(x89931,x89932,x89933,x89934)),f353(x89931,x89932,x89933,x89934)),x89934)+~P1(f318(f318(f226(a1),f2(a1)),x89933))+~P1(f318(f318(f320(a1),x89932),x89931))+~P1(f318(f318(f226(a1),x89934),x89932))+P1(f318(f318(f226(a1),f318(f318(f73(a1),x89934),x89933)),x89932))
% 109.14/108.86 [9067]~P1(f318(x90671,x90672))+~P1(f318(f318(f225(a1),f2(a1)),x90673))+~P1(f318(f318(f226(a1),f2(a1)),x90674))+~P1(f318(x90671,f318(f318(f3(a1),f385(x90673,x90671,x90674)),x90674)))+P1(f318(x90671,f318(f318(f3(a1),x90672),f318(f318(f74(a1),x90673),x90674))))
% 109.14/108.86 [9068]~P1(f318(x90681,x90682))+~P1(f318(f318(f225(a1),f2(a1)),x90683))+~P1(f318(f318(f226(a1),f2(a1)),x90684))+~P1(f318(x90681,f318(f318(f73(a1),f390(x90683,x90681,x90684)),x90684)))+P1(f318(x90681,f318(f318(f73(a1),x90682),f318(f318(f74(a1),x90683),x90684))))
% 109.14/108.86 [9212]~P1(f318(f318(f226(a1),f2(a1)),x92123))+~P1(f318(f318(f320(a1),x92122),x92121))+~P1(f318(f318(f226(a1),x92124),x92122))+P1(f318(f318(f320(a1),f352(x92121,x92122,x92123,x92124)),x92121))+P1(f318(f318(f226(a1),f318(f318(f73(a1),x92124),x92123)),x92122))
% 109.14/108.86 [9226]E(f318(f318(f3(a1),f335(x92261,x92262,x92263,x92264)),f336(x92261,x92262,x92263,x92264)),x92264)+~P1(f318(f318(f226(a1),f2(a1)),x92263))+~P1(f318(f318(f225(a1),x92264),x92262))+~P1(f318(f318(f320(a1),f318(f318(f73(a1),x92262),f71(a1))),x92261))+P1(f318(f318(f225(a1),f318(f318(f73(a1),x92264),x92263)),x92262))
% 109.14/108.86 [9253]~P1(f318(f318(f226(a1),f2(a1)),x92532))+~P1(f318(f318(f320(a1),x92533),x92534))+~P1(f318(f318(f226(a1),x92531),x92533))+P1(f318(f318(f320(a1),f353(x92534,x92533,x92532,x92531)),f294(a1,f71(a1),x92532)))+P1(f318(f318(f226(a1),f318(f318(f73(a1),x92531),x92532)),x92533))
% 109.14/108.86 [9353]~P1(f318(f318(f226(a1),f2(a1)),x93533))+~P1(f318(f318(f225(a1),x93534),x93532))+P1(f318(f318(f320(a1),f335(x93531,x93532,x93533,x93534)),x93531))+~P1(f318(f318(f320(a1),f318(f318(f73(a1),x93532),f71(a1))),x93531))+P1(f318(f318(f225(a1),f318(f318(f73(a1),x93534),x93533)),x93532))
% 109.14/108.86 [9398]~P1(f318(f318(f226(a1),f2(a1)),x93982))+~P1(f318(f318(f225(a1),x93981),x93983))+P1(f318(f318(f320(a1),f336(x93984,x93983,x93982,x93981)),f294(a1,f71(a1),x93982)))+~P1(f318(f318(f320(a1),f318(f318(f73(a1),x93983),f71(a1))),x93984))+P1(f318(f318(f225(a1),f318(f318(f73(a1),x93981),x93982)),x93983))
% 109.14/108.86 [9705]~P39(x97051,x97053)+~P27(x97051,x97054)+P39(x97051,f318(f318(f101(f918(f917(x97051,x97051),a909)),x97052),x97053))+~P1(f318(f318(f225(f918(f917(x97051,x97051),a909)),x97052),f318(f242(f918(f917(x97051,x97051),a909),f918(f917(x97051,x97051),a909)),x97054)))+~P1(f318(f318(f225(f918(f917(x97051,x97051),a909)),x97053),f318(f247(f918(f917(x97051,x97051),a909),f918(f917(x97051,x97051),a909)),x97054)))
% 109.14/108.86 [10110]~P18(x101102,x101104,x101103)+E(x101101,f179(f918(x101102,a909)))+~P1(f318(f55(x101102),x101101))+P1(f318(f318(f320(x101102),f318(x101103,x101101)),x101101))+~P1(f318(f318(f320(x101102),f318(f318(x101104,f879(x101101,x101103,x101104,x101102)),f880(x101101,x101103,x101104,x101102))),f318(f318(f300(x101102),f879(x101101,x101103,x101104,x101102)),f318(f318(f300(x101102),f880(x101101,x101103,x101104,x101102)),f179(f918(x101102,a909))))))
% 109.14/108.86 [8697]~P5(x86971)+~P42(x86971,x86971,x86974)+~E(x86972,f86(x86971,x86974))+P1(f318(f318(f225(x86971),x86972),x86973))+~P1(f318(f318(f225(x86971),f318(x86974,f318(f318(f92(x86971),x86972),x86973))),x86973))
% 109.14/108.86 [8830]~P100(x88301)+~P74(x88301)+~P1(f318(f318(f226(x88301),f2(x88301)),x88303))+~P1(f318(f318(f225(x88301),f318(f94(x88301),x88302)),f318(f318(f282(x88301),x88304),x88303)))+P1(f318(f318(f225(x88301),f318(f318(f74(x88301),f318(f94(x88301),x88302)),x88303)),x88304))
% 109.14/108.86 [8831]~P100(x88311)+~P74(x88311)+~P1(f318(f318(f226(x88311),f2(x88311)),x88313))+~P1(f318(f318(f226(x88311),f318(f94(x88311),x88312)),f318(f318(f282(x88311),x88314),x88313)))+P1(f318(f318(f226(x88311),f318(f318(f74(x88311),f318(f94(x88311),x88312)),x88313)),x88314))
% 109.14/108.86 [8996]~P100(x89961)+~P74(x89961)+~P1(f318(f318(f226(x89961),f2(x89961)),x89964))+P1(f318(f318(f225(x89961),f318(f94(x89961),x89962)),f318(f318(f282(x89961),x89963),x89964)))+~P1(f318(f318(f225(x89961),f318(f318(f74(x89961),f318(f94(x89961),x89962)),x89964)),x89963))
% 109.14/108.86 [8997]~P100(x89971)+~P74(x89971)+~P1(f318(f318(f226(x89971),f2(x89971)),x89974))+P1(f318(f318(f226(x89971),f318(f94(x89971),x89972)),f318(f318(f282(x89971),x89973),x89974)))+~P1(f318(f318(f226(x89971),f318(f318(f74(x89971),f318(f94(x89971),x89972)),x89974)),x89973))
% 109.14/108.86 [10042]~P113(x100422)+~P71(x100421)+~P1(f318(f318(f225(f918(x100421,x100422)),x100423),x100424))+P1(f318(f318(f226(f918(x100421,x100422)),x100423),x100424))+~P1(f318(f50(x100421),f318(f318(f10(a909,a909,x100421),a313),f318(f318(f20(x100421,x100422,a909),f318(f318(f10(x100422,f918(x100422,a909),x100421),a315),x100423)),x100424))))
% 109.14/108.86 [5262]~P52(x52624,x52625,x52623)+E(x52621,x52622)+~P4(x52624)+~P113(x52625)+~E(f318(x52623,x52621),f318(x52623,x52622))
% 109.14/108.86 [9609]~P58(x96091,x96091,x96094)+P1(f318(f318(f320(f917(x96091,x96091)),f318(f318(f243(x96091,x96091),x96092),x96093)),f298(x96091,x96094)))+P1(f318(f318(f320(f917(x96091,x96091)),f318(f318(f243(x96091,x96091),x96093),x96092)),f298(x96091,x96094)))+~P1(f318(f318(f320(f917(x96091,x96091)),f318(f318(f243(x96091,x96091),x96095),x96092)),f298(x96091,x96094)))+~P1(f318(f318(f320(f917(x96091,x96091)),f318(f318(f243(x96091,x96091),x96095),x96093)),f298(x96091,x96094)))
% 109.14/108.86 [5753]E(x57531,f2(a911))+~E(f318(f29(x57532),x57535),x57531)+E(f318(f29(x57532),x57533),f318(a103,x57531))+~E(x57533,f318(f318(f300(x57532),x57534),x57535))+P1(f318(f318(f320(x57532),x57534),x57535))
% 109.14/108.86 [5876]~P73(x58762)+E(x58761,f2(x58762))+E(x58763,f2(x58762))+~E(f318(f318(f282(x58762),x58764),x58763),f318(f318(f282(x58762),x58765),x58761))+E(f318(f318(f74(x58762),x58764),x58761),f318(f318(f74(x58762),x58765),x58763))
% 109.14/108.86 [5877]~P73(x58772)+E(x58771,f2(x58772))+E(x58773,f2(x58772))+~E(f318(f318(f74(x58772),x58774),x58773),f318(f318(f74(x58772),x58775),x58771))+E(f318(f318(f282(x58772),x58774),x58771),f318(f318(f282(x58772),x58775),x58773))
% 109.14/108.86 [5946]~E(f318(f29(x59461),x59465),x59463)+~E(x59465,f179(f918(x59461,a909)))+E(f318(f29(x59461),x59462),f318(a103,x59463))+~E(x59462,f318(f318(f300(x59461),x59464),x59465))+P1(f318(f318(f320(x59461),x59464),x59465))
% 109.14/108.86 [6187]~P121(x61872)+~E(f318(x61873,x61875),f2(x61872))+E(f318(f318(f11(x61871,x61872),x61873),x61874),f2(x61872))+~P1(f318(f55(x61871),x61874))+~P1(f318(f318(f320(x61871),x61875),x61874))
% 109.14/108.86 [6556]~P4(x65563)+E(x65561,x65562)+~E(f318(f293(x65563,x65564),x65561),f318(f293(x65563,x65565),x65562))+~P1(f318(f318(f226(x65563),x65565),x65562))+~P1(f318(f318(f226(x65563),x65564),x65561))
% 109.14/108.86 [6557]~P4(x65573)+E(x65571,x65572)+~E(f318(f293(x65573,x65571),x65574),f318(f293(x65573,x65572),x65575))+~P1(f318(f318(f226(x65573),x65572),x65575))+~P1(f318(f318(f226(x65573),x65571),x65574))
% 109.14/108.86 [6558]~P4(x65583)+E(x65581,x65582)+~E(f318(f293(x65583,x65584),x65581),f318(f293(x65583,x65585),x65582))+~P1(f318(f318(f226(x65583),x65585),x65582))+~P1(f318(f318(f226(x65583),x65584),x65581))
% 109.14/108.86 [6559]~P4(x65593)+E(x65591,x65592)+~E(f318(f293(x65593,x65591),x65594),f318(f293(x65593,x65592),x65595))+~P1(f318(f318(f226(x65593),x65592),x65595))+~P1(f318(f318(f226(x65593),x65591),x65594))
% 109.14/108.86 [6723]~P113(x67231)+~P52(x67235,x67231,x67232)+~P4(x67235)+P1(f318(f318(f225(x67231),f318(x67232,x67233)),f318(x67232,x67234)))+~P1(f318(f318(f225(x67235),x67233),x67234))
% 109.14/108.86 [6724]~P113(x67241)+~P42(x67245,x67241,x67242)+~P113(x67245)+P1(f318(f318(f225(x67241),f318(x67242,x67243)),f318(x67242,x67244)))+~P1(f318(f318(f225(x67245),x67243),x67244))
% 109.14/108.86 [6725]~P113(x67251)+~P52(x67255,x67251,x67252)+~P4(x67255)+P1(f318(f318(f226(x67251),f318(x67252,x67253)),f318(x67252,x67254)))+~P1(f318(f318(f226(x67255),x67253),x67254))
% 109.14/108.86 [6726]~P113(x67261)+~P52(x67265,x67261,x67262)+~P113(x67265)+P1(f318(f318(f226(x67261),f318(x67262,x67263)),f318(x67262,x67264)))+~P1(f318(f318(f226(x67265),x67263),x67264))
% 109.14/108.86 [6970]~P4(x69701)+~P52(x69701,x69704,x69705)+~P113(x69704)+~P1(f318(f318(f225(x69704),f318(x69705,x69702)),f318(x69705,x69703)))+P1(f318(f318(f225(x69701),x69702),x69703))
% 109.14/108.86 [6971]~P4(x69711)+~P52(x69711,x69714,x69715)+~P113(x69714)+~P1(f318(f318(f226(x69714),f318(x69715,x69712)),f318(x69715,x69713)))+P1(f318(f318(f226(x69711),x69712),x69713))
% 109.14/108.86 [7614]~P4(x76141)+~P13(x76141,f318(f318(f125(x76141),x76144),x76145))+~P1(f318(f318(f320(x76141),x76143),f318(f163(x76141),x76145)))+~P1(f318(f318(f320(x76141),x76142),f318(f163(x76141),x76144)))+P1(f318(f318(f225(x76141),x76142),x76143))
% 109.14/108.86 [8707]~P113(x87071)+~P1(f318(f318(f226(f918(x87071,a909)),f294(x87071,x87075,x87072)),f294(x87071,x87074,x87073)))+~P1(f318(f318(f225(x87071),x87075),x87072))+P1(f318(f318(f226(x87071),x87072),x87073))+P1(f318(f318(f226(x87071),x87074),x87075))
% 109.14/108.86 [9741]~P42(f918(x97414,a909),f918(x97414,a909),x97415)+P1(f318(x97411,x97412))+~E(x97413,f86(f918(x97414,a909),x97415))+~P1(f318(x97411,f602(x97411,x97412,x97415,x97414,x97413)))+~P1(f318(f318(f320(x97414),x97412),x97413))
% 109.14/108.86 [10143]~P17(x101432,x101435,x101433)+E(x101431,f179(f918(x101432,a909)))+~E(f318(f318(x101435,f318(x101434,f902(x101431,x101434,x101433,x101435,x101432))),f318(x101434,f903(x101431,x101434,x101433,x101435,x101432))),f318(x101434,f318(f318(x101435,f902(x101431,x101434,x101433,x101435,x101432)),f903(x101431,x101434,x101433,x101435,x101432))))+E(f318(x101433,f318(f301(x101432,x101432,x101434),x101431)),f318(x101434,f318(x101433,x101431)))+~P1(f318(f55(x101432),x101431))
% 109.14/108.86 [6555]~P18(x65552,x65555,x65553)+E(x65551,f179(f918(x65552,a909)))+~P1(f318(f55(x65552),x65551))+E(f318(x65553,f318(f318(f300(x65552),x65554),x65551)),f318(f318(x65555,x65554),f318(x65553,x65551)))+P1(f318(f318(f320(x65552),x65554),x65551))
% 109.14/108.86 [7387]~P17(x73872,x73873,x73874)+E(f318(f318(x73873,f318(x73874,x73871)),f318(x73874,x73875)),f318(x73874,x73875))+E(x73871,f179(f918(x73872,a909)))+~P1(f318(f55(x73872),x73875))+~P1(f318(f318(f225(f918(x73872,a909)),x73871),x73875))
% 109.14/108.86 [7746]~P18(x77464,x77465,x77461)+E(f318(x77461,x77462),x77463)+~P1(f318(f55(x77464),x77462))+~E(f318(f318(f3(f918(x77464,a909)),x77462),f318(f318(f300(x77464),x77463),f179(f918(x77464,a909)))),f179(f918(x77464,a909)))+~P1(f318(f318(f320(x77464),x77463),x77462))
% 109.14/108.86 [8624]~P82(x86241)+~P124(x86241)+~P1(f318(f55(x86242),x86245))+P1(f318(f318(f278(x86241),f318(f318(f11(x86242,x86241),x86243),x86244)),f318(f318(f11(x86242,x86241),x86243),x86245)))+~P1(f318(f318(f225(f918(x86242,a909)),x86244),x86245))
% 109.14/108.86 [8676]E(x86761,x86762)+~P8(x86763,x86764,x86765)+E(f318(f318(f92(f918(x86763,a909)),x86761),x86762),f179(f918(x86763,a909)))+~P1(f318(f318(f320(f918(x86763,a909)),x86762),f318(f318(f54(x86763),x86764),x86765)))+~P1(f318(f318(f320(f918(x86763,a909)),x86761),f318(f318(f54(x86763),x86764),x86765)))
% 109.14/108.86 [9143]~P25(x91431,x91433,x91435,x91432)+~P1(f318(f55(x91433),x91434))+~P1(f318(f55(x91431),x91432))+P1(f318(f318(f225(a911),f318(f29(x91431),x91432)),f318(f29(x91433),x91434)))+~P1(f318(f318(f225(f918(x91433,a909)),f318(f301(x91431,x91433,x91435),x91432)),x91434))
% 109.14/108.86 [9485]~P76(x94852)+~E(f318(x94853,f878(x94853,x94854,x94855,x94851,x94852)),f2(x94852))+E(f318(f318(f8(x94851,x94852),x94853),x94854),f318(f318(f8(x94851,x94852),x94853),x94855))+~P1(f318(f55(x94851),x94855))+~P1(f318(f318(f225(f918(x94851,a909)),x94854),x94855))
% 109.14/108.86 [9486]~P76(x94862)+~E(f318(x94863,f881(x94863,x94864,x94865,x94861,x94862)),f2(x94862))+E(f318(f318(f8(x94861,x94862),x94863),x94864),f318(f318(f8(x94861,x94862),x94863),x94865))+~P1(f318(f55(x94861),x94865))+~P1(f318(f318(f225(f918(x94861,a909)),x94864),x94865))
% 109.14/108.86 [9487]~P82(x94872)+~E(f318(x94873,f416(x94873,x94874,x94875,x94871,x94872)),f71(x94872))+E(f318(f318(f11(x94871,x94872),x94873),x94874),f318(f318(f11(x94871,x94872),x94873),x94875))+~P1(f318(f55(x94871),x94875))+~P1(f318(f318(f225(f918(x94871,a909)),x94874),x94875))
% 109.14/108.86 [9488]~P82(x94882)+~E(f318(x94883,f420(x94883,x94884,x94885,x94881,x94882)),f71(x94882))+E(f318(f318(f11(x94881,x94882),x94883),x94884),f318(f318(f11(x94881,x94882),x94883),x94885))+~P1(f318(f55(x94881),x94885))+~P1(f318(f318(f225(f918(x94881,a909)),x94884),x94885))
% 109.14/108.86 [9942]~P42(f918(x99421,a909),f918(x99421,a909),f318(f318(f10(f918(x99421,a909),f918(x99421,a909),f918(x99421,a909)),f253(x99421)),x99424))+~P1(f318(f318(x99424,f318(f318(f101(f918(x99421,a909)),x99425),x99423)),f603(x99425,x99422,x99424,x99421,x99423)))+~E(x99423,f87(f918(x99421,a909),f318(f318(f10(f918(x99421,a909),f918(x99421,a909),f918(x99421,a909)),f253(x99421)),x99424)))+P1(f318(f318(f320(x99421),x99422),x99423))+~P1(f318(f318(f320(x99421),x99422),x99425))
% 109.14/108.86 [9947]~P42(f918(x99471,a909),f918(x99471,a909),f318(f318(f10(f918(x99471,a909),f918(x99471,a909),f918(x99471,a909)),f253(x99471)),x99475))+~E(x99473,f87(f918(x99471,a909),f318(f318(f10(f918(x99471,a909),f918(x99471,a909),f918(x99471,a909)),f253(x99471)),x99475)))+~P1(f318(f318(f320(x99471),x99472),x99474))+P1(f318(f318(f320(x99471),f603(x99474,x99472,x99475,x99471,x99473)),x99474))+P1(f318(f318(f320(x99471),x99472),x99473))
% 109.14/108.86 [10000]~P93(x100001)+~P1(f318(f55(x100002),x100005))+~P1(f318(f318(f225(x100001),f2(x100001)),f318(x100003,f868(x100003,x100004,x100005,x100002,x100001))))+P1(f318(f318(f225(x100001),f318(f318(f8(x100002,x100001),x100003),x100004)),f318(f318(f8(x100002,x100001),x100003),x100005)))+~P1(f318(f318(f225(f918(x100002,a909)),x100004),x100005))
% 109.14/108.86 [7611]E(x76111,f2(a911))+P1(f318(x76112,x76113))+~E(x76114,f318(f318(f73(a911),f318(f318(f74(a911),x76111),x76113)),x76115))+~P1(f318(f318(f226(a911),x76115),x76111))+~P1(f318(x76112,f318(f318(f30(a911),x76114),x76111)))
% 109.14/108.86 [7687]E(x76871,f2(a911))+P1(f318(x76872,x76873))+~P1(f318(x76872,f39(a911,x76874,x76871)))+~E(x76874,f318(f318(f73(a911),f318(f318(f74(a911),x76871),x76875)),x76873))+~P1(f318(f318(f226(a911),x76873),x76871))
% 109.14/108.86 [7982]~P73(x79823)+E(f318(x79821,x79822),f2(x79823))+~P1(f318(f55(x79824),x79825))+E(f318(f318(f11(x79824,x79823),x79821),f318(f318(f3(f918(x79824,a909)),x79825),f318(f318(f300(x79824),x79822),f179(f918(x79824,a909))))),f318(f318(f11(x79824,x79823),x79821),x79825))+P1(f318(f318(f320(x79824),x79822),x79825))
% 109.14/108.86 [8374]~P76(x83741)+~P1(f318(f55(x83742),x83745))+~P1(f318(f55(x83742),x83744))+~E(f318(f318(f92(f918(x83742,a909)),x83744),x83745),f179(f918(x83742,a909)))+E(f318(f318(f73(x83741),f318(f318(f8(x83742,x83741),x83743),x83744)),f318(f318(f8(x83742,x83741),x83743),x83745)),f318(f318(f8(x83742,x83741),x83743),f318(f318(f101(f918(x83742,a909)),x83744),x83745)))
% 109.14/108.86 [8375]~P82(x83751)+~P1(f318(f55(x83752),x83755))+~P1(f318(f55(x83752),x83754))+~E(f318(f318(f92(f918(x83752,a909)),x83754),x83755),f179(f918(x83752,a909)))+E(f318(f318(f74(x83751),f318(f318(f11(x83752,x83751),x83753),x83754)),f318(f318(f11(x83752,x83751),x83753),x83755)),f318(f318(f11(x83752,x83751),x83753),f318(f318(f101(f918(x83752,a909)),x83754),x83755)))
% 109.14/108.86 [8376]~P82(x83761)+~P1(f318(f55(x83762),x83765))+~P1(f318(f55(x83762),x83764))+~E(f318(f318(f92(f918(x83762,a909)),x83764),x83765),f179(f918(x83762,a909)))+E(f318(f318(f74(x83761),f318(f318(f11(x83762,x83761),x83763),x83764)),f318(f318(f11(x83762,x83761),x83763),x83765)),f318(f318(f11(x83762,x83761),x83763),f318(f318(f101(f918(x83762,a909)),x83764),x83765)))
% 109.14/108.86 [8475]~P73(x84753)+E(f318(x84751,x84752),f2(x84753))+~P1(f318(f55(x84754),x84755))+E(f318(f318(f11(x84754,x84753),x84751),f318(f318(f3(f918(x84754,a909)),x84755),f318(f318(f300(x84754),x84752),f179(f918(x84754,a909))))),f318(f318(f282(x84753),f318(f318(f11(x84754,x84753),x84751),x84755)),f318(x84751,x84752)))+~P1(f318(f318(f320(x84754),x84752),x84755))
% 109.14/108.86 [9012]~P8(x90121,x90125,x90124)+~E(f318(f276(x90121,x90121,x90124),f318(f318(f300(x90121),x90122),f179(f918(x90121,a909)))),f318(f276(x90121,x90121,x90124),f318(f318(f300(x90121),x90123),f179(f918(x90121,a909)))))+~P1(f318(f318(f320(x90121),x90123),x90125))+~P1(f318(f318(f320(x90121),x90122),x90125))+P1(f318(f318(f320(f917(x90121,x90121)),f318(f318(f243(x90121,x90121),x90122),x90123)),x90124))
% 109.14/108.86 [9013]~P8(x90131,x90135,x90134)+~E(f318(f276(x90131,x90131,x90134),f318(f318(f300(x90131),x90132),f179(f918(x90131,a909)))),f318(f276(x90131,x90131,x90134),f318(f318(f300(x90131),x90133),f179(f918(x90131,a909)))))+~P1(f318(f318(f320(x90131),x90133),x90135))+~P1(f318(f318(f320(x90131),x90132),x90135))+P1(f318(f318(f320(f917(x90131,x90131)),f318(f318(f243(x90131,x90131),x90132),x90133)),x90134))
% 109.14/108.86 [9107]~P8(x91071,x91075,x91072)+E(f318(f276(x91071,x91071,x91072),f318(f318(f300(x91071),x91073),f179(f918(x91071,a909)))),f318(f276(x91071,x91071,x91072),f318(f318(f300(x91071),x91074),f179(f918(x91071,a909)))))+~P1(f318(f318(f320(x91071),x91074),x91075))+~P1(f318(f318(f320(x91071),x91073),x91075))+~P1(f318(f318(f320(f917(x91071,x91071)),f318(f318(f243(x91071,x91071),x91073),x91074)),x91072))
% 109.14/108.86 [9195]~P8(x91951,x91955,x91954)+~E(f318(f318(f54(x91951),f318(f318(f300(x91951),x91952),f179(f918(x91951,a909)))),x91954),f318(f318(f54(x91951),f318(f318(f300(x91951),x91953),f179(f918(x91951,a909)))),x91954))+~P1(f318(f318(f320(x91951),x91953),x91955))+~P1(f318(f318(f320(x91951),x91952),x91955))+P1(f318(f318(f320(f917(x91951,x91951)),f318(f318(f243(x91951,x91951),x91952),x91953)),x91954))
% 109.14/108.86 [9211]~P8(x92111,x92115,x92113)+E(f318(f318(f54(x92111),f318(f318(f300(x92111),x92112),f179(f918(x92111,a909)))),x92113),f318(f318(f54(x92111),f318(f318(f300(x92111),x92114),f179(f918(x92111,a909)))),x92113))+~P1(f318(f318(f320(x92111),x92114),x92115))+~P1(f318(f318(f320(x92111),x92112),x92115))+~P1(f318(f318(f320(f917(x92111,x92111)),f318(f318(f243(x92111,x92111),x92112),x92114)),x92113))
% 109.14/108.86 [9514]~P82(x95141)+~P1(f318(f55(x95142),x95145))+~P1(f318(f55(x95142),x95144))+~E(f318(f318(f92(f918(x95142,a909)),x95144),x95145),f179(f918(x95142,a909)))+E(f318(f318(f74(x95141),f318(f318(f318(f59(x95141,x95142,f74(x95141)),x95143),f71(x95141)),x95144)),f318(f318(f318(f59(x95141,x95142,f74(x95141)),x95143),f71(x95141)),x95145)),f318(f318(f318(f59(x95141,x95142,f74(x95141)),x95143),f71(x95141)),f318(f318(f101(f918(x95142,a909)),x95144),x95145)))
% 109.14/108.86 [9525]~P76(x95251)+~E(f318(x95253,f866(x95253,x95255,x95254,x95252,x95251)),f2(x95251))+~P1(f318(f55(x95252),x95254))+~P1(f318(f55(x95252),x95255))+E(f318(f318(f73(x95251),f318(f318(f8(x95252,x95251),x95253),x95254)),f318(f318(f8(x95252,x95251),x95253),x95255)),f318(f318(f8(x95252,x95251),x95253),f318(f318(f101(f918(x95252,a909)),x95254),x95255)))
% 109.14/108.86 [9526]~P76(x95261)+~E(f318(x95263,f869(x95263,x95265,x95264,x95262,x95261)),f2(x95261))+~P1(f318(f55(x95262),x95264))+~P1(f318(f55(x95262),x95265))+E(f318(f318(f73(x95261),f318(f318(f8(x95262,x95261),x95263),x95264)),f318(f318(f8(x95262,x95261),x95263),x95265)),f318(f318(f8(x95262,x95261),x95263),f318(f318(f101(f918(x95262,a909)),x95264),x95265)))
% 109.14/108.86 [9527]~P82(x95271)+~E(f318(x95273,f417(x95273,x95275,x95274,x95272,x95271)),f71(x95271))+~P1(f318(f55(x95272),x95274))+~P1(f318(f55(x95272),x95275))+E(f318(f318(f74(x95271),f318(f318(f11(x95272,x95271),x95273),x95274)),f318(f318(f11(x95272,x95271),x95273),x95275)),f318(f318(f11(x95272,x95271),x95273),f318(f318(f101(f918(x95272,a909)),x95274),x95275)))
% 109.14/108.86 [9528]~P82(x95281)+~E(f318(x95283,f419(x95283,x95285,x95284,x95282,x95281)),f71(x95281))+~P1(f318(f55(x95282),x95284))+~P1(f318(f55(x95282),x95285))+E(f318(f318(f74(x95281),f318(f318(f11(x95282,x95281),x95283),x95284)),f318(f318(f11(x95282,x95281),x95283),x95285)),f318(f318(f11(x95282,x95281),x95283),f318(f318(f101(f918(x95282,a909)),x95284),x95285)))
% 109.14/108.86 [9747]~P82(x97471)+~E(f318(x97473,f392(x97473,x97475,x97474,x97472,x97471)),f71(x97471))+~P1(f318(f55(x97472),x97474))+~P1(f318(f55(x97472),x97475))+E(f318(f318(f74(x97471),f318(f318(f318(f59(x97471,x97472,f74(x97471)),x97473),f71(x97471)),x97474)),f318(f318(f318(f59(x97471,x97472,f74(x97471)),x97473),f71(x97471)),x97475)),f318(f318(f318(f59(x97471,x97472,f74(x97471)),x97473),f71(x97471)),f318(f318(f101(f918(x97472,a909)),x97474),x97475)))
% 109.14/108.86 [9871]~P76(x98712)+E(f318(f318(f8(x98711,x98712),x98713),x98714),f318(f318(f8(x98711,x98712),x98713),x98715))+~P1(f318(f55(x98711),x98715))+~P1(f318(f318(f225(f918(x98711,a909)),x98714),x98715))+P1(f318(f318(f320(x98711),f878(x98713,x98714,x98715,x98711,x98712)),f318(f318(f3(f918(x98711,a909)),x98715),x98714)))
% 109.14/108.86 [9872]~P76(x98722)+E(f318(f318(f8(x98721,x98722),x98723),x98724),f318(f318(f8(x98721,x98722),x98723),x98725))+~P1(f318(f55(x98721),x98725))+~P1(f318(f318(f225(f918(x98721,a909)),x98724),x98725))+P1(f318(f318(f320(x98721),f881(x98723,x98724,x98725,x98721,x98722)),f318(f318(f3(f918(x98721,a909)),x98725),x98724)))
% 109.14/108.86 [9873]~P82(x98732)+E(f318(f318(f11(x98731,x98732),x98733),x98734),f318(f318(f11(x98731,x98732),x98733),x98735))+~P1(f318(f55(x98731),x98735))+~P1(f318(f318(f225(f918(x98731,a909)),x98734),x98735))+P1(f318(f318(f320(x98731),f416(x98733,x98734,x98735,x98731,x98732)),f318(f318(f3(f918(x98731,a909)),x98735),x98734)))
% 109.14/108.86 [9874]~P82(x98742)+E(f318(f318(f11(x98741,x98742),x98743),x98744),f318(f318(f11(x98741,x98742),x98743),x98745))+~P1(f318(f55(x98741),x98745))+~P1(f318(f318(f225(f918(x98741,a909)),x98744),x98745))+P1(f318(f318(f320(x98741),f420(x98743,x98744,x98745,x98741,x98742)),f318(f318(f3(f918(x98741,a909)),x98745),x98744)))
% 109.14/108.86 [9893]~P76(x98931)+~P1(f318(f55(x98932),x98934))+~P1(f318(f55(x98932),x98935))+E(f318(f318(f73(x98931),f318(f318(f8(x98932,x98931),x98933),x98934)),f318(f318(f8(x98932,x98931),x98933),x98935)),f318(f318(f8(x98932,x98931),x98933),f318(f318(f101(f918(x98932,a909)),x98934),x98935)))+P1(f318(f318(f320(x98932),f866(x98933,x98935,x98934,x98932,x98931)),f318(f318(f92(f918(x98932,a909)),x98934),x98935)))
% 109.14/108.86 [9894]~P76(x98941)+~P1(f318(f55(x98942),x98944))+~P1(f318(f55(x98942),x98945))+E(f318(f318(f73(x98941),f318(f318(f8(x98942,x98941),x98943),x98944)),f318(f318(f8(x98942,x98941),x98943),x98945)),f318(f318(f8(x98942,x98941),x98943),f318(f318(f101(f918(x98942,a909)),x98944),x98945)))+P1(f318(f318(f320(x98942),f869(x98943,x98945,x98944,x98942,x98941)),f318(f318(f92(f918(x98942,a909)),x98944),x98945)))
% 109.14/108.86 [9895]~P82(x98951)+~P1(f318(f55(x98952),x98954))+~P1(f318(f55(x98952),x98955))+E(f318(f318(f74(x98951),f318(f318(f11(x98952,x98951),x98953),x98954)),f318(f318(f11(x98952,x98951),x98953),x98955)),f318(f318(f11(x98952,x98951),x98953),f318(f318(f101(f918(x98952,a909)),x98954),x98955)))+P1(f318(f318(f320(x98952),f417(x98953,x98955,x98954,x98952,x98951)),f318(f318(f92(f918(x98952,a909)),x98954),x98955)))
% 109.14/108.86 [9896]~P82(x98961)+~P1(f318(f55(x98962),x98964))+~P1(f318(f55(x98962),x98965))+E(f318(f318(f74(x98961),f318(f318(f11(x98962,x98961),x98963),x98964)),f318(f318(f11(x98962,x98961),x98963),x98965)),f318(f318(f11(x98962,x98961),x98963),f318(f318(f101(f918(x98962,a909)),x98964),x98965)))+P1(f318(f318(f320(x98962),f419(x98963,x98965,x98964,x98962,x98961)),f318(f318(f92(f918(x98962,a909)),x98964),x98965)))
% 109.14/108.86 [9899]~P42(f918(x98993,a909),f918(x98993,a909),x98994)+P1(f318(x98991,x98992))+~E(x98995,f86(f918(x98993,a909),x98994))+~P1(f318(f318(f320(x98993),x98992),x98995))+P1(f318(f318(f320(x98993),f602(x98991,x98992,x98994,x98993,x98995)),f318(x98994,f318(f318(f92(f918(x98993,a909)),x98995),f318(f253(x98993),x98991)))))
% 109.14/108.86 [9903]~P93(x99035)+~P1(f318(f55(x99031),x99034))+P1(f318(f318(f225(x99035),f318(f318(f8(x99031,x99035),x99032),x99033)),f318(f318(f8(x99031,x99035),x99032),x99034)))+~P1(f318(f318(f225(f918(x99031,a909)),x99033),x99034))+P1(f318(f318(f320(x99031),f868(x99032,x99033,x99034,x99031,x99035)),f318(f318(f3(f918(x99031,a909)),x99034),x99033)))
% 109.14/108.86 [9961]~P82(x99611)+~P1(f318(f55(x99612),x99614))+~P1(f318(f55(x99612),x99615))+E(f318(f318(f74(x99611),f318(f318(f318(f59(x99611,x99612,f74(x99611)),x99613),f71(x99611)),x99614)),f318(f318(f318(f59(x99611,x99612,f74(x99611)),x99613),f71(x99611)),x99615)),f318(f318(f318(f59(x99611,x99612,f74(x99611)),x99613),f71(x99611)),f318(f318(f101(f918(x99612,a909)),x99614),x99615)))+P1(f318(f318(f320(x99612),f392(x99613,x99615,x99614,x99612,x99611)),f318(f318(f92(f918(x99612,a909)),x99614),x99615)))
% 109.14/108.86 [8878]~P18(x88781,x88784,x88785)+~P1(f318(f55(x88781),x88782))+E(f318(f318(f3(f918(x88781,a909)),x88782),f318(f318(f300(x88781),x88783),f179(f918(x88781,a909)))),f179(f918(x88781,a909)))+~P1(f318(f318(f320(x88781),x88783),x88782))+E(f318(f318(x88784,x88783),f318(x88785,f318(f318(f3(f918(x88781,a909)),x88782),f318(f318(f300(x88781),x88783),f179(f918(x88781,a909)))))),f318(x88785,x88782))
% 109.14/108.86 [8956]~P18(x89561,x89564,x89565)+~P1(f318(f55(x89561),x89563))+~P1(f318(f55(x89561),x89562))+E(f318(f318(f92(f918(x89561,a909)),x89562),x89563),f179(f918(x89561,a909)))+E(f318(f318(x89564,f318(x89565,f318(f318(f101(f918(x89561,a909)),x89562),x89563))),f318(x89565,f318(f318(f92(f918(x89561,a909)),x89562),x89563))),f318(f318(x89564,f318(x89565,x89562)),f318(x89565,x89563)))
% 109.14/108.86 [9144]~P42(f918(x91441,a909),f918(x91441,a909),x91444)+~E(x91443,f87(f918(x91441,a909),x91444))+P1(f318(f318(f320(x91441),x91442),x91443))+~P1(f318(f318(f320(x91441),x91442),x91445))+~P1(f318(f318(f225(f918(x91441,a909)),x91445),f318(x91444,f318(f318(f101(f918(x91441,a909)),x91445),x91443))))
% 109.14/108.86 [9530]~P1(f318(f318(f225(a1),x95304),f2(a1)))+~P1(f318(f318(f226(a1),x95303),x95305))+P1(f318(f318(f225(a1),x95301),x95302))+~P1(f318(f318(f226(a1),x95303),x95304))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f74(a1),x95303),x95302)),x95305)),f318(f318(f73(a1),f318(f318(f74(a1),x95303),x95301)),x95304)))
% 109.14/108.86 [9536]~P1(f318(f318(f225(a1),f2(a1)),x95365))+P1(f318(f318(f225(a1),x95361),x95362))+~P1(f318(f318(f226(a1),x95363),x95364))+~P1(f318(f318(f226(a1),x95365),x95364))+~P1(f318(f318(f225(a1),f318(f318(f73(a1),f318(f318(f74(a1),x95364),x95361)),x95365)),f318(f318(f73(a1),f318(f318(f74(a1),x95364),x95362)),x95363)))
% 109.14/108.86 [9644]~P73(x96445)+E(f318(x96441,f418(x96441,x96442,x96443,x96444,x96445)),f2(x96445))+~P1(f318(f55(x96444),x96443))+~P1(f318(f55(x96444),x96442))+E(f318(f318(f282(x96445),f318(f318(f74(x96445),f318(f318(f11(x96444,x96445),x96441),x96443)),f318(f318(f11(x96444,x96445),x96441),x96442))),f318(f318(f11(x96444,x96445),x96441),f318(f318(f92(f918(x96444,a909)),x96443),x96442))),f318(f318(f11(x96444,x96445),x96441),f318(f318(f101(f918(x96444,a909)),x96443),x96442)))
% 109.14/108.86 [9953]~P73(x99531)+~P1(f318(f55(x99532),x99534))+~P1(f318(f55(x99532),x99535))+E(f318(f318(f282(x99531),f318(f318(f74(x99531),f318(f318(f11(x99532,x99531),x99533),x99534)),f318(f318(f11(x99532,x99531),x99533),x99535))),f318(f318(f11(x99532,x99531),x99533),f318(f318(f92(f918(x99532,a909)),x99534),x99535))),f318(f318(f11(x99532,x99531),x99533),f318(f318(f101(f918(x99532,a909)),x99534),x99535)))+P1(f318(f318(f320(x99532),f418(x99533,x99535,x99534,x99532,x99531)),f318(f318(f92(f918(x99532,a909)),x99534),x99535)))
% 109.14/108.86 [9225]E(f318(f318(f125(x92251),x92252),x92253),f318(f318(f125(x92251),x92254),x92255))+~E(f318(f318(f166(x92251),f318(f180(f912(x92251)),x92254)),x92252),x92254)+~E(f318(f318(f166(x92251),f318(f180(f912(x92251)),x92252)),x92254),x92252)+~E(x92255,f318(f318(f125(x92251),f318(f318(f129(x92251),f318(f180(f912(x92251)),x92254)),x92252)),x92253))+~E(f318(f318(f125(x92251),f318(f318(f129(x92251),f318(f180(f912(x92251)),x92252)),x92254)),x92255),x92253)
% 109.14/108.86 [9642]~P4(x96422)+E(f318(f318(f139(x96421,x96422,x96423),x96424),f161(x96421,x96424,x96425)),x96425)+~P13(x96422,f318(f318(f145(x96421,x96422),x96423),x96425))+~P1(f318(f318(f320(x96421),x96424),f318(f163(x96421),x96425)))+~E(f318(f132(x96421),f318(f127(x96421,f318(f318(f10(x96422,a909,x96421),f318(a315,f318(x96423,x96424))),x96423)),x96425)),x96424)
% 109.14/108.86 [10018]~P80(x100181)+~P1(f318(f60(x100181,x100181,f74(x100181),x100182,x100183),x100185))+~P1(f318(f318(f320(x100181),x100184),x100183))+P1(f318(f318(f320(x100181),x100182),x100183))+P1(f318(f60(x100181,x100181,f74(x100181),x100184,f318(f318(f300(x100181),x100182),f318(f318(f3(f918(x100181,a909)),x100183),f318(f318(f300(x100181),x100184),f179(f918(x100181,a909)))))),x100185))
% 109.14/108.86 [10389]~P42(f918(x103891,a909),f918(x103891,a909),x103894)+~E(x103893,f87(f918(x103891,a909),x103894))+P1(f318(f318(f320(x103891),x103892),x103893))+~P1(f318(f318(f320(x103891),x103892),x103895))+~P1(f318(f318(f225(f918(x103891,a909)),x103895),f318(x103894,f86(f918(x103891,a909),f318(f318(f9(f918(x103891,a909),f918(x103891,a909),f918(x103891,a909)),f318(f318(f10(f918(x103891,a909),f918(f918(x103891,a909),f918(x103891,a909)),f918(x103891,a909)),f101(f918(x103891,a909))),f318(f318(f9(f918(x103891,a909),f918(x103891,a909),f918(x103891,a909)),f318(f318(f10(f918(x103891,a909),f918(f918(x103891,a909),f918(x103891,a909)),f918(x103891,a909)),f101(f918(x103891,a909))),x103894)),x103895))),x103893)))))
% 109.14/108.86 [7392]E(x73921,x73922)+~P25(x73924,x73925,x73923,x73926)+~E(f318(x73923,x73921),f318(x73923,x73922))+~P1(f318(f318(f320(x73924),x73922),x73926))+~P1(f318(f318(f320(x73924),x73921),x73926))
% 109.14/108.86 [7393]E(x73931,x73932)+~P25(x73934,x73935,x73933,x73936)+~E(f318(x73933,x73931),f318(x73933,x73932))+~P1(f318(f318(f320(x73934),x73932),x73936))+~P1(f318(f318(f320(x73934),x73931),x73936))
% 109.14/108.86 [7394]E(x73941,x73942)+~P25(x73944,x73945,x73943,x73946)+~E(f318(x73943,x73941),f318(x73943,x73942))+~P1(f318(f318(f320(x73944),x73942),x73946))+~P1(f318(f318(f320(x73944),x73941),x73946))
% 109.14/108.86 [7395]E(x73951,x73952)+~P25(x73954,x73955,x73953,x73956)+~E(f318(x73953,x73951),f318(x73953,x73952))+~P1(f318(f318(f320(x73954),x73952),x73956))+~P1(f318(f318(f320(x73954),x73951),x73956))
% 109.14/108.86 [6648]~P149(x66484)+E(x66481,x66482)+~E(x66485,x66486)+E(x66483,f2(x66484))+~E(f318(f318(f73(x66484),x66485),f318(f318(f74(x66484),x66483),x66481)),f318(f318(f73(x66484),x66486),f318(f318(f74(x66484),x66483),x66482)))
% 109.14/108.86 [7667]~P4(x76671)+~P5(x76671)+~P1(f318(f318(f226(x76671),x76672),f318(x76675,x76676)))+~P1(f318(f318(f320(x76673),x76676),x76674))+P1(f318(f318(f226(x76671),x76672),f318(f318(f33(x76673,x76671),x76674),x76675)))
% 109.14/108.86 [10014]~P25(x100142,x100141,x100143,x100144)+~P25(x100141,x100142,x100146,x100145)+P26(x100141,x100142,f822(x100143,x100144,x100145,x100146,x100142,x100141),x100145,x100144)+~P1(f318(f318(f225(f918(x100142,a909)),f318(f301(x100141,x100142,x100146),x100145)),x100144))+~P1(f318(f318(f225(f918(x100141,a909)),f318(f301(x100142,x100141,x100143),x100144)),x100145))
% 109.14/108.86 [8348]~P4(x83481)+~P5(x83481)+~P1(f318(f318(f226(x83481),f318(x83484,x83486)),x83485))+~P1(f318(f318(f320(x83482),x83486),x83483))+P1(f318(f318(f226(x83481),f318(f318(f34(x83482,x83481),x83483),x83484)),x83485))
% 109.14/108.86 [8596]~P19(x85962,x85965,x85966,x85961)+~P1(f318(f55(x85962),x85964))+~P1(f318(f55(x85962),x85963))+~E(f318(f318(f92(f918(x85962,a909)),x85963),x85964),f179(f918(x85962,a909)))+E(f318(x85961,f318(f318(f101(f918(x85962,a909)),x85963),x85964)),f318(f66(x85965,x85965,x85965,f318(x85961,x85963)),f318(x85961,x85964)))
% 109.14/108.86 [10201]~P82(x102011)+~E(f808(x102014,x102015,x102013,x102016,x102012,x102011),f809(x102014,x102015,x102013,x102016,x102012,x102011))+~P1(f318(f55(x102012),x102016))+E(f318(f318(f318(f59(x102011,x102012,f74(x102011)),f318(f318(f10(f918(x102013,a909),x102011,x102012),f318(f318(f59(x102011,x102013,f74(x102011)),x102014),f71(x102011))),x102015)),f71(x102011)),x102016),f318(f318(f318(f59(x102011,x102013,f74(x102011)),x102014),f71(x102011)),f318(f318(f33(x102012,f918(x102013,a909)),x102016),x102015)))+P1(f318(f318(f320(x102012),f807(x102014,x102015,x102013,x102016,x102012,x102011)),x102016))
% 109.14/108.86 [10227]~P82(x102271)+~E(f808(x102274,x102275,x102273,x102276,x102272,x102271),f809(x102274,x102275,x102273,x102276,x102272,x102271))+~P1(f318(f55(x102272),x102276))+E(f318(f318(f318(f59(x102271,x102272,f74(x102271)),f318(f318(f10(f918(x102273,a909),x102271,x102272),f318(f318(f59(x102271,x102273,f74(x102271)),x102274),f71(x102271))),x102275)),f71(x102271)),x102276),f318(f318(f318(f59(x102271,x102273,f74(x102271)),x102274),f71(x102271)),f318(f318(f33(x102272,f918(x102273,a909)),x102276),x102275)))+~P1(f318(f55(x102273),f318(x102275,f807(x102274,x102275,x102273,x102276,x102272,x102271))))
% 109.14/108.86 [10230]~P82(x102301)+~P1(f318(f55(x102302),x102306))+E(f318(f318(f318(f59(x102301,x102302,f74(x102301)),f318(f318(f10(f918(x102303,a909),x102301,x102302),f318(f318(f59(x102301,x102303,f74(x102301)),x102304),f71(x102301))),x102305)),f71(x102301)),x102306),f318(f318(f318(f59(x102301,x102303,f74(x102301)),x102304),f71(x102301)),f318(f318(f33(x102302,f918(x102303,a909)),x102306),x102305)))+P1(f318(f318(f320(x102302),f807(x102304,x102305,x102303,x102306,x102302,x102301)),x102306))+P1(f318(f318(f320(x102302),f809(x102304,x102305,x102303,x102306,x102302,x102301)),x102306))
% 109.14/108.86 [10231]~P82(x102311)+~P1(f318(f55(x102312),x102316))+E(f318(f318(f318(f59(x102311,x102312,f74(x102311)),f318(f318(f10(f918(x102313,a909),x102311,x102312),f318(f318(f59(x102311,x102313,f74(x102311)),x102314),f71(x102311))),x102315)),f71(x102311)),x102316),f318(f318(f318(f59(x102311,x102313,f74(x102311)),x102314),f71(x102311)),f318(f318(f33(x102312,f918(x102313,a909)),x102316),x102315)))+P1(f318(f318(f320(x102312),f807(x102314,x102315,x102313,x102316,x102312,x102311)),x102316))+P1(f318(f318(f320(x102312),f808(x102314,x102315,x102313,x102316,x102312,x102311)),x102316))
% 109.14/108.86 [10248]~P82(x102481)+~P1(f318(f55(x102482),x102486))+E(f318(f318(f318(f59(x102481,x102482,f74(x102481)),f318(f318(f10(f918(x102483,a909),x102481,x102482),f318(f318(f59(x102481,x102483,f74(x102481)),x102484),f71(x102481))),x102485)),f71(x102481)),x102486),f318(f318(f318(f59(x102481,x102483,f74(x102481)),x102484),f71(x102481)),f318(f318(f33(x102482,f918(x102483,a909)),x102486),x102485)))+P1(f318(f318(f320(x102482),f809(x102484,x102485,x102483,x102486,x102482,x102481)),x102486))+~P1(f318(f55(x102483),f318(x102485,f807(x102484,x102485,x102483,x102486,x102482,x102481))))
% 109.14/108.86 [10249]~P82(x102491)+~P1(f318(f55(x102492),x102496))+E(f318(f318(f318(f59(x102491,x102492,f74(x102491)),f318(f318(f10(f918(x102493,a909),x102491,x102492),f318(f318(f59(x102491,x102493,f74(x102491)),x102494),f71(x102491))),x102495)),f71(x102491)),x102496),f318(f318(f318(f59(x102491,x102493,f74(x102491)),x102494),f71(x102491)),f318(f318(f33(x102492,f918(x102493,a909)),x102496),x102495)))+P1(f318(f318(f320(x102492),f808(x102494,x102495,x102493,x102496,x102492,x102491)),x102496))+~P1(f318(f55(x102493),f318(x102495,f807(x102494,x102495,x102493,x102496,x102492,x102491))))
% 109.14/108.86 [10269]~P82(x102691)+~E(f318(f318(f92(f918(x102693,a909)),f318(x102695,f809(x102694,x102695,x102693,x102696,x102692,x102691))),f318(x102695,f808(x102694,x102695,x102693,x102696,x102692,x102691))),f179(f918(x102693,a909)))+~P1(f318(f55(x102692),x102696))+E(f318(f318(f318(f59(x102691,x102692,f74(x102691)),f318(f318(f10(f918(x102693,a909),x102691,x102692),f318(f318(f59(x102691,x102693,f74(x102691)),x102694),f71(x102691))),x102695)),f71(x102691)),x102696),f318(f318(f318(f59(x102691,x102693,f74(x102691)),x102694),f71(x102691)),f318(f318(f33(x102692,f918(x102693,a909)),x102696),x102695)))+P1(f318(f318(f320(x102692),f807(x102694,x102695,x102693,x102696,x102692,x102691)),x102696))
% 109.14/108.86 [10279]~P82(x102791)+~E(f318(f318(f92(f918(x102793,a909)),f318(x102795,f809(x102794,x102795,x102793,x102796,x102792,x102791))),f318(x102795,f808(x102794,x102795,x102793,x102796,x102792,x102791))),f179(f918(x102793,a909)))+~P1(f318(f55(x102792),x102796))+E(f318(f318(f318(f59(x102791,x102792,f74(x102791)),f318(f318(f10(f918(x102793,a909),x102791,x102792),f318(f318(f59(x102791,x102793,f74(x102791)),x102794),f71(x102791))),x102795)),f71(x102791)),x102796),f318(f318(f318(f59(x102791,x102793,f74(x102791)),x102794),f71(x102791)),f318(f318(f33(x102792,f918(x102793,a909)),x102796),x102795)))+~P1(f318(f55(x102793),f318(x102795,f807(x102794,x102795,x102793,x102796,x102792,x102791))))
% 109.14/108.86 [9324]~P124(x93241)+~P120(x93241)+~P1(f318(f318(f278(x93241),x93242),x93245))+~P1(f318(f318(f278(x93241),x93242),f318(f318(f73(x93241),x93243),x93246)))+P1(f318(f318(f278(x93241),x93242),f318(f318(f73(x93241),f318(f318(f3(x93241),x93243),f318(f318(f74(x93241),x93244),x93245))),x93246)))
% 109.14/108.86 [9325]~P124(x93251)+~P120(x93251)+~P1(f318(f318(f278(x93251),x93252),x93255))+~P1(f318(f318(f278(x93251),x93252),f318(f318(f73(x93251),x93253),x93256)))+P1(f318(f318(f278(x93251),x93252),f318(f318(f73(x93251),f318(f318(f3(x93251),x93253),f318(f318(f74(x93251),x93254),x93255))),x93256)))
% 109.14/108.86 [9518]~P124(x95181)+~P120(x95181)+~P1(f318(f318(f278(x95181),x95182),x95185))+P1(f318(f318(f278(x95181),x95182),f318(f318(f73(x95181),x95183),x95184)))+~P1(f318(f318(f278(x95181),x95182),f318(f318(f73(x95181),f318(f318(f3(x95181),x95183),f318(f318(f74(x95181),x95186),x95185))),x95184)))
% 109.14/108.86 [9519]~P124(x95191)+~P120(x95191)+~P1(f318(f318(f278(x95191),x95192),x95195))+P1(f318(f318(f278(x95191),x95192),f318(f318(f73(x95191),x95193),x95194)))+~P1(f318(f318(f278(x95191),x95192),f318(f318(f73(x95191),f318(f318(f3(x95191),x95193),f318(f318(f74(x95191),x95196),x95195))),x95194)))
% 109.14/108.86 [8926]E(x89261,x89262)+~P60(x89264,x89265,x89266,x89263,x89267)+~E(f318(x89263,x89261),f318(x89263,x89262))+~P1(f318(f318(f320(x89265),x89262),x89267))+~P1(f318(f318(f320(x89265),x89261),x89267))
% 109.14/108.86 [9641]~P26(x96411,x96412,x96413,x96415,x96417)+~P26(x96411,x96412,x96413,x96414,x96416)+P26(x96411,x96412,x96413,f318(f318(f101(f918(x96411,a909)),x96414),x96415),f318(f318(f101(f918(x96412,a909)),x96416),x96417))+~E(f318(f318(f92(f918(x96412,a909)),x96416),x96417),f179(f918(x96412,a909)))+~E(f318(f318(f92(f918(x96411,a909)),x96414),x96415),f179(f918(x96411,a909)))
% 109.14/108.86 [10239]~P1(f318(x102392,x102394))+~E(x102395,f318(f127(x102391,x102392),x102397))+E(f318(f127(x102391,x102392),x102393),f318(f318(f142(x102391),x102394),x102395))+~E(x102393,f318(f318(f125(x102391),x102396),f318(f318(f142(x102391),x102394),x102397)))+P1(f318(x102392,f742(x102395,x102394,x102393,x102392,x102391,x102396,x102397)))
% 109.14/108.86 [10240]~P1(f318(x102404,x102402))+~E(x102403,f318(f127(x102401,x102404),x102407))+E(f318(f318(f142(x102401),x102402),x102403),f318(f127(x102401,x102404),x102405))+~E(x102405,f318(f318(f125(x102401),x102406),f318(f318(f142(x102401),x102402),x102407)))+P1(f318(x102404,f743(x102405,x102404,x102403,x102402,x102401,x102406,x102407)))
% 109.14/108.86 [10290]~P1(f318(x102902,x102904))+~E(x102905,f318(f127(x102901,x102902),x102907))+E(f318(f127(x102901,x102902),x102903),f318(f318(f142(x102901),x102904),x102905))+~E(x102903,f318(f318(f125(x102901),x102906),f318(f318(f142(x102901),x102904),x102907)))+P1(f318(f318(f320(x102901),f742(x102905,x102904,x102903,x102902,x102901,x102906,x102907)),f318(f163(x102901),x102906)))
% 109.14/108.86 [10291]~P1(f318(x102914,x102912))+~E(x102913,f318(f127(x102911,x102914),x102917))+E(f318(f318(f142(x102911),x102912),x102913),f318(f127(x102911,x102914),x102915))+~E(x102915,f318(f318(f125(x102911),x102916),f318(f318(f142(x102911),x102912),x102917)))+P1(f318(f318(f320(x102911),f743(x102915,x102914,x102913,x102912,x102911,x102916,x102917)),f318(f163(x102911),x102916)))
% 109.14/108.86 [10296]~P8(x102961,x102967,x102966)+~P11(x102961,f918(x102965,a909),x102966,x102964)+P1(f318(f318(f320(x102961),f528(x102962,x102963,x102964,x102965,x102966,x102967,x102961)),x102967))+~P1(f318(f318(f320(f918(x102961,a909)),x102963),f318(f318(f54(x102961),x102967),x102966)))+P1(f318(f318(f320(f918(x102965,a909)),f318(f318(f33(x102961,f918(x102965,a909)),x102963),x102964)),x102962))
% 109.14/108.86 [10376]~P8(x103762,x103766,x103767)+~P11(x103762,f918(x103761,a909),x103767,x103764)+~P1(f318(f318(f320(f918(x103762,a909)),x103763),f318(f318(f54(x103762),x103766),x103767)))+~P1(f318(f318(f320(f918(x103761,a909)),f318(x103764,f528(x103765,x103763,x103764,x103761,x103767,x103766,x103762))),x103765))+P1(f318(f318(f320(f918(x103761,a909)),f318(f318(f33(x103762,f918(x103761,a909)),x103763),x103764)),x103765))
% 109.14/108.86 [8514]~P82(x85142)+~P25(x85141,x85145,x85148,x85144)+~E(x85143,f318(f66(x85145,x85142,x85141,x85146),x85148))+~E(x85147,f318(f301(x85141,x85145,x85148),x85144))+E(f318(f318(f11(x85141,x85142),x85143),x85144),f318(f318(f11(x85145,x85142),x85146),x85147))
% 109.14/108.86 [10385]~P82(x103852)+~P25(x103855,x103851,x103858,x103857)+~E(f318(x103856,f511(x103853,x103856,x103854,x103857,x103858,x103851,x103855,x103852)),f318(f318(f66(x103851,x103852,x103855,x103853),x103858),f511(x103853,x103856,x103854,x103857,x103858,x103851,x103855,x103852)))+~E(x103854,f318(f301(x103855,x103851,x103858),x103857))+E(f318(f318(f11(x103851,x103852),x103853),x103854),f318(f318(f11(x103855,x103852),x103856),x103857))
% 109.14/108.86 [10394]~P76(x103942)+~P25(x103941,x103945,x103948,x103944)+~E(x103947,f318(f301(x103941,x103945,x103948),x103944))+E(f318(f318(f8(x103941,x103942),x103943),x103944),f318(f318(f8(x103945,x103942),x103946),x103947))+P1(f318(f318(f320(x103941),f907(x103946,x103943,x103947,x103944,x103948,x103945,x103941,x103942)),x103944))
% 109.14/108.86 [10395]~P82(x103952)+~P25(x103951,x103955,x103958,x103954)+~E(x103957,f318(f301(x103951,x103955,x103958),x103954))+E(f318(f318(f11(x103951,x103952),x103953),x103954),f318(f318(f11(x103955,x103952),x103956),x103957))+P1(f318(f318(f320(x103951),f511(x103956,x103953,x103957,x103954,x103958,x103955,x103951,x103952)),x103954))
% 109.14/108.86 [10400]~P76(x104002)+~P25(x104005,x104001,x104008,x104007)+~E(x104004,f318(f301(x104005,x104001,x104008),x104007))+~E(f318(x104006,f907(x104003,x104006,x104004,x104007,x104008,x104001,x104005,x104002)),f318(x104003,f318(x104008,f907(x104003,x104006,x104004,x104007,x104008,x104001,x104005,x104002))))+E(f318(f318(f8(x104001,x104002),x104003),x104004),f318(f318(f8(x104005,x104002),x104006),x104007))
% 109.14/108.86 [9836]~P23(x98366,x98362,x98365,x98367,x98368,x98361)+~P1(f318(f55(x98362),x98364))+~P1(f318(f55(x98362),x98363))+~E(f318(f318(f92(f918(x98362,a909)),x98363),x98364),f179(f918(x98362,a909)))+E(f318(x98361,f318(f318(f101(f918(x98362,a909)),x98363),x98364)),f318(f318(x98365,f318(x98361,x98363)),f318(x98361,x98364)))
% 109.14/108.86 [10226]~P23(x102268,x102262,x102265,x102267,x102266,x102261)+~E(f318(x102266,f904(x102264,x102263,x102261,x102266,x102267,x102265,x102262)),x102267)+~P1(f318(f55(x102262),x102263))+~P1(f318(f55(x102262),x102264))+E(f318(x102261,f318(f318(f101(f918(x102262,a909)),x102263),x102264)),f318(f318(x102265,f318(x102261,x102263)),f318(x102261,x102264)))
% 109.14/108.86 [10303]~P23(x103038,x103032,x103035,x103037,x103036,x103031)+~P1(f318(f55(x103032),x103033))+~P1(f318(f55(x103032),x103034))+E(f318(x103031,f318(f318(f101(f918(x103032,a909)),x103033),x103034)),f318(f318(x103035,f318(x103031,x103033)),f318(x103031,x103034)))+P1(f318(f318(f320(x103032),f904(x103034,x103033,x103031,x103036,x103037,x103035,x103032)),f318(f318(f92(f918(x103032,a909)),x103033),x103034)))
% 109.14/108.86 [10005]~P8(x100054,x100058,x100055)+~P8(x100051,x100059,x100053)+~P12(x100051,x100054,f918(x100052,a909),x100053,x100055,x100057)+P11(x100051,f918(x100052,a909),x100053,f318(f318(f10(f918(x100054,f918(x100052,a909)),f918(x100052,a909),x100051),f318(f33(x100054,f918(x100052,a909)),f318(f276(x100054,x100054,x100055),f318(f318(f300(x100054),x100056),f179(f918(x100054,a909)))))),x100057))+~P1(f318(f318(f320(x100054),x100056),x100058))
% 109.14/108.86 [5550]~P4(x55503)+~P13(x55503,x55501)+E(x55501,f720(x55502,x55503))+~E(f318(f163(x55503),x55501),x55502)+~P1(f318(f55(x55503),x55502))+~P1(f318(f128(x55503),x55501))
% 109.14/108.86 [7386]P15(x73861,x73862)+~E(f318(x73862,f801(x73862)),f318(x73862,f802(x73862)))+~P1(f318(f318(x73862,f801(x73862)),f801(x73862)))+~P1(f318(f318(x73862,f801(x73862)),f802(x73862)))+~P1(f318(f318(x73862,f802(x73862)),f802(x73862)))+~P1(f318(f318(x73862,x73863),x73863))
% 109.14/108.86 [5171]~P150(x51712)+~P118(x51712)+~P133(x51712)+~P138(x51712)+E(x51711,f2(x51712))+~E(f318(f318(f235(x51712),x51711),x51713),f2(x51712))
% 109.14/108.86 [5172]~P150(x51722)+~P118(x51722)+~P133(x51722)+~P138(x51722)+~E(x51721,f2(a911))+~E(f318(f318(f235(x51722),x51723),x51721),f2(x51722))
% 109.14/108.86 [6630]~P93(x66301)+~E(x66303,f2(x66301))+~E(x66302,f2(x66301))+E(f318(f318(f73(x66301),x66302),x66303),f2(x66301))+~P1(f318(f318(f225(x66301),f2(x66301)),x66303))+~P1(f318(f318(f225(x66301),f2(x66301)),x66302))
% 109.14/108.86 [8978]E(x89781,f2(a911))+~E(x89782,f318(f318(f73(a911),f318(f318(f74(a911),f318(f242(a911,a911),x89783)),x89781)),f318(f247(a911,a911),x89783)))+P1(f318(f42(x89782,x89781),x89783))+~P1(f318(f318(f225(a911),f318(f247(a911,a911),x89783)),f2(a911)))+P1(f318(f318(f226(a911),f2(a911)),x89781))+~P1(f318(f318(f226(a911),x89781),f318(f247(a911,a911),x89783)))
% 109.14/108.86 [8998]~E(f318(f242(a911,a911),x89983),f2(a911))+~E(x89981,f318(f318(f73(a911),f318(f318(f74(a911),f318(f242(a911,a911),x89983)),x89982)),f318(f247(a911,a911),x89983)))+P1(f318(f42(x89981,x89982),x89983))+~P1(f318(f318(f225(a911),f318(f247(a911,a911),x89983)),f2(a911)))+P1(f318(f318(f226(a911),f2(a911)),x89982))+~P1(f318(f318(f226(a911),x89982),f318(f247(a911,a911),x89983)))
% 109.14/108.86 [9006]E(x90061,f2(a911))+~E(x90062,f318(f318(f73(a911),f318(f318(f74(a911),f318(f242(a911,a911),x90063)),x90061)),f318(f247(a911,a911),x90063)))+P1(f318(f42(x90062,x90061),x90063))+~P1(f318(f318(f226(a911),f2(a911)),x90061))+~P1(f318(f318(f225(a911),f2(a911)),f318(f247(a911,a911),x90063)))+~P1(f318(f318(f226(a911),f318(f247(a911,a911),x90063)),x90061))
% 109.14/108.86 [9025]~E(f318(f242(a911,a911),x90253),f2(a911))+~E(x90251,f318(f318(f73(a911),f318(f318(f74(a911),f318(f242(a911,a911),x90253)),x90252)),f318(f247(a911,a911),x90253)))+P1(f318(f42(x90251,x90252),x90253))+~P1(f318(f318(f226(a911),f2(a911)),x90252))+~P1(f318(f318(f225(a911),f2(a911)),f318(f247(a911,a911),x90253)))+~P1(f318(f318(f226(a911),f318(f247(a911,a911),x90253)),x90252))
% 109.14/108.86 [7011]~P103(x70112)+E(x70111,f179(f918(x70112,a909)))+E(x70113,f179(f918(x70112,a909)))+~P1(f318(f55(x70112),x70111))+~P1(f318(f55(x70112),x70113))+E(f12(x70112,f318(f318(f101(f918(x70112,a909)),x70113),x70111)),f318(f318(f92(x70112),f12(x70112,x70113)),f12(x70112,x70111)))
% 109.14/108.86 [7012]~P103(x70122)+E(x70121,f179(f918(x70122,a909)))+E(x70123,f179(f918(x70122,a909)))+~P1(f318(f55(x70122),x70121))+~P1(f318(f55(x70122),x70123))+E(f15(x70122,f318(f318(f101(f918(x70122,a909)),x70123),x70121)),f318(f318(f101(x70122),f15(x70122,x70123)),f15(x70122,x70121)))
% 109.14/108.86 [7013]~P4(x70132)+E(x70131,f179(f918(x70132,a909)))+E(x70133,f179(f918(x70132,a909)))+~P1(f318(f55(x70132),x70131))+~P1(f318(f55(x70132),x70133))+E(f16(x70132,f318(f318(f101(f918(x70132,a909)),x70133),x70131)),f318(f318(f223(x70132),f16(x70132,x70133)),f16(x70132,x70131)))
% 109.14/108.86 [7014]~P4(x70142)+E(x70141,f179(f918(x70142,a909)))+E(x70143,f179(f918(x70142,a909)))+~P1(f318(f55(x70142),x70141))+~P1(f318(f55(x70142),x70143))+E(f17(x70142,f318(f318(f101(f918(x70142,a909)),x70143),x70141)),f318(f318(f224(x70142),f17(x70142,x70143)),f17(x70142,x70141)))
% 109.14/108.86 [7642]~P101(x76422)+E(x76421,f179(f918(x76422,a909)))+E(x76423,f179(f918(x76422,a909)))+~P1(f318(f55(x76422),x76421))+~P1(f318(f55(x76422),x76423))+E(f318(f318(f74(x76422),f318(f57(x76422,f74(x76422)),x76423)),f318(f57(x76422,f74(x76422)),x76421)),f318(f57(x76422,f74(x76422)),f318(f318(f101(f918(x76422,a909)),x76423),x76421)))
% 109.14/108.86 [7800]~P4(x78002)+E(x78001,f179(f918(x78002,a909)))+E(x78003,f179(f918(x78002,a909)))+~P1(f318(f55(x78002),x78001))+~P1(f318(f55(x78002),x78003))+E(f318(f318(f223(x78002),f13(x78002,f223(x78002),x78003)),f13(x78002,f223(x78002),x78001)),f13(x78002,f223(x78002),f318(f318(f101(f918(x78002,a909)),x78003),x78001)))
% 109.14/108.86 [7801]~P4(x78012)+E(x78011,f179(f918(x78012,a909)))+E(x78013,f179(f918(x78012,a909)))+~P1(f318(f55(x78012),x78011))+~P1(f318(f55(x78012),x78013))+E(f318(f318(f224(x78012),f14(x78012,f224(x78012),x78013)),f14(x78012,f224(x78012),x78011)),f14(x78012,f224(x78012),f318(f318(f101(f918(x78012,a909)),x78013),x78011)))
% 109.14/108.86 [8828]~P1(f318(x88281,x88283))+P1(f318(x88281,f381(x88281,x88282)))+P1(f318(x88281,f377(x88281,x88282)))+~P1(f318(f318(f226(a1),f2(a1)),x88282))+~P1(f318(f318(f320(a1),x88283),f294(a1,f71(a1),x88282)))+P1(f318(x88281,f318(f318(f3(a1),f377(x88281,x88282)),f318(f318(f74(a1),f379(x88281,x88282)),x88282))))
% 109.14/108.86 [9135]~P1(f318(x91351,x91353))+~P1(f318(x91351,f377(x91351,x91352)))+P1(f318(x91351,f381(x91351,x91352)))+~P1(f318(f318(f226(a1),f2(a1)),x91352))+~P1(f318(f318(f320(a1),x91353),f294(a1,f71(a1),x91352)))+~P1(f318(x91351,f318(f318(f3(a1),f377(x91351,x91352)),f318(f318(f74(a1),f379(x91351,x91352)),x91352))))
% 109.14/108.86 [10437]~P107(x104372)+E(x104371,f179(f918(x104372,a909)))+E(x104373,f179(f918(x104372,a909)))+~P1(f318(f55(x104372),x104371))+~P1(f318(f55(x104372),x104373))+E(f12(x104372,f318(f253(x104372),f318(f318(f10(f918(x104372,a909),a909,x104372),f79(x104372)),f318(f318(f10(f918(x104372,f918(x104372,a909)),f918(x104372,a909),x104372),f318(f10(f918(x104372,a909),a909,x104372),f79(x104372))),f318(f318(f9(x104372,f918(x104372,f918(x104372,a909)),f918(x104372,f918(x104372,a909))),f318(f318(f10(f918(x104372,f918(f918(x104372,a909),f918(x104372,a909))),f918(f918(x104372,f918(x104372,a909)),f918(x104372,f918(x104372,a909))),x104372),f20(x104372,f918(x104372,a909),f918(x104372,a909))),f318(f318(f10(f918(x104372,f918(x104372,f918(a909,a909))),f918(x104372,f918(f918(x104372,a909),f918(x104372,a909))),x104372),f318(f10(f918(x104372,f918(a909,a909)),f918(f918(x104372,a909),f918(x104372,a909)),x104372),f20(x104372,a909,a909))),f318(f318(f10(f918(x104372,f918(x104372,a909)),f918(x104372,f918(x104372,f918(a909,a909))),x104372),f318(f10(f918(x104372,a909),f918(x104372,f918(a909,a909)),x104372),f318(f10(a909,f918(a909,a909),x104372),a316))),f318(f318(f9(x104372,f918(x104372,f918(x104372,x104372)),f918(x104372,f918(x104372,a909))),f318(f318(f10(f918(f918(x104372,x104372),f918(x104372,a909)),f918(f918(x104372,f918(x104372,x104372)),f918(x104372,f918(x104372,a909))),x104372),f10(f918(x104372,x104372),f918(x104372,a909),x104372)),f318(f318(f10(f918(x104372,a909),f918(f918(x104372,x104372),f918(x104372,a909)),x104372),f10(x104372,a909,x104372)),a315))),f101(x104372)))))),f318(f318(f9(x104372,f918(x104372,a909),f918(x104372,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x104372,a909),f918(x104372,a909)),x104372),f10(a909,a909,x104372)),f318(f318(f10(a909,f918(a909,a909),x104372),a316),f318(f318(f9(x104372,f918(x104372,a909),a909),f320(x104372)),x104373)))),f318(f318(f9(x104372,f918(x104372,a909),a909),f320(x104372)),x104371))))))),f318(f318(f101(x104372),f12(x104372,x104373)),f12(x104372,x104371)))
% 109.14/108.86 [10438]~P107(x104382)+E(x104381,f179(f918(x104382,a909)))+E(x104383,f179(f918(x104382,a909)))+~P1(f318(f55(x104382),x104381))+~P1(f318(f55(x104382),x104383))+E(f15(x104382,f318(f253(x104382),f318(f318(f10(f918(x104382,a909),a909,x104382),f79(x104382)),f318(f318(f10(f918(x104382,f918(x104382,a909)),f918(x104382,a909),x104382),f318(f10(f918(x104382,a909),a909,x104382),f79(x104382))),f318(f318(f9(x104382,f918(x104382,f918(x104382,a909)),f918(x104382,f918(x104382,a909))),f318(f318(f10(f918(x104382,f918(f918(x104382,a909),f918(x104382,a909))),f918(f918(x104382,f918(x104382,a909)),f918(x104382,f918(x104382,a909))),x104382),f20(x104382,f918(x104382,a909),f918(x104382,a909))),f318(f318(f10(f918(x104382,f918(x104382,f918(a909,a909))),f918(x104382,f918(f918(x104382,a909),f918(x104382,a909))),x104382),f318(f10(f918(x104382,f918(a909,a909)),f918(f918(x104382,a909),f918(x104382,a909)),x104382),f20(x104382,a909,a909))),f318(f318(f10(f918(x104382,f918(x104382,a909)),f918(x104382,f918(x104382,f918(a909,a909))),x104382),f318(f10(f918(x104382,a909),f918(x104382,f918(a909,a909)),x104382),f318(f10(a909,f918(a909,a909),x104382),a316))),f318(f318(f9(x104382,f918(x104382,f918(x104382,x104382)),f918(x104382,f918(x104382,a909))),f318(f318(f10(f918(f918(x104382,x104382),f918(x104382,a909)),f918(f918(x104382,f918(x104382,x104382)),f918(x104382,f918(x104382,a909))),x104382),f10(f918(x104382,x104382),f918(x104382,a909),x104382)),f318(f318(f10(f918(x104382,a909),f918(f918(x104382,x104382),f918(x104382,a909)),x104382),f10(x104382,a909,x104382)),a315))),f92(x104382)))))),f318(f318(f9(x104382,f918(x104382,a909),f918(x104382,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x104382,a909),f918(x104382,a909)),x104382),f10(a909,a909,x104382)),f318(f318(f10(a909,f918(a909,a909),x104382),a316),f318(f318(f9(x104382,f918(x104382,a909),a909),f320(x104382)),x104383)))),f318(f318(f9(x104382,f918(x104382,a909),a909),f320(x104382)),x104381))))))),f318(f318(f92(x104382),f15(x104382,x104383)),f15(x104382,x104381)))
% 109.14/108.86 [10439]~P4(x104392)+E(x104391,f179(f918(x104392,a909)))+E(x104393,f179(f918(x104392,a909)))+~P1(f318(f55(x104392),x104391))+~P1(f318(f55(x104392),x104393))+E(f14(x104392,f224(x104392),f318(f253(x104392),f318(f318(f10(f918(x104392,a909),a909,x104392),f79(x104392)),f318(f318(f10(f918(x104392,f918(x104392,a909)),f918(x104392,a909),x104392),f318(f10(f918(x104392,a909),a909,x104392),f79(x104392))),f318(f318(f9(x104392,f918(x104392,f918(x104392,a909)),f918(x104392,f918(x104392,a909))),f318(f318(f10(f918(x104392,f918(f918(x104392,a909),f918(x104392,a909))),f918(f918(x104392,f918(x104392,a909)),f918(x104392,f918(x104392,a909))),x104392),f20(x104392,f918(x104392,a909),f918(x104392,a909))),f318(f318(f10(f918(x104392,f918(x104392,f918(a909,a909))),f918(x104392,f918(f918(x104392,a909),f918(x104392,a909))),x104392),f318(f10(f918(x104392,f918(a909,a909)),f918(f918(x104392,a909),f918(x104392,a909)),x104392),f20(x104392,a909,a909))),f318(f318(f10(f918(x104392,f918(x104392,a909)),f918(x104392,f918(x104392,f918(a909,a909))),x104392),f318(f10(f918(x104392,a909),f918(x104392,f918(a909,a909)),x104392),f318(f10(a909,f918(a909,a909),x104392),a316))),f318(f318(f9(x104392,f918(x104392,f918(x104392,x104392)),f918(x104392,f918(x104392,a909))),f318(f318(f10(f918(f918(x104392,x104392),f918(x104392,a909)),f918(f918(x104392,f918(x104392,x104392)),f918(x104392,f918(x104392,a909))),x104392),f10(f918(x104392,x104392),f918(x104392,a909),x104392)),f318(f318(f10(f918(x104392,a909),f918(f918(x104392,x104392),f918(x104392,a909)),x104392),f10(x104392,a909,x104392)),a315))),f223(x104392)))))),f318(f318(f9(x104392,f918(x104392,a909),f918(x104392,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x104392,a909),f918(x104392,a909)),x104392),f10(a909,a909,x104392)),f318(f318(f10(a909,f918(a909,a909),x104392),a316),f318(f318(f9(x104392,f918(x104392,a909),a909),f320(x104392)),x104393)))),f318(f318(f9(x104392,f918(x104392,a909),a909),f320(x104392)),x104391))))))),f318(f318(f223(x104392),f14(x104392,f224(x104392),x104393)),f14(x104392,f224(x104392),x104391)))
% 109.14/108.86 [10440]~P4(x104402)+E(x104401,f179(f918(x104402,a909)))+E(x104403,f179(f918(x104402,a909)))+~P1(f318(f55(x104402),x104401))+~P1(f318(f55(x104402),x104403))+E(f13(x104402,f223(x104402),f318(f253(x104402),f318(f318(f10(f918(x104402,a909),a909,x104402),f79(x104402)),f318(f318(f10(f918(x104402,f918(x104402,a909)),f918(x104402,a909),x104402),f318(f10(f918(x104402,a909),a909,x104402),f79(x104402))),f318(f318(f9(x104402,f918(x104402,f918(x104402,a909)),f918(x104402,f918(x104402,a909))),f318(f318(f10(f918(x104402,f918(f918(x104402,a909),f918(x104402,a909))),f918(f918(x104402,f918(x104402,a909)),f918(x104402,f918(x104402,a909))),x104402),f20(x104402,f918(x104402,a909),f918(x104402,a909))),f318(f318(f10(f918(x104402,f918(x104402,f918(a909,a909))),f918(x104402,f918(f918(x104402,a909),f918(x104402,a909))),x104402),f318(f10(f918(x104402,f918(a909,a909)),f918(f918(x104402,a909),f918(x104402,a909)),x104402),f20(x104402,a909,a909))),f318(f318(f10(f918(x104402,f918(x104402,a909)),f918(x104402,f918(x104402,f918(a909,a909))),x104402),f318(f10(f918(x104402,a909),f918(x104402,f918(a909,a909)),x104402),f318(f10(a909,f918(a909,a909),x104402),a316))),f318(f318(f9(x104402,f918(x104402,f918(x104402,x104402)),f918(x104402,f918(x104402,a909))),f318(f318(f10(f918(f918(x104402,x104402),f918(x104402,a909)),f918(f918(x104402,f918(x104402,x104402)),f918(x104402,f918(x104402,a909))),x104402),f10(f918(x104402,x104402),f918(x104402,a909),x104402)),f318(f318(f10(f918(x104402,a909),f918(f918(x104402,x104402),f918(x104402,a909)),x104402),f10(x104402,a909,x104402)),a315))),f224(x104402)))))),f318(f318(f9(x104402,f918(x104402,a909),f918(x104402,a909)),f318(f318(f10(f918(a909,a909),f918(f918(x104402,a909),f918(x104402,a909)),x104402),f10(a909,a909,x104402)),f318(f318(f10(a909,f918(a909,a909),x104402),a316),f318(f318(f9(x104402,f918(x104402,a909),a909),f320(x104402)),x104403)))),f318(f318(f9(x104402,f918(x104402,a909),a909),f320(x104402)),x104401))))))),f318(f318(f224(x104402),f13(x104402,f223(x104402),x104403)),f13(x104402,f223(x104402),x104401)))
% 109.14/108.86 [7342]~P130(x73423)+E(x73421,x73422)+~E(f318(f318(f235(x73423),x73421),x73424),f318(f318(f235(x73423),x73422),x73424))+~P1(f318(f318(f225(x73423),f2(x73423)),x73422))+~P1(f318(f318(f225(x73423),f2(x73423)),x73421))+~P1(f318(f318(f226(a911),f2(a911)),x73424))
% 109.14/108.86 [8144]~P100(x81441)+~P74(x81441)+P1(f318(f318(f226(x81441),x81442),f2(x81441)))+P1(f318(f318(f226(x81441),f2(x81441)),x81442))+P1(f318(f318(f225(x81441),f318(f318(f282(x81441),x81443),x81442)),f318(f94(x81441),x81444)))+~P1(f318(f318(f225(x81441),f2(x81441)),f318(f94(x81441),x81444)))
% 109.14/108.86 [8145]~P100(x81451)+~P74(x81451)+P1(f318(f318(f226(x81451),x81452),f2(x81451)))+P1(f318(f318(f226(x81451),f2(x81451)),x81452))+P1(f318(f318(f226(x81451),f318(f318(f282(x81451),x81453),x81452)),f318(f94(x81451),x81454)))+~P1(f318(f318(f226(x81451),f2(x81451)),f318(f94(x81451),x81454)))
% 109.14/108.86 [8392]~P100(x83921)+~P74(x83921)+P1(f318(f318(f226(x83921),x83922),f2(x83921)))+P1(f318(f318(f226(x83921),f2(x83921)),x83922))+~P1(f318(f318(f225(x83921),f318(f318(f282(x83921),x83924),x83922)),f318(f94(x83921),x83923)))+P1(f318(f318(f225(x83921),f2(x83921)),f318(f94(x83921),x83923)))
% 109.14/108.86 [8393]~P100(x83931)+~P74(x83931)+P1(f318(f318(f226(x83931),x83932),f2(x83931)))+P1(f318(f318(f226(x83931),f2(x83931)),x83932))+~P1(f318(f318(f226(x83931),f318(f318(f282(x83931),x83934),x83932)),f318(f94(x83931),x83933)))+P1(f318(f318(f226(x83931),f2(x83931)),f318(f94(x83931),x83933)))
% 109.14/108.86 [9266]~P1(f318(x92662,x92663))+~P1(f318(x92661,x92664))+E(f229(a911,x92661),f318(a103,f229(a911,x92662)))+P1(f318(x92662,f821(x92663,x92662,x92664,x92661)))+P1(f318(x92661,f2(a911)))+P1(f318(x92661,f318(a103,f821(x92663,x92662,x92664,x92661))))
% 109.14/108.86 [9537]~P1(f318(x95372,x95373))+~P1(f318(x95371,x95374))+E(f229(a911,x95371),f318(a103,f229(a911,x95372)))+~P1(f318(x95372,f821(x95373,x95372,x95374,x95371)))+P1(f318(x95371,f2(a911)))+~P1(f318(x95371,f318(a103,f821(x95373,x95372,x95374,x95371))))
% 109.14/108.86 [7603]~P4(x76032)+E(x76031,f179(f918(x76032,a909)))+~P1(f318(f55(x76032),x76031))+~P1(f318(f318(f320(x76032),x76034),x76031))+P1(f318(f318(f225(x76032),x76033),x76034))+~P1(f318(f318(f225(x76032),x76033),f318(f57(x76032,f223(x76032)),x76031)))
% 109.14/108.86 [7604]~P108(x76042)+E(x76041,f179(f918(x76042,a909)))+~P1(f318(f55(x76042),x76041))+~P1(f318(f318(f320(x76042),x76044),x76041))+P1(f318(f318(f225(x76042),x76043),x76044))+~P1(f318(f318(f225(x76042),x76043),f318(f57(x76042,f92(x76042)),x76041)))
% 109.14/108.86 [7605]~P4(x76052)+E(x76051,f179(f918(x76052,a909)))+~P1(f318(f55(x76052),x76051))+~P1(f318(f318(f320(x76052),x76054),x76051))+P1(f318(f318(f226(x76052),x76053),x76054))+~P1(f318(f318(f226(x76052),x76053),f318(f57(x76052,f223(x76052)),x76051)))
% 109.14/108.86 [8101]~P100(x81011)+~P74(x81011)+P1(f318(f318(f226(x81011),f318(f94(x81011),x81012)),f2(x81011)))+~P1(f318(f318(f225(x81011),x81013),f2(x81011)))+P1(f318(f318(f226(x81011),f2(x81011)),f318(f94(x81011),x81012)))+P1(f318(f318(f225(x81011),x81013),f318(f318(f282(x81011),x81014),f318(f94(x81011),x81012))))
% 109.14/108.86 [8102]~P100(x81021)+~P74(x81021)+P1(f318(f318(f226(x81021),f318(f94(x81021),x81022)),f2(x81021)))+~P1(f318(f318(f226(x81021),x81023),f2(x81021)))+P1(f318(f318(f226(x81021),f2(x81021)),f318(f94(x81021),x81022)))+P1(f318(f318(f226(x81021),x81023),f318(f318(f282(x81021),x81024),f318(f94(x81021),x81022))))
% 109.14/108.86 [8113]~P100(x81131)+~P74(x81131)+P1(f318(f318(f226(x81131),x81132),f2(x81131)))+~P1(f318(f318(f225(x81131),f318(f94(x81131),x81133)),f2(x81131)))+P1(f318(f318(f226(x81131),f2(x81131)),x81132))+P1(f318(f318(f225(x81131),f318(f94(x81131),x81133)),f318(f318(f282(x81131),x81134),x81132)))
% 109.14/108.86 [8114]~P100(x81141)+~P74(x81141)+P1(f318(f318(f226(x81141),x81142),f2(x81141)))+~P1(f318(f318(f226(x81141),f318(f94(x81141),x81143)),f2(x81141)))+P1(f318(f318(f226(x81141),f2(x81141)),x81142))+P1(f318(f318(f226(x81141),f318(f94(x81141),x81143)),f318(f318(f282(x81141),x81144),x81142)))
% 109.14/108.86 [8268]~P100(x82681)+~P74(x82681)+P1(f318(f318(f226(x82681),x82682),f2(x82681)))+P1(f318(f318(f225(x82681),f318(f94(x82681),x82683)),f2(x82681)))+P1(f318(f318(f226(x82681),f2(x82681)),x82682))+~P1(f318(f318(f225(x82681),f318(f94(x82681),x82683)),f318(f318(f282(x82681),x82684),x82682)))
% 109.14/108.86 [8269]~P100(x82691)+~P74(x82691)+P1(f318(f318(f226(x82691),x82692),f2(x82691)))+P1(f318(f318(f226(x82691),f318(f94(x82691),x82693)),f2(x82691)))+P1(f318(f318(f226(x82691),f2(x82691)),x82692))+~P1(f318(f318(f226(x82691),f318(f94(x82691),x82693)),f318(f318(f282(x82691),x82694),x82692)))
% 109.14/108.86 [8342]~P100(x83421)+~P74(x83421)+P1(f318(f318(f225(x83421),x83422),f2(x83421)))+P1(f318(f318(f226(x83421),f318(f94(x83421),x83423)),f2(x83421)))+P1(f318(f318(f226(x83421),f2(x83421)),f318(f94(x83421),x83423)))+~P1(f318(f318(f225(x83421),x83422),f318(f318(f282(x83421),x83424),f318(f94(x83421),x83423))))
% 109.14/108.86 [8343]~P100(x83431)+~P74(x83431)+P1(f318(f318(f226(x83431),x83432),f2(x83431)))+P1(f318(f318(f226(x83431),f318(f94(x83431),x83433)),f2(x83431)))+P1(f318(f318(f226(x83431),f2(x83431)),f318(f94(x83431),x83433)))+~P1(f318(f318(f226(x83431),x83432),f318(f318(f282(x83431),x83434),f318(f94(x83431),x83433))))
% 109.14/108.86 [8529]~P100(x85291)+~P74(x85291)+~P1(f318(f318(f225(x85291),x85293),f2(x85291)))+P1(f318(f318(f226(x85291),f2(x85291)),f318(f94(x85291),x85292)))+~P1(f318(f318(f225(x85291),x85294),f318(f318(f74(x85291),x85293),f318(f94(x85291),x85292))))+P1(f318(f318(f225(x85291),x85293),f318(f318(f282(x85291),x85294),f318(f94(x85291),x85292))))
% 109.14/108.86 [8530]~P100(x85301)+~P74(x85301)+~P1(f318(f318(f226(x85301),x85303),f2(x85301)))+P1(f318(f318(f226(x85301),f2(x85301)),f318(f94(x85301),x85302)))+~P1(f318(f318(f226(x85301),x85304),f318(f318(f74(x85301),x85303),f318(f94(x85301),x85302))))+P1(f318(f318(f226(x85301),x85303),f318(f318(f282(x85301),x85304),f318(f94(x85301),x85302))))
% 109.14/108.86 [8700]~P100(x87001)+~P74(x87001)+~P1(f318(f318(f226(x87001),f318(f94(x87001),x87002)),f2(x87001)))+P1(f318(f318(f226(x87001),f2(x87001)),f318(f94(x87001),x87002)))+~P1(f318(f318(f225(x87001),x87004),f318(f318(f74(x87001),x87003),f318(f94(x87001),x87002))))+P1(f318(f318(f225(x87001),x87003),f318(f318(f282(x87001),x87004),f318(f94(x87001),x87002))))
% 109.14/108.86 [8701]~P100(x87011)+~P74(x87011)+~P1(f318(f318(f226(x87011),f318(f94(x87011),x87012)),f2(x87011)))+P1(f318(f318(f226(x87011),f2(x87011)),f318(f94(x87011),x87012)))+~P1(f318(f318(f225(x87011),x87014),f318(f318(f282(x87011),x87013),f318(f94(x87011),x87012))))+P1(f318(f318(f225(x87011),x87013),f318(f318(f74(x87011),x87014),f318(f94(x87011),x87012))))
% 109.14/108.86 [8702]~P100(x87021)+~P74(x87021)+~P1(f318(f318(f226(x87021),f318(f94(x87021),x87022)),f2(x87021)))+P1(f318(f318(f226(x87021),f2(x87021)),f318(f94(x87021),x87022)))+~P1(f318(f318(f226(x87021),x87024),f318(f318(f74(x87021),x87023),f318(f94(x87021),x87022))))+P1(f318(f318(f226(x87021),x87023),f318(f318(f282(x87021),x87024),f318(f94(x87021),x87022))))
% 109.14/108.86 [8703]~P100(x87031)+~P74(x87031)+~P1(f318(f318(f226(x87031),f318(f94(x87031),x87032)),f2(x87031)))+P1(f318(f318(f226(x87031),f2(x87031)),f318(f94(x87031),x87032)))+~P1(f318(f318(f226(x87031),x87034),f318(f318(f282(x87031),x87033),f318(f94(x87031),x87032))))+P1(f318(f318(f226(x87031),x87033),f318(f318(f74(x87031),x87034),f318(f94(x87031),x87032))))
% 109.14/108.86 [7512]E(x75121,f2(a1))+E(f318(f318(f30(a1),x75122),x75121),x75123)+~P1(f318(f318(f225(a1),x75124),f2(a1)))+~E(x75122,f318(f318(f73(a1),f318(f318(f74(a1),x75121),x75123)),x75124))+P1(f318(f318(f226(a1),f2(a1)),x75121))+~P1(f318(f318(f226(a1),x75121),x75124))
% 109.14/108.86 [7526]E(f39(a1,x75262,x75261),x75263)+E(x75261,f2(a1))+~P1(f318(f318(f225(a1),x75263),f2(a1)))+~E(x75262,f318(f318(f73(a1),f318(f318(f74(a1),x75261),x75264)),x75263))+P1(f318(f318(f226(a1),f2(a1)),x75261))+~P1(f318(f318(f226(a1),x75261),x75263))
% 109.14/108.86 [7641]E(x76411,f2(a1))+E(f318(f318(f30(a1),x76412),x76411),x76413)+~E(x76412,f318(f318(f73(a1),f318(f318(f74(a1),x76411),x76413)),x76414))+~P1(f318(f318(f225(a1),f2(a1)),x76414))+~P1(f318(f318(f226(a1),f2(a1)),x76411))+~P1(f318(f318(f226(a1),x76414),x76411))
% 109.14/108.86 [7663]E(f39(a1,x76632,x76631),x76633)+E(x76631,f2(a1))+~E(x76632,f318(f318(f73(a1),f318(f318(f74(a1),x76631),x76634)),x76633))+~P1(f318(f318(f225(a1),f2(a1)),x76633))+~P1(f318(f318(f226(a1),f2(a1)),x76631))+~P1(f318(f318(f226(a1),x76633),x76631))
% 109.14/108.86 [7804]~P4(x78042)+E(x78041,f179(f918(x78042,a909)))+~P1(f318(f55(x78042),x78041))+~P1(f318(f318(f320(x78042),x78044),x78041))+~P1(f318(f318(f225(x78042),x78044),x78043))+P1(f318(f318(f225(x78042),f318(f57(x78042,f223(x78042)),x78041)),x78043))
% 109.14/108.86 [7805]~P4(x78052)+E(x78051,f179(f918(x78052,a909)))+~P1(f318(f55(x78052),x78051))+~P1(f318(f318(f226(x78052),x78054),x78053))+~P1(f318(f318(f320(x78052),x78054),x78051))+P1(f318(f318(f226(x78052),f318(f57(x78052,f223(x78052)),x78051)),x78053))
% 109.14/108.86 [8370]~P1(f318(f318(f225(a1),x83704),f2(a1)))+~E(x83701,f318(f318(f73(a1),f318(f318(f74(a1),x83702),x83703)),x83704))+~P1(f318(f318(f225(a1),f2(a1)),x83704))+~P1(f318(f318(f226(a1),x83704),x83702))+~P1(f318(f318(f226(a1),x83702),x83704))+P1(f318(f43(x83701,x83702),f318(f318(f243(a1,a1),x83703),x83704)))
% 109.14/108.86 [8491]~P100(x84911)+~P74(x84911)+P1(f318(f318(f226(x84911),f318(f94(x84911),x84912)),f2(x84911)))+~P1(f318(f318(f225(x84911),f2(x84911)),x84914))+P1(f318(f318(f226(x84911),f2(x84911)),f318(f94(x84911),x84912)))+P1(f318(f318(f225(x84911),f318(f318(f282(x84911),x84913),f318(f94(x84911),x84912))),x84914))
% 109.14/108.86 [8492]~P100(x84921)+~P74(x84921)+P1(f318(f318(f226(x84921),f318(f94(x84921),x84922)),f2(x84921)))+~P1(f318(f318(f226(x84921),f2(x84921)),x84924))+P1(f318(f318(f226(x84921),f2(x84921)),f318(f94(x84921),x84922)))+P1(f318(f318(f226(x84921),f318(f318(f282(x84921),x84923),f318(f94(x84921),x84922))),x84924))
% 109.14/108.86 [8604]~P100(x86041)+~P74(x86041)+~P1(f318(f318(f226(x86041),x86042),f2(x86041)))+P1(f318(f318(f226(x86041),f2(x86041)),x86042))+~P1(f318(f318(f225(x86041),f318(f94(x86041),x86044)),f318(f318(f282(x86041),x86043),x86042)))+P1(f318(f318(f225(x86041),x86043),f318(f318(f74(x86041),f318(f94(x86041),x86044)),x86042)))
% 109.14/108.86 [8605]~P100(x86051)+~P74(x86051)+~P1(f318(f318(f226(x86051),x86052),f2(x86051)))+P1(f318(f318(f226(x86051),f2(x86051)),x86052))+~P1(f318(f318(f226(x86051),f318(f94(x86051),x86054)),f318(f318(f282(x86051),x86053),x86052)))+P1(f318(f318(f226(x86051),x86053),f318(f318(f74(x86051),f318(f94(x86051),x86054)),x86052)))
% 109.14/108.86 [8641]~P100(x86411)+~P74(x86411)+~P1(f318(f318(f226(x86411),x86412),f2(x86411)))+P1(f318(f318(f226(x86411),f2(x86411)),x86412))+P1(f318(f318(f225(x86411),f318(f94(x86411),x86413)),f318(f318(f282(x86411),x86414),x86412)))+~P1(f318(f318(f225(x86411),x86414),f318(f318(f74(x86411),f318(f94(x86411),x86413)),x86412)))
% 109.14/108.86 [8642]~P100(x86421)+~P74(x86421)+~P1(f318(f318(f226(x86421),x86422),f2(x86421)))+P1(f318(f318(f226(x86421),f2(x86421)),x86422))+P1(f318(f318(f226(x86421),f318(f94(x86421),x86423)),f318(f318(f282(x86421),x86424),x86422)))+~P1(f318(f318(f226(x86421),x86424),f318(f318(f74(x86421),f318(f94(x86421),x86423)),x86422)))
% 109.14/108.86 [8739]~P100(x87391)+~P74(x87391)+P1(f318(f318(f226(x87391),f318(f94(x87391),x87393)),f2(x87391)))+P1(f318(f318(f225(x87391),f2(x87391)),x87392))+P1(f318(f318(f226(x87391),f2(x87391)),f318(f94(x87391),x87393)))+~P1(f318(f318(f225(x87391),f318(f318(f282(x87391),x87394),f318(f94(x87391),x87393))),x87392))
% 109.14/108.86 [8740]~P100(x87401)+~P74(x87401)+P1(f318(f318(f226(x87401),f318(f94(x87401),x87403)),f2(x87401)))+P1(f318(f318(f226(x87401),f2(x87401)),x87402))+P1(f318(f318(f226(x87401),f2(x87401)),f318(f94(x87401),x87403)))+~P1(f318(f318(f226(x87401),f318(f318(f282(x87401),x87404),f318(f94(x87401),x87403))),x87402))
% 109.14/108.86 [8791]~P100(x87911)+~P74(x87911)+~P1(f318(f318(f225(x87911),f318(f94(x87911),x87913)),f2(x87911)))+P1(f318(f318(f226(x87911),f2(x87911)),x87912))+P1(f318(f318(f225(x87911),f318(f94(x87911),x87913)),f318(f318(f282(x87911),x87914),x87912)))+~P1(f318(f318(f225(x87911),x87914),f318(f318(f74(x87911),f318(f94(x87911),x87913)),x87912)))
% 109.14/108.86 [8792]~P100(x87921)+~P74(x87921)+~P1(f318(f318(f226(x87921),f318(f94(x87921),x87923)),f2(x87921)))+P1(f318(f318(f226(x87921),f2(x87921)),x87922))+P1(f318(f318(f226(x87921),f318(f94(x87921),x87923)),f318(f318(f282(x87921),x87924),x87922)))+~P1(f318(f318(f226(x87921),x87924),f318(f318(f74(x87921),f318(f94(x87921),x87923)),x87922)))
% 109.14/108.86 [8800]~P100(x88001)+~P74(x88001)+P1(f318(f318(f226(x88001),x88002),f2(x88001)))+P1(f318(f318(f225(x88001),f318(f318(f282(x88001),x88003),x88002)),f318(f94(x88001),x88004)))+~P1(f318(f318(f225(x88001),f2(x88001)),f318(f94(x88001),x88004)))+~P1(f318(f318(f225(x88001),x88003),f318(f318(f74(x88001),f318(f94(x88001),x88004)),x88002)))
% 109.14/108.86 [8801]~P100(x88011)+~P74(x88011)+P1(f318(f318(f226(x88011),x88012),f2(x88011)))+P1(f318(f318(f226(x88011),f318(f318(f282(x88011),x88013),x88012)),f318(f94(x88011),x88014)))+~P1(f318(f318(f226(x88011),f2(x88011)),f318(f94(x88011),x88014)))+~P1(f318(f318(f226(x88011),x88013),f318(f318(f74(x88011),f318(f94(x88011),x88014)),x88012)))
% 109.14/108.86 [8816]~P100(x88161)+~P74(x88161)+P1(f318(f318(f226(x88161),f318(f94(x88161),x88162)),f2(x88161)))+~P1(f318(f318(f225(x88161),f2(x88161)),x88164))+~P1(f318(f318(f225(x88161),x88163),f318(f318(f74(x88161),x88164),f318(f94(x88161),x88162))))+P1(f318(f318(f225(x88161),f318(f318(f282(x88161),x88163),f318(f94(x88161),x88162))),x88164))
% 109.14/108.86 [8817]~P100(x88171)+~P74(x88171)+P1(f318(f318(f226(x88171),f318(f94(x88171),x88172)),f2(x88171)))+~P1(f318(f318(f226(x88171),f2(x88171)),x88174))+~P1(f318(f318(f226(x88171),x88173),f318(f318(f74(x88171),x88174),f318(f94(x88171),x88172))))+P1(f318(f318(f226(x88171),f318(f318(f282(x88171),x88173),f318(f94(x88171),x88172))),x88174))
% 109.14/108.86 [8902]~P100(x89021)+~P74(x89021)+P1(f318(f318(f226(x89021),f318(f94(x89021),x89022)),f2(x89021)))+~P1(f318(f318(f225(x89021),x89023),f2(x89021)))+P1(f318(f318(f225(x89021),x89023),f318(f318(f282(x89021),x89024),f318(f94(x89021),x89022))))+~P1(f318(f318(f225(x89021),f318(f318(f74(x89021),x89023),f318(f94(x89021),x89022))),x89024))
% 109.14/108.86 [8903]~P100(x89031)+~P74(x89031)+P1(f318(f318(f226(x89031),f318(f94(x89031),x89032)),f2(x89031)))+~P1(f318(f318(f226(x89031),x89033),f2(x89031)))+P1(f318(f318(f226(x89031),x89033),f318(f318(f282(x89031),x89034),f318(f94(x89031),x89032))))+~P1(f318(f318(f226(x89031),f318(f318(f74(x89031),x89033),f318(f94(x89031),x89032))),x89034))
% 109.14/108.86 [9030]~P100(x90301)+~P74(x90301)+~P1(f318(f318(f225(x90301),f2(x90301)),x90304))+P1(f318(f318(f226(x90301),f2(x90301)),f318(f94(x90301),x90302)))+~P1(f318(f318(f225(x90301),f318(f318(f74(x90301),x90304),f318(f94(x90301),x90302))),x90303))+P1(f318(f318(f225(x90301),f318(f318(f282(x90301),x90303),f318(f94(x90301),x90302))),x90304))
% 109.14/108.86 [9031]~P100(x90311)+~P74(x90311)+~P1(f318(f318(f226(x90311),f2(x90311)),x90314))+P1(f318(f318(f226(x90311),f2(x90311)),f318(f94(x90311),x90312)))+~P1(f318(f318(f226(x90311),f318(f318(f74(x90311),x90314),f318(f94(x90311),x90312))),x90313))+P1(f318(f318(f226(x90311),f318(f318(f282(x90311),x90313),f318(f94(x90311),x90312))),x90314))
% 109.14/108.86 [9088]~P100(x90881)+~P74(x90881)+~P1(f318(f318(f225(x90881),x90882),f2(x90881)))+P1(f318(f318(f225(x90881),x90882),f318(f318(f282(x90881),x90883),f318(f94(x90881),x90884))))+~P1(f318(f318(f225(x90881),x90883),f318(f318(f74(x90881),x90882),f318(f94(x90881),x90884))))+~P1(f318(f318(f225(x90881),f318(f318(f74(x90881),x90882),f318(f94(x90881),x90884))),x90883))
% 109.14/108.86 [9089]~P100(x90891)+~P74(x90891)+~P1(f318(f318(f226(x90891),x90892),f2(x90891)))+P1(f318(f318(f226(x90891),x90892),f318(f318(f282(x90891),x90893),f318(f94(x90891),x90894))))+~P1(f318(f318(f226(x90891),x90893),f318(f318(f74(x90891),x90892),f318(f94(x90891),x90894))))+~P1(f318(f318(f226(x90891),f318(f318(f74(x90891),x90892),f318(f94(x90891),x90894))),x90893))
% 109.14/108.86 [9117]~P100(x91171)+~P74(x91171)+~P1(f318(f318(f226(x91171),f318(f94(x91171),x91172)),f2(x91171)))+P1(f318(f318(f226(x91171),f2(x91171)),f318(f94(x91171),x91172)))+~P1(f318(f318(f225(x91171),f318(f318(f282(x91171),x91174),f318(f94(x91171),x91172))),x91173))+P1(f318(f318(f225(x91171),f318(f318(f74(x91171),x91173),f318(f94(x91171),x91172))),x91174))
% 109.14/108.86 [9118]~P100(x91181)+~P74(x91181)+~P1(f318(f318(f226(x91181),f318(f94(x91181),x91182)),f2(x91181)))+P1(f318(f318(f226(x91181),f2(x91181)),f318(f94(x91181),x91182)))+~P1(f318(f318(f225(x91181),f318(f318(f74(x91181),x91184),f318(f94(x91181),x91182))),x91183))+P1(f318(f318(f225(x91181),f318(f318(f282(x91181),x91183),f318(f94(x91181),x91182))),x91184))
% 109.14/108.86 [9119]~P100(x91191)+~P74(x91191)+~P1(f318(f318(f226(x91191),f318(f94(x91191),x91192)),f2(x91191)))+P1(f318(f318(f226(x91191),f2(x91191)),f318(f94(x91191),x91192)))+~P1(f318(f318(f226(x91191),f318(f318(f282(x91191),x91194),f318(f94(x91191),x91192))),x91193))+P1(f318(f318(f226(x91191),f318(f318(f74(x91191),x91193),f318(f94(x91191),x91192))),x91194))
% 109.14/108.86 [9120]~P100(x91201)+~P74(x91201)+~P1(f318(f318(f226(x91201),f318(f94(x91201),x91202)),f2(x91201)))+P1(f318(f318(f226(x91201),f2(x91201)),f318(f94(x91201),x91202)))+~P1(f318(f318(f226(x91201),f318(f318(f74(x91201),x91204),f318(f94(x91201),x91202))),x91203))+P1(f318(f318(f226(x91201),f318(f318(f282(x91201),x91203),f318(f94(x91201),x91202))),x91204))
% 109.14/108.86 [9196]~P100(x91961)+~P74(x91961)+~P1(f318(f318(f226(x91961),f318(f94(x91961),x91964)),f2(x91961)))+P1(f318(f318(f225(x91961),x91962),f318(f318(f282(x91961),x91963),f318(f94(x91961),x91964))))+~P1(f318(f318(f225(x91961),x91963),f318(f318(f74(x91961),x91962),f318(f94(x91961),x91964))))+~P1(f318(f318(f225(x91961),f318(f318(f74(x91961),x91962),f318(f94(x91961),x91964))),x91963))
% 109.14/108.86 [9197]~P100(x91971)+~P74(x91971)+~P1(f318(f318(f226(x91971),f318(f94(x91971),x91974)),f2(x91971)))+P1(f318(f318(f226(x91971),x91972),f318(f318(f282(x91971),x91973),f318(f94(x91971),x91974))))+~P1(f318(f318(f226(x91971),x91973),f318(f318(f74(x91971),x91972),f318(f94(x91971),x91974))))+~P1(f318(f318(f226(x91971),f318(f318(f74(x91971),x91972),f318(f94(x91971),x91974))),x91973))
% 109.14/108.86 [9230]~P100(x92301)+~P74(x92301)+~P1(f318(f318(f225(x92301),f2(x92301)),x92304))+~P1(f318(f318(f225(x92301),x92302),f318(f318(f74(x92301),x92304),f318(f94(x92301),x92303))))+~P1(f318(f318(f225(x92301),f318(f318(f74(x92301),x92304),f318(f94(x92301),x92303))),x92302))+P1(f318(f318(f225(x92301),f318(f318(f282(x92301),x92302),f318(f94(x92301),x92303))),x92304))
% 109.14/108.86 [9231]~P100(x92311)+~P74(x92311)+~P1(f318(f318(f226(x92311),f2(x92311)),x92314))+~P1(f318(f318(f226(x92311),x92312),f318(f318(f74(x92311),x92314),f318(f94(x92311),x92313))))+~P1(f318(f318(f226(x92311),f318(f318(f74(x92311),x92314),f318(f94(x92311),x92313))),x92312))+P1(f318(f318(f226(x92311),f318(f318(f282(x92311),x92312),f318(f94(x92311),x92313))),x92314))
% 109.14/108.86 [9272]~P100(x92721)+~P74(x92721)+~P1(f318(f318(f226(x92721),f318(f94(x92721),x92723)),f2(x92721)))+~P1(f318(f318(f225(x92721),x92722),f318(f318(f74(x92721),x92724),f318(f94(x92721),x92723))))+~P1(f318(f318(f225(x92721),f318(f318(f74(x92721),x92724),f318(f94(x92721),x92723))),x92722))+P1(f318(f318(f225(x92721),f318(f318(f282(x92721),x92722),f318(f94(x92721),x92723))),x92724))
% 109.14/108.86 [9273]~P100(x92731)+~P74(x92731)+~P1(f318(f318(f226(x92731),f318(f94(x92731),x92733)),f2(x92731)))+~P1(f318(f318(f226(x92731),x92732),f318(f318(f74(x92731),x92734),f318(f94(x92731),x92733))))+~P1(f318(f318(f226(x92731),f318(f318(f74(x92731),x92734),f318(f94(x92731),x92733))),x92732))+P1(f318(f318(f226(x92731),f318(f318(f282(x92731),x92732),f318(f94(x92731),x92733))),x92734))
% 109.14/108.86 [8973]~P100(x89731)+~P74(x89731)+~P1(f318(f318(f226(x89731),x89732),f2(x89731)))+~P1(f318(f318(f225(x89731),f318(f318(f282(x89731),x89734),x89732)),f318(f94(x89731),x89733)))+P1(f318(f318(f226(x89731),f2(x89731)),x89732))+P1(f318(f318(f225(x89731),f318(f318(f74(x89731),f318(f94(x89731),x89733)),x89732)),x89734))
% 109.14/108.86 [8974]~P100(x89741)+~P74(x89741)+~P1(f318(f318(f226(x89741),x89742),f2(x89741)))+~P1(f318(f318(f226(x89741),f318(f318(f282(x89741),x89744),x89742)),f318(f94(x89741),x89743)))+P1(f318(f318(f226(x89741),f2(x89741)),x89742))+P1(f318(f318(f226(x89741),f318(f318(f74(x89741),f318(f94(x89741),x89743)),x89742)),x89744))
% 109.14/108.86 [9092]~P100(x90921)+~P74(x90921)+~P1(f318(f318(f226(x90921),x90922),f2(x90921)))+P1(f318(f318(f226(x90921),f2(x90921)),x90922))+P1(f318(f318(f225(x90921),f318(f318(f282(x90921),x90923),x90922)),f318(f94(x90921),x90924)))+~P1(f318(f318(f225(x90921),f318(f318(f74(x90921),f318(f94(x90921),x90924)),x90922)),x90923))
% 109.14/108.86 [9093]~P100(x90931)+~P74(x90931)+~P1(f318(f318(f226(x90931),x90932),f2(x90931)))+P1(f318(f318(f226(x90931),f2(x90931)),x90932))+P1(f318(f318(f226(x90931),f318(f318(f282(x90931),x90933),x90932)),f318(f94(x90931),x90934)))+~P1(f318(f318(f226(x90931),f318(f318(f74(x90931),f318(f94(x90931),x90934)),x90932)),x90933))
% 109.14/108.86 [9131]~P100(x91311)+~P74(x91311)+P1(f318(f318(f226(x91311),x91312),f2(x91311)))+~P1(f318(f318(f225(x91311),f318(f94(x91311),x91313)),f2(x91311)))+P1(f318(f318(f225(x91311),f318(f94(x91311),x91313)),f318(f318(f282(x91311),x91314),x91312)))+~P1(f318(f318(f225(x91311),f318(f318(f74(x91311),f318(f94(x91311),x91313)),x91312)),x91314))
% 109.14/108.86 [9132]~P100(x91321)+~P74(x91321)+P1(f318(f318(f226(x91321),x91322),f2(x91321)))+~P1(f318(f318(f226(x91321),f318(f94(x91321),x91323)),f2(x91321)))+P1(f318(f318(f226(x91321),f318(f94(x91321),x91323)),f318(f318(f282(x91321),x91324),x91322)))+~P1(f318(f318(f226(x91321),f318(f318(f74(x91321),f318(f94(x91321),x91323)),x91322)),x91324))
% 109.14/108.86 [9147]~P100(x91471)+~P74(x91471)+P1(f318(f318(f226(x91471),f2(x91471)),x91472))+P1(f318(f318(f225(x91471),f318(f318(f282(x91471),x91473),x91472)),f318(f94(x91471),x91474)))+~P1(f318(f318(f225(x91471),f2(x91471)),f318(f94(x91471),x91474)))+~P1(f318(f318(f225(x91471),f318(f318(f74(x91471),f318(f94(x91471),x91474)),x91472)),x91473))
% 109.14/108.86 [9148]~P100(x91481)+~P74(x91481)+P1(f318(f318(f226(x91481),f2(x91481)),x91482))+P1(f318(f318(f226(x91481),f318(f318(f282(x91481),x91483),x91482)),f318(f94(x91481),x91484)))+~P1(f318(f318(f226(x91481),f2(x91481)),f318(f94(x91481),x91484)))+~P1(f318(f318(f226(x91481),f318(f318(f74(x91481),f318(f94(x91481),x91484)),x91482)),x91483))
% 109.14/108.86 [9305]~P100(x93051)+~P74(x93051)+~P1(f318(f318(f226(x93051),x93054),f2(x93051)))+P1(f318(f318(f225(x93051),f318(f94(x93051),x93052)),f318(f318(f282(x93051),x93053),x93054)))+~P1(f318(f318(f225(x93051),x93053),f318(f318(f74(x93051),f318(f94(x93051),x93052)),x93054)))+~P1(f318(f318(f225(x93051),f318(f318(f74(x93051),f318(f94(x93051),x93052)),x93054)),x93053))
% 109.14/108.86 [9306]~P100(x93061)+~P74(x93061)+~P1(f318(f318(f226(x93061),x93064),f2(x93061)))+P1(f318(f318(f226(x93061),f318(f94(x93061),x93062)),f318(f318(f282(x93061),x93063),x93064)))+~P1(f318(f318(f226(x93061),x93063),f318(f318(f74(x93061),f318(f94(x93061),x93062)),x93064)))+~P1(f318(f318(f226(x93061),f318(f318(f74(x93061),f318(f94(x93061),x93062)),x93064)),x93063))
% 109.14/108.86 [9343]~P100(x93431)+~P74(x93431)+~P1(f318(f318(f226(x93431),x93433),f2(x93431)))+P1(f318(f318(f225(x93431),f318(f318(f282(x93431),x93432),x93433)),f318(f94(x93431),x93434)))+~P1(f318(f318(f225(x93431),x93432),f318(f318(f74(x93431),f318(f94(x93431),x93434)),x93433)))+~P1(f318(f318(f225(x93431),f318(f318(f74(x93431),f318(f94(x93431),x93434)),x93433)),x93432))
% 109.14/108.86 [9344]~P100(x93441)+~P74(x93441)+~P1(f318(f318(f226(x93441),x93443),f2(x93441)))+P1(f318(f318(f226(x93441),f318(f318(f282(x93441),x93442),x93443)),f318(f94(x93441),x93444)))+~P1(f318(f318(f226(x93441),x93442),f318(f318(f74(x93441),f318(f94(x93441),x93444)),x93443)))+~P1(f318(f318(f226(x93441),f318(f318(f74(x93441),f318(f94(x93441),x93444)),x93443)),x93442))
% 109.14/108.86 [9363]~P100(x93631)+~P74(x93631)+~P1(f318(f318(f225(x93631),f318(f94(x93631),x93632)),f2(x93631)))+P1(f318(f318(f225(x93631),f318(f94(x93631),x93632)),f318(f318(f282(x93631),x93633),x93634)))+~P1(f318(f318(f225(x93631),x93633),f318(f318(f74(x93631),f318(f94(x93631),x93632)),x93634)))+~P1(f318(f318(f225(x93631),f318(f318(f74(x93631),f318(f94(x93631),x93632)),x93634)),x93633))
% 109.14/108.86 [9364]~P100(x93641)+~P74(x93641)+~P1(f318(f318(f226(x93641),f318(f94(x93641),x93642)),f2(x93641)))+P1(f318(f318(f226(x93641),f318(f94(x93641),x93642)),f318(f318(f282(x93641),x93643),x93644)))+~P1(f318(f318(f226(x93641),x93643),f318(f318(f74(x93641),f318(f94(x93641),x93642)),x93644)))+~P1(f318(f318(f226(x93641),f318(f318(f74(x93641),f318(f94(x93641),x93642)),x93644)),x93643))
% 109.14/108.86 [9368]~P100(x93681)+~P74(x93681)+P1(f318(f318(f225(x93681),f318(f318(f282(x93681),x93682),x93683)),f318(f94(x93681),x93684)))+~P1(f318(f318(f225(x93681),f2(x93681)),f318(f94(x93681),x93684)))+~P1(f318(f318(f225(x93681),x93682),f318(f318(f74(x93681),f318(f94(x93681),x93684)),x93683)))+~P1(f318(f318(f225(x93681),f318(f318(f74(x93681),f318(f94(x93681),x93684)),x93683)),x93682))
% 109.14/108.86 [9369]~P100(x93691)+~P74(x93691)+P1(f318(f318(f226(x93691),f318(f318(f282(x93691),x93692),x93693)),f318(f94(x93691),x93694)))+~P1(f318(f318(f226(x93691),f2(x93691)),f318(f94(x93691),x93694)))+~P1(f318(f318(f226(x93691),x93692),f318(f318(f74(x93691),f318(f94(x93691),x93694)),x93693)))+~P1(f318(f318(f226(x93691),f318(f318(f74(x93691),f318(f94(x93691),x93694)),x93693)),x93692))
% 109.14/108.86 [6206]~P121(x62062)+~P138(x62062)+~E(f318(x62063,x62065),f2(x62062))+E(f318(f318(f11(x62061,x62062),x62063),x62064),f2(x62062))+~P1(f318(f55(x62061),x62064))+~P1(f318(f318(f320(x62061),x62065),x62064))
% 109.14/108.86 [8534]~P113(x85341)+P1(f318(f318(f226(f918(x85341,a909)),f294(x85341,x85342,x85343)),f294(x85341,x85344,x85345)))+~P1(f318(f318(f225(x85341),x85344),x85342))+~P1(f318(f318(f225(x85341),x85344),x85345))+~P1(f318(f318(f225(x85341),x85343),x85345))+~P1(f318(f318(f226(x85341),x85343),x85345))
% 109.14/108.86 [8535]~P113(x85351)+P1(f318(f318(f226(f918(x85351,a909)),f294(x85351,x85352,x85353)),f294(x85351,x85354,x85355)))+~P1(f318(f318(f225(x85351),x85353),x85355))+~P1(f318(f318(f225(x85351),x85354),x85355))+~P1(f318(f318(f225(x85351),x85354),x85352))+~P1(f318(f318(f226(x85351),x85354),x85352))
% 109.14/108.86 [9393]P62(x93932,x93933,x93934,x93931)+E(x93931,f179(f918(x93932,a909)))+~P1(f318(f55(x93932),x93934))+~P1(f318(f55(x93932),x93931))+~P1(f318(f318(x93933,f535(x93931,x93934,x93933,x93932)),x93935))+~P1(f318(f318(f320(x93932),x93935),x93931))
% 109.14/108.86 [9394]P62(x93942,x93943,x93944,x93941)+E(x93941,f179(f918(x93942,a909)))+~P1(f318(f55(x93942),x93944))+~P1(f318(f55(x93942),x93941))+~P1(f318(f318(x93943,f792(x93943,x93941,x93944,x93942)),x93945))+~P1(f318(f318(f320(x93942),x93945),x93941))
% 109.14/108.86 [9395]P62(x93952,x93953,x93954,x93951)+E(x93951,f179(f918(x93952,a909)))+~P1(f318(f55(x93952),x93954))+~P1(f318(f55(x93952),x93951))+~P1(f318(f318(x93953,f793(x93951,x93954,x93953,x93952)),x93955))+~P1(f318(f318(f320(x93952),x93955),x93951))
% 109.14/108.86 [9553]~E(x95533,x95535)+~P76(x95531)+~P82(x95531)+~P43(x95533)+E(f318(f318(f8(a1,x95531),x95532),x95533),f318(f318(f8(a1,x95531),x95534),x95535))+P1(f318(f318(f225(a1),f2(a1)),f533(x95532,x95534,x95533,x95535,x95531)))
% 109.14/108.86 [9554]~E(x95543,x95545)+~P76(x95541)+~P82(x95541)+~P43(x95543)+E(f318(f318(f11(a1,x95541),x95542),x95543),f318(f318(f11(a1,x95541),x95544),x95545))+P1(f318(f318(f225(a1),f2(a1)),f513(x95542,x95544,x95543,x95545,x95541)))
% 109.14/108.86 [9731]~E(x97315,x97313)+~P76(x97311)+~P82(x97311)+~P43(x97315)+~E(f318(x97312,f533(x97314,x97312,x97315,x97313,x97311)),f318(x97314,f533(x97314,x97312,x97315,x97313,x97311)))+E(f318(f318(f8(a1,x97311),x97312),x97313),f318(f318(f8(a1,x97311),x97314),x97315))
% 109.14/108.86 [9732]~E(x97325,x97323)+~P76(x97321)+~P82(x97321)+~P43(x97325)+~E(f318(x97322,f513(x97324,x97322,x97325,x97323,x97321)),f318(x97324,f513(x97324,x97322,x97325,x97323,x97321)))+E(f318(f318(f11(a1,x97321),x97322),x97323),f318(f318(f11(a1,x97321),x97324),x97325))
% 109.14/108.86 [9834]~P65(x98343)+E(f318(x98341,x98342),f2(x98343))+~E(f318(f318(f8(x98344,x98343),x98341),x98345),f2(x98343))+~P1(f318(f55(x98344),x98345))+P1(f318(f318(f320(x98344),f503(x98342,x98341,x98345,x98344,x98343)),x98345))+~P1(f318(f318(f320(x98344),x98342),x98345))
% 109.14/108.86 [9978]~P65(x99783)+E(f318(x99781,x99782),f2(x99783))+~E(f318(f318(f8(x99784,x99783),x99781),x99785),f2(x99783))+~P1(f318(f55(x99784),x99785))+~P1(f318(f318(f320(x99784),x99782),x99785))+~P1(f318(f318(f225(x99783),f2(x99783)),f318(x99781,f503(x99782,x99781,x99785,x99784,x99783))))
% 109.14/108.86 [8455]~P142(x84551)+~P1(f318(f318(f225(x84551),x84553),x84555))+~P1(f318(f318(f225(x84551),x84552),x84554))+~P1(f318(f318(f225(x84551),f2(x84551)),x84553))+~P1(f318(f318(f225(x84551),f2(x84551)),x84554))+P1(f318(f318(f225(x84551),f318(f318(f74(x84551),x84552),x84553)),f318(f318(f74(x84551),x84554),x84555)))
% 109.14/108.86 [8456]~P142(x84561)+~P1(f318(f318(f225(x84561),x84563),x84565))+~P1(f318(f318(f225(x84561),x84562),x84564))+~P1(f318(f318(f225(x84561),f2(x84561)),x84563))+~P1(f318(f318(f225(x84561),f2(x84561)),x84562))+P1(f318(f318(f225(x84561),f318(f318(f74(x84561),x84562),x84563)),f318(f318(f74(x84561),x84564),x84565)))
% 109.14/108.86 [8457]~P75(x84571)+~P1(f318(f318(f226(x84571),f2(x84571)),x84575))+~P1(f318(f318(f225(x84571),x84575),x84573))+~P1(f318(f318(f225(x84571),x84572),x84574))+~P1(f318(f318(f225(x84571),f2(x84571)),x84572))+P1(f318(f318(f225(x84571),f318(f318(f282(x84571),x84572),x84573)),f318(f318(f282(x84571),x84574),x84575)))
% 109.14/108.86 [8458]~P134(x84581)+~P1(f318(f318(f225(x84581),x84583),x84585))+~P1(f318(f318(f225(x84581),f2(x84581)),x84582))+~P1(f318(f318(f226(x84581),x84582),x84584))+~P1(f318(f318(f226(x84581),f2(x84581)),x84583))+P1(f318(f318(f226(x84581),f318(f318(f74(x84581),x84582),x84583)),f318(f318(f74(x84581),x84584),x84585)))
% 109.14/108.86 [8459]~P134(x84591)+~P1(f318(f318(f225(x84591),x84592),x84594))+~P1(f318(f318(f225(x84591),f2(x84591)),x84593))+~P1(f318(f318(f226(x84591),x84593),x84595))+~P1(f318(f318(f226(x84591),f2(x84591)),x84592))+P1(f318(f318(f226(x84591),f318(f318(f74(x84591),x84592),x84593)),f318(f318(f74(x84591),x84594),x84595)))
% 109.14/108.86 [8460]~P134(x84601)+~P1(f318(f318(f225(x84601),f2(x84601)),x84603))+~P1(f318(f318(f225(x84601),f2(x84601)),x84602))+~P1(f318(f318(f226(x84601),x84603),x84605))+~P1(f318(f318(f226(x84601),x84602),x84604))+P1(f318(f318(f226(x84601),f318(f318(f74(x84601),x84602),x84603)),f318(f318(f74(x84601),x84604),x84605)))
% 109.14/108.86 [8461]~P134(x84611)+~P1(f318(f318(f225(x84611),f2(x84611)),x84613))+~P1(f318(f318(f226(x84611),x84613),x84615))+~P1(f318(f318(f226(x84611),x84612),x84614))+~P1(f318(f318(f226(x84611),f2(x84611)),x84614))+P1(f318(f318(f226(x84611),f318(f318(f74(x84611),x84612),x84613)),f318(f318(f74(x84611),x84614),x84615)))
% 109.14/108.86 [8462]~P75(x84621)+~P1(f318(f318(f225(x84621),x84625),x84623))+~P1(f318(f318(f225(x84621),f2(x84621)),x84622))+~P1(f318(f318(f226(x84621),x84622),x84624))+~P1(f318(f318(f226(x84621),f2(x84621)),x84625))+P1(f318(f318(f226(x84621),f318(f318(f282(x84621),x84622),x84623)),f318(f318(f282(x84621),x84624),x84625)))
% 109.14/108.86 [8463]~P75(x84631)+~P1(f318(f318(f225(x84631),x84632),x84634))+~P1(f318(f318(f226(x84631),x84635),x84633))+~P1(f318(f318(f226(x84631),f2(x84631)),x84635))+~P1(f318(f318(f226(x84631),f2(x84631)),x84632))+P1(f318(f318(f226(x84631),f318(f318(f282(x84631),x84632),x84633)),f318(f318(f282(x84631),x84634),x84635)))
% 109.14/108.86 [9876]~P76(x98765)+~P92(x98765)+E(x98761,f179(f918(x98762,a909)))+~P1(f318(f55(x98762),x98761))+P1(f318(f318(f320(x98762),f901(x98763,x98764,x98761,x98762,x98765)),x98761))+P1(f318(f318(f226(x98765),f318(f318(f8(x98762,x98765),x98764),x98761)),f318(f318(f8(x98762,x98765),x98763),x98761)))
% 109.14/108.86 [10001]~P76(x100011)+~P90(x100011)+~P1(f318(f55(x100012),x100015))+~P1(f318(f318(f225(x100011),f2(x100011)),f318(x100013,f871(x100013,x100014,x100015,x100012,x100011))))+P1(f318(f318(f225(x100011),f318(f318(f8(x100012,x100011),x100013),x100014)),f318(f318(f8(x100012,x100011),x100013),x100015)))+~P1(f318(f318(f225(f918(x100012,a909)),x100014),x100015))
% 109.14/108.86 [10148]~P76(x101483)+~P92(x101483)+E(x101481,f179(f918(x101482,a909)))+~P1(f318(f55(x101482),x101481))+~P1(f318(f318(f226(x101483),f318(x101484,f901(x101485,x101484,x101481,x101482,x101483))),f318(x101485,f901(x101485,x101484,x101481,x101482,x101483))))+P1(f318(f318(f226(x101483),f318(f318(f8(x101482,x101483),x101484),x101481)),f318(f318(f8(x101482,x101483),x101485),x101481)))
% 109.14/108.86 [7197]~P17(x71972,x71975,x71974)+E(x71971,f179(f918(x71972,a909)))+E(x71973,f179(f918(x71972,a909)))+~P1(f318(f55(x71972),x71971))+~P1(f318(f55(x71972),x71973))+E(f318(x71974,f318(f318(f101(f918(x71972,a909)),x71973),x71971)),f318(f318(x71975,f318(x71974,x71973)),f318(x71974,x71971)))
% 109.14/108.86 [7770]~P152(x77701,x77703,x77704)+P1(f318(x77701,x77702))+~P1(f318(f318(f226(a1),x77704),f2(a1)))+~P1(f318(f318(f225(a1),x77705),f2(a1)))+~E(x77703,f318(f318(f73(a1),f318(f318(f74(a1),x77704),x77702)),x77705))+~P1(f318(f318(f226(a1),x77704),x77705))
% 109.14/108.86 [7771]~P151(x77711,x77713,x77714)+P1(f318(x77711,x77712))+~P1(f318(f318(f226(a1),x77714),f2(a1)))+~P1(f318(f318(f225(a1),x77712),f2(a1)))+~E(x77713,f318(f318(f73(a1),f318(f318(f74(a1),x77714),x77715)),x77712))+~P1(f318(f318(f226(a1),x77714),x77712))
% 109.14/108.86 [7814]~P152(x78141,x78143,x78144)+P1(f318(x78141,x78142))+~E(x78143,f318(f318(f73(a1),f318(f318(f74(a1),x78144),x78142)),x78145))+~P1(f318(f318(f225(a1),f2(a1)),x78145))+~P1(f318(f318(f226(a1),f2(a1)),x78144))+~P1(f318(f318(f226(a1),x78145),x78144))
% 109.14/108.86 [7815]~P151(x78151,x78153,x78154)+P1(f318(x78151,x78152))+~E(x78153,f318(f318(f73(a1),f318(f318(f74(a1),x78154),x78155)),x78152))+~P1(f318(f318(f225(a1),f2(a1)),x78152))+~P1(f318(f318(f226(a1),f2(a1)),x78154))+~P1(f318(f318(f226(a1),x78152),x78154))
% 109.14/108.86 [8746]P1(f318(f318(x87461,x87462),x87463))+~P1(f318(f318(x87461,f318(f318(f30(a1),x87464),x87465)),f39(a1,x87464,x87465)))+~P1(f318(f318(f226(a1),x87465),f2(a1)))+~P1(f318(f318(f225(a1),x87463),f2(a1)))+~E(x87464,f318(f318(f73(a1),f318(f318(f74(a1),x87465),x87462)),x87463))+~P1(f318(f318(f226(a1),x87465),x87463))
% 109.14/108.86 [8755]P1(f318(f318(x87551,x87552),x87553))+~P1(f318(f318(x87551,f318(f318(f30(a1),x87554),x87555)),f39(a1,x87554,x87555)))+~E(x87554,f318(f318(f73(a1),f318(f318(f74(a1),x87555),x87552)),x87553))+~P1(f318(f318(f225(a1),f2(a1)),x87553))+~P1(f318(f318(f226(a1),f2(a1)),x87555))+~P1(f318(f318(f226(a1),x87553),x87555))
% 109.14/108.86 [9015]E(x90151,x90152)+~P59(x90153,x90155,x90154)+~P1(f318(f318(f320(x90153),x90152),x90155))+~P1(f318(f318(f320(x90153),x90151),x90155))+P1(f318(f318(f320(f917(x90153,x90153)),f318(f318(f243(x90153,x90153),x90151),x90152)),x90154))+P1(f318(f318(f320(f917(x90153,x90153)),f318(f318(f243(x90153,x90153),x90152),x90151)),x90154))
% 109.14/108.86 [9850]~P113(x98501)+~P113(x98502)+~P42(x98502,x98501,x98503)+~P1(f318(f318(f225(x98502),x98505),f504(x98504,x98503,x98502,x98501,x98505)))+E(f229(x98501,f318(f318(f9(x98501,f918(x98501,a909),a909),f320(x98501)),f318(f301(x98502,x98501,x98503),x98504))),f318(x98503,f229(x98502,f318(f318(f9(x98502,f918(x98502,a909),a909),f320(x98502)),x98504))))+~P1(f318(f318(f320(x98502),x98505),x98504))
% 109.14/108.86 [9904]~P76(x99045)+~P90(x99045)+~P1(f318(f55(x99041),x99044))+P1(f318(f318(f225(x99045),f318(f318(f8(x99041,x99045),x99042),x99043)),f318(f318(f8(x99041,x99045),x99042),x99044)))+~P1(f318(f318(f225(f918(x99041,a909)),x99043),x99044))+P1(f318(f318(f320(x99041),f871(x99042,x99043,x99044,x99041,x99045)),f318(f318(f3(f918(x99041,a909)),x99044),x99043)))
% 109.14/108.86 [9920]~P113(x99201)+~P113(x99202)+~P42(x99202,x99201,x99203)+E(f229(x99201,f318(f318(f9(x99201,f918(x99201,a909),a909),f320(x99201)),f318(f301(x99202,x99201,x99203),x99204))),f318(x99203,f229(x99202,f318(f318(f9(x99202,f918(x99202,a909),a909),f320(x99202)),x99204))))+~P1(f318(f318(f320(x99202),x99205),x99204))+P1(f318(f318(f320(x99202),f504(x99204,x99203,x99202,x99201,x99205)),x99204))
% 109.14/108.86 [10009]E(x100091,f179(f918(x100092,a909)))+~P1(f318(f55(x100092),x100093))+~P1(f318(f55(x100092),x100091))+P1(f318(f318(f320(f917(f918(x100092,a909),f918(x100092,a909))),f318(f318(f243(f918(x100092,a909),f918(x100092,a909)),x100093),x100091)),f310(x100092,x100094)))+~P1(f318(f318(f320(x100092),x100095),x100091))+~P1(f318(f318(f320(f917(x100092,x100092)),f318(f318(f243(x100092,x100092),f537(x100094,x100091,x100093,x100092)),x100095)),x100094))
% 109.14/108.86 [10010]E(x100101,f179(f918(x100102,a909)))+~P1(f318(f55(x100102),x100103))+~P1(f318(f55(x100102),x100101))+P1(f318(f318(f320(f917(f918(x100102,a909),f918(x100102,a909))),f318(f318(f243(f918(x100102,a909),f918(x100102,a909)),x100103),x100101)),f310(x100102,x100104)))+~P1(f318(f318(f320(x100102),x100105),x100101))+~P1(f318(f318(f320(f917(x100102,x100102)),f318(f318(f243(x100102,x100102),f600(x100104,x100101,x100103,x100102)),x100105)),x100104))
% 109.14/108.86 [10152]~P65(x101521)+~E(f318(f318(f8(x101525,x101521),x101522),x101526),x101524)+~P1(f318(f55(x101525),x101526))+P1(f318(f318(f320(x101525),f509(x101523,x101524,x101522,x101526,x101525,x101521)),x101526))+P1(f318(f318(f225(x101521),f318(x101522,x101523)),x101524))+~P1(f318(f318(f320(x101525),x101523),x101526))
% 109.14/108.86 [10198]~P65(x101981)+~E(f318(f318(f8(x101985,x101981),x101982),x101986),x101984)+~P1(f318(f55(x101985),x101986))+~P1(f318(f318(f320(x101985),x101983),x101986))+~P1(f318(f318(f225(x101981),f2(x101981)),f318(x101982,f509(x101983,x101984,x101982,x101986,x101985,x101981))))+P1(f318(f318(f225(x101981),f318(x101982,x101983)),x101984))
% 109.14/108.86 [10361]~E(x103615,x103618)+~E(x103614,x103617)+~P3(x103611)+~P76(x103612)+E(f318(f318(f8(x103611,x103612),x103613),f318(f293(x103611,x103614),x103615)),f318(f318(f8(x103611,x103612),x103616),f318(f293(x103611,x103617),x103618)))+P1(f318(f318(f225(x103611),x103614),f330(x103613,x103616,x103615,x103618,x103614,x103617,x103611,x103612)))
% 109.14/108.86 [10384]~E(x103847,x103844)+~E(x103848,x103845)+~P3(x103841)+~P76(x103842)+~E(f318(x103843,f330(x103846,x103843,x103848,x103845,x103847,x103844,x103841,x103842)),f318(x103846,f330(x103846,x103843,x103848,x103845,x103847,x103844,x103841,x103842)))+E(f318(f318(f8(x103841,x103842),x103843),f318(f293(x103841,x103844),x103845)),f318(f318(f8(x103841,x103842),x103846),f318(f293(x103841,x103847),x103848)))
% 109.14/108.86 [10393]~E(x103934,x103937)+~E(x103935,x103938)+~P3(x103931)+~P76(x103932)+E(f318(f318(f8(x103931,x103932),x103933),f318(f293(x103931,x103934),x103935)),f318(f318(f8(x103931,x103932),x103936),f318(f293(x103931,x103937),x103938)))+P1(f318(f318(f226(x103931),f330(x103933,x103936,x103935,x103938,x103934,x103937,x103931,x103932)),x103935))
% 109.14/108.86 [10016]~P8(x100165,x100169,x100166)+~P8(x100161,x1001610,x100163)+~P12(x100161,x100165,f918(x100162,a909),x100163,x100166,x100168)+~P1(f318(f318(f320(x100165),x100167),x100169))+~P1(f318(f318(f320(x100161),x100164),x1001610))+E(f318(f318(f33(x100161,f918(x100162,a909)),f318(f276(x100161,x100161,x100163),f318(f318(f300(x100161),x100164),f179(f918(x100161,a909))))),f318(f318(f10(f918(x100165,f918(x100162,a909)),f918(x100162,a909),x100161),f318(f33(x100165,f918(x100162,a909)),f318(f276(x100165,x100165,x100166),f318(f318(f300(x100165),x100167),f179(f918(x100165,a909)))))),x100168)),f318(f318(x100168,x100164),x100167))
% 109.14/108.86 [5721]~P4(x57213)+~P13(x57213,x57212)+~P13(x57213,x57211)+E(x57211,x57212)+~E(f318(f163(x57213),x57211),f318(f163(x57213),x57212))+~P1(f318(f128(x57213),x57212))+~P1(f318(f128(x57213),x57211))
% 109.14/108.86 [5049]~P150(x50492)+~P118(x50492)+~P133(x50492)+~P138(x50492)+~E(x50493,f2(x50492))+E(x50491,f2(a911))+E(f318(f318(f235(x50492),x50493),x50491),f2(x50492))
% 109.14/108.86 [9261]E(x92611,f2(a911))+~E(x92612,f318(f318(f73(a911),f318(f318(f74(a911),f318(f242(a911,a911),x92613)),x92611)),f318(f247(a911,a911),x92613)))+P1(f318(f42(x92612,x92611),x92613))+~P1(f318(f318(f225(a911),f318(f247(a911,a911),x92613)),f2(a911)))+~P1(f318(f318(f225(a911),f2(a911)),f318(f247(a911,a911),x92613)))+~P1(f318(f318(f226(a911),x92611),f318(f247(a911,a911),x92613)))+~P1(f318(f318(f226(a911),f318(f247(a911,a911),x92613)),x92611))
% 109.14/108.86 [9275]~E(f318(f242(a911,a911),x92753),f2(a911))+~E(x92751,f318(f318(f73(a911),f318(f318(f74(a911),f318(f242(a911,a911),x92753)),x92752)),f318(f247(a911,a911),x92753)))+P1(f318(f42(x92751,x92752),x92753))+~P1(f318(f318(f225(a911),f318(f247(a911,a911),x92753)),f2(a911)))+~P1(f318(f318(f225(a911),f2(a911)),f318(f247(a911,a911),x92753)))+~P1(f318(f318(f226(a911),x92752),f318(f247(a911,a911),x92753)))+~P1(f318(f318(f226(a911),f318(f247(a911,a911),x92753)),x92752))
% 109.14/108.86 [7653]~P103(x76532)+E(x76531,f179(f918(x76532,a909)))+E(x76533,f179(f918(x76532,a909)))+~P1(f318(f55(x76532),x76531))+~P1(f318(f55(x76532),x76533))+~E(f318(f318(f92(f918(x76532,a909)),x76533),x76531),f179(f918(x76532,a909)))+E(f12(x76532,f318(f318(f101(f918(x76532,a909)),x76533),x76531)),f318(f318(f92(x76532),f12(x76532,x76533)),f12(x76532,x76531)))
% 109.14/108.86 [7654]~P103(x76542)+E(x76541,f179(f918(x76542,a909)))+E(x76543,f179(f918(x76542,a909)))+~P1(f318(f55(x76542),x76541))+~P1(f318(f55(x76542),x76543))+~E(f318(f318(f92(f918(x76542,a909)),x76543),x76541),f179(f918(x76542,a909)))+E(f15(x76542,f318(f318(f101(f918(x76542,a909)),x76543),x76541)),f318(f318(f101(x76542),f15(x76542,x76543)),f15(x76542,x76541)))
% 109.14/108.86 [7655]~P4(x76552)+E(x76551,f179(f918(x76552,a909)))+E(x76553,f179(f918(x76552,a909)))+~P1(f318(f55(x76552),x76551))+~P1(f318(f55(x76552),x76553))+~E(f318(f318(f92(f918(x76552,a909)),x76553),x76551),f179(f918(x76552,a909)))+E(f16(x76552,f318(f318(f101(f918(x76552,a909)),x76553),x76551)),f318(f318(f223(x76552),f16(x76552,x76553)),f16(x76552,x76551)))
% 109.14/108.86 [7656]~P4(x76562)+E(x76561,f179(f918(x76562,a909)))+E(x76563,f179(f918(x76562,a909)))+~P1(f318(f55(x76562),x76561))+~P1(f318(f55(x76562),x76563))+~E(f318(f318(f92(f918(x76562,a909)),x76563),x76561),f179(f918(x76562,a909)))+E(f17(x76562,f318(f318(f101(f918(x76562,a909)),x76563),x76561)),f318(f318(f224(x76562),f17(x76562,x76563)),f17(x76562,x76561)))
% 109.14/108.86 [8119]~P80(x81192)+E(x81191,f179(f918(x81192,a909)))+E(x81193,f179(f918(x81192,a909)))+~P1(f318(f55(x81192),x81191))+~P1(f318(f55(x81192),x81193))+~E(f318(f318(f92(f918(x81192,a909)),x81193),x81191),f179(f918(x81192,a909)))+E(f318(f318(f74(x81192),f318(f57(x81192,f74(x81192)),x81193)),f318(f57(x81192,f74(x81192)),x81191)),f318(f57(x81192,f74(x81192)),f318(f318(f101(f918(x81192,a909)),x81193),x81191)))
% 109.14/108.86 [8193]~P4(x81932)+E(x81931,f179(f918(x81932,a909)))+E(x81933,f179(f918(x81932,a909)))+~P1(f318(f55(x81932),x81931))+~P1(f318(f55(x81932),x81933))+~E(f318(f318(f92(f918(x81932,a909)),x81933),x81931),f179(f918(x81932,a909)))+E(f318(f318(f223(x81932),f13(x81932,f223(x81932),x81933)),f13(x81932,f223(x81932),x81931)),f13(x81932,f223(x81932),f318(f318(f101(f918(x81932,a909)),x81933),x81931)))
% 109.14/108.86 [8194]~P4(x81942)+E(x81941,f179(f918(x81942,a909)))+E(x81943,f179(f918(x81942,a909)))+~P1(f318(f55(x81942),x81941))+~P1(f318(f55(x81942),x81943))+~E(f318(f318(f92(f918(x81942,a909)),x81943),x81941),f179(f918(x81942,a909)))+E(f318(f318(f224(x81942),f14(x81942,f224(x81942),x81943)),f14(x81942,f224(x81942),x81941)),f14(x81942,f224(x81942),f318(f318(f101(f918(x81942,a909)),x81943),x81941)))
% 109.14/108.86 [7909]E(x79091,f2(a1))+E(f318(f318(f30(a1),x79092),x79091),x79093)+~P1(f318(f318(f225(a1),x79094),f2(a1)))+~E(x79092,f318(f318(f73(a1),f318(f318(f74(a1),x79091),x79093)),x79094))+~P1(f318(f318(f225(a1),f2(a1)),x79094))+~P1(f318(f318(f226(a1),x79094),x79091))+~P1(f318(f318(f226(a1),x79091),x79094))
% 109.14/108.86 [7917]E(f39(a1,x79172,x79171),x79173)+E(x79171,f2(a1))+~P1(f318(f318(f225(a1),x79173),f2(a1)))+~E(x79172,f318(f318(f73(a1),f318(f318(f74(a1),x79171),x79174)),x79173))+~P1(f318(f318(f225(a1),f2(a1)),x79173))+~P1(f318(f318(f226(a1),x79173),x79171))+~P1(f318(f318(f226(a1),x79171),x79173))
% 109.14/108.86 [6978]~P69(x69782)+E(x69781,f2(x69782))+E(x69783,f2(x69782))+~E(f318(f318(f30(x69782),x69784),x69783),f318(f318(f30(x69782),x69785),x69781))+E(f318(f318(f74(x69782),x69784),x69781),f318(f318(f74(x69782),x69783),x69785))+~P1(f318(f318(f278(x69782),x69781),x69785))+~P1(f318(f318(f278(x69782),x69783),x69784))
% 109.14/108.86 [6979]~P69(x69792)+E(x69791,f2(x69792))+E(x69793,f2(x69792))+~E(f318(f318(f74(x69792),x69794),x69793),f318(f318(f74(x69792),x69791),x69795))+E(f318(f318(f30(x69792),x69794),x69791),f318(f318(f30(x69792),x69795),x69793))+~P1(f318(f318(f278(x69792),x69791),x69794))+~P1(f318(f318(f278(x69792),x69793),x69795))
% 109.14/108.86 [7824]~P18(x78242,x78245,x78244)+E(x78241,f179(f918(x78242,a909)))+E(x78243,f179(f918(x78242,a909)))+~P1(f318(f55(x78242),x78241))+~P1(f318(f55(x78242),x78243))+~E(f318(f318(f92(f918(x78242,a909)),x78243),x78241),f179(f918(x78242,a909)))+E(f318(x78244,f318(f318(f101(f918(x78242,a909)),x78243),x78241)),f318(f318(x78245,f318(x78244,x78243)),f318(x78244,x78241)))
% 109.14/108.86 [9521]~P25(x95213,x95211,x95215,x95214)+~P25(x95211,x95213,x95216,x95212)+E(f318(f29(x95211),x95212),f318(f29(x95213),x95214))+~P1(f318(f55(x95213),x95214))+~P1(f318(f55(x95211),x95212))+~P1(f318(f318(f225(f918(x95213,a909)),f318(f301(x95211,x95213,x95216),x95212)),x95214))+~P1(f318(f318(f225(f918(x95211,a909)),f318(f301(x95213,x95211,x95215),x95214)),x95212))
% 109.14/108.86 [9467]~P1(f318(f318(f226(a1),f318(f318(f73(a1),f318(f318(f74(a1),x94675),x94671)),x94676)),f2(a1)))+~E(f318(f318(f73(a1),f318(f318(f74(a1),x94673),x94672)),x94674),f318(f318(f73(a1),f318(f318(f74(a1),x94675),x94671)),x94676))+~P1(f318(f318(f225(a1),f2(a1)),x94676))+~P1(f318(f318(f226(a1),f2(a1)),x94675))+~P1(f318(f318(f225(a1),x94675),x94673))+~P1(f318(f318(f226(a1),x94674),x94673))+P1(f318(f318(f225(a1),x94671),x94672))
% 109.14/108.86 [9217]~E(f318(f318(f73(a1),f318(f318(f74(a1),x92173),x92171)),x92174),f318(f318(f73(a1),f318(f318(f74(a1),x92175),x92172)),x92176))+~P1(f318(f318(f225(a1),f2(a1)),x92174))+~P1(f318(f318(f226(a1),f2(a1)),x92175))+~P1(f318(f318(f225(a1),x92175),x92173))+~P1(f318(f318(f226(a1),x92176),x92175))+P1(f318(f318(f225(a1),x92171),x92172))+~P1(f318(f318(f225(a1),f2(a1)),f318(f318(f73(a1),f318(f318(f74(a1),x92175),x92172)),x92176)))
% 109.14/108.86 [9399]~P136(x93991)+~E(f318(f318(f73(x93991),x93992),x93994),f71(x93991))+~P1(f318(f318(f225(x93991),x93995),x93996))+~P1(f318(f318(f225(x93991),x93993),x93996))+~P1(f318(f318(f225(x93991),f2(x93991)),x93994))+~P1(f318(f318(f225(x93991),f2(x93991)),x93992))+P1(f318(f318(f225(x93991),f318(f318(f73(x93991),f318(f318(f74(x93991),x93992),x93993)),f318(f318(f74(x93991),x93994),x93995))),x93996))
% 109.14/108.86 [9400]~P137(x94001)+~E(f318(f318(f73(x94001),x94002),x94004),f71(x94001))+~P1(f318(f318(f225(x94001),f2(x94001)),x94004))+~P1(f318(f318(f225(x94001),f2(x94001)),x94002))+~P1(f318(f318(f226(x94001),x94005),x94006))+~P1(f318(f318(f226(x94001),x94003),x94006))+P1(f318(f318(f226(x94001),f318(f318(f73(x94001),f318(f318(f74(x94001),x94002),x94003)),f318(f318(f74(x94001),x94004),x94005))),x94006))
% 109.14/108.86 [10242]~P8(x102427,x102426,x102425)+E(x102421,x102422)+~P11(x102427,f918(x102424,a909),x102425,x102423)+E(f318(x102423,f526(x102421,x102422,x102423,x102424,x102425,x102426,x102427)),f318(x102423,f527(x102421,x102422,x102423,x102424,x102425,x102426,x102427)))+~E(f318(f318(f33(x102427,f918(x102424,a909)),x102421),x102423),f318(f318(f33(x102427,f918(x102424,a909)),x102422),x102423))+~P1(f318(f318(f320(f918(x102427,a909)),x102422),f318(f318(f54(x102427),x102426),x102425)))+~P1(f318(f318(f320(f918(x102427,a909)),x102421),f318(f318(f54(x102427),x102426),x102425)))
% 109.14/108.86 [10294]~P8(x102943,x102947,x102946)+E(x102941,x102942)+~P11(x102943,f918(x102945,a909),x102946,x102944)+~E(f318(f318(f33(x102943,f918(x102945,a909)),x102941),x102944),f318(f318(f33(x102943,f918(x102945,a909)),x102942),x102944))+P1(f318(f318(f320(x102943),f527(x102941,x102942,x102944,x102945,x102946,x102947,x102943)),x102947))+~P1(f318(f318(f320(f918(x102943,a909)),x102942),f318(f318(f54(x102943),x102947),x102946)))+~P1(f318(f318(f320(f918(x102943,a909)),x102941),f318(f318(f54(x102943),x102947),x102946)))
% 109.14/108.86 [10295]~P8(x102953,x102957,x102956)+E(x102951,x102952)+~P11(x102953,f918(x102955,a909),x102956,x102954)+~E(f318(f318(f33(x102953,f918(x102955,a909)),x102951),x102954),f318(f318(f33(x102953,f918(x102955,a909)),x102952),x102954))+P1(f318(f318(f320(x102953),f526(x102951,x102952,x102954,x102955,x102956,x102957,x102953)),x102957))+~P1(f318(f318(f320(f918(x102953,a909)),x102952),f318(f318(f54(x102953),x102957),x102956)))+~P1(f318(f318(f320(f918(x102953,a909)),x102951),f318(f318(f54(x102953),x102957),x102956)))
% 109.14/108.86 [10414]E(x104141,x104142)+~P8(x104143,x104146,x104147)+~P11(x104143,f918(x104144,a909),x104147,x104145)+~E(f318(f318(f33(x104143,f918(x104144,a909)),x104141),x104145),f318(f318(f33(x104143,f918(x104144,a909)),x104142),x104145))+~P1(f318(f318(f320(f917(x104143,x104143)),f318(f318(f243(x104143,x104143),f527(x104141,x104142,x104145,x104144,x104147,x104146,x104143)),f526(x104141,x104142,x104145,x104144,x104147,x104146,x104143))),x104147))+~P1(f318(f318(f320(f918(x104143,a909)),x104142),f318(f318(f54(x104143),x104146),x104147)))+~P1(f318(f318(f320(f918(x104143,a909)),x104141),f318(f318(f54(x104143),x104146),x104147)))
% 109.14/108.86 [9216]~P8(x92161,x92167,x92164)+~E(x92165,x92166)+~P1(f318(f318(f320(x92161),x92163),x92166))+~P1(f318(f318(f320(x92161),x92162),x92165))+~P1(f318(f318(f320(f918(x92161,a909)),x92166),f318(f318(f54(x92161),x92167),x92164)))+~P1(f318(f318(f320(f918(x92161,a909)),x92165),f318(f318(f54(x92161),x92167),x92164)))+P1(f318(f318(f320(f917(x92161,x92161)),f318(f318(f243(x92161,x92161),x92162),x92163)),x92164))
% 109.14/108.86 [9357]E(x93571,x93572)+~P8(x93573,x93574,x93575)+~P1(f318(f318(f320(x93573),x93576),x93572))+~P1(f318(f318(f320(x93573),x93577),x93571))+~P1(f318(f318(f320(f918(x93573,a909)),x93572),f318(f318(f54(x93573),x93574),x93575)))+~P1(f318(f318(f320(f918(x93573,a909)),x93571),f318(f318(f54(x93573),x93574),x93575)))+~P1(f318(f318(f320(f917(x93573,x93573)),f318(f318(f243(x93573,x93573),x93577),x93576)),x93575))
% 109.14/108.86 [9358]E(x93581,x93582)+~P8(x93583,x93584,x93585)+~P1(f318(f318(f320(x93583),x93586),x93582))+~P1(f318(f318(f320(x93583),x93587),x93581))+~P1(f318(f318(f320(f918(x93583,a909)),x93582),f318(f318(f54(x93583),x93584),x93585)))+~P1(f318(f318(f320(f918(x93583,a909)),x93581),f318(f318(f54(x93583),x93584),x93585)))+~P1(f318(f318(f320(f917(x93583,x93583)),f318(f318(f243(x93583,x93583),x93587),x93586)),x93585))
% 109.14/108.86 [10446]~P8(x104469,x104468,x104467)+~P8(x104461,x1044611,x1044610)+~P12(x104461,x104469,f918(x104466,a909),x1044610,x104467,x104465)+P1(f318(f318(f320(x104461),f529(x104462,x104463,x104464,x104465,x104466,x104467,x104468,x104469,x1044610,x1044611,x104461)),x1044611))+~P1(f318(f318(f320(f918(x104469,a909)),x104463),f318(f318(f54(x104469),x104468),x104467)))+~P1(f318(f318(f320(f918(x104461,a909)),x104464),f318(f318(f54(x104461),x1044611),x1044610)))+P1(f318(f318(f320(f918(x104466,a909)),f318(f318(f33(x104461,f918(x104466,a909)),x104464),f318(f318(f10(f918(x104469,f918(x104466,a909)),f918(x104466,a909),x104461),f318(f33(x104469,f918(x104466,a909)),x104463)),x104465))),x104462))
% 109.14/108.86 [10447]~P8(x1044711,x1044710,x104479)+~P8(x104471,x104478,x104477)+~P12(x1044711,x104471,f918(x104476,a909),x104479,x104477,x104475)+P1(f318(f318(f320(x104471),f530(x104472,x104473,x104474,x104475,x104476,x104477,x104478,x104471,x104479,x1044710,x1044711)),x104478))+~P1(f318(f318(f320(f918(x1044711,a909)),x104474),f318(f318(f54(x1044711),x1044710),x104479)))+~P1(f318(f318(f320(f918(x104471,a909)),x104473),f318(f318(f54(x104471),x104478),x104477)))+P1(f318(f318(f320(f918(x104476,a909)),f318(f318(f33(x1044711,f918(x104476,a909)),x104474),f318(f318(f10(f918(x104471,f918(x104476,a909)),f918(x104476,a909),x1044711),f318(f33(x104471,f918(x104476,a909)),x104473)),x104475))),x104472))
% 109.14/108.86 [10448]~P8(x104482,x104488,x104489)+~P8(x104484,x1044810,x1044811)+~P12(x104482,x104484,f918(x104481,a909),x104489,x1044811,x104486)+~P1(f318(f318(f320(f918(x104482,a909)),x104483),f318(f318(f54(x104482),x104488),x104489)))+~P1(f318(f318(f320(f918(x104484,a909)),x104485),f318(f318(f54(x104484),x1044810),x1044811)))+~P1(f318(f318(f320(f918(x104481,a909)),f318(f318(x104486,f529(x104487,x104485,x104483,x104486,x104481,x1044811,x1044810,x104484,x104489,x104488,x104482)),f530(x104487,x104485,x104483,x104486,x104481,x1044811,x1044810,x104484,x104489,x104488,x104482))),x104487))+P1(f318(f318(f320(f918(x104481,a909)),f318(f318(f33(x104482,f918(x104481,a909)),x104483),f318(f318(f10(f918(x104484,f918(x104481,a909)),f918(x104481,a909),x104482),f318(f33(x104484,f918(x104481,a909)),x104485)),x104486))),x104487))
% 109.14/108.86 [9246]E(x92461,x92462)+~P4(x92464)+~P25(x92463,x92464,x92465,f318(f318(f101(f918(x92463,a909)),f318(f163(x92463),x92461)),f318(f163(x92463),x92462)))+~E(f318(f163(x92463),x92461),f318(f163(x92463),x92462))+~P13(x92464,f318(f318(f145(x92463,x92464),x92465),x92462))+~P13(x92464,f318(f318(f145(x92463,x92464),x92465),x92461))+~P1(f318(f128(x92464),f318(f318(f145(x92463,x92464),x92465),x92462)))+~P1(f318(f128(x92464),f318(f318(f145(x92463,x92464),x92465),x92461)))
% 109.14/108.86 %EqnAxiom
% 109.14/108.86 [1]E(x11,x11)
% 109.14/108.86 [2]E(x22,x21)+~E(x21,x22)
% 109.14/108.86 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 109.14/108.86 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 109.14/108.86 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 109.14/108.86 [6]~E(x61,x62)+E(f91(x61),f91(x62))
% 109.14/108.86 [7]~E(x71,x72)+E(f179(x71),f179(x72))
% 109.14/108.86 [8]~E(x81,x82)+E(f318(x81,x83),f318(x82,x83))
% 109.14/108.86 [9]~E(x91,x92)+E(f318(x93,x91),f318(x93,x92))
% 109.14/108.86 [10]~E(x101,x102)+E(f92(x101),f92(x102))
% 109.14/108.86 [11]~E(x111,x112)+E(f223(x111),f223(x112))
% 109.14/108.86 [12]~E(x121,x122)+E(f101(x121),f101(x122))
% 109.14/108.86 [13]~E(x131,x132)+E(f224(x131),f224(x132))
% 109.14/108.86 [14]~E(x141,x142)+E(f93(x141),f93(x142))
% 109.14/108.86 [15]~E(x151,x152)+E(f25(x151),f25(x152))
% 109.14/108.86 [16]~E(x161,x162)+E(f77(x161),f77(x162))
% 109.14/108.86 [17]~E(x171,x172)+E(f73(x171),f73(x172))
% 109.14/108.86 [18]~E(x181,x182)+E(f100(x181),f100(x182))
% 109.14/108.86 [19]~E(x191,x192)+E(f229(x191,x193),f229(x192,x193))
% 109.14/108.86 [20]~E(x201,x202)+E(f229(x203,x201),f229(x203,x202))
% 109.14/108.86 [21]~E(x211,x212)+E(f530(x211,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112),f530(x212,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112))
% 109.14/108.86 [22]~E(x221,x222)+E(f530(x223,x221,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f530(x223,x222,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212))
% 109.14/108.86 [23]~E(x231,x232)+E(f530(x233,x234,x231,x235,x236,x237,x238,x239,x2310,x2311,x2312),f530(x233,x234,x232,x235,x236,x237,x238,x239,x2310,x2311,x2312))
% 109.14/108.86 [24]~E(x241,x242)+E(f530(x243,x244,x245,x241,x246,x247,x248,x249,x2410,x2411,x2412),f530(x243,x244,x245,x242,x246,x247,x248,x249,x2410,x2411,x2412))
% 109.14/108.86 [25]~E(x251,x252)+E(f530(x253,x254,x255,x256,x251,x257,x258,x259,x2510,x2511,x2512),f530(x253,x254,x255,x256,x252,x257,x258,x259,x2510,x2511,x2512))
% 109.14/108.86 [26]~E(x261,x262)+E(f530(x263,x264,x265,x266,x267,x261,x268,x269,x2610,x2611,x2612),f530(x263,x264,x265,x266,x267,x262,x268,x269,x2610,x2611,x2612))
% 109.14/108.86 [27]~E(x271,x272)+E(f530(x273,x274,x275,x276,x277,x278,x271,x279,x2710,x2711,x2712),f530(x273,x274,x275,x276,x277,x278,x272,x279,x2710,x2711,x2712))
% 109.14/108.86 [28]~E(x281,x282)+E(f530(x283,x284,x285,x286,x287,x288,x289,x281,x2810,x2811,x2812),f530(x283,x284,x285,x286,x287,x288,x289,x282,x2810,x2811,x2812))
% 109.14/108.86 [29]~E(x291,x292)+E(f530(x293,x294,x295,x296,x297,x298,x299,x2910,x291,x2911,x2912),f530(x293,x294,x295,x296,x297,x298,x299,x2910,x292,x2911,x2912))
% 109.14/108.86 [30]~E(x301,x302)+E(f530(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x301,x3012),f530(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x302,x3012))
% 109.14/108.86 [31]~E(x311,x312)+E(f530(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x311),f530(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x312))
% 109.14/108.86 [32]~E(x321,x322)+E(f71(x321),f71(x322))
% 109.14/108.86 [33]~E(x331,x332)+E(f320(x331),f320(x332))
% 109.14/108.86 [34]~E(x341,x342)+E(f6(x341),f6(x342))
% 109.14/108.86 [35]~E(x351,x352)+E(f529(x351,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f529(x352,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512))
% 109.14/108.86 [36]~E(x361,x362)+E(f529(x363,x361,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f529(x363,x362,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612))
% 109.14/108.86 [37]~E(x371,x372)+E(f529(x373,x374,x371,x375,x376,x377,x378,x379,x3710,x3711,x3712),f529(x373,x374,x372,x375,x376,x377,x378,x379,x3710,x3711,x3712))
% 109.14/108.86 [38]~E(x381,x382)+E(f529(x383,x384,x385,x381,x386,x387,x388,x389,x3810,x3811,x3812),f529(x383,x384,x385,x382,x386,x387,x388,x389,x3810,x3811,x3812))
% 109.14/108.86 [39]~E(x391,x392)+E(f529(x393,x394,x395,x396,x391,x397,x398,x399,x3910,x3911,x3912),f529(x393,x394,x395,x396,x392,x397,x398,x399,x3910,x3911,x3912))
% 109.14/108.86 [40]~E(x401,x402)+E(f529(x403,x404,x405,x406,x407,x401,x408,x409,x4010,x4011,x4012),f529(x403,x404,x405,x406,x407,x402,x408,x409,x4010,x4011,x4012))
% 109.14/108.86 [41]~E(x411,x412)+E(f529(x413,x414,x415,x416,x417,x418,x411,x419,x4110,x4111,x4112),f529(x413,x414,x415,x416,x417,x418,x412,x419,x4110,x4111,x4112))
% 109.14/108.86 [42]~E(x421,x422)+E(f529(x423,x424,x425,x426,x427,x428,x429,x421,x4210,x4211,x4212),f529(x423,x424,x425,x426,x427,x428,x429,x422,x4210,x4211,x4212))
% 109.14/108.86 [43]~E(x431,x432)+E(f529(x433,x434,x435,x436,x437,x438,x439,x4310,x431,x4311,x4312),f529(x433,x434,x435,x436,x437,x438,x439,x4310,x432,x4311,x4312))
% 109.14/108.86 [44]~E(x441,x442)+E(f529(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x441,x4412),f529(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x442,x4412))
% 109.14/108.86 [45]~E(x451,x452)+E(f529(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x451),f529(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x452))
% 109.14/108.86 [46]~E(x461,x462)+E(f243(x461,x463),f243(x462,x463))
% 109.14/108.86 [47]~E(x471,x472)+E(f243(x473,x471),f243(x473,x472))
% 109.14/108.86 [48]~E(x481,x482)+E(f102(x481),f102(x482))
% 109.14/108.86 [49]~E(x491,x492)+E(f918(x491,x493),f918(x492,x493))
% 109.14/108.86 [50]~E(x501,x502)+E(f918(x503,x501),f918(x503,x502))
% 109.14/108.86 [51]~E(x511,x512)+E(f910(x511),f910(x512))
% 109.14/108.86 [52]~E(x521,x522)+E(f915(x521),f915(x522))
% 109.14/108.86 [53]~E(x531,x532)+E(f912(x531),f912(x532))
% 109.14/108.86 [54]~E(x541,x542)+E(f913(x541),f913(x542))
% 109.14/108.86 [55]~E(x551,x552)+E(f72(x551),f72(x552))
% 109.14/108.86 [56]~E(x561,x562)+E(f94(x561),f94(x562))
% 109.14/108.86 [57]~E(x571,x572)+E(f11(x571,x573),f11(x572,x573))
% 109.14/108.86 [58]~E(x581,x582)+E(f11(x583,x581),f11(x583,x582))
% 109.14/108.86 [59]~E(x591,x592)+E(f235(x591),f235(x592))
% 109.14/108.86 [60]~E(x601,x602)+E(f180(x601),f180(x602))
% 109.14/108.86 [61]~E(x611,x612)+E(f225(x611),f225(x612))
% 109.14/108.86 [62]~E(x621,x622)+E(f226(x621),f226(x622))
% 109.14/108.86 [63]~E(x631,x632)+E(f29(x631),f29(x632))
% 109.14/108.86 [64]~E(x641,x642)+E(f277(x641,x643),f277(x642,x643))
% 109.14/108.86 [65]~E(x651,x652)+E(f277(x653,x651),f277(x653,x652))
% 109.14/108.86 [66]~E(x661,x662)+E(f55(x661),f55(x662))
% 109.14/108.86 [67]~E(x671,x672)+E(f298(x671,x673),f298(x672,x673))
% 109.14/108.86 [68]~E(x681,x682)+E(f298(x683,x681),f298(x683,x682))
% 109.14/108.86 [69]~E(x691,x692)+E(f54(x691),f54(x692))
% 109.14/108.86 [70]~E(x701,x702)+E(f917(x701,x703),f917(x702,x703))
% 109.14/108.86 [71]~E(x711,x712)+E(f917(x713,x711),f917(x713,x712))
% 109.14/108.86 [72]~E(x721,x722)+E(f234(x721,x723,x724),f234(x722,x723,x724))
% 109.14/108.86 [73]~E(x731,x732)+E(f234(x733,x731,x734),f234(x733,x732,x734))
% 109.14/108.86 [74]~E(x741,x742)+E(f234(x743,x744,x741),f234(x743,x744,x742))
% 109.14/108.86 [75]~E(x751,x752)+E(f247(x751,x753),f247(x752,x753))
% 109.14/108.86 [76]~E(x761,x762)+E(f247(x763,x761),f247(x763,x762))
% 109.14/108.86 [77]~E(x771,x772)+E(f278(x771),f278(x772))
% 109.14/108.86 [78]~E(x781,x782)+E(f245(x781,x783),f245(x782,x783))
% 109.14/108.86 [79]~E(x791,x792)+E(f245(x793,x791),f245(x793,x792))
% 109.14/108.86 [80]~E(x801,x802)+E(f104(x801),f104(x802))
% 109.14/108.86 [81]~E(x811,x812)+E(f426(x811,x813,x814,x815),f426(x812,x813,x814,x815))
% 109.14/108.86 [82]~E(x821,x822)+E(f426(x823,x821,x824,x825),f426(x823,x822,x824,x825))
% 109.14/108.86 [83]~E(x831,x832)+E(f426(x833,x834,x831,x835),f426(x833,x834,x832,x835))
% 109.14/108.86 [84]~E(x841,x842)+E(f426(x843,x844,x845,x841),f426(x843,x844,x845,x842))
% 109.14/108.86 [85]~E(x851,x852)+E(f30(x851),f30(x852))
% 109.14/108.86 [86]~E(x861,x862)+E(f74(x861),f74(x862))
% 109.14/108.86 [87]~E(x871,x872)+E(f601(x871,x873,x874,x875,x876),f601(x872,x873,x874,x875,x876))
% 109.14/108.86 [88]~E(x881,x882)+E(f601(x883,x881,x884,x885,x886),f601(x883,x882,x884,x885,x886))
% 109.14/108.86 [89]~E(x891,x892)+E(f601(x893,x894,x891,x895,x896),f601(x893,x894,x892,x895,x896))
% 109.14/108.86 [90]~E(x901,x902)+E(f601(x903,x904,x905,x901,x906),f601(x903,x904,x905,x902,x906))
% 109.14/108.86 [91]~E(x911,x912)+E(f601(x913,x914,x915,x916,x911),f601(x913,x914,x915,x916,x912))
% 109.14/108.86 [92]~E(x921,x922)+E(f248(x921,x923,x924),f248(x922,x923,x924))
% 109.14/108.86 [93]~E(x931,x932)+E(f248(x933,x931,x934),f248(x933,x932,x934))
% 109.14/108.86 [94]~E(x941,x942)+E(f248(x943,x944,x941),f248(x943,x944,x942))
% 109.14/108.86 [95]~E(x951,x952)+E(f130(x951,x953),f130(x952,x953))
% 109.14/108.86 [96]~E(x961,x962)+E(f130(x963,x961),f130(x963,x962))
% 109.14/108.86 [97]~E(x971,x972)+E(f280(x971,x973,x974),f280(x972,x973,x974))
% 109.14/108.86 [98]~E(x981,x982)+E(f280(x983,x981,x984),f280(x983,x982,x984))
% 109.14/108.86 [99]~E(x991,x992)+E(f280(x993,x994,x991),f280(x993,x994,x992))
% 109.14/108.86 [100]~E(x1001,x1002)+E(f10(x1001,x1003,x1004),f10(x1002,x1003,x1004))
% 109.14/108.86 [101]~E(x1011,x1012)+E(f10(x1013,x1011,x1014),f10(x1013,x1012,x1014))
% 109.14/108.86 [102]~E(x1021,x1022)+E(f10(x1023,x1024,x1021),f10(x1023,x1024,x1022))
% 109.14/108.86 [103]~E(x1031,x1032)+E(f160(x1031,x1033,x1034),f160(x1032,x1033,x1034))
% 109.14/108.86 [104]~E(x1041,x1042)+E(f160(x1043,x1041,x1044),f160(x1043,x1042,x1044))
% 109.14/108.86 [105]~E(x1051,x1052)+E(f160(x1053,x1054,x1051),f160(x1053,x1054,x1052))
% 109.14/108.86 [106]~E(x1061,x1062)+E(f163(x1061),f163(x1062))
% 109.14/108.86 [107]~E(x1071,x1072)+E(f349(x1071,x1073,x1074),f349(x1072,x1073,x1074))
% 109.14/108.86 [108]~E(x1081,x1082)+E(f349(x1083,x1081,x1084),f349(x1083,x1082,x1084))
% 109.14/108.86 [109]~E(x1091,x1092)+E(f349(x1093,x1094,x1091),f349(x1093,x1094,x1092))
% 109.14/108.86 [110]~E(x1101,x1102)+E(f282(x1101),f282(x1102))
% 109.14/108.86 [111]~E(x1111,x1112)+E(f39(x1111,x1113,x1114),f39(x1112,x1113,x1114))
% 109.14/108.86 [112]~E(x1121,x1122)+E(f39(x1123,x1121,x1124),f39(x1123,x1122,x1124))
% 109.14/108.86 [113]~E(x1131,x1132)+E(f39(x1133,x1134,x1131),f39(x1133,x1134,x1132))
% 109.14/108.86 [114]~E(x1141,x1142)+E(f375(x1141,x1143,x1144),f375(x1142,x1143,x1144))
% 109.14/108.86 [115]~E(x1151,x1152)+E(f375(x1153,x1151,x1154),f375(x1153,x1152,x1154))
% 109.14/108.86 [116]~E(x1161,x1162)+E(f375(x1163,x1164,x1161),f375(x1163,x1164,x1162))
% 109.14/108.86 [117]~E(x1171,x1172)+E(f294(x1171,x1173,x1174),f294(x1172,x1173,x1174))
% 109.14/108.86 [118]~E(x1181,x1182)+E(f294(x1183,x1181,x1184),f294(x1183,x1182,x1184))
% 109.14/108.86 [119]~E(x1191,x1192)+E(f294(x1193,x1194,x1191),f294(x1193,x1194,x1192))
% 109.14/108.86 [120]~E(x1201,x1202)+E(f432(x1201,x1203,x1204,x1205),f432(x1202,x1203,x1204,x1205))
% 109.14/108.86 [121]~E(x1211,x1212)+E(f432(x1213,x1211,x1214,x1215),f432(x1213,x1212,x1214,x1215))
% 109.14/108.86 [122]~E(x1221,x1222)+E(f432(x1223,x1224,x1221,x1225),f432(x1223,x1224,x1222,x1225))
% 109.14/108.86 [123]~E(x1231,x1232)+E(f432(x1233,x1234,x1235,x1231),f432(x1233,x1234,x1235,x1232))
% 109.14/108.86 [124]~E(x1241,x1242)+E(f66(x1241,x1243,x1244,x1245),f66(x1242,x1243,x1244,x1245))
% 109.14/108.86 [125]~E(x1251,x1252)+E(f66(x1253,x1251,x1254,x1255),f66(x1253,x1252,x1254,x1255))
% 109.14/108.86 [126]~E(x1261,x1262)+E(f66(x1263,x1264,x1261,x1265),f66(x1263,x1264,x1262,x1265))
% 109.14/108.86 [127]~E(x1271,x1272)+E(f66(x1273,x1274,x1275,x1271),f66(x1273,x1274,x1275,x1272))
% 109.14/108.86 [128]~E(x1281,x1282)+E(f656(x1281,x1283,x1284,x1285),f656(x1282,x1283,x1284,x1285))
% 109.14/108.86 [129]~E(x1291,x1292)+E(f656(x1293,x1291,x1294,x1295),f656(x1293,x1292,x1294,x1295))
% 109.14/108.86 [130]~E(x1301,x1302)+E(f656(x1303,x1304,x1301,x1305),f656(x1303,x1304,x1302,x1305))
% 109.14/108.86 [131]~E(x1311,x1312)+E(f656(x1313,x1314,x1315,x1311),f656(x1313,x1314,x1315,x1312))
% 109.14/108.86 [132]~E(x1321,x1322)+E(f311(x1321,x1323,x1324,x1325),f311(x1322,x1323,x1324,x1325))
% 109.14/108.86 [133]~E(x1331,x1332)+E(f311(x1333,x1331,x1334,x1335),f311(x1333,x1332,x1334,x1335))
% 109.14/108.86 [134]~E(x1341,x1342)+E(f311(x1343,x1344,x1341,x1345),f311(x1343,x1344,x1342,x1345))
% 109.14/108.86 [135]~E(x1351,x1352)+E(f311(x1353,x1354,x1355,x1351),f311(x1353,x1354,x1355,x1352))
% 109.14/108.86 [136]~E(x1361,x1362)+E(f18(x1361,x1363),f18(x1362,x1363))
% 109.14/108.86 [137]~E(x1371,x1372)+E(f18(x1373,x1371),f18(x1373,x1372))
% 109.14/108.86 [138]~E(x1381,x1382)+E(f275(x1381,x1383),f275(x1382,x1383))
% 109.14/108.86 [139]~E(x1391,x1392)+E(f275(x1393,x1391),f275(x1393,x1392))
% 109.14/108.86 [140]~E(x1401,x1402)+E(f16(x1401,x1403),f16(x1402,x1403))
% 109.14/108.86 [141]~E(x1411,x1412)+E(f16(x1413,x1411),f16(x1413,x1412))
% 109.14/108.86 [142]~E(x1421,x1422)+E(f266(x1421,x1423),f266(x1422,x1423))
% 109.14/108.86 [143]~E(x1431,x1432)+E(f266(x1433,x1431),f266(x1433,x1432))
% 109.14/108.86 [144]~E(x1441,x1442)+E(f233(x1441),f233(x1442))
% 109.14/108.86 [145]~E(x1451,x1452)+E(f96(x1451),f96(x1452))
% 109.14/108.86 [146]~E(x1461,x1462)+E(f98(x1461),f98(x1462))
% 109.14/108.86 [147]~E(x1471,x1472)+E(f319(x1471),f319(x1472))
% 109.14/108.86 [148]~E(x1481,x1482)+E(f419(x1481,x1483,x1484,x1485,x1486),f419(x1482,x1483,x1484,x1485,x1486))
% 109.14/108.86 [149]~E(x1491,x1492)+E(f419(x1493,x1491,x1494,x1495,x1496),f419(x1493,x1492,x1494,x1495,x1496))
% 109.14/108.86 [150]~E(x1501,x1502)+E(f419(x1503,x1504,x1501,x1505,x1506),f419(x1503,x1504,x1502,x1505,x1506))
% 109.14/108.86 [151]~E(x1511,x1512)+E(f419(x1513,x1514,x1515,x1511,x1516),f419(x1513,x1514,x1515,x1512,x1516))
% 109.14/108.86 [152]~E(x1521,x1522)+E(f419(x1523,x1524,x1525,x1526,x1521),f419(x1523,x1524,x1525,x1526,x1522))
% 109.14/108.86 [153]~E(x1531,x1532)+E(f575(x1531),f575(x1532))
% 109.14/108.86 [154]~E(x1541,x1542)+E(f20(x1541,x1543,x1544),f20(x1542,x1543,x1544))
% 109.14/108.86 [155]~E(x1551,x1552)+E(f20(x1553,x1551,x1554),f20(x1553,x1552,x1554))
% 109.14/108.86 [156]~E(x1561,x1562)+E(f20(x1563,x1564,x1561),f20(x1563,x1564,x1562))
% 109.14/108.86 [157]~E(x1571,x1572)+E(f459(x1571,x1573,x1574),f459(x1572,x1573,x1574))
% 109.14/108.86 [158]~E(x1581,x1582)+E(f459(x1583,x1581,x1584),f459(x1583,x1582,x1584))
% 109.14/108.86 [159]~E(x1591,x1592)+E(f459(x1593,x1594,x1591),f459(x1593,x1594,x1592))
% 109.14/108.86 [160]~E(x1601,x1602)+E(f232(x1601,x1603),f232(x1602,x1603))
% 109.14/108.86 [161]~E(x1611,x1612)+E(f232(x1613,x1611),f232(x1613,x1612))
% 109.14/108.86 [162]~E(x1621,x1622)+E(f301(x1621,x1623,x1624),f301(x1622,x1623,x1624))
% 109.14/108.86 [163]~E(x1631,x1632)+E(f301(x1633,x1631,x1634),f301(x1633,x1632,x1634))
% 109.14/108.86 [164]~E(x1641,x1642)+E(f301(x1643,x1644,x1641),f301(x1643,x1644,x1642))
% 109.14/108.86 [165]~E(x1651,x1652)+E(f9(x1651,x1653,x1654),f9(x1652,x1653,x1654))
% 109.14/108.86 [166]~E(x1661,x1662)+E(f9(x1663,x1661,x1664),f9(x1663,x1662,x1664))
% 109.14/108.86 [167]~E(x1671,x1672)+E(f9(x1673,x1674,x1671),f9(x1673,x1674,x1672))
% 109.14/108.86 [168]~E(x1681,x1682)+E(f430(x1681,x1683,x1684,x1685),f430(x1682,x1683,x1684,x1685))
% 109.14/108.86 [169]~E(x1691,x1692)+E(f430(x1693,x1691,x1694,x1695),f430(x1693,x1692,x1694,x1695))
% 109.14/108.86 [170]~E(x1701,x1702)+E(f430(x1703,x1704,x1701,x1705),f430(x1703,x1704,x1702,x1705))
% 109.14/108.86 [171]~E(x1711,x1712)+E(f430(x1713,x1714,x1715,x1711),f430(x1713,x1714,x1715,x1712))
% 109.14/108.86 [172]~E(x1721,x1722)+E(f159(x1721),f159(x1722))
% 109.14/108.86 [173]~E(x1731,x1732)+E(f7(x1731),f7(x1732))
% 109.14/108.86 [174]~E(x1741,x1742)+E(f142(x1741),f142(x1742))
% 109.14/108.86 [175]~E(x1751,x1752)+E(f253(x1751),f253(x1752))
% 109.14/108.86 [176]~E(x1761,x1762)+E(f174(x1761,x1763),f174(x1762,x1763))
% 109.14/108.86 [177]~E(x1771,x1772)+E(f174(x1773,x1771),f174(x1773,x1772))
% 109.14/108.86 [178]~E(x1781,x1782)+E(f33(x1781,x1783),f33(x1782,x1783))
% 109.14/108.86 [179]~E(x1791,x1792)+E(f33(x1793,x1791),f33(x1793,x1792))
% 109.14/108.86 [180]~E(x1801,x1802)+E(f56(x1801,x1803,x1804),f56(x1802,x1803,x1804))
% 109.14/108.86 [181]~E(x1811,x1812)+E(f56(x1813,x1811,x1814),f56(x1813,x1812,x1814))
% 109.14/108.86 [182]~E(x1821,x1822)+E(f56(x1823,x1824,x1821),f56(x1823,x1824,x1822))
% 109.14/108.86 [183]~E(x1831,x1832)+E(f293(x1831,x1833),f293(x1832,x1833))
% 109.14/108.86 [184]~E(x1841,x1842)+E(f293(x1843,x1841),f293(x1843,x1842))
% 109.14/108.86 [185]~E(x1851,x1852)+E(f166(x1851),f166(x1852))
% 109.14/108.86 [186]~E(x1861,x1862)+E(f151(x1861,x1863),f151(x1862,x1863))
% 109.14/108.86 [187]~E(x1871,x1872)+E(f151(x1873,x1871),f151(x1873,x1872))
% 109.14/108.86 [188]~E(x1881,x1882)+E(f161(x1881,x1883,x1884),f161(x1882,x1883,x1884))
% 109.14/108.86 [189]~E(x1891,x1892)+E(f161(x1893,x1891,x1894),f161(x1893,x1892,x1894))
% 109.14/108.86 [190]~E(x1901,x1902)+E(f161(x1903,x1904,x1901),f161(x1903,x1904,x1902))
% 109.14/108.86 [191]~E(x1911,x1912)+E(f145(x1911,x1913),f145(x1912,x1913))
% 109.14/108.86 [192]~E(x1921,x1922)+E(f145(x1923,x1921),f145(x1923,x1922))
% 109.14/108.86 [193]~E(x1931,x1932)+E(f125(x1931),f125(x1932))
% 109.14/108.86 [194]~E(x1941,x1942)+E(f666(x1941,x1943),f666(x1942,x1943))
% 109.14/108.86 [195]~E(x1951,x1952)+E(f666(x1953,x1951),f666(x1953,x1952))
% 109.14/108.86 [196]~E(x1961,x1962)+E(f855(x1961,x1963,x1964),f855(x1962,x1963,x1964))
% 109.14/108.86 [197]~E(x1971,x1972)+E(f855(x1973,x1971,x1974),f855(x1973,x1972,x1974))
% 109.14/108.86 [198]~E(x1981,x1982)+E(f855(x1983,x1984,x1981),f855(x1983,x1984,x1982))
% 109.14/108.86 [199]~E(x1991,x1992)+E(f296(x1991,x1993,x1994),f296(x1992,x1993,x1994))
% 109.14/108.86 [200]~E(x2001,x2002)+E(f296(x2003,x2001,x2004),f296(x2003,x2002,x2004))
% 109.14/108.86 [201]~E(x2011,x2012)+E(f296(x2013,x2014,x2011),f296(x2013,x2014,x2012))
% 109.14/108.86 [202]~E(x2021,x2022)+E(f17(x2021,x2023),f17(x2022,x2023))
% 109.14/108.86 [203]~E(x2031,x2032)+E(f17(x2033,x2031),f17(x2033,x2032))
% 109.14/108.86 [204]~E(x2041,x2042)+E(f613(x2041,x2043,x2044),f613(x2042,x2043,x2044))
% 109.14/108.86 [205]~E(x2051,x2052)+E(f613(x2053,x2051,x2054),f613(x2053,x2052,x2054))
% 109.14/108.86 [206]~E(x2061,x2062)+E(f613(x2063,x2064,x2061),f613(x2063,x2064,x2062))
% 109.14/108.86 [207]~E(x2071,x2072)+E(f168(x2071,x2073,x2074),f168(x2072,x2073,x2074))
% 109.14/108.86 [208]~E(x2081,x2082)+E(f168(x2083,x2081,x2084),f168(x2083,x2082,x2084))
% 109.14/108.86 [209]~E(x2091,x2092)+E(f168(x2093,x2094,x2091),f168(x2093,x2094,x2092))
% 109.14/108.86 [210]~E(x2101,x2102)+E(f69(x2101),f69(x2102))
% 109.14/108.86 [211]~E(x2111,x2112)+E(f80(x2111),f80(x2112))
% 109.14/108.86 [212]~E(x2121,x2122)+E(f772(x2121,x2123,x2124,x2125),f772(x2122,x2123,x2124,x2125))
% 109.14/108.86 [213]~E(x2131,x2132)+E(f772(x2133,x2131,x2134,x2135),f772(x2133,x2132,x2134,x2135))
% 109.14/108.86 [214]~E(x2141,x2142)+E(f772(x2143,x2144,x2141,x2145),f772(x2143,x2144,x2142,x2145))
% 109.14/108.86 [215]~E(x2151,x2152)+E(f772(x2153,x2154,x2155,x2151),f772(x2153,x2154,x2155,x2152))
% 109.14/108.86 [216]~E(x2161,x2162)+E(f508(x2161,x2163,x2164,x2165,x2166,x2167),f508(x2162,x2163,x2164,x2165,x2166,x2167))
% 109.14/108.86 [217]~E(x2171,x2172)+E(f508(x2173,x2171,x2174,x2175,x2176,x2177),f508(x2173,x2172,x2174,x2175,x2176,x2177))
% 109.14/108.86 [218]~E(x2181,x2182)+E(f508(x2183,x2184,x2181,x2185,x2186,x2187),f508(x2183,x2184,x2182,x2185,x2186,x2187))
% 109.14/108.86 [219]~E(x2191,x2192)+E(f508(x2193,x2194,x2195,x2191,x2196,x2197),f508(x2193,x2194,x2195,x2192,x2196,x2197))
% 109.14/108.86 [220]~E(x2201,x2202)+E(f508(x2203,x2204,x2205,x2206,x2201,x2207),f508(x2203,x2204,x2205,x2206,x2202,x2207))
% 109.14/108.86 [221]~E(x2211,x2212)+E(f508(x2213,x2214,x2215,x2216,x2217,x2211),f508(x2213,x2214,x2215,x2216,x2217,x2212))
% 109.14/108.86 [222]~E(x2221,x2222)+E(f466(x2221,x2223),f466(x2222,x2223))
% 109.14/108.86 [223]~E(x2231,x2232)+E(f466(x2233,x2231),f466(x2233,x2232))
% 109.14/108.86 [224]~E(x2241,x2242)+E(f825(x2241,x2243,x2244),f825(x2242,x2243,x2244))
% 109.14/108.86 [225]~E(x2251,x2252)+E(f825(x2253,x2251,x2254),f825(x2253,x2252,x2254))
% 109.14/108.86 [226]~E(x2261,x2262)+E(f825(x2263,x2264,x2261),f825(x2263,x2264,x2262))
% 109.14/108.86 [227]~E(x2271,x2272)+E(f719(x2271,x2273,x2274,x2275),f719(x2272,x2273,x2274,x2275))
% 109.14/108.86 [228]~E(x2281,x2282)+E(f719(x2283,x2281,x2284,x2285),f719(x2283,x2282,x2284,x2285))
% 109.14/108.86 [229]~E(x2291,x2292)+E(f719(x2293,x2294,x2291,x2295),f719(x2293,x2294,x2292,x2295))
% 109.14/108.86 [230]~E(x2301,x2302)+E(f719(x2303,x2304,x2305,x2301),f719(x2303,x2304,x2305,x2302))
% 109.14/108.86 [231]~E(x2311,x2312)+E(f261(x2311,x2313),f261(x2312,x2313))
% 109.14/108.86 [232]~E(x2321,x2322)+E(f261(x2323,x2321),f261(x2323,x2322))
% 109.14/108.86 [233]~E(x2331,x2332)+E(f273(x2331),f273(x2332))
% 109.14/108.86 [234]~E(x2341,x2342)+E(f170(x2341,x2343),f170(x2342,x2343))
% 109.14/108.86 [235]~E(x2351,x2352)+E(f170(x2353,x2351),f170(x2353,x2352))
% 109.14/108.86 [236]~E(x2361,x2362)+E(f447(x2361,x2363,x2364),f447(x2362,x2363,x2364))
% 109.14/108.86 [237]~E(x2371,x2372)+E(f447(x2373,x2371,x2374),f447(x2373,x2372,x2374))
% 109.14/108.86 [238]~E(x2381,x2382)+E(f447(x2383,x2384,x2381),f447(x2383,x2384,x2382))
% 109.14/108.86 [239]~E(x2391,x2392)+E(f68(x2391,x2393,x2394,x2395,x2396),f68(x2392,x2393,x2394,x2395,x2396))
% 109.14/108.86 [240]~E(x2401,x2402)+E(f68(x2403,x2401,x2404,x2405,x2406),f68(x2403,x2402,x2404,x2405,x2406))
% 109.14/108.86 [241]~E(x2411,x2412)+E(f68(x2413,x2414,x2411,x2415,x2416),f68(x2413,x2414,x2412,x2415,x2416))
% 109.14/108.86 [242]~E(x2421,x2422)+E(f68(x2423,x2424,x2425,x2421,x2426),f68(x2423,x2424,x2425,x2422,x2426))
% 109.14/108.86 [243]~E(x2431,x2432)+E(f68(x2433,x2434,x2435,x2436,x2431),f68(x2433,x2434,x2435,x2436,x2432))
% 109.14/108.86 [244]~E(x2441,x2442)+E(f528(x2441,x2443,x2444,x2445,x2446,x2447,x2448),f528(x2442,x2443,x2444,x2445,x2446,x2447,x2448))
% 109.14/108.86 [245]~E(x2451,x2452)+E(f528(x2453,x2451,x2454,x2455,x2456,x2457,x2458),f528(x2453,x2452,x2454,x2455,x2456,x2457,x2458))
% 109.14/108.86 [246]~E(x2461,x2462)+E(f528(x2463,x2464,x2461,x2465,x2466,x2467,x2468),f528(x2463,x2464,x2462,x2465,x2466,x2467,x2468))
% 109.14/108.86 [247]~E(x2471,x2472)+E(f528(x2473,x2474,x2475,x2471,x2476,x2477,x2478),f528(x2473,x2474,x2475,x2472,x2476,x2477,x2478))
% 109.14/108.86 [248]~E(x2481,x2482)+E(f528(x2483,x2484,x2485,x2486,x2481,x2487,x2488),f528(x2483,x2484,x2485,x2486,x2482,x2487,x2488))
% 109.14/108.86 [249]~E(x2491,x2492)+E(f528(x2493,x2494,x2495,x2496,x2497,x2491,x2498),f528(x2493,x2494,x2495,x2496,x2497,x2492,x2498))
% 109.14/108.86 [250]~E(x2501,x2502)+E(f528(x2503,x2504,x2505,x2506,x2507,x2508,x2501),f528(x2503,x2504,x2505,x2506,x2507,x2508,x2502))
% 109.14/108.86 [251]~E(x2511,x2512)+E(f889(x2511,x2513,x2514,x2515),f889(x2512,x2513,x2514,x2515))
% 109.14/108.86 [252]~E(x2521,x2522)+E(f889(x2523,x2521,x2524,x2525),f889(x2523,x2522,x2524,x2525))
% 109.14/108.86 [253]~E(x2531,x2532)+E(f889(x2533,x2534,x2531,x2535),f889(x2533,x2534,x2532,x2535))
% 109.14/108.86 [254]~E(x2541,x2542)+E(f889(x2543,x2544,x2545,x2541),f889(x2543,x2544,x2545,x2542))
% 109.14/108.86 [255]~E(x2551,x2552)+E(f436(x2551,x2553,x2554),f436(x2552,x2553,x2554))
% 109.14/108.86 [256]~E(x2561,x2562)+E(f436(x2563,x2561,x2564),f436(x2563,x2562,x2564))
% 109.14/108.86 [257]~E(x2571,x2572)+E(f436(x2573,x2574,x2571),f436(x2573,x2574,x2572))
% 109.14/108.86 [258]~E(x2581,x2582)+E(f79(x2581),f79(x2582))
% 109.14/108.86 [259]~E(x2591,x2592)+E(f240(x2591,x2593,x2594),f240(x2592,x2593,x2594))
% 109.14/108.86 [260]~E(x2601,x2602)+E(f240(x2603,x2601,x2604),f240(x2603,x2602,x2604))
% 109.14/108.86 [261]~E(x2611,x2612)+E(f240(x2613,x2614,x2611),f240(x2613,x2614,x2612))
% 109.14/108.86 [262]~E(x2621,x2622)+E(f807(x2621,x2623,x2624,x2625,x2626,x2627),f807(x2622,x2623,x2624,x2625,x2626,x2627))
% 109.14/108.86 [263]~E(x2631,x2632)+E(f807(x2633,x2631,x2634,x2635,x2636,x2637),f807(x2633,x2632,x2634,x2635,x2636,x2637))
% 109.14/108.86 [264]~E(x2641,x2642)+E(f807(x2643,x2644,x2641,x2645,x2646,x2647),f807(x2643,x2644,x2642,x2645,x2646,x2647))
% 109.14/108.86 [265]~E(x2651,x2652)+E(f807(x2653,x2654,x2655,x2651,x2656,x2657),f807(x2653,x2654,x2655,x2652,x2656,x2657))
% 109.14/108.86 [266]~E(x2661,x2662)+E(f807(x2663,x2664,x2665,x2666,x2661,x2667),f807(x2663,x2664,x2665,x2666,x2662,x2667))
% 109.14/108.86 [267]~E(x2671,x2672)+E(f807(x2673,x2674,x2675,x2676,x2677,x2671),f807(x2673,x2674,x2675,x2676,x2677,x2672))
% 109.14/108.86 [268]~E(x2681,x2682)+E(f327(x2681),f327(x2682))
% 109.14/108.86 [269]~E(x2691,x2692)+E(f105(x2691,x2693),f105(x2692,x2693))
% 109.14/108.86 [270]~E(x2701,x2702)+E(f105(x2703,x2701),f105(x2703,x2702))
% 109.14/108.86 [271]~E(x2711,x2712)+E(f594(x2711,x2713),f594(x2712,x2713))
% 109.14/108.86 [272]~E(x2721,x2722)+E(f594(x2723,x2721),f594(x2723,x2722))
% 109.14/108.86 [273]~E(x2731,x2732)+E(f41(x2731,x2733),f41(x2732,x2733))
% 109.14/108.86 [274]~E(x2741,x2742)+E(f41(x2743,x2741),f41(x2743,x2742))
% 109.14/108.86 [275]~E(x2751,x2752)+E(f143(x2751,x2753),f143(x2752,x2753))
% 109.14/108.86 [276]~E(x2761,x2762)+E(f143(x2763,x2761),f143(x2763,x2762))
% 109.14/108.86 [277]~E(x2771,x2772)+E(f85(x2771),f85(x2772))
% 109.14/108.86 [278]~E(x2781,x2782)+E(f182(x2781),f182(x2782))
% 109.14/108.86 [279]~E(x2791,x2792)+E(f254(x2791,x2793),f254(x2792,x2793))
% 109.14/108.86 [280]~E(x2801,x2802)+E(f254(x2803,x2801),f254(x2803,x2802))
% 109.14/108.86 [281]~E(x2811,x2812)+E(f106(x2811),f106(x2812))
% 109.14/108.86 [282]~E(x2821,x2822)+E(f132(x2821),f132(x2822))
% 109.14/108.86 [283]~E(x2831,x2832)+E(f919(x2831,x2833),f919(x2832,x2833))
% 109.14/108.86 [284]~E(x2841,x2842)+E(f919(x2843,x2841),f919(x2843,x2842))
% 109.14/108.86 [285]~E(x2851,x2852)+E(f916(x2851,x2853),f916(x2852,x2853))
% 109.14/108.86 [286]~E(x2861,x2862)+E(f916(x2863,x2861),f916(x2863,x2862))
% 109.14/108.86 [287]~E(x2871,x2872)+E(f158(x2871),f158(x2872))
% 109.14/108.86 [288]~E(x2881,x2882)+E(f300(x2881),f300(x2882))
% 109.14/108.86 [289]~E(x2891,x2892)+E(f127(x2891,x2893),f127(x2892,x2893))
% 109.14/108.86 [290]~E(x2901,x2902)+E(f127(x2903,x2901),f127(x2903,x2902))
% 109.14/108.86 [291]~E(x2911,x2912)+E(f149(x2911,x2913),f149(x2912,x2913))
% 109.14/108.86 [292]~E(x2921,x2922)+E(f149(x2923,x2921),f149(x2923,x2922))
% 109.14/108.86 [293]~E(x2931,x2932)+E(f162(x2931),f162(x2932))
% 109.14/108.86 [294]~E(x2941,x2942)+E(f81(x2941,x2943),f81(x2942,x2943))
% 109.14/108.86 [295]~E(x2951,x2952)+E(f81(x2953,x2951),f81(x2953,x2952))
% 109.14/108.86 [296]~E(x2961,x2962)+E(f614(x2961,x2963,x2964),f614(x2962,x2963,x2964))
% 109.14/108.86 [297]~E(x2971,x2972)+E(f614(x2973,x2971,x2974),f614(x2973,x2972,x2974))
% 109.14/108.86 [298]~E(x2981,x2982)+E(f614(x2983,x2984,x2981),f614(x2983,x2984,x2982))
% 109.14/108.86 [299]~E(x2991,x2992)+E(f8(x2991,x2993),f8(x2992,x2993))
% 109.14/108.86 [300]~E(x3001,x3002)+E(f8(x3003,x3001),f8(x3003,x3002))
% 109.14/108.86 [301]~E(x3011,x3012)+E(f129(x3011),f129(x3012))
% 109.14/108.86 [302]~E(x3021,x3022)+E(f249(x3021,x3023,x3024,x3025,x3026,x3027),f249(x3022,x3023,x3024,x3025,x3026,x3027))
% 109.14/108.86 [303]~E(x3031,x3032)+E(f249(x3033,x3031,x3034,x3035,x3036,x3037),f249(x3033,x3032,x3034,x3035,x3036,x3037))
% 109.14/108.86 [304]~E(x3041,x3042)+E(f249(x3043,x3044,x3041,x3045,x3046,x3047),f249(x3043,x3044,x3042,x3045,x3046,x3047))
% 109.14/108.86 [305]~E(x3051,x3052)+E(f249(x3053,x3054,x3055,x3051,x3056,x3057),f249(x3053,x3054,x3055,x3052,x3056,x3057))
% 109.14/108.86 [306]~E(x3061,x3062)+E(f249(x3063,x3064,x3065,x3066,x3061,x3067),f249(x3063,x3064,x3065,x3066,x3062,x3067))
% 109.14/108.86 [307]~E(x3071,x3072)+E(f249(x3073,x3074,x3075,x3076,x3077,x3071),f249(x3073,x3074,x3075,x3076,x3077,x3072))
% 109.14/108.86 [308]~E(x3081,x3082)+E(f156(x3081),f156(x3082))
% 109.14/108.86 [309]~E(x3091,x3092)+E(f155(x3091),f155(x3092))
% 109.14/108.86 [310]~E(x3101,x3102)+E(f877(x3101,x3103,x3104,x3105),f877(x3102,x3103,x3104,x3105))
% 109.14/108.86 [311]~E(x3111,x3112)+E(f877(x3113,x3111,x3114,x3115),f877(x3113,x3112,x3114,x3115))
% 109.14/108.86 [312]~E(x3121,x3122)+E(f877(x3123,x3124,x3121,x3125),f877(x3123,x3124,x3122,x3125))
% 109.14/108.86 [313]~E(x3131,x3132)+E(f877(x3133,x3134,x3135,x3131),f877(x3133,x3134,x3135,x3132))
% 109.14/108.86 [314]~E(x3141,x3142)+E(f371(x3141,x3143),f371(x3142,x3143))
% 109.14/108.86 [315]~E(x3151,x3152)+E(f371(x3153,x3151),f371(x3153,x3152))
% 109.14/108.86 [316]~E(x3161,x3162)+E(f128(x3161),f128(x3162))
% 109.14/108.86 [317]~E(x3171,x3172)+E(f376(x3171,x3173,x3174),f376(x3172,x3173,x3174))
% 109.14/108.86 [318]~E(x3181,x3182)+E(f376(x3183,x3181,x3184),f376(x3183,x3182,x3184))
% 109.14/108.86 [319]~E(x3191,x3192)+E(f376(x3193,x3194,x3191),f376(x3193,x3194,x3192))
% 109.14/108.86 [320]~E(x3201,x3202)+E(f353(x3201,x3203,x3204,x3205),f353(x3202,x3203,x3204,x3205))
% 109.14/108.86 [321]~E(x3211,x3212)+E(f353(x3213,x3211,x3214,x3215),f353(x3213,x3212,x3214,x3215))
% 109.14/108.86 [322]~E(x3221,x3222)+E(f353(x3223,x3224,x3221,x3225),f353(x3223,x3224,x3222,x3225))
% 109.14/108.86 [323]~E(x3231,x3232)+E(f353(x3233,x3234,x3235,x3231),f353(x3233,x3234,x3235,x3232))
% 109.14/108.86 [324]~E(x3241,x3242)+E(f309(x3241,x3243),f309(x3242,x3243))
% 109.14/108.86 [325]~E(x3251,x3252)+E(f309(x3253,x3251),f309(x3253,x3252))
% 109.14/108.86 [326]~E(x3261,x3262)+E(f796(x3261,x3263),f796(x3262,x3263))
% 109.14/108.86 [327]~E(x3271,x3272)+E(f796(x3273,x3271),f796(x3273,x3272))
% 109.14/108.86 [328]~E(x3281,x3282)+E(f310(x3281,x3283),f310(x3282,x3283))
% 109.14/108.86 [329]~E(x3291,x3292)+E(f310(x3293,x3291),f310(x3293,x3292))
% 109.14/108.86 [330]~E(x3301,x3302)+E(f826(x3301,x3303,x3304,x3305),f826(x3302,x3303,x3304,x3305))
% 109.14/108.86 [331]~E(x3311,x3312)+E(f826(x3313,x3311,x3314,x3315),f826(x3313,x3312,x3314,x3315))
% 109.14/108.86 [332]~E(x3321,x3322)+E(f826(x3323,x3324,x3321,x3325),f826(x3323,x3324,x3322,x3325))
% 109.14/108.86 [333]~E(x3331,x3332)+E(f826(x3333,x3334,x3335,x3331),f826(x3333,x3334,x3335,x3332))
% 109.14/108.86 [334]~E(x3341,x3342)+E(f133(x3341,x3343,x3344,x3345),f133(x3342,x3343,x3344,x3345))
% 109.14/108.86 [335]~E(x3351,x3352)+E(f133(x3353,x3351,x3354,x3355),f133(x3353,x3352,x3354,x3355))
% 109.14/108.86 [336]~E(x3361,x3362)+E(f133(x3363,x3364,x3361,x3365),f133(x3363,x3364,x3362,x3365))
% 109.14/108.86 [337]~E(x3371,x3372)+E(f133(x3373,x3374,x3375,x3371),f133(x3373,x3374,x3375,x3372))
% 109.14/108.86 [338]~E(x3381,x3382)+E(f31(x3381,x3383),f31(x3382,x3383))
% 109.14/108.86 [339]~E(x3391,x3392)+E(f31(x3393,x3391),f31(x3393,x3392))
% 109.14/108.86 [340]~E(x3401,x3402)+E(f444(x3401,x3403,x3404,x3405,x3406,x3407,x3408),f444(x3402,x3403,x3404,x3405,x3406,x3407,x3408))
% 109.14/108.86 [341]~E(x3411,x3412)+E(f444(x3413,x3411,x3414,x3415,x3416,x3417,x3418),f444(x3413,x3412,x3414,x3415,x3416,x3417,x3418))
% 109.14/108.86 [342]~E(x3421,x3422)+E(f444(x3423,x3424,x3421,x3425,x3426,x3427,x3428),f444(x3423,x3424,x3422,x3425,x3426,x3427,x3428))
% 109.14/108.86 [343]~E(x3431,x3432)+E(f444(x3433,x3434,x3435,x3431,x3436,x3437,x3438),f444(x3433,x3434,x3435,x3432,x3436,x3437,x3438))
% 109.14/108.86 [344]~E(x3441,x3442)+E(f444(x3443,x3444,x3445,x3446,x3441,x3447,x3448),f444(x3443,x3444,x3445,x3446,x3442,x3447,x3448))
% 109.14/108.86 [345]~E(x3451,x3452)+E(f444(x3453,x3454,x3455,x3456,x3457,x3451,x3458),f444(x3453,x3454,x3455,x3456,x3457,x3452,x3458))
% 109.14/108.86 [346]~E(x3461,x3462)+E(f444(x3463,x3464,x3465,x3466,x3467,x3468,x3461),f444(x3463,x3464,x3465,x3466,x3467,x3468,x3462))
% 109.14/108.86 [347]~E(x3471,x3472)+E(f306(x3471,x3473),f306(x3472,x3473))
% 109.14/108.86 [348]~E(x3481,x3482)+E(f306(x3483,x3481),f306(x3483,x3482))
% 109.14/108.86 [349]~E(x3491,x3492)+E(f84(x3491,x3493,x3494,x3495),f84(x3492,x3493,x3494,x3495))
% 109.14/108.86 [350]~E(x3501,x3502)+E(f84(x3503,x3501,x3504,x3505),f84(x3503,x3502,x3504,x3505))
% 109.14/108.86 [351]~E(x3511,x3512)+E(f84(x3513,x3514,x3511,x3515),f84(x3513,x3514,x3512,x3515))
% 109.14/108.86 [352]~E(x3521,x3522)+E(f84(x3523,x3524,x3525,x3521),f84(x3523,x3524,x3525,x3522))
% 109.14/108.86 [353]~E(x3531,x3532)+E(f778(x3531,x3533,x3534,x3535,x3536,x3537,x3538),f778(x3532,x3533,x3534,x3535,x3536,x3537,x3538))
% 109.14/108.86 [354]~E(x3541,x3542)+E(f778(x3543,x3541,x3544,x3545,x3546,x3547,x3548),f778(x3543,x3542,x3544,x3545,x3546,x3547,x3548))
% 109.14/108.86 [355]~E(x3551,x3552)+E(f778(x3553,x3554,x3551,x3555,x3556,x3557,x3558),f778(x3553,x3554,x3552,x3555,x3556,x3557,x3558))
% 109.14/108.86 [356]~E(x3561,x3562)+E(f778(x3563,x3564,x3565,x3561,x3566,x3567,x3568),f778(x3563,x3564,x3565,x3562,x3566,x3567,x3568))
% 109.14/108.86 [357]~E(x3571,x3572)+E(f778(x3573,x3574,x3575,x3576,x3571,x3577,x3578),f778(x3573,x3574,x3575,x3576,x3572,x3577,x3578))
% 109.14/108.86 [358]~E(x3581,x3582)+E(f778(x3583,x3584,x3585,x3586,x3587,x3581,x3588),f778(x3583,x3584,x3585,x3586,x3587,x3582,x3588))
% 109.14/108.86 [359]~E(x3591,x3592)+E(f778(x3593,x3594,x3595,x3596,x3597,x3598,x3591),f778(x3593,x3594,x3595,x3596,x3597,x3598,x3592))
% 109.14/108.86 [360]~E(x3601,x3602)+E(f34(x3601,x3603),f34(x3602,x3603))
% 109.14/108.86 [361]~E(x3611,x3612)+E(f34(x3613,x3611),f34(x3613,x3612))
% 109.14/108.86 [362]~E(x3621,x3622)+E(f110(x3621),f110(x3622))
% 109.14/108.86 [363]~E(x3631,x3632)+E(f860(x3631,x3633,x3634),f860(x3632,x3633,x3634))
% 109.14/108.86 [364]~E(x3641,x3642)+E(f860(x3643,x3641,x3644),f860(x3643,x3642,x3644))
% 109.14/108.86 [365]~E(x3651,x3652)+E(f860(x3653,x3654,x3651),f860(x3653,x3654,x3652))
% 109.14/108.86 [366]~E(x3661,x3662)+E(f483(x3661,x3663,x3664,x3665,x3666,x3667,x3668),f483(x3662,x3663,x3664,x3665,x3666,x3667,x3668))
% 109.14/108.86 [367]~E(x3671,x3672)+E(f483(x3673,x3671,x3674,x3675,x3676,x3677,x3678),f483(x3673,x3672,x3674,x3675,x3676,x3677,x3678))
% 109.14/108.86 [368]~E(x3681,x3682)+E(f483(x3683,x3684,x3681,x3685,x3686,x3687,x3688),f483(x3683,x3684,x3682,x3685,x3686,x3687,x3688))
% 109.14/108.86 [369]~E(x3691,x3692)+E(f483(x3693,x3694,x3695,x3691,x3696,x3697,x3698),f483(x3693,x3694,x3695,x3692,x3696,x3697,x3698))
% 109.14/108.86 [370]~E(x3701,x3702)+E(f483(x3703,x3704,x3705,x3706,x3701,x3707,x3708),f483(x3703,x3704,x3705,x3706,x3702,x3707,x3708))
% 109.14/108.86 [371]~E(x3711,x3712)+E(f483(x3713,x3714,x3715,x3716,x3717,x3711,x3718),f483(x3713,x3714,x3715,x3716,x3717,x3712,x3718))
% 109.14/108.86 [372]~E(x3721,x3722)+E(f483(x3723,x3724,x3725,x3726,x3727,x3728,x3721),f483(x3723,x3724,x3725,x3726,x3727,x3728,x3722))
% 109.14/108.86 [373]~E(x3731,x3732)+E(f255(x3731,x3733),f255(x3732,x3733))
% 109.14/108.86 [374]~E(x3741,x3742)+E(f255(x3743,x3741),f255(x3743,x3742))
% 109.14/108.86 [375]~E(x3751,x3752)+E(f58(x3751,x3753,x3754),f58(x3752,x3753,x3754))
% 109.14/108.86 [376]~E(x3761,x3762)+E(f58(x3763,x3761,x3764),f58(x3763,x3762,x3764))
% 109.14/108.86 [377]~E(x3771,x3772)+E(f58(x3773,x3774,x3771),f58(x3773,x3774,x3772))
% 109.14/108.86 [378]~E(x3781,x3782)+E(f12(x3781,x3783),f12(x3782,x3783))
% 109.14/108.86 [379]~E(x3791,x3792)+E(f12(x3793,x3791),f12(x3793,x3792))
% 109.14/108.86 [380]~E(x3801,x3802)+E(f847(x3801,x3803,x3804,x3805,x3806,x3807),f847(x3802,x3803,x3804,x3805,x3806,x3807))
% 109.14/108.86 [381]~E(x3811,x3812)+E(f847(x3813,x3811,x3814,x3815,x3816,x3817),f847(x3813,x3812,x3814,x3815,x3816,x3817))
% 109.14/108.86 [382]~E(x3821,x3822)+E(f847(x3823,x3824,x3821,x3825,x3826,x3827),f847(x3823,x3824,x3822,x3825,x3826,x3827))
% 109.14/108.86 [383]~E(x3831,x3832)+E(f847(x3833,x3834,x3835,x3831,x3836,x3837),f847(x3833,x3834,x3835,x3832,x3836,x3837))
% 109.14/108.86 [384]~E(x3841,x3842)+E(f847(x3843,x3844,x3845,x3846,x3841,x3847),f847(x3843,x3844,x3845,x3846,x3842,x3847))
% 109.14/108.86 [385]~E(x3851,x3852)+E(f847(x3853,x3854,x3855,x3856,x3857,x3851),f847(x3853,x3854,x3855,x3856,x3857,x3852))
% 109.14/108.86 [386]~E(x3861,x3862)+E(f111(x3861,x3863),f111(x3862,x3863))
% 109.14/108.86 [387]~E(x3871,x3872)+E(f111(x3873,x3871),f111(x3873,x3872))
% 109.14/108.86 [388]~E(x3881,x3882)+E(f138(x3881,x3883),f138(x3882,x3883))
% 109.14/108.86 [389]~E(x3891,x3892)+E(f138(x3893,x3891),f138(x3893,x3892))
% 109.14/108.86 [390]~E(x3901,x3902)+E(f211(x3901,x3903,x3904,x3905),f211(x3902,x3903,x3904,x3905))
% 109.14/108.86 [391]~E(x3911,x3912)+E(f211(x3913,x3911,x3914,x3915),f211(x3913,x3912,x3914,x3915))
% 109.14/108.86 [392]~E(x3921,x3922)+E(f211(x3923,x3924,x3921,x3925),f211(x3923,x3924,x3922,x3925))
% 109.14/108.86 [393]~E(x3931,x3932)+E(f211(x3933,x3934,x3935,x3931),f211(x3933,x3934,x3935,x3932))
% 109.14/108.86 [394]~E(x3941,x3942)+E(f387(x3941,x3943,x3944),f387(x3942,x3943,x3944))
% 109.14/108.86 [395]~E(x3951,x3952)+E(f387(x3953,x3951,x3954),f387(x3953,x3952,x3954))
% 109.14/108.86 [396]~E(x3961,x3962)+E(f387(x3963,x3964,x3961),f387(x3963,x3964,x3962))
% 109.14/108.86 [397]~E(x3971,x3972)+E(f497(x3971,x3973,x3974),f497(x3972,x3973,x3974))
% 109.14/108.86 [398]~E(x3981,x3982)+E(f497(x3983,x3981,x3984),f497(x3983,x3982,x3984))
% 109.14/108.86 [399]~E(x3991,x3992)+E(f497(x3993,x3994,x3991),f497(x3993,x3994,x3992))
% 109.14/108.86 [400]~E(x4001,x4002)+E(f78(x4001,x4003),f78(x4002,x4003))
% 109.14/108.86 [401]~E(x4011,x4012)+E(f78(x4013,x4011),f78(x4013,x4012))
% 109.14/108.86 [402]~E(x4021,x4022)+E(f13(x4021,x4023,x4024),f13(x4022,x4023,x4024))
% 109.14/108.86 [403]~E(x4031,x4032)+E(f13(x4033,x4031,x4034),f13(x4033,x4032,x4034))
% 109.14/108.86 [404]~E(x4041,x4042)+E(f13(x4043,x4044,x4041),f13(x4043,x4044,x4042))
% 109.14/108.86 [405]~E(x4051,x4052)+E(f83(x4051,x4053),f83(x4052,x4053))
% 109.14/108.86 [406]~E(x4061,x4062)+E(f83(x4063,x4061),f83(x4063,x4062))
% 109.14/108.86 [407]~E(x4071,x4072)+E(f169(x4071,x4073),f169(x4072,x4073))
% 109.14/108.86 [408]~E(x4081,x4082)+E(f169(x4083,x4081),f169(x4083,x4082))
% 109.14/108.86 [409]~E(x4091,x4092)+E(f144(x4091,x4093),f144(x4092,x4093))
% 109.14/108.86 [410]~E(x4101,x4102)+E(f144(x4103,x4101),f144(x4103,x4102))
% 109.14/108.86 [411]~E(x4111,x4112)+E(f878(x4111,x4113,x4114,x4115,x4116),f878(x4112,x4113,x4114,x4115,x4116))
% 109.14/108.86 [412]~E(x4121,x4122)+E(f878(x4123,x4121,x4124,x4125,x4126),f878(x4123,x4122,x4124,x4125,x4126))
% 109.14/108.86 [413]~E(x4131,x4132)+E(f878(x4133,x4134,x4131,x4135,x4136),f878(x4133,x4134,x4132,x4135,x4136))
% 109.14/108.86 [414]~E(x4141,x4142)+E(f878(x4143,x4144,x4145,x4141,x4146),f878(x4143,x4144,x4145,x4142,x4146))
% 109.14/108.86 [415]~E(x4151,x4152)+E(f878(x4153,x4154,x4155,x4156,x4151),f878(x4153,x4154,x4155,x4156,x4152))
% 109.14/108.86 [416]~E(x4161,x4162)+E(f798(x4161,x4163),f798(x4162,x4163))
% 109.14/108.86 [417]~E(x4171,x4172)+E(f798(x4173,x4171),f798(x4173,x4172))
% 109.14/108.86 [418]~E(x4181,x4182)+E(f591(x4181,x4183,x4184),f591(x4182,x4183,x4184))
% 109.14/108.86 [419]~E(x4191,x4192)+E(f591(x4193,x4191,x4194),f591(x4193,x4192,x4194))
% 109.14/108.86 [420]~E(x4201,x4202)+E(f591(x4203,x4204,x4201),f591(x4203,x4204,x4202))
% 109.14/108.86 [421]~E(x4211,x4212)+E(f32(x4211,x4213),f32(x4212,x4213))
% 109.14/108.86 [422]~E(x4221,x4222)+E(f32(x4223,x4221),f32(x4223,x4222))
% 109.14/108.86 [423]~E(x4231,x4232)+E(f14(x4231,x4233,x4234),f14(x4232,x4233,x4234))
% 109.14/108.86 [424]~E(x4241,x4242)+E(f14(x4243,x4241,x4244),f14(x4243,x4242,x4244))
% 109.14/108.86 [425]~E(x4251,x4252)+E(f14(x4253,x4254,x4251),f14(x4253,x4254,x4252))
% 109.14/108.86 [426]~E(x4261,x4262)+E(f441(x4261,x4263),f441(x4262,x4263))
% 109.14/108.86 [427]~E(x4271,x4272)+E(f441(x4273,x4271),f441(x4273,x4272))
% 109.14/108.86 [428]~E(x4281,x4282)+E(f415(x4281,x4283,x4284,x4285),f415(x4282,x4283,x4284,x4285))
% 109.14/108.86 [429]~E(x4291,x4292)+E(f415(x4293,x4291,x4294,x4295),f415(x4293,x4292,x4294,x4295))
% 109.14/108.86 [430]~E(x4301,x4302)+E(f415(x4303,x4304,x4301,x4305),f415(x4303,x4304,x4302,x4305))
% 109.14/108.86 [431]~E(x4311,x4312)+E(f415(x4313,x4314,x4315,x4311),f415(x4313,x4314,x4315,x4312))
% 109.14/108.86 [432]~E(x4321,x4322)+E(f150(x4321,x4323),f150(x4322,x4323))
% 109.14/108.86 [433]~E(x4331,x4332)+E(f150(x4333,x4331),f150(x4333,x4332))
% 109.14/108.86 [434]~E(x4341,x4342)+E(f242(x4341,x4343),f242(x4342,x4343))
% 109.14/108.86 [435]~E(x4351,x4352)+E(f242(x4353,x4351),f242(x4353,x4352))
% 109.14/108.86 [436]~E(x4361,x4362)+E(f346(x4361,x4363,x4364,x4365),f346(x4362,x4363,x4364,x4365))
% 109.14/108.86 [437]~E(x4371,x4372)+E(f346(x4373,x4371,x4374,x4375),f346(x4373,x4372,x4374,x4375))
% 109.14/108.86 [438]~E(x4381,x4382)+E(f346(x4383,x4384,x4381,x4385),f346(x4383,x4384,x4382,x4385))
% 109.14/108.86 [439]~E(x4391,x4392)+E(f346(x4393,x4394,x4395,x4391),f346(x4393,x4394,x4395,x4392))
% 109.14/108.86 [440]~E(x4401,x4402)+E(f446(x4401,x4403),f446(x4402,x4403))
% 109.14/108.86 [441]~E(x4411,x4412)+E(f446(x4413,x4411),f446(x4413,x4412))
% 109.14/108.86 [442]~E(x4421,x4422)+E(f15(x4421,x4423),f15(x4422,x4423))
% 109.14/108.86 [443]~E(x4431,x4432)+E(f15(x4433,x4431),f15(x4433,x4432))
% 109.14/108.86 [444]~E(x4441,x4442)+E(f50(x4441),f50(x4442))
% 109.14/108.86 [445]~E(x4451,x4452)+E(f324(x4451),f324(x4452))
% 109.14/108.86 [446]~E(x4461,x4462)+E(f244(x4461,x4463,x4464,x4465,x4466),f244(x4462,x4463,x4464,x4465,x4466))
% 109.14/108.86 [447]~E(x4471,x4472)+E(f244(x4473,x4471,x4474,x4475,x4476),f244(x4473,x4472,x4474,x4475,x4476))
% 109.14/108.86 [448]~E(x4481,x4482)+E(f244(x4483,x4484,x4481,x4485,x4486),f244(x4483,x4484,x4482,x4485,x4486))
% 109.14/108.86 [449]~E(x4491,x4492)+E(f244(x4493,x4494,x4495,x4491,x4496),f244(x4493,x4494,x4495,x4492,x4496))
% 109.14/108.86 [450]~E(x4501,x4502)+E(f244(x4503,x4504,x4505,x4506,x4501),f244(x4503,x4504,x4505,x4506,x4502))
% 109.14/108.86 [451]~E(x4511,x4512)+E(f75(x4511,x4513),f75(x4512,x4513))
% 109.14/108.86 [452]~E(x4521,x4522)+E(f75(x4523,x4521),f75(x4523,x4522))
% 109.14/108.86 [453]~E(x4531,x4532)+E(f636(x4531,x4533),f636(x4532,x4533))
% 109.14/108.86 [454]~E(x4541,x4542)+E(f636(x4543,x4541),f636(x4543,x4542))
% 109.14/108.86 [455]~E(x4551,x4552)+E(f829(x4551,x4553,x4554,x4555),f829(x4552,x4553,x4554,x4555))
% 109.14/108.86 [456]~E(x4561,x4562)+E(f829(x4563,x4561,x4564,x4565),f829(x4563,x4562,x4564,x4565))
% 109.14/108.86 [457]~E(x4571,x4572)+E(f829(x4573,x4574,x4571,x4575),f829(x4573,x4574,x4572,x4575))
% 109.14/108.86 [458]~E(x4581,x4582)+E(f829(x4583,x4584,x4585,x4581),f829(x4583,x4584,x4585,x4582))
% 109.14/108.86 [459]~E(x4591,x4592)+E(f858(x4591,x4593,x4594),f858(x4592,x4593,x4594))
% 109.14/108.86 [460]~E(x4601,x4602)+E(f858(x4603,x4601,x4604),f858(x4603,x4602,x4604))
% 109.14/108.86 [461]~E(x4611,x4612)+E(f858(x4613,x4614,x4611),f858(x4613,x4614,x4612))
% 109.14/108.86 [462]~E(x4621,x4622)+E(f469(x4621,x4623,x4624,x4625),f469(x4622,x4623,x4624,x4625))
% 109.14/108.86 [463]~E(x4631,x4632)+E(f469(x4633,x4631,x4634,x4635),f469(x4633,x4632,x4634,x4635))
% 109.14/108.86 [464]~E(x4641,x4642)+E(f469(x4643,x4644,x4641,x4645),f469(x4643,x4644,x4642,x4645))
% 109.14/108.86 [465]~E(x4651,x4652)+E(f469(x4653,x4654,x4655,x4651),f469(x4653,x4654,x4655,x4652))
% 109.14/108.86 [466]~E(x4661,x4662)+E(f859(x4661,x4663,x4664),f859(x4662,x4663,x4664))
% 109.14/108.86 [467]~E(x4671,x4672)+E(f859(x4673,x4671,x4674),f859(x4673,x4672,x4674))
% 109.14/108.86 [468]~E(x4681,x4682)+E(f859(x4683,x4684,x4681),f859(x4683,x4684,x4682))
% 109.14/108.86 [469]~E(x4691,x4692)+E(f850(x4691,x4693,x4694,x4695,x4696,x4697,x4698),f850(x4692,x4693,x4694,x4695,x4696,x4697,x4698))
% 109.14/108.86 [470]~E(x4701,x4702)+E(f850(x4703,x4701,x4704,x4705,x4706,x4707,x4708),f850(x4703,x4702,x4704,x4705,x4706,x4707,x4708))
% 109.14/108.86 [471]~E(x4711,x4712)+E(f850(x4713,x4714,x4711,x4715,x4716,x4717,x4718),f850(x4713,x4714,x4712,x4715,x4716,x4717,x4718))
% 109.14/108.86 [472]~E(x4721,x4722)+E(f850(x4723,x4724,x4725,x4721,x4726,x4727,x4728),f850(x4723,x4724,x4725,x4722,x4726,x4727,x4728))
% 109.14/108.86 [473]~E(x4731,x4732)+E(f850(x4733,x4734,x4735,x4736,x4731,x4737,x4738),f850(x4733,x4734,x4735,x4736,x4732,x4737,x4738))
% 109.14/108.86 [474]~E(x4741,x4742)+E(f850(x4743,x4744,x4745,x4746,x4747,x4741,x4748),f850(x4743,x4744,x4745,x4746,x4747,x4742,x4748))
% 109.14/108.86 [475]~E(x4751,x4752)+E(f850(x4753,x4754,x4755,x4756,x4757,x4758,x4751),f850(x4753,x4754,x4755,x4756,x4757,x4758,x4752))
% 109.14/108.86 [476]~E(x4761,x4762)+E(f299(x4761),f299(x4762))
% 109.14/108.86 [477]~E(x4771,x4772)+E(f699(x4771,x4773,x4774),f699(x4772,x4773,x4774))
% 109.14/108.86 [478]~E(x4781,x4782)+E(f699(x4783,x4781,x4784),f699(x4783,x4782,x4784))
% 109.14/108.86 [479]~E(x4791,x4792)+E(f699(x4793,x4794,x4791),f699(x4793,x4794,x4792))
% 109.14/108.86 [480]~E(x4801,x4802)+E(f141(x4801,x4803,x4804,x4805),f141(x4802,x4803,x4804,x4805))
% 109.14/108.86 [481]~E(x4811,x4812)+E(f141(x4813,x4811,x4814,x4815),f141(x4813,x4812,x4814,x4815))
% 109.14/108.86 [482]~E(x4821,x4822)+E(f141(x4823,x4824,x4821,x4825),f141(x4823,x4824,x4822,x4825))
% 109.14/108.86 [483]~E(x4831,x4832)+E(f141(x4833,x4834,x4835,x4831),f141(x4833,x4834,x4835,x4832))
% 109.14/108.86 [484]~E(x4841,x4842)+E(f152(x4841,x4843),f152(x4842,x4843))
% 109.14/108.86 [485]~E(x4851,x4852)+E(f152(x4853,x4851),f152(x4853,x4852))
% 109.14/108.86 [486]~E(x4861,x4862)+E(f305(x4861),f305(x4862))
% 109.14/108.86 [487]~E(x4871,x4872)+E(f400(x4871,x4873,x4874),f400(x4872,x4873,x4874))
% 109.14/108.86 [488]~E(x4881,x4882)+E(f400(x4883,x4881,x4884),f400(x4883,x4882,x4884))
% 109.14/108.86 [489]~E(x4891,x4892)+E(f400(x4893,x4894,x4891),f400(x4893,x4894,x4892))
% 109.14/108.86 [490]~E(x4901,x4902)+E(f307(x4901,x4903),f307(x4902,x4903))
% 109.14/108.86 [491]~E(x4911,x4912)+E(f307(x4913,x4911),f307(x4913,x4912))
% 109.14/108.86 [492]~E(x4921,x4922)+E(f177(x4921),f177(x4922))
% 109.14/108.86 [493]~E(x4931,x4932)+E(f139(x4931,x4933,x4934),f139(x4932,x4933,x4934))
% 109.14/108.86 [494]~E(x4941,x4942)+E(f139(x4943,x4941,x4944),f139(x4943,x4942,x4944))
% 109.14/108.86 [495]~E(x4951,x4952)+E(f139(x4953,x4954,x4951),f139(x4953,x4954,x4952))
% 109.14/108.86 [496]~E(x4961,x4962)+E(f830(x4961,x4963,x4964,x4965,x4966),f830(x4962,x4963,x4964,x4965,x4966))
% 109.14/108.86 [497]~E(x4971,x4972)+E(f830(x4973,x4971,x4974,x4975,x4976),f830(x4973,x4972,x4974,x4975,x4976))
% 109.14/108.86 [498]~E(x4981,x4982)+E(f830(x4983,x4984,x4981,x4985,x4986),f830(x4983,x4984,x4982,x4985,x4986))
% 109.14/108.86 [499]~E(x4991,x4992)+E(f830(x4993,x4994,x4995,x4991,x4996),f830(x4993,x4994,x4995,x4992,x4996))
% 109.14/108.86 [500]~E(x5001,x5002)+E(f830(x5003,x5004,x5005,x5006,x5001),f830(x5003,x5004,x5005,x5006,x5002))
% 109.14/108.86 [501]~E(x5011,x5012)+E(f49(x5011,x5013,x5014),f49(x5012,x5013,x5014))
% 109.14/108.86 [502]~E(x5021,x5022)+E(f49(x5023,x5021,x5024),f49(x5023,x5022,x5024))
% 109.14/108.86 [503]~E(x5031,x5032)+E(f49(x5033,x5034,x5031),f49(x5033,x5034,x5032))
% 109.14/108.86 [504]~E(x5041,x5042)+E(f833(x5041,x5043,x5044),f833(x5042,x5043,x5044))
% 109.14/108.86 [505]~E(x5051,x5052)+E(f833(x5053,x5051,x5054),f833(x5053,x5052,x5054))
% 109.14/108.86 [506]~E(x5061,x5062)+E(f833(x5063,x5064,x5061),f833(x5063,x5064,x5062))
% 109.14/108.86 [507]~E(x5071,x5072)+E(f372(x5071,x5073,x5074),f372(x5072,x5073,x5074))
% 109.14/108.86 [508]~E(x5081,x5082)+E(f372(x5083,x5081,x5084),f372(x5083,x5082,x5084))
% 109.14/108.86 [509]~E(x5091,x5092)+E(f372(x5093,x5094,x5091),f372(x5093,x5094,x5092))
% 109.14/108.86 [510]~E(x5101,x5102)+E(f302(x5101,x5103,x5104),f302(x5102,x5103,x5104))
% 109.14/108.86 [511]~E(x5111,x5112)+E(f302(x5113,x5111,x5114),f302(x5113,x5112,x5114))
% 109.14/108.86 [512]~E(x5121,x5122)+E(f302(x5123,x5124,x5121),f302(x5123,x5124,x5122))
% 109.14/108.86 [513]~E(x5131,x5132)+E(f126(x5131),f126(x5132))
% 109.14/108.86 [514]~E(x5141,x5142)+E(f609(x5141,x5143,x5144),f609(x5142,x5143,x5144))
% 109.14/108.86 [515]~E(x5151,x5152)+E(f609(x5153,x5151,x5154),f609(x5153,x5152,x5154))
% 109.14/108.86 [516]~E(x5161,x5162)+E(f609(x5163,x5164,x5161),f609(x5163,x5164,x5162))
% 109.14/108.86 [517]~E(x5171,x5172)+E(f291(x5171,x5173,x5174,x5175,x5176),f291(x5172,x5173,x5174,x5175,x5176))
% 109.14/108.86 [518]~E(x5181,x5182)+E(f291(x5183,x5181,x5184,x5185,x5186),f291(x5183,x5182,x5184,x5185,x5186))
% 109.14/108.86 [519]~E(x5191,x5192)+E(f291(x5193,x5194,x5191,x5195,x5196),f291(x5193,x5194,x5192,x5195,x5196))
% 109.14/108.86 [520]~E(x5201,x5202)+E(f291(x5203,x5204,x5205,x5201,x5206),f291(x5203,x5204,x5205,x5202,x5206))
% 109.14/108.86 [521]~E(x5211,x5212)+E(f291(x5213,x5214,x5215,x5216,x5211),f291(x5213,x5214,x5215,x5216,x5212))
% 109.14/108.86 [522]~E(x5221,x5222)+E(f352(x5221,x5223,x5224,x5225),f352(x5222,x5223,x5224,x5225))
% 109.14/108.86 [523]~E(x5231,x5232)+E(f352(x5233,x5231,x5234,x5235),f352(x5233,x5232,x5234,x5235))
% 109.14/108.86 [524]~E(x5241,x5242)+E(f352(x5243,x5244,x5241,x5245),f352(x5243,x5244,x5242,x5245))
% 109.14/108.86 [525]~E(x5251,x5252)+E(f352(x5253,x5254,x5255,x5251),f352(x5253,x5254,x5255,x5252))
% 109.14/108.86 [526]~E(x5261,x5262)+E(f274(x5261),f274(x5262))
% 109.14/108.86 [527]~E(x5271,x5272)+E(f44(x5271,x5273),f44(x5272,x5273))
% 109.14/108.86 [528]~E(x5281,x5282)+E(f44(x5283,x5281),f44(x5283,x5282))
% 109.14/108.86 [529]~E(x5291,x5292)+E(f425(x5291,x5293,x5294,x5295),f425(x5292,x5293,x5294,x5295))
% 109.14/108.86 [530]~E(x5301,x5302)+E(f425(x5303,x5301,x5304,x5305),f425(x5303,x5302,x5304,x5305))
% 109.14/108.86 [531]~E(x5311,x5312)+E(f425(x5313,x5314,x5311,x5315),f425(x5313,x5314,x5312,x5315))
% 109.14/108.86 [532]~E(x5321,x5322)+E(f425(x5323,x5324,x5325,x5321),f425(x5323,x5324,x5325,x5322))
% 109.14/108.86 [533]~E(x5331,x5332)+E(f638(x5331,x5333,x5334,x5335),f638(x5332,x5333,x5334,x5335))
% 109.14/108.86 [534]~E(x5341,x5342)+E(f638(x5343,x5341,x5344,x5345),f638(x5343,x5342,x5344,x5345))
% 109.14/108.86 [535]~E(x5351,x5352)+E(f638(x5353,x5354,x5351,x5355),f638(x5353,x5354,x5352,x5355))
% 109.14/108.86 [536]~E(x5361,x5362)+E(f638(x5363,x5364,x5365,x5361),f638(x5363,x5364,x5365,x5362))
% 109.14/108.86 [537]~E(x5371,x5372)+E(f831(x5371,x5373,x5374,x5375,x5376,x5377),f831(x5372,x5373,x5374,x5375,x5376,x5377))
% 109.14/108.86 [538]~E(x5381,x5382)+E(f831(x5383,x5381,x5384,x5385,x5386,x5387),f831(x5383,x5382,x5384,x5385,x5386,x5387))
% 109.14/108.86 [539]~E(x5391,x5392)+E(f831(x5393,x5394,x5391,x5395,x5396,x5397),f831(x5393,x5394,x5392,x5395,x5396,x5397))
% 109.14/108.86 [540]~E(x5401,x5402)+E(f831(x5403,x5404,x5405,x5401,x5406,x5407),f831(x5403,x5404,x5405,x5402,x5406,x5407))
% 109.14/108.86 [541]~E(x5411,x5412)+E(f831(x5413,x5414,x5415,x5416,x5411,x5417),f831(x5413,x5414,x5415,x5416,x5412,x5417))
% 109.14/108.86 [542]~E(x5421,x5422)+E(f831(x5423,x5424,x5425,x5426,x5427,x5421),f831(x5423,x5424,x5425,x5426,x5427,x5422))
% 109.14/108.86 [543]~E(x5431,x5432)+E(f585(x5431,x5433,x5434),f585(x5432,x5433,x5434))
% 109.14/108.86 [544]~E(x5441,x5442)+E(f585(x5443,x5441,x5444),f585(x5443,x5442,x5444))
% 109.14/108.86 [545]~E(x5451,x5452)+E(f585(x5453,x5454,x5451),f585(x5453,x5454,x5452))
% 109.14/108.86 [546]~E(x5461,x5462)+E(f297(x5461,x5463,x5464),f297(x5462,x5463,x5464))
% 109.14/108.86 [547]~E(x5471,x5472)+E(f297(x5473,x5471,x5474),f297(x5473,x5472,x5474))
% 109.14/108.86 [548]~E(x5481,x5482)+E(f297(x5483,x5484,x5481),f297(x5483,x5484,x5482))
% 109.14/108.86 [549]~E(x5491,x5492)+E(f246(x5491,x5493,x5494,x5495),f246(x5492,x5493,x5494,x5495))
% 109.14/108.86 [550]~E(x5501,x5502)+E(f246(x5503,x5501,x5504,x5505),f246(x5503,x5502,x5504,x5505))
% 109.14/108.86 [551]~E(x5511,x5512)+E(f246(x5513,x5514,x5511,x5515),f246(x5513,x5514,x5512,x5515))
% 109.14/108.86 [552]~E(x5521,x5522)+E(f246(x5523,x5524,x5525,x5521),f246(x5523,x5524,x5525,x5522))
% 109.14/108.86 [553]~E(x5531,x5532)+E(f57(x5531,x5533),f57(x5532,x5533))
% 109.14/108.86 [554]~E(x5541,x5542)+E(f57(x5543,x5541),f57(x5543,x5542))
% 109.14/108.86 [555]~E(x5551,x5552)+E(f272(x5551),f272(x5552))
% 109.14/108.86 [556]~E(x5561,x5562)+E(f59(x5561,x5563,x5564),f59(x5562,x5563,x5564))
% 109.14/108.86 [557]~E(x5571,x5572)+E(f59(x5573,x5571,x5574),f59(x5573,x5572,x5574))
% 109.14/108.86 [558]~E(x5581,x5582)+E(f59(x5583,x5584,x5581),f59(x5583,x5584,x5582))
% 109.14/108.86 [559]~E(x5591,x5592)+E(f863(x5591,x5593),f863(x5592,x5593))
% 109.14/108.86 [560]~E(x5601,x5602)+E(f863(x5603,x5601),f863(x5603,x5602))
% 109.14/108.86 [561]~E(x5611,x5612)+E(f362(x5611,x5613,x5614),f362(x5612,x5613,x5614))
% 109.14/108.86 [562]~E(x5621,x5622)+E(f362(x5623,x5621,x5624),f362(x5623,x5622,x5624))
% 109.14/108.86 [563]~E(x5631,x5632)+E(f362(x5633,x5634,x5631),f362(x5633,x5634,x5632))
% 109.14/108.86 [564]~E(x5641,x5642)+E(f140(x5641,x5643,x5644,x5645,x5646),f140(x5642,x5643,x5644,x5645,x5646))
% 109.14/108.86 [565]~E(x5651,x5652)+E(f140(x5653,x5651,x5654,x5655,x5656),f140(x5653,x5652,x5654,x5655,x5656))
% 109.14/108.86 [566]~E(x5661,x5662)+E(f140(x5663,x5664,x5661,x5665,x5666),f140(x5663,x5664,x5662,x5665,x5666))
% 109.14/108.86 [567]~E(x5671,x5672)+E(f140(x5673,x5674,x5675,x5671,x5676),f140(x5673,x5674,x5675,x5672,x5676))
% 109.14/108.86 [568]~E(x5681,x5682)+E(f140(x5683,x5684,x5685,x5686,x5681),f140(x5683,x5684,x5685,x5686,x5682))
% 109.14/108.86 [569]~E(x5691,x5692)+E(f116(x5691,x5693),f116(x5692,x5693))
% 109.14/108.86 [570]~E(x5701,x5702)+E(f116(x5703,x5701),f116(x5703,x5702))
% 109.14/108.86 [571]~E(x5711,x5712)+E(f279(x5711,x5713),f279(x5712,x5713))
% 109.14/108.86 [572]~E(x5721,x5722)+E(f279(x5723,x5721),f279(x5723,x5722))
% 109.14/108.86 [573]~E(x5731,x5732)+E(f167(x5731,x5733,x5734),f167(x5732,x5733,x5734))
% 109.14/108.86 [574]~E(x5741,x5742)+E(f167(x5743,x5741,x5744),f167(x5743,x5742,x5744))
% 109.14/108.86 [575]~E(x5751,x5752)+E(f167(x5753,x5754,x5751),f167(x5753,x5754,x5752))
% 109.14/108.86 [576]~E(x5761,x5762)+E(f276(x5761,x5763,x5764),f276(x5762,x5763,x5764))
% 109.14/108.86 [577]~E(x5771,x5772)+E(f276(x5773,x5771,x5774),f276(x5773,x5772,x5774))
% 109.14/108.86 [578]~E(x5781,x5782)+E(f276(x5783,x5784,x5781),f276(x5783,x5784,x5782))
% 109.14/108.86 [579]~E(x5791,x5792)+E(f378(x5791,x5793),f378(x5792,x5793))
% 109.14/108.86 [580]~E(x5801,x5802)+E(f378(x5803,x5801),f378(x5803,x5802))
% 109.14/108.86 [581]~E(x5811,x5812)+E(f484(x5811,x5813,x5814,x5815,x5816,x5817,x5818),f484(x5812,x5813,x5814,x5815,x5816,x5817,x5818))
% 109.14/108.86 [582]~E(x5821,x5822)+E(f484(x5823,x5821,x5824,x5825,x5826,x5827,x5828),f484(x5823,x5822,x5824,x5825,x5826,x5827,x5828))
% 109.14/108.86 [583]~E(x5831,x5832)+E(f484(x5833,x5834,x5831,x5835,x5836,x5837,x5838),f484(x5833,x5834,x5832,x5835,x5836,x5837,x5838))
% 109.14/108.86 [584]~E(x5841,x5842)+E(f484(x5843,x5844,x5845,x5841,x5846,x5847,x5848),f484(x5843,x5844,x5845,x5842,x5846,x5847,x5848))
% 109.14/108.86 [585]~E(x5851,x5852)+E(f484(x5853,x5854,x5855,x5856,x5851,x5857,x5858),f484(x5853,x5854,x5855,x5856,x5852,x5857,x5858))
% 109.14/108.86 [586]~E(x5861,x5862)+E(f484(x5863,x5864,x5865,x5866,x5867,x5861,x5868),f484(x5863,x5864,x5865,x5866,x5867,x5862,x5868))
% 109.14/108.86 [587]~E(x5871,x5872)+E(f484(x5873,x5874,x5875,x5876,x5877,x5878,x5871),f484(x5873,x5874,x5875,x5876,x5877,x5878,x5872))
% 109.14/108.86 [588]~E(x5881,x5882)+E(f70(x5881,x5883,x5884,x5885),f70(x5882,x5883,x5884,x5885))
% 109.14/108.86 [589]~E(x5891,x5892)+E(f70(x5893,x5891,x5894,x5895),f70(x5893,x5892,x5894,x5895))
% 109.14/108.86 [590]~E(x5901,x5902)+E(f70(x5903,x5904,x5901,x5905),f70(x5903,x5904,x5902,x5905))
% 109.14/108.86 [591]~E(x5911,x5912)+E(f70(x5913,x5914,x5915,x5911),f70(x5913,x5914,x5915,x5912))
% 109.14/108.86 [592]~E(x5921,x5922)+E(f43(x5921,x5923),f43(x5922,x5923))
% 109.14/108.86 [593]~E(x5931,x5932)+E(f43(x5933,x5931),f43(x5933,x5932))
% 109.14/108.86 [594]~E(x5941,x5942)+E(f885(x5941,x5943),f885(x5942,x5943))
% 109.14/108.86 [595]~E(x5951,x5952)+E(f885(x5953,x5951),f885(x5953,x5952))
% 109.14/108.86 [596]~E(x5961,x5962)+E(f285(x5961,x5963,x5964),f285(x5962,x5963,x5964))
% 109.14/108.86 [597]~E(x5971,x5972)+E(f285(x5973,x5971,x5974),f285(x5973,x5972,x5974))
% 109.14/108.86 [598]~E(x5981,x5982)+E(f285(x5983,x5984,x5981),f285(x5983,x5984,x5982))
% 109.14/108.86 [599]~E(x5991,x5992)+E(f118(x5991,x5993,x5994,x5995,x5996),f118(x5992,x5993,x5994,x5995,x5996))
% 109.14/108.86 [600]~E(x6001,x6002)+E(f118(x6003,x6001,x6004,x6005,x6006),f118(x6003,x6002,x6004,x6005,x6006))
% 109.14/108.86 [601]~E(x6011,x6012)+E(f118(x6013,x6014,x6011,x6015,x6016),f118(x6013,x6014,x6012,x6015,x6016))
% 109.14/108.86 [602]~E(x6021,x6022)+E(f118(x6023,x6024,x6025,x6021,x6026),f118(x6023,x6024,x6025,x6022,x6026))
% 109.14/108.86 [603]~E(x6031,x6032)+E(f118(x6033,x6034,x6035,x6036,x6031),f118(x6033,x6034,x6035,x6036,x6032))
% 109.14/108.86 [604]~E(x6041,x6042)+E(f856(x6041,x6043,x6044),f856(x6042,x6043,x6044))
% 109.14/108.86 [605]~E(x6051,x6052)+E(f856(x6053,x6051,x6054),f856(x6053,x6052,x6054))
% 109.14/108.86 [606]~E(x6061,x6062)+E(f856(x6063,x6064,x6061),f856(x6063,x6064,x6062))
% 109.14/108.86 [607]~E(x6071,x6072)+E(f213(x6071,x6073,x6074),f213(x6072,x6073,x6074))
% 109.14/108.86 [608]~E(x6081,x6082)+E(f213(x6083,x6081,x6084),f213(x6083,x6082,x6084))
% 109.14/108.86 [609]~E(x6091,x6092)+E(f213(x6093,x6094,x6091),f213(x6093,x6094,x6092))
% 109.14/108.86 [610]~E(x6101,x6102)+E(f720(x6101,x6103),f720(x6102,x6103))
% 109.14/108.86 [611]~E(x6111,x6112)+E(f720(x6113,x6111),f720(x6113,x6112))
% 109.14/108.86 [612]~E(x6121,x6122)+E(f135(x6121,x6123),f135(x6122,x6123))
% 109.14/108.86 [613]~E(x6131,x6132)+E(f135(x6133,x6131),f135(x6133,x6132))
% 109.14/108.86 [614]~E(x6141,x6142)+E(f60(x6141,x6143,x6144,x6145,x6146),f60(x6142,x6143,x6144,x6145,x6146))
% 109.14/108.86 [615]~E(x6151,x6152)+E(f60(x6153,x6151,x6154,x6155,x6156),f60(x6153,x6152,x6154,x6155,x6156))
% 109.14/108.86 [616]~E(x6161,x6162)+E(f60(x6163,x6164,x6161,x6165,x6166),f60(x6163,x6164,x6162,x6165,x6166))
% 109.14/108.86 [617]~E(x6171,x6172)+E(f60(x6173,x6174,x6175,x6171,x6176),f60(x6173,x6174,x6175,x6172,x6176))
% 109.14/108.86 [618]~E(x6181,x6182)+E(f60(x6183,x6184,x6185,x6186,x6181),f60(x6183,x6184,x6185,x6186,x6182))
% 109.14/108.86 [619]~E(x6191,x6192)+E(f385(x6191,x6193,x6194),f385(x6192,x6193,x6194))
% 109.14/108.86 [620]~E(x6201,x6202)+E(f385(x6203,x6201,x6204),f385(x6203,x6202,x6204))
% 109.14/108.86 [621]~E(x6211,x6212)+E(f385(x6213,x6214,x6211),f385(x6213,x6214,x6212))
% 109.14/108.86 [622]~E(x6221,x6222)+E(f820(x6221,x6223,x6224,x6225),f820(x6222,x6223,x6224,x6225))
% 109.14/108.86 [623]~E(x6231,x6232)+E(f820(x6233,x6231,x6234,x6235),f820(x6233,x6232,x6234,x6235))
% 109.14/108.86 [624]~E(x6241,x6242)+E(f820(x6243,x6244,x6241,x6245),f820(x6243,x6244,x6242,x6245))
% 109.14/108.86 [625]~E(x6251,x6252)+E(f820(x6253,x6254,x6255,x6251),f820(x6253,x6254,x6255,x6252))
% 109.14/108.86 [626]~E(x6261,x6262)+E(f477(x6261,x6263,x6264,x6265,x6266),f477(x6262,x6263,x6264,x6265,x6266))
% 109.14/108.86 [627]~E(x6271,x6272)+E(f477(x6273,x6271,x6274,x6275,x6276),f477(x6273,x6272,x6274,x6275,x6276))
% 109.14/108.86 [628]~E(x6281,x6282)+E(f477(x6283,x6284,x6281,x6285,x6286),f477(x6283,x6284,x6282,x6285,x6286))
% 109.14/108.86 [629]~E(x6291,x6292)+E(f477(x6293,x6294,x6295,x6291,x6296),f477(x6293,x6294,x6295,x6292,x6296))
% 109.14/108.86 [630]~E(x6301,x6302)+E(f477(x6303,x6304,x6305,x6306,x6301),f477(x6303,x6304,x6305,x6306,x6302))
% 109.14/108.86 [631]~E(x6311,x6312)+E(f586(x6311,x6313,x6314,x6315,x6316,x6317),f586(x6312,x6313,x6314,x6315,x6316,x6317))
% 109.14/108.86 [632]~E(x6321,x6322)+E(f586(x6323,x6321,x6324,x6325,x6326,x6327),f586(x6323,x6322,x6324,x6325,x6326,x6327))
% 109.14/108.86 [633]~E(x6331,x6332)+E(f586(x6333,x6334,x6331,x6335,x6336,x6337),f586(x6333,x6334,x6332,x6335,x6336,x6337))
% 109.14/108.86 [634]~E(x6341,x6342)+E(f586(x6343,x6344,x6345,x6341,x6346,x6347),f586(x6343,x6344,x6345,x6342,x6346,x6347))
% 109.14/108.86 [635]~E(x6351,x6352)+E(f586(x6353,x6354,x6355,x6356,x6351,x6357),f586(x6353,x6354,x6355,x6356,x6352,x6357))
% 109.14/108.86 [636]~E(x6361,x6362)+E(f586(x6363,x6364,x6365,x6366,x6367,x6361),f586(x6363,x6364,x6365,x6366,x6367,x6362))
% 109.14/108.86 [637]~E(x6371,x6372)+E(f621(x6371,x6373,x6374,x6375,x6376),f621(x6372,x6373,x6374,x6375,x6376))
% 109.14/108.86 [638]~E(x6381,x6382)+E(f621(x6383,x6381,x6384,x6385,x6386),f621(x6383,x6382,x6384,x6385,x6386))
% 109.14/108.86 [639]~E(x6391,x6392)+E(f621(x6393,x6394,x6391,x6395,x6396),f621(x6393,x6394,x6392,x6395,x6396))
% 109.14/108.86 [640]~E(x6401,x6402)+E(f621(x6403,x6404,x6405,x6401,x6406),f621(x6403,x6404,x6405,x6402,x6406))
% 109.14/108.86 [641]~E(x6411,x6412)+E(f621(x6413,x6414,x6415,x6416,x6411),f621(x6413,x6414,x6415,x6416,x6412))
% 109.14/108.86 [642]~E(x6421,x6422)+E(f292(x6421),f292(x6422))
% 109.14/108.86 [643]~E(x6431,x6432)+E(f651(x6431,x6433,x6434,x6435,x6436),f651(x6432,x6433,x6434,x6435,x6436))
% 109.14/108.86 [644]~E(x6441,x6442)+E(f651(x6443,x6441,x6444,x6445,x6446),f651(x6443,x6442,x6444,x6445,x6446))
% 109.14/108.86 [645]~E(x6451,x6452)+E(f651(x6453,x6454,x6451,x6455,x6456),f651(x6453,x6454,x6452,x6455,x6456))
% 109.14/108.86 [646]~E(x6461,x6462)+E(f651(x6463,x6464,x6465,x6461,x6466),f651(x6463,x6464,x6465,x6462,x6466))
% 109.14/108.86 [647]~E(x6471,x6472)+E(f651(x6473,x6474,x6475,x6476,x6471),f651(x6473,x6474,x6475,x6476,x6472))
% 109.14/108.86 [648]~E(x6481,x6482)+E(f809(x6481,x6483,x6484,x6485,x6486,x6487),f809(x6482,x6483,x6484,x6485,x6486,x6487))
% 109.14/108.86 [649]~E(x6491,x6492)+E(f809(x6493,x6491,x6494,x6495,x6496,x6497),f809(x6493,x6492,x6494,x6495,x6496,x6497))
% 109.14/108.86 [650]~E(x6501,x6502)+E(f809(x6503,x6504,x6501,x6505,x6506,x6507),f809(x6503,x6504,x6502,x6505,x6506,x6507))
% 109.14/108.86 [651]~E(x6511,x6512)+E(f809(x6513,x6514,x6515,x6511,x6516,x6517),f809(x6513,x6514,x6515,x6512,x6516,x6517))
% 109.14/108.86 [652]~E(x6521,x6522)+E(f809(x6523,x6524,x6525,x6526,x6521,x6527),f809(x6523,x6524,x6525,x6526,x6522,x6527))
% 109.14/108.86 [653]~E(x6531,x6532)+E(f809(x6533,x6534,x6535,x6536,x6537,x6531),f809(x6533,x6534,x6535,x6536,x6537,x6532))
% 109.14/108.86 [654]~E(x6541,x6542)+E(f705(x6541,x6543),f705(x6542,x6543))
% 109.14/108.86 [655]~E(x6551,x6552)+E(f705(x6553,x6551),f705(x6553,x6552))
% 109.14/108.86 [656]~E(x6561,x6562)+E(f148(x6561,x6563),f148(x6562,x6563))
% 109.14/108.86 [657]~E(x6571,x6572)+E(f148(x6573,x6571),f148(x6573,x6572))
% 109.14/108.86 [658]~E(x6581,x6582)+E(f620(x6581,x6583,x6584,x6585,x6586),f620(x6582,x6583,x6584,x6585,x6586))
% 109.14/108.86 [659]~E(x6591,x6592)+E(f620(x6593,x6591,x6594,x6595,x6596),f620(x6593,x6592,x6594,x6595,x6596))
% 109.14/108.86 [660]~E(x6601,x6602)+E(f620(x6603,x6604,x6601,x6605,x6606),f620(x6603,x6604,x6602,x6605,x6606))
% 109.14/108.86 [661]~E(x6611,x6612)+E(f620(x6613,x6614,x6615,x6611,x6616),f620(x6613,x6614,x6615,x6612,x6616))
% 109.14/108.86 [662]~E(x6621,x6622)+E(f620(x6623,x6624,x6625,x6626,x6621),f620(x6623,x6624,x6625,x6626,x6622))
% 109.14/108.86 [663]~E(x6631,x6632)+E(f589(x6631,x6633,x6634,x6635,x6636,x6637),f589(x6632,x6633,x6634,x6635,x6636,x6637))
% 109.14/108.86 [664]~E(x6641,x6642)+E(f589(x6643,x6641,x6644,x6645,x6646,x6647),f589(x6643,x6642,x6644,x6645,x6646,x6647))
% 109.14/108.86 [665]~E(x6651,x6652)+E(f589(x6653,x6654,x6651,x6655,x6656,x6657),f589(x6653,x6654,x6652,x6655,x6656,x6657))
% 109.14/108.86 [666]~E(x6661,x6662)+E(f589(x6663,x6664,x6665,x6661,x6666,x6667),f589(x6663,x6664,x6665,x6662,x6666,x6667))
% 109.14/108.86 [667]~E(x6671,x6672)+E(f589(x6673,x6674,x6675,x6676,x6671,x6677),f589(x6673,x6674,x6675,x6676,x6672,x6677))
% 109.14/108.86 [668]~E(x6681,x6682)+E(f589(x6683,x6684,x6685,x6686,x6687,x6681),f589(x6683,x6684,x6685,x6686,x6687,x6682))
% 109.14/108.86 [669]~E(x6691,x6692)+E(f214(x6691,x6693,x6694,x6695,x6696),f214(x6692,x6693,x6694,x6695,x6696))
% 109.14/108.86 [670]~E(x6701,x6702)+E(f214(x6703,x6701,x6704,x6705,x6706),f214(x6703,x6702,x6704,x6705,x6706))
% 109.14/108.86 [671]~E(x6711,x6712)+E(f214(x6713,x6714,x6711,x6715,x6716),f214(x6713,x6714,x6712,x6715,x6716))
% 109.14/108.86 [672]~E(x6721,x6722)+E(f214(x6723,x6724,x6725,x6721,x6726),f214(x6723,x6724,x6725,x6722,x6726))
% 109.14/108.86 [673]~E(x6731,x6732)+E(f214(x6733,x6734,x6735,x6736,x6731),f214(x6733,x6734,x6735,x6736,x6732))
% 109.14/108.86 [674]~E(x6741,x6742)+E(f679(x6741,x6743,x6744),f679(x6742,x6743,x6744))
% 109.14/108.86 [675]~E(x6751,x6752)+E(f679(x6753,x6751,x6754),f679(x6753,x6752,x6754))
% 109.14/108.86 [676]~E(x6761,x6762)+E(f679(x6763,x6764,x6761),f679(x6763,x6764,x6762))
% 109.14/108.86 [677]~E(x6771,x6772)+E(f172(x6771,x6773),f172(x6772,x6773))
% 109.14/108.86 [678]~E(x6781,x6782)+E(f172(x6783,x6781),f172(x6783,x6782))
% 109.14/108.86 [679]~E(x6791,x6792)+E(f775(x6791,x6793,x6794,x6795),f775(x6792,x6793,x6794,x6795))
% 109.14/108.86 [680]~E(x6801,x6802)+E(f775(x6803,x6801,x6804,x6805),f775(x6803,x6802,x6804,x6805))
% 109.14/108.86 [681]~E(x6811,x6812)+E(f775(x6813,x6814,x6811,x6815),f775(x6813,x6814,x6812,x6815))
% 109.14/108.86 [682]~E(x6821,x6822)+E(f775(x6823,x6824,x6825,x6821),f775(x6823,x6824,x6825,x6822))
% 109.14/108.86 [683]~E(x6831,x6832)+E(f480(x6831,x6833,x6834,x6835,x6836),f480(x6832,x6833,x6834,x6835,x6836))
% 109.14/108.86 [684]~E(x6841,x6842)+E(f480(x6843,x6841,x6844,x6845,x6846),f480(x6843,x6842,x6844,x6845,x6846))
% 109.14/108.86 [685]~E(x6851,x6852)+E(f480(x6853,x6854,x6851,x6855,x6856),f480(x6853,x6854,x6852,x6855,x6856))
% 109.14/108.86 [686]~E(x6861,x6862)+E(f480(x6863,x6864,x6865,x6861,x6866),f480(x6863,x6864,x6865,x6862,x6866))
% 109.14/108.86 [687]~E(x6871,x6872)+E(f480(x6873,x6874,x6875,x6876,x6871),f480(x6873,x6874,x6875,x6876,x6872))
% 109.14/108.86 [688]~E(x6881,x6882)+E(f808(x6881,x6883,x6884,x6885,x6886,x6887),f808(x6882,x6883,x6884,x6885,x6886,x6887))
% 109.14/108.86 [689]~E(x6891,x6892)+E(f808(x6893,x6891,x6894,x6895,x6896,x6897),f808(x6893,x6892,x6894,x6895,x6896,x6897))
% 109.14/108.86 [690]~E(x6901,x6902)+E(f808(x6903,x6904,x6901,x6905,x6906,x6907),f808(x6903,x6904,x6902,x6905,x6906,x6907))
% 109.14/108.86 [691]~E(x6911,x6912)+E(f808(x6913,x6914,x6915,x6911,x6916,x6917),f808(x6913,x6914,x6915,x6912,x6916,x6917))
% 109.14/108.86 [692]~E(x6921,x6922)+E(f808(x6923,x6924,x6925,x6926,x6921,x6927),f808(x6923,x6924,x6925,x6926,x6922,x6927))
% 109.14/108.86 [693]~E(x6931,x6932)+E(f808(x6933,x6934,x6935,x6936,x6937,x6931),f808(x6933,x6934,x6935,x6936,x6937,x6932))
% 109.14/108.86 [694]~E(x6941,x6942)+E(f263(x6941,x6943),f263(x6942,x6943))
% 109.14/108.86 [695]~E(x6951,x6952)+E(f263(x6953,x6951),f263(x6953,x6952))
% 109.14/108.86 [696]~E(x6961,x6962)+E(f238(x6961,x6963,x6964),f238(x6962,x6963,x6964))
% 109.14/108.86 [697]~E(x6971,x6972)+E(f238(x6973,x6971,x6974),f238(x6973,x6972,x6974))
% 109.14/108.86 [698]~E(x6981,x6982)+E(f238(x6983,x6984,x6981),f238(x6983,x6984,x6982))
% 109.14/108.86 [699]~E(x6991,x6992)+E(f157(x6991,x6993,x6994),f157(x6992,x6993,x6994))
% 109.14/108.86 [700]~E(x7001,x7002)+E(f157(x7003,x7001,x7004),f157(x7003,x7002,x7004))
% 109.14/108.86 [701]~E(x7011,x7012)+E(f157(x7013,x7014,x7011),f157(x7013,x7014,x7012))
% 109.14/108.86 [702]~E(x7021,x7022)+E(f482(x7021,x7023,x7024,x7025,x7026),f482(x7022,x7023,x7024,x7025,x7026))
% 109.14/108.86 [703]~E(x7031,x7032)+E(f482(x7033,x7031,x7034,x7035,x7036),f482(x7033,x7032,x7034,x7035,x7036))
% 109.14/108.86 [704]~E(x7041,x7042)+E(f482(x7043,x7044,x7041,x7045,x7046),f482(x7043,x7044,x7042,x7045,x7046))
% 109.14/108.86 [705]~E(x7051,x7052)+E(f482(x7053,x7054,x7055,x7051,x7056),f482(x7053,x7054,x7055,x7052,x7056))
% 109.14/108.86 [706]~E(x7061,x7062)+E(f482(x7063,x7064,x7065,x7066,x7061),f482(x7063,x7064,x7065,x7066,x7062))
% 109.14/108.86 [707]~E(x7071,x7072)+E(f842(x7071,x7073,x7074,x7075,x7076,x7077,x7078,x7079),f842(x7072,x7073,x7074,x7075,x7076,x7077,x7078,x7079))
% 109.14/108.86 [708]~E(x7081,x7082)+E(f842(x7083,x7081,x7084,x7085,x7086,x7087,x7088,x7089),f842(x7083,x7082,x7084,x7085,x7086,x7087,x7088,x7089))
% 109.14/108.86 [709]~E(x7091,x7092)+E(f842(x7093,x7094,x7091,x7095,x7096,x7097,x7098,x7099),f842(x7093,x7094,x7092,x7095,x7096,x7097,x7098,x7099))
% 109.14/108.86 [710]~E(x7101,x7102)+E(f842(x7103,x7104,x7105,x7101,x7106,x7107,x7108,x7109),f842(x7103,x7104,x7105,x7102,x7106,x7107,x7108,x7109))
% 109.14/108.86 [711]~E(x7111,x7112)+E(f842(x7113,x7114,x7115,x7116,x7111,x7117,x7118,x7119),f842(x7113,x7114,x7115,x7116,x7112,x7117,x7118,x7119))
% 109.14/108.86 [712]~E(x7121,x7122)+E(f842(x7123,x7124,x7125,x7126,x7127,x7121,x7128,x7129),f842(x7123,x7124,x7125,x7126,x7127,x7122,x7128,x7129))
% 109.14/108.86 [713]~E(x7131,x7132)+E(f842(x7133,x7134,x7135,x7136,x7137,x7138,x7131,x7139),f842(x7133,x7134,x7135,x7136,x7137,x7138,x7132,x7139))
% 109.14/108.86 [714]~E(x7141,x7142)+E(f842(x7143,x7144,x7145,x7146,x7147,x7148,x7149,x7141),f842(x7143,x7144,x7145,x7146,x7147,x7148,x7149,x7142))
% 109.14/108.86 [715]~E(x7151,x7152)+E(f473(x7151,x7153,x7154,x7155,x7156),f473(x7152,x7153,x7154,x7155,x7156))
% 109.14/108.86 [716]~E(x7161,x7162)+E(f473(x7163,x7161,x7164,x7165,x7166),f473(x7163,x7162,x7164,x7165,x7166))
% 109.14/108.86 [717]~E(x7171,x7172)+E(f473(x7173,x7174,x7171,x7175,x7176),f473(x7173,x7174,x7172,x7175,x7176))
% 109.14/108.86 [718]~E(x7181,x7182)+E(f473(x7183,x7184,x7185,x7181,x7186),f473(x7183,x7184,x7185,x7182,x7186))
% 109.14/108.86 [719]~E(x7191,x7192)+E(f473(x7193,x7194,x7195,x7196,x7191),f473(x7193,x7194,x7195,x7196,x7192))
% 109.14/108.86 [720]~E(x7201,x7202)+E(f747(x7201,x7203,x7204),f747(x7202,x7203,x7204))
% 109.14/108.86 [721]~E(x7211,x7212)+E(f747(x7213,x7211,x7214),f747(x7213,x7212,x7214))
% 109.14/108.86 [722]~E(x7221,x7222)+E(f747(x7223,x7224,x7221),f747(x7223,x7224,x7222))
% 109.14/108.86 [723]~E(x7231,x7232)+E(f423(x7231,x7233,x7234),f423(x7232,x7233,x7234))
% 109.14/108.86 [724]~E(x7241,x7242)+E(f423(x7243,x7241,x7244),f423(x7243,x7242,x7244))
% 109.14/108.86 [725]~E(x7251,x7252)+E(f423(x7253,x7254,x7251),f423(x7253,x7254,x7252))
% 109.14/108.86 [726]~E(x7261,x7262)+E(f824(x7261,x7263,x7264,x7265,x7266),f824(x7262,x7263,x7264,x7265,x7266))
% 109.14/108.86 [727]~E(x7271,x7272)+E(f824(x7273,x7271,x7274,x7275,x7276),f824(x7273,x7272,x7274,x7275,x7276))
% 109.14/108.86 [728]~E(x7281,x7282)+E(f824(x7283,x7284,x7281,x7285,x7286),f824(x7283,x7284,x7282,x7285,x7286))
% 109.14/108.86 [729]~E(x7291,x7292)+E(f824(x7293,x7294,x7295,x7291,x7296),f824(x7293,x7294,x7295,x7292,x7296))
% 109.14/108.86 [730]~E(x7301,x7302)+E(f824(x7303,x7304,x7305,x7306,x7301),f824(x7303,x7304,x7305,x7306,x7302))
% 109.14/108.86 [731]~E(x7311,x7312)+E(f765(x7311,x7313,x7314,x7315),f765(x7312,x7313,x7314,x7315))
% 109.14/108.86 [732]~E(x7321,x7322)+E(f765(x7323,x7321,x7324,x7325),f765(x7323,x7322,x7324,x7325))
% 109.14/108.86 [733]~E(x7331,x7332)+E(f765(x7333,x7334,x7331,x7335),f765(x7333,x7334,x7332,x7335))
% 109.14/108.86 [734]~E(x7341,x7342)+E(f765(x7343,x7344,x7345,x7341),f765(x7343,x7344,x7345,x7342))
% 109.14/108.86 [735]~E(x7351,x7352)+E(f500(x7351,x7353,x7354),f500(x7352,x7353,x7354))
% 109.14/108.86 [736]~E(x7361,x7362)+E(f500(x7363,x7361,x7364),f500(x7363,x7362,x7364))
% 109.14/108.86 [737]~E(x7371,x7372)+E(f500(x7373,x7374,x7371),f500(x7373,x7374,x7372))
% 109.14/108.86 [738]~E(x7381,x7382)+E(f670(x7381,x7383,x7384,x7385),f670(x7382,x7383,x7384,x7385))
% 109.14/108.86 [739]~E(x7391,x7392)+E(f670(x7393,x7391,x7394,x7395),f670(x7393,x7392,x7394,x7395))
% 109.14/108.86 [740]~E(x7401,x7402)+E(f670(x7403,x7404,x7401,x7405),f670(x7403,x7404,x7402,x7405))
% 109.14/108.86 [741]~E(x7411,x7412)+E(f670(x7413,x7414,x7415,x7411),f670(x7413,x7414,x7415,x7412))
% 109.14/108.86 [742]~E(x7421,x7422)+E(f108(x7421,x7423,x7424),f108(x7422,x7423,x7424))
% 109.14/108.86 [743]~E(x7431,x7432)+E(f108(x7433,x7431,x7434),f108(x7433,x7432,x7434))
% 109.14/108.86 [744]~E(x7441,x7442)+E(f108(x7443,x7444,x7441),f108(x7443,x7444,x7442))
% 109.14/108.86 [745]~E(x7451,x7452)+E(f42(x7451,x7453),f42(x7452,x7453))
% 109.14/108.86 [746]~E(x7461,x7462)+E(f42(x7463,x7461),f42(x7463,x7462))
% 109.14/108.86 [747]~E(x7471,x7472)+E(f576(x7471),f576(x7472))
% 109.14/108.86 [748]~E(x7481,x7482)+E(f759(x7481,x7483,x7484),f759(x7482,x7483,x7484))
% 109.14/108.86 [749]~E(x7491,x7492)+E(f759(x7493,x7491,x7494),f759(x7493,x7492,x7494))
% 109.14/108.86 [750]~E(x7501,x7502)+E(f759(x7503,x7504,x7501),f759(x7503,x7504,x7502))
% 109.14/108.86 [751]~E(x7511,x7512)+E(f702(x7511,x7513),f702(x7512,x7513))
% 109.14/108.86 [752]~E(x7521,x7522)+E(f702(x7523,x7521),f702(x7523,x7522))
% 109.14/108.86 [753]~E(x7531,x7532)+E(f203(x7531),f203(x7532))
% 109.14/108.86 [754]~E(x7541,x7542)+E(f136(x7541,x7543),f136(x7542,x7543))
% 109.14/108.86 [755]~E(x7551,x7552)+E(f136(x7553,x7551),f136(x7553,x7552))
% 109.14/108.86 [756]~E(x7561,x7562)+E(f659(x7561,x7563,x7564),f659(x7562,x7563,x7564))
% 109.14/108.86 [757]~E(x7571,x7572)+E(f659(x7573,x7571,x7574),f659(x7573,x7572,x7574))
% 109.14/108.86 [758]~E(x7581,x7582)+E(f659(x7583,x7584,x7581),f659(x7583,x7584,x7582))
% 109.14/108.86 [759]~E(x7591,x7592)+E(f48(x7591,x7593),f48(x7592,x7593))
% 109.14/108.86 [760]~E(x7601,x7602)+E(f48(x7603,x7601),f48(x7603,x7602))
% 109.14/108.86 [761]~E(x7611,x7612)+E(f147(x7611,x7613,x7614,x7615),f147(x7612,x7613,x7614,x7615))
% 109.14/108.86 [762]~E(x7621,x7622)+E(f147(x7623,x7621,x7624,x7625),f147(x7623,x7622,x7624,x7625))
% 109.14/108.86 [763]~E(x7631,x7632)+E(f147(x7633,x7634,x7631,x7635),f147(x7633,x7634,x7632,x7635))
% 109.14/108.86 [764]~E(x7641,x7642)+E(f147(x7643,x7644,x7645,x7641),f147(x7643,x7644,x7645,x7642))
% 109.14/108.86 [765]~E(x7651,x7652)+E(f507(x7651,x7653,x7654,x7655,x7656,x7657),f507(x7652,x7653,x7654,x7655,x7656,x7657))
% 109.14/108.86 [766]~E(x7661,x7662)+E(f507(x7663,x7661,x7664,x7665,x7666,x7667),f507(x7663,x7662,x7664,x7665,x7666,x7667))
% 109.14/108.86 [767]~E(x7671,x7672)+E(f507(x7673,x7674,x7671,x7675,x7676,x7677),f507(x7673,x7674,x7672,x7675,x7676,x7677))
% 109.14/108.86 [768]~E(x7681,x7682)+E(f507(x7683,x7684,x7685,x7681,x7686,x7687),f507(x7683,x7684,x7685,x7682,x7686,x7687))
% 109.14/108.86 [769]~E(x7691,x7692)+E(f507(x7693,x7694,x7695,x7696,x7691,x7697),f507(x7693,x7694,x7695,x7696,x7692,x7697))
% 109.14/108.86 [770]~E(x7701,x7702)+E(f507(x7703,x7704,x7705,x7706,x7707,x7701),f507(x7703,x7704,x7705,x7706,x7707,x7702))
% 109.14/108.86 [771]~E(x7711,x7712)+E(f21(x7711,x7713,x7714,x7715),f21(x7712,x7713,x7714,x7715))
% 109.14/108.86 [772]~E(x7721,x7722)+E(f21(x7723,x7721,x7724,x7725),f21(x7723,x7722,x7724,x7725))
% 109.14/108.86 [773]~E(x7731,x7732)+E(f21(x7733,x7734,x7731,x7735),f21(x7733,x7734,x7732,x7735))
% 109.14/108.86 [774]~E(x7741,x7742)+E(f21(x7743,x7744,x7745,x7741),f21(x7743,x7744,x7745,x7742))
% 109.14/108.86 [775]~E(x7751,x7752)+E(f492(x7751,x7753,x7754),f492(x7752,x7753,x7754))
% 109.14/108.86 [776]~E(x7761,x7762)+E(f492(x7763,x7761,x7764),f492(x7763,x7762,x7764))
% 109.14/108.86 [777]~E(x7771,x7772)+E(f492(x7773,x7774,x7771),f492(x7773,x7774,x7772))
% 109.14/108.86 [778]~E(x7781,x7782)+E(f801(x7781),f801(x7782))
% 109.14/108.86 [779]~E(x7791,x7792)+E(f708(x7791,x7793,x7794),f708(x7792,x7793,x7794))
% 109.14/108.86 [780]~E(x7801,x7802)+E(f708(x7803,x7801,x7804),f708(x7803,x7802,x7804))
% 109.14/108.86 [781]~E(x7811,x7812)+E(f708(x7813,x7814,x7811),f708(x7813,x7814,x7812))
% 109.14/108.86 [782]~E(x7821,x7822)+E(f629(x7821,x7823,x7824,x7825,x7826),f629(x7822,x7823,x7824,x7825,x7826))
% 109.14/108.86 [783]~E(x7831,x7832)+E(f629(x7833,x7831,x7834,x7835,x7836),f629(x7833,x7832,x7834,x7835,x7836))
% 109.14/108.86 [784]~E(x7841,x7842)+E(f629(x7843,x7844,x7841,x7845,x7846),f629(x7843,x7844,x7842,x7845,x7846))
% 109.14/108.86 [785]~E(x7851,x7852)+E(f629(x7853,x7854,x7855,x7851,x7856),f629(x7853,x7854,x7855,x7852,x7856))
% 109.14/108.86 [786]~E(x7861,x7862)+E(f629(x7863,x7864,x7865,x7866,x7861),f629(x7863,x7864,x7865,x7866,x7862))
% 109.14/108.86 [787]~E(x7871,x7872)+E(f389(x7871,x7873,x7874),f389(x7872,x7873,x7874))
% 109.14/108.86 [788]~E(x7881,x7882)+E(f389(x7883,x7881,x7884),f389(x7883,x7882,x7884))
% 109.14/108.86 [789]~E(x7891,x7892)+E(f389(x7893,x7894,x7891),f389(x7893,x7894,x7892))
% 109.14/108.86 [790]~E(x7901,x7902)+E(f562(x7901,x7903,x7904,x7905,x7906,x7907),f562(x7902,x7903,x7904,x7905,x7906,x7907))
% 109.14/108.86 [791]~E(x7911,x7912)+E(f562(x7913,x7911,x7914,x7915,x7916,x7917),f562(x7913,x7912,x7914,x7915,x7916,x7917))
% 109.14/108.86 [792]~E(x7921,x7922)+E(f562(x7923,x7924,x7921,x7925,x7926,x7927),f562(x7923,x7924,x7922,x7925,x7926,x7927))
% 109.14/108.86 [793]~E(x7931,x7932)+E(f562(x7933,x7934,x7935,x7931,x7936,x7937),f562(x7933,x7934,x7935,x7932,x7936,x7937))
% 109.14/108.86 [794]~E(x7941,x7942)+E(f562(x7943,x7944,x7945,x7946,x7941,x7947),f562(x7943,x7944,x7945,x7946,x7942,x7947))
% 109.14/108.86 [795]~E(x7951,x7952)+E(f562(x7953,x7954,x7955,x7956,x7957,x7951),f562(x7953,x7954,x7955,x7956,x7957,x7952))
% 109.14/108.86 [796]~E(x7961,x7962)+E(f622(x7961,x7963,x7964,x7965,x7966),f622(x7962,x7963,x7964,x7965,x7966))
% 109.14/108.86 [797]~E(x7971,x7972)+E(f622(x7973,x7971,x7974,x7975,x7976),f622(x7973,x7972,x7974,x7975,x7976))
% 109.14/108.86 [798]~E(x7981,x7982)+E(f622(x7983,x7984,x7981,x7985,x7986),f622(x7983,x7984,x7982,x7985,x7986))
% 109.14/108.86 [799]~E(x7991,x7992)+E(f622(x7993,x7994,x7995,x7991,x7996),f622(x7993,x7994,x7995,x7992,x7996))
% 109.14/108.86 [800]~E(x8001,x8002)+E(f622(x8003,x8004,x8005,x8006,x8001),f622(x8003,x8004,x8005,x8006,x8002))
% 109.14/108.86 [801]~E(x8011,x8012)+E(f888(x8011,x8013,x8014),f888(x8012,x8013,x8014))
% 109.14/108.86 [802]~E(x8021,x8022)+E(f888(x8023,x8021,x8024),f888(x8023,x8022,x8024))
% 109.14/108.86 [803]~E(x8031,x8032)+E(f888(x8033,x8034,x8031),f888(x8033,x8034,x8032))
% 109.14/108.86 [804]~E(x8041,x8042)+E(f792(x8041,x8043,x8044,x8045),f792(x8042,x8043,x8044,x8045))
% 109.14/108.86 [805]~E(x8051,x8052)+E(f792(x8053,x8051,x8054,x8055),f792(x8053,x8052,x8054,x8055))
% 109.14/108.86 [806]~E(x8061,x8062)+E(f792(x8063,x8064,x8061,x8065),f792(x8063,x8064,x8062,x8065))
% 109.14/108.86 [807]~E(x8071,x8072)+E(f792(x8073,x8074,x8075,x8071),f792(x8073,x8074,x8075,x8072))
% 109.14/108.86 [808]~E(x8081,x8082)+E(f87(x8081,x8083),f87(x8082,x8083))
% 109.14/108.86 [809]~E(x8091,x8092)+E(f87(x8093,x8091),f87(x8093,x8092))
% 109.14/108.86 [810]~E(x8101,x8102)+E(f443(x8101,x8103,x8104,x8105,x8106,x8107,x8108),f443(x8102,x8103,x8104,x8105,x8106,x8107,x8108))
% 109.14/108.86 [811]~E(x8111,x8112)+E(f443(x8113,x8111,x8114,x8115,x8116,x8117,x8118),f443(x8113,x8112,x8114,x8115,x8116,x8117,x8118))
% 109.14/108.86 [812]~E(x8121,x8122)+E(f443(x8123,x8124,x8121,x8125,x8126,x8127,x8128),f443(x8123,x8124,x8122,x8125,x8126,x8127,x8128))
% 109.14/108.86 [813]~E(x8131,x8132)+E(f443(x8133,x8134,x8135,x8131,x8136,x8137,x8138),f443(x8133,x8134,x8135,x8132,x8136,x8137,x8138))
% 109.14/108.86 [814]~E(x8141,x8142)+E(f443(x8143,x8144,x8145,x8146,x8141,x8147,x8148),f443(x8143,x8144,x8145,x8146,x8142,x8147,x8148))
% 109.14/108.86 [815]~E(x8151,x8152)+E(f443(x8153,x8154,x8155,x8156,x8157,x8151,x8158),f443(x8153,x8154,x8155,x8156,x8157,x8152,x8158))
% 109.14/108.86 [816]~E(x8161,x8162)+E(f443(x8163,x8164,x8165,x8166,x8167,x8168,x8161),f443(x8163,x8164,x8165,x8166,x8167,x8168,x8162))
% 109.14/108.86 [817]~E(x8171,x8172)+E(f460(x8171,x8173,x8174),f460(x8172,x8173,x8174))
% 109.14/108.86 [818]~E(x8181,x8182)+E(f460(x8183,x8181,x8184),f460(x8183,x8182,x8184))
% 109.14/108.86 [819]~E(x8191,x8192)+E(f460(x8193,x8194,x8191),f460(x8193,x8194,x8192))
% 109.14/108.86 [820]~E(x8201,x8202)+E(f334(x8201,x8203,x8204,x8205),f334(x8202,x8203,x8204,x8205))
% 109.14/108.86 [821]~E(x8211,x8212)+E(f334(x8213,x8211,x8214,x8215),f334(x8213,x8212,x8214,x8215))
% 109.14/108.86 [822]~E(x8221,x8222)+E(f334(x8223,x8224,x8221,x8225),f334(x8223,x8224,x8222,x8225))
% 109.14/108.86 [823]~E(x8231,x8232)+E(f334(x8233,x8234,x8235,x8231),f334(x8233,x8234,x8235,x8232))
% 109.14/108.86 [824]~E(x8241,x8242)+E(f464(x8241,x8243,x8244,x8245),f464(x8242,x8243,x8244,x8245))
% 109.14/108.86 [825]~E(x8251,x8252)+E(f464(x8253,x8251,x8254,x8255),f464(x8253,x8252,x8254,x8255))
% 109.14/108.86 [826]~E(x8261,x8262)+E(f464(x8263,x8264,x8261,x8265),f464(x8263,x8264,x8262,x8265))
% 109.14/108.86 [827]~E(x8271,x8272)+E(f464(x8273,x8274,x8275,x8271),f464(x8273,x8274,x8275,x8272))
% 109.14/108.86 [828]~E(x8281,x8282)+E(f805(x8281,x8283),f805(x8282,x8283))
% 109.14/108.86 [829]~E(x8291,x8292)+E(f805(x8293,x8291),f805(x8293,x8292))
% 109.14/108.86 [830]~E(x8301,x8302)+E(f706(x8301,x8303,x8304),f706(x8302,x8303,x8304))
% 109.14/108.86 [831]~E(x8311,x8312)+E(f706(x8313,x8311,x8314),f706(x8313,x8312,x8314))
% 109.14/108.86 [832]~E(x8321,x8322)+E(f706(x8323,x8324,x8321),f706(x8323,x8324,x8322))
% 109.14/108.86 [833]~E(x8331,x8332)+E(f605(x8331,x8333,x8334),f605(x8332,x8333,x8334))
% 109.14/108.86 [834]~E(x8341,x8342)+E(f605(x8343,x8341,x8344),f605(x8343,x8342,x8344))
% 109.14/108.86 [835]~E(x8351,x8352)+E(f605(x8353,x8354,x8351),f605(x8353,x8354,x8352))
% 109.14/108.86 [836]~E(x8361,x8362)+E(f879(x8361,x8363,x8364,x8365),f879(x8362,x8363,x8364,x8365))
% 109.14/108.86 [837]~E(x8371,x8372)+E(f879(x8373,x8371,x8374,x8375),f879(x8373,x8372,x8374,x8375))
% 109.14/108.86 [838]~E(x8381,x8382)+E(f879(x8383,x8384,x8381,x8385),f879(x8383,x8384,x8382,x8385))
% 109.14/108.86 [839]~E(x8391,x8392)+E(f879(x8393,x8394,x8395,x8391),f879(x8393,x8394,x8395,x8392))
% 109.14/108.86 [840]~E(x8401,x8402)+E(f697(x8401,x8403),f697(x8402,x8403))
% 109.14/108.86 [841]~E(x8411,x8412)+E(f697(x8413,x8411),f697(x8413,x8412))
% 109.14/108.86 [842]~E(x8421,x8422)+E(f131(x8421,x8423,x8424),f131(x8422,x8423,x8424))
% 109.14/108.86 [843]~E(x8431,x8432)+E(f131(x8433,x8431,x8434),f131(x8433,x8432,x8434))
% 109.14/108.86 [844]~E(x8441,x8442)+E(f131(x8443,x8444,x8441),f131(x8443,x8444,x8442))
% 109.14/108.86 [845]~E(x8451,x8452)+E(f414(x8451,x8453,x8454),f414(x8452,x8453,x8454))
% 109.14/108.86 [846]~E(x8461,x8462)+E(f414(x8463,x8461,x8464),f414(x8463,x8462,x8464))
% 109.14/108.86 [847]~E(x8471,x8472)+E(f414(x8473,x8474,x8471),f414(x8473,x8474,x8472))
% 109.14/108.86 [848]~E(x8481,x8482)+E(f333(x8481,x8483,x8484,x8485),f333(x8482,x8483,x8484,x8485))
% 109.14/108.86 [849]~E(x8491,x8492)+E(f333(x8493,x8491,x8494,x8495),f333(x8493,x8492,x8494,x8495))
% 109.14/108.86 [850]~E(x8501,x8502)+E(f333(x8503,x8504,x8501,x8505),f333(x8503,x8504,x8502,x8505))
% 109.14/108.86 [851]~E(x8511,x8512)+E(f333(x8513,x8514,x8515,x8511),f333(x8513,x8514,x8515,x8512))
% 109.14/108.86 [852]~E(x8521,x8522)+E(f185(x8521,x8523),f185(x8522,x8523))
% 109.14/108.86 [853]~E(x8531,x8532)+E(f185(x8533,x8531),f185(x8533,x8532))
% 109.14/108.86 [854]~E(x8541,x8542)+E(f849(x8541,x8543,x8544,x8545,x8546,x8547),f849(x8542,x8543,x8544,x8545,x8546,x8547))
% 109.14/108.86 [855]~E(x8551,x8552)+E(f849(x8553,x8551,x8554,x8555,x8556,x8557),f849(x8553,x8552,x8554,x8555,x8556,x8557))
% 109.14/108.86 [856]~E(x8561,x8562)+E(f849(x8563,x8564,x8561,x8565,x8566,x8567),f849(x8563,x8564,x8562,x8565,x8566,x8567))
% 109.14/108.86 [857]~E(x8571,x8572)+E(f849(x8573,x8574,x8575,x8571,x8576,x8577),f849(x8573,x8574,x8575,x8572,x8576,x8577))
% 109.14/108.86 [858]~E(x8581,x8582)+E(f849(x8583,x8584,x8585,x8586,x8581,x8587),f849(x8583,x8584,x8585,x8586,x8582,x8587))
% 109.14/108.86 [859]~E(x8591,x8592)+E(f849(x8593,x8594,x8595,x8596,x8597,x8591),f849(x8593,x8594,x8595,x8596,x8597,x8592))
% 109.14/108.86 [860]~E(x8601,x8602)+E(f628(x8601,x8603,x8604,x8605,x8606),f628(x8602,x8603,x8604,x8605,x8606))
% 109.14/108.86 [861]~E(x8611,x8612)+E(f628(x8613,x8611,x8614,x8615,x8616),f628(x8613,x8612,x8614,x8615,x8616))
% 109.14/108.86 [862]~E(x8621,x8622)+E(f628(x8623,x8624,x8621,x8625,x8626),f628(x8623,x8624,x8622,x8625,x8626))
% 109.14/108.86 [863]~E(x8631,x8632)+E(f628(x8633,x8634,x8635,x8631,x8636),f628(x8633,x8634,x8635,x8632,x8636))
% 109.14/108.86 [864]~E(x8641,x8642)+E(f628(x8643,x8644,x8645,x8646,x8641),f628(x8643,x8644,x8645,x8646,x8642))
% 109.14/108.86 [865]~E(x8651,x8652)+E(f722(x8651,x8653),f722(x8652,x8653))
% 109.14/108.86 [866]~E(x8661,x8662)+E(f722(x8663,x8661),f722(x8663,x8662))
% 109.14/108.86 [867]~E(x8671,x8672)+E(f86(x8671,x8673),f86(x8672,x8673))
% 109.14/108.86 [868]~E(x8681,x8682)+E(f86(x8683,x8681),f86(x8683,x8682))
% 109.14/108.86 [869]~E(x8691,x8692)+E(f19(x8691,x8693,x8694,x8695),f19(x8692,x8693,x8694,x8695))
% 109.14/108.86 [870]~E(x8701,x8702)+E(f19(x8703,x8701,x8704,x8705),f19(x8703,x8702,x8704,x8705))
% 109.14/108.86 [871]~E(x8711,x8712)+E(f19(x8713,x8714,x8711,x8715),f19(x8713,x8714,x8712,x8715))
% 109.14/108.86 [872]~E(x8721,x8722)+E(f19(x8723,x8724,x8725,x8721),f19(x8723,x8724,x8725,x8722))
% 109.14/108.86 [873]~E(x8731,x8732)+E(f519(x8731),f519(x8732))
% 109.14/108.86 [874]~E(x8741,x8742)+E(f408(x8741,x8743,x8744),f408(x8742,x8743,x8744))
% 109.14/108.86 [875]~E(x8751,x8752)+E(f408(x8753,x8751,x8754),f408(x8753,x8752,x8754))
% 109.14/108.86 [876]~E(x8761,x8762)+E(f408(x8763,x8764,x8761),f408(x8763,x8764,x8762))
% 109.14/108.86 [877]~E(x8771,x8772)+E(f250(x8771,x8773,x8774,x8775),f250(x8772,x8773,x8774,x8775))
% 109.14/108.86 [878]~E(x8781,x8782)+E(f250(x8783,x8781,x8784,x8785),f250(x8783,x8782,x8784,x8785))
% 109.14/108.86 [879]~E(x8791,x8792)+E(f250(x8793,x8794,x8791,x8795),f250(x8793,x8794,x8792,x8795))
% 109.14/108.86 [880]~E(x8801,x8802)+E(f250(x8803,x8804,x8805,x8801),f250(x8803,x8804,x8805,x8802))
% 109.14/108.86 [881]~E(x8811,x8812)+E(f269(x8811),f269(x8812))
% 109.14/108.86 [882]~E(x8821,x8822)+E(f864(x8821,x8823,x8824,x8825),f864(x8822,x8823,x8824,x8825))
% 109.14/108.86 [883]~E(x8831,x8832)+E(f864(x8833,x8831,x8834,x8835),f864(x8833,x8832,x8834,x8835))
% 109.14/108.86 [884]~E(x8841,x8842)+E(f864(x8843,x8844,x8841,x8845),f864(x8843,x8844,x8842,x8845))
% 109.14/108.86 [885]~E(x8851,x8852)+E(f864(x8853,x8854,x8855,x8851),f864(x8853,x8854,x8855,x8852))
% 109.14/108.86 [886]~E(x8861,x8862)+E(f117(x8861,x8863,x8864),f117(x8862,x8863,x8864))
% 109.14/108.86 [887]~E(x8871,x8872)+E(f117(x8873,x8871,x8874),f117(x8873,x8872,x8874))
% 109.14/108.86 [888]~E(x8881,x8882)+E(f117(x8883,x8884,x8881),f117(x8883,x8884,x8882))
% 109.14/108.86 [889]~E(x8891,x8892)+E(f51(x8891),f51(x8892))
% 109.14/108.86 [890]~E(x8901,x8902)+E(f567(x8901,x8903,x8904),f567(x8902,x8903,x8904))
% 109.14/108.86 [891]~E(x8911,x8912)+E(f567(x8913,x8911,x8914),f567(x8913,x8912,x8914))
% 109.14/108.86 [892]~E(x8921,x8922)+E(f567(x8923,x8924,x8921),f567(x8923,x8924,x8922))
% 109.14/108.86 [893]~E(x8931,x8932)+E(f640(x8931,x8933,x8934,x8935,x8936),f640(x8932,x8933,x8934,x8935,x8936))
% 109.14/108.86 [894]~E(x8941,x8942)+E(f640(x8943,x8941,x8944,x8945,x8946),f640(x8943,x8942,x8944,x8945,x8946))
% 109.14/108.86 [895]~E(x8951,x8952)+E(f640(x8953,x8954,x8951,x8955,x8956),f640(x8953,x8954,x8952,x8955,x8956))
% 109.14/108.86 [896]~E(x8961,x8962)+E(f640(x8963,x8964,x8965,x8961,x8966),f640(x8963,x8964,x8965,x8962,x8966))
% 109.14/108.86 [897]~E(x8971,x8972)+E(f640(x8973,x8974,x8975,x8976,x8971),f640(x8973,x8974,x8975,x8976,x8972))
% 109.14/108.86 [898]~E(x8981,x8982)+E(f848(x8981,x8983,x8984,x8985,x8986,x8987),f848(x8982,x8983,x8984,x8985,x8986,x8987))
% 109.14/108.86 [899]~E(x8991,x8992)+E(f848(x8993,x8991,x8994,x8995,x8996,x8997),f848(x8993,x8992,x8994,x8995,x8996,x8997))
% 109.14/108.86 [900]~E(x9001,x9002)+E(f848(x9003,x9004,x9001,x9005,x9006,x9007),f848(x9003,x9004,x9002,x9005,x9006,x9007))
% 109.14/108.86 [901]~E(x9011,x9012)+E(f848(x9013,x9014,x9015,x9011,x9016,x9017),f848(x9013,x9014,x9015,x9012,x9016,x9017))
% 109.14/108.86 [902]~E(x9021,x9022)+E(f848(x9023,x9024,x9025,x9026,x9021,x9027),f848(x9023,x9024,x9025,x9026,x9022,x9027))
% 109.14/108.86 [903]~E(x9031,x9032)+E(f848(x9033,x9034,x9035,x9036,x9037,x9031),f848(x9033,x9034,x9035,x9036,x9037,x9032))
% 109.14/108.86 [904]~E(x9041,x9042)+E(f377(x9041,x9043),f377(x9042,x9043))
% 109.14/108.86 [905]~E(x9051,x9052)+E(f377(x9053,x9051),f377(x9053,x9052))
% 109.14/108.86 [906]~E(x9061,x9062)+E(f506(x9061,x9063,x9064,x9065),f506(x9062,x9063,x9064,x9065))
% 109.14/108.86 [907]~E(x9071,x9072)+E(f506(x9073,x9071,x9074,x9075),f506(x9073,x9072,x9074,x9075))
% 109.14/108.86 [908]~E(x9081,x9082)+E(f506(x9083,x9084,x9081,x9085),f506(x9083,x9084,x9082,x9085))
% 109.14/108.86 [909]~E(x9091,x9092)+E(f506(x9093,x9094,x9095,x9091),f506(x9093,x9094,x9095,x9092))
% 109.14/108.86 [910]~E(x9101,x9102)+E(f183(x9101,x9103),f183(x9102,x9103))
% 109.14/108.86 [911]~E(x9111,x9112)+E(f183(x9113,x9111),f183(x9113,x9112))
% 109.14/108.86 [912]~E(x9121,x9122)+E(f753(x9121,x9123,x9124),f753(x9122,x9123,x9124))
% 109.14/108.86 [913]~E(x9131,x9132)+E(f753(x9133,x9131,x9134),f753(x9133,x9132,x9134))
% 109.14/108.86 [914]~E(x9141,x9142)+E(f753(x9143,x9144,x9141),f753(x9143,x9144,x9142))
% 109.14/108.86 [915]~E(x9151,x9152)+E(f112(x9151,x9153),f112(x9152,x9153))
% 109.14/108.86 [916]~E(x9161,x9162)+E(f112(x9163,x9161),f112(x9163,x9162))
% 109.14/108.86 [917]~E(x9171,x9172)+E(f523(x9171,x9173,x9174),f523(x9172,x9173,x9174))
% 109.14/108.86 [918]~E(x9181,x9182)+E(f523(x9183,x9181,x9184),f523(x9183,x9182,x9184))
% 109.14/108.86 [919]~E(x9191,x9192)+E(f523(x9193,x9194,x9191),f523(x9193,x9194,x9192))
% 109.14/108.86 [920]~E(x9201,x9202)+E(f394(x9201,x9203,x9204),f394(x9202,x9203,x9204))
% 109.14/108.86 [921]~E(x9211,x9212)+E(f394(x9213,x9211,x9214),f394(x9213,x9212,x9214))
% 109.14/108.86 [922]~E(x9221,x9222)+E(f394(x9223,x9224,x9221),f394(x9223,x9224,x9222))
% 109.14/108.86 [923]~E(x9231,x9232)+E(f439(x9231,x9233,x9234),f439(x9232,x9233,x9234))
% 109.14/108.86 [924]~E(x9241,x9242)+E(f439(x9243,x9241,x9244),f439(x9243,x9242,x9244))
% 109.14/108.86 [925]~E(x9251,x9252)+E(f439(x9253,x9254,x9251),f439(x9253,x9254,x9252))
% 109.14/108.86 [926]~E(x9261,x9262)+E(f876(x9261,x9263,x9264),f876(x9262,x9263,x9264))
% 109.14/108.86 [927]~E(x9271,x9272)+E(f876(x9273,x9271,x9274),f876(x9273,x9272,x9274))
% 109.14/108.86 [928]~E(x9281,x9282)+E(f876(x9283,x9284,x9281),f876(x9283,x9284,x9282))
% 109.14/108.86 [929]~E(x9291,x9292)+E(f872(x9291,x9293,x9294,x9295,x9296),f872(x9292,x9293,x9294,x9295,x9296))
% 109.14/108.86 [930]~E(x9301,x9302)+E(f872(x9303,x9301,x9304,x9305,x9306),f872(x9303,x9302,x9304,x9305,x9306))
% 109.14/108.86 [931]~E(x9311,x9312)+E(f872(x9313,x9314,x9311,x9315,x9316),f872(x9313,x9314,x9312,x9315,x9316))
% 109.14/108.86 [932]~E(x9321,x9322)+E(f872(x9323,x9324,x9325,x9321,x9326),f872(x9323,x9324,x9325,x9322,x9326))
% 109.14/108.86 [933]~E(x9331,x9332)+E(f872(x9333,x9334,x9335,x9336,x9331),f872(x9333,x9334,x9335,x9336,x9332))
% 109.14/108.86 [934]~E(x9341,x9342)+E(f516(x9341),f516(x9342))
% 109.14/108.86 [935]~E(x9351,x9352)+E(f654(x9351,x9353,x9354,x9355),f654(x9352,x9353,x9354,x9355))
% 109.14/108.86 [936]~E(x9361,x9362)+E(f654(x9363,x9361,x9364,x9365),f654(x9363,x9362,x9364,x9365))
% 109.14/108.86 [937]~E(x9371,x9372)+E(f654(x9373,x9374,x9371,x9375),f654(x9373,x9374,x9372,x9375))
% 109.14/108.86 [938]~E(x9381,x9382)+E(f654(x9383,x9384,x9385,x9381),f654(x9383,x9384,x9385,x9382))
% 109.14/108.86 [939]~E(x9391,x9392)+E(f542(x9391,x9393,x9394,x9395,x9396,x9397),f542(x9392,x9393,x9394,x9395,x9396,x9397))
% 109.14/108.86 [940]~E(x9401,x9402)+E(f542(x9403,x9401,x9404,x9405,x9406,x9407),f542(x9403,x9402,x9404,x9405,x9406,x9407))
% 109.14/108.86 [941]~E(x9411,x9412)+E(f542(x9413,x9414,x9411,x9415,x9416,x9417),f542(x9413,x9414,x9412,x9415,x9416,x9417))
% 109.14/108.86 [942]~E(x9421,x9422)+E(f542(x9423,x9424,x9425,x9421,x9426,x9427),f542(x9423,x9424,x9425,x9422,x9426,x9427))
% 109.14/108.86 [943]~E(x9431,x9432)+E(f542(x9433,x9434,x9435,x9436,x9431,x9437),f542(x9433,x9434,x9435,x9436,x9432,x9437))
% 109.14/108.86 [944]~E(x9441,x9442)+E(f542(x9443,x9444,x9445,x9446,x9447,x9441),f542(x9443,x9444,x9445,x9446,x9447,x9442))
% 109.14/108.86 [945]~E(x9451,x9452)+E(f257(x9451,x9453),f257(x9452,x9453))
% 109.14/108.86 [946]~E(x9461,x9462)+E(f257(x9463,x9461),f257(x9463,x9462))
% 109.14/108.86 [947]~E(x9471,x9472)+E(f726(x9471,x9473),f726(x9472,x9473))
% 109.14/108.86 [948]~E(x9481,x9482)+E(f726(x9483,x9481),f726(x9483,x9482))
% 109.14/108.86 [949]~E(x9491,x9492)+E(f498(x9491,x9493,x9494),f498(x9492,x9493,x9494))
% 109.14/108.86 [950]~E(x9501,x9502)+E(f498(x9503,x9501,x9504),f498(x9503,x9502,x9504))
% 109.14/108.86 [951]~E(x9511,x9512)+E(f498(x9513,x9514,x9511),f498(x9513,x9514,x9512))
% 109.14/108.86 [952]~E(x9521,x9522)+E(f902(x9521,x9523,x9524,x9525,x9526),f902(x9522,x9523,x9524,x9525,x9526))
% 109.14/108.86 [953]~E(x9531,x9532)+E(f902(x9533,x9531,x9534,x9535,x9536),f902(x9533,x9532,x9534,x9535,x9536))
% 109.14/108.86 [954]~E(x9541,x9542)+E(f902(x9543,x9544,x9541,x9545,x9546),f902(x9543,x9544,x9542,x9545,x9546))
% 109.14/108.86 [955]~E(x9551,x9552)+E(f902(x9553,x9554,x9555,x9551,x9556),f902(x9553,x9554,x9555,x9552,x9556))
% 109.14/108.86 [956]~E(x9561,x9562)+E(f902(x9563,x9564,x9565,x9566,x9561),f902(x9563,x9564,x9565,x9566,x9562))
% 109.14/108.86 [957]~E(x9571,x9572)+E(f743(x9571,x9573,x9574,x9575,x9576,x9577,x9578),f743(x9572,x9573,x9574,x9575,x9576,x9577,x9578))
% 109.14/108.86 [958]~E(x9581,x9582)+E(f743(x9583,x9581,x9584,x9585,x9586,x9587,x9588),f743(x9583,x9582,x9584,x9585,x9586,x9587,x9588))
% 109.14/108.86 [959]~E(x9591,x9592)+E(f743(x9593,x9594,x9591,x9595,x9596,x9597,x9598),f743(x9593,x9594,x9592,x9595,x9596,x9597,x9598))
% 109.14/108.86 [960]~E(x9601,x9602)+E(f743(x9603,x9604,x9605,x9601,x9606,x9607,x9608),f743(x9603,x9604,x9605,x9602,x9606,x9607,x9608))
% 109.14/108.86 [961]~E(x9611,x9612)+E(f743(x9613,x9614,x9615,x9616,x9611,x9617,x9618),f743(x9613,x9614,x9615,x9616,x9612,x9617,x9618))
% 109.14/108.86 [962]~E(x9621,x9622)+E(f743(x9623,x9624,x9625,x9626,x9627,x9621,x9628),f743(x9623,x9624,x9625,x9626,x9627,x9622,x9628))
% 109.14/108.86 [963]~E(x9631,x9632)+E(f743(x9633,x9634,x9635,x9636,x9637,x9638,x9631),f743(x9633,x9634,x9635,x9636,x9637,x9638,x9632))
% 109.14/108.86 [964]~E(x9641,x9642)+E(f176(x9641,x9643,x9644,x9645),f176(x9642,x9643,x9644,x9645))
% 109.14/108.86 [965]~E(x9651,x9652)+E(f176(x9653,x9651,x9654,x9655),f176(x9653,x9652,x9654,x9655))
% 109.14/108.86 [966]~E(x9661,x9662)+E(f176(x9663,x9664,x9661,x9665),f176(x9663,x9664,x9662,x9665))
% 109.14/108.86 [967]~E(x9671,x9672)+E(f176(x9673,x9674,x9675,x9671),f176(x9673,x9674,x9675,x9672))
% 109.14/108.86 [968]~E(x9681,x9682)+E(f653(x9681,x9683,x9684,x9685),f653(x9682,x9683,x9684,x9685))
% 109.14/108.86 [969]~E(x9691,x9692)+E(f653(x9693,x9691,x9694,x9695),f653(x9693,x9692,x9694,x9695))
% 109.14/108.86 [970]~E(x9701,x9702)+E(f653(x9703,x9704,x9701,x9705),f653(x9703,x9704,x9702,x9705))
% 109.14/108.86 [971]~E(x9711,x9712)+E(f653(x9713,x9714,x9715,x9711),f653(x9713,x9714,x9715,x9712))
% 109.14/108.86 [972]~E(x9721,x9722)+E(f289(x9721,x9723,x9724),f289(x9722,x9723,x9724))
% 109.14/108.86 [973]~E(x9731,x9732)+E(f289(x9733,x9731,x9734),f289(x9733,x9732,x9734))
% 109.14/108.86 [974]~E(x9741,x9742)+E(f289(x9743,x9744,x9741),f289(x9743,x9744,x9742))
% 109.14/108.86 [975]~E(x9751,x9752)+E(f786(x9751,x9753),f786(x9752,x9753))
% 109.14/108.86 [976]~E(x9761,x9762)+E(f786(x9763,x9761),f786(x9763,x9762))
% 109.14/108.86 [977]~E(x9771,x9772)+E(f267(x9771,x9773,x9774,x9775),f267(x9772,x9773,x9774,x9775))
% 109.14/108.86 [978]~E(x9781,x9782)+E(f267(x9783,x9781,x9784,x9785),f267(x9783,x9782,x9784,x9785))
% 109.14/108.86 [979]~E(x9791,x9792)+E(f267(x9793,x9794,x9791,x9795),f267(x9793,x9794,x9792,x9795))
% 109.14/108.86 [980]~E(x9801,x9802)+E(f267(x9803,x9804,x9805,x9801),f267(x9803,x9804,x9805,x9802))
% 109.14/108.86 [981]~E(x9811,x9812)+E(f701(x9811,x9813),f701(x9812,x9813))
% 109.14/108.86 [982]~E(x9821,x9822)+E(f701(x9823,x9821),f701(x9823,x9822))
% 109.14/108.86 [983]~E(x9831,x9832)+E(f767(x9831,x9833,x9834),f767(x9832,x9833,x9834))
% 109.14/108.86 [984]~E(x9841,x9842)+E(f767(x9843,x9841,x9844),f767(x9843,x9842,x9844))
% 109.14/108.86 [985]~E(x9851,x9852)+E(f767(x9853,x9854,x9851),f767(x9853,x9854,x9852))
% 109.14/108.86 [986]~E(x9861,x9862)+E(f827(x9861,x9863,x9864),f827(x9862,x9863,x9864))
% 109.14/108.86 [987]~E(x9871,x9872)+E(f827(x9873,x9871,x9874),f827(x9873,x9872,x9874))
% 109.14/108.86 [988]~E(x9881,x9882)+E(f827(x9883,x9884,x9881),f827(x9883,x9884,x9882))
% 109.14/108.86 [989]~E(x9891,x9892)+E(f192(x9891),f192(x9892))
% 109.14/108.86 [990]~E(x9901,x9902)+E(f61(x9901,x9903,x9904),f61(x9902,x9903,x9904))
% 109.14/108.86 [991]~E(x9911,x9912)+E(f61(x9913,x9911,x9914),f61(x9913,x9912,x9914))
% 109.14/108.86 [992]~E(x9921,x9922)+E(f61(x9923,x9924,x9921),f61(x9923,x9924,x9922))
% 109.14/108.86 [993]~E(x9931,x9932)+E(f671(x9931,x9933,x9934),f671(x9932,x9933,x9934))
% 109.14/108.86 [994]~E(x9941,x9942)+E(f671(x9943,x9941,x9944),f671(x9943,x9942,x9944))
% 109.14/108.86 [995]~E(x9951,x9952)+E(f671(x9953,x9954,x9951),f671(x9953,x9954,x9952))
% 109.14/108.86 [996]~E(x9961,x9962)+E(f804(x9961,x9963,x9964),f804(x9962,x9963,x9964))
% 109.14/108.86 [997]~E(x9971,x9972)+E(f804(x9973,x9971,x9974),f804(x9973,x9972,x9974))
% 109.14/108.86 [998]~E(x9981,x9982)+E(f804(x9983,x9984,x9981),f804(x9983,x9984,x9982))
% 109.14/108.86 [999]~E(x9991,x9992)+E(f205(x9991,x9993),f205(x9992,x9993))
% 109.14/108.86 [1000]~E(x10001,x10002)+E(f205(x10003,x10001),f205(x10003,x10002))
% 109.14/108.86 [1001]~E(x10011,x10012)+E(f358(x10011),f358(x10012))
% 109.14/108.86 [1002]~E(x10021,x10022)+E(f791(x10021,x10023,x10024),f791(x10022,x10023,x10024))
% 109.14/108.86 [1003]~E(x10031,x10032)+E(f791(x10033,x10031,x10034),f791(x10033,x10032,x10034))
% 109.14/108.86 [1004]~E(x10041,x10042)+E(f791(x10043,x10044,x10041),f791(x10043,x10044,x10042))
% 109.14/108.86 [1005]~E(x10051,x10052)+E(f258(x10051),f258(x10052))
% 109.14/108.86 [1006]~E(x10061,x10062)+E(f330(x10061,x10063,x10064,x10065,x10066,x10067,x10068,x10069),f330(x10062,x10063,x10064,x10065,x10066,x10067,x10068,x10069))
% 109.14/108.86 [1007]~E(x10071,x10072)+E(f330(x10073,x10071,x10074,x10075,x10076,x10077,x10078,x10079),f330(x10073,x10072,x10074,x10075,x10076,x10077,x10078,x10079))
% 109.14/108.86 [1008]~E(x10081,x10082)+E(f330(x10083,x10084,x10081,x10085,x10086,x10087,x10088,x10089),f330(x10083,x10084,x10082,x10085,x10086,x10087,x10088,x10089))
% 109.14/108.86 [1009]~E(x10091,x10092)+E(f330(x10093,x10094,x10095,x10091,x10096,x10097,x10098,x10099),f330(x10093,x10094,x10095,x10092,x10096,x10097,x10098,x10099))
% 109.14/108.86 [1010]~E(x10101,x10102)+E(f330(x10103,x10104,x10105,x10106,x10101,x10107,x10108,x10109),f330(x10103,x10104,x10105,x10106,x10102,x10107,x10108,x10109))
% 109.14/108.86 [1011]~E(x10111,x10112)+E(f330(x10113,x10114,x10115,x10116,x10117,x10111,x10118,x10119),f330(x10113,x10114,x10115,x10116,x10117,x10112,x10118,x10119))
% 109.14/108.86 [1012]~E(x10121,x10122)+E(f330(x10123,x10124,x10125,x10126,x10127,x10128,x10121,x10129),f330(x10123,x10124,x10125,x10126,x10127,x10128,x10122,x10129))
% 109.14/108.86 [1013]~E(x10131,x10132)+E(f330(x10133,x10134,x10135,x10136,x10137,x10138,x10139,x10131),f330(x10133,x10134,x10135,x10136,x10137,x10138,x10139,x10132))
% 109.14/108.86 [1014]~E(x10141,x10142)+E(f873(x10141,x10143,x10144,x10145,x10146),f873(x10142,x10143,x10144,x10145,x10146))
% 109.14/108.86 [1015]~E(x10151,x10152)+E(f873(x10153,x10151,x10154,x10155,x10156),f873(x10153,x10152,x10154,x10155,x10156))
% 109.14/108.86 [1016]~E(x10161,x10162)+E(f873(x10163,x10164,x10161,x10165,x10166),f873(x10163,x10164,x10162,x10165,x10166))
% 109.14/108.86 [1017]~E(x10171,x10172)+E(f873(x10173,x10174,x10175,x10171,x10176),f873(x10173,x10174,x10175,x10172,x10176))
% 109.14/108.86 [1018]~E(x10181,x10182)+E(f873(x10183,x10184,x10185,x10186,x10181),f873(x10183,x10184,x10185,x10186,x10182))
% 109.14/108.86 [1019]~E(x10191,x10192)+E(f881(x10191,x10193,x10194,x10195,x10196),f881(x10192,x10193,x10194,x10195,x10196))
% 109.14/108.86 [1020]~E(x10201,x10202)+E(f881(x10203,x10201,x10204,x10205,x10206),f881(x10203,x10202,x10204,x10205,x10206))
% 109.14/108.86 [1021]~E(x10211,x10212)+E(f881(x10213,x10214,x10211,x10215,x10216),f881(x10213,x10214,x10212,x10215,x10216))
% 109.14/108.86 [1022]~E(x10221,x10222)+E(f881(x10223,x10224,x10225,x10221,x10226),f881(x10223,x10224,x10225,x10222,x10226))
% 109.14/108.86 [1023]~E(x10231,x10232)+E(f881(x10233,x10234,x10235,x10236,x10231),f881(x10233,x10234,x10235,x10236,x10232))
% 109.14/108.86 [1024]~E(x10241,x10242)+E(f401(x10241,x10243,x10244,x10245),f401(x10242,x10243,x10244,x10245))
% 109.14/108.86 [1025]~E(x10251,x10252)+E(f401(x10253,x10251,x10254,x10255),f401(x10253,x10252,x10254,x10255))
% 109.14/108.86 [1026]~E(x10261,x10262)+E(f401(x10263,x10264,x10261,x10265),f401(x10263,x10264,x10262,x10265))
% 109.14/108.86 [1027]~E(x10271,x10272)+E(f401(x10273,x10274,x10275,x10271),f401(x10273,x10274,x10275,x10272))
% 109.14/108.86 [1028]~E(x10281,x10282)+E(f295(x10281),f295(x10282))
% 109.14/108.86 [1029]~E(x10291,x10292)+E(f565(x10291,x10293,x10294,x10295),f565(x10292,x10293,x10294,x10295))
% 109.14/108.86 [1030]~E(x10301,x10302)+E(f565(x10303,x10301,x10304,x10305),f565(x10303,x10302,x10304,x10305))
% 109.14/108.86 [1031]~E(x10311,x10312)+E(f565(x10313,x10314,x10311,x10315),f565(x10313,x10314,x10312,x10315))
% 109.14/108.86 [1032]~E(x10321,x10322)+E(f565(x10323,x10324,x10325,x10321),f565(x10323,x10324,x10325,x10322))
% 109.14/108.86 [1033]~E(x10331,x10332)+E(f472(x10331,x10333,x10334,x10335),f472(x10332,x10333,x10334,x10335))
% 109.14/108.86 [1034]~E(x10341,x10342)+E(f472(x10343,x10341,x10344,x10345),f472(x10343,x10342,x10344,x10345))
% 109.14/108.86 [1035]~E(x10351,x10352)+E(f472(x10353,x10354,x10351,x10355),f472(x10353,x10354,x10352,x10355))
% 109.14/108.86 [1036]~E(x10361,x10362)+E(f472(x10363,x10364,x10365,x10361),f472(x10363,x10364,x10365,x10362))
% 109.14/108.86 [1037]~E(x10371,x10372)+E(f555(x10371,x10373),f555(x10372,x10373))
% 109.14/108.86 [1038]~E(x10381,x10382)+E(f555(x10383,x10381),f555(x10383,x10382))
% 109.14/108.86 [1039]~E(x10391,x10392)+E(f836(x10391,x10393,x10394,x10395,x10396,x10397,x10398,x10399),f836(x10392,x10393,x10394,x10395,x10396,x10397,x10398,x10399))
% 109.14/108.86 [1040]~E(x10401,x10402)+E(f836(x10403,x10401,x10404,x10405,x10406,x10407,x10408,x10409),f836(x10403,x10402,x10404,x10405,x10406,x10407,x10408,x10409))
% 109.14/108.86 [1041]~E(x10411,x10412)+E(f836(x10413,x10414,x10411,x10415,x10416,x10417,x10418,x10419),f836(x10413,x10414,x10412,x10415,x10416,x10417,x10418,x10419))
% 109.14/108.86 [1042]~E(x10421,x10422)+E(f836(x10423,x10424,x10425,x10421,x10426,x10427,x10428,x10429),f836(x10423,x10424,x10425,x10422,x10426,x10427,x10428,x10429))
% 109.14/108.86 [1043]~E(x10431,x10432)+E(f836(x10433,x10434,x10435,x10436,x10431,x10437,x10438,x10439),f836(x10433,x10434,x10435,x10436,x10432,x10437,x10438,x10439))
% 109.14/108.86 [1044]~E(x10441,x10442)+E(f836(x10443,x10444,x10445,x10446,x10447,x10441,x10448,x10449),f836(x10443,x10444,x10445,x10446,x10447,x10442,x10448,x10449))
% 109.14/108.86 [1045]~E(x10451,x10452)+E(f836(x10453,x10454,x10455,x10456,x10457,x10458,x10451,x10459),f836(x10453,x10454,x10455,x10456,x10457,x10458,x10452,x10459))
% 109.14/108.86 [1046]~E(x10461,x10462)+E(f836(x10463,x10464,x10465,x10466,x10467,x10468,x10469,x10461),f836(x10463,x10464,x10465,x10466,x10467,x10468,x10469,x10462))
% 109.14/108.86 [1047]~E(x10471,x10472)+E(f113(x10471,x10473,x10474,x10475),f113(x10472,x10473,x10474,x10475))
% 109.14/108.86 [1048]~E(x10481,x10482)+E(f113(x10483,x10481,x10484,x10485),f113(x10483,x10482,x10484,x10485))
% 109.14/108.86 [1049]~E(x10491,x10492)+E(f113(x10493,x10494,x10491,x10495),f113(x10493,x10494,x10492,x10495))
% 109.14/108.86 [1050]~E(x10501,x10502)+E(f113(x10503,x10504,x10505,x10501),f113(x10503,x10504,x10505,x10502))
% 109.14/108.86 [1051]~E(x10511,x10512)+E(f857(x10511,x10513,x10514),f857(x10512,x10513,x10514))
% 109.14/108.86 [1052]~E(x10521,x10522)+E(f857(x10523,x10521,x10524),f857(x10523,x10522,x10524))
% 109.14/108.86 [1053]~E(x10531,x10532)+E(f857(x10533,x10534,x10531),f857(x10533,x10534,x10532))
% 109.14/108.86 [1054]~E(x10541,x10542)+E(f690(x10541,x10543,x10544,x10545,x10546),f690(x10542,x10543,x10544,x10545,x10546))
% 109.14/108.86 [1055]~E(x10551,x10552)+E(f690(x10553,x10551,x10554,x10555,x10556),f690(x10553,x10552,x10554,x10555,x10556))
% 109.14/108.86 [1056]~E(x10561,x10562)+E(f690(x10563,x10564,x10561,x10565,x10566),f690(x10563,x10564,x10562,x10565,x10566))
% 109.14/108.86 [1057]~E(x10571,x10572)+E(f690(x10573,x10574,x10575,x10571,x10576),f690(x10573,x10574,x10575,x10572,x10576))
% 109.14/108.86 [1058]~E(x10581,x10582)+E(f690(x10583,x10584,x10585,x10586,x10581),f690(x10583,x10584,x10585,x10586,x10582))
% 109.14/108.86 [1059]~E(x10591,x10592)+E(f686(x10591,x10593,x10594),f686(x10592,x10593,x10594))
% 109.14/108.86 [1060]~E(x10601,x10602)+E(f686(x10603,x10601,x10604),f686(x10603,x10602,x10604))
% 109.14/108.86 [1061]~E(x10611,x10612)+E(f686(x10613,x10614,x10611),f686(x10613,x10614,x10612))
% 109.14/108.86 [1062]~E(x10621,x10622)+E(f623(x10621,x10623,x10624,x10625,x10626),f623(x10622,x10623,x10624,x10625,x10626))
% 109.14/108.86 [1063]~E(x10631,x10632)+E(f623(x10633,x10631,x10634,x10635,x10636),f623(x10633,x10632,x10634,x10635,x10636))
% 109.14/108.86 [1064]~E(x10641,x10642)+E(f623(x10643,x10644,x10641,x10645,x10646),f623(x10643,x10644,x10642,x10645,x10646))
% 109.14/108.86 [1065]~E(x10651,x10652)+E(f623(x10653,x10654,x10655,x10651,x10656),f623(x10653,x10654,x10655,x10652,x10656))
% 109.14/108.86 [1066]~E(x10661,x10662)+E(f623(x10663,x10664,x10665,x10666,x10661),f623(x10663,x10664,x10665,x10666,x10662))
% 109.14/108.86 [1067]~E(x10671,x10672)+E(f284(x10671,x10673),f284(x10672,x10673))
% 109.14/108.86 [1068]~E(x10681,x10682)+E(f284(x10683,x10681),f284(x10683,x10682))
% 109.14/108.86 [1069]~E(x10691,x10692)+E(f802(x10691),f802(x10692))
% 109.14/108.86 [1070]~E(x10701,x10702)+E(f727(x10701,x10703),f727(x10702,x10703))
% 109.14/108.86 [1071]~E(x10711,x10712)+E(f727(x10713,x10711),f727(x10713,x10712))
% 109.14/108.86 [1072]~E(x10721,x10722)+E(f712(x10721,x10723,x10724),f712(x10722,x10723,x10724))
% 109.14/108.86 [1073]~E(x10731,x10732)+E(f712(x10733,x10731,x10734),f712(x10733,x10732,x10734))
% 109.14/108.86 [1074]~E(x10741,x10742)+E(f712(x10743,x10744,x10741),f712(x10743,x10744,x10742))
% 109.14/108.86 [1075]~E(x10751,x10752)+E(f732(x10751,x10753),f732(x10752,x10753))
% 109.14/108.86 [1076]~E(x10761,x10762)+E(f732(x10763,x10761),f732(x10763,x10762))
% 109.14/108.86 [1077]~E(x10771,x10772)+E(f373(x10771,x10773,x10774),f373(x10772,x10773,x10774))
% 109.14/108.86 [1078]~E(x10781,x10782)+E(f373(x10783,x10781,x10784),f373(x10783,x10782,x10784))
% 109.14/108.86 [1079]~E(x10791,x10792)+E(f373(x10793,x10794,x10791),f373(x10793,x10794,x10792))
% 109.14/108.86 [1080]~E(x10801,x10802)+E(f773(x10801,x10803,x10804,x10805),f773(x10802,x10803,x10804,x10805))
% 109.14/108.86 [1081]~E(x10811,x10812)+E(f773(x10813,x10811,x10814,x10815),f773(x10813,x10812,x10814,x10815))
% 109.14/108.86 [1082]~E(x10821,x10822)+E(f773(x10823,x10824,x10821,x10825),f773(x10823,x10824,x10822,x10825))
% 109.14/108.86 [1083]~E(x10831,x10832)+E(f773(x10833,x10834,x10835,x10831),f773(x10833,x10834,x10835,x10832))
% 109.14/108.86 [1084]~E(x10841,x10842)+E(f115(x10841),f115(x10842))
% 109.14/108.86 [1085]~E(x10851,x10852)+E(f281(x10851,x10853,x10854,x10855),f281(x10852,x10853,x10854,x10855))
% 109.14/108.86 [1086]~E(x10861,x10862)+E(f281(x10863,x10861,x10864,x10865),f281(x10863,x10862,x10864,x10865))
% 109.14/108.86 [1087]~E(x10871,x10872)+E(f281(x10873,x10874,x10871,x10875),f281(x10873,x10874,x10872,x10875))
% 109.14/108.86 [1088]~E(x10881,x10882)+E(f281(x10883,x10884,x10885,x10881),f281(x10883,x10884,x10885,x10882))
% 109.14/108.86 [1089]~E(x10891,x10892)+E(f109(x10891,x10893,x10894),f109(x10892,x10893,x10894))
% 109.14/108.86 [1090]~E(x10901,x10902)+E(f109(x10903,x10901,x10904),f109(x10903,x10902,x10904))
% 109.14/108.86 [1091]~E(x10911,x10912)+E(f109(x10913,x10914,x10911),f109(x10913,x10914,x10912))
% 109.14/108.86 [1092]~E(x10921,x10922)+E(f366(x10921),f366(x10922))
% 109.14/108.86 [1093]~E(x10931,x10932)+E(f606(x10931,x10933,x10934,x10935,x10936,x10937),f606(x10932,x10933,x10934,x10935,x10936,x10937))
% 109.14/108.86 [1094]~E(x10941,x10942)+E(f606(x10943,x10941,x10944,x10945,x10946,x10947),f606(x10943,x10942,x10944,x10945,x10946,x10947))
% 109.14/108.86 [1095]~E(x10951,x10952)+E(f606(x10953,x10954,x10951,x10955,x10956,x10957),f606(x10953,x10954,x10952,x10955,x10956,x10957))
% 109.14/108.86 [1096]~E(x10961,x10962)+E(f606(x10963,x10964,x10965,x10961,x10966,x10967),f606(x10963,x10964,x10965,x10962,x10966,x10967))
% 109.14/108.86 [1097]~E(x10971,x10972)+E(f606(x10973,x10974,x10975,x10976,x10971,x10977),f606(x10973,x10974,x10975,x10976,x10972,x10977))
% 109.14/108.86 [1098]~E(x10981,x10982)+E(f606(x10983,x10984,x10985,x10986,x10987,x10981),f606(x10983,x10984,x10985,x10986,x10987,x10982))
% 109.14/108.86 [1099]~E(x10991,x10992)+E(f384(x10991),f384(x10992))
% 109.14/108.86 [1100]~E(x11001,x11002)+E(f379(x11001,x11003),f379(x11002,x11003))
% 109.14/108.86 [1101]~E(x11011,x11012)+E(f379(x11013,x11011),f379(x11013,x11012))
% 109.14/108.86 [1102]~E(x11021,x11022)+E(f652(x11021,x11023,x11024,x11025),f652(x11022,x11023,x11024,x11025))
% 109.14/108.86 [1103]~E(x11031,x11032)+E(f652(x11033,x11031,x11034,x11035),f652(x11033,x11032,x11034,x11035))
% 109.14/108.86 [1104]~E(x11041,x11042)+E(f652(x11043,x11044,x11041,x11045),f652(x11043,x11044,x11042,x11045))
% 109.14/108.86 [1105]~E(x11051,x11052)+E(f652(x11053,x11054,x11055,x11051),f652(x11053,x11054,x11055,x11052))
% 109.14/108.86 [1106]~E(x11061,x11062)+E(f37(x11061),f37(x11062))
% 109.14/108.86 [1107]~E(x11071,x11072)+E(f662(x11071,x11073),f662(x11072,x11073))
% 109.14/108.86 [1108]~E(x11081,x11082)+E(f662(x11083,x11081),f662(x11083,x11082))
% 109.14/108.86 [1109]~E(x11091,x11092)+E(f587(x11091,x11093,x11094,x11095,x11096,x11097),f587(x11092,x11093,x11094,x11095,x11096,x11097))
% 109.14/108.86 [1110]~E(x11101,x11102)+E(f587(x11103,x11101,x11104,x11105,x11106,x11107),f587(x11103,x11102,x11104,x11105,x11106,x11107))
% 109.14/108.86 [1111]~E(x11111,x11112)+E(f587(x11113,x11114,x11111,x11115,x11116,x11117),f587(x11113,x11114,x11112,x11115,x11116,x11117))
% 109.14/108.86 [1112]~E(x11121,x11122)+E(f587(x11123,x11124,x11125,x11121,x11126,x11127),f587(x11123,x11124,x11125,x11122,x11126,x11127))
% 109.14/108.86 [1113]~E(x11131,x11132)+E(f587(x11133,x11134,x11135,x11136,x11131,x11137),f587(x11133,x11134,x11135,x11136,x11132,x11137))
% 109.14/108.86 [1114]~E(x11141,x11142)+E(f587(x11143,x11144,x11145,x11146,x11147,x11141),f587(x11143,x11144,x11145,x11146,x11147,x11142))
% 109.14/108.86 [1115]~E(x11151,x11152)+E(f875(x11151,x11153,x11154),f875(x11152,x11153,x11154))
% 109.14/108.86 [1116]~E(x11161,x11162)+E(f875(x11163,x11161,x11164),f875(x11163,x11162,x11164))
% 109.14/108.86 [1117]~E(x11171,x11172)+E(f875(x11173,x11174,x11171),f875(x11173,x11174,x11172))
% 109.14/108.86 [1118]~E(x11181,x11182)+E(f568(x11181,x11183),f568(x11182,x11183))
% 109.14/108.86 [1119]~E(x11191,x11192)+E(f568(x11193,x11191),f568(x11193,x11192))
% 109.14/108.86 [1120]~E(x11201,x11202)+E(f119(x11201,x11203),f119(x11202,x11203))
% 109.14/108.86 [1121]~E(x11211,x11212)+E(f119(x11213,x11211),f119(x11213,x11212))
% 109.14/108.86 [1122]~E(x11221,x11222)+E(f123(x11221,x11223),f123(x11222,x11223))
% 109.14/108.86 [1123]~E(x11231,x11232)+E(f123(x11233,x11231),f123(x11233,x11232))
% 109.14/108.86 [1124]~E(x11241,x11242)+E(f740(x11241,x11243,x11244,x11245,x11246),f740(x11242,x11243,x11244,x11245,x11246))
% 109.14/108.86 [1125]~E(x11251,x11252)+E(f740(x11253,x11251,x11254,x11255,x11256),f740(x11253,x11252,x11254,x11255,x11256))
% 109.14/108.86 [1126]~E(x11261,x11262)+E(f740(x11263,x11264,x11261,x11265,x11266),f740(x11263,x11264,x11262,x11265,x11266))
% 109.14/108.86 [1127]~E(x11271,x11272)+E(f740(x11273,x11274,x11275,x11271,x11276),f740(x11273,x11274,x11275,x11272,x11276))
% 109.14/108.86 [1128]~E(x11281,x11282)+E(f740(x11283,x11284,x11285,x11286,x11281),f740(x11283,x11284,x11285,x11286,x11282))
% 109.14/108.86 [1129]~E(x11291,x11292)+E(f583(x11291,x11293,x11294),f583(x11292,x11293,x11294))
% 109.14/108.86 [1130]~E(x11301,x11302)+E(f583(x11303,x11301,x11304),f583(x11303,x11302,x11304))
% 109.14/108.86 [1131]~E(x11311,x11312)+E(f583(x11313,x11314,x11311),f583(x11313,x11314,x11312))
% 109.14/108.86 [1132]~E(x11321,x11322)+E(f557(x11321,x11323,x11324),f557(x11322,x11323,x11324))
% 109.14/108.86 [1133]~E(x11331,x11332)+E(f557(x11333,x11331,x11334),f557(x11333,x11332,x11334))
% 109.14/108.86 [1134]~E(x11341,x11342)+E(f557(x11343,x11344,x11341),f557(x11343,x11344,x11342))
% 109.14/108.86 [1135]~E(x11351,x11352)+E(f463(x11351,x11353,x11354),f463(x11352,x11353,x11354))
% 109.14/108.86 [1136]~E(x11361,x11362)+E(f463(x11363,x11361,x11364),f463(x11363,x11362,x11364))
% 109.14/108.86 [1137]~E(x11371,x11372)+E(f463(x11373,x11374,x11371),f463(x11373,x11374,x11372))
% 109.14/108.86 [1138]~E(x11381,x11382)+E(f607(x11381,x11383,x11384,x11385,x11386,x11387),f607(x11382,x11383,x11384,x11385,x11386,x11387))
% 109.14/108.86 [1139]~E(x11391,x11392)+E(f607(x11393,x11391,x11394,x11395,x11396,x11397),f607(x11393,x11392,x11394,x11395,x11396,x11397))
% 109.14/108.86 [1140]~E(x11401,x11402)+E(f607(x11403,x11404,x11401,x11405,x11406,x11407),f607(x11403,x11404,x11402,x11405,x11406,x11407))
% 109.14/108.86 [1141]~E(x11411,x11412)+E(f607(x11413,x11414,x11415,x11411,x11416,x11417),f607(x11413,x11414,x11415,x11412,x11416,x11417))
% 109.14/108.86 [1142]~E(x11421,x11422)+E(f607(x11423,x11424,x11425,x11426,x11421,x11427),f607(x11423,x11424,x11425,x11426,x11422,x11427))
% 109.14/108.86 [1143]~E(x11431,x11432)+E(f607(x11433,x11434,x11435,x11436,x11437,x11431),f607(x11433,x11434,x11435,x11436,x11437,x11432))
% 109.14/108.86 [1144]~E(x11441,x11442)+E(f718(x11441,x11443,x11444,x11445),f718(x11442,x11443,x11444,x11445))
% 109.14/108.86 [1145]~E(x11451,x11452)+E(f718(x11453,x11451,x11454,x11455),f718(x11453,x11452,x11454,x11455))
% 109.14/108.86 [1146]~E(x11461,x11462)+E(f718(x11463,x11464,x11461,x11465),f718(x11463,x11464,x11462,x11465))
% 109.14/108.86 [1147]~E(x11471,x11472)+E(f718(x11473,x11474,x11475,x11471),f718(x11473,x11474,x11475,x11472))
% 109.14/108.86 [1148]~E(x11481,x11482)+E(f896(x11481,x11483,x11484),f896(x11482,x11483,x11484))
% 109.14/108.86 [1149]~E(x11491,x11492)+E(f896(x11493,x11491,x11494),f896(x11493,x11492,x11494))
% 109.14/108.86 [1150]~E(x11501,x11502)+E(f896(x11503,x11504,x11501),f896(x11503,x11504,x11502))
% 109.14/108.86 [1151]~E(x11511,x11512)+E(f865(x11511,x11513,x11514,x11515),f865(x11512,x11513,x11514,x11515))
% 109.14/108.86 [1152]~E(x11521,x11522)+E(f865(x11523,x11521,x11524,x11525),f865(x11523,x11522,x11524,x11525))
% 109.14/108.86 [1153]~E(x11531,x11532)+E(f865(x11533,x11534,x11531,x11535),f865(x11533,x11534,x11532,x11535))
% 109.14/108.86 [1154]~E(x11541,x11542)+E(f865(x11543,x11544,x11545,x11541),f865(x11543,x11544,x11545,x11542))
% 109.14/108.86 [1155]~E(x11551,x11552)+E(f785(x11551,x11553,x11554,x11555,x11556,x11557,x11558),f785(x11552,x11553,x11554,x11555,x11556,x11557,x11558))
% 109.14/108.86 [1156]~E(x11561,x11562)+E(f785(x11563,x11561,x11564,x11565,x11566,x11567,x11568),f785(x11563,x11562,x11564,x11565,x11566,x11567,x11568))
% 109.14/108.86 [1157]~E(x11571,x11572)+E(f785(x11573,x11574,x11571,x11575,x11576,x11577,x11578),f785(x11573,x11574,x11572,x11575,x11576,x11577,x11578))
% 109.14/108.86 [1158]~E(x11581,x11582)+E(f785(x11583,x11584,x11585,x11581,x11586,x11587,x11588),f785(x11583,x11584,x11585,x11582,x11586,x11587,x11588))
% 109.14/108.86 [1159]~E(x11591,x11592)+E(f785(x11593,x11594,x11595,x11596,x11591,x11597,x11598),f785(x11593,x11594,x11595,x11596,x11592,x11597,x11598))
% 109.14/108.86 [1160]~E(x11601,x11602)+E(f785(x11603,x11604,x11605,x11606,x11607,x11601,x11608),f785(x11603,x11604,x11605,x11606,x11607,x11602,x11608))
% 109.14/108.86 [1161]~E(x11611,x11612)+E(f785(x11613,x11614,x11615,x11616,x11617,x11618,x11611),f785(x11613,x11614,x11615,x11616,x11617,x11618,x11612))
% 109.14/108.86 [1162]~E(x11621,x11622)+E(f312(x11621,x11623,x11624),f312(x11622,x11623,x11624))
% 109.14/108.86 [1163]~E(x11631,x11632)+E(f312(x11633,x11631,x11634),f312(x11633,x11632,x11634))
% 109.14/108.86 [1164]~E(x11641,x11642)+E(f312(x11643,x11644,x11641),f312(x11643,x11644,x11642))
% 109.14/108.86 [1165]~E(x11651,x11652)+E(f413(x11651,x11653,x11654),f413(x11652,x11653,x11654))
% 109.14/108.86 [1166]~E(x11661,x11662)+E(f413(x11663,x11661,x11664),f413(x11663,x11662,x11664))
% 109.14/108.86 [1167]~E(x11671,x11672)+E(f413(x11673,x11674,x11671),f413(x11673,x11674,x11672))
% 109.14/108.86 [1168]~E(x11681,x11682)+E(f239(x11681,x11683),f239(x11682,x11683))
% 109.14/108.86 [1169]~E(x11691,x11692)+E(f239(x11693,x11691),f239(x11693,x11692))
% 109.14/108.86 [1170]~E(x11701,x11702)+E(f190(x11701,x11703),f190(x11702,x11703))
% 109.14/108.86 [1171]~E(x11711,x11712)+E(f190(x11713,x11711),f190(x11713,x11712))
% 109.14/108.86 [1172]~E(x11721,x11722)+E(f341(x11721,x11723,x11724),f341(x11722,x11723,x11724))
% 109.14/108.86 [1173]~E(x11731,x11732)+E(f341(x11733,x11731,x11734),f341(x11733,x11732,x11734))
% 109.14/108.86 [1174]~E(x11741,x11742)+E(f341(x11743,x11744,x11741),f341(x11743,x11744,x11742))
% 109.14/108.86 [1175]~E(x11751,x11752)+E(f120(x11751),f120(x11752))
% 109.14/108.86 [1176]~E(x11761,x11762)+E(f904(x11761,x11763,x11764,x11765,x11766,x11767,x11768),f904(x11762,x11763,x11764,x11765,x11766,x11767,x11768))
% 109.14/108.86 [1177]~E(x11771,x11772)+E(f904(x11773,x11771,x11774,x11775,x11776,x11777,x11778),f904(x11773,x11772,x11774,x11775,x11776,x11777,x11778))
% 109.14/108.86 [1178]~E(x11781,x11782)+E(f904(x11783,x11784,x11781,x11785,x11786,x11787,x11788),f904(x11783,x11784,x11782,x11785,x11786,x11787,x11788))
% 109.14/108.86 [1179]~E(x11791,x11792)+E(f904(x11793,x11794,x11795,x11791,x11796,x11797,x11798),f904(x11793,x11794,x11795,x11792,x11796,x11797,x11798))
% 109.14/108.86 [1180]~E(x11801,x11802)+E(f904(x11803,x11804,x11805,x11806,x11801,x11807,x11808),f904(x11803,x11804,x11805,x11806,x11802,x11807,x11808))
% 109.14/108.86 [1181]~E(x11811,x11812)+E(f904(x11813,x11814,x11815,x11816,x11817,x11811,x11818),f904(x11813,x11814,x11815,x11816,x11817,x11812,x11818))
% 109.14/108.86 [1182]~E(x11821,x11822)+E(f904(x11823,x11824,x11825,x11826,x11827,x11828,x11821),f904(x11823,x11824,x11825,x11826,x11827,x11828,x11822))
% 109.14/108.86 [1183]~E(x11831,x11832)+E(f647(x11831,x11833,x11834,x11835),f647(x11832,x11833,x11834,x11835))
% 109.14/108.86 [1184]~E(x11841,x11842)+E(f647(x11843,x11841,x11844,x11845),f647(x11843,x11842,x11844,x11845))
% 109.14/108.86 [1185]~E(x11851,x11852)+E(f647(x11853,x11854,x11851,x11855),f647(x11853,x11854,x11852,x11855))
% 109.14/108.86 [1186]~E(x11861,x11862)+E(f647(x11863,x11864,x11865,x11861),f647(x11863,x11864,x11865,x11862))
% 109.14/108.86 [1187]~E(x11871,x11872)+E(f784(x11871,x11873,x11874,x11875,x11876,x11877,x11878),f784(x11872,x11873,x11874,x11875,x11876,x11877,x11878))
% 109.14/108.86 [1188]~E(x11881,x11882)+E(f784(x11883,x11881,x11884,x11885,x11886,x11887,x11888),f784(x11883,x11882,x11884,x11885,x11886,x11887,x11888))
% 109.14/108.86 [1189]~E(x11891,x11892)+E(f784(x11893,x11894,x11891,x11895,x11896,x11897,x11898),f784(x11893,x11894,x11892,x11895,x11896,x11897,x11898))
% 109.14/108.86 [1190]~E(x11901,x11902)+E(f784(x11903,x11904,x11905,x11901,x11906,x11907,x11908),f784(x11903,x11904,x11905,x11902,x11906,x11907,x11908))
% 109.14/108.86 [1191]~E(x11911,x11912)+E(f784(x11913,x11914,x11915,x11916,x11911,x11917,x11918),f784(x11913,x11914,x11915,x11916,x11912,x11917,x11918))
% 109.14/108.86 [1192]~E(x11921,x11922)+E(f784(x11923,x11924,x11925,x11926,x11927,x11921,x11928),f784(x11923,x11924,x11925,x11926,x11927,x11922,x11928))
% 109.14/108.86 [1193]~E(x11931,x11932)+E(f784(x11933,x11934,x11935,x11936,x11937,x11938,x11931),f784(x11933,x11934,x11935,x11936,x11937,x11938,x11932))
% 109.14/108.86 [1194]~E(x11941,x11942)+E(f286(x11941,x11943,x11944),f286(x11942,x11943,x11944))
% 109.14/108.86 [1195]~E(x11951,x11952)+E(f286(x11953,x11951,x11954),f286(x11953,x11952,x11954))
% 109.14/108.86 [1196]~E(x11961,x11962)+E(f286(x11963,x11964,x11961),f286(x11963,x11964,x11962))
% 109.14/108.86 [1197]~E(x11971,x11972)+E(f761(x11971,x11973,x11974),f761(x11972,x11973,x11974))
% 109.14/108.86 [1198]~E(x11981,x11982)+E(f761(x11983,x11981,x11984),f761(x11983,x11982,x11984))
% 109.14/108.86 [1199]~E(x11991,x11992)+E(f761(x11993,x11994,x11991),f761(x11993,x11994,x11992))
% 109.14/108.86 [1200]~E(x12001,x12002)+E(f348(x12001,x12003,x12004),f348(x12002,x12003,x12004))
% 109.14/108.86 [1201]~E(x12011,x12012)+E(f348(x12013,x12011,x12014),f348(x12013,x12012,x12014))
% 109.14/108.86 [1202]~E(x12021,x12022)+E(f348(x12023,x12024,x12021),f348(x12023,x12024,x12022))
% 109.14/108.86 [1203]~E(x12031,x12032)+E(f774(x12031,x12033,x12034,x12035),f774(x12032,x12033,x12034,x12035))
% 109.14/108.86 [1204]~E(x12041,x12042)+E(f774(x12043,x12041,x12044,x12045),f774(x12043,x12042,x12044,x12045))
% 109.14/108.86 [1205]~E(x12051,x12052)+E(f774(x12053,x12054,x12051,x12055),f774(x12053,x12054,x12052,x12055))
% 109.14/108.86 [1206]~E(x12061,x12062)+E(f774(x12063,x12064,x12065,x12061),f774(x12063,x12064,x12065,x12062))
% 109.14/108.86 [1207]~E(x12071,x12072)+E(f578(x12071),f578(x12072))
% 109.14/108.86 [1208]~E(x12081,x12082)+E(f445(x12081,x12083),f445(x12082,x12083))
% 109.14/108.86 [1209]~E(x12091,x12092)+E(f445(x12093,x12091),f445(x12093,x12092))
% 109.14/108.86 [1210]~E(x12101,x12102)+E(f175(x12101,x12103,x12104),f175(x12102,x12103,x12104))
% 109.14/108.86 [1211]~E(x12111,x12112)+E(f175(x12113,x12111,x12114),f175(x12113,x12112,x12114))
% 109.14/108.86 [1212]~E(x12121,x12122)+E(f175(x12123,x12124,x12121),f175(x12123,x12124,x12122))
% 109.14/108.86 [1213]~E(x12131,x12132)+E(f749(x12131,x12133,x12134,x12135),f749(x12132,x12133,x12134,x12135))
% 109.14/108.86 [1214]~E(x12141,x12142)+E(f749(x12143,x12141,x12144,x12145),f749(x12143,x12142,x12144,x12145))
% 109.14/108.86 [1215]~E(x12151,x12152)+E(f749(x12153,x12154,x12151,x12155),f749(x12153,x12154,x12152,x12155))
% 109.14/108.86 [1216]~E(x12161,x12162)+E(f749(x12163,x12164,x12165,x12161),f749(x12163,x12164,x12165,x12162))
% 109.14/108.86 [1217]~E(x12171,x12172)+E(f486(x12171,x12173),f486(x12172,x12173))
% 109.14/108.86 [1218]~E(x12181,x12182)+E(f486(x12183,x12181),f486(x12183,x12182))
% 109.14/108.86 [1219]~E(x12191,x12192)+E(f736(x12191,x12193,x12194,x12195),f736(x12192,x12193,x12194,x12195))
% 109.14/108.86 [1220]~E(x12201,x12202)+E(f736(x12203,x12201,x12204,x12205),f736(x12203,x12202,x12204,x12205))
% 109.14/108.86 [1221]~E(x12211,x12212)+E(f736(x12213,x12214,x12211,x12215),f736(x12213,x12214,x12212,x12215))
% 109.14/108.86 [1222]~E(x12221,x12222)+E(f736(x12223,x12224,x12225,x12221),f736(x12223,x12224,x12225,x12222))
% 109.14/108.86 [1223]~E(x12231,x12232)+E(f164(x12231,x12233,x12234),f164(x12232,x12233,x12234))
% 109.14/108.86 [1224]~E(x12241,x12242)+E(f164(x12243,x12241,x12244),f164(x12243,x12242,x12244))
% 109.14/108.86 [1225]~E(x12251,x12252)+E(f164(x12253,x12254,x12251),f164(x12253,x12254,x12252))
% 109.14/108.86 [1226]~E(x12261,x12262)+E(f360(x12261,x12263,x12264,x12265),f360(x12262,x12263,x12264,x12265))
% 109.14/108.86 [1227]~E(x12271,x12272)+E(f360(x12273,x12271,x12274,x12275),f360(x12273,x12272,x12274,x12275))
% 109.14/108.86 [1228]~E(x12281,x12282)+E(f360(x12283,x12284,x12281,x12285),f360(x12283,x12284,x12282,x12285))
% 109.14/108.86 [1229]~E(x12291,x12292)+E(f360(x12293,x12294,x12295,x12291),f360(x12293,x12294,x12295,x12292))
% 109.14/108.86 [1230]~E(x12301,x12302)+E(f541(x12301,x12303,x12304),f541(x12302,x12303,x12304))
% 109.14/108.86 [1231]~E(x12311,x12312)+E(f541(x12313,x12311,x12314),f541(x12313,x12312,x12314))
% 109.14/108.86 [1232]~E(x12321,x12322)+E(f541(x12323,x12324,x12321),f541(x12323,x12324,x12322))
% 109.14/108.86 [1233]~E(x12331,x12332)+E(f503(x12331,x12333,x12334,x12335,x12336),f503(x12332,x12333,x12334,x12335,x12336))
% 109.14/108.86 [1234]~E(x12341,x12342)+E(f503(x12343,x12341,x12344,x12345,x12346),f503(x12343,x12342,x12344,x12345,x12346))
% 109.14/108.86 [1235]~E(x12351,x12352)+E(f503(x12353,x12354,x12351,x12355,x12356),f503(x12353,x12354,x12352,x12355,x12356))
% 109.14/108.86 [1236]~E(x12361,x12362)+E(f503(x12363,x12364,x12365,x12361,x12366),f503(x12363,x12364,x12365,x12362,x12366))
% 109.14/108.86 [1237]~E(x12371,x12372)+E(f503(x12373,x12374,x12375,x12376,x12371),f503(x12373,x12374,x12375,x12376,x12372))
% 109.14/108.86 [1238]~E(x12381,x12382)+E(f107(x12381,x12383,x12384),f107(x12382,x12383,x12384))
% 109.14/108.87 [1239]~E(x12391,x12392)+E(f107(x12393,x12391,x12394),f107(x12393,x12392,x12394))
% 109.14/108.87 [1240]~E(x12401,x12402)+E(f107(x12403,x12404,x12401),f107(x12403,x12404,x12402))
% 109.14/108.87 [1241]~E(x12411,x12412)+E(f770(x12411,x12413,x12414),f770(x12412,x12413,x12414))
% 109.14/108.87 [1242]~E(x12421,x12422)+E(f770(x12423,x12421,x12424),f770(x12423,x12422,x12424))
% 109.14/108.87 [1243]~E(x12431,x12432)+E(f770(x12433,x12434,x12431),f770(x12433,x12434,x12432))
% 109.14/108.87 [1244]~E(x12441,x12442)+E(f745(x12441,x12443),f745(x12442,x12443))
% 109.14/108.87 [1245]~E(x12451,x12452)+E(f745(x12453,x12451),f745(x12453,x12452))
% 109.14/108.87 [1246]~E(x12461,x12462)+E(f228(x12461,x12463),f228(x12462,x12463))
% 109.14/108.87 [1247]~E(x12471,x12472)+E(f228(x12473,x12471),f228(x12473,x12472))
% 109.14/108.87 [1248]~E(x12481,x12482)+E(f539(x12481),f539(x12482))
% 109.14/108.87 [1249]~E(x12491,x12492)+E(f776(x12491,x12493,x12494,x12495),f776(x12492,x12493,x12494,x12495))
% 109.14/108.87 [1250]~E(x12501,x12502)+E(f776(x12503,x12501,x12504,x12505),f776(x12503,x12502,x12504,x12505))
% 109.14/108.87 [1251]~E(x12511,x12512)+E(f776(x12513,x12514,x12511,x12515),f776(x12513,x12514,x12512,x12515))
% 109.14/108.87 [1252]~E(x12521,x12522)+E(f776(x12523,x12524,x12525,x12521),f776(x12523,x12524,x12525,x12522))
% 109.14/108.87 [1253]~E(x12531,x12532)+E(f374(x12531,x12533,x12534),f374(x12532,x12533,x12534))
% 109.14/108.87 [1254]~E(x12541,x12542)+E(f374(x12543,x12541,x12544),f374(x12543,x12542,x12544))
% 109.14/108.87 [1255]~E(x12551,x12552)+E(f374(x12553,x12554,x12551),f374(x12553,x12554,x12552))
% 109.14/108.87 [1256]~E(x12561,x12562)+E(f454(x12561,x12563),f454(x12562,x12563))
% 109.14/108.87 [1257]~E(x12571,x12572)+E(f454(x12573,x12571),f454(x12573,x12572))
% 109.14/108.87 [1258]~E(x12581,x12582)+E(f329(x12581,x12583,x12584),f329(x12582,x12583,x12584))
% 109.14/108.87 [1259]~E(x12591,x12592)+E(f329(x12593,x12591,x12594),f329(x12593,x12592,x12594))
% 109.14/108.87 [1260]~E(x12601,x12602)+E(f329(x12603,x12604,x12601),f329(x12603,x12604,x12602))
% 109.14/108.87 [1261]~E(x12611,x12612)+E(f655(x12611,x12613,x12614),f655(x12612,x12613,x12614))
% 109.14/108.87 [1262]~E(x12621,x12622)+E(f655(x12623,x12621,x12624),f655(x12623,x12622,x12624))
% 109.14/108.87 [1263]~E(x12631,x12632)+E(f655(x12633,x12634,x12631),f655(x12633,x12634,x12632))
% 109.14/108.87 [1264]~E(x12641,x12642)+E(f515(x12641),f515(x12642))
% 109.14/108.87 [1265]~E(x12651,x12652)+E(f841(x12651,x12653,x12654,x12655,x12656,x12657,x12658,x12659),f841(x12652,x12653,x12654,x12655,x12656,x12657,x12658,x12659))
% 109.14/108.87 [1266]~E(x12661,x12662)+E(f841(x12663,x12661,x12664,x12665,x12666,x12667,x12668,x12669),f841(x12663,x12662,x12664,x12665,x12666,x12667,x12668,x12669))
% 109.14/108.87 [1267]~E(x12671,x12672)+E(f841(x12673,x12674,x12671,x12675,x12676,x12677,x12678,x12679),f841(x12673,x12674,x12672,x12675,x12676,x12677,x12678,x12679))
% 109.14/108.87 [1268]~E(x12681,x12682)+E(f841(x12683,x12684,x12685,x12681,x12686,x12687,x12688,x12689),f841(x12683,x12684,x12685,x12682,x12686,x12687,x12688,x12689))
% 109.14/108.87 [1269]~E(x12691,x12692)+E(f841(x12693,x12694,x12695,x12696,x12691,x12697,x12698,x12699),f841(x12693,x12694,x12695,x12696,x12692,x12697,x12698,x12699))
% 109.14/108.87 [1270]~E(x12701,x12702)+E(f841(x12703,x12704,x12705,x12706,x12707,x12701,x12708,x12709),f841(x12703,x12704,x12705,x12706,x12707,x12702,x12708,x12709))
% 109.14/108.87 [1271]~E(x12711,x12712)+E(f841(x12713,x12714,x12715,x12716,x12717,x12718,x12711,x12719),f841(x12713,x12714,x12715,x12716,x12717,x12718,x12712,x12719))
% 109.14/108.87 [1272]~E(x12721,x12722)+E(f841(x12723,x12724,x12725,x12726,x12727,x12728,x12729,x12721),f841(x12723,x12724,x12725,x12726,x12727,x12728,x12729,x12722))
% 109.14/108.87 [1273]~E(x12731,x12732)+E(f742(x12731,x12733,x12734,x12735,x12736,x12737,x12738),f742(x12732,x12733,x12734,x12735,x12736,x12737,x12738))
% 109.14/108.87 [1274]~E(x12741,x12742)+E(f742(x12743,x12741,x12744,x12745,x12746,x12747,x12748),f742(x12743,x12742,x12744,x12745,x12746,x12747,x12748))
% 109.14/108.87 [1275]~E(x12751,x12752)+E(f742(x12753,x12754,x12751,x12755,x12756,x12757,x12758),f742(x12753,x12754,x12752,x12755,x12756,x12757,x12758))
% 109.14/108.87 [1276]~E(x12761,x12762)+E(f742(x12763,x12764,x12765,x12761,x12766,x12767,x12768),f742(x12763,x12764,x12765,x12762,x12766,x12767,x12768))
% 109.14/108.87 [1277]~E(x12771,x12772)+E(f742(x12773,x12774,x12775,x12776,x12771,x12777,x12778),f742(x12773,x12774,x12775,x12776,x12772,x12777,x12778))
% 109.14/108.87 [1278]~E(x12781,x12782)+E(f742(x12783,x12784,x12785,x12786,x12787,x12781,x12788),f742(x12783,x12784,x12785,x12786,x12787,x12782,x12788))
% 109.14/108.87 [1279]~E(x12791,x12792)+E(f742(x12793,x12794,x12795,x12796,x12797,x12798,x12791),f742(x12793,x12794,x12795,x12796,x12797,x12798,x12792))
% 109.14/108.87 [1280]~E(x12801,x12802)+E(f592(x12801,x12803,x12804),f592(x12802,x12803,x12804))
% 109.14/108.87 [1281]~E(x12811,x12812)+E(f592(x12813,x12811,x12814),f592(x12813,x12812,x12814))
% 109.14/108.87 [1282]~E(x12821,x12822)+E(f592(x12823,x12824,x12821),f592(x12823,x12824,x12822))
% 109.14/108.87 [1283]~E(x12831,x12832)+E(f431(x12831,x12833,x12834,x12835),f431(x12832,x12833,x12834,x12835))
% 109.14/108.87 [1284]~E(x12841,x12842)+E(f431(x12843,x12841,x12844,x12845),f431(x12843,x12842,x12844,x12845))
% 109.14/108.87 [1285]~E(x12851,x12852)+E(f431(x12853,x12854,x12851,x12855),f431(x12853,x12854,x12852,x12855))
% 109.14/108.87 [1286]~E(x12861,x12862)+E(f431(x12863,x12864,x12865,x12861),f431(x12863,x12864,x12865,x12862))
% 109.14/108.87 [1287]~E(x12871,x12872)+E(f350(x12871,x12873,x12874,x12875),f350(x12872,x12873,x12874,x12875))
% 109.14/108.87 [1288]~E(x12881,x12882)+E(f350(x12883,x12881,x12884,x12885),f350(x12883,x12882,x12884,x12885))
% 109.14/108.87 [1289]~E(x12891,x12892)+E(f350(x12893,x12894,x12891,x12895),f350(x12893,x12894,x12892,x12895))
% 109.14/108.87 [1290]~E(x12901,x12902)+E(f350(x12903,x12904,x12905,x12901),f350(x12903,x12904,x12905,x12902))
% 109.14/108.87 [1291]~E(x12911,x12912)+E(f262(x12911,x12913,x12914,x12915),f262(x12912,x12913,x12914,x12915))
% 109.14/108.87 [1292]~E(x12921,x12922)+E(f262(x12923,x12921,x12924,x12925),f262(x12923,x12922,x12924,x12925))
% 109.14/108.87 [1293]~E(x12931,x12932)+E(f262(x12933,x12934,x12931,x12935),f262(x12933,x12934,x12932,x12935))
% 109.14/108.87 [1294]~E(x12941,x12942)+E(f262(x12943,x12944,x12945,x12941),f262(x12943,x12944,x12945,x12942))
% 109.14/108.87 [1295]~E(x12951,x12952)+E(f390(x12951,x12953,x12954),f390(x12952,x12953,x12954))
% 109.14/108.87 [1296]~E(x12961,x12962)+E(f390(x12963,x12961,x12964),f390(x12963,x12962,x12964))
% 109.14/108.87 [1297]~E(x12971,x12972)+E(f390(x12973,x12974,x12971),f390(x12973,x12974,x12972))
% 109.14/108.87 [1298]~E(x12981,x12982)+E(f303(x12981,x12983),f303(x12982,x12983))
% 109.14/108.87 [1299]~E(x12991,x12992)+E(f303(x12993,x12991),f303(x12993,x12992))
% 109.14/108.87 [1300]~E(x13001,x13002)+E(f619(x13001,x13003,x13004),f619(x13002,x13003,x13004))
% 109.14/108.87 [1301]~E(x13011,x13012)+E(f619(x13013,x13011,x13014),f619(x13013,x13012,x13014))
% 109.14/108.87 [1302]~E(x13021,x13022)+E(f619(x13023,x13024,x13021),f619(x13023,x13024,x13022))
% 109.14/108.87 [1303]~E(x13031,x13032)+E(f146(x13031,x13033,x13034),f146(x13032,x13033,x13034))
% 109.14/108.87 [1304]~E(x13041,x13042)+E(f146(x13043,x13041,x13044),f146(x13043,x13042,x13044))
% 109.14/108.87 [1305]~E(x13051,x13052)+E(f146(x13053,x13054,x13051),f146(x13053,x13054,x13052))
% 109.14/108.87 [1306]~E(x13061,x13062)+E(f222(x13061,x13063,x13064,x13065),f222(x13062,x13063,x13064,x13065))
% 109.14/108.87 [1307]~E(x13071,x13072)+E(f222(x13073,x13071,x13074,x13075),f222(x13073,x13072,x13074,x13075))
% 109.14/108.87 [1308]~E(x13081,x13082)+E(f222(x13083,x13084,x13081,x13085),f222(x13083,x13084,x13082,x13085))
% 109.14/108.87 [1309]~E(x13091,x13092)+E(f222(x13093,x13094,x13095,x13091),f222(x13093,x13094,x13095,x13092))
% 109.14/108.87 [1310]~E(x13101,x13102)+E(f122(x13101,x13103,x13104,x13105),f122(x13102,x13103,x13104,x13105))
% 109.14/108.87 [1311]~E(x13111,x13112)+E(f122(x13113,x13111,x13114,x13115),f122(x13113,x13112,x13114,x13115))
% 109.14/108.87 [1312]~E(x13121,x13122)+E(f122(x13123,x13124,x13121,x13125),f122(x13123,x13124,x13122,x13125))
% 109.14/108.87 [1313]~E(x13131,x13132)+E(f122(x13133,x13134,x13135,x13131),f122(x13133,x13134,x13135,x13132))
% 109.14/108.87 [1314]~E(x13141,x13142)+E(f674(x13141,x13143,x13144,x13145,x13146),f674(x13142,x13143,x13144,x13145,x13146))
% 109.14/108.87 [1315]~E(x13151,x13152)+E(f674(x13153,x13151,x13154,x13155,x13156),f674(x13153,x13152,x13154,x13155,x13156))
% 109.14/108.87 [1316]~E(x13161,x13162)+E(f674(x13163,x13164,x13161,x13165,x13166),f674(x13163,x13164,x13162,x13165,x13166))
% 109.14/108.87 [1317]~E(x13171,x13172)+E(f674(x13173,x13174,x13175,x13171,x13176),f674(x13173,x13174,x13175,x13172,x13176))
% 109.14/108.87 [1318]~E(x13181,x13182)+E(f674(x13183,x13184,x13185,x13186,x13181),f674(x13183,x13184,x13185,x13186,x13182))
% 109.14/108.87 [1319]~E(x13191,x13192)+E(f552(x13191,x13193,x13194,x13195,x13196,x13197,x13198,x13199),f552(x13192,x13193,x13194,x13195,x13196,x13197,x13198,x13199))
% 109.14/108.87 [1320]~E(x13201,x13202)+E(f552(x13203,x13201,x13204,x13205,x13206,x13207,x13208,x13209),f552(x13203,x13202,x13204,x13205,x13206,x13207,x13208,x13209))
% 109.14/108.87 [1321]~E(x13211,x13212)+E(f552(x13213,x13214,x13211,x13215,x13216,x13217,x13218,x13219),f552(x13213,x13214,x13212,x13215,x13216,x13217,x13218,x13219))
% 109.14/108.87 [1322]~E(x13221,x13222)+E(f552(x13223,x13224,x13225,x13221,x13226,x13227,x13228,x13229),f552(x13223,x13224,x13225,x13222,x13226,x13227,x13228,x13229))
% 109.14/108.87 [1323]~E(x13231,x13232)+E(f552(x13233,x13234,x13235,x13236,x13231,x13237,x13238,x13239),f552(x13233,x13234,x13235,x13236,x13232,x13237,x13238,x13239))
% 109.14/108.87 [1324]~E(x13241,x13242)+E(f552(x13243,x13244,x13245,x13246,x13247,x13241,x13248,x13249),f552(x13243,x13244,x13245,x13246,x13247,x13242,x13248,x13249))
% 109.14/108.87 [1325]~E(x13251,x13252)+E(f552(x13253,x13254,x13255,x13256,x13257,x13258,x13251,x13259),f552(x13253,x13254,x13255,x13256,x13257,x13258,x13252,x13259))
% 109.14/108.87 [1326]~E(x13261,x13262)+E(f552(x13263,x13264,x13265,x13266,x13267,x13268,x13269,x13261),f552(x13263,x13264,x13265,x13266,x13267,x13268,x13269,x13262))
% 109.14/108.87 [1327]~E(x13271,x13272)+E(f617(x13271,x13273,x13274),f617(x13272,x13273,x13274))
% 109.14/108.87 [1328]~E(x13281,x13282)+E(f617(x13283,x13281,x13284),f617(x13283,x13282,x13284))
% 109.14/108.87 [1329]~E(x13291,x13292)+E(f617(x13293,x13294,x13291),f617(x13293,x13294,x13292))
% 109.14/108.87 [1330]~E(x13301,x13302)+E(f369(x13301,x13303,x13304,x13305),f369(x13302,x13303,x13304,x13305))
% 109.14/108.87 [1331]~E(x13311,x13312)+E(f369(x13313,x13311,x13314,x13315),f369(x13313,x13312,x13314,x13315))
% 109.14/108.87 [1332]~E(x13321,x13322)+E(f369(x13323,x13324,x13321,x13325),f369(x13323,x13324,x13322,x13325))
% 109.14/108.87 [1333]~E(x13331,x13332)+E(f369(x13333,x13334,x13335,x13331),f369(x13333,x13334,x13335,x13332))
% 109.14/108.87 [1334]~E(x13341,x13342)+E(f579(x13341,x13343),f579(x13342,x13343))
% 109.14/108.87 [1335]~E(x13351,x13352)+E(f579(x13353,x13351),f579(x13353,x13352))
% 109.14/108.87 [1336]~E(x13361,x13362)+E(f584(x13361,x13363,x13364),f584(x13362,x13363,x13364))
% 109.14/108.87 [1337]~E(x13371,x13372)+E(f584(x13373,x13371,x13374),f584(x13373,x13372,x13374))
% 109.14/108.87 [1338]~E(x13381,x13382)+E(f584(x13383,x13384,x13381),f584(x13383,x13384,x13382))
% 109.14/108.87 [1339]~E(x13391,x13392)+E(f861(x13391,x13393,x13394),f861(x13392,x13393,x13394))
% 109.14/108.87 [1340]~E(x13401,x13402)+E(f861(x13403,x13401,x13404),f861(x13403,x13402,x13404))
% 109.14/108.87 [1341]~E(x13411,x13412)+E(f861(x13413,x13414,x13411),f861(x13413,x13414,x13412))
% 109.14/108.87 [1342]~E(x13421,x13422)+E(f252(x13421,x13423,x13424,x13425,x13426),f252(x13422,x13423,x13424,x13425,x13426))
% 109.14/108.87 [1343]~E(x13431,x13432)+E(f252(x13433,x13431,x13434,x13435,x13436),f252(x13433,x13432,x13434,x13435,x13436))
% 109.14/108.87 [1344]~E(x13441,x13442)+E(f252(x13443,x13444,x13441,x13445,x13446),f252(x13443,x13444,x13442,x13445,x13446))
% 109.14/108.87 [1345]~E(x13451,x13452)+E(f252(x13453,x13454,x13455,x13451,x13456),f252(x13453,x13454,x13455,x13452,x13456))
% 109.14/108.87 [1346]~E(x13461,x13462)+E(f252(x13463,x13464,x13465,x13466,x13461),f252(x13463,x13464,x13465,x13466,x13462))
% 109.14/108.87 [1347]~E(x13471,x13472)+E(f553(x13471),f553(x13472))
% 109.14/108.87 [1348]~E(x13481,x13482)+E(f53(x13481,x13483,x13484,x13485),f53(x13482,x13483,x13484,x13485))
% 109.14/108.87 [1349]~E(x13491,x13492)+E(f53(x13493,x13491,x13494,x13495),f53(x13493,x13492,x13494,x13495))
% 109.14/108.87 [1350]~E(x13501,x13502)+E(f53(x13503,x13504,x13501,x13505),f53(x13503,x13504,x13502,x13505))
% 109.14/108.87 [1351]~E(x13511,x13512)+E(f53(x13513,x13514,x13515,x13511),f53(x13513,x13514,x13515,x13512))
% 109.14/108.87 [1352]~E(x13521,x13522)+E(f783(x13521,x13523),f783(x13522,x13523))
% 109.14/108.87 [1353]~E(x13531,x13532)+E(f783(x13533,x13531),f783(x13533,x13532))
% 109.14/108.87 [1354]~E(x13541,x13542)+E(f648(x13541,x13543,x13544,x13545,x13546),f648(x13542,x13543,x13544,x13545,x13546))
% 109.14/108.87 [1355]~E(x13551,x13552)+E(f648(x13553,x13551,x13554,x13555,x13556),f648(x13553,x13552,x13554,x13555,x13556))
% 109.14/108.87 [1356]~E(x13561,x13562)+E(f648(x13563,x13564,x13561,x13565,x13566),f648(x13563,x13564,x13562,x13565,x13566))
% 109.14/108.87 [1357]~E(x13571,x13572)+E(f648(x13573,x13574,x13575,x13571,x13576),f648(x13573,x13574,x13575,x13572,x13576))
% 109.14/108.87 [1358]~E(x13581,x13582)+E(f648(x13583,x13584,x13585,x13586,x13581),f648(x13583,x13584,x13585,x13586,x13582))
% 109.14/108.87 [1359]~E(x13591,x13592)+E(f380(x13591,x13593,x13594,x13595),f380(x13592,x13593,x13594,x13595))
% 109.14/108.87 [1360]~E(x13601,x13602)+E(f380(x13603,x13601,x13604,x13605),f380(x13603,x13602,x13604,x13605))
% 109.14/108.87 [1361]~E(x13611,x13612)+E(f380(x13613,x13614,x13611,x13615),f380(x13613,x13614,x13612,x13615))
% 109.14/108.87 [1362]~E(x13621,x13622)+E(f380(x13623,x13624,x13625,x13621),f380(x13623,x13624,x13625,x13622))
% 109.14/108.87 [1363]~E(x13631,x13632)+E(f852(x13631,x13633,x13634),f852(x13632,x13633,x13634))
% 109.14/108.87 [1364]~E(x13641,x13642)+E(f852(x13643,x13641,x13644),f852(x13643,x13642,x13644))
% 109.14/108.87 [1365]~E(x13651,x13652)+E(f852(x13653,x13654,x13651),f852(x13653,x13654,x13652))
% 109.14/108.87 [1366]~E(x13661,x13662)+E(f757(x13661,x13663,x13664),f757(x13662,x13663,x13664))
% 109.14/108.87 [1367]~E(x13671,x13672)+E(f757(x13673,x13671,x13674),f757(x13673,x13672,x13674))
% 109.14/108.87 [1368]~E(x13681,x13682)+E(f757(x13683,x13684,x13681),f757(x13683,x13684,x13682))
% 109.14/108.87 [1369]~E(x13691,x13692)+E(f611(x13691,x13693,x13694),f611(x13692,x13693,x13694))
% 109.14/108.87 [1370]~E(x13701,x13702)+E(f611(x13703,x13701,x13704),f611(x13703,x13702,x13704))
% 109.14/108.87 [1371]~E(x13711,x13712)+E(f611(x13713,x13714,x13711),f611(x13713,x13714,x13712))
% 109.14/108.87 [1372]~E(x13721,x13722)+E(f625(x13721,x13723,x13724,x13725),f625(x13722,x13723,x13724,x13725))
% 109.14/108.87 [1373]~E(x13731,x13732)+E(f625(x13733,x13731,x13734,x13735),f625(x13733,x13732,x13734,x13735))
% 109.14/108.87 [1374]~E(x13741,x13742)+E(f625(x13743,x13744,x13741,x13745),f625(x13743,x13744,x13742,x13745))
% 109.14/108.87 [1375]~E(x13751,x13752)+E(f625(x13753,x13754,x13755,x13751),f625(x13753,x13754,x13755,x13752))
% 109.14/108.87 [1376]~E(x13761,x13762)+E(f396(x13761,x13763,x13764),f396(x13762,x13763,x13764))
% 109.14/108.87 [1377]~E(x13771,x13772)+E(f396(x13773,x13771,x13774),f396(x13773,x13772,x13774))
% 109.14/108.87 [1378]~E(x13781,x13782)+E(f396(x13783,x13784,x13781),f396(x13783,x13784,x13782))
% 109.14/108.87 [1379]~E(x13791,x13792)+E(f264(x13791,x13793,x13794,x13795),f264(x13792,x13793,x13794,x13795))
% 109.14/108.87 [1380]~E(x13801,x13802)+E(f264(x13803,x13801,x13804,x13805),f264(x13803,x13802,x13804,x13805))
% 109.14/108.87 [1381]~E(x13811,x13812)+E(f264(x13813,x13814,x13811,x13815),f264(x13813,x13814,x13812,x13815))
% 109.14/108.87 [1382]~E(x13821,x13822)+E(f264(x13823,x13824,x13825,x13821),f264(x13823,x13824,x13825,x13822))
% 109.14/108.87 [1383]~E(x13831,x13832)+E(f338(x13831,x13833,x13834,x13835),f338(x13832,x13833,x13834,x13835))
% 109.14/108.87 [1384]~E(x13841,x13842)+E(f338(x13843,x13841,x13844,x13845),f338(x13843,x13842,x13844,x13845))
% 109.14/108.87 [1385]~E(x13851,x13852)+E(f338(x13853,x13854,x13851,x13855),f338(x13853,x13854,x13852,x13855))
% 109.14/108.87 [1386]~E(x13861,x13862)+E(f338(x13863,x13864,x13865,x13861),f338(x13863,x13864,x13865,x13862))
% 109.14/108.87 [1387]~E(x13871,x13872)+E(f715(x13871,x13873,x13874,x13875,x13876),f715(x13872,x13873,x13874,x13875,x13876))
% 109.14/108.87 [1388]~E(x13881,x13882)+E(f715(x13883,x13881,x13884,x13885,x13886),f715(x13883,x13882,x13884,x13885,x13886))
% 109.14/108.87 [1389]~E(x13891,x13892)+E(f715(x13893,x13894,x13891,x13895,x13896),f715(x13893,x13894,x13892,x13895,x13896))
% 109.14/108.87 [1390]~E(x13901,x13902)+E(f715(x13903,x13904,x13905,x13901,x13906),f715(x13903,x13904,x13905,x13902,x13906))
% 109.14/108.87 [1391]~E(x13911,x13912)+E(f715(x13913,x13914,x13915,x13916,x13911),f715(x13913,x13914,x13915,x13916,x13912))
% 109.14/108.87 [1392]~E(x13921,x13922)+E(f540(x13921,x13923,x13924,x13925),f540(x13922,x13923,x13924,x13925))
% 109.14/108.87 [1393]~E(x13931,x13932)+E(f540(x13933,x13931,x13934,x13935),f540(x13933,x13932,x13934,x13935))
% 109.14/108.87 [1394]~E(x13941,x13942)+E(f540(x13943,x13944,x13941,x13945),f540(x13943,x13944,x13942,x13945))
% 109.14/108.87 [1395]~E(x13951,x13952)+E(f540(x13953,x13954,x13955,x13951),f540(x13953,x13954,x13955,x13952))
% 109.14/108.87 [1396]~E(x13961,x13962)+E(f551(x13961,x13963,x13964,x13965,x13966,x13967,x13968,x13969),f551(x13962,x13963,x13964,x13965,x13966,x13967,x13968,x13969))
% 109.14/108.87 [1397]~E(x13971,x13972)+E(f551(x13973,x13971,x13974,x13975,x13976,x13977,x13978,x13979),f551(x13973,x13972,x13974,x13975,x13976,x13977,x13978,x13979))
% 109.14/108.87 [1398]~E(x13981,x13982)+E(f551(x13983,x13984,x13981,x13985,x13986,x13987,x13988,x13989),f551(x13983,x13984,x13982,x13985,x13986,x13987,x13988,x13989))
% 109.14/108.87 [1399]~E(x13991,x13992)+E(f551(x13993,x13994,x13995,x13991,x13996,x13997,x13998,x13999),f551(x13993,x13994,x13995,x13992,x13996,x13997,x13998,x13999))
% 109.14/108.87 [1400]~E(x14001,x14002)+E(f551(x14003,x14004,x14005,x14006,x14001,x14007,x14008,x14009),f551(x14003,x14004,x14005,x14006,x14002,x14007,x14008,x14009))
% 109.14/108.87 [1401]~E(x14011,x14012)+E(f551(x14013,x14014,x14015,x14016,x14017,x14011,x14018,x14019),f551(x14013,x14014,x14015,x14016,x14017,x14012,x14018,x14019))
% 109.14/108.87 [1402]~E(x14021,x14022)+E(f551(x14023,x14024,x14025,x14026,x14027,x14028,x14021,x14029),f551(x14023,x14024,x14025,x14026,x14027,x14028,x14022,x14029))
% 109.14/108.87 [1403]~E(x14031,x14032)+E(f551(x14033,x14034,x14035,x14036,x14037,x14038,x14039,x14031),f551(x14033,x14034,x14035,x14036,x14037,x14038,x14039,x14032))
% 109.14/108.87 [1404]~E(x14041,x14042)+E(f525(x14041,x14043,x14044),f525(x14042,x14043,x14044))
% 109.14/108.87 [1405]~E(x14051,x14052)+E(f525(x14053,x14051,x14054),f525(x14053,x14052,x14054))
% 109.14/108.87 [1406]~E(x14061,x14062)+E(f525(x14063,x14064,x14061),f525(x14063,x14064,x14062))
% 109.14/108.87 [1407]~E(x14071,x14072)+E(f451(x14071,x14073,x14074),f451(x14072,x14073,x14074))
% 109.14/108.87 [1408]~E(x14081,x14082)+E(f451(x14083,x14081,x14084),f451(x14083,x14082,x14084))
% 109.14/108.87 [1409]~E(x14091,x14092)+E(f451(x14093,x14094,x14091),f451(x14093,x14094,x14092))
% 109.14/108.87 [1410]~E(x14101,x14102)+E(f794(x14101,x14103,x14104,x14105,x14106),f794(x14102,x14103,x14104,x14105,x14106))
% 109.14/108.87 [1411]~E(x14111,x14112)+E(f794(x14113,x14111,x14114,x14115,x14116),f794(x14113,x14112,x14114,x14115,x14116))
% 109.14/108.87 [1412]~E(x14121,x14122)+E(f794(x14123,x14124,x14121,x14125,x14126),f794(x14123,x14124,x14122,x14125,x14126))
% 109.14/108.87 [1413]~E(x14131,x14132)+E(f794(x14133,x14134,x14135,x14131,x14136),f794(x14133,x14134,x14135,x14132,x14136))
% 109.14/108.87 [1414]~E(x14141,x14142)+E(f794(x14143,x14144,x14145,x14146,x14141),f794(x14143,x14144,x14145,x14146,x14142))
% 109.14/108.87 [1415]~E(x14151,x14152)+E(f725(x14151,x14153),f725(x14152,x14153))
% 109.14/108.87 [1416]~E(x14161,x14162)+E(f725(x14163,x14161),f725(x14163,x14162))
% 109.14/108.87 [1417]~E(x14171,x14172)+E(f388(x14171,x14173,x14174),f388(x14172,x14173,x14174))
% 109.14/108.87 [1418]~E(x14181,x14182)+E(f388(x14183,x14181,x14184),f388(x14183,x14182,x14184))
% 109.14/108.87 [1419]~E(x14191,x14192)+E(f388(x14193,x14194,x14191),f388(x14193,x14194,x14192))
% 109.14/108.87 [1420]~E(x14201,x14202)+E(f763(x14201,x14203,x14204,x14205),f763(x14202,x14203,x14204,x14205))
% 109.14/108.87 [1421]~E(x14211,x14212)+E(f763(x14213,x14211,x14214,x14215),f763(x14213,x14212,x14214,x14215))
% 109.14/108.87 [1422]~E(x14221,x14222)+E(f763(x14223,x14224,x14221,x14225),f763(x14223,x14224,x14222,x14225))
% 109.14/108.87 [1423]~E(x14231,x14232)+E(f763(x14233,x14234,x14235,x14231),f763(x14233,x14234,x14235,x14232))
% 109.14/108.87 [1424]~E(x14241,x14242)+E(f411(x14241,x14243,x14244),f411(x14242,x14243,x14244))
% 109.14/108.87 [1425]~E(x14251,x14252)+E(f411(x14253,x14251,x14254),f411(x14253,x14252,x14254))
% 109.14/108.87 [1426]~E(x14261,x14262)+E(f411(x14263,x14264,x14261),f411(x14263,x14264,x14262))
% 109.14/108.87 [1427]~E(x14271,x14272)+E(f403(x14271,x14273,x14274,x14275,x14276),f403(x14272,x14273,x14274,x14275,x14276))
% 109.14/108.87 [1428]~E(x14281,x14282)+E(f403(x14283,x14281,x14284,x14285,x14286),f403(x14283,x14282,x14284,x14285,x14286))
% 109.14/108.87 [1429]~E(x14291,x14292)+E(f403(x14293,x14294,x14291,x14295,x14296),f403(x14293,x14294,x14292,x14295,x14296))
% 109.14/108.87 [1430]~E(x14301,x14302)+E(f403(x14303,x14304,x14305,x14301,x14306),f403(x14303,x14304,x14305,x14302,x14306))
% 109.14/108.87 [1431]~E(x14311,x14312)+E(f403(x14313,x14314,x14315,x14316,x14311),f403(x14313,x14314,x14315,x14316,x14312))
% 109.14/108.87 [1432]~E(x14321,x14322)+E(f416(x14321,x14323,x14324,x14325,x14326),f416(x14322,x14323,x14324,x14325,x14326))
% 109.14/108.87 [1433]~E(x14331,x14332)+E(f416(x14333,x14331,x14334,x14335,x14336),f416(x14333,x14332,x14334,x14335,x14336))
% 109.14/108.87 [1434]~E(x14341,x14342)+E(f416(x14343,x14344,x14341,x14345,x14346),f416(x14343,x14344,x14342,x14345,x14346))
% 109.14/108.87 [1435]~E(x14351,x14352)+E(f416(x14353,x14354,x14355,x14351,x14356),f416(x14353,x14354,x14355,x14352,x14356))
% 109.14/108.87 [1436]~E(x14361,x14362)+E(f416(x14363,x14364,x14365,x14366,x14361),f416(x14363,x14364,x14365,x14366,x14362))
% 109.14/108.87 [1437]~E(x14371,x14372)+E(f479(x14371,x14373,x14374,x14375,x14376),f479(x14372,x14373,x14374,x14375,x14376))
% 109.14/108.87 [1438]~E(x14381,x14382)+E(f479(x14383,x14381,x14384,x14385,x14386),f479(x14383,x14382,x14384,x14385,x14386))
% 109.14/108.87 [1439]~E(x14391,x14392)+E(f479(x14393,x14394,x14391,x14395,x14396),f479(x14393,x14394,x14392,x14395,x14396))
% 109.14/108.87 [1440]~E(x14401,x14402)+E(f479(x14403,x14404,x14405,x14401,x14406),f479(x14403,x14404,x14405,x14402,x14406))
% 109.14/108.87 [1441]~E(x14411,x14412)+E(f479(x14413,x14414,x14415,x14416,x14411),f479(x14413,x14414,x14415,x14416,x14412))
% 109.14/108.87 [1442]~E(x14421,x14422)+E(f689(x14421,x14423,x14424,x14425),f689(x14422,x14423,x14424,x14425))
% 109.14/108.87 [1443]~E(x14431,x14432)+E(f689(x14433,x14431,x14434,x14435),f689(x14433,x14432,x14434,x14435))
% 109.14/108.87 [1444]~E(x14441,x14442)+E(f689(x14443,x14444,x14441,x14445),f689(x14443,x14444,x14442,x14445))
% 109.14/108.87 [1445]~E(x14451,x14452)+E(f689(x14453,x14454,x14455,x14451),f689(x14453,x14454,x14455,x14452))
% 109.14/108.87 [1446]~E(x14461,x14462)+E(f417(x14461,x14463,x14464,x14465,x14466),f417(x14462,x14463,x14464,x14465,x14466))
% 109.14/108.87 [1447]~E(x14471,x14472)+E(f417(x14473,x14471,x14474,x14475,x14476),f417(x14473,x14472,x14474,x14475,x14476))
% 109.14/108.87 [1448]~E(x14481,x14482)+E(f417(x14483,x14484,x14481,x14485,x14486),f417(x14483,x14484,x14482,x14485,x14486))
% 109.14/108.87 [1449]~E(x14491,x14492)+E(f417(x14493,x14494,x14495,x14491,x14496),f417(x14493,x14494,x14495,x14492,x14496))
% 109.14/108.87 [1450]~E(x14501,x14502)+E(f417(x14503,x14504,x14505,x14506,x14501),f417(x14503,x14504,x14505,x14506,x14502))
% 109.14/108.87 [1451]~E(x14511,x14512)+E(f495(x14511,x14513,x14514),f495(x14512,x14513,x14514))
% 109.14/108.87 [1452]~E(x14521,x14522)+E(f495(x14523,x14521,x14524),f495(x14523,x14522,x14524))
% 109.14/108.87 [1453]~E(x14531,x14532)+E(f495(x14533,x14534,x14531),f495(x14533,x14534,x14532))
% 109.14/108.87 [1454]~E(x14541,x14542)+E(f491(x14541,x14543,x14544),f491(x14542,x14543,x14544))
% 109.14/108.87 [1455]~E(x14551,x14552)+E(f491(x14553,x14551,x14554),f491(x14553,x14552,x14554))
% 109.14/108.87 [1456]~E(x14561,x14562)+E(f491(x14563,x14564,x14561),f491(x14563,x14564,x14562))
% 109.14/108.87 [1457]~E(x14571,x14572)+E(f449(x14571,x14573,x14574),f449(x14572,x14573,x14574))
% 109.14/108.87 [1458]~E(x14581,x14582)+E(f449(x14583,x14581,x14584),f449(x14583,x14582,x14584))
% 109.14/108.87 [1459]~E(x14591,x14592)+E(f449(x14593,x14594,x14591),f449(x14593,x14594,x14592))
% 109.14/108.87 [1460]~E(x14601,x14602)+E(f520(x14601,x14603,x14604),f520(x14602,x14603,x14604))
% 109.14/108.87 [1461]~E(x14611,x14612)+E(f520(x14613,x14611,x14614),f520(x14613,x14612,x14614))
% 109.14/108.87 [1462]~E(x14621,x14622)+E(f520(x14623,x14624,x14621),f520(x14623,x14624,x14622))
% 109.14/108.87 [1463]~E(x14631,x14632)+E(f658(x14631,x14633,x14634),f658(x14632,x14633,x14634))
% 109.14/108.87 [1464]~E(x14641,x14642)+E(f658(x14643,x14641,x14644),f658(x14643,x14642,x14644))
% 109.14/108.87 [1465]~E(x14651,x14652)+E(f658(x14653,x14654,x14651),f658(x14653,x14654,x14652))
% 109.14/108.87 [1466]~E(x14661,x14662)+E(f36(x14661),f36(x14662))
% 109.14/108.87 [1467]~E(x14671,x14672)+E(f673(x14671,x14673,x14674,x14675,x14676),f673(x14672,x14673,x14674,x14675,x14676))
% 109.14/108.87 [1468]~E(x14681,x14682)+E(f673(x14683,x14681,x14684,x14685,x14686),f673(x14683,x14682,x14684,x14685,x14686))
% 109.14/108.87 [1469]~E(x14691,x14692)+E(f673(x14693,x14694,x14691,x14695,x14696),f673(x14693,x14694,x14692,x14695,x14696))
% 109.14/108.87 [1470]~E(x14701,x14702)+E(f673(x14703,x14704,x14705,x14701,x14706),f673(x14703,x14704,x14705,x14702,x14706))
% 109.14/108.87 [1471]~E(x14711,x14712)+E(f673(x14713,x14714,x14715,x14716,x14711),f673(x14713,x14714,x14715,x14716,x14712))
% 109.14/108.87 [1472]~E(x14721,x14722)+E(f206(x14721,x14723),f206(x14722,x14723))
% 109.14/108.87 [1473]~E(x14731,x14732)+E(f206(x14733,x14731),f206(x14733,x14732))
% 109.14/108.87 [1474]~E(x14741,x14742)+E(f187(x14741,x14743,x14744,x14745),f187(x14742,x14743,x14744,x14745))
% 109.14/108.87 [1475]~E(x14751,x14752)+E(f187(x14753,x14751,x14754,x14755),f187(x14753,x14752,x14754,x14755))
% 109.14/108.87 [1476]~E(x14761,x14762)+E(f187(x14763,x14764,x14761,x14765),f187(x14763,x14764,x14762,x14765))
% 109.14/108.87 [1477]~E(x14771,x14772)+E(f187(x14773,x14774,x14775,x14771),f187(x14773,x14774,x14775,x14772))
% 109.14/108.87 [1478]~E(x14781,x14782)+E(f788(x14781,x14783,x14784,x14785),f788(x14782,x14783,x14784,x14785))
% 109.14/108.87 [1479]~E(x14791,x14792)+E(f788(x14793,x14791,x14794,x14795),f788(x14793,x14792,x14794,x14795))
% 109.14/108.87 [1480]~E(x14801,x14802)+E(f788(x14803,x14804,x14801,x14805),f788(x14803,x14804,x14802,x14805))
% 109.14/108.87 [1481]~E(x14811,x14812)+E(f788(x14813,x14814,x14815,x14811),f788(x14813,x14814,x14815,x14812))
% 109.14/108.87 [1482]~E(x14821,x14822)+E(f663(x14821,x14823,x14824,x14825),f663(x14822,x14823,x14824,x14825))
% 109.14/108.87 [1483]~E(x14831,x14832)+E(f663(x14833,x14831,x14834,x14835),f663(x14833,x14832,x14834,x14835))
% 109.14/108.87 [1484]~E(x14841,x14842)+E(f663(x14843,x14844,x14841,x14845),f663(x14843,x14844,x14842,x14845))
% 109.14/108.87 [1485]~E(x14851,x14852)+E(f663(x14853,x14854,x14855,x14851),f663(x14853,x14854,x14855,x14852))
% 109.14/108.87 [1486]~E(x14861,x14862)+E(f221(x14861,x14863,x14864),f221(x14862,x14863,x14864))
% 109.14/108.87 [1487]~E(x14871,x14872)+E(f221(x14873,x14871,x14874),f221(x14873,x14872,x14874))
% 109.14/108.87 [1488]~E(x14881,x14882)+E(f221(x14883,x14884,x14881),f221(x14883,x14884,x14882))
% 109.14/108.87 [1489]~E(x14891,x14892)+E(f368(x14891),f368(x14892))
% 109.14/108.87 [1490]~E(x14901,x14902)+E(f870(x14901,x14903,x14904,x14905,x14906),f870(x14902,x14903,x14904,x14905,x14906))
% 109.14/108.87 [1491]~E(x14911,x14912)+E(f870(x14913,x14911,x14914,x14915,x14916),f870(x14913,x14912,x14914,x14915,x14916))
% 109.14/108.87 [1492]~E(x14921,x14922)+E(f870(x14923,x14924,x14921,x14925,x14926),f870(x14923,x14924,x14922,x14925,x14926))
% 109.14/108.87 [1493]~E(x14931,x14932)+E(f870(x14933,x14934,x14935,x14931,x14936),f870(x14933,x14934,x14935,x14932,x14936))
% 109.14/108.87 [1494]~E(x14941,x14942)+E(f870(x14943,x14944,x14945,x14946,x14941),f870(x14943,x14944,x14945,x14946,x14942))
% 109.14/108.87 [1495]~E(x14951,x14952)+E(f514(x14951,x14953,x14954,x14955,x14956),f514(x14952,x14953,x14954,x14955,x14956))
% 109.14/108.87 [1496]~E(x14961,x14962)+E(f514(x14963,x14961,x14964,x14965,x14966),f514(x14963,x14962,x14964,x14965,x14966))
% 109.14/108.87 [1497]~E(x14971,x14972)+E(f514(x14973,x14974,x14971,x14975,x14976),f514(x14973,x14974,x14972,x14975,x14976))
% 109.14/108.87 [1498]~E(x14981,x14982)+E(f514(x14983,x14984,x14985,x14981,x14986),f514(x14983,x14984,x14985,x14982,x14986))
% 109.14/108.87 [1499]~E(x14991,x14992)+E(f514(x14993,x14994,x14995,x14996,x14991),f514(x14993,x14994,x14995,x14996,x14992))
% 109.14/108.87 [1500]~E(x15001,x15002)+E(f517(x15001,x15003,x15004,x15005),f517(x15002,x15003,x15004,x15005))
% 109.14/108.87 [1501]~E(x15011,x15012)+E(f517(x15013,x15011,x15014,x15015),f517(x15013,x15012,x15014,x15015))
% 109.14/108.87 [1502]~E(x15021,x15022)+E(f517(x15023,x15024,x15021,x15025),f517(x15023,x15024,x15022,x15025))
% 109.14/108.87 [1503]~E(x15031,x15032)+E(f517(x15033,x15034,x15035,x15031),f517(x15033,x15034,x15035,x15032))
% 109.14/108.87 [1504]~E(x15041,x15042)+E(f548(x15041,x15043,x15044,x15045,x15046),f548(x15042,x15043,x15044,x15045,x15046))
% 109.14/108.87 [1505]~E(x15051,x15052)+E(f548(x15053,x15051,x15054,x15055,x15056),f548(x15053,x15052,x15054,x15055,x15056))
% 109.14/108.87 [1506]~E(x15061,x15062)+E(f548(x15063,x15064,x15061,x15065,x15066),f548(x15063,x15064,x15062,x15065,x15066))
% 109.14/108.87 [1507]~E(x15071,x15072)+E(f548(x15073,x15074,x15075,x15071,x15076),f548(x15073,x15074,x15075,x15072,x15076))
% 109.14/108.87 [1508]~E(x15081,x15082)+E(f548(x15083,x15084,x15085,x15086,x15081),f548(x15083,x15084,x15085,x15086,x15082))
% 109.14/108.87 [1509]~E(x15091,x15092)+E(f429(x15091,x15093,x15094,x15095,x15096,x15097),f429(x15092,x15093,x15094,x15095,x15096,x15097))
% 109.14/108.87 [1510]~E(x15101,x15102)+E(f429(x15103,x15101,x15104,x15105,x15106,x15107),f429(x15103,x15102,x15104,x15105,x15106,x15107))
% 109.14/108.87 [1511]~E(x15111,x15112)+E(f429(x15113,x15114,x15111,x15115,x15116,x15117),f429(x15113,x15114,x15112,x15115,x15116,x15117))
% 109.14/108.87 [1512]~E(x15121,x15122)+E(f429(x15123,x15124,x15125,x15121,x15126,x15127),f429(x15123,x15124,x15125,x15122,x15126,x15127))
% 109.14/108.87 [1513]~E(x15131,x15132)+E(f429(x15133,x15134,x15135,x15136,x15131,x15137),f429(x15133,x15134,x15135,x15136,x15132,x15137))
% 109.14/108.87 [1514]~E(x15141,x15142)+E(f429(x15143,x15144,x15145,x15146,x15147,x15141),f429(x15143,x15144,x15145,x15146,x15147,x15142))
% 109.14/108.87 [1515]~E(x15151,x15152)+E(f304(x15151,x15153,x15154,x15155),f304(x15152,x15153,x15154,x15155))
% 109.14/108.87 [1516]~E(x15161,x15162)+E(f304(x15163,x15161,x15164,x15165),f304(x15163,x15162,x15164,x15165))
% 109.14/108.87 [1517]~E(x15171,x15172)+E(f304(x15173,x15174,x15171,x15175),f304(x15173,x15174,x15172,x15175))
% 109.14/108.87 [1518]~E(x15181,x15182)+E(f304(x15183,x15184,x15185,x15181),f304(x15183,x15184,x15185,x15182))
% 109.14/108.87 [1519]~E(x15191,x15192)+E(f532(x15191,x15193,x15194),f532(x15192,x15193,x15194))
% 109.14/108.87 [1520]~E(x15201,x15202)+E(f532(x15203,x15201,x15204),f532(x15203,x15202,x15204))
% 109.14/108.87 [1521]~E(x15211,x15212)+E(f532(x15213,x15214,x15211),f532(x15213,x15214,x15212))
% 109.14/108.87 [1522]~E(x15221,x15222)+E(f433(x15221,x15223,x15224),f433(x15222,x15223,x15224))
% 109.14/108.87 [1523]~E(x15231,x15232)+E(f433(x15233,x15231,x15234),f433(x15233,x15232,x15234))
% 109.14/108.87 [1524]~E(x15241,x15242)+E(f433(x15243,x15244,x15241),f433(x15243,x15244,x15242))
% 109.14/108.87 [1525]~E(x15251,x15252)+E(f838(x15251,x15253,x15254,x15255,x15256,x15257,x15258,x15259),f838(x15252,x15253,x15254,x15255,x15256,x15257,x15258,x15259))
% 109.14/108.87 [1526]~E(x15261,x15262)+E(f838(x15263,x15261,x15264,x15265,x15266,x15267,x15268,x15269),f838(x15263,x15262,x15264,x15265,x15266,x15267,x15268,x15269))
% 109.14/108.87 [1527]~E(x15271,x15272)+E(f838(x15273,x15274,x15271,x15275,x15276,x15277,x15278,x15279),f838(x15273,x15274,x15272,x15275,x15276,x15277,x15278,x15279))
% 109.14/108.87 [1528]~E(x15281,x15282)+E(f838(x15283,x15284,x15285,x15281,x15286,x15287,x15288,x15289),f838(x15283,x15284,x15285,x15282,x15286,x15287,x15288,x15289))
% 109.14/108.87 [1529]~E(x15291,x15292)+E(f838(x15293,x15294,x15295,x15296,x15291,x15297,x15298,x15299),f838(x15293,x15294,x15295,x15296,x15292,x15297,x15298,x15299))
% 109.14/108.87 [1530]~E(x15301,x15302)+E(f838(x15303,x15304,x15305,x15306,x15307,x15301,x15308,x15309),f838(x15303,x15304,x15305,x15306,x15307,x15302,x15308,x15309))
% 109.14/108.87 [1531]~E(x15311,x15312)+E(f838(x15313,x15314,x15315,x15316,x15317,x15318,x15311,x15319),f838(x15313,x15314,x15315,x15316,x15317,x15318,x15312,x15319))
% 109.14/108.87 [1532]~E(x15321,x15322)+E(f838(x15323,x15324,x15325,x15326,x15327,x15328,x15329,x15321),f838(x15323,x15324,x15325,x15326,x15327,x15328,x15329,x15322))
% 109.14/108.87 [1533]~E(x15331,x15332)+E(f803(x15331,x15333),f803(x15332,x15333))
% 109.14/108.87 [1534]~E(x15341,x15342)+E(f803(x15343,x15341),f803(x15343,x15342))
% 109.14/108.87 [1535]~E(x15351,x15352)+E(f288(x15351,x15353,x15354,x15355,x15356),f288(x15352,x15353,x15354,x15355,x15356))
% 109.14/108.87 [1536]~E(x15361,x15362)+E(f288(x15363,x15361,x15364,x15365,x15366),f288(x15363,x15362,x15364,x15365,x15366))
% 109.14/108.87 [1537]~E(x15371,x15372)+E(f288(x15373,x15374,x15371,x15375,x15376),f288(x15373,x15374,x15372,x15375,x15376))
% 109.14/108.87 [1538]~E(x15381,x15382)+E(f288(x15383,x15384,x15385,x15381,x15386),f288(x15383,x15384,x15385,x15382,x15386))
% 109.14/108.87 [1539]~E(x15391,x15392)+E(f288(x15393,x15394,x15395,x15396,x15391),f288(x15393,x15394,x15395,x15396,x15392))
% 109.14/108.87 [1540]~E(x15401,x15402)+E(f681(x15401,x15403),f681(x15402,x15403))
% 109.14/108.87 [1541]~E(x15411,x15412)+E(f681(x15413,x15411),f681(x15413,x15412))
% 109.14/108.87 [1542]~E(x15421,x15422)+E(f669(x15421,x15423,x15424),f669(x15422,x15423,x15424))
% 109.14/108.87 [1543]~E(x15431,x15432)+E(f669(x15433,x15431,x15434),f669(x15433,x15432,x15434))
% 109.14/108.87 [1544]~E(x15441,x15442)+E(f669(x15443,x15444,x15441),f669(x15443,x15444,x15442))
% 109.14/108.87 [1545]~E(x15451,x15452)+E(f340(x15451,x15453,x15454),f340(x15452,x15453,x15454))
% 109.14/108.87 [1546]~E(x15461,x15462)+E(f340(x15463,x15461,x15464),f340(x15463,x15462,x15464))
% 109.14/108.87 [1547]~E(x15471,x15472)+E(f340(x15473,x15474,x15471),f340(x15473,x15474,x15472))
% 109.14/108.87 [1548]~E(x15481,x15482)+E(f363(x15481,x15483,x15484),f363(x15482,x15483,x15484))
% 109.14/108.87 [1549]~E(x15491,x15492)+E(f363(x15493,x15491,x15494),f363(x15493,x15492,x15494))
% 109.14/108.87 [1550]~E(x15501,x15502)+E(f363(x15503,x15504,x15501),f363(x15503,x15504,x15502))
% 109.14/108.87 [1551]~E(x15511,x15512)+E(f577(x15511,x15513),f577(x15512,x15513))
% 109.14/108.87 [1552]~E(x15521,x15522)+E(f577(x15523,x15521),f577(x15523,x15522))
% 109.14/108.87 [1553]~E(x15531,x15532)+E(f780(x15531),f780(x15532))
% 109.14/108.87 [1554]~E(x15541,x15542)+E(f420(x15541,x15543,x15544,x15545,x15546),f420(x15542,x15543,x15544,x15545,x15546))
% 109.14/108.87 [1555]~E(x15551,x15552)+E(f420(x15553,x15551,x15554,x15555,x15556),f420(x15553,x15552,x15554,x15555,x15556))
% 109.14/108.87 [1556]~E(x15561,x15562)+E(f420(x15563,x15564,x15561,x15565,x15566),f420(x15563,x15564,x15562,x15565,x15566))
% 109.14/108.87 [1557]~E(x15571,x15572)+E(f420(x15573,x15574,x15575,x15571,x15576),f420(x15573,x15574,x15575,x15572,x15576))
% 109.14/108.87 [1558]~E(x15581,x15582)+E(f420(x15583,x15584,x15585,x15586,x15581),f420(x15583,x15584,x15585,x15586,x15582))
% 109.14/108.87 [1559]~E(x15591,x15592)+E(f218(x15591,x15593),f218(x15592,x15593))
% 109.14/108.87 [1560]~E(x15601,x15602)+E(f218(x15603,x15601),f218(x15603,x15602))
% 109.14/108.87 [1561]~E(x15611,x15612)+E(f493(x15611,x15613,x15614),f493(x15612,x15613,x15614))
% 109.14/108.87 [1562]~E(x15621,x15622)+E(f493(x15623,x15621,x15624),f493(x15623,x15622,x15624))
% 109.14/108.87 [1563]~E(x15631,x15632)+E(f493(x15633,x15634,x15631),f493(x15633,x15634,x15632))
% 109.14/108.87 [1564]~E(x15641,x15642)+E(f512(x15641,x15643),f512(x15642,x15643))
% 109.14/108.87 [1565]~E(x15651,x15652)+E(f512(x15653,x15651),f512(x15653,x15652))
% 109.14/108.87 [1566]~E(x15661,x15662)+E(f456(x15661,x15663),f456(x15662,x15663))
% 109.14/108.87 [1567]~E(x15671,x15672)+E(f456(x15673,x15671),f456(x15673,x15672))
% 109.14/108.87 [1568]~E(x15681,x15682)+E(f683(x15681,x15683,x15684,x15685),f683(x15682,x15683,x15684,x15685))
% 109.14/108.87 [1569]~E(x15691,x15692)+E(f683(x15693,x15691,x15694,x15695),f683(x15693,x15692,x15694,x15695))
% 109.14/108.87 [1570]~E(x15701,x15702)+E(f683(x15703,x15704,x15701,x15705),f683(x15703,x15704,x15702,x15705))
% 109.14/108.87 [1571]~E(x15711,x15712)+E(f683(x15713,x15714,x15715,x15711),f683(x15713,x15714,x15715,x15712))
% 109.14/108.87 [1572]~E(x15721,x15722)+E(f608(x15721,x15723),f608(x15722,x15723))
% 109.14/108.87 [1573]~E(x15731,x15732)+E(f608(x15733,x15731),f608(x15733,x15732))
% 109.14/108.87 [1574]~E(x15741,x15742)+E(f511(x15741,x15743,x15744,x15745,x15746,x15747,x15748,x15749),f511(x15742,x15743,x15744,x15745,x15746,x15747,x15748,x15749))
% 109.14/108.87 [1575]~E(x15751,x15752)+E(f511(x15753,x15751,x15754,x15755,x15756,x15757,x15758,x15759),f511(x15753,x15752,x15754,x15755,x15756,x15757,x15758,x15759))
% 109.14/108.87 [1576]~E(x15761,x15762)+E(f511(x15763,x15764,x15761,x15765,x15766,x15767,x15768,x15769),f511(x15763,x15764,x15762,x15765,x15766,x15767,x15768,x15769))
% 109.14/108.87 [1577]~E(x15771,x15772)+E(f511(x15773,x15774,x15775,x15771,x15776,x15777,x15778,x15779),f511(x15773,x15774,x15775,x15772,x15776,x15777,x15778,x15779))
% 109.14/108.87 [1578]~E(x15781,x15782)+E(f511(x15783,x15784,x15785,x15786,x15781,x15787,x15788,x15789),f511(x15783,x15784,x15785,x15786,x15782,x15787,x15788,x15789))
% 109.14/108.87 [1579]~E(x15791,x15792)+E(f511(x15793,x15794,x15795,x15796,x15797,x15791,x15798,x15799),f511(x15793,x15794,x15795,x15796,x15797,x15792,x15798,x15799))
% 109.14/108.87 [1580]~E(x15801,x15802)+E(f511(x15803,x15804,x15805,x15806,x15807,x15808,x15801,x15809),f511(x15803,x15804,x15805,x15806,x15807,x15808,x15802,x15809))
% 109.14/108.87 [1581]~E(x15811,x15812)+E(f511(x15813,x15814,x15815,x15816,x15817,x15818,x15819,x15811),f511(x15813,x15814,x15815,x15816,x15817,x15818,x15819,x15812))
% 109.14/108.87 [1582]~E(x15821,x15822)+E(f241(x15821,x15823,x15824),f241(x15822,x15823,x15824))
% 109.14/108.87 [1583]~E(x15831,x15832)+E(f241(x15833,x15831,x15834),f241(x15833,x15832,x15834))
% 109.14/108.87 [1584]~E(x15841,x15842)+E(f241(x15843,x15844,x15841),f241(x15843,x15844,x15842))
% 109.14/108.87 [1585]~E(x15851,x15852)+E(f665(x15851,x15853,x15854,x15855),f665(x15852,x15853,x15854,x15855))
% 109.14/108.87 [1586]~E(x15861,x15862)+E(f665(x15863,x15861,x15864,x15865),f665(x15863,x15862,x15864,x15865))
% 109.14/108.87 [1587]~E(x15871,x15872)+E(f665(x15873,x15874,x15871,x15875),f665(x15873,x15874,x15872,x15875))
% 109.14/108.87 [1588]~E(x15881,x15882)+E(f665(x15883,x15884,x15885,x15881),f665(x15883,x15884,x15885,x15882))
% 109.14/108.87 [1589]~E(x15891,x15892)+E(f574(x15891,x15893,x15894,x15895),f574(x15892,x15893,x15894,x15895))
% 109.14/108.87 [1590]~E(x15901,x15902)+E(f574(x15903,x15901,x15904,x15905),f574(x15903,x15902,x15904,x15905))
% 109.14/108.87 [1591]~E(x15911,x15912)+E(f574(x15913,x15914,x15911,x15915),f574(x15913,x15914,x15912,x15915))
% 109.14/108.87 [1592]~E(x15921,x15922)+E(f574(x15923,x15924,x15925,x15921),f574(x15923,x15924,x15925,x15922))
% 109.14/108.87 [1593]~E(x15931,x15932)+E(f196(x15931,x15933,x15934,x15935),f196(x15932,x15933,x15934,x15935))
% 109.14/108.87 [1594]~E(x15941,x15942)+E(f196(x15943,x15941,x15944,x15945),f196(x15943,x15942,x15944,x15945))
% 109.14/108.87 [1595]~E(x15951,x15952)+E(f196(x15953,x15954,x15951,x15955),f196(x15953,x15954,x15952,x15955))
% 109.14/108.87 [1596]~E(x15961,x15962)+E(f196(x15963,x15964,x15965,x15961),f196(x15963,x15964,x15965,x15962))
% 109.14/108.87 [1597]~E(x15971,x15972)+E(f38(x15971),f38(x15972))
% 109.14/108.87 [1598]~E(x15981,x15982)+E(f40(x15981,x15983),f40(x15982,x15983))
% 109.14/108.87 [1599]~E(x15991,x15992)+E(f40(x15993,x15991),f40(x15993,x15992))
% 109.14/108.87 [1600]~E(x16001,x16002)+E(f572(x16001,x16003,x16004,x16005),f572(x16002,x16003,x16004,x16005))
% 109.14/108.87 [1601]~E(x16011,x16012)+E(f572(x16013,x16011,x16014,x16015),f572(x16013,x16012,x16014,x16015))
% 109.14/108.87 [1602]~E(x16021,x16022)+E(f572(x16023,x16024,x16021,x16025),f572(x16023,x16024,x16022,x16025))
% 109.14/108.87 [1603]~E(x16031,x16032)+E(f572(x16033,x16034,x16035,x16031),f572(x16033,x16034,x16035,x16032))
% 109.14/108.87 [1604]~E(x16041,x16042)+E(f597(x16041,x16043,x16044,x16045,x16046,x16047),f597(x16042,x16043,x16044,x16045,x16046,x16047))
% 109.14/108.87 [1605]~E(x16051,x16052)+E(f597(x16053,x16051,x16054,x16055,x16056,x16057),f597(x16053,x16052,x16054,x16055,x16056,x16057))
% 109.14/108.87 [1606]~E(x16061,x16062)+E(f597(x16063,x16064,x16061,x16065,x16066,x16067),f597(x16063,x16064,x16062,x16065,x16066,x16067))
% 109.14/108.87 [1607]~E(x16071,x16072)+E(f597(x16073,x16074,x16075,x16071,x16076,x16077),f597(x16073,x16074,x16075,x16072,x16076,x16077))
% 109.14/108.87 [1608]~E(x16081,x16082)+E(f597(x16083,x16084,x16085,x16086,x16081,x16087),f597(x16083,x16084,x16085,x16086,x16082,x16087))
% 109.14/108.87 [1609]~E(x16091,x16092)+E(f597(x16093,x16094,x16095,x16096,x16097,x16091),f597(x16093,x16094,x16095,x16096,x16097,x16092))
% 109.14/108.87 [1610]~E(x16101,x16102)+E(f700(x16101,x16103,x16104,x16105),f700(x16102,x16103,x16104,x16105))
% 109.14/108.87 [1611]~E(x16111,x16112)+E(f700(x16113,x16111,x16114,x16115),f700(x16113,x16112,x16114,x16115))
% 109.14/108.87 [1612]~E(x16121,x16122)+E(f700(x16123,x16124,x16121,x16125),f700(x16123,x16124,x16122,x16125))
% 109.14/108.87 [1613]~E(x16131,x16132)+E(f700(x16133,x16134,x16135,x16131),f700(x16133,x16134,x16135,x16132))
% 109.14/108.87 [1614]~E(x16141,x16142)+E(f787(x16141,x16143),f787(x16142,x16143))
% 109.14/108.87 [1615]~E(x16151,x16152)+E(f787(x16153,x16151),f787(x16153,x16152))
% 109.14/108.87 [1616]~E(x16161,x16162)+E(f457(x16161,x16163),f457(x16162,x16163))
% 109.14/108.87 [1617]~E(x16171,x16172)+E(f457(x16173,x16171),f457(x16173,x16172))
% 109.14/108.87 [1618]~E(x16181,x16182)+E(f538(x16181,x16183,x16184),f538(x16182,x16183,x16184))
% 109.14/108.87 [1619]~E(x16191,x16192)+E(f538(x16193,x16191,x16194),f538(x16193,x16192,x16194))
% 109.14/108.87 [1620]~E(x16201,x16202)+E(f538(x16203,x16204,x16201),f538(x16203,x16204,x16202))
% 109.14/108.87 [1621]~E(x16211,x16212)+E(f766(x16211,x16213,x16214),f766(x16212,x16213,x16214))
% 109.14/108.87 [1622]~E(x16221,x16222)+E(f766(x16223,x16221,x16224),f766(x16223,x16222,x16224))
% 109.14/108.87 [1623]~E(x16231,x16232)+E(f766(x16233,x16234,x16231),f766(x16233,x16234,x16232))
% 109.14/108.87 [1624]~E(x16241,x16242)+E(f550(x16241,x16243,x16244,x16245,x16246,x16247),f550(x16242,x16243,x16244,x16245,x16246,x16247))
% 109.14/108.87 [1625]~E(x16251,x16252)+E(f550(x16253,x16251,x16254,x16255,x16256,x16257),f550(x16253,x16252,x16254,x16255,x16256,x16257))
% 109.14/108.87 [1626]~E(x16261,x16262)+E(f550(x16263,x16264,x16261,x16265,x16266,x16267),f550(x16263,x16264,x16262,x16265,x16266,x16267))
% 109.14/108.87 [1627]~E(x16271,x16272)+E(f550(x16273,x16274,x16275,x16271,x16276,x16277),f550(x16273,x16274,x16275,x16272,x16276,x16277))
% 109.14/108.87 [1628]~E(x16281,x16282)+E(f550(x16283,x16284,x16285,x16286,x16281,x16287),f550(x16283,x16284,x16285,x16286,x16282,x16287))
% 109.14/108.87 [1629]~E(x16291,x16292)+E(f550(x16293,x16294,x16295,x16296,x16297,x16291),f550(x16293,x16294,x16295,x16296,x16297,x16292))
% 109.14/108.87 [1630]~E(x16301,x16302)+E(f260(x16301,x16303),f260(x16302,x16303))
% 109.14/108.87 [1631]~E(x16311,x16312)+E(f260(x16313,x16311),f260(x16313,x16312))
% 109.14/108.87 [1632]~E(x16321,x16322)+E(f337(x16321,x16323,x16324,x16325),f337(x16322,x16323,x16324,x16325))
% 109.14/108.87 [1633]~E(x16331,x16332)+E(f337(x16333,x16331,x16334,x16335),f337(x16333,x16332,x16334,x16335))
% 109.14/108.87 [1634]~E(x16341,x16342)+E(f337(x16343,x16344,x16341,x16345),f337(x16343,x16344,x16342,x16345))
% 109.14/108.87 [1635]~E(x16351,x16352)+E(f337(x16353,x16354,x16355,x16351),f337(x16353,x16354,x16355,x16352))
% 109.14/108.87 [1636]~E(x16361,x16362)+E(f527(x16361,x16363,x16364,x16365,x16366,x16367,x16368),f527(x16362,x16363,x16364,x16365,x16366,x16367,x16368))
% 109.14/108.87 [1637]~E(x16371,x16372)+E(f527(x16373,x16371,x16374,x16375,x16376,x16377,x16378),f527(x16373,x16372,x16374,x16375,x16376,x16377,x16378))
% 109.14/108.87 [1638]~E(x16381,x16382)+E(f527(x16383,x16384,x16381,x16385,x16386,x16387,x16388),f527(x16383,x16384,x16382,x16385,x16386,x16387,x16388))
% 109.14/108.87 [1639]~E(x16391,x16392)+E(f527(x16393,x16394,x16395,x16391,x16396,x16397,x16398),f527(x16393,x16394,x16395,x16392,x16396,x16397,x16398))
% 109.14/108.87 [1640]~E(x16401,x16402)+E(f527(x16403,x16404,x16405,x16406,x16401,x16407,x16408),f527(x16403,x16404,x16405,x16406,x16402,x16407,x16408))
% 109.14/108.87 [1641]~E(x16411,x16412)+E(f527(x16413,x16414,x16415,x16416,x16417,x16411,x16418),f527(x16413,x16414,x16415,x16416,x16417,x16412,x16418))
% 109.14/108.87 [1642]~E(x16421,x16422)+E(f527(x16423,x16424,x16425,x16426,x16427,x16428,x16421),f527(x16423,x16424,x16425,x16426,x16427,x16428,x16422))
% 109.14/108.87 [1643]~E(x16431,x16432)+E(f868(x16431,x16433,x16434,x16435,x16436),f868(x16432,x16433,x16434,x16435,x16436))
% 109.14/108.87 [1644]~E(x16441,x16442)+E(f868(x16443,x16441,x16444,x16445,x16446),f868(x16443,x16442,x16444,x16445,x16446))
% 109.14/108.87 [1645]~E(x16451,x16452)+E(f868(x16453,x16454,x16451,x16455,x16456),f868(x16453,x16454,x16452,x16455,x16456))
% 109.14/108.87 [1646]~E(x16461,x16462)+E(f868(x16463,x16464,x16465,x16461,x16466),f868(x16463,x16464,x16465,x16462,x16466))
% 109.14/108.87 [1647]~E(x16471,x16472)+E(f868(x16473,x16474,x16475,x16476,x16471),f868(x16473,x16474,x16475,x16476,x16472))
% 109.14/108.87 [1648]~E(x16481,x16482)+E(f862(x16481,x16483,x16484),f862(x16482,x16483,x16484))
% 109.14/108.87 [1649]~E(x16491,x16492)+E(f862(x16493,x16491,x16494),f862(x16493,x16492,x16494))
% 109.14/108.87 [1650]~E(x16501,x16502)+E(f862(x16503,x16504,x16501),f862(x16503,x16504,x16502))
% 109.14/108.87 [1651]~E(x16511,x16512)+E(f616(x16511,x16513),f616(x16512,x16513))
% 109.14/108.87 [1652]~E(x16521,x16522)+E(f616(x16523,x16521),f616(x16523,x16522))
% 109.14/108.87 [1653]~E(x16531,x16532)+E(f410(x16531,x16533,x16534),f410(x16532,x16533,x16534))
% 109.14/108.87 [1654]~E(x16541,x16542)+E(f410(x16543,x16541,x16544),f410(x16543,x16542,x16544))
% 109.14/108.87 [1655]~E(x16551,x16552)+E(f410(x16553,x16554,x16551),f410(x16553,x16554,x16552))
% 109.14/108.87 [1656]~E(x16561,x16562)+E(f354(x16561,x16563,x16564,x16565),f354(x16562,x16563,x16564,x16565))
% 109.14/108.87 [1657]~E(x16571,x16572)+E(f354(x16573,x16571,x16574,x16575),f354(x16573,x16572,x16574,x16575))
% 109.14/108.87 [1658]~E(x16581,x16582)+E(f354(x16583,x16584,x16581,x16585),f354(x16583,x16584,x16582,x16585))
% 109.14/108.87 [1659]~E(x16591,x16592)+E(f354(x16593,x16594,x16595,x16591),f354(x16593,x16594,x16595,x16592))
% 109.14/108.87 [1660]~E(x16601,x16602)+E(f165(x16601,x16603,x16604),f165(x16602,x16603,x16604))
% 109.14/108.87 [1661]~E(x16611,x16612)+E(f165(x16613,x16611,x16614),f165(x16613,x16612,x16614))
% 109.14/108.87 [1662]~E(x16621,x16622)+E(f165(x16623,x16624,x16621),f165(x16623,x16624,x16622))
% 109.14/108.87 [1663]~E(x16631,x16632)+E(f688(x16631,x16633,x16634),f688(x16632,x16633,x16634))
% 109.14/108.87 [1664]~E(x16641,x16642)+E(f688(x16643,x16641,x16644),f688(x16643,x16642,x16644))
% 109.14/108.87 [1665]~E(x16651,x16652)+E(f688(x16653,x16654,x16651),f688(x16653,x16654,x16652))
% 109.14/108.87 [1666]~E(x16661,x16662)+E(f823(x16661,x16663,x16664),f823(x16662,x16663,x16664))
% 109.14/108.87 [1667]~E(x16671,x16672)+E(f823(x16673,x16671,x16674),f823(x16673,x16672,x16674))
% 109.14/108.87 [1668]~E(x16681,x16682)+E(f823(x16683,x16684,x16681),f823(x16683,x16684,x16682))
% 109.14/108.87 [1669]~E(x16691,x16692)+E(f137(x16691,x16693),f137(x16692,x16693))
% 109.14/108.87 [1670]~E(x16701,x16702)+E(f137(x16703,x16701),f137(x16703,x16702))
% 109.14/108.87 [1671]~E(x16711,x16712)+E(f504(x16711,x16713,x16714,x16715,x16716),f504(x16712,x16713,x16714,x16715,x16716))
% 109.14/108.87 [1672]~E(x16721,x16722)+E(f504(x16723,x16721,x16724,x16725,x16726),f504(x16723,x16722,x16724,x16725,x16726))
% 109.14/108.87 [1673]~E(x16731,x16732)+E(f504(x16733,x16734,x16731,x16735,x16736),f504(x16733,x16734,x16732,x16735,x16736))
% 109.14/108.87 [1674]~E(x16741,x16742)+E(f504(x16743,x16744,x16745,x16741,x16746),f504(x16743,x16744,x16745,x16742,x16746))
% 109.14/108.87 [1675]~E(x16751,x16752)+E(f504(x16753,x16754,x16755,x16756,x16751),f504(x16753,x16754,x16755,x16756,x16752))
% 109.14/108.87 [1676]~E(x16761,x16762)+E(f259(x16761,x16763),f259(x16762,x16763))
% 109.14/108.87 [1677]~E(x16771,x16772)+E(f259(x16773,x16771),f259(x16773,x16772))
% 109.14/108.87 [1678]~E(x16781,x16782)+E(f901(x16781,x16783,x16784,x16785,x16786),f901(x16782,x16783,x16784,x16785,x16786))
% 109.14/108.87 [1679]~E(x16791,x16792)+E(f901(x16793,x16791,x16794,x16795,x16796),f901(x16793,x16792,x16794,x16795,x16796))
% 109.14/108.87 [1680]~E(x16801,x16802)+E(f901(x16803,x16804,x16801,x16805,x16806),f901(x16803,x16804,x16802,x16805,x16806))
% 109.14/108.87 [1681]~E(x16811,x16812)+E(f901(x16813,x16814,x16815,x16811,x16816),f901(x16813,x16814,x16815,x16812,x16816))
% 109.14/108.87 [1682]~E(x16821,x16822)+E(f901(x16823,x16824,x16825,x16826,x16821),f901(x16823,x16824,x16825,x16826,x16822))
% 109.14/108.87 [1683]~E(x16831,x16832)+E(f799(x16831,x16833),f799(x16832,x16833))
% 109.14/108.87 [1684]~E(x16841,x16842)+E(f799(x16843,x16841),f799(x16843,x16842))
% 109.14/108.87 [1685]~E(x16851,x16852)+E(f713(x16851,x16853,x16854),f713(x16852,x16853,x16854))
% 109.14/108.87 [1686]~E(x16861,x16862)+E(f713(x16863,x16861,x16864),f713(x16863,x16862,x16864))
% 109.14/108.87 [1687]~E(x16871,x16872)+E(f713(x16873,x16874,x16871),f713(x16873,x16874,x16872))
% 109.14/108.87 [1688]~E(x16881,x16882)+E(f345(x16881,x16883,x16884,x16885),f345(x16882,x16883,x16884,x16885))
% 109.14/108.87 [1689]~E(x16891,x16892)+E(f345(x16893,x16891,x16894,x16895),f345(x16893,x16892,x16894,x16895))
% 109.14/108.87 [1690]~E(x16901,x16902)+E(f345(x16903,x16904,x16901,x16905),f345(x16903,x16904,x16902,x16905))
% 109.14/108.87 [1691]~E(x16911,x16912)+E(f345(x16913,x16914,x16915,x16911),f345(x16913,x16914,x16915,x16912))
% 109.14/108.87 [1692]~E(x16921,x16922)+E(f365(x16921,x16923,x16924),f365(x16922,x16923,x16924))
% 109.14/108.87 [1693]~E(x16931,x16932)+E(f365(x16933,x16931,x16934),f365(x16933,x16932,x16934))
% 109.14/108.87 [1694]~E(x16941,x16942)+E(f365(x16943,x16944,x16941),f365(x16943,x16944,x16942))
% 109.14/108.87 [1695]~E(x16951,x16952)+E(f835(x16951,x16953,x16954,x16955,x16956,x16957,x16958,x16959),f835(x16952,x16953,x16954,x16955,x16956,x16957,x16958,x16959))
% 109.14/108.87 [1696]~E(x16961,x16962)+E(f835(x16963,x16961,x16964,x16965,x16966,x16967,x16968,x16969),f835(x16963,x16962,x16964,x16965,x16966,x16967,x16968,x16969))
% 109.14/108.87 [1697]~E(x16971,x16972)+E(f835(x16973,x16974,x16971,x16975,x16976,x16977,x16978,x16979),f835(x16973,x16974,x16972,x16975,x16976,x16977,x16978,x16979))
% 109.14/108.87 [1698]~E(x16981,x16982)+E(f835(x16983,x16984,x16985,x16981,x16986,x16987,x16988,x16989),f835(x16983,x16984,x16985,x16982,x16986,x16987,x16988,x16989))
% 109.14/108.87 [1699]~E(x16991,x16992)+E(f835(x16993,x16994,x16995,x16996,x16991,x16997,x16998,x16999),f835(x16993,x16994,x16995,x16996,x16992,x16997,x16998,x16999))
% 109.14/108.87 [1700]~E(x17001,x17002)+E(f835(x17003,x17004,x17005,x17006,x17007,x17001,x17008,x17009),f835(x17003,x17004,x17005,x17006,x17007,x17002,x17008,x17009))
% 109.14/108.87 [1701]~E(x17011,x17012)+E(f835(x17013,x17014,x17015,x17016,x17017,x17018,x17011,x17019),f835(x17013,x17014,x17015,x17016,x17017,x17018,x17012,x17019))
% 109.14/108.87 [1702]~E(x17021,x17022)+E(f835(x17023,x17024,x17025,x17026,x17027,x17028,x17029,x17021),f835(x17023,x17024,x17025,x17026,x17027,x17028,x17029,x17022))
% 109.14/108.87 [1703]~E(x17031,x17032)+E(f453(x17031,x17033,x17034),f453(x17032,x17033,x17034))
% 109.14/108.87 [1704]~E(x17041,x17042)+E(f453(x17043,x17041,x17044),f453(x17043,x17042,x17044))
% 109.14/108.87 [1705]~E(x17051,x17052)+E(f453(x17053,x17054,x17051),f453(x17053,x17054,x17052))
% 109.14/108.87 [1706]~E(x17061,x17062)+E(f189(x17061,x17063,x17064,x17065),f189(x17062,x17063,x17064,x17065))
% 109.14/108.87 [1707]~E(x17071,x17072)+E(f189(x17073,x17071,x17074,x17075),f189(x17073,x17072,x17074,x17075))
% 109.14/108.87 [1708]~E(x17081,x17082)+E(f189(x17083,x17084,x17081,x17085),f189(x17083,x17084,x17082,x17085))
% 109.14/108.87 [1709]~E(x17091,x17092)+E(f189(x17093,x17094,x17095,x17091),f189(x17093,x17094,x17095,x17092))
% 109.14/108.87 [1710]~E(x17101,x17102)+E(f47(x17101,x17103),f47(x17102,x17103))
% 109.14/108.87 [1711]~E(x17111,x17112)+E(f47(x17113,x17111),f47(x17113,x17112))
% 109.14/108.87 [1712]~E(x17121,x17122)+E(f171(x17121),f171(x17122))
% 109.14/108.87 [1713]~E(x17131,x17132)+E(f748(x17131,x17133,x17134,x17135),f748(x17132,x17133,x17134,x17135))
% 109.14/108.87 [1714]~E(x17141,x17142)+E(f748(x17143,x17141,x17144,x17145),f748(x17143,x17142,x17144,x17145))
% 109.14/108.87 [1715]~E(x17151,x17152)+E(f748(x17153,x17154,x17151,x17155),f748(x17153,x17154,x17152,x17155))
% 109.14/108.87 [1716]~E(x17161,x17162)+E(f748(x17163,x17164,x17165,x17161),f748(x17163,x17164,x17165,x17162))
% 109.14/108.87 [1717]~E(x17171,x17172)+E(f521(x17171,x17173,x17174,x17175),f521(x17172,x17173,x17174,x17175))
% 109.14/108.87 [1718]~E(x17181,x17182)+E(f521(x17183,x17181,x17184,x17185),f521(x17183,x17182,x17184,x17185))
% 109.14/108.87 [1719]~E(x17191,x17192)+E(f521(x17193,x17194,x17191,x17195),f521(x17193,x17194,x17192,x17195))
% 109.14/108.87 [1720]~E(x17201,x17202)+E(f521(x17203,x17204,x17205,x17201),f521(x17203,x17204,x17205,x17202))
% 109.14/108.87 [1721]~E(x17211,x17212)+E(f731(x17211,x17213,x17214,x17215,x17216),f731(x17212,x17213,x17214,x17215,x17216))
% 109.14/108.87 [1722]~E(x17221,x17222)+E(f731(x17223,x17221,x17224,x17225,x17226),f731(x17223,x17222,x17224,x17225,x17226))
% 109.14/108.87 [1723]~E(x17231,x17232)+E(f731(x17233,x17234,x17231,x17235,x17236),f731(x17233,x17234,x17232,x17235,x17236))
% 109.14/108.87 [1724]~E(x17241,x17242)+E(f731(x17243,x17244,x17245,x17241,x17246),f731(x17243,x17244,x17245,x17242,x17246))
% 109.14/108.87 [1725]~E(x17251,x17252)+E(f731(x17253,x17254,x17255,x17256,x17251),f731(x17253,x17254,x17255,x17256,x17252))
% 109.14/108.87 [1726]~E(x17261,x17262)+E(f854(x17261,x17263,x17264),f854(x17262,x17263,x17264))
% 109.14/108.87 [1727]~E(x17271,x17272)+E(f854(x17273,x17271,x17274),f854(x17273,x17272,x17274))
% 109.14/108.87 [1728]~E(x17281,x17282)+E(f854(x17283,x17284,x17281),f854(x17283,x17284,x17282))
% 109.14/108.87 [1729]~E(x17291,x17292)+E(f392(x17291,x17293,x17294,x17295,x17296),f392(x17292,x17293,x17294,x17295,x17296))
% 109.14/108.87 [1730]~E(x17301,x17302)+E(f392(x17303,x17301,x17304,x17305,x17306),f392(x17303,x17302,x17304,x17305,x17306))
% 109.14/108.87 [1731]~E(x17311,x17312)+E(f392(x17313,x17314,x17311,x17315,x17316),f392(x17313,x17314,x17312,x17315,x17316))
% 109.14/108.87 [1732]~E(x17321,x17322)+E(f392(x17323,x17324,x17325,x17321,x17326),f392(x17323,x17324,x17325,x17322,x17326))
% 109.14/108.87 [1733]~E(x17331,x17332)+E(f392(x17333,x17334,x17335,x17336,x17331),f392(x17333,x17334,x17335,x17336,x17332))
% 109.14/108.87 [1734]~E(x17341,x17342)+E(f35(x17341),f35(x17342))
% 109.14/108.87 [1735]~E(x17351,x17352)+E(f207(x17351,x17353),f207(x17352,x17353))
% 109.14/108.87 [1736]~E(x17361,x17362)+E(f207(x17363,x17361),f207(x17363,x17362))
% 109.14/108.87 [1737]~E(x17371,x17372)+E(f600(x17371,x17373,x17374,x17375),f600(x17372,x17373,x17374,x17375))
% 109.14/108.87 [1738]~E(x17381,x17382)+E(f600(x17383,x17381,x17384,x17385),f600(x17383,x17382,x17384,x17385))
% 109.14/108.87 [1739]~E(x17391,x17392)+E(f600(x17393,x17394,x17391,x17395),f600(x17393,x17394,x17392,x17395))
% 109.14/108.87 [1740]~E(x17401,x17402)+E(f600(x17403,x17404,x17405,x17401),f600(x17403,x17404,x17405,x17402))
% 109.14/108.87 [1741]~E(x17411,x17412)+E(f782(x17411,x17413),f782(x17412,x17413))
% 109.14/108.87 [1742]~E(x17421,x17422)+E(f782(x17423,x17421),f782(x17423,x17422))
% 109.14/108.87 [1743]~E(x17431,x17432)+E(f710(x17431,x17433,x17434),f710(x17432,x17433,x17434))
% 109.14/108.87 [1744]~E(x17441,x17442)+E(f710(x17443,x17441,x17444),f710(x17443,x17442,x17444))
% 109.14/108.87 [1745]~E(x17451,x17452)+E(f710(x17453,x17454,x17451),f710(x17453,x17454,x17452))
% 109.14/108.87 [1746]~E(x17461,x17462)+E(f730(x17461,x17463,x17464,x17465),f730(x17462,x17463,x17464,x17465))
% 109.14/108.87 [1747]~E(x17471,x17472)+E(f730(x17473,x17471,x17474,x17475),f730(x17473,x17472,x17474,x17475))
% 109.14/108.87 [1748]~E(x17481,x17482)+E(f730(x17483,x17484,x17481,x17485),f730(x17483,x17484,x17482,x17485))
% 109.14/108.87 [1749]~E(x17491,x17492)+E(f730(x17493,x17494,x17495,x17491),f730(x17493,x17494,x17495,x17492))
% 109.14/108.87 [1750]~E(x17501,x17502)+E(f631(x17501,x17503,x17504,x17505,x17506),f631(x17502,x17503,x17504,x17505,x17506))
% 109.14/108.87 [1751]~E(x17511,x17512)+E(f631(x17513,x17511,x17514,x17515,x17516),f631(x17513,x17512,x17514,x17515,x17516))
% 109.14/108.87 [1752]~E(x17521,x17522)+E(f631(x17523,x17524,x17521,x17525,x17526),f631(x17523,x17524,x17522,x17525,x17526))
% 109.14/108.87 [1753]~E(x17531,x17532)+E(f631(x17533,x17534,x17535,x17531,x17536),f631(x17533,x17534,x17535,x17532,x17536))
% 109.14/108.87 [1754]~E(x17541,x17542)+E(f631(x17543,x17544,x17545,x17546,x17541),f631(x17543,x17544,x17545,x17546,x17542))
% 109.14/108.87 [1755]~E(x17551,x17552)+E(f741(x17551,x17553,x17554,x17555,x17556),f741(x17552,x17553,x17554,x17555,x17556))
% 109.14/108.87 [1756]~E(x17561,x17562)+E(f741(x17563,x17561,x17564,x17565,x17566),f741(x17563,x17562,x17564,x17565,x17566))
% 109.14/108.87 [1757]~E(x17571,x17572)+E(f741(x17573,x17574,x17571,x17575,x17576),f741(x17573,x17574,x17572,x17575,x17576))
% 109.14/108.87 [1758]~E(x17581,x17582)+E(f741(x17583,x17584,x17585,x17581,x17586),f741(x17583,x17584,x17585,x17582,x17586))
% 109.14/108.87 [1759]~E(x17591,x17592)+E(f741(x17593,x17594,x17595,x17596,x17591),f741(x17593,x17594,x17595,x17596,x17592))
% 109.14/108.87 [1760]~E(x17601,x17602)+E(f711(x17601,x17603),f711(x17602,x17603))
% 109.14/108.87 [1761]~E(x17611,x17612)+E(f711(x17613,x17611),f711(x17613,x17612))
% 109.14/108.87 [1762]~E(x17621,x17622)+E(f336(x17621,x17623,x17624,x17625),f336(x17622,x17623,x17624,x17625))
% 109.14/108.87 [1763]~E(x17631,x17632)+E(f336(x17633,x17631,x17634,x17635),f336(x17633,x17632,x17634,x17635))
% 109.14/108.87 [1764]~E(x17641,x17642)+E(f336(x17643,x17644,x17641,x17645),f336(x17643,x17644,x17642,x17645))
% 109.14/108.87 [1765]~E(x17651,x17652)+E(f336(x17653,x17654,x17655,x17651),f336(x17653,x17654,x17655,x17652))
% 109.14/108.87 [1766]~E(x17661,x17662)+E(f195(x17661),f195(x17662))
% 109.14/108.87 [1767]~E(x17671,x17672)+E(f361(x17671,x17673),f361(x17672,x17673))
% 109.14/108.87 [1768]~E(x17681,x17682)+E(f361(x17683,x17681),f361(x17683,x17682))
% 109.14/108.87 [1769]~E(x17691,x17692)+E(f723(x17691,x17693,x17694,x17695),f723(x17692,x17693,x17694,x17695))
% 109.14/108.87 [1770]~E(x17701,x17702)+E(f723(x17703,x17701,x17704,x17705),f723(x17703,x17702,x17704,x17705))
% 109.14/108.87 [1771]~E(x17711,x17712)+E(f723(x17713,x17714,x17711,x17715),f723(x17713,x17714,x17712,x17715))
% 109.14/108.87 [1772]~E(x17721,x17722)+E(f723(x17723,x17724,x17725,x17721),f723(x17723,x17724,x17725,x17722))
% 109.14/108.87 [1773]~E(x17731,x17732)+E(f326(x17731,x17733),f326(x17732,x17733))
% 109.14/108.87 [1774]~E(x17741,x17742)+E(f326(x17743,x17741),f326(x17743,x17742))
% 109.14/108.87 [1775]~E(x17751,x17752)+E(f884(x17751,x17753),f884(x17752,x17753))
% 109.14/108.87 [1776]~E(x17761,x17762)+E(f884(x17763,x17761),f884(x17763,x17762))
% 109.14/108.87 [1777]~E(x17771,x17772)+E(f287(x17771,x17773,x17774),f287(x17772,x17773,x17774))
% 109.14/108.87 [1778]~E(x17781,x17782)+E(f287(x17783,x17781,x17784),f287(x17783,x17782,x17784))
% 109.14/108.87 [1779]~E(x17791,x17792)+E(f287(x17793,x17794,x17791),f287(x17793,x17794,x17792))
% 109.14/108.87 [1780]~E(x17801,x17802)+E(f452(x17801,x17803,x17804,x17805),f452(x17802,x17803,x17804,x17805))
% 109.14/108.87 [1781]~E(x17811,x17812)+E(f452(x17813,x17811,x17814,x17815),f452(x17813,x17812,x17814,x17815))
% 109.14/108.87 [1782]~E(x17821,x17822)+E(f452(x17823,x17824,x17821,x17825),f452(x17823,x17824,x17822,x17825))
% 109.14/108.87 [1783]~E(x17831,x17832)+E(f452(x17833,x17834,x17835,x17831),f452(x17833,x17834,x17835,x17832))
% 109.14/108.87 [1784]~E(x17841,x17842)+E(f270(x17841,x17843,x17844,x17845),f270(x17842,x17843,x17844,x17845))
% 109.14/108.87 [1785]~E(x17851,x17852)+E(f270(x17853,x17851,x17854,x17855),f270(x17853,x17852,x17854,x17855))
% 109.14/108.87 [1786]~E(x17861,x17862)+E(f270(x17863,x17864,x17861,x17865),f270(x17863,x17864,x17862,x17865))
% 109.14/108.87 [1787]~E(x17871,x17872)+E(f270(x17873,x17874,x17875,x17871),f270(x17873,x17874,x17875,x17872))
% 109.14/108.87 [1788]~E(x17881,x17882)+E(f475(x17881,x17883,x17884,x17885,x17886),f475(x17882,x17883,x17884,x17885,x17886))
% 109.14/108.87 [1789]~E(x17891,x17892)+E(f475(x17893,x17891,x17894,x17895,x17896),f475(x17893,x17892,x17894,x17895,x17896))
% 109.14/108.87 [1790]~E(x17901,x17902)+E(f475(x17903,x17904,x17901,x17905,x17906),f475(x17903,x17904,x17902,x17905,x17906))
% 109.14/108.87 [1791]~E(x17911,x17912)+E(f475(x17913,x17914,x17915,x17911,x17916),f475(x17913,x17914,x17915,x17912,x17916))
% 109.14/108.87 [1792]~E(x17921,x17922)+E(f475(x17923,x17924,x17925,x17926,x17921),f475(x17923,x17924,x17925,x17926,x17922))
% 109.14/108.87 [1793]~E(x17931,x17932)+E(f344(x17931,x17933,x17934,x17935),f344(x17932,x17933,x17934,x17935))
% 109.14/108.87 [1794]~E(x17941,x17942)+E(f344(x17943,x17941,x17944,x17945),f344(x17943,x17942,x17944,x17945))
% 109.14/108.87 [1795]~E(x17951,x17952)+E(f344(x17953,x17954,x17951,x17955),f344(x17953,x17954,x17952,x17955))
% 109.14/108.87 [1796]~E(x17961,x17962)+E(f344(x17963,x17964,x17965,x17961),f344(x17963,x17964,x17965,x17962))
% 109.14/108.87 [1797]~E(x17971,x17972)+E(f668(x17971,x17973),f668(x17972,x17973))
% 109.14/108.87 [1798]~E(x17981,x17982)+E(f668(x17983,x17981),f668(x17983,x17982))
% 109.14/108.87 [1799]~E(x17991,x17992)+E(f762(x17991,x17993,x17994),f762(x17992,x17993,x17994))
% 109.14/108.87 [1800]~E(x18001,x18002)+E(f762(x18003,x18001,x18004),f762(x18003,x18002,x18004))
% 109.14/108.87 [1801]~E(x18011,x18012)+E(f762(x18013,x18014,x18011),f762(x18013,x18014,x18012))
% 109.14/108.87 [1802]~E(x18021,x18022)+E(f707(x18021,x18023,x18024),f707(x18022,x18023,x18024))
% 109.14/108.87 [1803]~E(x18031,x18032)+E(f707(x18033,x18031,x18034),f707(x18033,x18032,x18034))
% 109.14/108.87 [1804]~E(x18041,x18042)+E(f707(x18043,x18044,x18041),f707(x18043,x18044,x18042))
% 109.14/108.87 [1805]~E(x18051,x18052)+E(f887(x18051,x18053),f887(x18052,x18053))
% 109.14/108.87 [1806]~E(x18061,x18062)+E(f887(x18063,x18061),f887(x18063,x18062))
% 109.14/108.87 [1807]~E(x18071,x18072)+E(f906(x18071,x18073),f906(x18072,x18073))
% 109.14/108.87 [1808]~E(x18081,x18082)+E(f906(x18083,x18081),f906(x18083,x18082))
% 109.14/108.87 [1809]~E(x18091,x18092)+E(f691(x18091,x18093,x18094,x18095,x18096),f691(x18092,x18093,x18094,x18095,x18096))
% 109.14/108.87 [1810]~E(x18101,x18102)+E(f691(x18103,x18101,x18104,x18105,x18106),f691(x18103,x18102,x18104,x18105,x18106))
% 109.14/108.87 [1811]~E(x18111,x18112)+E(f691(x18113,x18114,x18111,x18115,x18116),f691(x18113,x18114,x18112,x18115,x18116))
% 109.14/108.87 [1812]~E(x18121,x18122)+E(f691(x18123,x18124,x18125,x18121,x18126),f691(x18123,x18124,x18125,x18122,x18126))
% 109.14/108.87 [1813]~E(x18131,x18132)+E(f691(x18133,x18134,x18135,x18136,x18131),f691(x18133,x18134,x18135,x18136,x18132))
% 109.14/108.87 [1814]~E(x18141,x18142)+E(f455(x18141,x18143),f455(x18142,x18143))
% 109.14/108.87 [1815]~E(x18151,x18152)+E(f455(x18153,x18151),f455(x18153,x18152))
% 109.14/108.87 [1816]~E(x18161,x18162)+E(f610(x18161,x18163),f610(x18162,x18163))
% 109.14/108.87 [1817]~E(x18171,x18172)+E(f610(x18173,x18171),f610(x18173,x18172))
% 109.14/108.87 [1818]~E(x18181,x18182)+E(f356(x18181),f356(x18182))
% 109.14/108.87 [1819]~E(x18191,x18192)+E(f900(x18191,x18193,x18194,x18195),f900(x18192,x18193,x18194,x18195))
% 109.14/108.87 [1820]~E(x18201,x18202)+E(f900(x18203,x18201,x18204,x18205),f900(x18203,x18202,x18204,x18205))
% 109.14/108.87 [1821]~E(x18211,x18212)+E(f900(x18213,x18214,x18211,x18215),f900(x18213,x18214,x18212,x18215))
% 109.14/108.87 [1822]~E(x18221,x18222)+E(f900(x18223,x18224,x18225,x18221),f900(x18223,x18224,x18225,x18222))
% 109.14/108.87 [1823]~E(x18231,x18232)+E(f692(x18231,x18233),f692(x18232,x18233))
% 109.14/108.87 [1824]~E(x18241,x18242)+E(f692(x18243,x18241),f692(x18243,x18242))
% 109.14/108.87 [1825]~E(x18251,x18252)+E(f832(x18251,x18253,x18254,x18255,x18256,x18257,x18258),f832(x18252,x18253,x18254,x18255,x18256,x18257,x18258))
% 109.14/108.87 [1826]~E(x18261,x18262)+E(f832(x18263,x18261,x18264,x18265,x18266,x18267,x18268),f832(x18263,x18262,x18264,x18265,x18266,x18267,x18268))
% 109.14/108.87 [1827]~E(x18271,x18272)+E(f832(x18273,x18274,x18271,x18275,x18276,x18277,x18278),f832(x18273,x18274,x18272,x18275,x18276,x18277,x18278))
% 109.14/108.87 [1828]~E(x18281,x18282)+E(f832(x18283,x18284,x18285,x18281,x18286,x18287,x18288),f832(x18283,x18284,x18285,x18282,x18286,x18287,x18288))
% 109.14/108.87 [1829]~E(x18291,x18292)+E(f832(x18293,x18294,x18295,x18296,x18291,x18297,x18298),f832(x18293,x18294,x18295,x18296,x18292,x18297,x18298))
% 109.14/108.87 [1830]~E(x18301,x18302)+E(f832(x18303,x18304,x18305,x18306,x18307,x18301,x18308),f832(x18303,x18304,x18305,x18306,x18307,x18302,x18308))
% 109.14/108.87 [1831]~E(x18311,x18312)+E(f832(x18313,x18314,x18315,x18316,x18317,x18318,x18311),f832(x18313,x18314,x18315,x18316,x18317,x18318,x18312))
% 109.14/108.87 [1832]~E(x18321,x18322)+E(f490(x18321,x18323,x18324),f490(x18322,x18323,x18324))
% 109.14/108.87 [1833]~E(x18331,x18332)+E(f490(x18333,x18331,x18334),f490(x18333,x18332,x18334))
% 109.14/108.87 [1834]~E(x18341,x18342)+E(f490(x18343,x18344,x18341),f490(x18343,x18344,x18342))
% 109.14/108.87 [1835]~E(x18351,x18352)+E(f543(x18351,x18353,x18354,x18355,x18356,x18357),f543(x18352,x18353,x18354,x18355,x18356,x18357))
% 109.14/108.87 [1836]~E(x18361,x18362)+E(f543(x18363,x18361,x18364,x18365,x18366,x18367),f543(x18363,x18362,x18364,x18365,x18366,x18367))
% 109.14/108.87 [1837]~E(x18371,x18372)+E(f543(x18373,x18374,x18371,x18375,x18376,x18377),f543(x18373,x18374,x18372,x18375,x18376,x18377))
% 109.14/108.87 [1838]~E(x18381,x18382)+E(f543(x18383,x18384,x18385,x18381,x18386,x18387),f543(x18383,x18384,x18385,x18382,x18386,x18387))
% 109.14/108.87 [1839]~E(x18391,x18392)+E(f543(x18393,x18394,x18395,x18396,x18391,x18397),f543(x18393,x18394,x18395,x18396,x18392,x18397))
% 109.14/108.87 [1840]~E(x18401,x18402)+E(f543(x18403,x18404,x18405,x18406,x18407,x18401),f543(x18403,x18404,x18405,x18406,x18407,x18402))
% 109.14/108.87 [1841]~E(x18411,x18412)+E(f524(x18411,x18413,x18414),f524(x18412,x18413,x18414))
% 109.14/108.87 [1842]~E(x18421,x18422)+E(f524(x18423,x18421,x18424),f524(x18423,x18422,x18424))
% 109.14/108.87 [1843]~E(x18431,x18432)+E(f524(x18433,x18434,x18431),f524(x18433,x18434,x18432))
% 109.14/108.87 [1844]~E(x18441,x18442)+E(f471(x18441,x18443,x18444,x18445),f471(x18442,x18443,x18444,x18445))
% 109.14/108.87 [1845]~E(x18451,x18452)+E(f471(x18453,x18451,x18454,x18455),f471(x18453,x18452,x18454,x18455))
% 109.14/108.87 [1846]~E(x18461,x18462)+E(f471(x18463,x18464,x18461,x18465),f471(x18463,x18464,x18462,x18465))
% 109.14/108.87 [1847]~E(x18471,x18472)+E(f471(x18473,x18474,x18475,x18471),f471(x18473,x18474,x18475,x18472))
% 109.14/108.87 [1848]~E(x18481,x18482)+E(f837(x18481,x18483,x18484,x18485,x18486,x18487,x18488),f837(x18482,x18483,x18484,x18485,x18486,x18487,x18488))
% 109.14/108.87 [1849]~E(x18491,x18492)+E(f837(x18493,x18491,x18494,x18495,x18496,x18497,x18498),f837(x18493,x18492,x18494,x18495,x18496,x18497,x18498))
% 109.14/108.87 [1850]~E(x18501,x18502)+E(f837(x18503,x18504,x18501,x18505,x18506,x18507,x18508),f837(x18503,x18504,x18502,x18505,x18506,x18507,x18508))
% 109.14/108.87 [1851]~E(x18511,x18512)+E(f837(x18513,x18514,x18515,x18511,x18516,x18517,x18518),f837(x18513,x18514,x18515,x18512,x18516,x18517,x18518))
% 109.14/108.87 [1852]~E(x18521,x18522)+E(f837(x18523,x18524,x18525,x18526,x18521,x18527,x18528),f837(x18523,x18524,x18525,x18526,x18522,x18527,x18528))
% 109.14/108.87 [1853]~E(x18531,x18532)+E(f837(x18533,x18534,x18535,x18536,x18537,x18531,x18538),f837(x18533,x18534,x18535,x18536,x18537,x18532,x18538))
% 109.14/108.87 [1854]~E(x18541,x18542)+E(f837(x18543,x18544,x18545,x18546,x18547,x18548,x18541),f837(x18543,x18544,x18545,x18546,x18547,x18548,x18542))
% 109.14/108.87 [1855]~E(x18551,x18552)+E(f646(x18551,x18553,x18554,x18555,x18556,x18557),f646(x18552,x18553,x18554,x18555,x18556,x18557))
% 109.14/108.87 [1856]~E(x18561,x18562)+E(f646(x18563,x18561,x18564,x18565,x18566,x18567),f646(x18563,x18562,x18564,x18565,x18566,x18567))
% 109.14/108.87 [1857]~E(x18571,x18572)+E(f646(x18573,x18574,x18571,x18575,x18576,x18577),f646(x18573,x18574,x18572,x18575,x18576,x18577))
% 109.14/108.87 [1858]~E(x18581,x18582)+E(f646(x18583,x18584,x18585,x18581,x18586,x18587),f646(x18583,x18584,x18585,x18582,x18586,x18587))
% 109.14/108.87 [1859]~E(x18591,x18592)+E(f646(x18593,x18594,x18595,x18596,x18591,x18597),f646(x18593,x18594,x18595,x18596,x18592,x18597))
% 109.14/108.87 [1860]~E(x18601,x18602)+E(f646(x18603,x18604,x18605,x18606,x18607,x18601),f646(x18603,x18604,x18605,x18606,x18607,x18602))
% 109.14/108.87 [1861]~E(x18611,x18612)+E(f402(x18611,x18613,x18614,x18615,x18616),f402(x18612,x18613,x18614,x18615,x18616))
% 109.14/108.87 [1862]~E(x18621,x18622)+E(f402(x18623,x18621,x18624,x18625,x18626),f402(x18623,x18622,x18624,x18625,x18626))
% 109.14/108.87 [1863]~E(x18631,x18632)+E(f402(x18633,x18634,x18631,x18635,x18636),f402(x18633,x18634,x18632,x18635,x18636))
% 109.14/108.87 [1864]~E(x18641,x18642)+E(f402(x18643,x18644,x18645,x18641,x18646),f402(x18643,x18644,x18645,x18642,x18646))
% 109.14/108.87 [1865]~E(x18651,x18652)+E(f402(x18653,x18654,x18655,x18656,x18651),f402(x18653,x18654,x18655,x18656,x18652))
% 109.14/108.87 [1866]~E(x18661,x18662)+E(f547(x18661,x18663,x18664,x18665,x18666,x18667),f547(x18662,x18663,x18664,x18665,x18666,x18667))
% 109.14/108.87 [1867]~E(x18671,x18672)+E(f547(x18673,x18671,x18674,x18675,x18676,x18677),f547(x18673,x18672,x18674,x18675,x18676,x18677))
% 109.14/108.87 [1868]~E(x18681,x18682)+E(f547(x18683,x18684,x18681,x18685,x18686,x18687),f547(x18683,x18684,x18682,x18685,x18686,x18687))
% 109.14/108.87 [1869]~E(x18691,x18692)+E(f547(x18693,x18694,x18695,x18691,x18696,x18697),f547(x18693,x18694,x18695,x18692,x18696,x18697))
% 109.14/108.87 [1870]~E(x18701,x18702)+E(f547(x18703,x18704,x18705,x18706,x18701,x18707),f547(x18703,x18704,x18705,x18706,x18702,x18707))
% 109.14/108.87 [1871]~E(x18711,x18712)+E(f547(x18713,x18714,x18715,x18716,x18717,x18711),f547(x18713,x18714,x18715,x18716,x18717,x18712))
% 109.14/108.87 [1872]~E(x18721,x18722)+E(f649(x18721,x18723,x18724,x18725,x18726),f649(x18722,x18723,x18724,x18725,x18726))
% 109.14/108.87 [1873]~E(x18731,x18732)+E(f649(x18733,x18731,x18734,x18735,x18736),f649(x18733,x18732,x18734,x18735,x18736))
% 109.14/108.87 [1874]~E(x18741,x18742)+E(f649(x18743,x18744,x18741,x18745,x18746),f649(x18743,x18744,x18742,x18745,x18746))
% 109.14/108.87 [1875]~E(x18751,x18752)+E(f649(x18753,x18754,x18755,x18751,x18756),f649(x18753,x18754,x18755,x18752,x18756))
% 109.14/108.87 [1876]~E(x18761,x18762)+E(f649(x18763,x18764,x18765,x18766,x18761),f649(x18763,x18764,x18765,x18766,x18762))
% 109.14/108.87 [1877]~E(x18771,x18772)+E(f461(x18771,x18773,x18774),f461(x18772,x18773,x18774))
% 109.14/108.87 [1878]~E(x18781,x18782)+E(f461(x18783,x18781,x18784),f461(x18783,x18782,x18784))
% 109.14/108.87 [1879]~E(x18791,x18792)+E(f461(x18793,x18794,x18791),f461(x18793,x18794,x18792))
% 109.14/108.87 [1880]~E(x18801,x18802)+E(f675(x18801,x18803,x18804,x18805,x18806),f675(x18802,x18803,x18804,x18805,x18806))
% 109.14/108.87 [1881]~E(x18811,x18812)+E(f675(x18813,x18811,x18814,x18815,x18816),f675(x18813,x18812,x18814,x18815,x18816))
% 109.14/108.87 [1882]~E(x18821,x18822)+E(f675(x18823,x18824,x18821,x18825,x18826),f675(x18823,x18824,x18822,x18825,x18826))
% 109.14/108.87 [1883]~E(x18831,x18832)+E(f675(x18833,x18834,x18835,x18831,x18836),f675(x18833,x18834,x18835,x18832,x18836))
% 109.14/108.87 [1884]~E(x18841,x18842)+E(f675(x18843,x18844,x18845,x18846,x18841),f675(x18843,x18844,x18845,x18846,x18842))
% 109.14/108.87 [1885]~E(x18851,x18852)+E(f627(x18851,x18853,x18854,x18855,x18856),f627(x18852,x18853,x18854,x18855,x18856))
% 109.14/108.87 [1886]~E(x18861,x18862)+E(f627(x18863,x18861,x18864,x18865,x18866),f627(x18863,x18862,x18864,x18865,x18866))
% 109.14/108.87 [1887]~E(x18871,x18872)+E(f627(x18873,x18874,x18871,x18875,x18876),f627(x18873,x18874,x18872,x18875,x18876))
% 109.14/108.87 [1888]~E(x18881,x18882)+E(f627(x18883,x18884,x18885,x18881,x18886),f627(x18883,x18884,x18885,x18882,x18886))
% 109.14/108.87 [1889]~E(x18891,x18892)+E(f627(x18893,x18894,x18895,x18896,x18891),f627(x18893,x18894,x18895,x18896,x18892))
% 109.14/108.87 [1890]~E(x18901,x18902)+E(f685(x18901,x18903,x18904),f685(x18902,x18903,x18904))
% 109.14/108.87 [1891]~E(x18911,x18912)+E(f685(x18913,x18911,x18914),f685(x18913,x18912,x18914))
% 109.14/108.87 [1892]~E(x18921,x18922)+E(f685(x18923,x18924,x18921),f685(x18923,x18924,x18922))
% 109.14/108.87 [1893]~E(x18931,x18932)+E(f644(x18931,x18933,x18934,x18935,x18936,x18937),f644(x18932,x18933,x18934,x18935,x18936,x18937))
% 109.14/108.87 [1894]~E(x18941,x18942)+E(f644(x18943,x18941,x18944,x18945,x18946,x18947),f644(x18943,x18942,x18944,x18945,x18946,x18947))
% 109.14/108.87 [1895]~E(x18951,x18952)+E(f644(x18953,x18954,x18951,x18955,x18956,x18957),f644(x18953,x18954,x18952,x18955,x18956,x18957))
% 109.14/108.87 [1896]~E(x18961,x18962)+E(f644(x18963,x18964,x18965,x18961,x18966,x18967),f644(x18963,x18964,x18965,x18962,x18966,x18967))
% 109.14/108.87 [1897]~E(x18971,x18972)+E(f644(x18973,x18974,x18975,x18976,x18971,x18977),f644(x18973,x18974,x18975,x18976,x18972,x18977))
% 109.14/108.87 [1898]~E(x18981,x18982)+E(f644(x18983,x18984,x18985,x18986,x18987,x18981),f644(x18983,x18984,x18985,x18986,x18987,x18982))
% 109.14/108.87 [1899]~E(x18991,x18992)+E(f695(x18991,x18993,x18994,x18995,x18996),f695(x18992,x18993,x18994,x18995,x18996))
% 109.14/108.87 [1900]~E(x19001,x19002)+E(f695(x19003,x19001,x19004,x19005,x19006),f695(x19003,x19002,x19004,x19005,x19006))
% 109.14/108.87 [1901]~E(x19011,x19012)+E(f695(x19013,x19014,x19011,x19015,x19016),f695(x19013,x19014,x19012,x19015,x19016))
% 109.14/108.87 [1902]~E(x19021,x19022)+E(f695(x19023,x19024,x19025,x19021,x19026),f695(x19023,x19024,x19025,x19022,x19026))
% 109.14/108.87 [1903]~E(x19031,x19032)+E(f695(x19033,x19034,x19035,x19036,x19031),f695(x19033,x19034,x19035,x19036,x19032))
% 109.14/108.87 [1904]~E(x19041,x19042)+E(f62(x19041,x19043,x19044),f62(x19042,x19043,x19044))
% 109.14/108.87 [1905]~E(x19051,x19052)+E(f62(x19053,x19051,x19054),f62(x19053,x19052,x19054))
% 109.14/108.87 [1906]~E(x19061,x19062)+E(f62(x19063,x19064,x19061),f62(x19063,x19064,x19062))
% 109.14/108.87 [1907]~E(x19071,x19072)+E(f193(x19071,x19073),f193(x19072,x19073))
% 109.14/108.87 [1908]~E(x19081,x19082)+E(f193(x19083,x19081),f193(x19083,x19082))
% 109.14/108.87 [1909]~E(x19091,x19092)+E(f395(x19091,x19093,x19094),f395(x19092,x19093,x19094))
% 109.14/108.87 [1910]~E(x19101,x19102)+E(f395(x19103,x19101,x19104),f395(x19103,x19102,x19104))
% 109.14/108.87 [1911]~E(x19111,x19112)+E(f395(x19113,x19114,x19111),f395(x19113,x19114,x19112))
% 109.14/108.87 [1912]~E(x19121,x19122)+E(f828(x19121,x19123,x19124),f828(x19122,x19123,x19124))
% 109.14/108.87 [1913]~E(x19131,x19132)+E(f828(x19133,x19131,x19134),f828(x19133,x19132,x19134))
% 109.14/108.87 [1914]~E(x19141,x19142)+E(f828(x19143,x19144,x19141),f828(x19143,x19144,x19142))
% 109.14/108.87 [1915]~E(x19151,x19152)+E(f409(x19151,x19153,x19154),f409(x19152,x19153,x19154))
% 109.14/108.87 [1916]~E(x19161,x19162)+E(f409(x19163,x19161,x19164),f409(x19163,x19162,x19164))
% 109.14/108.87 [1917]~E(x19171,x19172)+E(f409(x19173,x19174,x19171),f409(x19173,x19174,x19172))
% 109.14/108.87 [1918]~E(x19181,x19182)+E(f851(x19181,x19183,x19184),f851(x19182,x19183,x19184))
% 109.14/108.87 [1919]~E(x19191,x19192)+E(f851(x19193,x19191,x19194),f851(x19193,x19192,x19194))
% 109.14/108.87 [1920]~E(x19201,x19202)+E(f851(x19203,x19204,x19201),f851(x19203,x19204,x19202))
% 109.14/108.87 [1921]~E(x19211,x19212)+E(f191(x19211),f191(x19212))
% 109.14/108.87 [1922]~E(x19221,x19222)+E(f526(x19221,x19223,x19224,x19225,x19226,x19227,x19228),f526(x19222,x19223,x19224,x19225,x19226,x19227,x19228))
% 109.14/108.87 [1923]~E(x19231,x19232)+E(f526(x19233,x19231,x19234,x19235,x19236,x19237,x19238),f526(x19233,x19232,x19234,x19235,x19236,x19237,x19238))
% 109.14/108.87 [1924]~E(x19241,x19242)+E(f526(x19243,x19244,x19241,x19245,x19246,x19247,x19248),f526(x19243,x19244,x19242,x19245,x19246,x19247,x19248))
% 109.14/108.87 [1925]~E(x19251,x19252)+E(f526(x19253,x19254,x19255,x19251,x19256,x19257,x19258),f526(x19253,x19254,x19255,x19252,x19256,x19257,x19258))
% 109.14/108.87 [1926]~E(x19261,x19262)+E(f526(x19263,x19264,x19265,x19266,x19261,x19267,x19268),f526(x19263,x19264,x19265,x19266,x19262,x19267,x19268))
% 109.14/108.87 [1927]~E(x19271,x19272)+E(f526(x19273,x19274,x19275,x19276,x19277,x19271,x19278),f526(x19273,x19274,x19275,x19276,x19277,x19272,x19278))
% 109.14/108.87 [1928]~E(x19281,x19282)+E(f526(x19283,x19284,x19285,x19286,x19287,x19288,x19281),f526(x19283,x19284,x19285,x19286,x19287,x19288,x19282))
% 109.14/108.87 [1929]~E(x19291,x19292)+E(f328(x19291),f328(x19292))
% 109.14/108.87 [1930]~E(x19301,x19302)+E(f121(x19301,x19303,x19304,x19305),f121(x19302,x19303,x19304,x19305))
% 109.14/108.87 [1931]~E(x19311,x19312)+E(f121(x19313,x19311,x19314,x19315),f121(x19313,x19312,x19314,x19315))
% 109.14/108.87 [1932]~E(x19321,x19322)+E(f121(x19323,x19324,x19321,x19325),f121(x19323,x19324,x19322,x19325))
% 109.14/108.87 [1933]~E(x19331,x19332)+E(f121(x19333,x19334,x19335,x19331),f121(x19333,x19334,x19335,x19332))
% 109.14/108.87 [1934]~E(x19341,x19342)+E(f399(x19341,x19343),f399(x19342,x19343))
% 109.14/108.87 [1935]~E(x19351,x19352)+E(f399(x19353,x19351),f399(x19353,x19352))
% 109.14/108.87 [1936]~E(x19361,x19362)+E(f764(x19361,x19363,x19364,x19365),f764(x19362,x19363,x19364,x19365))
% 109.14/108.87 [1937]~E(x19371,x19372)+E(f764(x19373,x19371,x19374,x19375),f764(x19373,x19372,x19374,x19375))
% 109.14/108.87 [1938]~E(x19381,x19382)+E(f764(x19383,x19384,x19381,x19385),f764(x19383,x19384,x19382,x19385))
% 109.14/108.87 [1939]~E(x19391,x19392)+E(f764(x19393,x19394,x19395,x19391),f764(x19393,x19394,x19395,x19392))
% 109.14/108.87 [1940]~E(x19401,x19402)+E(f283(x19401,x19403),f283(x19402,x19403))
% 109.14/108.87 [1941]~E(x19411,x19412)+E(f283(x19413,x19411),f283(x19413,x19412))
% 109.14/108.87 [1942]~E(x19421,x19422)+E(f391(x19421,x19423,x19424,x19425),f391(x19422,x19423,x19424,x19425))
% 109.14/108.87 [1943]~E(x19431,x19432)+E(f391(x19433,x19431,x19434,x19435),f391(x19433,x19432,x19434,x19435))
% 109.14/108.87 [1944]~E(x19441,x19442)+E(f391(x19443,x19444,x19441,x19445),f391(x19443,x19444,x19442,x19445))
% 109.14/108.87 [1945]~E(x19451,x19452)+E(f391(x19453,x19454,x19455,x19451),f391(x19453,x19454,x19455,x19452))
% 109.14/108.87 [1946]~E(x19461,x19462)+E(f268(x19461,x19463,x19464,x19465),f268(x19462,x19463,x19464,x19465))
% 109.14/108.87 [1947]~E(x19471,x19472)+E(f268(x19473,x19471,x19474,x19475),f268(x19473,x19472,x19474,x19475))
% 109.14/108.87 [1948]~E(x19481,x19482)+E(f268(x19483,x19484,x19481,x19485),f268(x19483,x19484,x19482,x19485))
% 109.14/108.87 [1949]~E(x19491,x19492)+E(f268(x19493,x19494,x19495,x19491),f268(x19493,x19494,x19495,x19492))
% 109.14/108.87 [1950]~E(x19501,x19502)+E(f290(x19501,x19503,x19504,x19505),f290(x19502,x19503,x19504,x19505))
% 109.14/108.87 [1951]~E(x19511,x19512)+E(f290(x19513,x19511,x19514,x19515),f290(x19513,x19512,x19514,x19515))
% 109.14/108.87 [1952]~E(x19521,x19522)+E(f290(x19523,x19524,x19521,x19525),f290(x19523,x19524,x19522,x19525))
% 109.14/108.87 [1953]~E(x19531,x19532)+E(f290(x19533,x19534,x19535,x19531),f290(x19533,x19534,x19535,x19532))
% 109.14/108.87 [1954]~E(x19541,x19542)+E(f513(x19541,x19543,x19544,x19545,x19546),f513(x19542,x19543,x19544,x19545,x19546))
% 109.14/108.87 [1955]~E(x19551,x19552)+E(f513(x19553,x19551,x19554,x19555,x19556),f513(x19553,x19552,x19554,x19555,x19556))
% 109.14/108.87 [1956]~E(x19561,x19562)+E(f513(x19563,x19564,x19561,x19565,x19566),f513(x19563,x19564,x19562,x19565,x19566))
% 109.14/108.87 [1957]~E(x19571,x19572)+E(f513(x19573,x19574,x19575,x19571,x19576),f513(x19573,x19574,x19575,x19572,x19576))
% 109.14/108.87 [1958]~E(x19581,x19582)+E(f513(x19583,x19584,x19585,x19586,x19581),f513(x19583,x19584,x19585,x19586,x19582))
% 109.14/108.87 [1959]~E(x19591,x19592)+E(f549(x19591,x19593,x19594,x19595,x19596),f549(x19592,x19593,x19594,x19595,x19596))
% 109.14/108.87 [1960]~E(x19601,x19602)+E(f549(x19603,x19601,x19604,x19605,x19606),f549(x19603,x19602,x19604,x19605,x19606))
% 109.14/108.87 [1961]~E(x19611,x19612)+E(f549(x19613,x19614,x19611,x19615,x19616),f549(x19613,x19614,x19612,x19615,x19616))
% 109.14/108.87 [1962]~E(x19621,x19622)+E(f549(x19623,x19624,x19625,x19621,x19626),f549(x19623,x19624,x19625,x19622,x19626))
% 109.14/108.87 [1963]~E(x19631,x19632)+E(f549(x19633,x19634,x19635,x19636,x19631),f549(x19633,x19634,x19635,x19636,x19632))
% 109.14/108.87 [1964]~E(x19641,x19642)+E(f588(x19641,x19643,x19644,x19645,x19646,x19647),f588(x19642,x19643,x19644,x19645,x19646,x19647))
% 109.14/108.87 [1965]~E(x19651,x19652)+E(f588(x19653,x19651,x19654,x19655,x19656,x19657),f588(x19653,x19652,x19654,x19655,x19656,x19657))
% 109.14/108.87 [1966]~E(x19661,x19662)+E(f588(x19663,x19664,x19661,x19665,x19666,x19667),f588(x19663,x19664,x19662,x19665,x19666,x19667))
% 109.14/108.87 [1967]~E(x19671,x19672)+E(f588(x19673,x19674,x19675,x19671,x19676,x19677),f588(x19673,x19674,x19675,x19672,x19676,x19677))
% 109.14/108.87 [1968]~E(x19681,x19682)+E(f588(x19683,x19684,x19685,x19686,x19681,x19687),f588(x19683,x19684,x19685,x19686,x19682,x19687))
% 109.14/108.87 [1969]~E(x19691,x19692)+E(f588(x19693,x19694,x19695,x19696,x19697,x19691),f588(x19693,x19694,x19695,x19696,x19697,x19692))
% 109.14/108.87 [1970]~E(x19701,x19702)+E(f582(x19701,x19703,x19704,x19705),f582(x19702,x19703,x19704,x19705))
% 109.14/108.87 [1971]~E(x19711,x19712)+E(f582(x19713,x19711,x19714,x19715),f582(x19713,x19712,x19714,x19715))
% 109.14/108.87 [1972]~E(x19721,x19722)+E(f582(x19723,x19724,x19721,x19725),f582(x19723,x19724,x19722,x19725))
% 109.14/108.87 [1973]~E(x19731,x19732)+E(f582(x19733,x19734,x19735,x19731),f582(x19733,x19734,x19735,x19732))
% 109.14/108.87 [1974]~E(x19741,x19742)+E(f546(x19741,x19743,x19744,x19745),f546(x19742,x19743,x19744,x19745))
% 109.14/108.87 [1975]~E(x19751,x19752)+E(f546(x19753,x19751,x19754,x19755),f546(x19753,x19752,x19754,x19755))
% 109.14/108.87 [1976]~E(x19761,x19762)+E(f546(x19763,x19764,x19761,x19765),f546(x19763,x19764,x19762,x19765))
% 109.14/108.87 [1977]~E(x19771,x19772)+E(f546(x19773,x19774,x19775,x19771),f546(x19773,x19774,x19775,x19772))
% 109.14/108.87 [1978]~E(x19781,x19782)+E(f843(x19781,x19783,x19784,x19785,x19786,x19787,x19788,x19789),f843(x19782,x19783,x19784,x19785,x19786,x19787,x19788,x19789))
% 109.14/108.87 [1979]~E(x19791,x19792)+E(f843(x19793,x19791,x19794,x19795,x19796,x19797,x19798,x19799),f843(x19793,x19792,x19794,x19795,x19796,x19797,x19798,x19799))
% 109.14/108.87 [1980]~E(x19801,x19802)+E(f843(x19803,x19804,x19801,x19805,x19806,x19807,x19808,x19809),f843(x19803,x19804,x19802,x19805,x19806,x19807,x19808,x19809))
% 109.14/108.87 [1981]~E(x19811,x19812)+E(f843(x19813,x19814,x19815,x19811,x19816,x19817,x19818,x19819),f843(x19813,x19814,x19815,x19812,x19816,x19817,x19818,x19819))
% 109.14/108.87 [1982]~E(x19821,x19822)+E(f843(x19823,x19824,x19825,x19826,x19821,x19827,x19828,x19829),f843(x19823,x19824,x19825,x19826,x19822,x19827,x19828,x19829))
% 109.14/108.87 [1983]~E(x19831,x19832)+E(f843(x19833,x19834,x19835,x19836,x19837,x19831,x19838,x19839),f843(x19833,x19834,x19835,x19836,x19837,x19832,x19838,x19839))
% 109.14/108.87 [1984]~E(x19841,x19842)+E(f843(x19843,x19844,x19845,x19846,x19847,x19848,x19841,x19849),f843(x19843,x19844,x19845,x19846,x19847,x19848,x19842,x19849))
% 109.14/108.87 [1985]~E(x19851,x19852)+E(f843(x19853,x19854,x19855,x19856,x19857,x19858,x19859,x19851),f843(x19853,x19854,x19855,x19856,x19857,x19858,x19859,x19852))
% 109.14/108.87 [1986]~E(x19861,x19862)+E(f114(x19861),f114(x19862))
% 109.14/108.87 [1987]~E(x19871,x19872)+E(f398(x19871,x19873,x19874,x19875,x19876,x19877,x19878),f398(x19872,x19873,x19874,x19875,x19876,x19877,x19878))
% 109.14/108.87 [1988]~E(x19881,x19882)+E(f398(x19883,x19881,x19884,x19885,x19886,x19887,x19888),f398(x19883,x19882,x19884,x19885,x19886,x19887,x19888))
% 109.14/108.87 [1989]~E(x19891,x19892)+E(f398(x19893,x19894,x19891,x19895,x19896,x19897,x19898),f398(x19893,x19894,x19892,x19895,x19896,x19897,x19898))
% 109.14/108.87 [1990]~E(x19901,x19902)+E(f398(x19903,x19904,x19905,x19901,x19906,x19907,x19908),f398(x19903,x19904,x19905,x19902,x19906,x19907,x19908))
% 109.14/108.87 [1991]~E(x19911,x19912)+E(f398(x19913,x19914,x19915,x19916,x19911,x19917,x19918),f398(x19913,x19914,x19915,x19916,x19912,x19917,x19918))
% 109.14/108.87 [1992]~E(x19921,x19922)+E(f398(x19923,x19924,x19925,x19926,x19927,x19921,x19928),f398(x19923,x19924,x19925,x19926,x19927,x19922,x19928))
% 109.14/108.87 [1993]~E(x19931,x19932)+E(f398(x19933,x19934,x19935,x19936,x19937,x19938,x19931),f398(x19933,x19934,x19935,x19936,x19937,x19938,x19932))
% 109.14/108.87 [1994]~E(x19941,x19942)+E(f728(x19941,x19943,x19944,x19945,x19946,x19947,x19948,x19949),f728(x19942,x19943,x19944,x19945,x19946,x19947,x19948,x19949))
% 109.14/108.87 [1995]~E(x19951,x19952)+E(f728(x19953,x19951,x19954,x19955,x19956,x19957,x19958,x19959),f728(x19953,x19952,x19954,x19955,x19956,x19957,x19958,x19959))
% 109.14/108.87 [1996]~E(x19961,x19962)+E(f728(x19963,x19964,x19961,x19965,x19966,x19967,x19968,x19969),f728(x19963,x19964,x19962,x19965,x19966,x19967,x19968,x19969))
% 109.14/108.87 [1997]~E(x19971,x19972)+E(f728(x19973,x19974,x19975,x19971,x19976,x19977,x19978,x19979),f728(x19973,x19974,x19975,x19972,x19976,x19977,x19978,x19979))
% 109.14/108.87 [1998]~E(x19981,x19982)+E(f728(x19983,x19984,x19985,x19986,x19981,x19987,x19988,x19989),f728(x19983,x19984,x19985,x19986,x19982,x19987,x19988,x19989))
% 109.14/108.87 [1999]~E(x19991,x19992)+E(f728(x19993,x19994,x19995,x19996,x19997,x19991,x19998,x19999),f728(x19993,x19994,x19995,x19996,x19997,x19992,x19998,x19999))
% 109.14/108.87 [2000]~E(x20001,x20002)+E(f728(x20003,x20004,x20005,x20006,x20007,x20008,x20001,x20009),f728(x20003,x20004,x20005,x20006,x20007,x20008,x20002,x20009))
% 109.14/108.87 [2001]~E(x20011,x20012)+E(f728(x20013,x20014,x20015,x20016,x20017,x20018,x20019,x20011),f728(x20013,x20014,x20015,x20016,x20017,x20018,x20019,x20012))
% 109.14/108.87 [2002]~E(x20021,x20022)+E(f779(x20021,x20023,x20024,x20025,x20026,x20027,x20028),f779(x20022,x20023,x20024,x20025,x20026,x20027,x20028))
% 109.14/108.87 [2003]~E(x20031,x20032)+E(f779(x20033,x20031,x20034,x20035,x20036,x20037,x20038),f779(x20033,x20032,x20034,x20035,x20036,x20037,x20038))
% 109.14/108.87 [2004]~E(x20041,x20042)+E(f779(x20043,x20044,x20041,x20045,x20046,x20047,x20048),f779(x20043,x20044,x20042,x20045,x20046,x20047,x20048))
% 109.14/108.87 [2005]~E(x20051,x20052)+E(f779(x20053,x20054,x20055,x20051,x20056,x20057,x20058),f779(x20053,x20054,x20055,x20052,x20056,x20057,x20058))
% 109.14/108.87 [2006]~E(x20061,x20062)+E(f779(x20063,x20064,x20065,x20066,x20061,x20067,x20068),f779(x20063,x20064,x20065,x20066,x20062,x20067,x20068))
% 109.14/108.87 [2007]~E(x20071,x20072)+E(f779(x20073,x20074,x20075,x20076,x20077,x20071,x20078),f779(x20073,x20074,x20075,x20076,x20077,x20072,x20078))
% 109.14/108.87 [2008]~E(x20081,x20082)+E(f779(x20083,x20084,x20085,x20086,x20087,x20088,x20081),f779(x20083,x20084,x20085,x20086,x20087,x20088,x20082))
% 109.14/108.87 [2009]~E(x20091,x20092)+E(f476(x20091,x20093,x20094,x20095,x20096),f476(x20092,x20093,x20094,x20095,x20096))
% 109.14/108.87 [2010]~E(x20101,x20102)+E(f476(x20103,x20101,x20104,x20105,x20106),f476(x20103,x20102,x20104,x20105,x20106))
% 109.14/108.87 [2011]~E(x20111,x20112)+E(f476(x20113,x20114,x20111,x20115,x20116),f476(x20113,x20114,x20112,x20115,x20116))
% 109.14/108.87 [2012]~E(x20121,x20122)+E(f476(x20123,x20124,x20125,x20121,x20126),f476(x20123,x20124,x20125,x20122,x20126))
% 109.14/108.87 [2013]~E(x20131,x20132)+E(f476(x20133,x20134,x20135,x20136,x20131),f476(x20133,x20134,x20135,x20136,x20132))
% 109.14/108.87 [2014]~E(x20141,x20142)+E(f485(x20141,x20143,x20144),f485(x20142,x20143,x20144))
% 109.14/108.87 [2015]~E(x20151,x20152)+E(f485(x20153,x20151,x20154),f485(x20153,x20152,x20154))
% 109.14/108.87 [2016]~E(x20161,x20162)+E(f485(x20163,x20164,x20161),f485(x20163,x20164,x20162))
% 109.14/108.87 [2017]~E(x20171,x20172)+E(f194(x20171,x20173,x20174),f194(x20172,x20173,x20174))
% 109.14/108.87 [2018]~E(x20181,x20182)+E(f194(x20183,x20181,x20184),f194(x20183,x20182,x20184))
% 109.14/108.87 [2019]~E(x20191,x20192)+E(f194(x20193,x20194,x20191),f194(x20193,x20194,x20192))
% 109.14/108.87 [2020]~E(x20201,x20202)+E(f558(x20201,x20203),f558(x20202,x20203))
% 109.14/108.87 [2021]~E(x20211,x20212)+E(f558(x20213,x20211),f558(x20213,x20212))
% 109.14/108.87 [2022]~E(x20221,x20222)+E(f626(x20221,x20223,x20224,x20225,x20226),f626(x20222,x20223,x20224,x20225,x20226))
% 109.14/108.87 [2023]~E(x20231,x20232)+E(f626(x20233,x20231,x20234,x20235,x20236),f626(x20233,x20232,x20234,x20235,x20236))
% 109.14/108.87 [2024]~E(x20241,x20242)+E(f626(x20243,x20244,x20241,x20245,x20246),f626(x20243,x20244,x20242,x20245,x20246))
% 109.14/108.87 [2025]~E(x20251,x20252)+E(f626(x20253,x20254,x20255,x20251,x20256),f626(x20253,x20254,x20255,x20252,x20256))
% 109.14/108.87 [2026]~E(x20261,x20262)+E(f626(x20263,x20264,x20265,x20266,x20261),f626(x20263,x20264,x20265,x20266,x20262))
% 109.14/108.87 [2027]~E(x20271,x20272)+E(f771(x20271,x20273,x20274,x20275),f771(x20272,x20273,x20274,x20275))
% 109.14/108.87 [2028]~E(x20281,x20282)+E(f771(x20283,x20281,x20284,x20285),f771(x20283,x20282,x20284,x20285))
% 109.14/108.87 [2029]~E(x20291,x20292)+E(f771(x20293,x20294,x20291,x20295),f771(x20293,x20294,x20292,x20295))
% 109.14/108.87 [2030]~E(x20301,x20302)+E(f771(x20303,x20304,x20305,x20301),f771(x20303,x20304,x20305,x20302))
% 109.14/108.87 [2031]~E(x20311,x20312)+E(f510(x20311,x20313,x20314,x20315,x20316,x20317,x20318,x20319),f510(x20312,x20313,x20314,x20315,x20316,x20317,x20318,x20319))
% 109.14/108.87 [2032]~E(x20321,x20322)+E(f510(x20323,x20321,x20324,x20325,x20326,x20327,x20328,x20329),f510(x20323,x20322,x20324,x20325,x20326,x20327,x20328,x20329))
% 109.14/108.87 [2033]~E(x20331,x20332)+E(f510(x20333,x20334,x20331,x20335,x20336,x20337,x20338,x20339),f510(x20333,x20334,x20332,x20335,x20336,x20337,x20338,x20339))
% 109.14/108.87 [2034]~E(x20341,x20342)+E(f510(x20343,x20344,x20345,x20341,x20346,x20347,x20348,x20349),f510(x20343,x20344,x20345,x20342,x20346,x20347,x20348,x20349))
% 109.14/108.87 [2035]~E(x20351,x20352)+E(f510(x20353,x20354,x20355,x20356,x20351,x20357,x20358,x20359),f510(x20353,x20354,x20355,x20356,x20352,x20357,x20358,x20359))
% 109.14/108.87 [2036]~E(x20361,x20362)+E(f510(x20363,x20364,x20365,x20366,x20367,x20361,x20368,x20369),f510(x20363,x20364,x20365,x20366,x20367,x20362,x20368,x20369))
% 109.14/108.87 [2037]~E(x20371,x20372)+E(f510(x20373,x20374,x20375,x20376,x20377,x20378,x20371,x20379),f510(x20373,x20374,x20375,x20376,x20377,x20378,x20372,x20379))
% 109.14/108.87 [2038]~E(x20381,x20382)+E(f510(x20383,x20384,x20385,x20386,x20387,x20388,x20389,x20381),f510(x20383,x20384,x20385,x20386,x20387,x20388,x20389,x20382))
% 109.14/108.87 [2039]~E(x20391,x20392)+E(f721(x20391,x20393),f721(x20392,x20393))
% 109.14/108.87 [2040]~E(x20401,x20402)+E(f721(x20403,x20401),f721(x20403,x20402))
% 109.14/108.87 [2041]~E(x20411,x20412)+E(f265(x20411,x20413,x20414),f265(x20412,x20413,x20414))
% 109.14/108.87 [2042]~E(x20421,x20422)+E(f265(x20423,x20421,x20424),f265(x20423,x20422,x20424))
% 109.14/108.87 [2043]~E(x20431,x20432)+E(f265(x20433,x20434,x20431),f265(x20433,x20434,x20432))
% 109.14/108.87 [2044]~E(x20441,x20442)+E(f545(x20441,x20443,x20444,x20445),f545(x20442,x20443,x20444,x20445))
% 109.14/108.87 [2045]~E(x20451,x20452)+E(f545(x20453,x20451,x20454,x20455),f545(x20453,x20452,x20454,x20455))
% 109.14/108.87 [2046]~E(x20461,x20462)+E(f545(x20463,x20464,x20461,x20465),f545(x20463,x20464,x20462,x20465))
% 109.14/108.87 [2047]~E(x20471,x20472)+E(f545(x20473,x20474,x20475,x20471),f545(x20473,x20474,x20475,x20472))
% 109.14/108.87 [2048]~E(x20481,x20482)+E(f325(x20481),f325(x20482))
% 109.14/108.87 [2049]~E(x20491,x20492)+E(f598(x20491,x20493,x20494),f598(x20492,x20493,x20494))
% 109.14/108.87 [2050]~E(x20501,x20502)+E(f598(x20503,x20501,x20504),f598(x20503,x20502,x20504))
% 109.14/108.87 [2051]~E(x20511,x20512)+E(f598(x20513,x20514,x20511),f598(x20513,x20514,x20512))
% 109.14/108.87 [2052]~E(x20521,x20522)+E(f181(x20521,x20523,x20524,x20525),f181(x20522,x20523,x20524,x20525))
% 109.14/108.87 [2053]~E(x20531,x20532)+E(f181(x20533,x20531,x20534,x20535),f181(x20533,x20532,x20534,x20535))
% 109.14/108.87 [2054]~E(x20541,x20542)+E(f181(x20543,x20544,x20541,x20545),f181(x20543,x20544,x20542,x20545))
% 109.14/108.87 [2055]~E(x20551,x20552)+E(f181(x20553,x20554,x20555,x20551),f181(x20553,x20554,x20555,x20552))
% 109.14/108.87 [2056]~E(x20561,x20562)+E(f684(x20561,x20563,x20564,x20565,x20566),f684(x20562,x20563,x20564,x20565,x20566))
% 109.14/108.87 [2057]~E(x20571,x20572)+E(f684(x20573,x20571,x20574,x20575,x20576),f684(x20573,x20572,x20574,x20575,x20576))
% 109.14/108.87 [2058]~E(x20581,x20582)+E(f684(x20583,x20584,x20581,x20585,x20586),f684(x20583,x20584,x20582,x20585,x20586))
% 109.14/108.87 [2059]~E(x20591,x20592)+E(f684(x20593,x20594,x20595,x20591,x20596),f684(x20593,x20594,x20595,x20592,x20596))
% 109.14/108.87 [2060]~E(x20601,x20602)+E(f684(x20603,x20604,x20605,x20606,x20601),f684(x20603,x20604,x20605,x20606,x20602))
% 109.14/108.87 [2061]~E(x20611,x20612)+E(f789(x20611),f789(x20612))
% 109.14/108.87 [2062]~E(x20621,x20622)+E(f342(x20621,x20623,x20624,x20625),f342(x20622,x20623,x20624,x20625))
% 109.14/108.87 [2063]~E(x20631,x20632)+E(f342(x20633,x20631,x20634,x20635),f342(x20633,x20632,x20634,x20635))
% 109.14/108.87 [2064]~E(x20641,x20642)+E(f342(x20643,x20644,x20641,x20645),f342(x20643,x20644,x20642,x20645))
% 109.14/108.87 [2065]~E(x20651,x20652)+E(f342(x20653,x20654,x20655,x20651),f342(x20653,x20654,x20655,x20652))
% 109.14/108.87 [2066]~E(x20661,x20662)+E(f355(x20661,x20663,x20664,x20665),f355(x20662,x20663,x20664,x20665))
% 109.14/108.87 [2067]~E(x20671,x20672)+E(f355(x20673,x20671,x20674,x20675),f355(x20673,x20672,x20674,x20675))
% 109.14/108.87 [2068]~E(x20681,x20682)+E(f355(x20683,x20684,x20681,x20685),f355(x20683,x20684,x20682,x20685))
% 109.14/108.87 [2069]~E(x20691,x20692)+E(f355(x20693,x20694,x20695,x20691),f355(x20693,x20694,x20695,x20692))
% 109.14/108.87 [2070]~E(x20701,x20702)+E(f404(x20701,x20703,x20704,x20705,x20706),f404(x20702,x20703,x20704,x20705,x20706))
% 109.14/108.87 [2071]~E(x20711,x20712)+E(f404(x20713,x20711,x20714,x20715,x20716),f404(x20713,x20712,x20714,x20715,x20716))
% 109.14/108.87 [2072]~E(x20721,x20722)+E(f404(x20723,x20724,x20721,x20725,x20726),f404(x20723,x20724,x20722,x20725,x20726))
% 109.14/108.87 [2073]~E(x20731,x20732)+E(f404(x20733,x20734,x20735,x20731,x20736),f404(x20733,x20734,x20735,x20732,x20736))
% 109.14/108.87 [2074]~E(x20741,x20742)+E(f404(x20743,x20744,x20745,x20746,x20741),f404(x20743,x20744,x20745,x20746,x20742))
% 109.14/108.87 [2075]~E(x20751,x20752)+E(f438(x20751,x20753,x20754),f438(x20752,x20753,x20754))
% 109.14/108.87 [2076]~E(x20761,x20762)+E(f438(x20763,x20761,x20764),f438(x20763,x20762,x20764))
% 109.14/108.87 [2077]~E(x20771,x20772)+E(f438(x20773,x20774,x20771),f438(x20773,x20774,x20772))
% 109.14/108.87 [2078]~E(x20781,x20782)+E(f615(x20781,x20783),f615(x20782,x20783))
% 109.14/108.87 [2079]~E(x20791,x20792)+E(f615(x20793,x20791),f615(x20793,x20792))
% 109.14/108.87 [2080]~E(x20801,x20802)+E(f199(x20801),f199(x20802))
% 109.14/108.87 [2081]~E(x20811,x20812)+E(f533(x20811,x20813,x20814,x20815,x20816),f533(x20812,x20813,x20814,x20815,x20816))
% 109.14/108.87 [2082]~E(x20821,x20822)+E(f533(x20823,x20821,x20824,x20825,x20826),f533(x20823,x20822,x20824,x20825,x20826))
% 109.14/108.87 [2083]~E(x20831,x20832)+E(f533(x20833,x20834,x20831,x20835,x20836),f533(x20833,x20834,x20832,x20835,x20836))
% 109.14/108.87 [2084]~E(x20841,x20842)+E(f533(x20843,x20844,x20845,x20841,x20846),f533(x20843,x20844,x20845,x20842,x20846))
% 109.14/108.87 [2085]~E(x20851,x20852)+E(f533(x20853,x20854,x20855,x20856,x20851),f533(x20853,x20854,x20855,x20856,x20852))
% 109.14/108.87 [2086]~E(x20861,x20862)+E(f537(x20861,x20863,x20864,x20865),f537(x20862,x20863,x20864,x20865))
% 109.14/108.87 [2087]~E(x20871,x20872)+E(f537(x20873,x20871,x20874,x20875),f537(x20873,x20872,x20874,x20875))
% 109.14/108.87 [2088]~E(x20881,x20882)+E(f537(x20883,x20884,x20881,x20885),f537(x20883,x20884,x20882,x20885))
% 109.14/108.87 [2089]~E(x20891,x20892)+E(f537(x20893,x20894,x20895,x20891),f537(x20893,x20894,x20895,x20892))
% 109.14/108.87 [2090]~E(x20901,x20902)+E(f343(x20901,x20903,x20904,x20905),f343(x20902,x20903,x20904,x20905))
% 109.14/108.87 [2091]~E(x20911,x20912)+E(f343(x20913,x20911,x20914,x20915),f343(x20913,x20912,x20914,x20915))
% 109.14/108.87 [2092]~E(x20921,x20922)+E(f343(x20923,x20924,x20921,x20925),f343(x20923,x20924,x20922,x20925))
% 109.14/108.87 [2093]~E(x20931,x20932)+E(f343(x20933,x20934,x20935,x20931),f343(x20933,x20934,x20935,x20932))
% 109.14/108.87 [2094]~E(x20941,x20942)+E(f630(x20941,x20943,x20944,x20945,x20946),f630(x20942,x20943,x20944,x20945,x20946))
% 109.14/108.87 [2095]~E(x20951,x20952)+E(f630(x20953,x20951,x20954,x20955,x20956),f630(x20953,x20952,x20954,x20955,x20956))
% 109.14/108.87 [2096]~E(x20961,x20962)+E(f630(x20963,x20964,x20961,x20965,x20966),f630(x20963,x20964,x20962,x20965,x20966))
% 109.14/108.87 [2097]~E(x20971,x20972)+E(f630(x20973,x20974,x20975,x20971,x20976),f630(x20973,x20974,x20975,x20972,x20976))
% 109.14/108.87 [2098]~E(x20981,x20982)+E(f630(x20983,x20984,x20985,x20986,x20981),f630(x20983,x20984,x20985,x20986,x20982))
% 109.14/108.87 [2099]~E(x20991,x20992)+E(f899(x20991,x20993,x20994,x20995),f899(x20992,x20993,x20994,x20995))
% 109.14/108.87 [2100]~E(x21001,x21002)+E(f899(x21003,x21001,x21004,x21005),f899(x21003,x21002,x21004,x21005))
% 109.14/108.87 [2101]~E(x21011,x21012)+E(f899(x21013,x21014,x21011,x21015),f899(x21013,x21014,x21012,x21015))
% 109.14/108.87 [2102]~E(x21021,x21022)+E(f899(x21023,x21024,x21025,x21021),f899(x21023,x21024,x21025,x21022))
% 109.14/108.87 [2103]~E(x21031,x21032)+E(f468(x21031,x21033,x21034,x21035),f468(x21032,x21033,x21034,x21035))
% 109.14/108.87 [2104]~E(x21041,x21042)+E(f468(x21043,x21041,x21044,x21045),f468(x21043,x21042,x21044,x21045))
% 109.14/108.87 [2105]~E(x21051,x21052)+E(f468(x21053,x21054,x21051,x21055),f468(x21053,x21054,x21052,x21055))
% 109.14/108.87 [2106]~E(x21061,x21062)+E(f468(x21063,x21064,x21065,x21061),f468(x21063,x21064,x21065,x21062))
% 109.14/108.87 [2107]~E(x21071,x21072)+E(f894(x21071,x21073,x21074),f894(x21072,x21073,x21074))
% 109.14/108.87 [2108]~E(x21081,x21082)+E(f894(x21083,x21081,x21084),f894(x21083,x21082,x21084))
% 109.14/108.87 [2109]~E(x21091,x21092)+E(f894(x21093,x21094,x21091),f894(x21093,x21094,x21092))
% 109.14/108.87 [2110]~E(x21101,x21102)+E(f866(x21101,x21103,x21104,x21105,x21106),f866(x21102,x21103,x21104,x21105,x21106))
% 109.14/108.87 [2111]~E(x21111,x21112)+E(f866(x21113,x21111,x21114,x21115,x21116),f866(x21113,x21112,x21114,x21115,x21116))
% 109.14/108.87 [2112]~E(x21121,x21122)+E(f866(x21123,x21124,x21121,x21125,x21126),f866(x21123,x21124,x21122,x21125,x21126))
% 109.14/108.87 [2113]~E(x21131,x21132)+E(f866(x21133,x21134,x21135,x21131,x21136),f866(x21133,x21134,x21135,x21132,x21136))
% 109.14/108.87 [2114]~E(x21141,x21142)+E(f866(x21143,x21144,x21145,x21146,x21141),f866(x21143,x21144,x21145,x21146,x21142))
% 109.14/108.87 [2115]~E(x21151,x21152)+E(f751(x21151,x21153,x21154),f751(x21152,x21153,x21154))
% 109.14/108.87 [2116]~E(x21161,x21162)+E(f751(x21163,x21161,x21164),f751(x21163,x21162,x21164))
% 109.14/108.87 [2117]~E(x21171,x21172)+E(f751(x21173,x21174,x21171),f751(x21173,x21174,x21172))
% 109.14/108.87 [2118]~E(x21181,x21182)+E(f844(x21181,x21183,x21184),f844(x21182,x21183,x21184))
% 109.14/108.87 [2119]~E(x21191,x21192)+E(f844(x21193,x21191,x21194),f844(x21193,x21192,x21194))
% 109.14/108.87 [2120]~E(x21201,x21202)+E(f844(x21203,x21204,x21201),f844(x21203,x21204,x21202))
% 109.14/108.87 [2121]~E(x21211,x21212)+E(f618(x21211,x21213),f618(x21212,x21213))
% 109.14/108.87 [2122]~E(x21221,x21222)+E(f618(x21223,x21221),f618(x21223,x21222))
% 109.14/108.87 [2123]~E(x21231,x21232)+E(f351(x21231,x21233,x21234,x21235),f351(x21232,x21233,x21234,x21235))
% 109.14/108.87 [2124]~E(x21241,x21242)+E(f351(x21243,x21241,x21244,x21245),f351(x21243,x21242,x21244,x21245))
% 109.14/108.87 [2125]~E(x21251,x21252)+E(f351(x21253,x21254,x21251,x21255),f351(x21253,x21254,x21252,x21255))
% 109.14/108.87 [2126]~E(x21261,x21262)+E(f351(x21263,x21264,x21265,x21261),f351(x21263,x21264,x21265,x21262))
% 109.14/108.87 [2127]~E(x21271,x21272)+E(f678(x21271,x21273,x21274),f678(x21272,x21273,x21274))
% 109.14/108.87 [2128]~E(x21281,x21282)+E(f678(x21283,x21281,x21284),f678(x21283,x21282,x21284))
% 109.14/108.87 [2129]~E(x21291,x21292)+E(f678(x21293,x21294,x21291),f678(x21293,x21294,x21292))
% 109.14/108.87 [2130]~E(x21301,x21302)+E(f664(x21301,x21303,x21304,x21305),f664(x21302,x21303,x21304,x21305))
% 109.14/108.87 [2131]~E(x21311,x21312)+E(f664(x21313,x21311,x21314,x21315),f664(x21313,x21312,x21314,x21315))
% 109.14/108.87 [2132]~E(x21321,x21322)+E(f664(x21323,x21324,x21321,x21325),f664(x21323,x21324,x21322,x21325))
% 109.14/108.87 [2133]~E(x21331,x21332)+E(f664(x21333,x21334,x21335,x21331),f664(x21333,x21334,x21335,x21332))
% 109.14/108.87 [2134]~E(x21341,x21342)+E(f505(x21341,x21343,x21344),f505(x21342,x21343,x21344))
% 109.14/108.87 [2135]~E(x21351,x21352)+E(f505(x21353,x21351,x21354),f505(x21353,x21352,x21354))
% 109.14/108.87 [2136]~E(x21361,x21362)+E(f505(x21363,x21364,x21361),f505(x21363,x21364,x21362))
% 109.14/108.87 [2137]~E(x21371,x21372)+E(f839(x21371,x21373,x21374,x21375,x21376,x21377,x21378,x21379),f839(x21372,x21373,x21374,x21375,x21376,x21377,x21378,x21379))
% 109.14/108.87 [2138]~E(x21381,x21382)+E(f839(x21383,x21381,x21384,x21385,x21386,x21387,x21388,x21389),f839(x21383,x21382,x21384,x21385,x21386,x21387,x21388,x21389))
% 109.14/108.87 [2139]~E(x21391,x21392)+E(f839(x21393,x21394,x21391,x21395,x21396,x21397,x21398,x21399),f839(x21393,x21394,x21392,x21395,x21396,x21397,x21398,x21399))
% 109.14/108.87 [2140]~E(x21401,x21402)+E(f839(x21403,x21404,x21405,x21401,x21406,x21407,x21408,x21409),f839(x21403,x21404,x21405,x21402,x21406,x21407,x21408,x21409))
% 109.14/108.87 [2141]~E(x21411,x21412)+E(f839(x21413,x21414,x21415,x21416,x21411,x21417,x21418,x21419),f839(x21413,x21414,x21415,x21416,x21412,x21417,x21418,x21419))
% 109.14/108.87 [2142]~E(x21421,x21422)+E(f839(x21423,x21424,x21425,x21426,x21427,x21421,x21428,x21429),f839(x21423,x21424,x21425,x21426,x21427,x21422,x21428,x21429))
% 109.14/108.87 [2143]~E(x21431,x21432)+E(f839(x21433,x21434,x21435,x21436,x21437,x21438,x21431,x21439),f839(x21433,x21434,x21435,x21436,x21437,x21438,x21432,x21439))
% 109.14/108.87 [2144]~E(x21441,x21442)+E(f839(x21443,x21444,x21445,x21446,x21447,x21448,x21449,x21441),f839(x21443,x21444,x21445,x21446,x21447,x21448,x21449,x21442))
% 109.14/108.87 [2145]~E(x21451,x21452)+E(f364(x21451,x21453,x21454),f364(x21452,x21453,x21454))
% 109.14/108.87 [2146]~E(x21461,x21462)+E(f364(x21463,x21461,x21464),f364(x21463,x21462,x21464))
% 109.14/108.87 [2147]~E(x21471,x21472)+E(f364(x21473,x21474,x21471),f364(x21473,x21474,x21472))
% 109.14/108.87 [2148]~E(x21481,x21482)+E(f604(x21481,x21483,x21484),f604(x21482,x21483,x21484))
% 109.14/108.87 [2149]~E(x21491,x21492)+E(f604(x21493,x21491,x21494),f604(x21493,x21492,x21494))
% 109.14/108.87 [2150]~E(x21501,x21502)+E(f604(x21503,x21504,x21501),f604(x21503,x21504,x21502))
% 109.14/108.87 [2151]~E(x21511,x21512)+E(f729(x21511,x21513),f729(x21512,x21513))
% 109.14/108.87 [2152]~E(x21521,x21522)+E(f729(x21523,x21521),f729(x21523,x21522))
% 109.14/108.87 [2153]~E(x21531,x21532)+E(f907(x21531,x21533,x21534,x21535,x21536,x21537,x21538,x21539),f907(x21532,x21533,x21534,x21535,x21536,x21537,x21538,x21539))
% 109.14/108.87 [2154]~E(x21541,x21542)+E(f907(x21543,x21541,x21544,x21545,x21546,x21547,x21548,x21549),f907(x21543,x21542,x21544,x21545,x21546,x21547,x21548,x21549))
% 109.14/108.87 [2155]~E(x21551,x21552)+E(f907(x21553,x21554,x21551,x21555,x21556,x21557,x21558,x21559),f907(x21553,x21554,x21552,x21555,x21556,x21557,x21558,x21559))
% 109.14/108.87 [2156]~E(x21561,x21562)+E(f907(x21563,x21564,x21565,x21561,x21566,x21567,x21568,x21569),f907(x21563,x21564,x21565,x21562,x21566,x21567,x21568,x21569))
% 109.14/108.87 [2157]~E(x21571,x21572)+E(f907(x21573,x21574,x21575,x21576,x21571,x21577,x21578,x21579),f907(x21573,x21574,x21575,x21576,x21572,x21577,x21578,x21579))
% 109.14/108.87 [2158]~E(x21581,x21582)+E(f907(x21583,x21584,x21585,x21586,x21587,x21581,x21588,x21589),f907(x21583,x21584,x21585,x21586,x21587,x21582,x21588,x21589))
% 109.14/108.87 [2159]~E(x21591,x21592)+E(f907(x21593,x21594,x21595,x21596,x21597,x21598,x21591,x21599),f907(x21593,x21594,x21595,x21596,x21597,x21598,x21592,x21599))
% 109.14/108.87 [2160]~E(x21601,x21602)+E(f907(x21603,x21604,x21605,x21606,x21607,x21608,x21609,x21601),f907(x21603,x21604,x21605,x21606,x21607,x21608,x21609,x21602))
% 109.14/108.87 [2161]~E(x21611,x21612)+E(f590(x21611,x21613),f590(x21612,x21613))
% 109.14/108.87 [2162]~E(x21621,x21622)+E(f590(x21623,x21621),f590(x21623,x21622))
% 109.14/108.87 [2163]~E(x21631,x21632)+E(f465(x21631,x21633,x21634),f465(x21632,x21633,x21634))
% 109.14/108.87 [2164]~E(x21641,x21642)+E(f465(x21643,x21641,x21644),f465(x21643,x21642,x21644))
% 109.14/108.87 [2165]~E(x21651,x21652)+E(f465(x21653,x21654,x21651),f465(x21653,x21654,x21652))
% 109.14/108.87 [2166]~E(x21661,x21662)+E(f236(x21661,x21663,x21664),f236(x21662,x21663,x21664))
% 109.14/108.87 [2167]~E(x21671,x21672)+E(f236(x21673,x21671,x21674),f236(x21673,x21672,x21674))
% 109.14/108.87 [2168]~E(x21681,x21682)+E(f236(x21683,x21684,x21681),f236(x21683,x21684,x21682))
% 109.14/108.87 [2169]~E(x21691,x21692)+E(f752(x21691,x21693,x21694),f752(x21692,x21693,x21694))
% 109.14/108.87 [2170]~E(x21701,x21702)+E(f752(x21703,x21701,x21704),f752(x21703,x21702,x21704))
% 109.14/108.87 [2171]~E(x21711,x21712)+E(f752(x21713,x21714,x21711),f752(x21713,x21714,x21712))
% 109.14/108.87 [2172]~E(x21721,x21722)+E(f816(x21721,x21723,x21724),f816(x21722,x21723,x21724))
% 109.14/108.87 [2173]~E(x21731,x21732)+E(f816(x21733,x21731,x21734),f816(x21733,x21732,x21734))
% 109.14/108.87 [2174]~E(x21741,x21742)+E(f816(x21743,x21744,x21741),f816(x21743,x21744,x21742))
% 109.14/108.87 [2175]~E(x21751,x21752)+E(f331(x21751,x21753,x21754,x21755),f331(x21752,x21753,x21754,x21755))
% 109.14/108.87 [2176]~E(x21761,x21762)+E(f331(x21763,x21761,x21764,x21765),f331(x21763,x21762,x21764,x21765))
% 109.14/108.87 [2177]~E(x21771,x21772)+E(f331(x21773,x21774,x21771,x21775),f331(x21773,x21774,x21772,x21775))
% 109.14/108.87 [2178]~E(x21781,x21782)+E(f331(x21783,x21784,x21785,x21781),f331(x21783,x21784,x21785,x21782))
% 109.14/108.87 [2179]~E(x21791,x21792)+E(f612(x21791,x21793,x21794,x21795,x21796),f612(x21792,x21793,x21794,x21795,x21796))
% 109.14/108.87 [2180]~E(x21801,x21802)+E(f612(x21803,x21801,x21804,x21805,x21806),f612(x21803,x21802,x21804,x21805,x21806))
% 109.14/108.87 [2181]~E(x21811,x21812)+E(f612(x21813,x21814,x21811,x21815,x21816),f612(x21813,x21814,x21812,x21815,x21816))
% 109.14/108.87 [2182]~E(x21821,x21822)+E(f612(x21823,x21824,x21825,x21821,x21826),f612(x21823,x21824,x21825,x21822,x21826))
% 109.14/108.87 [2183]~E(x21831,x21832)+E(f612(x21833,x21834,x21835,x21836,x21831),f612(x21833,x21834,x21835,x21836,x21832))
% 109.14/108.87 [2184]~E(x21841,x21842)+E(f462(x21841,x21843,x21844),f462(x21842,x21843,x21844))
% 109.14/108.87 [2185]~E(x21851,x21852)+E(f462(x21853,x21851,x21854),f462(x21853,x21852,x21854))
% 109.14/108.87 [2186]~E(x21861,x21862)+E(f462(x21863,x21864,x21861),f462(x21863,x21864,x21862))
% 109.14/108.87 [2187]~E(x21871,x21872)+E(f339(x21871,x21873,x21874),f339(x21872,x21873,x21874))
% 109.14/108.87 [2188]~E(x21881,x21882)+E(f339(x21883,x21881,x21884),f339(x21883,x21882,x21884))
% 109.14/108.87 [2189]~E(x21891,x21892)+E(f339(x21893,x21894,x21891),f339(x21893,x21894,x21892))
% 109.14/108.87 [2190]~E(x21901,x21902)+E(f534(x21901,x21903),f534(x21902,x21903))
% 109.14/108.87 [2191]~E(x21911,x21912)+E(f534(x21913,x21911),f534(x21913,x21912))
% 109.14/108.87 [2192]~E(x21921,x21922)+E(f450(x21921,x21923,x21924),f450(x21922,x21923,x21924))
% 109.14/108.87 [2193]~E(x21931,x21932)+E(f450(x21933,x21931,x21934),f450(x21933,x21932,x21934))
% 109.14/108.87 [2194]~E(x21941,x21942)+E(f450(x21943,x21944,x21941),f450(x21943,x21944,x21942))
% 109.14/108.87 [2195]~E(x21951,x21952)+E(f817(x21951,x21953),f817(x21952,x21953))
% 109.14/108.87 [2196]~E(x21961,x21962)+E(f817(x21963,x21961),f817(x21963,x21962))
% 109.14/108.87 [2197]~E(x21971,x21972)+E(f733(x21971,x21973,x21974),f733(x21972,x21973,x21974))
% 109.14/108.87 [2198]~E(x21981,x21982)+E(f733(x21983,x21981,x21984),f733(x21983,x21982,x21984))
% 109.14/108.87 [2199]~E(x21991,x21992)+E(f733(x21993,x21994,x21991),f733(x21993,x21994,x21992))
% 109.14/108.87 [2200]~E(x22001,x22002)+E(f595(x22001,x22003),f595(x22002,x22003))
% 109.14/108.87 [2201]~E(x22011,x22012)+E(f595(x22013,x22011),f595(x22013,x22012))
% 109.14/108.87 [2202]~E(x22021,x22022)+E(f815(x22021,x22023,x22024),f815(x22022,x22023,x22024))
% 109.14/108.87 [2203]~E(x22031,x22032)+E(f815(x22033,x22031,x22034),f815(x22033,x22032,x22034))
% 109.14/108.87 [2204]~E(x22041,x22042)+E(f815(x22043,x22044,x22041),f815(x22043,x22044,x22042))
% 109.14/108.87 [2205]~E(x22051,x22052)+E(f882(x22051,x22053),f882(x22052,x22053))
% 109.14/108.87 [2206]~E(x22061,x22062)+E(f882(x22063,x22061),f882(x22063,x22062))
% 109.14/108.87 [2207]~E(x22071,x22072)+E(f437(x22071,x22073,x22074),f437(x22072,x22073,x22074))
% 109.14/108.87 [2208]~E(x22081,x22082)+E(f437(x22083,x22081,x22084),f437(x22083,x22082,x22084))
% 109.14/108.87 [2209]~E(x22091,x22092)+E(f437(x22093,x22094,x22091),f437(x22093,x22094,x22092))
% 109.14/108.87 [2210]~E(x22101,x22102)+E(f405(x22101,x22103,x22104,x22105,x22106),f405(x22102,x22103,x22104,x22105,x22106))
% 109.14/108.87 [2211]~E(x22111,x22112)+E(f405(x22113,x22111,x22114,x22115,x22116),f405(x22113,x22112,x22114,x22115,x22116))
% 109.14/108.87 [2212]~E(x22121,x22122)+E(f405(x22123,x22124,x22121,x22125,x22126),f405(x22123,x22124,x22122,x22125,x22126))
% 109.14/108.87 [2213]~E(x22131,x22132)+E(f405(x22133,x22134,x22135,x22131,x22136),f405(x22133,x22134,x22135,x22132,x22136))
% 109.14/108.87 [2214]~E(x22141,x22142)+E(f405(x22143,x22144,x22145,x22146,x22141),f405(x22143,x22144,x22145,x22146,x22142))
% 109.14/108.87 [2215]~E(x22151,x22152)+E(f370(x22151,x22153),f370(x22152,x22153))
% 109.14/108.87 [2216]~E(x22161,x22162)+E(f370(x22163,x22161),f370(x22163,x22162))
% 109.14/108.87 [2217]~E(x22171,x22172)+E(f427(x22171,x22173,x22174,x22175),f427(x22172,x22173,x22174,x22175))
% 109.14/108.87 [2218]~E(x22181,x22182)+E(f427(x22183,x22181,x22184,x22185),f427(x22183,x22182,x22184,x22185))
% 109.14/108.87 [2219]~E(x22191,x22192)+E(f427(x22193,x22194,x22191,x22195),f427(x22193,x22194,x22192,x22195))
% 109.14/108.87 [2220]~E(x22201,x22202)+E(f427(x22203,x22204,x22205,x22201),f427(x22203,x22204,x22205,x22202))
% 109.14/108.87 [2221]~E(x22211,x22212)+E(f698(x22211,x22213,x22214),f698(x22212,x22213,x22214))
% 109.14/108.87 [2222]~E(x22221,x22222)+E(f698(x22223,x22221,x22224),f698(x22223,x22222,x22224))
% 109.14/108.87 [2223]~E(x22231,x22232)+E(f698(x22233,x22234,x22231),f698(x22233,x22234,x22232))
% 109.14/108.87 [2224]~E(x22241,x22242)+E(f624(x22241,x22243,x22244,x22245),f624(x22242,x22243,x22244,x22245))
% 109.14/108.87 [2225]~E(x22251,x22252)+E(f624(x22253,x22251,x22254,x22255),f624(x22253,x22252,x22254,x22255))
% 109.14/108.87 [2226]~E(x22261,x22262)+E(f624(x22263,x22264,x22261,x22265),f624(x22263,x22264,x22262,x22265))
% 109.14/108.87 [2227]~E(x22271,x22272)+E(f624(x22273,x22274,x22275,x22271),f624(x22273,x22274,x22275,x22272))
% 109.14/108.87 [2228]~E(x22281,x22282)+E(f790(x22281,x22283,x22284),f790(x22282,x22283,x22284))
% 109.14/108.87 [2229]~E(x22291,x22292)+E(f790(x22293,x22291,x22294),f790(x22293,x22292,x22294))
% 109.14/108.87 [2230]~E(x22301,x22302)+E(f790(x22303,x22304,x22301),f790(x22303,x22304,x22302))
% 109.14/108.87 [2231]~E(x22311,x22312)+E(f556(x22311,x22313),f556(x22312,x22313))
% 109.14/108.87 [2232]~E(x22321,x22322)+E(f556(x22323,x22321),f556(x22323,x22322))
% 109.14/108.87 [2233]~E(x22331,x22332)+E(f735(x22331,x22333,x22334),f735(x22332,x22333,x22334))
% 109.14/108.87 [2234]~E(x22341,x22342)+E(f735(x22343,x22341,x22344),f735(x22343,x22342,x22344))
% 109.14/108.87 [2235]~E(x22351,x22352)+E(f735(x22353,x22354,x22351),f735(x22353,x22354,x22352))
% 109.14/108.87 [2236]~E(x22361,x22362)+E(f200(x22361,x22363,x22364,x22365),f200(x22362,x22363,x22364,x22365))
% 109.14/108.87 [2237]~E(x22371,x22372)+E(f200(x22373,x22371,x22374,x22375),f200(x22373,x22372,x22374,x22375))
% 109.14/108.87 [2238]~E(x22381,x22382)+E(f200(x22383,x22384,x22381,x22385),f200(x22383,x22384,x22382,x22385))
% 109.14/108.87 [2239]~E(x22391,x22392)+E(f200(x22393,x22394,x22395,x22391),f200(x22393,x22394,x22395,x22392))
% 109.14/108.87 [2240]~E(x22401,x22402)+E(f645(x22401,x22403,x22404,x22405,x22406,x22407),f645(x22402,x22403,x22404,x22405,x22406,x22407))
% 109.14/108.87 [2241]~E(x22411,x22412)+E(f645(x22413,x22411,x22414,x22415,x22416,x22417),f645(x22413,x22412,x22414,x22415,x22416,x22417))
% 109.14/108.87 [2242]~E(x22421,x22422)+E(f645(x22423,x22424,x22421,x22425,x22426,x22427),f645(x22423,x22424,x22422,x22425,x22426,x22427))
% 109.14/108.87 [2243]~E(x22431,x22432)+E(f645(x22433,x22434,x22435,x22431,x22436,x22437),f645(x22433,x22434,x22435,x22432,x22436,x22437))
% 109.14/108.87 [2244]~E(x22441,x22442)+E(f645(x22443,x22444,x22445,x22446,x22441,x22447),f645(x22443,x22444,x22445,x22446,x22442,x22447))
% 109.14/108.87 [2245]~E(x22451,x22452)+E(f645(x22453,x22454,x22455,x22456,x22457,x22451),f645(x22453,x22454,x22455,x22456,x22457,x22452))
% 109.14/108.87 [2246]~E(x22461,x22462)+E(f821(x22461,x22463,x22464,x22465),f821(x22462,x22463,x22464,x22465))
% 109.14/108.87 [2247]~E(x22471,x22472)+E(f821(x22473,x22471,x22474,x22475),f821(x22473,x22472,x22474,x22475))
% 109.14/108.87 [2248]~E(x22481,x22482)+E(f821(x22483,x22484,x22481,x22485),f821(x22483,x22484,x22482,x22485))
% 109.14/108.87 [2249]~E(x22491,x22492)+E(f821(x22493,x22494,x22495,x22491),f821(x22493,x22494,x22495,x22492))
% 109.14/108.87 [2250]~E(x22501,x22502)+E(f217(x22501,x22503,x22504,x22505,x22506),f217(x22502,x22503,x22504,x22505,x22506))
% 109.14/108.87 [2251]~E(x22511,x22512)+E(f217(x22513,x22511,x22514,x22515,x22516),f217(x22513,x22512,x22514,x22515,x22516))
% 109.14/108.87 [2252]~E(x22521,x22522)+E(f217(x22523,x22524,x22521,x22525,x22526),f217(x22523,x22524,x22522,x22525,x22526))
% 109.14/108.87 [2253]~E(x22531,x22532)+E(f217(x22533,x22534,x22535,x22531,x22536),f217(x22533,x22534,x22535,x22532,x22536))
% 109.14/108.87 [2254]~E(x22541,x22542)+E(f217(x22543,x22544,x22545,x22546,x22541),f217(x22543,x22544,x22545,x22546,x22542))
% 109.14/108.87 [2255]~E(x22551,x22552)+E(f153(x22551,x22553),f153(x22552,x22553))
% 109.14/108.87 [2256]~E(x22561,x22562)+E(f153(x22563,x22561),f153(x22563,x22562))
% 109.14/108.87 [2257]~E(x22571,x22572)+E(f440(x22571,x22573,x22574),f440(x22572,x22573,x22574))
% 109.14/108.87 [2258]~E(x22581,x22582)+E(f440(x22583,x22581,x22584),f440(x22583,x22582,x22584))
% 109.14/108.87 [2259]~E(x22591,x22592)+E(f440(x22593,x22594,x22591),f440(x22593,x22594,x22592))
% 109.14/108.87 [2260]~E(x22601,x22602)+E(f739(x22601,x22603,x22604,x22605,x22606),f739(x22602,x22603,x22604,x22605,x22606))
% 109.14/108.87 [2261]~E(x22611,x22612)+E(f739(x22613,x22611,x22614,x22615,x22616),f739(x22613,x22612,x22614,x22615,x22616))
% 109.14/108.87 [2262]~E(x22621,x22622)+E(f739(x22623,x22624,x22621,x22625,x22626),f739(x22623,x22624,x22622,x22625,x22626))
% 109.14/108.87 [2263]~E(x22631,x22632)+E(f739(x22633,x22634,x22635,x22631,x22636),f739(x22633,x22634,x22635,x22632,x22636))
% 109.14/108.87 [2264]~E(x22641,x22642)+E(f739(x22643,x22644,x22645,x22646,x22641),f739(x22643,x22644,x22645,x22646,x22642))
% 109.14/108.87 [2265]~E(x22651,x22652)+E(f642(x22651,x22653,x22654),f642(x22652,x22653,x22654))
% 109.14/108.87 [2266]~E(x22661,x22662)+E(f642(x22663,x22661,x22664),f642(x22663,x22662,x22664))
% 109.14/108.87 [2267]~E(x22671,x22672)+E(f642(x22673,x22674,x22671),f642(x22673,x22674,x22672))
% 109.14/108.87 [2268]~E(x22681,x22682)+E(f800(x22681,x22683),f800(x22682,x22683))
% 109.14/108.87 [2269]~E(x22691,x22692)+E(f800(x22693,x22691),f800(x22693,x22692))
% 109.14/108.87 [2270]~E(x22701,x22702)+E(f570(x22701,x22703,x22704,x22705),f570(x22702,x22703,x22704,x22705))
% 109.14/108.87 [2271]~E(x22711,x22712)+E(f570(x22713,x22711,x22714,x22715),f570(x22713,x22712,x22714,x22715))
% 109.14/108.87 [2272]~E(x22721,x22722)+E(f570(x22723,x22724,x22721,x22725),f570(x22723,x22724,x22722,x22725))
% 109.14/108.87 [2273]~E(x22731,x22732)+E(f570(x22733,x22734,x22735,x22731),f570(x22733,x22734,x22735,x22732))
% 109.14/108.87 [2274]~E(x22741,x22742)+E(f874(x22741,x22743,x22744),f874(x22742,x22743,x22744))
% 109.14/108.87 [2275]~E(x22751,x22752)+E(f874(x22753,x22751,x22754),f874(x22753,x22752,x22754))
% 109.14/108.87 [2276]~E(x22761,x22762)+E(f874(x22763,x22764,x22761),f874(x22763,x22764,x22762))
% 109.14/108.87 [2277]~E(x22771,x22772)+E(f560(x22771,x22773,x22774,x22775),f560(x22772,x22773,x22774,x22775))
% 109.14/108.87 [2278]~E(x22781,x22782)+E(f560(x22783,x22781,x22784,x22785),f560(x22783,x22782,x22784,x22785))
% 109.14/108.87 [2279]~E(x22791,x22792)+E(f560(x22793,x22794,x22791,x22795),f560(x22793,x22794,x22792,x22795))
% 109.14/108.87 [2280]~E(x22801,x22802)+E(f560(x22803,x22804,x22805,x22801),f560(x22803,x22804,x22805,x22802))
% 109.14/108.87 [2281]~E(x22811,x22812)+E(f569(x22811,x22813,x22814),f569(x22812,x22813,x22814))
% 109.14/108.87 [2282]~E(x22821,x22822)+E(f569(x22823,x22821,x22824),f569(x22823,x22822,x22824))
% 109.14/108.87 [2283]~E(x22831,x22832)+E(f569(x22833,x22834,x22831),f569(x22833,x22834,x22832))
% 109.14/108.87 [2284]~E(x22841,x22842)+E(f834(x22841,x22843,x22844,x22845),f834(x22842,x22843,x22844,x22845))
% 109.14/108.87 [2285]~E(x22851,x22852)+E(f834(x22853,x22851,x22854,x22855),f834(x22853,x22852,x22854,x22855))
% 109.14/108.87 [2286]~E(x22861,x22862)+E(f834(x22863,x22864,x22861,x22865),f834(x22863,x22864,x22862,x22865))
% 109.14/108.87 [2287]~E(x22871,x22872)+E(f834(x22873,x22874,x22875,x22871),f834(x22873,x22874,x22875,x22872))
% 109.14/108.87 [2288]~E(x22881,x22882)+E(f703(x22881,x22883),f703(x22882,x22883))
% 109.14/108.87 [2289]~E(x22891,x22892)+E(f703(x22893,x22891),f703(x22893,x22892))
% 109.14/108.87 [2290]~E(x22901,x22902)+E(f893(x22901,x22903,x22904),f893(x22902,x22903,x22904))
% 109.14/108.87 [2291]~E(x22911,x22912)+E(f893(x22913,x22911,x22914),f893(x22913,x22912,x22914))
% 109.14/108.87 [2292]~E(x22921,x22922)+E(f893(x22923,x22924,x22921),f893(x22923,x22924,x22922))
% 109.14/108.87 [2293]~E(x22931,x22932)+E(f635(x22931,x22933,x22934),f635(x22932,x22933,x22934))
% 109.14/108.87 [2294]~E(x22941,x22942)+E(f635(x22943,x22941,x22944),f635(x22943,x22942,x22944))
% 109.14/108.87 [2295]~E(x22951,x22952)+E(f635(x22953,x22954,x22951),f635(x22953,x22954,x22952))
% 109.14/108.87 [2296]~E(x22961,x22962)+E(f154(x22961,x22963,x22964,x22965),f154(x22962,x22963,x22964,x22965))
% 109.14/108.87 [2297]~E(x22971,x22972)+E(f154(x22973,x22971,x22974,x22975),f154(x22973,x22972,x22974,x22975))
% 109.14/108.87 [2298]~E(x22981,x22982)+E(f154(x22983,x22984,x22981,x22985),f154(x22983,x22984,x22982,x22985))
% 109.14/108.87 [2299]~E(x22991,x22992)+E(f154(x22993,x22994,x22995,x22991),f154(x22993,x22994,x22995,x22992))
% 109.14/108.87 [2300]~E(x23001,x23002)+E(f488(x23001,x23003,x23004),f488(x23002,x23003,x23004))
% 109.14/108.87 [2301]~E(x23011,x23012)+E(f488(x23013,x23011,x23014),f488(x23013,x23012,x23014))
% 109.14/108.87 [2302]~E(x23021,x23022)+E(f488(x23023,x23024,x23021),f488(x23023,x23024,x23022))
% 109.14/108.87 [2303]~E(x23031,x23032)+E(f581(x23031,x23033),f581(x23032,x23033))
% 109.14/108.87 [2304]~E(x23041,x23042)+E(f581(x23043,x23041),f581(x23043,x23042))
% 109.14/108.87 [2305]~E(x23051,x23052)+E(f738(x23051,x23053,x23054,x23055,x23056),f738(x23052,x23053,x23054,x23055,x23056))
% 109.14/108.87 [2306]~E(x23061,x23062)+E(f738(x23063,x23061,x23064,x23065,x23066),f738(x23063,x23062,x23064,x23065,x23066))
% 109.14/108.87 [2307]~E(x23071,x23072)+E(f738(x23073,x23074,x23071,x23075,x23076),f738(x23073,x23074,x23072,x23075,x23076))
% 109.14/108.87 [2308]~E(x23081,x23082)+E(f738(x23083,x23084,x23085,x23081,x23086),f738(x23083,x23084,x23085,x23082,x23086))
% 109.14/108.87 [2309]~E(x23091,x23092)+E(f738(x23093,x23094,x23095,x23096,x23091),f738(x23093,x23094,x23095,x23096,x23092))
% 109.14/108.87 [2310]~E(x23101,x23102)+E(f509(x23101,x23103,x23104,x23105,x23106,x23107),f509(x23102,x23103,x23104,x23105,x23106,x23107))
% 109.14/108.87 [2311]~E(x23111,x23112)+E(f509(x23113,x23111,x23114,x23115,x23116,x23117),f509(x23113,x23112,x23114,x23115,x23116,x23117))
% 109.14/108.87 [2312]~E(x23121,x23122)+E(f509(x23123,x23124,x23121,x23125,x23126,x23127),f509(x23123,x23124,x23122,x23125,x23126,x23127))
% 109.14/108.87 [2313]~E(x23131,x23132)+E(f509(x23133,x23134,x23135,x23131,x23136,x23137),f509(x23133,x23134,x23135,x23132,x23136,x23137))
% 109.14/108.87 [2314]~E(x23141,x23142)+E(f509(x23143,x23144,x23145,x23146,x23141,x23147),f509(x23143,x23144,x23145,x23146,x23142,x23147))
% 109.14/108.87 [2315]~E(x23151,x23152)+E(f509(x23153,x23154,x23155,x23156,x23157,x23151),f509(x23153,x23154,x23155,x23156,x23157,x23152))
% 109.14/108.87 [2316]~E(x23161,x23162)+E(f672(x23161,x23163,x23164,x23165,x23166),f672(x23162,x23163,x23164,x23165,x23166))
% 109.14/108.87 [2317]~E(x23171,x23172)+E(f672(x23173,x23171,x23174,x23175,x23176),f672(x23173,x23172,x23174,x23175,x23176))
% 109.14/108.87 [2318]~E(x23181,x23182)+E(f672(x23183,x23184,x23181,x23185,x23186),f672(x23183,x23184,x23182,x23185,x23186))
% 109.14/108.87 [2319]~E(x23191,x23192)+E(f672(x23193,x23194,x23195,x23191,x23196),f672(x23193,x23194,x23195,x23192,x23196))
% 109.14/108.87 [2320]~E(x23201,x23202)+E(f672(x23203,x23204,x23205,x23206,x23201),f672(x23203,x23204,x23205,x23206,x23202))
% 109.14/108.87 [2321]~E(x23211,x23212)+E(f406(x23211,x23213,x23214,x23215),f406(x23212,x23213,x23214,x23215))
% 109.14/108.87 [2322]~E(x23221,x23222)+E(f406(x23223,x23221,x23224,x23225),f406(x23223,x23222,x23224,x23225))
% 109.14/108.87 [2323]~E(x23231,x23232)+E(f406(x23233,x23234,x23231,x23235),f406(x23233,x23234,x23232,x23235))
% 109.14/108.87 [2324]~E(x23241,x23242)+E(f406(x23243,x23244,x23245,x23241),f406(x23243,x23244,x23245,x23242))
% 109.14/108.87 [2325]~E(x23251,x23252)+E(f332(x23251,x23253,x23254,x23255),f332(x23252,x23253,x23254,x23255))
% 109.14/108.87 [2326]~E(x23261,x23262)+E(f332(x23263,x23261,x23264,x23265),f332(x23263,x23262,x23264,x23265))
% 109.14/108.87 [2327]~E(x23271,x23272)+E(f332(x23273,x23274,x23271,x23275),f332(x23273,x23274,x23272,x23275))
% 109.14/108.87 [2328]~E(x23281,x23282)+E(f332(x23283,x23284,x23285,x23281),f332(x23283,x23284,x23285,x23282))
% 109.14/108.87 [2329]~E(x23291,x23292)+E(f602(x23291,x23293,x23294,x23295,x23296),f602(x23292,x23293,x23294,x23295,x23296))
% 109.14/108.87 [2330]~E(x23301,x23302)+E(f602(x23303,x23301,x23304,x23305,x23306),f602(x23303,x23302,x23304,x23305,x23306))
% 109.14/108.87 [2331]~E(x23311,x23312)+E(f602(x23313,x23314,x23311,x23315,x23316),f602(x23313,x23314,x23312,x23315,x23316))
% 109.14/108.87 [2332]~E(x23321,x23322)+E(f602(x23323,x23324,x23325,x23321,x23326),f602(x23323,x23324,x23325,x23322,x23326))
% 109.14/108.87 [2333]~E(x23331,x23332)+E(f602(x23333,x23334,x23335,x23336,x23331),f602(x23333,x23334,x23335,x23336,x23332))
% 109.14/108.87 [2334]~E(x23341,x23342)+E(f381(x23341,x23343),f381(x23342,x23343))
% 109.14/108.87 [2335]~E(x23351,x23352)+E(f381(x23353,x23351),f381(x23353,x23352))
% 109.14/108.87 [2336]~E(x23361,x23362)+E(f693(x23361,x23363,x23364,x23365),f693(x23362,x23363,x23364,x23365))
% 109.14/108.87 [2337]~E(x23371,x23372)+E(f693(x23373,x23371,x23374,x23375),f693(x23373,x23372,x23374,x23375))
% 109.14/108.87 [2338]~E(x23381,x23382)+E(f693(x23383,x23384,x23381,x23385),f693(x23383,x23384,x23382,x23385))
% 109.14/108.87 [2339]~E(x23391,x23392)+E(f693(x23393,x23394,x23395,x23391),f693(x23393,x23394,x23395,x23392))
% 109.14/108.87 [2340]~E(x23401,x23402)+E(f603(x23401,x23403,x23404,x23405,x23406),f603(x23402,x23403,x23404,x23405,x23406))
% 109.14/108.87 [2341]~E(x23411,x23412)+E(f603(x23413,x23411,x23414,x23415,x23416),f603(x23413,x23412,x23414,x23415,x23416))
% 109.14/108.87 [2342]~E(x23421,x23422)+E(f603(x23423,x23424,x23421,x23425,x23426),f603(x23423,x23424,x23422,x23425,x23426))
% 109.14/108.87 [2343]~E(x23431,x23432)+E(f603(x23433,x23434,x23435,x23431,x23436),f603(x23433,x23434,x23435,x23432,x23436))
% 109.14/108.87 [2344]~E(x23441,x23442)+E(f603(x23443,x23444,x23445,x23446,x23441),f603(x23443,x23444,x23445,x23446,x23442))
% 109.14/108.87 [2345]~E(x23451,x23452)+E(f501(x23451,x23453),f501(x23452,x23453))
% 109.14/108.87 [2346]~E(x23461,x23462)+E(f501(x23463,x23461),f501(x23463,x23462))
% 109.14/108.87 [2347]~E(x23471,x23472)+E(f871(x23471,x23473,x23474,x23475,x23476),f871(x23472,x23473,x23474,x23475,x23476))
% 109.14/108.87 [2348]~E(x23481,x23482)+E(f871(x23483,x23481,x23484,x23485,x23486),f871(x23483,x23482,x23484,x23485,x23486))
% 109.14/108.87 [2349]~E(x23491,x23492)+E(f871(x23493,x23494,x23491,x23495,x23496),f871(x23493,x23494,x23492,x23495,x23496))
% 109.14/108.87 [2350]~E(x23501,x23502)+E(f871(x23503,x23504,x23505,x23501,x23506),f871(x23503,x23504,x23505,x23502,x23506))
% 109.14/108.87 [2351]~E(x23511,x23512)+E(f871(x23513,x23514,x23515,x23516,x23511),f871(x23513,x23514,x23515,x23516,x23512))
% 109.14/108.87 [2352]~E(x23521,x23522)+E(f386(x23521,x23523,x23524,x23525,x23526),f386(x23522,x23523,x23524,x23525,x23526))
% 109.14/108.87 [2353]~E(x23531,x23532)+E(f386(x23533,x23531,x23534,x23535,x23536),f386(x23533,x23532,x23534,x23535,x23536))
% 109.14/108.87 [2354]~E(x23541,x23542)+E(f386(x23543,x23544,x23541,x23545,x23546),f386(x23543,x23544,x23542,x23545,x23546))
% 109.14/108.87 [2355]~E(x23551,x23552)+E(f386(x23553,x23554,x23555,x23551,x23556),f386(x23553,x23554,x23555,x23552,x23556))
% 109.14/108.87 [2356]~E(x23561,x23562)+E(f386(x23563,x23564,x23565,x23566,x23561),f386(x23563,x23564,x23565,x23566,x23562))
% 109.14/108.87 [2357]~E(x23571,x23572)+E(f478(x23571,x23573,x23574,x23575,x23576),f478(x23572,x23573,x23574,x23575,x23576))
% 109.14/108.87 [2358]~E(x23581,x23582)+E(f478(x23583,x23581,x23584,x23585,x23586),f478(x23583,x23582,x23584,x23585,x23586))
% 109.14/108.87 [2359]~E(x23591,x23592)+E(f478(x23593,x23594,x23591,x23595,x23596),f478(x23593,x23594,x23592,x23595,x23596))
% 109.14/108.87 [2360]~E(x23601,x23602)+E(f478(x23603,x23604,x23605,x23601,x23606),f478(x23603,x23604,x23605,x23602,x23606))
% 109.14/108.87 [2361]~E(x23611,x23612)+E(f478(x23613,x23614,x23615,x23616,x23611),f478(x23613,x23614,x23615,x23616,x23612))
% 109.14/108.87 [2362]~E(x23621,x23622)+E(f435(x23621,x23623),f435(x23622,x23623))
% 109.14/108.87 [2363]~E(x23631,x23632)+E(f435(x23633,x23631),f435(x23633,x23632))
% 109.14/108.87 [2364]~E(x23641,x23642)+E(f682(x23641,x23643,x23644,x23645),f682(x23642,x23643,x23644,x23645))
% 109.14/108.87 [2365]~E(x23651,x23652)+E(f682(x23653,x23651,x23654,x23655),f682(x23653,x23652,x23654,x23655))
% 109.14/108.87 [2366]~E(x23661,x23662)+E(f682(x23663,x23664,x23661,x23665),f682(x23663,x23664,x23662,x23665))
% 109.14/108.87 [2367]~E(x23671,x23672)+E(f682(x23673,x23674,x23675,x23671),f682(x23673,x23674,x23675,x23672))
% 109.14/108.87 [2368]~E(x23681,x23682)+E(f641(x23681,x23683,x23684,x23685),f641(x23682,x23683,x23684,x23685))
% 109.14/108.87 [2369]~E(x23691,x23692)+E(f641(x23693,x23691,x23694,x23695),f641(x23693,x23692,x23694,x23695))
% 109.14/108.87 [2370]~E(x23701,x23702)+E(f641(x23703,x23704,x23701,x23705),f641(x23703,x23704,x23702,x23705))
% 109.14/108.87 [2371]~E(x23711,x23712)+E(f641(x23713,x23714,x23715,x23711),f641(x23713,x23714,x23715,x23712))
% 109.14/108.87 [2372]~E(x23721,x23722)+E(f418(x23721,x23723,x23724,x23725,x23726),f418(x23722,x23723,x23724,x23725,x23726))
% 109.14/108.87 [2373]~E(x23731,x23732)+E(f418(x23733,x23731,x23734,x23735,x23736),f418(x23733,x23732,x23734,x23735,x23736))
% 109.14/108.87 [2374]~E(x23741,x23742)+E(f418(x23743,x23744,x23741,x23745,x23746),f418(x23743,x23744,x23742,x23745,x23746))
% 109.14/108.87 [2375]~E(x23751,x23752)+E(f418(x23753,x23754,x23755,x23751,x23756),f418(x23753,x23754,x23755,x23752,x23756))
% 109.14/108.87 [2376]~E(x23761,x23762)+E(f418(x23763,x23764,x23765,x23766,x23761),f418(x23763,x23764,x23765,x23766,x23762))
% 109.14/108.87 [2377]~E(x23771,x23772)+E(f704(x23771,x23773),f704(x23772,x23773))
% 109.14/108.87 [2378]~E(x23781,x23782)+E(f704(x23783,x23781),f704(x23783,x23782))
% 109.14/108.87 [2379]~E(x23791,x23792)+E(f428(x23791,x23793,x23794,x23795,x23796),f428(x23792,x23793,x23794,x23795,x23796))
% 109.14/108.87 [2380]~E(x23801,x23802)+E(f428(x23803,x23801,x23804,x23805,x23806),f428(x23803,x23802,x23804,x23805,x23806))
% 109.14/108.87 [2381]~E(x23811,x23812)+E(f428(x23813,x23814,x23811,x23815,x23816),f428(x23813,x23814,x23812,x23815,x23816))
% 109.14/108.87 [2382]~E(x23821,x23822)+E(f428(x23823,x23824,x23825,x23821,x23826),f428(x23823,x23824,x23825,x23822,x23826))
% 109.14/108.87 [2383]~E(x23831,x23832)+E(f428(x23833,x23834,x23835,x23836,x23831),f428(x23833,x23834,x23835,x23836,x23832))
% 109.14/108.87 [2384]~E(x23841,x23842)+E(f754(x23841,x23843,x23844),f754(x23842,x23843,x23844))
% 109.14/108.87 [2385]~E(x23851,x23852)+E(f754(x23853,x23851,x23854),f754(x23853,x23852,x23854))
% 109.14/108.87 [2386]~E(x23861,x23862)+E(f754(x23863,x23864,x23861),f754(x23863,x23864,x23862))
% 109.14/108.87 [2387]~E(x23871,x23872)+E(f880(x23871,x23873,x23874,x23875),f880(x23872,x23873,x23874,x23875))
% 109.14/108.87 [2388]~E(x23881,x23882)+E(f880(x23883,x23881,x23884,x23885),f880(x23883,x23882,x23884,x23885))
% 109.14/108.87 [2389]~E(x23891,x23892)+E(f880(x23893,x23894,x23891,x23895),f880(x23893,x23894,x23892,x23895))
% 109.14/108.87 [2390]~E(x23901,x23902)+E(f880(x23903,x23904,x23905,x23901),f880(x23903,x23904,x23905,x23902))
% 109.14/108.87 [2391]~E(x23911,x23912)+E(f421(x23911,x23913,x23914,x23915,x23916,x23917,x23918),f421(x23912,x23913,x23914,x23915,x23916,x23917,x23918))
% 109.14/108.87 [2392]~E(x23921,x23922)+E(f421(x23923,x23921,x23924,x23925,x23926,x23927,x23928),f421(x23923,x23922,x23924,x23925,x23926,x23927,x23928))
% 109.14/108.87 [2393]~E(x23931,x23932)+E(f421(x23933,x23934,x23931,x23935,x23936,x23937,x23938),f421(x23933,x23934,x23932,x23935,x23936,x23937,x23938))
% 109.14/108.87 [2394]~E(x23941,x23942)+E(f421(x23943,x23944,x23945,x23941,x23946,x23947,x23948),f421(x23943,x23944,x23945,x23942,x23946,x23947,x23948))
% 109.14/108.87 [2395]~E(x23951,x23952)+E(f421(x23953,x23954,x23955,x23956,x23951,x23957,x23958),f421(x23953,x23954,x23955,x23956,x23952,x23957,x23958))
% 109.14/108.87 [2396]~E(x23961,x23962)+E(f421(x23963,x23964,x23965,x23966,x23967,x23961,x23968),f421(x23963,x23964,x23965,x23966,x23967,x23962,x23968))
% 109.14/108.87 [2397]~E(x23971,x23972)+E(f421(x23973,x23974,x23975,x23976,x23977,x23978,x23971),f421(x23973,x23974,x23975,x23976,x23977,x23978,x23972))
% 109.14/108.87 [2398]~E(x23981,x23982)+E(f393(x23981,x23983,x23984),f393(x23982,x23983,x23984))
% 109.14/108.87 [2399]~E(x23991,x23992)+E(f393(x23993,x23991,x23994),f393(x23993,x23992,x23994))
% 109.14/108.87 [2400]~E(x24001,x24002)+E(f393(x24003,x24004,x24001),f393(x24003,x24004,x24002))
% 109.14/108.87 [2401]~E(x24011,x24012)+E(f559(x24011,x24013),f559(x24012,x24013))
% 109.14/108.87 [2402]~E(x24021,x24022)+E(f559(x24023,x24021),f559(x24023,x24022))
% 109.14/108.87 [2403]~E(x24031,x24032)+E(f891(x24031,x24033,x24034),f891(x24032,x24033,x24034))
% 109.14/108.87 [2404]~E(x24041,x24042)+E(f891(x24043,x24041,x24044),f891(x24043,x24042,x24044))
% 109.14/108.87 [2405]~E(x24051,x24052)+E(f891(x24053,x24054,x24051),f891(x24053,x24054,x24052))
% 109.14/108.87 [2406]~E(x24061,x24062)+E(f489(x24061,x24063,x24064),f489(x24062,x24063,x24064))
% 109.14/108.87 [2407]~E(x24071,x24072)+E(f489(x24073,x24071,x24074),f489(x24073,x24072,x24074))
% 109.14/108.87 [2408]~E(x24081,x24082)+E(f489(x24083,x24084,x24081),f489(x24083,x24084,x24082))
% 109.14/108.87 [2409]~E(x24091,x24092)+E(f467(x24091,x24093,x24094),f467(x24092,x24093,x24094))
% 109.14/108.87 [2410]~E(x24101,x24102)+E(f467(x24103,x24101,x24104),f467(x24103,x24102,x24104))
% 109.14/108.87 [2411]~E(x24111,x24112)+E(f467(x24113,x24114,x24111),f467(x24113,x24114,x24112))
% 109.14/108.87 [2412]~E(x24121,x24122)+E(f661(x24121,x24123),f661(x24122,x24123))
% 109.14/108.87 [2413]~E(x24131,x24132)+E(f661(x24133,x24131),f661(x24133,x24132))
% 109.14/108.87 [2414]~E(x24141,x24142)+E(f502(x24141,x24143,x24144),f502(x24142,x24143,x24144))
% 109.14/108.87 [2415]~E(x24151,x24152)+E(f502(x24153,x24151,x24154),f502(x24153,x24152,x24154))
% 109.14/108.87 [2416]~E(x24161,x24162)+E(f502(x24163,x24164,x24161),f502(x24163,x24164,x24162))
% 109.14/108.87 [2417]~E(x24171,x24172)+E(f867(x24171,x24173,x24174,x24175),f867(x24172,x24173,x24174,x24175))
% 109.14/108.87 [2418]~E(x24181,x24182)+E(f867(x24183,x24181,x24184,x24185),f867(x24183,x24182,x24184,x24185))
% 109.14/108.87 [2419]~E(x24191,x24192)+E(f867(x24193,x24194,x24191,x24195),f867(x24193,x24194,x24192,x24195))
% 109.14/108.87 [2420]~E(x24201,x24202)+E(f867(x24203,x24204,x24205,x24201),f867(x24203,x24204,x24205,x24202))
% 109.14/108.87 [2421]~E(x24211,x24212)+E(f219(x24211,x24213,x24214),f219(x24212,x24213,x24214))
% 109.14/108.87 [2422]~E(x24221,x24222)+E(f219(x24223,x24221,x24224),f219(x24223,x24222,x24224))
% 109.14/108.87 [2423]~E(x24231,x24232)+E(f219(x24233,x24234,x24231),f219(x24233,x24234,x24232))
% 109.14/108.87 [2424]~E(x24241,x24242)+E(f750(x24241,x24243,x24244),f750(x24242,x24243,x24244))
% 109.14/108.87 [2425]~E(x24251,x24252)+E(f750(x24253,x24251,x24254),f750(x24253,x24252,x24254))
% 109.14/108.87 [2426]~E(x24261,x24262)+E(f750(x24263,x24264,x24261),f750(x24263,x24264,x24262))
% 109.14/108.87 [2427]~E(x24271,x24272)+E(f535(x24271,x24273,x24274,x24275),f535(x24272,x24273,x24274,x24275))
% 109.14/108.87 [2428]~E(x24281,x24282)+E(f535(x24283,x24281,x24284,x24285),f535(x24283,x24282,x24284,x24285))
% 109.14/108.87 [2429]~E(x24291,x24292)+E(f535(x24293,x24294,x24291,x24295),f535(x24293,x24294,x24292,x24295))
% 109.14/108.87 [2430]~E(x24301,x24302)+E(f535(x24303,x24304,x24305,x24301),f535(x24303,x24304,x24305,x24302))
% 109.14/108.87 [2431]~E(x24311,x24312)+E(f716(x24311,x24313),f716(x24312,x24313))
% 109.14/108.87 [2432]~E(x24321,x24322)+E(f716(x24323,x24321),f716(x24323,x24322))
% 109.14/108.87 [2433]~E(x24331,x24332)+E(f554(x24331,x24333),f554(x24332,x24333))
% 109.14/108.87 [2434]~E(x24341,x24342)+E(f554(x24343,x24341),f554(x24343,x24342))
% 109.14/108.87 [2435]~E(x24351,x24352)+E(f734(x24351,x24353),f734(x24352,x24353))
% 109.14/108.87 [2436]~E(x24361,x24362)+E(f734(x24363,x24361),f734(x24363,x24362))
% 109.14/108.87 [2437]~E(x24371,x24372)+E(f442(x24371,x24373),f442(x24372,x24373))
% 109.14/108.87 [2438]~E(x24381,x24382)+E(f442(x24383,x24381),f442(x24383,x24382))
% 109.14/108.87 [2439]~E(x24391,x24392)+E(f696(x24391,x24393,x24394,x24395,x24396),f696(x24392,x24393,x24394,x24395,x24396))
% 109.14/108.87 [2440]~E(x24401,x24402)+E(f696(x24403,x24401,x24404,x24405,x24406),f696(x24403,x24402,x24404,x24405,x24406))
% 109.14/108.87 [2441]~E(x24411,x24412)+E(f696(x24413,x24414,x24411,x24415,x24416),f696(x24413,x24414,x24412,x24415,x24416))
% 109.14/108.87 [2442]~E(x24421,x24422)+E(f696(x24423,x24424,x24425,x24421,x24426),f696(x24423,x24424,x24425,x24422,x24426))
% 109.14/108.87 [2443]~E(x24431,x24432)+E(f696(x24433,x24434,x24435,x24436,x24431),f696(x24433,x24434,x24435,x24436,x24432))
% 109.14/108.87 [2444]~E(x24441,x24442)+E(f188(x24441,x24443,x24444,x24445),f188(x24442,x24443,x24444,x24445))
% 109.14/108.87 [2445]~E(x24451,x24452)+E(f188(x24453,x24451,x24454,x24455),f188(x24453,x24452,x24454,x24455))
% 109.14/108.87 [2446]~E(x24461,x24462)+E(f188(x24463,x24464,x24461,x24465),f188(x24463,x24464,x24462,x24465))
% 109.14/108.87 [2447]~E(x24471,x24472)+E(f188(x24473,x24474,x24475,x24471),f188(x24473,x24474,x24475,x24472))
% 109.14/108.87 [2448]~E(x24481,x24482)+E(f903(x24481,x24483,x24484,x24485,x24486),f903(x24482,x24483,x24484,x24485,x24486))
% 109.14/108.87 [2449]~E(x24491,x24492)+E(f903(x24493,x24491,x24494,x24495,x24496),f903(x24493,x24492,x24494,x24495,x24496))
% 109.14/108.87 [2450]~E(x24501,x24502)+E(f903(x24503,x24504,x24501,x24505,x24506),f903(x24503,x24504,x24502,x24505,x24506))
% 109.14/108.87 [2451]~E(x24511,x24512)+E(f903(x24513,x24514,x24515,x24511,x24516),f903(x24513,x24514,x24515,x24512,x24516))
% 109.14/108.87 [2452]~E(x24521,x24522)+E(f903(x24523,x24524,x24525,x24526,x24521),f903(x24523,x24524,x24525,x24526,x24522))
% 109.14/108.87 [2453]~E(x24531,x24532)+E(f580(x24531,x24533),f580(x24532,x24533))
% 109.14/108.87 [2454]~E(x24541,x24542)+E(f580(x24543,x24541),f580(x24543,x24542))
% 109.14/108.87 [2455]~E(x24551,x24552)+E(f599(x24551,x24553,x24554,x24555),f599(x24552,x24553,x24554,x24555))
% 109.14/108.87 [2456]~E(x24561,x24562)+E(f599(x24563,x24561,x24564,x24565),f599(x24563,x24562,x24564,x24565))
% 109.14/108.87 [2457]~E(x24571,x24572)+E(f599(x24573,x24574,x24571,x24575),f599(x24573,x24574,x24572,x24575))
% 109.14/108.87 [2458]~E(x24581,x24582)+E(f599(x24583,x24584,x24585,x24581),f599(x24583,x24584,x24585,x24582))
% 109.14/108.87 [2459]~E(x24591,x24592)+E(f717(x24591,x24593,x24594),f717(x24592,x24593,x24594))
% 109.14/108.87 [2460]~E(x24601,x24602)+E(f717(x24603,x24601,x24604),f717(x24603,x24602,x24604))
% 109.14/108.87 [2461]~E(x24611,x24612)+E(f717(x24613,x24614,x24611),f717(x24613,x24614,x24612))
% 109.14/108.87 [2462]~E(x24621,x24622)+E(f637(x24621,x24623,x24624,x24625),f637(x24622,x24623,x24624,x24625))
% 109.14/108.87 [2463]~E(x24631,x24632)+E(f637(x24633,x24631,x24634,x24635),f637(x24633,x24632,x24634,x24635))
% 109.14/108.87 [2464]~E(x24641,x24642)+E(f637(x24643,x24644,x24641,x24645),f637(x24643,x24644,x24642,x24645))
% 109.14/108.87 [2465]~E(x24651,x24652)+E(f637(x24653,x24654,x24655,x24651),f637(x24653,x24654,x24655,x24652))
% 109.14/108.87 [2466]~E(x24661,x24662)+E(f768(x24661,x24663,x24664,x24665,x24666),f768(x24662,x24663,x24664,x24665,x24666))
% 109.14/108.87 [2467]~E(x24671,x24672)+E(f768(x24673,x24671,x24674,x24675,x24676),f768(x24673,x24672,x24674,x24675,x24676))
% 109.14/108.87 [2468]~E(x24681,x24682)+E(f768(x24683,x24684,x24681,x24685,x24686),f768(x24683,x24684,x24682,x24685,x24686))
% 109.14/108.87 [2469]~E(x24691,x24692)+E(f768(x24693,x24694,x24695,x24691,x24696),f768(x24693,x24694,x24695,x24692,x24696))
% 109.14/108.87 [2470]~E(x24701,x24702)+E(f768(x24703,x24704,x24705,x24706,x24701),f768(x24703,x24704,x24705,x24706,x24702))
% 109.14/108.87 [2471]~E(x24711,x24712)+E(f573(x24711,x24713,x24714,x24715),f573(x24712,x24713,x24714,x24715))
% 109.14/108.87 [2472]~E(x24721,x24722)+E(f573(x24723,x24721,x24724,x24725),f573(x24723,x24722,x24724,x24725))
% 109.14/108.87 [2473]~E(x24731,x24732)+E(f573(x24733,x24734,x24731,x24735),f573(x24733,x24734,x24732,x24735))
% 109.14/108.87 [2474]~E(x24741,x24742)+E(f573(x24743,x24744,x24745,x24741),f573(x24743,x24744,x24745,x24742))
% 109.14/108.87 [2475]~E(x24751,x24752)+E(f650(x24751,x24753,x24754,x24755,x24756),f650(x24752,x24753,x24754,x24755,x24756))
% 109.14/108.87 [2476]~E(x24761,x24762)+E(f650(x24763,x24761,x24764,x24765,x24766),f650(x24763,x24762,x24764,x24765,x24766))
% 109.14/108.87 [2477]~E(x24771,x24772)+E(f650(x24773,x24774,x24771,x24775,x24776),f650(x24773,x24774,x24772,x24775,x24776))
% 109.14/108.87 [2478]~E(x24781,x24782)+E(f650(x24783,x24784,x24785,x24781,x24786),f650(x24783,x24784,x24785,x24782,x24786))
% 109.14/108.87 [2479]~E(x24791,x24792)+E(f650(x24793,x24794,x24795,x24796,x24791),f650(x24793,x24794,x24795,x24796,x24792))
% 109.14/108.87 [2480]~E(x24801,x24802)+E(f596(x24801,x24803,x24804),f596(x24802,x24803,x24804))
% 109.14/108.87 [2481]~E(x24811,x24812)+E(f596(x24813,x24811,x24814),f596(x24813,x24812,x24814))
% 109.14/108.87 [2482]~E(x24821,x24822)+E(f596(x24823,x24824,x24821),f596(x24823,x24824,x24822))
% 109.14/108.87 [2483]~E(x24831,x24832)+E(f639(x24831,x24833),f639(x24832,x24833))
% 109.14/108.87 [2484]~E(x24841,x24842)+E(f639(x24843,x24841),f639(x24843,x24842))
% 109.14/108.87 [2485]~E(x24851,x24852)+E(f819(x24851,x24853),f819(x24852,x24853))
% 109.14/108.87 [2486]~E(x24861,x24862)+E(f819(x24863,x24861),f819(x24863,x24862))
% 109.14/108.87 [2487]~E(x24871,x24872)+E(f814(x24871,x24873),f814(x24872,x24873))
% 109.14/108.87 [2488]~E(x24881,x24882)+E(f814(x24883,x24881),f814(x24883,x24882))
% 109.14/108.87 [2489]~E(x24891,x24892)+E(f795(x24891),f795(x24892))
% 109.14/108.87 [2490]~E(x24901,x24902)+E(f811(x24901,x24903),f811(x24902,x24903))
% 109.14/108.87 [2491]~E(x24911,x24912)+E(f811(x24913,x24911),f811(x24913,x24912))
% 109.14/108.87 [2492]~E(x24921,x24922)+E(f458(x24921,x24923),f458(x24922,x24923))
% 109.14/108.87 [2493]~E(x24931,x24932)+E(f458(x24933,x24931),f458(x24933,x24932))
% 109.14/108.87 [2494]~E(x24941,x24942)+E(f845(x24941,x24943,x24944,x24945),f845(x24942,x24943,x24944,x24945))
% 109.14/108.87 [2495]~E(x24951,x24952)+E(f845(x24953,x24951,x24954,x24955),f845(x24953,x24952,x24954,x24955))
% 109.14/108.87 [2496]~E(x24961,x24962)+E(f845(x24963,x24964,x24961,x24965),f845(x24963,x24964,x24962,x24965))
% 109.14/108.87 [2497]~E(x24971,x24972)+E(f845(x24973,x24974,x24975,x24971),f845(x24973,x24974,x24975,x24972))
% 109.14/108.87 [2498]~E(x24981,x24982)+E(f657(x24981,x24983,x24984),f657(x24982,x24983,x24984))
% 109.14/108.87 [2499]~E(x24991,x24992)+E(f657(x24993,x24991,x24994),f657(x24993,x24992,x24994))
% 109.14/108.87 [2500]~E(x25001,x25002)+E(f657(x25003,x25004,x25001),f657(x25003,x25004,x25002))
% 109.14/108.87 [2501]~E(x25011,x25012)+E(f755(x25011,x25013,x25014),f755(x25012,x25013,x25014))
% 109.14/108.87 [2502]~E(x25021,x25022)+E(f755(x25023,x25021,x25024),f755(x25023,x25022,x25024))
% 109.14/108.87 [2503]~E(x25031,x25032)+E(f755(x25033,x25034,x25031),f755(x25033,x25034,x25032))
% 109.14/108.87 [2504]~E(x25041,x25042)+E(f694(x25041,x25043,x25044,x25045,x25046),f694(x25042,x25043,x25044,x25045,x25046))
% 109.14/108.87 [2505]~E(x25051,x25052)+E(f694(x25053,x25051,x25054,x25055,x25056),f694(x25053,x25052,x25054,x25055,x25056))
% 109.14/108.87 [2506]~E(x25061,x25062)+E(f694(x25063,x25064,x25061,x25065,x25066),f694(x25063,x25064,x25062,x25065,x25066))
% 109.14/108.87 [2507]~E(x25071,x25072)+E(f694(x25073,x25074,x25075,x25071,x25076),f694(x25073,x25074,x25075,x25072,x25076))
% 109.14/108.87 [2508]~E(x25081,x25082)+E(f694(x25083,x25084,x25085,x25086,x25081),f694(x25083,x25084,x25085,x25086,x25082))
% 109.14/108.87 [2509]~E(x25091,x25092)+E(f198(x25091,x25093,x25094,x25095,x25096,x25097,x25098),f198(x25092,x25093,x25094,x25095,x25096,x25097,x25098))
% 109.14/108.87 [2510]~E(x25101,x25102)+E(f198(x25103,x25101,x25104,x25105,x25106,x25107,x25108),f198(x25103,x25102,x25104,x25105,x25106,x25107,x25108))
% 109.14/108.87 [2511]~E(x25111,x25112)+E(f198(x25113,x25114,x25111,x25115,x25116,x25117,x25118),f198(x25113,x25114,x25112,x25115,x25116,x25117,x25118))
% 109.14/108.87 [2512]~E(x25121,x25122)+E(f198(x25123,x25124,x25125,x25121,x25126,x25127,x25128),f198(x25123,x25124,x25125,x25122,x25126,x25127,x25128))
% 109.14/108.87 [2513]~E(x25131,x25132)+E(f198(x25133,x25134,x25135,x25136,x25131,x25137,x25138),f198(x25133,x25134,x25135,x25136,x25132,x25137,x25138))
% 109.14/108.87 [2514]~E(x25141,x25142)+E(f198(x25143,x25144,x25145,x25146,x25147,x25141,x25148),f198(x25143,x25144,x25145,x25146,x25147,x25142,x25148))
% 109.14/108.87 [2515]~E(x25151,x25152)+E(f198(x25153,x25154,x25155,x25156,x25157,x25158,x25151),f198(x25153,x25154,x25155,x25156,x25157,x25158,x25152))
% 109.14/108.87 [2516]~E(x25161,x25162)+E(f677(x25161,x25163,x25164,x25165),f677(x25162,x25163,x25164,x25165))
% 109.14/108.87 [2517]~E(x25171,x25172)+E(f677(x25173,x25171,x25174,x25175),f677(x25173,x25172,x25174,x25175))
% 109.14/108.87 [2518]~E(x25181,x25182)+E(f677(x25183,x25184,x25181,x25185),f677(x25183,x25184,x25182,x25185))
% 109.14/108.87 [2519]~E(x25191,x25192)+E(f677(x25193,x25194,x25195,x25191),f677(x25193,x25194,x25195,x25192))
% 109.14/108.87 [2520]~E(x25201,x25202)+E(f407(x25201,x25203,x25204),f407(x25202,x25203,x25204))
% 109.14/108.87 [2521]~E(x25211,x25212)+E(f407(x25213,x25211,x25214),f407(x25213,x25212,x25214))
% 109.14/108.87 [2522]~E(x25221,x25222)+E(f407(x25223,x25224,x25221),f407(x25223,x25224,x25222))
% 109.14/108.87 [2523]~E(x25231,x25232)+E(f769(x25231,x25233,x25234),f769(x25232,x25233,x25234))
% 109.14/108.87 [2524]~E(x25241,x25242)+E(f769(x25243,x25241,x25244),f769(x25243,x25242,x25244))
% 109.14/108.87 [2525]~E(x25251,x25252)+E(f769(x25253,x25254,x25251),f769(x25253,x25254,x25252))
% 109.14/108.87 [2526]~E(x25261,x25262)+E(f227(x25261,x25263),f227(x25262,x25263))
% 109.14/108.87 [2527]~E(x25271,x25272)+E(f227(x25273,x25271),f227(x25273,x25272))
% 109.14/108.87 [2528]~E(x25281,x25282)+E(f724(x25281,x25283,x25284,x25285),f724(x25282,x25283,x25284,x25285))
% 109.14/108.87 [2529]~E(x25291,x25292)+E(f724(x25293,x25291,x25294,x25295),f724(x25293,x25292,x25294,x25295))
% 109.14/108.87 [2530]~E(x25301,x25302)+E(f724(x25303,x25304,x25301,x25305),f724(x25303,x25304,x25302,x25305))
% 109.14/108.87 [2531]~E(x25311,x25312)+E(f724(x25313,x25314,x25315,x25311),f724(x25313,x25314,x25315,x25312))
% 109.14/108.87 [2532]~E(x25321,x25322)+E(f571(x25321,x25323,x25324,x25325),f571(x25322,x25323,x25324,x25325))
% 109.14/108.87 [2533]~E(x25331,x25332)+E(f571(x25333,x25331,x25334,x25335),f571(x25333,x25332,x25334,x25335))
% 109.14/108.87 [2534]~E(x25341,x25342)+E(f571(x25343,x25344,x25341,x25345),f571(x25343,x25344,x25342,x25345))
% 109.14/108.87 [2535]~E(x25351,x25352)+E(f571(x25353,x25354,x25355,x25351),f571(x25353,x25354,x25355,x25352))
% 109.14/108.87 [2536]~E(x25361,x25362)+E(f566(x25361,x25363),f566(x25362,x25363))
% 109.14/108.87 [2537]~E(x25371,x25372)+E(f566(x25373,x25371),f566(x25373,x25372))
% 109.14/108.87 [2538]~E(x25381,x25382)+E(f840(x25381,x25383,x25384,x25385,x25386,x25387,x25388,x25389),f840(x25382,x25383,x25384,x25385,x25386,x25387,x25388,x25389))
% 109.14/108.87 [2539]~E(x25391,x25392)+E(f840(x25393,x25391,x25394,x25395,x25396,x25397,x25398,x25399),f840(x25393,x25392,x25394,x25395,x25396,x25397,x25398,x25399))
% 109.14/108.87 [2540]~E(x25401,x25402)+E(f840(x25403,x25404,x25401,x25405,x25406,x25407,x25408,x25409),f840(x25403,x25404,x25402,x25405,x25406,x25407,x25408,x25409))
% 109.14/108.87 [2541]~E(x25411,x25412)+E(f840(x25413,x25414,x25415,x25411,x25416,x25417,x25418,x25419),f840(x25413,x25414,x25415,x25412,x25416,x25417,x25418,x25419))
% 109.14/108.87 [2542]~E(x25421,x25422)+E(f840(x25423,x25424,x25425,x25426,x25421,x25427,x25428,x25429),f840(x25423,x25424,x25425,x25426,x25422,x25427,x25428,x25429))
% 109.14/108.87 [2543]~E(x25431,x25432)+E(f840(x25433,x25434,x25435,x25436,x25437,x25431,x25438,x25439),f840(x25433,x25434,x25435,x25436,x25437,x25432,x25438,x25439))
% 109.14/108.87 [2544]~E(x25441,x25442)+E(f840(x25443,x25444,x25445,x25446,x25447,x25448,x25441,x25449),f840(x25443,x25444,x25445,x25446,x25447,x25448,x25442,x25449))
% 109.14/108.87 [2545]~E(x25451,x25452)+E(f840(x25453,x25454,x25455,x25456,x25457,x25458,x25459,x25451),f840(x25453,x25454,x25455,x25456,x25457,x25458,x25459,x25452))
% 109.14/108.87 [2546]~E(x25461,x25462)+E(f777(x25461,x25463),f777(x25462,x25463))
% 109.14/108.87 [2547]~E(x25471,x25472)+E(f777(x25473,x25471),f777(x25473,x25472))
% 109.14/108.87 [2548]~E(x25481,x25482)+E(f271(x25481,x25483,x25484,x25485),f271(x25482,x25483,x25484,x25485))
% 109.14/108.87 [2549]~E(x25491,x25492)+E(f271(x25493,x25491,x25494,x25495),f271(x25493,x25492,x25494,x25495))
% 109.14/108.87 [2550]~E(x25501,x25502)+E(f271(x25503,x25504,x25501,x25505),f271(x25503,x25504,x25502,x25505))
% 109.14/108.87 [2551]~E(x25511,x25512)+E(f271(x25513,x25514,x25515,x25511),f271(x25513,x25514,x25515,x25512))
% 109.14/108.87 [2552]~E(x25521,x25522)+E(f134(x25521,x25523),f134(x25522,x25523))
% 109.14/108.87 [2553]~E(x25531,x25532)+E(f134(x25533,x25531),f134(x25533,x25532))
% 109.14/108.87 [2554]~E(x25541,x25542)+E(f781(x25541,x25543,x25544),f781(x25542,x25543,x25544))
% 109.14/108.87 [2555]~E(x25551,x25552)+E(f781(x25553,x25551,x25554),f781(x25553,x25552,x25554))
% 109.14/108.87 [2556]~E(x25561,x25562)+E(f781(x25563,x25564,x25561),f781(x25563,x25564,x25562))
% 109.14/108.87 [2557]~E(x25571,x25572)+E(f905(x25571,x25573,x25574),f905(x25572,x25573,x25574))
% 109.14/108.87 [2558]~E(x25581,x25582)+E(f905(x25583,x25581,x25584),f905(x25583,x25582,x25584))
% 109.14/108.87 [2559]~E(x25591,x25592)+E(f905(x25593,x25594,x25591),f905(x25593,x25594,x25592))
% 109.14/108.87 [2560]~E(x25601,x25602)+E(f883(x25601,x25603),f883(x25602,x25603))
% 109.14/108.87 [2561]~E(x25611,x25612)+E(f883(x25613,x25611),f883(x25613,x25612))
% 109.14/108.87 [2562]~E(x25621,x25622)+E(f487(x25621,x25623,x25624),f487(x25622,x25623,x25624))
% 109.14/108.87 [2563]~E(x25631,x25632)+E(f487(x25633,x25631,x25634),f487(x25633,x25632,x25634))
% 109.14/108.87 [2564]~E(x25641,x25642)+E(f487(x25643,x25644,x25641),f487(x25643,x25644,x25642))
% 109.14/108.87 [2565]~E(x25651,x25652)+E(f897(x25651,x25653,x25654),f897(x25652,x25653,x25654))
% 109.14/108.87 [2566]~E(x25661,x25662)+E(f897(x25663,x25661,x25664),f897(x25663,x25662,x25664))
% 109.14/108.87 [2567]~E(x25671,x25672)+E(f897(x25673,x25674,x25671),f897(x25673,x25674,x25672))
% 109.14/108.87 [2568]~E(x25681,x25682)+E(f383(x25681),f383(x25682))
% 109.14/108.87 [2569]~E(x25691,x25692)+E(f810(x25691),f810(x25692))
% 109.14/108.87 [2570]~E(x25701,x25702)+E(f347(x25701,x25703,x25704,x25705),f347(x25702,x25703,x25704,x25705))
% 109.14/108.87 [2571]~E(x25711,x25712)+E(f347(x25713,x25711,x25714,x25715),f347(x25713,x25712,x25714,x25715))
% 109.14/108.87 [2572]~E(x25721,x25722)+E(f347(x25723,x25724,x25721,x25725),f347(x25723,x25724,x25722,x25725))
% 109.14/108.87 [2573]~E(x25731,x25732)+E(f347(x25733,x25734,x25735,x25731),f347(x25733,x25734,x25735,x25732))
% 109.14/108.87 [2574]~E(x25741,x25742)+E(f397(x25741,x25743),f397(x25742,x25743))
% 109.14/108.87 [2575]~E(x25751,x25752)+E(f397(x25753,x25751),f397(x25753,x25752))
% 109.14/108.87 [2576]~E(x25761,x25762)+E(f563(x25761,x25763,x25764,x25765),f563(x25762,x25763,x25764,x25765))
% 109.14/108.87 [2577]~E(x25771,x25772)+E(f563(x25773,x25771,x25774,x25775),f563(x25773,x25772,x25774,x25775))
% 109.14/108.87 [2578]~E(x25781,x25782)+E(f563(x25783,x25784,x25781,x25785),f563(x25783,x25784,x25782,x25785))
% 109.14/108.87 [2579]~E(x25791,x25792)+E(f563(x25793,x25794,x25795,x25791),f563(x25793,x25794,x25795,x25792))
% 109.14/108.87 [2580]~E(x25801,x25802)+E(f898(x25801,x25803,x25804,x25805),f898(x25802,x25803,x25804,x25805))
% 109.14/108.87 [2581]~E(x25811,x25812)+E(f898(x25813,x25811,x25814,x25815),f898(x25813,x25812,x25814,x25815))
% 109.14/108.87 [2582]~E(x25821,x25822)+E(f898(x25823,x25824,x25821,x25825),f898(x25823,x25824,x25822,x25825))
% 109.14/108.87 [2583]~E(x25831,x25832)+E(f898(x25833,x25834,x25835,x25831),f898(x25833,x25834,x25835,x25832))
% 109.14/108.87 [2584]~E(x25841,x25842)+E(f676(x25841,x25843,x25844,x25845),f676(x25842,x25843,x25844,x25845))
% 109.14/108.87 [2585]~E(x25851,x25852)+E(f676(x25853,x25851,x25854,x25855),f676(x25853,x25852,x25854,x25855))
% 109.14/108.87 [2586]~E(x25861,x25862)+E(f676(x25863,x25864,x25861,x25865),f676(x25863,x25864,x25862,x25865))
% 109.14/108.87 [2587]~E(x25871,x25872)+E(f676(x25873,x25874,x25875,x25871),f676(x25873,x25874,x25875,x25872))
% 109.14/108.87 [2588]~E(x25881,x25882)+E(f237(x25881,x25883,x25884,x25885,x25886,x25887),f237(x25882,x25883,x25884,x25885,x25886,x25887))
% 109.14/108.87 [2589]~E(x25891,x25892)+E(f237(x25893,x25891,x25894,x25895,x25896,x25897),f237(x25893,x25892,x25894,x25895,x25896,x25897))
% 109.14/108.87 [2590]~E(x25901,x25902)+E(f237(x25903,x25904,x25901,x25905,x25906,x25907),f237(x25903,x25904,x25902,x25905,x25906,x25907))
% 109.14/108.87 [2591]~E(x25911,x25912)+E(f237(x25913,x25914,x25915,x25911,x25916,x25917),f237(x25913,x25914,x25915,x25912,x25916,x25917))
% 109.14/108.87 [2592]~E(x25921,x25922)+E(f237(x25923,x25924,x25925,x25926,x25921,x25927),f237(x25923,x25924,x25925,x25926,x25922,x25927))
% 109.14/108.87 [2593]~E(x25931,x25932)+E(f237(x25933,x25934,x25935,x25936,x25937,x25931),f237(x25933,x25934,x25935,x25936,x25937,x25932))
% 109.14/108.87 [2594]~E(x25941,x25942)+E(f382(x25941,x25943),f382(x25942,x25943))
% 109.14/108.87 [2595]~E(x25951,x25952)+E(f382(x25953,x25951),f382(x25953,x25952))
% 109.14/108.87 [2596]~E(x25961,x25962)+E(f660(x25961,x25963,x25964,x25965),f660(x25962,x25963,x25964,x25965))
% 109.14/108.87 [2597]~E(x25971,x25972)+E(f660(x25973,x25971,x25974,x25975),f660(x25973,x25972,x25974,x25975))
% 109.14/108.87 [2598]~E(x25981,x25982)+E(f660(x25983,x25984,x25981,x25985),f660(x25983,x25984,x25982,x25985))
% 109.14/108.87 [2599]~E(x25991,x25992)+E(f660(x25993,x25994,x25995,x25991),f660(x25993,x25994,x25995,x25992))
% 109.14/108.87 [2600]~E(x26001,x26002)+E(f806(x26001,x26003,x26004,x26005,x26006),f806(x26002,x26003,x26004,x26005,x26006))
% 109.14/108.87 [2601]~E(x26011,x26012)+E(f806(x26013,x26011,x26014,x26015,x26016),f806(x26013,x26012,x26014,x26015,x26016))
% 109.14/108.87 [2602]~E(x26021,x26022)+E(f806(x26023,x26024,x26021,x26025,x26026),f806(x26023,x26024,x26022,x26025,x26026))
% 109.14/108.87 [2603]~E(x26031,x26032)+E(f806(x26033,x26034,x26035,x26031,x26036),f806(x26033,x26034,x26035,x26032,x26036))
% 109.14/108.87 [2604]~E(x26041,x26042)+E(f806(x26043,x26044,x26045,x26046,x26041),f806(x26043,x26044,x26045,x26046,x26042))
% 109.14/108.87 [2605]~E(x26051,x26052)+E(f709(x26051,x26053,x26054),f709(x26052,x26053,x26054))
% 109.14/108.87 [2606]~E(x26061,x26062)+E(f709(x26063,x26061,x26064),f709(x26063,x26062,x26064))
% 109.14/108.87 [2607]~E(x26071,x26072)+E(f709(x26073,x26074,x26071),f709(x26073,x26074,x26072))
% 109.14/108.87 [2608]~E(x26081,x26082)+E(f634(x26081,x26083,x26084),f634(x26082,x26083,x26084))
% 109.14/108.87 [2609]~E(x26091,x26092)+E(f634(x26093,x26091,x26094),f634(x26093,x26092,x26094))
% 109.14/108.87 [2610]~E(x26101,x26102)+E(f634(x26103,x26104,x26101),f634(x26103,x26104,x26102))
% 109.14/108.87 [2611]~E(x26111,x26112)+E(f474(x26111,x26113,x26114,x26115,x26116),f474(x26112,x26113,x26114,x26115,x26116))
% 109.14/108.87 [2612]~E(x26121,x26122)+E(f474(x26123,x26121,x26124,x26125,x26126),f474(x26123,x26122,x26124,x26125,x26126))
% 109.14/108.87 [2613]~E(x26131,x26132)+E(f474(x26133,x26134,x26131,x26135,x26136),f474(x26133,x26134,x26132,x26135,x26136))
% 109.14/108.87 [2614]~E(x26141,x26142)+E(f474(x26143,x26144,x26145,x26141,x26146),f474(x26143,x26144,x26145,x26142,x26146))
% 109.14/108.87 [2615]~E(x26151,x26152)+E(f474(x26153,x26154,x26155,x26156,x26151),f474(x26153,x26154,x26155,x26156,x26152))
% 109.14/108.87 [2616]~E(x26161,x26162)+E(f470(x26161,x26163,x26164,x26165,x26166),f470(x26162,x26163,x26164,x26165,x26166))
% 109.14/108.87 [2617]~E(x26171,x26172)+E(f470(x26173,x26171,x26174,x26175,x26176),f470(x26173,x26172,x26174,x26175,x26176))
% 109.14/108.87 [2618]~E(x26181,x26182)+E(f470(x26183,x26184,x26181,x26185,x26186),f470(x26183,x26184,x26182,x26185,x26186))
% 109.14/108.87 [2619]~E(x26191,x26192)+E(f470(x26193,x26194,x26195,x26191,x26196),f470(x26193,x26194,x26195,x26192,x26196))
% 109.14/108.87 [2620]~E(x26201,x26202)+E(f470(x26203,x26204,x26205,x26206,x26201),f470(x26203,x26204,x26205,x26206,x26202))
% 109.14/108.87 [2621]~E(x26211,x26212)+E(f793(x26211,x26213,x26214,x26215),f793(x26212,x26213,x26214,x26215))
% 109.14/108.87 [2622]~E(x26221,x26222)+E(f793(x26223,x26221,x26224,x26225),f793(x26223,x26222,x26224,x26225))
% 109.14/108.87 [2623]~E(x26231,x26232)+E(f793(x26233,x26234,x26231,x26235),f793(x26233,x26234,x26232,x26235))
% 109.14/108.87 [2624]~E(x26241,x26242)+E(f793(x26243,x26244,x26245,x26241),f793(x26243,x26244,x26245,x26242))
% 109.14/108.87 [2625]~E(x26251,x26252)+E(f518(x26251,x26253,x26254,x26255,x26256),f518(x26252,x26253,x26254,x26255,x26256))
% 109.14/108.87 [2626]~E(x26261,x26262)+E(f518(x26263,x26261,x26264,x26265,x26266),f518(x26263,x26262,x26264,x26265,x26266))
% 109.14/108.87 [2627]~E(x26271,x26272)+E(f518(x26273,x26274,x26271,x26275,x26276),f518(x26273,x26274,x26272,x26275,x26276))
% 109.14/108.87 [2628]~E(x26281,x26282)+E(f518(x26283,x26284,x26285,x26281,x26286),f518(x26283,x26284,x26285,x26282,x26286))
% 109.14/108.87 [2629]~E(x26291,x26292)+E(f518(x26293,x26294,x26295,x26296,x26291),f518(x26293,x26294,x26295,x26296,x26292))
% 109.14/108.87 [2630]~E(x26301,x26302)+E(f322(x26301,x26303,x26304,x26305),f322(x26302,x26303,x26304,x26305))
% 109.14/108.87 [2631]~E(x26311,x26312)+E(f322(x26313,x26311,x26314,x26315),f322(x26313,x26312,x26314,x26315))
% 109.14/108.87 [2632]~E(x26321,x26322)+E(f322(x26323,x26324,x26321,x26325),f322(x26323,x26324,x26322,x26325))
% 109.14/108.87 [2633]~E(x26331,x26332)+E(f322(x26333,x26334,x26335,x26331),f322(x26333,x26334,x26335,x26332))
% 109.14/108.87 [2634]~E(x26341,x26342)+E(f886(x26341,x26343,x26344,x26345),f886(x26342,x26343,x26344,x26345))
% 109.14/108.87 [2635]~E(x26351,x26352)+E(f886(x26353,x26351,x26354,x26355),f886(x26353,x26352,x26354,x26355))
% 109.14/108.87 [2636]~E(x26361,x26362)+E(f886(x26363,x26364,x26361,x26365),f886(x26363,x26364,x26362,x26365))
% 109.14/108.87 [2637]~E(x26371,x26372)+E(f886(x26373,x26374,x26375,x26371),f886(x26373,x26374,x26375,x26372))
% 109.14/108.87 [2638]~E(x26381,x26382)+E(f201(x26381,x26383,x26384,x26385),f201(x26382,x26383,x26384,x26385))
% 109.14/108.87 [2639]~E(x26391,x26392)+E(f201(x26393,x26391,x26394,x26395),f201(x26393,x26392,x26394,x26395))
% 109.14/108.87 [2640]~E(x26401,x26402)+E(f201(x26403,x26404,x26401,x26405),f201(x26403,x26404,x26402,x26405))
% 109.14/108.87 [2641]~E(x26411,x26412)+E(f201(x26413,x26414,x26415,x26411),f201(x26413,x26414,x26415,x26412))
% 109.14/108.87 [2642]~E(x26421,x26422)+E(f895(x26421,x26423),f895(x26422,x26423))
% 109.14/108.87 [2643]~E(x26431,x26432)+E(f895(x26433,x26431),f895(x26433,x26432))
% 109.14/108.87 [2644]~E(x26441,x26442)+E(f209(x26441,x26443),f209(x26442,x26443))
% 109.14/108.87 [2645]~E(x26451,x26452)+E(f209(x26453,x26451),f209(x26453,x26452))
% 109.14/108.87 [2646]~E(x26461,x26462)+E(f448(x26461,x26463,x26464),f448(x26462,x26463,x26464))
% 109.14/108.87 [2647]~E(x26471,x26472)+E(f448(x26473,x26471,x26474),f448(x26473,x26472,x26474))
% 109.14/108.87 [2648]~E(x26481,x26482)+E(f448(x26483,x26484,x26481),f448(x26483,x26484,x26482))
% 109.14/108.87 [2649]~E(x26491,x26492)+E(f593(x26491,x26493),f593(x26492,x26493))
% 109.14/108.87 [2650]~E(x26501,x26502)+E(f593(x26503,x26501),f593(x26503,x26502))
% 109.14/108.87 [2651]~E(x26511,x26512)+E(f186(x26511,x26513,x26514,x26515),f186(x26512,x26513,x26514,x26515))
% 109.14/108.87 [2652]~E(x26521,x26522)+E(f186(x26523,x26521,x26524,x26525),f186(x26523,x26522,x26524,x26525))
% 109.14/108.87 [2653]~E(x26531,x26532)+E(f186(x26533,x26534,x26531,x26535),f186(x26533,x26534,x26532,x26535))
% 109.14/108.87 [2654]~E(x26541,x26542)+E(f186(x26543,x26544,x26545,x26541),f186(x26543,x26544,x26545,x26542))
% 109.14/108.87 [2655]~E(x26551,x26552)+E(f422(x26551,x26553,x26554,x26555),f422(x26552,x26553,x26554,x26555))
% 109.14/108.87 [2656]~E(x26561,x26562)+E(f422(x26563,x26561,x26564,x26565),f422(x26563,x26562,x26564,x26565))
% 109.14/108.87 [2657]~E(x26571,x26572)+E(f422(x26573,x26574,x26571,x26575),f422(x26573,x26574,x26572,x26575))
% 109.14/108.87 [2658]~E(x26581,x26582)+E(f422(x26583,x26584,x26585,x26581),f422(x26583,x26584,x26585,x26582))
% 109.14/108.87 [2659]~E(x26591,x26592)+E(f481(x26591,x26593,x26594),f481(x26592,x26593,x26594))
% 109.14/108.87 [2660]~E(x26601,x26602)+E(f481(x26603,x26601,x26604),f481(x26603,x26602,x26604))
% 109.14/108.87 [2661]~E(x26611,x26612)+E(f481(x26613,x26614,x26611),f481(x26613,x26614,x26612))
% 109.14/108.87 [2662]~E(x26621,x26622)+E(f424(x26621,x26623,x26624),f424(x26622,x26623,x26624))
% 109.14/108.87 [2663]~E(x26631,x26632)+E(f424(x26633,x26631,x26634),f424(x26633,x26632,x26634))
% 109.14/108.87 [2664]~E(x26641,x26642)+E(f424(x26643,x26644,x26641),f424(x26643,x26644,x26642))
% 109.14/108.87 [2665]~E(x26651,x26652)+E(f797(x26651,x26653),f797(x26652,x26653))
% 109.14/108.87 [2666]~E(x26661,x26662)+E(f797(x26663,x26661),f797(x26663,x26662))
% 109.14/108.87 [2667]~E(x26671,x26672)+E(f758(x26671),f758(x26672))
% 109.14/108.87 [2668]~E(x26681,x26682)+E(f746(x26681,x26683,x26684),f746(x26682,x26683,x26684))
% 109.14/108.87 [2669]~E(x26691,x26692)+E(f746(x26693,x26691,x26694),f746(x26693,x26692,x26694))
% 109.14/108.87 [2670]~E(x26701,x26702)+E(f746(x26703,x26704,x26701),f746(x26703,x26704,x26702))
% 109.14/108.87 [2671]~E(x26711,x26712)+E(f846(x26711,x26713,x26714,x26715,x26716,x26717),f846(x26712,x26713,x26714,x26715,x26716,x26717))
% 109.14/108.87 [2672]~E(x26721,x26722)+E(f846(x26723,x26721,x26724,x26725,x26726,x26727),f846(x26723,x26722,x26724,x26725,x26726,x26727))
% 109.14/108.87 [2673]~E(x26731,x26732)+E(f846(x26733,x26734,x26731,x26735,x26736,x26737),f846(x26733,x26734,x26732,x26735,x26736,x26737))
% 109.14/108.87 [2674]~E(x26741,x26742)+E(f846(x26743,x26744,x26745,x26741,x26746,x26747),f846(x26743,x26744,x26745,x26742,x26746,x26747))
% 109.14/108.87 [2675]~E(x26751,x26752)+E(f846(x26753,x26754,x26755,x26756,x26751,x26757),f846(x26753,x26754,x26755,x26756,x26752,x26757))
% 109.14/108.87 [2676]~E(x26761,x26762)+E(f846(x26763,x26764,x26765,x26766,x26767,x26761),f846(x26763,x26764,x26765,x26766,x26767,x26762))
% 109.14/108.87 [2677]~E(x26771,x26772)+E(f499(x26771,x26773,x26774,x26775),f499(x26772,x26773,x26774,x26775))
% 109.14/108.87 [2678]~E(x26781,x26782)+E(f499(x26783,x26781,x26784,x26785),f499(x26783,x26782,x26784,x26785))
% 109.14/108.87 [2679]~E(x26791,x26792)+E(f499(x26793,x26794,x26791,x26795),f499(x26793,x26794,x26792,x26795))
% 109.14/108.87 [2680]~E(x26801,x26802)+E(f499(x26803,x26804,x26805,x26801),f499(x26803,x26804,x26805,x26802))
% 109.14/108.87 [2681]~E(x26811,x26812)+E(f494(x26811,x26813,x26814),f494(x26812,x26813,x26814))
% 109.14/108.87 [2682]~E(x26821,x26822)+E(f494(x26823,x26821,x26824),f494(x26823,x26822,x26824))
% 109.14/108.87 [2683]~E(x26831,x26832)+E(f494(x26833,x26834,x26831),f494(x26833,x26834,x26832))
% 109.14/108.87 [2684]~E(x26841,x26842)+E(f714(x26841,x26843,x26844,x26845,x26846),f714(x26842,x26843,x26844,x26845,x26846))
% 109.14/108.87 [2685]~E(x26851,x26852)+E(f714(x26853,x26851,x26854,x26855,x26856),f714(x26853,x26852,x26854,x26855,x26856))
% 109.14/108.87 [2686]~E(x26861,x26862)+E(f714(x26863,x26864,x26861,x26865,x26866),f714(x26863,x26864,x26862,x26865,x26866))
% 109.14/108.87 [2687]~E(x26871,x26872)+E(f714(x26873,x26874,x26875,x26871,x26876),f714(x26873,x26874,x26875,x26872,x26876))
% 109.14/108.87 [2688]~E(x26881,x26882)+E(f714(x26883,x26884,x26885,x26886,x26881),f714(x26883,x26884,x26885,x26886,x26882))
% 109.14/108.87 [2689]~E(x26891,x26892)+E(f335(x26891,x26893,x26894,x26895),f335(x26892,x26893,x26894,x26895))
% 109.14/108.87 [2690]~E(x26901,x26902)+E(f335(x26903,x26901,x26904,x26905),f335(x26903,x26902,x26904,x26905))
% 109.14/108.87 [2691]~E(x26911,x26912)+E(f335(x26913,x26914,x26911,x26915),f335(x26913,x26914,x26912,x26915))
% 109.14/108.87 [2692]~E(x26921,x26922)+E(f335(x26923,x26924,x26925,x26921),f335(x26923,x26924,x26925,x26922))
% 109.14/108.87 [2693]~E(x26931,x26932)+E(f67(x26931,x26933),f67(x26932,x26933))
% 109.14/108.87 [2694]~E(x26941,x26942)+E(f67(x26943,x26941),f67(x26943,x26942))
% 109.14/108.87 [2695]~E(x26951,x26952)+E(f531(x26951,x26953,x26954,x26955),f531(x26952,x26953,x26954,x26955))
% 109.14/108.87 [2696]~E(x26961,x26962)+E(f531(x26963,x26961,x26964,x26965),f531(x26963,x26962,x26964,x26965))
% 109.14/108.87 [2697]~E(x26971,x26972)+E(f531(x26973,x26974,x26971,x26975),f531(x26973,x26974,x26972,x26975))
% 109.14/108.87 [2698]~E(x26981,x26982)+E(f531(x26983,x26984,x26985,x26981),f531(x26983,x26984,x26985,x26982))
% 109.14/108.87 [2699]~E(x26991,x26992)+E(f737(x26991,x26993,x26994,x26995,x26996),f737(x26992,x26993,x26994,x26995,x26996))
% 109.14/108.87 [2700]~E(x27001,x27002)+E(f737(x27003,x27001,x27004,x27005,x27006),f737(x27003,x27002,x27004,x27005,x27006))
% 109.14/108.87 [2701]~E(x27011,x27012)+E(f737(x27013,x27014,x27011,x27015,x27016),f737(x27013,x27014,x27012,x27015,x27016))
% 109.14/108.87 [2702]~E(x27021,x27022)+E(f737(x27023,x27024,x27025,x27021,x27026),f737(x27023,x27024,x27025,x27022,x27026))
% 109.14/108.87 [2703]~E(x27031,x27032)+E(f737(x27033,x27034,x27035,x27036,x27031),f737(x27033,x27034,x27035,x27036,x27032))
% 109.14/108.87 [2704]~E(x27041,x27042)+E(f680(x27041,x27043,x27044),f680(x27042,x27043,x27044))
% 109.14/108.87 [2705]~E(x27051,x27052)+E(f680(x27053,x27051,x27054),f680(x27053,x27052,x27054))
% 109.14/108.87 [2706]~E(x27061,x27062)+E(f680(x27063,x27064,x27061),f680(x27063,x27064,x27062))
% 109.14/108.87 [2707]~E(x27071,x27072)+E(f544(x27071,x27073,x27074,x27075),f544(x27072,x27073,x27074,x27075))
% 109.14/108.87 [2708]~E(x27081,x27082)+E(f544(x27083,x27081,x27084,x27085),f544(x27083,x27082,x27084,x27085))
% 109.14/108.87 [2709]~E(x27091,x27092)+E(f544(x27093,x27094,x27091,x27095),f544(x27093,x27094,x27092,x27095))
% 109.14/108.87 [2710]~E(x27101,x27102)+E(f544(x27103,x27104,x27105,x27101),f544(x27103,x27104,x27105,x27102))
% 109.14/108.87 [2711]~E(x27111,x27112)+E(f561(x27111,x27113,x27114,x27115,x27116,x27117),f561(x27112,x27113,x27114,x27115,x27116,x27117))
% 109.14/108.87 [2712]~E(x27121,x27122)+E(f561(x27123,x27121,x27124,x27125,x27126,x27127),f561(x27123,x27122,x27124,x27125,x27126,x27127))
% 109.14/108.87 [2713]~E(x27131,x27132)+E(f561(x27133,x27134,x27131,x27135,x27136,x27137),f561(x27133,x27134,x27132,x27135,x27136,x27137))
% 109.14/108.87 [2714]~E(x27141,x27142)+E(f561(x27143,x27144,x27145,x27141,x27146,x27147),f561(x27143,x27144,x27145,x27142,x27146,x27147))
% 109.14/108.87 [2715]~E(x27151,x27152)+E(f561(x27153,x27154,x27155,x27156,x27151,x27157),f561(x27153,x27154,x27155,x27156,x27152,x27157))
% 109.14/108.87 [2716]~E(x27161,x27162)+E(f561(x27163,x27164,x27165,x27166,x27167,x27161),f561(x27163,x27164,x27165,x27166,x27167,x27162))
% 109.14/108.87 [2717]~E(x27171,x27172)+E(f744(x27171,x27173),f744(x27172,x27173))
% 109.14/108.87 [2718]~E(x27181,x27182)+E(f744(x27183,x27181),f744(x27183,x27182))
% 109.14/108.87 [2719]~E(x27191,x27192)+E(f892(x27191,x27193,x27194),f892(x27192,x27193,x27194))
% 109.14/108.87 [2720]~E(x27201,x27202)+E(f892(x27203,x27201,x27204),f892(x27203,x27202,x27204))
% 109.14/108.87 [2721]~E(x27211,x27212)+E(f892(x27213,x27214,x27211),f892(x27213,x27214,x27212))
% 109.14/108.87 [2722]~E(x27221,x27222)+E(f869(x27221,x27223,x27224,x27225,x27226),f869(x27222,x27223,x27224,x27225,x27226))
% 109.14/108.87 [2723]~E(x27231,x27232)+E(f869(x27233,x27231,x27234,x27235,x27236),f869(x27233,x27232,x27234,x27235,x27236))
% 109.14/108.87 [2724]~E(x27241,x27242)+E(f869(x27243,x27244,x27241,x27245,x27246),f869(x27243,x27244,x27242,x27245,x27246))
% 109.14/108.87 [2725]~E(x27251,x27252)+E(f869(x27253,x27254,x27255,x27251,x27256),f869(x27253,x27254,x27255,x27252,x27256))
% 109.14/108.87 [2726]~E(x27261,x27262)+E(f869(x27263,x27264,x27265,x27266,x27261),f869(x27263,x27264,x27265,x27266,x27262))
% 109.14/108.87 [2727]~E(x27271,x27272)+E(f434(x27271,x27273,x27274),f434(x27272,x27273,x27274))
% 109.14/108.87 [2728]~E(x27281,x27282)+E(f434(x27283,x27281,x27284),f434(x27283,x27282,x27284))
% 109.14/108.87 [2729]~E(x27291,x27292)+E(f434(x27293,x27294,x27291),f434(x27293,x27294,x27292))
% 109.14/108.87 [2730]~E(x27301,x27302)+E(f412(x27301,x27303,x27304),f412(x27302,x27303,x27304))
% 109.14/108.87 [2731]~E(x27311,x27312)+E(f412(x27313,x27311,x27314),f412(x27313,x27312,x27314))
% 109.14/108.87 [2732]~E(x27321,x27322)+E(f412(x27323,x27324,x27321),f412(x27323,x27324,x27322))
% 109.14/108.87 [2733]~E(x27331,x27332)+E(f756(x27331,x27333,x27334),f756(x27332,x27333,x27334))
% 109.14/108.87 [2734]~E(x27341,x27342)+E(f756(x27343,x27341,x27344),f756(x27343,x27342,x27344))
% 109.14/108.87 [2735]~E(x27351,x27352)+E(f756(x27353,x27354,x27351),f756(x27353,x27354,x27352))
% 109.14/108.87 [2736]~E(x27361,x27362)+E(f853(x27361,x27363,x27364),f853(x27362,x27363,x27364))
% 109.14/108.87 [2737]~E(x27371,x27372)+E(f853(x27373,x27371,x27374),f853(x27373,x27372,x27374))
% 109.14/108.87 [2738]~E(x27381,x27382)+E(f853(x27383,x27384,x27381),f853(x27383,x27384,x27382))
% 109.14/108.87 [2739]~E(x27391,x27392)+E(f632(x27391,x27393,x27394,x27395,x27396),f632(x27392,x27393,x27394,x27395,x27396))
% 109.14/108.87 [2740]~E(x27401,x27402)+E(f632(x27403,x27401,x27404,x27405,x27406),f632(x27403,x27402,x27404,x27405,x27406))
% 109.14/108.87 [2741]~E(x27411,x27412)+E(f632(x27413,x27414,x27411,x27415,x27416),f632(x27413,x27414,x27412,x27415,x27416))
% 109.14/108.87 [2742]~E(x27421,x27422)+E(f632(x27423,x27424,x27425,x27421,x27426),f632(x27423,x27424,x27425,x27422,x27426))
% 109.14/108.87 [2743]~E(x27431,x27432)+E(f632(x27433,x27434,x27435,x27436,x27431),f632(x27433,x27434,x27435,x27436,x27432))
% 109.14/108.87 [2744]~E(x27441,x27442)+E(f359(x27441,x27443),f359(x27442,x27443))
% 109.14/108.87 [2745]~E(x27451,x27452)+E(f359(x27453,x27451),f359(x27453,x27452))
% 109.14/108.87 [2746]~E(x27461,x27462)+E(f256(x27461,x27463,x27464),f256(x27462,x27463,x27464))
% 109.14/108.87 [2747]~E(x27471,x27472)+E(f256(x27473,x27471,x27474),f256(x27473,x27472,x27474))
% 109.14/108.87 [2748]~E(x27481,x27482)+E(f256(x27483,x27484,x27481),f256(x27483,x27484,x27482))
% 109.14/108.87 [2749]~E(x27491,x27492)+E(f251(x27491,x27493,x27494,x27495,x27496),f251(x27492,x27493,x27494,x27495,x27496))
% 109.14/108.87 [2750]~E(x27501,x27502)+E(f251(x27503,x27501,x27504,x27505,x27506),f251(x27503,x27502,x27504,x27505,x27506))
% 109.14/108.87 [2751]~E(x27511,x27512)+E(f251(x27513,x27514,x27511,x27515,x27516),f251(x27513,x27514,x27512,x27515,x27516))
% 109.14/108.87 [2752]~E(x27521,x27522)+E(f251(x27523,x27524,x27525,x27521,x27526),f251(x27523,x27524,x27525,x27522,x27526))
% 109.14/108.87 [2753]~E(x27531,x27532)+E(f251(x27533,x27534,x27535,x27536,x27531),f251(x27533,x27534,x27535,x27536,x27532))
% 109.14/108.87 [2754]~E(x27541,x27542)+E(f536(x27541,x27543,x27544,x27545,x27546),f536(x27542,x27543,x27544,x27545,x27546))
% 109.14/108.87 [2755]~E(x27551,x27552)+E(f536(x27553,x27551,x27554,x27555,x27556),f536(x27553,x27552,x27554,x27555,x27556))
% 109.14/108.87 [2756]~E(x27561,x27562)+E(f536(x27563,x27564,x27561,x27565,x27566),f536(x27563,x27564,x27562,x27565,x27566))
% 109.14/108.87 [2757]~E(x27571,x27572)+E(f536(x27573,x27574,x27575,x27571,x27576),f536(x27573,x27574,x27575,x27572,x27576))
% 109.14/108.87 [2758]~E(x27581,x27582)+E(f536(x27583,x27584,x27585,x27586,x27581),f536(x27583,x27584,x27585,x27586,x27582))
% 109.14/108.87 [2759]~E(x27591,x27592)+E(f633(x27591,x27593,x27594),f633(x27592,x27593,x27594))
% 109.14/108.87 [2760]~E(x27601,x27602)+E(f633(x27603,x27601,x27604),f633(x27603,x27602,x27604))
% 109.14/108.87 [2761]~E(x27611,x27612)+E(f633(x27613,x27614,x27611),f633(x27613,x27614,x27612))
% 109.14/108.87 [2762]~E(x27621,x27622)+E(f23(x27621,x27623),f23(x27622,x27623))
% 109.14/108.87 [2763]~E(x27631,x27632)+E(f23(x27633,x27631),f23(x27633,x27632))
% 109.14/108.87 [2764]~E(x27641,x27642)+E(f822(x27641,x27643,x27644,x27645,x27646,x27647),f822(x27642,x27643,x27644,x27645,x27646,x27647))
% 109.14/108.87 [2765]~E(x27651,x27652)+E(f822(x27653,x27651,x27654,x27655,x27656,x27657),f822(x27653,x27652,x27654,x27655,x27656,x27657))
% 109.14/108.87 [2766]~E(x27661,x27662)+E(f822(x27663,x27664,x27661,x27665,x27666,x27667),f822(x27663,x27664,x27662,x27665,x27666,x27667))
% 109.14/108.87 [2767]~E(x27671,x27672)+E(f822(x27673,x27674,x27675,x27671,x27676,x27677),f822(x27673,x27674,x27675,x27672,x27676,x27677))
% 109.14/108.87 [2768]~E(x27681,x27682)+E(f822(x27683,x27684,x27685,x27686,x27681,x27687),f822(x27683,x27684,x27685,x27686,x27682,x27687))
% 109.14/108.87 [2769]~E(x27691,x27692)+E(f822(x27693,x27694,x27695,x27696,x27697,x27691),f822(x27693,x27694,x27695,x27696,x27697,x27692))
% 109.14/108.87 [2770]~E(x27701,x27702)+E(f496(x27701,x27703,x27704),f496(x27702,x27703,x27704))
% 109.14/108.87 [2771]~E(x27711,x27712)+E(f496(x27713,x27711,x27714),f496(x27713,x27712,x27714))
% 109.14/108.87 [2772]~E(x27721,x27722)+E(f496(x27723,x27724,x27721),f496(x27723,x27724,x27722))
% 109.14/108.87 [2773]~E(x27731,x27732)+E(f760(x27731,x27733,x27734),f760(x27732,x27733,x27734))
% 109.14/108.87 [2774]~E(x27741,x27742)+E(f760(x27743,x27741,x27744),f760(x27743,x27742,x27744))
% 109.14/108.87 [2775]~E(x27751,x27752)+E(f760(x27753,x27754,x27751),f760(x27753,x27754,x27752))
% 109.14/108.87 [2776]~E(x27761,x27762)+E(f522(x27761),f522(x27762))
% 109.14/108.87 [2777]~E(x27771,x27772)+E(f643(x27771,x27773),f643(x27772,x27773))
% 109.14/108.87 [2778]~E(x27781,x27782)+E(f643(x27783,x27781),f643(x27783,x27782))
% 109.14/108.87 [2779]~E(x27791,x27792)+E(f197(x27791,x27793,x27794,x27795),f197(x27792,x27793,x27794,x27795))
% 109.14/108.87 [2780]~E(x27801,x27802)+E(f197(x27803,x27801,x27804,x27805),f197(x27803,x27802,x27804,x27805))
% 109.14/108.87 [2781]~E(x27811,x27812)+E(f197(x27813,x27814,x27811,x27815),f197(x27813,x27814,x27812,x27815))
% 109.14/108.87 [2782]~E(x27821,x27822)+E(f197(x27823,x27824,x27825,x27821),f197(x27823,x27824,x27825,x27822))
% 109.14/108.87 [2783]~E(x27831,x27832)+E(f215(x27831,x27833,x27834,x27835,x27836),f215(x27832,x27833,x27834,x27835,x27836))
% 109.14/108.87 [2784]~E(x27841,x27842)+E(f215(x27843,x27841,x27844,x27845,x27846),f215(x27843,x27842,x27844,x27845,x27846))
% 109.14/108.87 [2785]~E(x27851,x27852)+E(f215(x27853,x27854,x27851,x27855,x27856),f215(x27853,x27854,x27852,x27855,x27856))
% 109.14/108.87 [2786]~E(x27861,x27862)+E(f215(x27863,x27864,x27865,x27861,x27866),f215(x27863,x27864,x27865,x27862,x27866))
% 109.14/108.87 [2787]~E(x27871,x27872)+E(f215(x27873,x27874,x27875,x27876,x27871),f215(x27873,x27874,x27875,x27876,x27872))
% 109.14/108.87 [2788]~E(x27881,x27882)+E(f687(x27881,x27883,x27884),f687(x27882,x27883,x27884))
% 109.14/108.87 [2789]~E(x27891,x27892)+E(f687(x27893,x27891,x27894),f687(x27893,x27892,x27894))
% 109.14/108.87 [2790]~E(x27901,x27902)+E(f687(x27903,x27904,x27901),f687(x27903,x27904,x27902))
% 109.14/108.87 [2791]~E(x27911,x27912)+E(f667(x27911,x27913),f667(x27912,x27913))
% 109.14/108.87 [2792]~E(x27921,x27922)+E(f667(x27923,x27921),f667(x27923,x27922))
% 109.14/108.87 [2793]~E(x27931,x27932)+E(f220(x27931,x27933,x27934,x27935),f220(x27932,x27933,x27934,x27935))
% 109.14/108.87 [2794]~E(x27941,x27942)+E(f220(x27943,x27941,x27944,x27945),f220(x27943,x27942,x27944,x27945))
% 109.14/108.87 [2795]~E(x27951,x27952)+E(f220(x27953,x27954,x27951,x27955),f220(x27953,x27954,x27952,x27955))
% 109.14/108.87 [2796]~E(x27961,x27962)+E(f220(x27963,x27964,x27965,x27961),f220(x27963,x27964,x27965,x27962))
% 109.14/108.87 [2797]~E(x27971,x27972)+E(f367(x27971),f367(x27972))
% 109.14/108.87 [2798]~E(x27981,x27982)+E(f323(x27981),f323(x27982))
% 109.14/108.87 [2799]~E(x27991,x27992)+E(f818(x27991,x27993),f818(x27992,x27993))
% 109.14/108.87 [2800]~E(x28001,x28002)+E(f818(x28003,x28001),f818(x28003,x28002))
% 109.14/108.87 [2801]~E(x28011,x28012)+E(f564(x28011,x28013,x28014,x28015),f564(x28012,x28013,x28014,x28015))
% 109.14/108.87 [2802]~E(x28021,x28022)+E(f564(x28023,x28021,x28024,x28025),f564(x28023,x28022,x28024,x28025))
% 109.14/108.87 [2803]~E(x28031,x28032)+E(f564(x28033,x28034,x28031,x28035),f564(x28033,x28034,x28032,x28035))
% 109.14/108.87 [2804]~E(x28041,x28042)+E(f564(x28043,x28044,x28045,x28041),f564(x28043,x28044,x28045,x28042))
% 109.14/108.87 [2805]~E(x28051,x28052)+E(f202(x28051,x28053,x28054,x28055,x28056,x28057,x28058),f202(x28052,x28053,x28054,x28055,x28056,x28057,x28058))
% 109.14/108.87 [2806]~E(x28061,x28062)+E(f202(x28063,x28061,x28064,x28065,x28066,x28067,x28068),f202(x28063,x28062,x28064,x28065,x28066,x28067,x28068))
% 109.14/108.87 [2807]~E(x28071,x28072)+E(f202(x28073,x28074,x28071,x28075,x28076,x28077,x28078),f202(x28073,x28074,x28072,x28075,x28076,x28077,x28078))
% 109.14/108.87 [2808]~E(x28081,x28082)+E(f202(x28083,x28084,x28085,x28081,x28086,x28087,x28088),f202(x28083,x28084,x28085,x28082,x28086,x28087,x28088))
% 109.14/108.87 [2809]~E(x28091,x28092)+E(f202(x28093,x28094,x28095,x28096,x28091,x28097,x28098),f202(x28093,x28094,x28095,x28096,x28092,x28097,x28098))
% 109.14/108.87 [2810]~E(x28101,x28102)+E(f202(x28103,x28104,x28105,x28106,x28107,x28101,x28108),f202(x28103,x28104,x28105,x28106,x28107,x28102,x28108))
% 109.14/108.87 [2811]~E(x28111,x28112)+E(f202(x28113,x28114,x28115,x28116,x28117,x28118,x28111),f202(x28113,x28114,x28115,x28116,x28117,x28118,x28112))
% 109.14/108.87 [2812]~E(x28121,x28122)+E(f357(x28121),f357(x28122))
% 109.14/108.87 [2813]~E(x28131,x28132)+E(f216(x28131,x28133,x28134,x28135,x28136),f216(x28132,x28133,x28134,x28135,x28136))
% 109.14/108.87 [2814]~E(x28141,x28142)+E(f216(x28143,x28141,x28144,x28145,x28146),f216(x28143,x28142,x28144,x28145,x28146))
% 109.14/108.87 [2815]~E(x28151,x28152)+E(f216(x28153,x28154,x28151,x28155,x28156),f216(x28153,x28154,x28152,x28155,x28156))
% 109.14/108.87 [2816]~E(x28161,x28162)+E(f216(x28163,x28164,x28165,x28161,x28166),f216(x28163,x28164,x28165,x28162,x28166))
% 109.14/108.87 [2817]~E(x28171,x28172)+E(f216(x28173,x28174,x28175,x28176,x28171),f216(x28173,x28174,x28175,x28176,x28172))
% 109.14/108.87 [2818]~E(x28181,x28182)+E(f890(x28181,x28183,x28184),f890(x28182,x28183,x28184))
% 109.14/108.87 [2819]~E(x28191,x28192)+E(f890(x28193,x28191,x28194),f890(x28193,x28192,x28194))
% 109.14/108.87 [2820]~E(x28201,x28202)+E(f890(x28203,x28204,x28201),f890(x28203,x28204,x28202))
% 109.14/108.87 [2821]~P1(x28211)+P1(x28212)+~E(x28211,x28212)
% 109.14/108.87 [2822]~P2(x28221)+P2(x28222)+~E(x28221,x28222)
% 109.14/108.87 [2823]~P65(x28231)+P65(x28232)+~E(x28231,x28232)
% 109.14/108.87 [2824]~P107(x28241)+P107(x28242)+~E(x28241,x28242)
% 109.14/108.87 [2825]~P80(x28251)+P80(x28252)+~E(x28251,x28252)
% 109.14/108.87 [2826]~P3(x28261)+P3(x28262)+~E(x28261,x28262)
% 109.14/108.87 [2827]~P119(x28271)+P119(x28272)+~E(x28271,x28272)
% 109.14/108.87 [2828]P7(x28282,x28283)+~E(x28281,x28282)+~P7(x28281,x28283)
% 109.14/108.87 [2829]P7(x28293,x28292)+~E(x28291,x28292)+~P7(x28293,x28291)
% 109.14/108.87 [2830]~P130(x28301)+P130(x28302)+~E(x28301,x28302)
% 109.14/108.87 [2831]~P4(x28311)+P4(x28312)+~E(x28311,x28312)
% 109.14/108.87 [2832]~P103(x28321)+P103(x28322)+~E(x28321,x28322)
% 109.14/108.87 [2833]P28(x28332,x28333,x28334)+~E(x28331,x28332)+~P28(x28331,x28333,x28334)
% 109.14/108.87 [2834]P28(x28343,x28342,x28344)+~E(x28341,x28342)+~P28(x28343,x28341,x28344)
% 109.14/108.87 [2835]P28(x28353,x28354,x28352)+~E(x28351,x28352)+~P28(x28353,x28354,x28351)
% 109.14/108.87 [2836]~P113(x28361)+P113(x28362)+~E(x28361,x28362)
% 109.14/108.87 [2837]~P116(x28371)+P116(x28372)+~E(x28371,x28372)
% 109.14/108.87 [2838]~P99(x28381)+P99(x28382)+~E(x28381,x28382)
% 109.14/108.87 [2839]~P69(x28391)+P69(x28392)+~E(x28391,x28392)
% 109.14/108.87 [2840]~P5(x28401)+P5(x28402)+~E(x28401,x28402)
% 109.14/108.87 [2841]~P114(x28411)+P114(x28412)+~E(x28411,x28412)
% 109.14/108.87 [2842]P152(x28422,x28423,x28424)+~E(x28421,x28422)+~P152(x28421,x28423,x28424)
% 109.14/108.87 [2843]P152(x28433,x28432,x28434)+~E(x28431,x28432)+~P152(x28433,x28431,x28434)
% 109.14/108.87 [2844]P152(x28443,x28444,x28442)+~E(x28441,x28442)+~P152(x28443,x28444,x28441)
% 109.14/108.87 [2845]P62(x28452,x28453,x28454,x28455)+~E(x28451,x28452)+~P62(x28451,x28453,x28454,x28455)
% 109.14/108.87 [2846]P62(x28463,x28462,x28464,x28465)+~E(x28461,x28462)+~P62(x28463,x28461,x28464,x28465)
% 109.14/108.87 [2847]P62(x28473,x28474,x28472,x28475)+~E(x28471,x28472)+~P62(x28473,x28474,x28471,x28475)
% 109.14/108.87 [2848]P62(x28483,x28484,x28485,x28482)+~E(x28481,x28482)+~P62(x28483,x28484,x28485,x28481)
% 109.14/108.87 [2849]~P64(x28491)+P64(x28492)+~E(x28491,x28492)
% 109.14/108.87 [2850]P39(x28502,x28503)+~E(x28501,x28502)+~P39(x28501,x28503)
% 109.14/108.87 [2851]P39(x28513,x28512)+~E(x28511,x28512)+~P39(x28513,x28511)
% 109.14/108.87 [2852]~P89(x28521)+P89(x28522)+~E(x28521,x28522)
% 109.14/108.87 [2853]~P96(x28531)+P96(x28532)+~E(x28531,x28532)
% 109.14/108.87 [2854]~P66(x28541)+P66(x28542)+~E(x28541,x28542)
% 109.14/108.87 [2855]~P102(x28551)+P102(x28552)+~E(x28551,x28552)
% 109.14/108.87 [2856]~P74(x28561)+P74(x28562)+~E(x28561,x28562)
% 109.14/108.87 [2857]~P108(x28571)+P108(x28572)+~E(x28571,x28572)
% 109.14/108.87 [2858]P14(x28582,x28583,x28584)+~E(x28581,x28582)+~P14(x28581,x28583,x28584)
% 109.14/108.87 [2859]P14(x28593,x28592,x28594)+~E(x28591,x28592)+~P14(x28593,x28591,x28594)
% 109.14/108.87 [2860]P14(x28603,x28604,x28602)+~E(x28601,x28602)+~P14(x28603,x28604,x28601)
% 109.14/108.87 [2861]~P90(x28611)+P90(x28612)+~E(x28611,x28612)
% 109.14/108.87 [2862]P58(x28622,x28623,x28624)+~E(x28621,x28622)+~P58(x28621,x28623,x28624)
% 109.14/108.87 [2863]P58(x28633,x28632,x28634)+~E(x28631,x28632)+~P58(x28633,x28631,x28634)
% 109.14/108.87 [2864]P58(x28643,x28644,x28642)+~E(x28641,x28642)+~P58(x28643,x28644,x28641)
% 109.14/108.87 [2865]~P104(x28651)+P104(x28652)+~E(x28651,x28652)
% 109.14/108.87 [2866]P26(x28662,x28663,x28664,x28665,x28666)+~E(x28661,x28662)+~P26(x28661,x28663,x28664,x28665,x28666)
% 109.14/108.87 [2867]P26(x28673,x28672,x28674,x28675,x28676)+~E(x28671,x28672)+~P26(x28673,x28671,x28674,x28675,x28676)
% 109.14/108.87 [2868]P26(x28683,x28684,x28682,x28685,x28686)+~E(x28681,x28682)+~P26(x28683,x28684,x28681,x28685,x28686)
% 109.14/108.87 [2869]P26(x28693,x28694,x28695,x28692,x28696)+~E(x28691,x28692)+~P26(x28693,x28694,x28695,x28691,x28696)
% 109.14/108.87 [2870]P26(x28703,x28704,x28705,x28706,x28702)+~E(x28701,x28702)+~P26(x28703,x28704,x28705,x28706,x28701)
% 109.14/108.87 [2871]P25(x28712,x28713,x28714,x28715)+~E(x28711,x28712)+~P25(x28711,x28713,x28714,x28715)
% 109.14/108.87 [2872]P25(x28723,x28722,x28724,x28725)+~E(x28721,x28722)+~P25(x28723,x28721,x28724,x28725)
% 109.14/108.87 [2873]P25(x28733,x28734,x28732,x28735)+~E(x28731,x28732)+~P25(x28733,x28734,x28731,x28735)
% 109.14/108.87 [2874]P25(x28743,x28744,x28745,x28742)+~E(x28741,x28742)+~P25(x28743,x28744,x28745,x28741)
% 109.14/108.87 [2875]P52(x28752,x28753,x28754)+~E(x28751,x28752)+~P52(x28751,x28753,x28754)
% 109.14/108.87 [2876]P52(x28763,x28762,x28764)+~E(x28761,x28762)+~P52(x28763,x28761,x28764)
% 109.14/108.87 [2877]P52(x28773,x28774,x28772)+~E(x28771,x28772)+~P52(x28773,x28774,x28771)
% 109.14/108.87 [2878]~P115(x28781)+P115(x28782)+~E(x28781,x28782)
% 109.14/108.87 [2879]P61(x28792,x28793)+~E(x28791,x28792)+~P61(x28791,x28793)
% 109.14/108.87 [2880]P61(x28803,x28802)+~E(x28801,x28802)+~P61(x28803,x28801)
% 109.14/108.87 [2881]P63(x28812,x28813)+~E(x28811,x28812)+~P63(x28811,x28813)
% 109.14/108.87 [2882]P63(x28823,x28822)+~E(x28821,x28822)+~P63(x28823,x28821)
% 109.14/108.87 [2883]P40(x28832,x28833)+~E(x28831,x28832)+~P40(x28831,x28833)
% 109.14/108.87 [2884]P40(x28843,x28842)+~E(x28841,x28842)+~P40(x28843,x28841)
% 109.14/108.87 [2885]~P109(x28851)+P109(x28852)+~E(x28851,x28852)
% 109.14/108.87 [2886]~P141(x28861)+P141(x28862)+~E(x28861,x28862)
% 109.14/108.87 [2887]~P97(x28871)+P97(x28872)+~E(x28871,x28872)
% 109.14/108.87 [2888]P151(x28882,x28883,x28884)+~E(x28881,x28882)+~P151(x28881,x28883,x28884)
% 109.14/108.87 [2889]P151(x28893,x28892,x28894)+~E(x28891,x28892)+~P151(x28893,x28891,x28894)
% 109.14/108.87 [2890]P151(x28903,x28904,x28902)+~E(x28901,x28902)+~P151(x28903,x28904,x28901)
% 109.14/108.87 [2891]P42(x28912,x28913,x28914)+~E(x28911,x28912)+~P42(x28911,x28913,x28914)
% 109.14/108.87 [2892]P42(x28923,x28922,x28924)+~E(x28921,x28922)+~P42(x28923,x28921,x28924)
% 109.14/108.87 [2893]P42(x28933,x28934,x28932)+~E(x28931,x28932)+~P42(x28933,x28934,x28931)
% 109.14/108.87 [2894]~P83(x28941)+P83(x28942)+~E(x28941,x28942)
% 109.14/108.87 [2895]~P105(x28951)+P105(x28952)+~E(x28951,x28952)
% 109.14/108.87 [2896]~P84(x28961)+P84(x28962)+~E(x28961,x28962)
% 109.14/108.87 [2897]P59(x28972,x28973,x28974)+~E(x28971,x28972)+~P59(x28971,x28973,x28974)
% 109.14/108.87 [2898]P59(x28983,x28982,x28984)+~E(x28981,x28982)+~P59(x28983,x28981,x28984)
% 109.14/108.87 [2899]P59(x28993,x28994,x28992)+~E(x28991,x28992)+~P59(x28993,x28994,x28991)
% 109.14/108.87 [2900]P36(x29002,x29003,x29004,x29005,x29006)+~E(x29001,x29002)+~P36(x29001,x29003,x29004,x29005,x29006)
% 109.14/108.87 [2901]P36(x29013,x29012,x29014,x29015,x29016)+~E(x29011,x29012)+~P36(x29013,x29011,x29014,x29015,x29016)
% 109.14/108.87 [2902]P36(x29023,x29024,x29022,x29025,x29026)+~E(x29021,x29022)+~P36(x29023,x29024,x29021,x29025,x29026)
% 109.14/108.87 [2903]P36(x29033,x29034,x29035,x29032,x29036)+~E(x29031,x29032)+~P36(x29033,x29034,x29035,x29031,x29036)
% 109.14/108.87 [2904]P36(x29043,x29044,x29045,x29046,x29042)+~E(x29041,x29042)+~P36(x29043,x29044,x29045,x29046,x29041)
% 109.14/108.87 [2905]P13(x29052,x29053)+~E(x29051,x29052)+~P13(x29051,x29053)
% 109.14/108.87 [2906]P13(x29063,x29062)+~E(x29061,x29062)+~P13(x29063,x29061)
% 109.14/108.87 [2907]~P67(x29071)+P67(x29072)+~E(x29071,x29072)
% 109.14/108.87 [2908]~P77(x29081)+P77(x29082)+~E(x29081,x29082)
% 109.14/108.87 [2909]~P76(x29091)+P76(x29092)+~E(x29091,x29092)
% 109.14/108.87 [2910]~P73(x29101)+P73(x29102)+~E(x29101,x29102)
% 109.14/108.87 [2911]~P93(x29111)+P93(x29112)+~E(x29111,x29112)
% 109.14/108.87 [2912]~P129(x29121)+P129(x29122)+~E(x29121,x29122)
% 109.14/108.87 [2913]~P118(x29131)+P118(x29132)+~E(x29131,x29132)
% 109.14/108.87 [2914]~P121(x29141)+P121(x29142)+~E(x29141,x29142)
% 109.14/108.87 [2915]~P82(x29151)+P82(x29152)+~E(x29151,x29152)
% 109.14/108.87 [2916]~P78(x29161)+P78(x29162)+~E(x29161,x29162)
% 109.14/108.87 [2917]P56(x29172,x29173,x29174)+~E(x29171,x29172)+~P56(x29171,x29173,x29174)
% 109.14/108.87 [2918]P56(x29183,x29182,x29184)+~E(x29181,x29182)+~P56(x29183,x29181,x29184)
% 109.14/108.87 [2919]P56(x29193,x29194,x29192)+~E(x29191,x29192)+~P56(x29193,x29194,x29191)
% 109.14/108.87 [2920]P30(x29202,x29203)+~E(x29201,x29202)+~P30(x29201,x29203)
% 109.14/108.87 [2921]P30(x29213,x29212)+~E(x29211,x29212)+~P30(x29213,x29211)
% 109.14/108.87 [2922]~P79(x29221)+P79(x29222)+~E(x29221,x29222)
% 109.14/108.87 [2923]~P94(x29231)+P94(x29232)+~E(x29231,x29232)
% 109.14/108.87 [2924]~P140(x29241)+P140(x29242)+~E(x29241,x29242)
% 109.14/108.87 [2925]~P131(x29251)+P131(x29252)+~E(x29251,x29252)
% 109.14/108.87 [2926]P8(x29262,x29263,x29264)+~E(x29261,x29262)+~P8(x29261,x29263,x29264)
% 109.14/108.87 [2927]P8(x29273,x29272,x29274)+~E(x29271,x29272)+~P8(x29273,x29271,x29274)
% 109.14/108.87 [2928]P8(x29283,x29284,x29282)+~E(x29281,x29282)+~P8(x29283,x29284,x29281)
% 109.14/108.87 [2929]P11(x29292,x29293,x29294,x29295)+~E(x29291,x29292)+~P11(x29291,x29293,x29294,x29295)
% 109.14/108.87 [2930]P11(x29303,x29302,x29304,x29305)+~E(x29301,x29302)+~P11(x29303,x29301,x29304,x29305)
% 109.14/108.87 [2931]P11(x29313,x29314,x29312,x29315)+~E(x29311,x29312)+~P11(x29313,x29314,x29311,x29315)
% 109.14/108.87 [2932]P11(x29323,x29324,x29325,x29322)+~E(x29321,x29322)+~P11(x29323,x29324,x29325,x29321)
% 109.14/108.87 [2933]P17(x29332,x29333,x29334)+~E(x29331,x29332)+~P17(x29331,x29333,x29334)
% 109.14/108.87 [2934]P17(x29343,x29342,x29344)+~E(x29341,x29342)+~P17(x29343,x29341,x29344)
% 109.14/108.87 [2935]P17(x29353,x29354,x29352)+~E(x29351,x29352)+~P17(x29353,x29354,x29351)
% 109.14/108.87 [2936]~P71(x29361)+P71(x29362)+~E(x29361,x29362)
% 109.14/108.87 [2937]~P88(x29371)+P88(x29372)+~E(x29371,x29372)
% 109.14/108.87 [2938]~P86(x29381)+P86(x29382)+~E(x29381,x29382)
% 109.14/108.87 [2939]~P100(x29391)+P100(x29392)+~E(x29391,x29392)
% 109.14/108.87 [2940]P21(x29402,x29403,x29404,x29405,x29406)+~E(x29401,x29402)+~P21(x29401,x29403,x29404,x29405,x29406)
% 109.14/108.87 [2941]P21(x29413,x29412,x29414,x29415,x29416)+~E(x29411,x29412)+~P21(x29413,x29411,x29414,x29415,x29416)
% 109.14/108.87 [2942]P21(x29423,x29424,x29422,x29425,x29426)+~E(x29421,x29422)+~P21(x29423,x29424,x29421,x29425,x29426)
% 109.14/108.87 [2943]P21(x29433,x29434,x29435,x29432,x29436)+~E(x29431,x29432)+~P21(x29433,x29434,x29435,x29431,x29436)
% 109.14/108.87 [2944]P21(x29443,x29444,x29445,x29446,x29442)+~E(x29441,x29442)+~P21(x29443,x29444,x29445,x29446,x29441)
% 109.14/108.87 [2945]~P92(x29451)+P92(x29452)+~E(x29451,x29452)
% 109.14/108.87 [2946]~P127(x29461)+P127(x29462)+~E(x29461,x29462)
% 109.14/108.87 [2947]~P75(x29471)+P75(x29472)+~E(x29471,x29472)
% 109.14/108.87 [2948]P33(x29482,x29483,x29484)+~E(x29481,x29482)+~P33(x29481,x29483,x29484)
% 109.14/108.87 [2949]P33(x29493,x29492,x29494)+~E(x29491,x29492)+~P33(x29493,x29491,x29494)
% 109.14/108.87 [2950]P33(x29503,x29504,x29502)+~E(x29501,x29502)+~P33(x29503,x29504,x29501)
% 109.14/108.87 [2951]P24(x29512,x29513,x29514)+~E(x29511,x29512)+~P24(x29511,x29513,x29514)
% 109.14/108.87 [2952]P24(x29523,x29522,x29524)+~E(x29521,x29522)+~P24(x29523,x29521,x29524)
% 109.14/108.87 [2953]P24(x29533,x29534,x29532)+~E(x29531,x29532)+~P24(x29533,x29534,x29531)
% 109.14/108.87 [2954]~P43(x29541)+P43(x29542)+~E(x29541,x29542)
% 109.14/108.87 [2955]P16(x29552,x29553,x29554)+~E(x29551,x29552)+~P16(x29551,x29553,x29554)
% 109.14/108.87 [2956]P16(x29563,x29562,x29564)+~E(x29561,x29562)+~P16(x29563,x29561,x29564)
% 109.14/108.87 [2957]P16(x29573,x29574,x29572)+~E(x29571,x29572)+~P16(x29573,x29574,x29571)
% 109.14/108.87 [2958]~P143(x29581)+P143(x29582)+~E(x29581,x29582)
% 109.14/108.87 [2959]~P91(x29591)+P91(x29592)+~E(x29591,x29592)
% 109.14/108.87 [2960]~P68(x29601)+P68(x29602)+~E(x29601,x29602)
% 109.14/108.87 [2961]~P72(x29611)+P72(x29612)+~E(x29611,x29612)
% 109.14/108.87 [2962]~P117(x29621)+P117(x29622)+~E(x29621,x29622)
% 109.14/108.87 [2963]P41(x29632,x29633)+~E(x29631,x29632)+~P41(x29631,x29633)
% 109.14/108.87 [2964]P41(x29643,x29642)+~E(x29641,x29642)+~P41(x29643,x29641)
% 109.14/108.87 [2965]P32(x29652,x29653,x29654)+~E(x29651,x29652)+~P32(x29651,x29653,x29654)
% 109.14/108.87 [2966]P32(x29663,x29662,x29664)+~E(x29661,x29662)+~P32(x29663,x29661,x29664)
% 109.14/108.87 [2967]P32(x29673,x29674,x29672)+~E(x29671,x29672)+~P32(x29673,x29674,x29671)
% 109.14/108.87 [2968]P23(x29682,x29683,x29684,x29685,x29686,x29687)+~E(x29681,x29682)+~P23(x29681,x29683,x29684,x29685,x29686,x29687)
% 109.14/108.87 [2969]P23(x29693,x29692,x29694,x29695,x29696,x29697)+~E(x29691,x29692)+~P23(x29693,x29691,x29694,x29695,x29696,x29697)
% 109.14/108.87 [2970]P23(x29703,x29704,x29702,x29705,x29706,x29707)+~E(x29701,x29702)+~P23(x29703,x29704,x29701,x29705,x29706,x29707)
% 109.14/108.87 [2971]P23(x29713,x29714,x29715,x29712,x29716,x29717)+~E(x29711,x29712)+~P23(x29713,x29714,x29715,x29711,x29716,x29717)
% 109.14/108.87 [2972]P23(x29723,x29724,x29725,x29726,x29722,x29727)+~E(x29721,x29722)+~P23(x29723,x29724,x29725,x29726,x29721,x29727)
% 109.14/108.87 [2973]P23(x29733,x29734,x29735,x29736,x29737,x29732)+~E(x29731,x29732)+~P23(x29733,x29734,x29735,x29736,x29737,x29731)
% 109.14/108.87 [2974]~P149(x29741)+P149(x29742)+~E(x29741,x29742)
% 109.14/108.87 [2975]~P125(x29751)+P125(x29752)+~E(x29751,x29752)
% 109.14/108.87 [2976]~P87(x29761)+P87(x29762)+~E(x29761,x29762)
% 109.14/108.87 [2977]P27(x29772,x29773)+~E(x29771,x29772)+~P27(x29771,x29773)
% 109.14/108.87 [2978]P27(x29783,x29782)+~E(x29781,x29782)+~P27(x29783,x29781)
% 109.14/108.87 [2979]~P123(x29791)+P123(x29792)+~E(x29791,x29792)
% 109.14/108.87 [2980]~P150(x29801)+P150(x29802)+~E(x29801,x29802)
% 109.14/108.87 [2981]P55(x29812,x29813)+~E(x29811,x29812)+~P55(x29811,x29813)
% 109.14/108.87 [2982]P55(x29823,x29822)+~E(x29821,x29822)+~P55(x29823,x29821)
% 109.14/108.87 [2983]~P134(x29831)+P134(x29832)+~E(x29831,x29832)
% 109.14/108.87 [2984]~P144(x29841)+P144(x29842)+~E(x29841,x29842)
% 109.14/108.87 [2985]~P98(x29851)+P98(x29852)+~E(x29851,x29852)
% 109.14/108.87 [2986]~P138(x29861)+P138(x29862)+~E(x29861,x29862)
% 109.14/108.87 [2987]~P124(x29871)+P124(x29872)+~E(x29871,x29872)
% 109.14/108.87 [2988]~P6(x29881)+P6(x29882)+~E(x29881,x29882)
% 109.14/108.87 [2989]P19(x29892,x29893,x29894,x29895)+~E(x29891,x29892)+~P19(x29891,x29893,x29894,x29895)
% 109.14/108.87 [2990]P19(x29903,x29902,x29904,x29905)+~E(x29901,x29902)+~P19(x29903,x29901,x29904,x29905)
% 109.14/108.87 [2991]P19(x29913,x29914,x29912,x29915)+~E(x29911,x29912)+~P19(x29913,x29914,x29911,x29915)
% 109.14/108.87 [2992]P19(x29923,x29924,x29925,x29922)+~E(x29921,x29922)+~P19(x29923,x29924,x29925,x29921)
% 109.14/108.87 [2993]P37(x29932,x29933,x29934)+~E(x29931,x29932)+~P37(x29931,x29933,x29934)
% 109.14/108.87 [2994]P37(x29943,x29942,x29944)+~E(x29941,x29942)+~P37(x29943,x29941,x29944)
% 109.14/108.87 [2995]P37(x29953,x29954,x29952)+~E(x29951,x29952)+~P37(x29953,x29954,x29951)
% 109.14/108.87 [2996]~P145(x29961)+P145(x29962)+~E(x29961,x29962)
% 109.14/108.87 [2997]P35(x29972,x29973,x29974)+~E(x29971,x29972)+~P35(x29971,x29973,x29974)
% 109.14/108.87 [2998]P35(x29983,x29982,x29984)+~E(x29981,x29982)+~P35(x29983,x29981,x29984)
% 109.14/108.87 [2999]P35(x29993,x29994,x29992)+~E(x29991,x29992)+~P35(x29993,x29994,x29991)
% 109.14/108.87 [3000]~P139(x30001)+P139(x30002)+~E(x30001,x30002)
% 109.14/108.87 [3001]P49(x30012,x30013,x30014)+~E(x30011,x30012)+~P49(x30011,x30013,x30014)
% 109.14/108.87 [3002]P49(x30023,x30022,x30024)+~E(x30021,x30022)+~P49(x30023,x30021,x30024)
% 109.14/108.87 [3003]P49(x30033,x30034,x30032)+~E(x30031,x30032)+~P49(x30033,x30034,x30031)
% 109.14/108.87 [3004]P60(x30042,x30043,x30044,x30045,x30046)+~E(x30041,x30042)+~P60(x30041,x30043,x30044,x30045,x30046)
% 109.14/108.87 [3005]P60(x30053,x30052,x30054,x30055,x30056)+~E(x30051,x30052)+~P60(x30053,x30051,x30054,x30055,x30056)
% 109.14/108.87 [3006]P60(x30063,x30064,x30062,x30065,x30066)+~E(x30061,x30062)+~P60(x30063,x30064,x30061,x30065,x30066)
% 109.14/108.87 [3007]P60(x30073,x30074,x30075,x30072,x30076)+~E(x30071,x30072)+~P60(x30073,x30074,x30075,x30071,x30076)
% 109.14/108.87 [3008]P60(x30083,x30084,x30085,x30086,x30082)+~E(x30081,x30082)+~P60(x30083,x30084,x30085,x30086,x30081)
% 109.14/108.87 [3009]P45(x30092,x30093,x30094,x30095,x30096,x30097)+~E(x30091,x30092)+~P45(x30091,x30093,x30094,x30095,x30096,x30097)
% 109.14/108.87 [3010]P45(x30103,x30102,x30104,x30105,x30106,x30107)+~E(x30101,x30102)+~P45(x30103,x30101,x30104,x30105,x30106,x30107)
% 109.14/108.87 [3011]P45(x30113,x30114,x30112,x30115,x30116,x30117)+~E(x30111,x30112)+~P45(x30113,x30114,x30111,x30115,x30116,x30117)
% 109.14/108.87 [3012]P45(x30123,x30124,x30125,x30122,x30126,x30127)+~E(x30121,x30122)+~P45(x30123,x30124,x30125,x30121,x30126,x30127)
% 109.14/108.87 [3013]P45(x30133,x30134,x30135,x30136,x30132,x30137)+~E(x30131,x30132)+~P45(x30133,x30134,x30135,x30136,x30131,x30137)
% 109.14/108.87 [3014]P45(x30143,x30144,x30145,x30146,x30147,x30142)+~E(x30141,x30142)+~P45(x30143,x30144,x30145,x30146,x30147,x30141)
% 109.14/108.87 [3015]~P70(x30151)+P70(x30152)+~E(x30151,x30152)
% 109.14/108.87 [3016]~P133(x30161)+P133(x30162)+~E(x30161,x30162)
% 109.14/108.87 [3017]~P142(x30171)+P142(x30172)+~E(x30171,x30172)
% 109.14/108.87 [3018]P34(x30182,x30183,x30184,x30185)+~E(x30181,x30182)+~P34(x30181,x30183,x30184,x30185)
% 109.14/108.87 [3019]P34(x30193,x30192,x30194,x30195)+~E(x30191,x30192)+~P34(x30193,x30191,x30194,x30195)
% 109.14/108.87 [3020]P34(x30203,x30204,x30202,x30205)+~E(x30201,x30202)+~P34(x30203,x30204,x30201,x30205)
% 109.14/108.87 [3021]P34(x30213,x30214,x30215,x30212)+~E(x30211,x30212)+~P34(x30213,x30214,x30215,x30211)
% 109.14/108.87 [3022]P15(x30222,x30223)+~E(x30221,x30222)+~P15(x30221,x30223)
% 109.14/108.87 [3023]P15(x30233,x30232)+~E(x30231,x30232)+~P15(x30233,x30231)
% 109.14/108.87 [3024]~P95(x30241)+P95(x30242)+~E(x30241,x30242)
% 109.14/108.87 [3025]P53(x30252,x30253)+~E(x30251,x30252)+~P53(x30251,x30253)
% 109.14/108.87 [3026]P53(x30263,x30262)+~E(x30261,x30262)+~P53(x30263,x30261)
% 109.14/108.87 [3027]~P146(x30271)+P146(x30272)+~E(x30271,x30272)
% 109.14/108.87 [3028]P54(x30282,x30283)+~E(x30281,x30282)+~P54(x30281,x30283)
% 109.14/108.87 [3029]P54(x30293,x30292)+~E(x30291,x30292)+~P54(x30293,x30291)
% 109.14/108.87 [3030]~P101(x30301)+P101(x30302)+~E(x30301,x30302)
% 109.14/108.87 [3031]~P110(x30311)+P110(x30312)+~E(x30311,x30312)
% 109.14/108.87 [3032]~P147(x30321)+P147(x30322)+~E(x30321,x30322)
% 109.14/108.87 [3033]~P122(x30331)+P122(x30332)+~E(x30331,x30332)
% 109.14/108.87 [3034]P57(x30342,x30343)+~E(x30341,x30342)+~P57(x30341,x30343)
% 109.14/108.87 [3035]P57(x30353,x30352)+~E(x30351,x30352)+~P57(x30353,x30351)
% 109.14/108.87 [3036]~P111(x30361)+P111(x30362)+~E(x30361,x30362)
% 109.14/108.87 [3037]P29(x30372,x30373,x30374)+~E(x30371,x30372)+~P29(x30371,x30373,x30374)
% 109.14/108.87 [3038]P29(x30383,x30382,x30384)+~E(x30381,x30382)+~P29(x30383,x30381,x30384)
% 109.14/108.87 [3039]P29(x30393,x30394,x30392)+~E(x30391,x30392)+~P29(x30393,x30394,x30391)
% 109.14/108.87 [3040]~P38(x30401)+P38(x30402)+~E(x30401,x30402)
% 109.14/108.87 [3041]~P148(x30411)+P148(x30412)+~E(x30411,x30412)
% 109.14/108.87 [3042]~P47(x30421)+P47(x30422)+~E(x30421,x30422)
% 109.14/108.87 [3043]P48(x30432,x30433)+~E(x30431,x30432)+~P48(x30431,x30433)
% 109.14/108.87 [3044]P48(x30443,x30442)+~E(x30441,x30442)+~P48(x30443,x30441)
% 109.14/108.87 [3045]P50(x30452,x30453,x30454)+~E(x30451,x30452)+~P50(x30451,x30453,x30454)
% 109.14/108.87 [3046]P50(x30463,x30462,x30464)+~E(x30461,x30462)+~P50(x30463,x30461,x30464)
% 109.14/108.87 [3047]P50(x30473,x30474,x30472)+~E(x30471,x30472)+~P50(x30473,x30474,x30471)
% 109.14/108.87 [3048]P31(x30482,x30483,x30484)+~E(x30481,x30482)+~P31(x30481,x30483,x30484)
% 109.14/108.87 [3049]P31(x30493,x30492,x30494)+~E(x30491,x30492)+~P31(x30493,x30491,x30494)
% 109.14/108.87 [3050]P31(x30503,x30504,x30502)+~E(x30501,x30502)+~P31(x30503,x30504,x30501)
% 109.14/108.87 [3051]P46(x30512,x30513)+~E(x30511,x30512)+~P46(x30511,x30513)
% 109.14/108.87 [3052]P46(x30523,x30522)+~E(x30521,x30522)+~P46(x30523,x30521)
% 109.14/108.87 [3053]P12(x30532,x30533,x30534,x30535,x30536,x30537)+~E(x30531,x30532)+~P12(x30531,x30533,x30534,x30535,x30536,x30537)
% 109.14/108.87 [3054]P12(x30543,x30542,x30544,x30545,x30546,x30547)+~E(x30541,x30542)+~P12(x30543,x30541,x30544,x30545,x30546,x30547)
% 109.14/108.87 [3055]P12(x30553,x30554,x30552,x30555,x30556,x30557)+~E(x30551,x30552)+~P12(x30553,x30554,x30551,x30555,x30556,x30557)
% 109.14/108.87 [3056]P12(x30563,x30564,x30565,x30562,x30566,x30567)+~E(x30561,x30562)+~P12(x30563,x30564,x30565,x30561,x30566,x30567)
% 109.14/108.87 [3057]P12(x30573,x30574,x30575,x30576,x30572,x30577)+~E(x30571,x30572)+~P12(x30573,x30574,x30575,x30576,x30571,x30577)
% 109.14/108.87 [3058]P12(x30583,x30584,x30585,x30586,x30587,x30582)+~E(x30581,x30582)+~P12(x30583,x30584,x30585,x30586,x30587,x30581)
% 109.14/108.87 [3059]P51(x30592,x30593)+~E(x30591,x30592)+~P51(x30591,x30593)
% 109.14/108.87 [3060]P51(x30603,x30602)+~E(x30601,x30602)+~P51(x30603,x30601)
% 109.14/108.87 [3061]P18(x30612,x30613,x30614)+~E(x30611,x30612)+~P18(x30611,x30613,x30614)
% 109.14/108.87 [3062]P18(x30623,x30622,x30624)+~E(x30621,x30622)+~P18(x30623,x30621,x30624)
% 109.14/108.87 [3063]P18(x30633,x30634,x30632)+~E(x30631,x30632)+~P18(x30633,x30634,x30631)
% 109.14/108.87 [3064]P44(x30642,x30643,x30644,x30645)+~E(x30641,x30642)+~P44(x30641,x30643,x30644,x30645)
% 109.14/108.87 [3065]P44(x30653,x30652,x30654,x30655)+~E(x30651,x30652)+~P44(x30653,x30651,x30654,x30655)
% 109.14/108.87 [3066]P44(x30663,x30664,x30662,x30665)+~E(x30661,x30662)+~P44(x30663,x30664,x30661,x30665)
% 109.14/108.87 [3067]P44(x30673,x30674,x30675,x30672)+~E(x30671,x30672)+~P44(x30673,x30674,x30675,x30671)
% 109.14/108.87 [3068]P22(x30682,x30683,x30684,x30685,x30686,x30687)+~E(x30681,x30682)+~P22(x30681,x30683,x30684,x30685,x30686,x30687)
% 109.14/108.87 [3069]P22(x30693,x30692,x30694,x30695,x30696,x30697)+~E(x30691,x30692)+~P22(x30693,x30691,x30694,x30695,x30696,x30697)
% 109.14/108.87 [3070]P22(x30703,x30704,x30702,x30705,x30706,x30707)+~E(x30701,x30702)+~P22(x30703,x30704,x30701,x30705,x30706,x30707)
% 109.14/108.87 [3071]P22(x30713,x30714,x30715,x30712,x30716,x30717)+~E(x30711,x30712)+~P22(x30713,x30714,x30715,x30711,x30716,x30717)
% 109.14/108.87 [3072]P22(x30723,x30724,x30725,x30726,x30722,x30727)+~E(x30721,x30722)+~P22(x30723,x30724,x30725,x30726,x30721,x30727)
% 109.14/108.87 [3073]P22(x30733,x30734,x30735,x30736,x30737,x30732)+~E(x30731,x30732)+~P22(x30733,x30734,x30735,x30736,x30737,x30731)
% 109.14/108.87 [3074]~P81(x30741)+P81(x30742)+~E(x30741,x30742)
% 109.14/108.87 [3075]~P112(x30751)+P112(x30752)+~E(x30751,x30752)
% 109.14/108.87 [3076]~P120(x30761)+P120(x30762)+~E(x30761,x30762)
% 109.14/108.87 [3077]~P128(x30771)+P128(x30772)+~E(x30771,x30772)
% 109.14/108.87 [3078]~P126(x30781)+P126(x30782)+~E(x30781,x30782)
% 109.14/108.87 [3079]P20(x30792,x30793,x30794,x30795)+~E(x30791,x30792)+~P20(x30791,x30793,x30794,x30795)
% 109.14/108.87 [3080]P20(x30803,x30802,x30804,x30805)+~E(x30801,x30802)+~P20(x30803,x30801,x30804,x30805)
% 109.14/108.87 [3081]P20(x30813,x30814,x30812,x30815)+~E(x30811,x30812)+~P20(x30813,x30814,x30811,x30815)
% 109.14/108.87 [3082]P20(x30823,x30824,x30825,x30822)+~E(x30821,x30822)+~P20(x30823,x30824,x30825,x30821)
% 109.14/108.87 [3083]~P137(x30831)+P137(x30832)+~E(x30831,x30832)
% 109.14/108.87 [3084]~P106(x30841)+P106(x30842)+~E(x30841,x30842)
% 109.14/108.87 [3085]~P135(x30851)+P135(x30852)+~E(x30851,x30852)
% 109.14/108.87 [3086]P10(x30862,x30863,x30864,x30865,x30866)+~E(x30861,x30862)+~P10(x30861,x30863,x30864,x30865,x30866)
% 109.14/108.87 [3087]P10(x30873,x30872,x30874,x30875,x30876)+~E(x30871,x30872)+~P10(x30873,x30871,x30874,x30875,x30876)
% 109.14/108.87 [3088]P10(x30883,x30884,x30882,x30885,x30886)+~E(x30881,x30882)+~P10(x30883,x30884,x30881,x30885,x30886)
% 109.14/108.87 [3089]P10(x30893,x30894,x30895,x30892,x30896)+~E(x30891,x30892)+~P10(x30893,x30894,x30895,x30891,x30896)
% 109.14/108.87 [3090]P10(x30903,x30904,x30905,x30906,x30902)+~E(x30901,x30902)+~P10(x30903,x30904,x30905,x30906,x30901)
% 109.14/108.87 [3091]~P132(x30911)+P132(x30912)+~E(x30911,x30912)
% 109.14/108.87 [3092]~P85(x30921)+P85(x30922)+~E(x30921,x30922)
% 109.14/108.87 [3093]P9(x30932,x30933,x30934)+~E(x30931,x30932)+~P9(x30931,x30933,x30934)
% 109.14/108.87 [3094]P9(x30943,x30942,x30944)+~E(x30941,x30942)+~P9(x30943,x30941,x30944)
% 109.14/108.87 [3095]P9(x30953,x30954,x30952)+~E(x30951,x30952)+~P9(x30953,x30954,x30951)
% 109.14/108.87 [3096]~P136(x30961)+P136(x30962)+~E(x30961,x30962)
% 109.14/108.87
% 109.14/108.87 %-------------------------------------------
% 109.25/108.93 cnf(10451,plain,
% 109.25/108.93 (~E(f318(f318(f142(x104511),x104512),x104513),x104513)),
% 109.25/108.93 inference(rename_variables,[],[4647])).
% 109.25/108.93 cnf(10460,plain,
% 109.25/108.93 (~E(f318(f318(f142(x104601),x104602),x104603),x104603)),
% 109.25/108.93 inference(rename_variables,[],[4647])).
% 109.25/108.93 cnf(10469,plain,
% 109.25/108.93 (~E(f318(a103,x104691),x104691)),
% 109.25/108.93 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(10476,plain,
% 109.25/108.94 (~E(f318(a103,x104761),x104761)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(10479,plain,
% 109.25/108.94 (~E(f318(a103,x104791),x104791)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(10486,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f39(a911,x104861,x104862)),x104861))),
% 109.25/108.94 inference(rename_variables,[],[3938])).
% 109.25/108.94 cnf(10489,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x104891),x104892)),x104892))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(10492,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x104921),x104922)),x104922))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(10495,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x104951),x104951))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(10498,plain,
% 109.25/108.94 (~E(f318(a103,x104981),x104981)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(10509,plain,
% 109.25/108.94 (~E(f318(a103,x105091),x105091)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(10512,plain,
% 109.25/108.94 (~E(f318(a103,x105121),x105121)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(10522,plain,
% 109.25/108.94 (P1(f318(f318(f320(x105221),x105222),f233(f918(x105221,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(10525,plain,
% 109.25/108.94 (~E(f318(a103,x105251),x105251)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(10528,plain,
% 109.25/108.94 (~E(f318(a103,x105281),f2(a911))),
% 109.25/108.94 inference(rename_variables,[],[4637])).
% 109.25/108.94 cnf(10533,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x105331),x105331))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(10554,plain,
% 109.25/108.94 (P1(f318(f318(f320(x105541),x105542),f233(f918(x105541,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(10559,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x105591),f318(a103,x105591)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(10564,plain,
% 109.25/108.94 (P1(f318(f318(f320(x105641),x105642),f233(f918(x105641,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(10567,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x105671),x105671))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(10589,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x105891),f318(a103,x105891)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(10598,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x105981),x105981))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(10613,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x106131),x106131))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(10628,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x106281),f318(a103,x106281)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(10655,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x106551),x106552)),x106552))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(10660,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x106601)),x106601))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(10663,plain,
% 109.25/108.94 (E(f318(f253(x106631),x106632),x106632)),
% 109.25/108.94 inference(rename_variables,[],[3328])).
% 109.25/108.94 cnf(10687,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x106871),x106872),f179(f918(x106871,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(10690,plain,
% 109.25/108.94 (E(f164(x106901,x106902,f104(x106901)),x106902)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(10693,plain,
% 109.25/108.94 (E(f164(x106931,f104(x106931),x106932),x106932)),
% 109.25/108.94 inference(rename_variables,[],[3430])).
% 109.25/108.94 cnf(10704,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x107041),f318(a103,x107041)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(10723,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x107231),x107231))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(10726,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x107261),f318(a103,x107261)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(10733,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x107331),f318(a103,x107331)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(10736,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x107361),f318(a103,x107361)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(10741,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x107411),x107411))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(10754,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x107541),x107541))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(10761,plain,
% 109.25/108.94 (~E(f318(a103,x107611),f2(a911))),
% 109.25/108.94 inference(rename_variables,[],[4637])).
% 109.25/108.94 cnf(10766,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x107661),x107661))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(10777,plain,
% 109.25/108.94 (~E(f318(a103,x107771),x107771)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(10780,plain,
% 109.25/108.94 (~E(f318(f318(f142(x107801),x107802),x107803),x107803)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(10787,plain,
% 109.25/108.94 (~E(f318(f318(f142(x107871),x107872),x107873),x107873)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(10808,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x108081),x108081))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(10813,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x108131),x108131))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(10821,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x108211),x108211))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(10826,plain,
% 109.25/108.94 (E(f164(x108261,x108262,f104(x108261)),x108262)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(10829,plain,
% 109.25/108.94 (E(f164(x108291,x108292,f104(x108291)),x108292)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(10832,plain,
% 109.25/108.94 (~E(f318(a103,x108321),x108321)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(10835,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x108351),f104(x108351)),x108352))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(10840,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x108401),f104(x108401)),x108402))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(10857,plain,
% 109.25/108.94 (~P1(f318(f318(f226(f918(x108571,a909)),x108572),f179(f918(x108571,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4685])).
% 109.25/108.94 cnf(10860,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x108601)),x108601))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(10863,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x108631)),x108631))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(10868,plain,
% 109.25/108.94 (~E(f318(f301(x108681,f918(x108681,a909),x108682),x108683),f318(f299(x108681),x108683))),
% 109.25/108.94 inference(rename_variables,[],[4677])).
% 109.25/108.94 cnf(10879,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x108791))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(10882,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x108821),x108821))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(10887,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x108871),f318(a103,f318(f318(f73(a911),x108872),x108871))))),
% 109.25/108.94 inference(rename_variables,[],[3927])).
% 109.25/108.94 cnf(10890,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x108901),f318(f318(f74(a911),x108901),x108901)))),
% 109.25/108.94 inference(rename_variables,[],[3749])).
% 109.25/108.94 cnf(10893,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x108931),f318(f318(f74(a911),x108931),x108931)))),
% 109.25/108.94 inference(rename_variables,[],[3749])).
% 109.25/108.94 cnf(10896,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x108961),f318(f318(f73(a911),x108962),x108961)))),
% 109.25/108.94 inference(rename_variables,[],[3747])).
% 109.25/108.94 cnf(10899,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x108991),f318(f318(f73(a911),x108992),x108991)))),
% 109.25/108.94 inference(rename_variables,[],[3747])).
% 109.25/108.94 cnf(10904,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x109041,a909)),f318(f301(x109042,x109041,x109043),f318(f302(x109042,x109041,x109043),x109044))),x109044))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(10909,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x109091),x109091))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(10916,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x109161),x109161))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(10919,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x109191),x109191))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(10938,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x109381),f318(f318(f74(a911),x109381),x109381)))),
% 109.25/108.94 inference(rename_variables,[],[3749])).
% 109.25/108.94 cnf(10941,plain,
% 109.25/108.94 (P1(f318(f233(f918(x109411,a909)),x109412))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(10944,plain,
% 109.25/108.94 (P1(f318(f233(f918(x109441,a909)),x109442))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(10947,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x109471))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(10950,plain,
% 109.25/108.94 (P1(f318(f318(f278(a911),f318(a103,f2(a911))),x109501))),
% 109.25/108.94 inference(rename_variables,[],[3642])).
% 109.25/108.94 cnf(10953,plain,
% 109.25/108.94 (P1(f318(f233(f918(x109531,a909)),x109532))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(10956,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x109561),x109562)),x109562))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(10959,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x109591),x109592)),x109591))),
% 109.25/108.94 inference(rename_variables,[],[4689])).
% 109.25/108.94 cnf(10962,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x109621),x109622)),x109622))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(10965,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x109651),x109652)),x109651))),
% 109.25/108.94 inference(rename_variables,[],[4689])).
% 109.25/108.94 cnf(10968,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x109681)),x109681))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(10973,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x109731)),x109731))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(10980,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x109801),f318(a103,x109801)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(10983,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x109831),f318(f318(f74(a911),x109831),x109831)))),
% 109.25/108.94 inference(rename_variables,[],[3749])).
% 109.25/108.94 cnf(10986,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x109861),f318(f318(f73(a911),x109862),x109861)))),
% 109.25/108.94 inference(rename_variables,[],[3747])).
% 109.25/108.94 cnf(10989,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x109891),f318(f318(f73(a911),x109891),x109892)))),
% 109.25/108.94 inference(rename_variables,[],[3748])).
% 109.25/108.94 cnf(10992,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x109921),x109921))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11017,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x110171),f104(x110171)),x110172))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(11020,plain,
% 109.25/108.94 (~P1(f318(f56(x110201,x110202,f179(f918(x110201,a909))),x110203))),
% 109.25/108.94 inference(rename_variables,[],[4687])).
% 109.25/108.94 cnf(11023,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x110231),f104(x110231)),x110232))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(11026,plain,
% 109.25/108.94 (~P1(f318(f56(x110261,x110262,f179(f918(x110261,a909))),x110263))),
% 109.25/108.94 inference(rename_variables,[],[4687])).
% 109.25/108.94 cnf(11029,plain,
% 109.25/108.94 (~P1(f318(f318(f179(f918(x110291,f918(x110292,a909))),x110293),x110294))),
% 109.25/108.94 inference(rename_variables,[],[4691])).
% 109.25/108.94 cnf(11052,plain,
% 109.25/108.94 (~E(f318(a103,x110521),f2(a911))),
% 109.25/108.94 inference(rename_variables,[],[4637])).
% 109.25/108.94 cnf(11127,plain,
% 109.25/108.94 (~E(f318(a103,x111271),x111271)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(11130,plain,
% 109.25/108.94 (~E(f318(a103,x111301),x111301)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(11133,plain,
% 109.25/108.94 (~E(f318(f318(f142(x111331),x111332),x111333),x111333)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(11150,plain,
% 109.25/108.94 (P1(f318(f318(f320(x111501),x111502),f233(f918(x111501,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11153,plain,
% 109.25/108.94 (P1(f318(f318(f320(x111531),x111532),f318(f318(f300(x111531),x111532),x111533)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(11156,plain,
% 109.25/108.94 (P1(f318(f318(f320(x111561),x111562),f233(f918(x111561,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11159,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x111591),x111592),f179(f918(x111591,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11164,plain,
% 109.25/108.94 (~E(f318(a103,x111641),x111641)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(11171,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x111711),x111712),f179(f918(x111711,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11204,plain,
% 109.25/108.94 (~P1(f318(f318(f179(f918(x112041,f918(x112042,a909))),x112043),x112044))),
% 109.25/108.94 inference(rename_variables,[],[4691])).
% 109.25/108.94 cnf(11246,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x112461,a909)),f179(f918(x112461,a909))),x112462))),
% 109.25/108.94 inference(rename_variables,[],[3926])).
% 109.25/108.94 cnf(11249,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x112491),f318(a103,x112491)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(11252,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x112521),x112521))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11257,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x112571),x112571))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(11260,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x112601),x112601))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11269,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x112691),x112691))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11286,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x112861),x112861))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11297,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x112971),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(11300,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x113001),f104(x113001)),x113002))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(11315,plain,
% 109.25/108.94 (E(f318(f318(f125(x113151),f104(x113151)),x113152),x113152)),
% 109.25/108.94 inference(rename_variables,[],[3447])).
% 109.25/108.94 cnf(11329,plain,
% 109.25/108.94 (E(f164(x113291,x113292,f104(x113291)),x113292)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(11332,plain,
% 109.25/108.94 (E(f164(x113321,x113322,f104(x113321)),x113322)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(11335,plain,
% 109.25/108.94 (~E(f318(a103,x113351),x113351)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(11338,plain,
% 109.25/108.94 (~E(f318(a103,x113381),x113381)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(11344,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x113441),x113442),f179(f918(x113441,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11351,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x113511,a909)),f179(f918(x113511,a909))),x113512))),
% 109.25/108.94 inference(rename_variables,[],[3926])).
% 109.25/108.94 cnf(11356,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x113561),f318(a103,x113561)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(11361,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x113611,a909)),x113612),f318(f318(f300(x113611),x113613),x113612)))),
% 109.25/108.94 inference(rename_variables,[],[3924])).
% 109.25/108.94 cnf(11364,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x113641,a909)),x113642),f318(f318(f300(x113641),x113643),x113642)))),
% 109.25/108.94 inference(rename_variables,[],[3924])).
% 109.25/108.94 cnf(11367,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x113671),x113671))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(11370,plain,
% 109.25/108.94 (P1(f318(f318(f320(x113701),x113702),f233(f918(x113701,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11379,plain,
% 109.25/108.94 (P1(f318(f318(f320(x113791),x113792),f233(f918(x113791,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11386,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x113861),x113861))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(11399,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x113991),x113991))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11402,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x114021),f318(f318(f74(a911),x114021),x114021)))),
% 109.25/108.94 inference(rename_variables,[],[3749])).
% 109.25/108.94 cnf(11405,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x114051),x114051))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11412,plain,
% 109.25/108.94 (P1(f318(f233(f918(x114121,a909)),x114122))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(11419,plain,
% 109.25/108.94 (P1(f318(f233(f918(x114191,a909)),x114192))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(11436,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x114361),f104(x114361)),x114362))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(11443,plain,
% 109.25/108.94 (~E(f318(a103,x114431),x114431)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(11448,plain,
% 109.25/108.94 (E(f318(f29(a911),f318(f273(a911),x114481)),x114481)),
% 109.25/108.94 inference(rename_variables,[],[3387])).
% 109.25/108.94 cnf(11453,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x114531),f912(x114531))),f318(f318(f243(f912(x114531),f912(x114531)),x114532),f104(x114531))),f138(x114531,x114533)))),
% 109.25/108.94 inference(rename_variables,[],[4698])).
% 109.25/108.94 cnf(11456,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x114561,a909)),f179(f918(x114561,a909))),x114562))),
% 109.25/108.94 inference(rename_variables,[],[3926])).
% 109.25/108.94 cnf(11459,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x114591,a909)),f179(f918(x114591,a909))),x114592))),
% 109.25/108.94 inference(rename_variables,[],[3926])).
% 109.25/108.94 cnf(11462,plain,
% 109.25/108.94 (~E(f318(f301(x114621,f918(x114621,a909),x114622),x114623),f318(f299(x114621),x114623))),
% 109.25/108.94 inference(rename_variables,[],[4677])).
% 109.25/108.94 cnf(11475,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x114751,a909)),x114752),x114752))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(11478,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x114781),f318(a103,x114781)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(11481,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x114811),x114812),f179(f918(x114811,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11488,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x114881,a909)),f318(f301(x114882,x114881,x114883),f318(f302(x114882,x114881,x114883),x114884))),x114884))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(11505,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x115051),x115052),f179(f918(x115051,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11508,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x115081),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(11511,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x115111),x115112),f179(f918(x115111,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11516,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x115161),f104(x115161)),x115162))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(11523,plain,
% 109.25/108.94 (~E(f318(a103,x115231),x115231)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(11537,plain,
% 109.25/108.94 (P1(f318(f318(f320(x115371),x115372),f233(f918(x115371,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11540,plain,
% 109.25/108.94 (P1(f318(f318(f320(x115401),x115402),f233(f918(x115401,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11543,plain,
% 109.25/108.94 (P1(f318(f318(f320(x115431),x115432),f233(f918(x115431,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11548,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x115481),x115482),f179(f918(x115481,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11551,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x115511,x115511)),f318(f318(f243(x115511,x115511),x115512),x115513)),f144(x115511,f104(f918(x115511,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11554,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x115541),x115542),f179(f918(x115541,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11557,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x115571,x115571)),f318(f318(f243(x115571,x115571),x115572),x115573)),f144(x115571,f104(f918(x115571,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11560,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x115601),x115602),f179(f918(x115601,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11563,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x115631,a909)),x115632),f233(f918(x115631,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(11566,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x115661,a909)),x115662),f233(f918(x115661,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(11571,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x115711),x115711))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11582,plain,
% 109.25/108.94 (P1(f318(f318(f320(x115821),x115822),f233(f918(x115821,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11585,plain,
% 109.25/108.94 (P1(f318(f318(f320(x115851),x115852),f233(f918(x115851,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11602,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x116021),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(11609,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x116091),x116091))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(11612,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x116121),f104(x116121)),x116122))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(11615,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x116151,a909)),x116152),x116152))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(11618,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x116181),x116182),f179(f918(x116181,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11621,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x116211),x116211))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11624,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x116241,a909)),x116242),f233(f918(x116241,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(11627,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x116271,a909)),x116272),f233(f918(x116271,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(11630,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x116301),x116302),f179(f918(x116301,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11635,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x116351,a909)),x116352),f233(f918(x116351,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(11638,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x116381,a909)),x116382),x116382))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(11643,plain,
% 109.25/108.94 (~E(f318(a103,x116431),f2(a911))),
% 109.25/108.94 inference(rename_variables,[],[4637])).
% 109.25/108.94 cnf(11646,plain,
% 109.25/108.94 (~E(f318(f318(f142(x116461),x116462),x116463),f104(x116461))),
% 109.25/108.94 inference(rename_variables,[],[4650])).
% 109.25/108.94 cnf(11649,plain,
% 109.25/108.94 (E(f318(f301(x116491,x116491,f7(x116491)),x116492),x116492)),
% 109.25/108.94 inference(rename_variables,[],[3548])).
% 109.25/108.94 cnf(11652,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x116521),x116522),f179(f918(x116521,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11655,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x116551),x116552),f179(f918(x116551,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11660,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x116601),x116601))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11665,plain,
% 109.25/108.94 (E(f318(f29(a911),f318(f273(a911),x116651)),x116651)),
% 109.25/108.94 inference(rename_variables,[],[3387])).
% 109.25/108.94 cnf(11670,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x116701),f104(x116701)),x116702))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(11677,plain,
% 109.25/108.94 (P1(f318(f318(f320(x116771),x116772),f233(f918(x116771,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11682,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x116821),x116822),f179(f918(x116821,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11685,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x116851,x116851)),f318(f318(f243(x116851,x116851),x116852),x116853)),f144(x116851,f104(f918(x116851,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11690,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x116901),x116902),f179(f918(x116901,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11697,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x116971,a909)),x116972),f233(f918(x116971,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(11700,plain,
% 109.25/108.94 (P1(f318(f318(f320(x117001),x117002),f233(f918(x117001,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11703,plain,
% 109.25/108.94 (P1(f318(f318(f320(x117031),x117032),f318(f318(f300(x117031),x117032),x117033)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(11706,plain,
% 109.25/108.94 (P1(f318(f318(f320(x117061),x117062),f233(f918(x117061,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11709,plain,
% 109.25/108.94 (P1(f318(f318(f320(x117091),x117092),f318(f318(f300(x117091),x117092),x117093)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(11712,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x117121,a909)),x117122),f233(f918(x117121,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(11721,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x117211),f104(x117211)),x117212))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(11736,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x117361),x117361))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(11739,plain,
% 109.25/108.94 (E(f318(f301(x117391,x117391,f7(x117391)),x117392),x117392)),
% 109.25/108.94 inference(rename_variables,[],[3548])).
% 109.25/108.94 cnf(11742,plain,
% 109.25/108.94 (E(f164(x117421,x117422,f104(x117421)),x117422)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(11745,plain,
% 109.25/108.94 (~E(f318(a103,x117451),x117451)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(11752,plain,
% 109.25/108.94 (P1(f318(f318(f320(x117521),x117522),f233(f918(x117521,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11757,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x117571),x117572),f179(f918(x117571,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11760,plain,
% 109.25/108.94 (P1(f318(f318(f320(f917(x117601,x117601)),f318(f318(f243(x117601,x117601),x117602),x117602)),f298(x117601,x117603)))),
% 109.25/108.94 inference(rename_variables,[],[4112])).
% 109.25/108.94 cnf(11769,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x117691,x117691)),f318(f318(f243(x117691,x117691),x117692),x117693)),f144(x117691,f104(f918(x117691,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11772,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x117721),x117722),f179(f918(x117721,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11779,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x117791,a909)),x117792),x117792))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(11782,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x117821),x117822),f179(f918(x117821,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11785,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x117851,x117851)),f318(f318(f243(x117851,x117851),x117852),x117853)),f144(x117851,f104(f918(x117851,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11788,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x117881),f912(x117881))),f318(f318(f243(f912(x117881),f912(x117881)),x117882),f104(x117881))),f136(x117881,x117883)))),
% 109.25/108.94 inference(rename_variables,[],[4697])).
% 109.25/108.94 cnf(11793,plain,
% 109.25/108.94 (P1(f318(f318(f320(x117931),x117932),f233(f918(x117931,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11796,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x117961),x117961))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(11799,plain,
% 109.25/108.94 (P1(f318(f318(f320(x117991),x117992),f233(f918(x117991,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11802,plain,
% 109.25/108.94 (P1(f318(f318(f320(x118021),x118022),f233(f918(x118021,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11805,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118051),x118052),f179(f918(x118051,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11808,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x118081,a909)),x118082),x118082))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(11811,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x118111),x118111))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11814,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118141),x118142),f179(f918(x118141,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11817,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x118171,x118171)),f318(f318(f243(x118171,x118171),x118172),x118173)),f144(x118171,f104(f918(x118171,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11820,plain,
% 109.25/108.94 (P1(f318(f233(f918(x118201,a909)),x118202))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(11823,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118231),x118232),f179(f918(x118231,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11826,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x118261,x118261)),f318(f318(f243(x118261,x118261),x118262),x118263)),f144(x118261,f104(f918(x118261,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11829,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118291),x118292),f179(f918(x118291,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11832,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118321),x118322),f179(f918(x118321,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11835,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x118351,a909)),x118352),x118352))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(11838,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x118381,a909)),x118382),x118382))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(11841,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118411),x118412),f179(f918(x118411,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11846,plain,
% 109.25/108.94 (P1(f318(f318(f320(x118461),x118462),f233(f918(x118461,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11849,plain,
% 109.25/108.94 (P1(f318(f318(f320(x118491),x118492),f318(f318(f300(x118491),x118492),x118493)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(11856,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118561),x118562),f179(f918(x118561,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11859,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118591),x118592),f179(f918(x118591,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11862,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118621),x118622),f179(f918(x118621,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11865,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x118651,x118651)),f318(f318(f243(x118651,x118651),x118652),x118653)),f144(x118651,f104(f918(x118651,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11872,plain,
% 109.25/108.94 (P1(f318(f318(f320(x118721),x118722),f233(f918(x118721,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11875,plain,
% 109.25/108.94 (P1(f318(f318(f320(x118751),x118752),f233(f918(x118751,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11878,plain,
% 109.25/108.94 (P1(f318(f318(f320(x118781),x118782),f233(f918(x118781,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11881,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x118811),x118811))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(11886,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118861),x118862),f179(f918(x118861,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11889,plain,
% 109.25/108.94 (P1(f318(f318(f320(x118891),x118892),f233(f918(x118891,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(11892,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x118921),x118922),f179(f918(x118921,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11897,plain,
% 109.25/108.94 (P1(f318(f318(f320(x118971),x118972),f318(f318(f300(x118971),x118972),x118973)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(11900,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x119001),x119001))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(11903,plain,
% 109.25/108.94 (~E(f318(f301(x119031,f918(x119031,a909),x119032),x119033),f318(f299(x119031),x119033))),
% 109.25/108.94 inference(rename_variables,[],[4677])).
% 109.25/108.94 cnf(11909,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x119091),f912(x119091))),f318(f318(f243(f912(x119091),f912(x119091)),x119092),f104(x119091))),f148(x119091,x119093)))),
% 109.25/108.94 inference(rename_variables,[],[4699])).
% 109.25/108.94 cnf(11914,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x119141),x119142),f179(f918(x119141,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11917,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x119171),x119172),f179(f918(x119171,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11920,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x119201),x119202),f179(f918(x119201,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11923,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x119231),x119232),f179(f918(x119231,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11926,plain,
% 109.25/108.94 (P1(f318(f318(f320(f917(f912(x119261),f912(x119261))),f318(f318(f243(f912(x119261),f912(x119261)),x119262),x119262)),f149(x119261,f298(x119261,x119263))))),
% 109.25/108.94 inference(rename_variables,[],[4240])).
% 109.25/108.94 cnf(11929,plain,
% 109.25/108.94 (P1(f318(f318(f320(f917(f912(x119291),f912(x119291))),f318(f318(f243(f912(x119291),f912(x119291)),x119292),x119292)),f149(x119291,f298(x119291,x119293))))),
% 109.25/108.94 inference(rename_variables,[],[4240])).
% 109.25/108.94 cnf(11932,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x119321,a909)),x119322),x119322))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(11937,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x119371),x119372),f179(f918(x119371,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11940,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x119401,x119401)),f318(f318(f243(x119401,x119401),x119402),x119403)),f144(x119401,f104(f918(x119401,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11947,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x119471,x119471)),f318(f318(f243(x119471,x119471),x119472),x119473)),f144(x119471,f104(f918(x119471,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(11954,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x119541,a909)),x119542),x119542))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(11957,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x119571),x119572),f179(f918(x119571,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11960,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x119601),x119602),f179(f918(x119601,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(11963,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x119631,a909)),x119632),f233(f918(x119631,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(11966,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x119661,a909)),x119662),f233(f918(x119661,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(11969,plain,
% 109.25/108.94 (P1(f318(f318(f320(x119691),f318(x119692,x119693)),f318(f301(x119694,x119691,x119692),f233(f918(x119694,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(11972,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x119721,x119721)),f318(f318(f243(x119721,x119721),x119722),x119723)),f144(x119721,f104(f918(x119721,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(12032,plain,
% 109.25/108.94 (E(f164(x120321,x120322,f104(x120321)),x120322)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12064,plain,
% 109.25/108.94 (E(f164(x120641,x120642,f104(x120641)),x120642)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12083,plain,
% 109.25/108.94 (E(f164(x120831,x120832,f104(x120831)),x120832)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12100,plain,
% 109.25/108.94 (E(f164(x121001,x121002,f104(x121001)),x121002)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12123,plain,
% 109.25/108.94 (E(f164(x121231,x121232,f104(x121231)),x121232)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12125,plain,
% 109.25/108.94 (~E(f318(a103,x121251),x121251)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12129,plain,
% 109.25/108.94 (P1(f318(f318(f320(x121291),x121292),f233(f918(x121291,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(12138,plain,
% 109.25/108.94 (~E(f318(a103,x121381),x121381)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12141,plain,
% 109.25/108.94 (~E(f318(a103,x121411),x121411)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12150,plain,
% 109.25/108.94 (P1(f318(f318(f320(x121501),x121502),f318(f318(f300(x121501),x121502),x121503)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(12153,plain,
% 109.25/108.94 (P1(f318(f318(f320(x121531),f318(x121532,x121533)),f318(f301(x121534,x121531,x121532),f233(f918(x121534,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(12178,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x121781),x121781))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12181,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x121811)),x121811))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(12188,plain,
% 109.25/108.94 (~E(f318(a103,x121881),x121881)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12196,plain,
% 109.25/108.94 (E(f164(x121961,x121962,f104(x121961)),x121962)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12199,plain,
% 109.25/108.94 (E(f164(x121991,x121992,f104(x121991)),x121992)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12202,plain,
% 109.25/108.94 (P1(f318(f55(a911),f294(a911,x122021,x122022)))),
% 109.25/108.94 inference(rename_variables,[],[3694])).
% 109.25/108.94 cnf(12207,plain,
% 109.25/108.94 (~E(f318(f318(f142(x122071),x122072),x122073),x122073)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(12210,plain,
% 109.25/108.94 (~E(f318(f318(f142(x122101),x122102),x122103),x122103)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(12213,plain,
% 109.25/108.94 (E(f318(f132(x122131),f318(f318(f142(x122131),x122132),x122133)),x122132)),
% 109.25/108.94 inference(rename_variables,[],[3536])).
% 109.25/108.94 cnf(12214,plain,
% 109.25/108.94 (~E(f318(f318(f142(x122141),x122142),x122143),x122143)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(12217,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x122171,a909)),x122172),f233(f918(x122171,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(12230,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x122301,a909)),f318(f301(x122302,x122301,x122303),f318(f302(x122302,x122301,x122303),x122304))),x122304))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(12238,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x122381),x122381))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12256,plain,
% 109.25/108.94 (P1(f318(f55(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),x122561)),f318(f318(f9(a911,a911,a909),f226(a911)),x122562)))))),
% 109.25/108.94 inference(rename_variables,[],[4499])).
% 109.25/108.94 cnf(12265,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x122651),x122651))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12268,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a1),f2(a1)),f318(f72(a1),f318(f91(a1),f318(a103,x122681)))))),
% 109.25/108.94 inference(rename_variables,[],[4690])).
% 109.25/108.94 cnf(12269,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x122691))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(12278,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),f318(f72(a1),f318(f91(a1),x122781))),f318(f91(a1),x122782)))),
% 109.25/108.94 inference(rename_variables,[],[3962])).
% 109.25/108.94 cnf(12283,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x122831),x122831))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12286,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x122861),x122861))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12289,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x122891),x122891))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12296,plain,
% 109.25/108.94 (~E(f318(a103,x122961),x122961)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12299,plain,
% 109.25/108.94 (E(f164(x122991,x122992,f104(x122991)),x122992)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12304,plain,
% 109.25/108.94 (E(f164(x123041,x123042,f104(x123041)),x123042)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12307,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x123071),x123071))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12308,plain,
% 109.25/108.94 (E(f164(x123081,x123082,f104(x123081)),x123082)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12322,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x123221),x123221))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12325,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x123251),x123251))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12330,plain,
% 109.25/108.94 (P1(f318(f318(f320(x123301),x123302),f233(f918(x123301,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(12331,plain,
% 109.25/108.94 (~E(f318(a103,x123311),f2(a911))),
% 109.25/108.94 inference(rename_variables,[],[4637])).
% 109.25/108.94 cnf(12334,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x123341,a909)),f318(f301(x123342,x123341,x123343),f318(f302(x123342,x123341,x123343),x123344))),x123344))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(12338,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x123381,a909)),f318(f301(x123382,x123381,x123383),f318(f302(x123382,x123381,x123383),x123384))),x123384))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(12342,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x123421,a909)),x123422),f318(f318(f300(x123421),x123423),x123422)))),
% 109.25/108.94 inference(rename_variables,[],[3924])).
% 109.25/108.94 cnf(12345,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x123451),x123451))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12348,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x123481),x123481))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12353,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x123531),x123531))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12360,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x123601),x123601))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12377,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x123771),f318(a103,x123771)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(12382,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x123821,a909)),x123822),f318(f318(f300(x123821),x123823),x123822)))),
% 109.25/108.94 inference(rename_variables,[],[3924])).
% 109.25/108.94 cnf(12385,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x123851),x123851))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12388,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x123881),x123881))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12423,plain,
% 109.25/108.94 (P1(f318(f55(x124231),f179(f918(x124231,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(12446,plain,
% 109.25/108.94 (~E(f318(a103,x124461),x124461)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12449,plain,
% 109.25/108.94 (~E(f318(f318(f142(x124491),x124492),x124493),x124493)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(12452,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),f318(f318(f3(a911),x124521),x124522)),f318(a103,x124521)))),
% 109.25/108.94 inference(rename_variables,[],[3929])).
% 109.25/108.94 cnf(12455,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x124551)),x124551))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(12456,plain,
% 109.25/108.94 (~E(f318(a103,x124561),x124561)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12461,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x124611),f318(a103,x124611)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(12484,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x124841),x124841))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12487,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x124871),x124871))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12490,plain,
% 109.25/108.94 (E(f164(x124901,x124902,f104(x124901)),x124902)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12495,plain,
% 109.25/108.94 (~P1(f318(f318(f163(x124951),f104(x124951)),x124952))),
% 109.25/108.94 inference(rename_variables,[],[4675])).
% 109.25/108.94 cnf(12501,plain,
% 109.25/108.94 (~E(f318(a103,x125011),x125011)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12504,plain,
% 109.25/108.94 (~E(f318(f318(f142(x125041),x125042),x125043),x125043)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(12516,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x125161),x125162)),x125162))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(12517,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x125171),f318(a103,x125171)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(12534,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a1),f318(f91(a1),x125341)),f318(f72(a1),f318(f91(a1),x125342))))),
% 109.25/108.94 inference(rename_variables,[],[4686])).
% 109.25/108.94 cnf(12547,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f39(a911,x125471,x125472)),x125471))),
% 109.25/108.94 inference(rename_variables,[],[3938])).
% 109.25/108.94 cnf(12548,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),f2(a911)),f318(a103,x125481)))),
% 109.25/108.94 inference(rename_variables,[],[3571])).
% 109.25/108.94 cnf(12573,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x125731),x125731))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12576,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),f2(a911)),f318(a103,x125761)))),
% 109.25/108.94 inference(rename_variables,[],[3571])).
% 109.25/108.94 cnf(12579,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),f2(a911)),f318(a103,x125791)))),
% 109.25/108.94 inference(rename_variables,[],[3571])).
% 109.25/108.94 cnf(12582,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),f2(a911)),f318(a103,x125821)))),
% 109.25/108.94 inference(rename_variables,[],[3571])).
% 109.25/108.94 cnf(12585,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),f2(a911)),f318(a103,x125851)))),
% 109.25/108.94 inference(rename_variables,[],[3571])).
% 109.25/108.94 cnf(12588,plain,
% 109.25/108.94 (P1(f318(f318(f320(x125881),f318(x125882,x125883)),f318(f301(x125884,x125881,x125882),f233(f918(x125884,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(12589,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x125891),x125892)),x125892))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(12592,plain,
% 109.25/108.94 (P1(f318(f318(f320(x125921),f318(x125922,x125923)),f318(f301(x125924,x125921,x125922),f233(f918(x125924,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(12593,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x125931)),x125931))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(12601,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x126011),f318(f318(f74(a911),x126011),x126011)))),
% 109.25/108.94 inference(rename_variables,[],[3749])).
% 109.25/108.94 cnf(12602,plain,
% 109.25/108.94 (E(f318(f318(f74(a911),x126021),f71(a911)),x126021)),
% 109.25/108.94 inference(rename_variables,[],[3391])).
% 109.25/108.94 cnf(12613,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a1),f318(f91(a1),x126131)),f318(f72(a1),f318(f91(a1),x126132))))),
% 109.25/108.94 inference(rename_variables,[],[4686])).
% 109.25/108.94 cnf(12616,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f39(a911,x126161,x126162)),x126161))),
% 109.25/108.94 inference(rename_variables,[],[3938])).
% 109.25/108.94 cnf(12619,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x126191),x126192)),x126192))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(12620,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x126201),x126202)),x126201))),
% 109.25/108.94 inference(rename_variables,[],[4689])).
% 109.25/108.94 cnf(12657,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x126571),x126571))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12682,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x126821),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(12685,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x126851),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(12698,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x126981,a909)),x126982),x126982))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(12701,plain,
% 109.25/108.94 (P25(x127011,x127011,f7(x127011),x127012)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(12704,plain,
% 109.25/108.94 (E(f164(x127041,x127042,f104(x127041)),x127042)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(12707,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),f2(a911)),f318(a103,x127071)))),
% 109.25/108.94 inference(rename_variables,[],[3571])).
% 109.25/108.94 cnf(12710,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x127101),x127101))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12711,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x127111),f318(a103,x127111)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(12716,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x127161),x127161))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12719,plain,
% 109.25/108.94 (E(f318(f318(f73(a1),a76),x127191),x127191)),
% 109.25/108.94 inference(rename_variables,[],[3374])).
% 109.25/108.94 cnf(12727,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x127271),x127271))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12728,plain,
% 109.25/108.94 (~E(f318(a103,x127281),x127281)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12731,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x127311),x127311))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12732,plain,
% 109.25/108.94 (~E(f318(a103,x127321),x127321)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12735,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x127351),x127351))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12736,plain,
% 109.25/108.94 (~E(f318(a103,x127361),x127361)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12748,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x127481),x127481))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12753,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x127531),x127531))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12764,plain,
% 109.25/108.94 (P34(x127641,x127642,f104(x127641),f104(x127641))),
% 109.25/108.94 inference(rename_variables,[],[3732])).
% 109.25/108.94 cnf(12770,plain,
% 109.25/108.94 (P1(f318(f318(f278(a911),x127701),x127701))),
% 109.25/108.94 inference(rename_variables,[],[3493])).
% 109.25/108.94 cnf(12773,plain,
% 109.25/108.94 (P1(f318(f318(f278(a911),x127731),x127731))),
% 109.25/108.94 inference(rename_variables,[],[3493])).
% 109.25/108.94 cnf(12776,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x127761),f318(a103,x127761)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(12779,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x127791),f318(a103,x127791)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(12782,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x127821),x127821))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12785,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x127851),x127851))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12788,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x127881),x127881))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12791,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x127911),x127911))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12794,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x127941),x127941))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12797,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x127971),x127971))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12800,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x128001),x128001))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12803,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x128031),x128031))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12810,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x128101,a909)),x128102),f318(f318(f300(x128101),x128103),x128102)))),
% 109.25/108.94 inference(rename_variables,[],[3924])).
% 109.25/108.94 cnf(12811,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x128111,a909)),x128112),f233(f918(x128111,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(12814,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x128141,a909)),f318(f301(x128142,x128141,x128143),f318(f302(x128142,x128141,x128143),x128144))),x128144))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(12815,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x128151,a909)),f179(f918(x128151,a909))),x128152))),
% 109.25/108.94 inference(rename_variables,[],[3926])).
% 109.25/108.94 cnf(12820,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x128201,a909)),x128202),f233(f918(x128201,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(12821,plain,
% 109.25/108.94 (~E(f318(a103,x128211),x128211)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12824,plain,
% 109.25/108.94 (~E(f318(a103,x128241),x128241)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12835,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x128351),x128351))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12840,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x128401),x128401))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12845,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x128451),x128451))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12848,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x128481),x128481))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12853,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x128531),x128531))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12856,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x128561),x128561))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12859,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x128591),x128591))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12862,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x128621),x128621))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12865,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x128651),x128651))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12868,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x128681),x128681))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12871,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x128711),x128711))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(12874,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x128741),x128741))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12877,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x128771,a909)),x128772),f318(f318(f300(x128771),x128773),x128772)))),
% 109.25/108.94 inference(rename_variables,[],[3924])).
% 109.25/108.94 cnf(12880,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x128801,a909)),f318(f301(x128802,x128801,x128803),f318(f302(x128802,x128801,x128803),x128804))),x128804))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(12883,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x128831),x128831))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(12888,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x128881),x128881))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12891,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x128911),x128912)),x128912))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(12894,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x128941),x128941))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12897,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),f318(f318(f73(a911),x128971),x128972)),x128972))),
% 109.25/108.94 inference(rename_variables,[],[4688])).
% 109.25/108.94 cnf(12900,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x129001),x129001))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12903,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x129031),x129031))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(12906,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x129061)),x129061))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(12911,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x129111)),x129111))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(12916,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x129161)),x129161))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(12919,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x129191)),x129191))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(12932,plain,
% 109.25/108.94 (P1(f318(f318(f320(x129321),x129322),f318(f318(f300(x129321),x129322),x129323)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(12973,plain,
% 109.25/108.94 (P1(f318(f55(a1),f294(a1,x129731,x129732)))),
% 109.25/108.94 inference(rename_variables,[],[3697])).
% 109.25/108.94 cnf(12978,plain,
% 109.25/108.94 (P1(f318(f318(f320(x129781),x129782),f233(f918(x129781,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(12981,plain,
% 109.25/108.94 (P25(x129811,x129811,f7(x129811),x129812)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(12986,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x129861)),x129861))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(12987,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x129871),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(12995,plain,
% 109.25/108.94 (P1(f318(f318(f320(x129951),x129952),f233(f918(x129951,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(12996,plain,
% 109.25/108.94 (~E(f318(a103,x129961),x129961)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(12999,plain,
% 109.25/108.94 (P1(f318(f318(f320(f918(x129991,a909)),x129992),f318(f299(x129991),x129992)))),
% 109.25/108.94 inference(rename_variables,[],[3850])).
% 109.25/108.94 cnf(13000,plain,
% 109.25/108.94 (~E(f318(a103,x130001),x130001)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13011,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x130111))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(13012,plain,
% 109.25/108.94 (~E(f318(a103,x130121),x130121)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13021,plain,
% 109.25/108.94 (P1(f318(f233(f918(x130211,a909)),x130212))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(13022,plain,
% 109.25/108.94 (~E(f318(a103,x130221),x130221)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13033,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x130331),x130331))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13034,plain,
% 109.25/108.94 (~E(f318(a103,x130341),x130341)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13040,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x130401),x130401))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13049,plain,
% 109.25/108.94 (~P1(f318(f318(f226(f918(x130491,a909)),x130492),f179(f918(x130491,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4685])).
% 109.25/108.94 cnf(13052,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x130521,a909)),x130522),f318(f318(f101(f918(x130521,a909)),x130523),x130522)))),
% 109.25/108.94 inference(rename_variables,[],[4063])).
% 109.25/108.94 cnf(13057,plain,
% 109.25/108.94 (~E(f318(a103,x130571),x130571)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13058,plain,
% 109.25/108.94 (E(f318(f301(x130581,x130581,f7(x130581)),x130582),x130582)),
% 109.25/108.94 inference(rename_variables,[],[3548])).
% 109.25/108.94 cnf(13065,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x130651,a909)),x130652),x130652))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13074,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x130741,a909)),x130742),f318(f318(f300(x130741),x130743),x130742)))),
% 109.25/108.94 inference(rename_variables,[],[3924])).
% 109.25/108.94 cnf(13077,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x130771,a909)),f318(f301(x130772,x130771,x130773),f318(f302(x130772,x130771,x130773),x130774))),x130774))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(13083,plain,
% 109.25/108.94 (P1(f318(f318(f320(x130831),x130832),f233(f918(x130831,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13090,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x130901),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(13091,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x130911),f318(a103,x130911)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(13122,plain,
% 109.25/108.94 (P1(f318(f55(x131221),f179(f918(x131221,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(13133,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x131331,a909)),x131332),x131332))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13136,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x131361,a909)),f318(f301(x131362,x131361,x131363),f318(f302(x131362,x131361,x131363),x131364))),x131364))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(13139,plain,
% 109.25/108.94 (~P1(f318(f318(f179(f918(x131391,f918(x131392,a909))),x131393),x131394))),
% 109.25/108.94 inference(rename_variables,[],[4691])).
% 109.25/108.94 cnf(13142,plain,
% 109.25/108.94 (P1(f318(f318(f320(x131421),x131422),f233(f918(x131421,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13145,plain,
% 109.25/108.94 (P1(f318(f318(f320(f918(x131451,a909)),x131452),f318(f299(x131451),x131452)))),
% 109.25/108.94 inference(rename_variables,[],[3850])).
% 109.25/108.94 cnf(13148,plain,
% 109.25/108.94 (~P1(f318(f318(f179(f918(x131481,f918(x131482,a909))),x131483),x131484))),
% 109.25/108.94 inference(rename_variables,[],[4691])).
% 109.25/108.94 cnf(13151,plain,
% 109.25/108.94 (P25(x131511,x131511,f7(x131511),x131512)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(13154,plain,
% 109.25/108.94 (P25(x131541,x131541,f7(x131541),x131542)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(13159,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a1),f318(f91(a1),x131591)),f2(a1)))),
% 109.25/108.94 inference(rename_variables,[],[4681])).
% 109.25/108.94 cnf(13170,plain,
% 109.25/108.94 (~P1(f318(f318(f179(f918(x131701,f918(x131702,a909))),x131703),x131704))),
% 109.25/108.94 inference(rename_variables,[],[4691])).
% 109.25/108.94 cnf(13173,plain,
% 109.25/108.94 (P1(f318(f318(f320(x131731),x131732),f233(f918(x131731,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13179,plain,
% 109.25/108.94 (E(f318(f180(f912(x131791)),f160(x131791,x131792,x131793)),x131792)),
% 109.25/108.94 inference(rename_variables,[],[3558])).
% 109.25/108.94 cnf(13186,plain,
% 109.25/108.94 (P1(f318(f318(f320(x131861),x131862),f233(f918(x131861,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13189,plain,
% 109.25/108.94 (P1(f318(f318(f320(x131891),x131892),f318(f318(f300(x131891),x131892),x131893)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(13192,plain,
% 109.25/108.94 (P1(f318(f318(f320(x131921),x131922),f233(f918(x131921,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13195,plain,
% 109.25/108.94 (P1(f318(f318(f320(x131951),x131952),f318(f318(f300(x131951),x131952),x131953)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(13198,plain,
% 109.25/108.94 (P25(x131981,x131981,f7(x131981),x131982)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(13201,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x132011),x132011))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13204,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x132041),x132041))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13208,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x132081))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(13213,plain,
% 109.25/108.94 (P1(f318(f318(f320(x132131),x132132),f233(f918(x132131,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13216,plain,
% 109.25/108.94 (P1(f318(f318(f320(f918(x132161,a909)),x132162),f318(f299(x132161),x132162)))),
% 109.25/108.94 inference(rename_variables,[],[3850])).
% 109.25/108.94 cnf(13219,plain,
% 109.25/108.94 (P1(f318(f318(f320(x132191),x132192),f233(f918(x132191,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13228,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x132281),x132281))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13229,plain,
% 109.25/108.94 (~E(f318(a103,x132291),x132291)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13232,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x132321),x132321))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13233,plain,
% 109.25/108.94 (~E(f318(a103,x132331),x132331)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13241,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x132411),x132412),f179(f918(x132411,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13250,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x132501),x132502),f179(f918(x132501,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13253,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(x132531,x132531)),f318(f318(f243(x132531,x132531),x132532),x132533)),f144(x132531,f104(f918(x132531,a911)))))),
% 109.25/108.94 inference(rename_variables,[],[4696])).
% 109.25/108.94 cnf(13256,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x132561),f912(x132561))),f318(f318(f243(f912(x132561),f912(x132561)),x132562),f104(x132561))),f136(x132561,x132563)))),
% 109.25/108.94 inference(rename_variables,[],[4697])).
% 109.25/108.94 cnf(13257,plain,
% 109.25/108.94 (P1(f318(f318(f320(x132571),x132572),f233(f918(x132571,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13262,plain,
% 109.25/108.94 (~P1(f318(f318(f179(f918(x132621,f918(x132622,a909))),x132623),x132624))),
% 109.25/108.94 inference(rename_variables,[],[4691])).
% 109.25/108.94 cnf(13265,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x132651),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(13266,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x132661),x132661))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13269,plain,
% 109.25/108.94 (P25(x132691,x132691,f7(x132691),x132692)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(13272,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x132721),x132721))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13275,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x132751),x132751))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13280,plain,
% 109.25/108.94 (P1(f318(f55(x132801),f318(f163(x132801),x132802)))),
% 109.25/108.94 inference(rename_variables,[],[3530])).
% 109.25/108.94 cnf(13283,plain,
% 109.25/108.94 (P1(f318(f55(x132831),f318(f163(x132831),x132832)))),
% 109.25/108.94 inference(rename_variables,[],[3530])).
% 109.25/108.94 cnf(13288,plain,
% 109.25/108.94 (E(f318(f318(f18(x132881,x132882),x132883),x132884),x132883)),
% 109.25/108.94 inference(rename_variables,[],[3482])).
% 109.25/108.94 cnf(13291,plain,
% 109.25/108.94 (E(f318(f318(f18(x132911,x132912),x132913),x132914),x132913)),
% 109.25/108.94 inference(rename_variables,[],[3482])).
% 109.25/108.94 cnf(13297,plain,
% 109.25/108.94 (E(f318(f301(x132971,x132971,f7(x132971)),x132972),x132972)),
% 109.25/108.94 inference(rename_variables,[],[3548])).
% 109.25/108.94 cnf(13298,plain,
% 109.25/108.94 (P25(x132981,x132981,f7(x132981),x132982)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(13301,plain,
% 109.25/108.94 (E(f164(x133011,x133012,f104(x133011)),x133012)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(13304,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x133041,a909)),f179(f918(x133041,a909))),x133042))),
% 109.25/108.94 inference(rename_variables,[],[3926])).
% 109.25/108.94 cnf(13329,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x133291),x133291))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13332,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x133321),x133321))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13335,plain,
% 109.25/108.94 (E(f164(x133351,x133352,f104(x133351)),x133352)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(13338,plain,
% 109.25/108.94 (E(f164(x133381,f104(x133381),x133382),x133382)),
% 109.25/108.94 inference(rename_variables,[],[3430])).
% 109.25/108.94 cnf(13341,plain,
% 109.25/108.94 (E(f164(x133411,x133412,f104(x133411)),x133412)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(13347,plain,
% 109.25/108.94 (E(f164(x133471,x133472,f104(x133471)),x133472)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(13350,plain,
% 109.25/108.94 (E(f164(x133501,x133502,f104(x133501)),x133502)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(13359,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x133591,a909)),x133592),f233(f918(x133591,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(13366,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x133661,a909)),x133662),f318(f318(f300(x133661),x133663),x133662)))),
% 109.25/108.94 inference(rename_variables,[],[3924])).
% 109.25/108.94 cnf(13369,plain,
% 109.25/108.94 (P25(x133691,x133691,f7(x133691),x133692)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(13372,plain,
% 109.25/108.94 (P1(f318(f318(f320(x133721),x133722),f233(f918(x133721,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13373,plain,
% 109.25/108.94 (P26(x133731,x133731,f25(x133731),x133732,x133732)),
% 109.25/108.94 inference(rename_variables,[],[4135])).
% 109.25/108.94 cnf(13374,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x133741),x133742),x133743))+E(f318(f84(x133744,x133741,x133745,f84(x133741,x133744,x133743,x133746)),x133742),f318(x133746,x133742))+~P26(x133741,x133744,x133746,x133743,x133745)),
% 109.25/108.94 inference(rename_variables,[],[9348])).
% 109.25/108.94 cnf(13376,plain,
% 109.25/108.94 (P26(x133761,x133761,f25(x133761),x133762,x133762)),
% 109.25/108.94 inference(rename_variables,[],[4135])).
% 109.25/108.94 cnf(13379,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x133791),x133791))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13380,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x133801),f318(a103,x133801)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(13386,plain,
% 109.25/108.94 (E(f164(x133861,x133862,f104(x133861)),x133862)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(13391,plain,
% 109.25/108.94 (~E(f318(a103,x133911),x133911)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13394,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x133941,a909)),x133942),x133942))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13399,plain,
% 109.25/108.94 (P1(f318(f318(f320(x133991),x133992),f233(f918(x133991,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13402,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x134021,a909)),f318(f301(x134022,x134021,x134023),f318(f302(x134022,x134021,x134023),x134024))),x134024))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(13408,plain,
% 109.25/108.94 (P1(f318(f55(x134081),f179(f918(x134081,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(13409,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x134091),x134092),f179(f918(x134091,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13412,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x134121),x134122),f179(f918(x134121,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13415,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x134151),x134152),f179(f918(x134151,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13418,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x134181),x134182),f179(f918(x134181,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13421,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x134211))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(13425,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x134251),f318(a103,x134251)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(13428,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x134281),x134281))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13431,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x134311),x134311))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13436,plain,
% 109.25/108.94 (P1(f318(f318(f320(x134361),x134362),f233(f918(x134361,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13445,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x134451),x134451))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13448,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x134481),x134481))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13451,plain,
% 109.25/108.94 (~P1(f318(f318(f225(a911),f318(a103,x134511)),x134511))),
% 109.25/108.94 inference(rename_variables,[],[4676])).
% 109.25/108.94 cnf(13454,plain,
% 109.25/108.94 (P1(f318(f318(f320(x134541),x134542),f233(f918(x134541,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13457,plain,
% 109.25/108.94 (P25(x134571,x134571,f7(x134571),x134572)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(13460,plain,
% 109.25/108.94 (~P1(f318(f318(f179(f918(x134601,f918(x134602,a909))),x134603),x134604))),
% 109.25/108.94 inference(rename_variables,[],[4691])).
% 109.25/108.94 cnf(13476,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x134761,a909)),x134762),x134762))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13479,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x134791,a909)),x134792),x134792))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13482,plain,
% 109.25/108.94 (P1(f318(f318(f320(x134821),x134822),f318(f318(f300(x134821),x134822),x134823)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(13485,plain,
% 109.25/108.94 (P1(f318(f318(f320(f917(f912(x134851),f912(x134851))),f318(f318(f243(f912(x134851),f912(x134851)),x134852),x134852)),f149(x134851,f298(x134851,x134853))))),
% 109.25/108.94 inference(rename_variables,[],[4240])).
% 109.25/108.94 cnf(13486,plain,
% 109.25/108.94 (P1(f318(f318(f320(x134861),x134862),f233(f918(x134861,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13493,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x134931),x134932),f179(f918(x134931,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13496,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x134961),x134962),f179(f918(x134961,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13499,plain,
% 109.25/108.94 (P1(f318(f55(x134991),f318(f163(x134991),x134992)))),
% 109.25/108.94 inference(rename_variables,[],[3530])).
% 109.25/108.94 cnf(13502,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x135021),f912(x135021))),f318(f318(f243(f912(x135021),f912(x135021)),x135022),f104(x135021))),f136(x135021,x135023)))),
% 109.25/108.94 inference(rename_variables,[],[4697])).
% 109.25/108.94 cnf(13503,plain,
% 109.25/108.94 (~E(f318(a103,x135031),x135031)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13506,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x135061),f912(x135061))),f318(f318(f243(f912(x135061),f912(x135061)),x135062),f104(x135061))),f136(x135061,x135063)))),
% 109.25/108.94 inference(rename_variables,[],[4697])).
% 109.25/108.94 cnf(13507,plain,
% 109.25/108.94 (~E(f318(a103,x135071),x135071)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13510,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x135101),x135102),f179(f918(x135101,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13513,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x135131),x135132),f179(f918(x135131,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13516,plain,
% 109.25/108.94 (E(f318(f318(f125(x135161),x135162),f104(x135161)),x135162)),
% 109.25/108.94 inference(rename_variables,[],[3423])).
% 109.25/108.94 cnf(13517,plain,
% 109.25/108.94 (~E(f318(f318(f142(x135171),x135172),x135173),x135173)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(13520,plain,
% 109.25/108.94 (E(f318(f318(f125(x135201),x135202),f104(x135201)),x135202)),
% 109.25/108.94 inference(rename_variables,[],[3423])).
% 109.25/108.94 cnf(13521,plain,
% 109.25/108.94 (~E(f318(f318(f142(x135211),x135212),x135213),x135213)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(13524,plain,
% 109.25/108.94 (E(f164(x135241,x135242,f104(x135241)),x135242)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(13525,plain,
% 109.25/108.94 (E(f318(f318(f166(x135251),x135252),f104(x135251)),f104(x135251))),
% 109.25/108.94 inference(rename_variables,[],[3438])).
% 109.25/108.94 cnf(13532,plain,
% 109.25/108.94 (~E(f318(f318(f142(x135321),x135322),x135323),x135323)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(13535,plain,
% 109.25/108.94 (E(f318(f301(x135351,x135351,f7(x135351)),x135352),x135352)),
% 109.25/108.94 inference(rename_variables,[],[3548])).
% 109.25/108.94 cnf(13538,plain,
% 109.25/108.94 (P1(f318(f318(f320(x135381),f318(x135382,x135383)),f318(f301(x135384,x135381,x135382),f233(f918(x135384,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(13541,plain,
% 109.25/108.94 (P1(f318(f318(f320(x135411),f318(x135412,x135413)),f318(f301(x135414,x135411,x135412),f233(f918(x135414,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(13546,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x135461),x135462),f179(f918(x135461,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13549,plain,
% 109.25/108.94 (P1(f318(f318(f320(f912(x135491)),f104(x135491)),f152(x135491,x135492)))),
% 109.25/108.94 inference(rename_variables,[],[3684])).
% 109.25/108.94 cnf(13552,plain,
% 109.25/108.94 (P1(f318(f318(f320(x135521),x135522),f233(f918(x135521,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13555,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x135551,a909)),x135552),x135552))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13558,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x135581,a909)),x135582),x135582))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13561,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x135611,a909)),x135612),f233(f918(x135611,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(13562,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x135621,a909)),x135622),x135622))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13565,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x135651,a909)),x135652),x135652))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13573,plain,
% 109.25/108.94 (P1(f318(f318(f320(x135731),f318(x135732,x135733)),f318(f301(x135734,x135731,x135732),f233(f918(x135734,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(13574,plain,
% 109.25/108.94 (P1(f318(f318(f320(x135741),f318(x135742,x135743)),f318(f301(x135744,x135741,x135742),f233(f918(x135744,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(13580,plain,
% 109.25/108.94 (E(f164(x135801,x135802,f104(x135801)),x135802)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(13583,plain,
% 109.25/108.94 (~E(f318(a103,x135831),x135831)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13586,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x135861),x135862),f179(f918(x135861,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13589,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x135891),x135892),f179(f918(x135891,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13592,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x135921),f912(x135921))),f318(f318(f243(f912(x135921),f912(x135921)),x135922),f104(x135921))),f136(x135921,x135923)))),
% 109.25/108.94 inference(rename_variables,[],[4697])).
% 109.25/108.94 cnf(13593,plain,
% 109.25/108.94 (~E(f318(a103,x135931),x135931)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13602,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x136021),x136022),f179(f918(x136021,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13605,plain,
% 109.25/108.94 (P1(f318(f318(f320(x136051),x136052),f233(f918(x136051,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13606,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x136061),x136061))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13609,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x136091,a909)),f179(f918(x136091,a909))),x136092))),
% 109.25/108.94 inference(rename_variables,[],[3926])).
% 109.25/108.94 cnf(13610,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x136101,a909)),x136102),x136102))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13613,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x136131),x136131))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13614,plain,
% 109.25/108.94 (P1(f318(f233(f918(x136141,a909)),x136142))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(13617,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x136171,a909)),x136172),x136172))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13620,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x136201,a909)),x136202),f233(f918(x136201,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(13623,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x136231,a909)),x136232),x136232))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13624,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x136241),x136242),f179(f918(x136241,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13627,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x136271,a909)),f318(f301(x136272,x136271,x136273),f318(f302(x136272,x136271,x136273),x136274))),x136274))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(13628,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x136281),x136282),f179(f918(x136281,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13631,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x136311,a909)),x136312),x136312))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13634,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x136341),x136341))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(13637,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x136371),x136372),f179(f918(x136371,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13640,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x136401),x136401))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(13643,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x136431),x136431))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13644,plain,
% 109.25/108.94 (P1(f318(f233(f918(x136441,a909)),x136442))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(13647,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x136471),x136471))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13648,plain,
% 109.25/108.94 (~E(f318(a103,x136481),x136481)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13652,plain,
% 109.25/108.94 (P1(f318(f318(f320(x136521),x136522),f233(f918(x136521,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13655,plain,
% 109.25/108.94 (E(f318(f318(f125(x136551),f318(f318(f142(x136551),x136552),x136553)),x136554),f318(f318(f142(x136551),x136552),f318(f318(f125(x136551),x136553),x136554)))),
% 109.25/108.94 inference(rename_variables,[],[3875])).
% 109.25/108.94 cnf(13658,plain,
% 109.25/108.94 (P1(f318(f55(x136581),f318(f163(x136581),x136582)))),
% 109.25/108.94 inference(rename_variables,[],[3530])).
% 109.25/108.94 cnf(13661,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x136611,a909)),x136612),x136612))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13662,plain,
% 109.25/108.94 (E(f318(f301(x136621,x136621,f7(x136621)),x136622),x136622)),
% 109.25/108.94 inference(rename_variables,[],[3548])).
% 109.25/108.94 cnf(13672,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x136721),x136721))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13673,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x136731),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(13676,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x136761),x136762),f179(f918(x136761,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13679,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x136791),x136792),f179(f918(x136791,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13680,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x136801),x136802),f179(f918(x136801,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13683,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x136831),x136831))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13686,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x136861),x136861))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(13689,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x136891),x136892),f179(f918(x136891,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13692,plain,
% 109.25/108.94 (P1(f318(f318(f320(x136921),x136922),f233(f918(x136921,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13693,plain,
% 109.25/108.94 (E(f318(f180(f912(x136931)),f160(x136931,x136932,x136933)),x136932)),
% 109.25/108.94 inference(rename_variables,[],[3558])).
% 109.25/108.94 cnf(13696,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x136961,a909)),x136962),f318(f318(f300(x136961),x136963),x136962)))),
% 109.25/108.94 inference(rename_variables,[],[3924])).
% 109.25/108.94 cnf(13699,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x136991),x136992),f179(f918(x136991,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13700,plain,
% 109.25/108.94 (P1(f318(f318(f320(f917(f912(x137001),f912(x137001))),f318(f318(f243(f912(x137001),f912(x137001)),f104(x137001)),f104(x137001))),f149(x137001,x137002)))),
% 109.25/108.94 inference(rename_variables,[],[4247])).
% 109.25/108.94 cnf(13704,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x137041,a909)),x137042),x137042))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13710,plain,
% 109.25/108.94 (P1(f318(f318(f320(x137101),x137102),f318(f318(f300(x137101),x137102),x137103)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(13711,plain,
% 109.25/108.94 (P1(f318(f318(f320(f917(x137111,x137111)),f318(f318(f243(x137111,x137111),x137112),x137112)),f298(x137111,x137113)))),
% 109.25/108.94 inference(rename_variables,[],[4112])).
% 109.25/108.94 cnf(13714,plain,
% 109.25/108.94 (P1(f318(f318(f320(x137141),f318(x137142,x137143)),f318(f301(x137144,x137141,x137142),f233(f918(x137144,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(13715,plain,
% 109.25/108.94 (P1(f318(f318(f320(f917(x137151,x137151)),f318(f318(f243(x137151,x137151),x137152),x137152)),f298(x137151,x137153)))),
% 109.25/108.94 inference(rename_variables,[],[4112])).
% 109.25/108.94 cnf(13718,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x137181,a909)),x137182),x137182))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(13721,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x137211),x137211))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13724,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x137241),x137241))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13727,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x137271),f912(x137271))),f318(f318(f243(f912(x137271),f912(x137271)),x137272),f104(x137271))),f148(x137271,x137273)))),
% 109.25/108.94 inference(rename_variables,[],[4699])).
% 109.25/108.94 cnf(13730,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x137301),x137302),f179(f918(x137301,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13731,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x137311),f912(x137311))),f318(f318(f243(f912(x137311),f912(x137311)),x137312),f104(x137311))),f138(x137311,x137313)))),
% 109.25/108.94 inference(rename_variables,[],[4698])).
% 109.25/108.94 cnf(13734,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x137341),x137342),f179(f918(x137341,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13735,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x137351),f912(x137351))),f318(f318(f243(f912(x137351),f912(x137351)),x137352),f104(x137351))),f136(x137351,x137353)))),
% 109.25/108.94 inference(rename_variables,[],[4697])).
% 109.25/108.94 cnf(13738,plain,
% 109.25/108.94 (P1(f318(f318(f320(x137381),x137382),f233(f918(x137381,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13742,plain,
% 109.25/108.94 (P1(f318(f318(f320(f917(x137421,x137421)),f318(f318(f243(x137421,x137421),x137422),x137422)),f318(f318(f174(f917(x137421,x137421),a909),f2(a911)),x137423)))),
% 109.25/108.94 inference(rename_variables,[],[4245])).
% 109.25/108.94 cnf(13743,plain,
% 109.25/108.94 (P1(f318(f318(f320(x137431),x137432),f233(f918(x137431,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13746,plain,
% 109.25/108.94 (P1(f318(f318(f320(x137461),x137462),f233(f918(x137461,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13751,plain,
% 109.25/108.94 (P1(f318(f318(f320(x137511),f318(x137512,x137513)),f318(f301(x137514,x137511,x137512),f233(f918(x137514,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(13752,plain,
% 109.25/108.94 (P1(f318(f318(f320(f917(x137521,x137521)),f318(f318(f243(x137521,x137521),x137522),x137522)),f298(x137521,x137523)))),
% 109.25/108.94 inference(rename_variables,[],[4112])).
% 109.25/108.94 cnf(13759,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x137591),x137592),f179(f918(x137591,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13762,plain,
% 109.25/108.94 (P1(f318(f318(f320(x137621),x137622),f233(f918(x137621,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13767,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x137671),x137671))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13770,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x137701),f912(x137701))),f318(f318(f243(f912(x137701),f912(x137701)),x137702),f104(x137701))),f148(x137701,x137703)))),
% 109.25/108.94 inference(rename_variables,[],[4699])).
% 109.25/108.94 cnf(13773,plain,
% 109.25/108.94 (P1(f318(f318(f320(x137731),x137732),f318(f318(f300(x137731),x137732),x137733)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(13776,plain,
% 109.25/108.94 (P1(f318(f318(f320(x137761),x137762),f318(f318(f300(x137761),x137762),x137763)))),
% 109.25/108.94 inference(rename_variables,[],[3797])).
% 109.25/108.94 cnf(13779,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x137791),x137792),f179(f918(x137791,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13780,plain,
% 109.25/108.94 (~P1(f318(f318(f320(f917(f912(x137801),f912(x137801))),f318(f318(f243(f912(x137801),f912(x137801)),x137802),f104(x137801))),f138(x137801,x137803)))),
% 109.25/108.94 inference(rename_variables,[],[4698])).
% 109.25/108.94 cnf(13790,plain,
% 109.25/108.94 (P43(f318(f301(a911,a1,f91(a1)),x137901))),
% 109.25/108.94 inference(rename_variables,[],[3700])).
% 109.25/108.94 cnf(13807,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x138071),x138071))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(13810,plain,
% 109.25/108.94 (~P1(f318(f318(f226(f918(x138101,a909)),x138102),f179(f918(x138101,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4685])).
% 109.25/108.94 cnf(13813,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x138131,a909)),f318(f301(x138132,x138131,x138133),f318(f302(x138132,x138131,x138133),x138134))),x138134))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(13814,plain,
% 109.25/108.94 (P43(f318(f301(a911,a1,f91(a1)),x138141))),
% 109.25/108.94 inference(rename_variables,[],[3700])).
% 109.25/108.94 cnf(13817,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x138171),x138171))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(13849,plain,
% 109.25/108.94 (P1(f318(f233(f918(x138491,a909)),x138492))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(13852,plain,
% 109.25/108.94 (P1(f318(f233(f918(x138521,a909)),x138522))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(13855,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a1),f318(f91(a1),x138551)),f2(a1)))),
% 109.25/108.94 inference(rename_variables,[],[4681])).
% 109.25/108.94 cnf(13856,plain,
% 109.25/108.94 (P1(f318(f233(f918(x138561,a909)),x138562))),
% 109.25/108.94 inference(rename_variables,[],[3552])).
% 109.25/108.94 cnf(13859,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a1),f318(f91(a1),x138591)),f2(a1)))),
% 109.25/108.94 inference(rename_variables,[],[4681])).
% 109.25/108.94 cnf(13868,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),f2(a1)),f318(f91(a1),x138681)))),
% 109.25/108.94 inference(rename_variables,[],[3591])).
% 109.25/108.94 cnf(13873,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f318(f318(f3(a911),x138731),x138732)),x138731))),
% 109.25/108.94 inference(rename_variables,[],[3903])).
% 109.25/108.94 cnf(13880,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x138801))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(13883,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f318(f318(f30(a911),x138831),x138832)),x138831))),
% 109.25/108.94 inference(rename_variables,[],[3904])).
% 109.25/108.94 cnf(13884,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x138841))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(13891,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x138911),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(13894,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f318(f180(f912(x138941)),f143(x138941,x138942))),f318(f180(f912(x138941)),x138942)))),
% 109.25/108.94 inference(rename_variables,[],[4024])).
% 109.25/108.94 cnf(13897,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x138971),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(13900,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x139001),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(13903,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x139031),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(13908,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x139081),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(13913,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f318(f180(f912(x139131)),f143(x139131,x139132))),f318(f180(f912(x139131)),x139132)))),
% 109.25/108.94 inference(rename_variables,[],[4024])).
% 109.25/108.94 cnf(13918,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x139181),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(13925,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x139251),x139251))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13928,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x139281),f318(a103,x139281)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(13932,plain,
% 109.25/108.94 (P1(f318(f318(f320(x139321),x139322),f233(f918(x139321,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13935,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x139351),f318(a103,x139351)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(13936,plain,
% 109.25/108.94 (~E(f318(a103,x139361),x139361)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(13943,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x139431),f318(a103,x139431)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(13944,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x139441),x139441))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13947,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x139471),x139471))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(13950,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x139501,a909)),f318(f301(x139502,x139501,x139503),f318(f302(x139502,x139501,x139503),x139504))),x139504))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(13958,plain,
% 109.25/108.94 (E(f318(f7(x139581),x139582),x139582)),
% 109.25/108.94 inference(rename_variables,[],[3327])).
% 109.25/108.94 cnf(13959,plain,
% 109.25/108.94 (P25(x139591,x139591,f7(x139591),x139592)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(13963,plain,
% 109.25/108.94 (P25(x139631,x139631,f7(x139631),x139632)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(13980,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x139801))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(13983,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x139831))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(13986,plain,
% 109.25/108.94 (P1(f318(f318(f320(x139861),x139862),f233(f918(x139861,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13987,plain,
% 109.25/108.94 (P1(f318(f318(f320(x139871),x139872),f233(f918(x139871,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(13988,plain,
% 109.25/108.94 (~E(f318(f318(f142(x139881),x139882),x139883),x139883)),
% 109.25/108.94 inference(rename_variables,[],[4647])).
% 109.25/108.94 cnf(13991,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x139911),x139912),f179(f918(x139911,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(13994,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x139941),f318(a103,x139941)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(13998,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x139981),x139981))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(13999,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x139991),x139991))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14000,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x140001),f318(a103,x140001)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(14003,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x140031))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(14004,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x140041))),
% 109.25/108.94 inference(rename_variables,[],[3511])).
% 109.25/108.94 cnf(14007,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x140071))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(14008,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x140081))),
% 109.25/108.94 inference(rename_variables,[],[3511])).
% 109.25/108.94 cnf(14011,plain,
% 109.25/108.94 (P1(f318(f318(f320(x140111),x140112),f233(f918(x140111,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(14012,plain,
% 109.25/108.94 (P1(f318(f318(f320(x140121),x140122),f233(f918(x140121,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(14015,plain,
% 109.25/108.94 (P1(f318(f318(f320(x140151),f318(x140152,x140153)),f318(f301(x140154,x140151,x140152),f233(f918(x140154,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(14016,plain,
% 109.25/108.94 (P1(f318(f318(f320(x140161),f318(x140162,x140163)),f318(f301(x140164,x140161,x140162),f233(f918(x140164,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(14019,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x140191),x140191))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14022,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x140221),x140222),f179(f918(x140221,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14025,plain,
% 109.25/108.94 (P1(f318(f55(x140251),f318(f163(x140251),x140252)))),
% 109.25/108.94 inference(rename_variables,[],[3530])).
% 109.25/108.94 cnf(14028,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x140281),x140282),f179(f918(x140281,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14031,plain,
% 109.25/108.94 (P1(f318(f55(x140311),f318(f163(x140311),x140312)))),
% 109.25/108.94 inference(rename_variables,[],[3530])).
% 109.25/108.94 cnf(14049,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x140491),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(14054,plain,
% 109.25/108.94 (P25(x140541,x140541,f7(x140541),x140542)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(14057,plain,
% 109.25/108.94 (P25(x140571,x140571,f7(x140571),x140572)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(14060,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x140601),x140601))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14063,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x140631),x140632),f179(f918(x140631,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14066,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x140661),f318(a103,x140661)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(14069,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x140691),x140691))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14072,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x140721),x140721))),
% 109.25/108.94 inference(rename_variables,[],[4667])).
% 109.25/108.94 cnf(14073,plain,
% 109.25/108.94 (P1(f318(f318(f226(a911),x140731),f318(a103,x140731)))),
% 109.25/108.94 inference(rename_variables,[],[3559])).
% 109.25/108.94 cnf(14076,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x140761),x140761))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14079,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x140791),x140791))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14082,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x140821),x140821))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14092,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x140921,a909)),x140922),x140922))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(14095,plain,
% 109.25/108.94 (E(f318(f318(f18(x140951,x140952),x140953),x140954),x140953)),
% 109.25/108.94 inference(rename_variables,[],[3482])).
% 109.25/108.94 cnf(14100,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x141001),x141002),f179(f918(x141001,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14104,plain,
% 109.25/108.94 (P1(f318(f318(f320(x141041),x141042),f233(f918(x141041,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(14132,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x141321,a909)),x141322),f233(f918(x141321,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3867])).
% 109.25/108.94 cnf(14135,plain,
% 109.25/108.94 (P1(f318(f55(a1),f294(a1,x141351,x141352)))),
% 109.25/108.94 inference(rename_variables,[],[3697])).
% 109.25/108.94 cnf(14138,plain,
% 109.25/108.94 (P1(f318(f55(a1),f294(a1,x141381,x141382)))),
% 109.25/108.94 inference(rename_variables,[],[3697])).
% 109.25/108.94 cnf(14141,plain,
% 109.25/108.94 (P1(f318(f55(a1),f294(a1,x141411,x141412)))),
% 109.25/108.94 inference(rename_variables,[],[3697])).
% 109.25/108.94 cnf(14144,plain,
% 109.25/108.94 (P1(f318(f55(a1),f294(a1,x141441,x141442)))),
% 109.25/108.94 inference(rename_variables,[],[3697])).
% 109.25/108.94 cnf(14147,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x141471,a909)),x141472),x141472))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(14148,plain,
% 109.25/108.94 (P25(x141481,x141481,f7(x141481),x141482)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(14151,plain,
% 109.25/108.94 (P1(f318(f318(f320(x141511),f318(x141512,x141513)),f318(f301(x141514,x141511,x141512),f233(f918(x141514,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(14181,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x141811),x141811))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(14186,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x141861),x141861))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14189,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x141891),x141891))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14197,plain,
% 109.25/108.94 (E(f164(x141971,x141972,f104(x141971)),x141972)),
% 109.25/108.94 inference(rename_variables,[],[3429])).
% 109.25/108.94 cnf(14200,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x142001),x142002),f179(f918(x142001,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14201,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x142011),x142011))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14204,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x142041),x142042),f179(f918(x142041,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14208,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x142081,a909)),x142082),x142082))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(14209,plain,
% 109.25/108.94 (~E(f318(a103,x142091),x142091)),
% 109.25/108.94 inference(rename_variables,[],[4635])).
% 109.25/108.94 cnf(14210,plain,
% 109.25/108.94 (P25(x142101,x142101,f7(x142101),x142102)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(14213,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x142131))),
% 109.25/108.94 inference(rename_variables,[],[3512])).
% 109.25/108.94 cnf(14214,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),f2(a911)),x142141))),
% 109.25/108.94 inference(rename_variables,[],[3511])).
% 109.25/108.94 cnf(14215,plain,
% 109.25/108.94 (P1(f318(f318(f225(a911),x142151),x142151))),
% 109.25/108.94 inference(rename_variables,[],[3491])).
% 109.25/108.94 cnf(14218,plain,
% 109.25/108.94 (E(f318(f318(f3(f918(x142181,a909)),f179(f918(x142181,a909))),x142182),f179(f918(x142181,a909)))),
% 109.25/108.94 inference(rename_variables,[],[3753])).
% 109.25/108.94 cnf(14219,plain,
% 109.25/108.94 (P1(f318(f55(x142191),f179(f918(x142191,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14222,plain,
% 109.25/108.94 (E(f318(f318(f3(f918(x142221,a909)),f179(f918(x142221,a909))),x142222),f179(f918(x142221,a909)))),
% 109.25/108.94 inference(rename_variables,[],[3753])).
% 109.25/108.94 cnf(14223,plain,
% 109.25/108.94 (P1(f318(f55(x142231),f179(f918(x142231,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14226,plain,
% 109.25/108.94 (E(f318(f318(f3(f918(x142261,a909)),f179(f918(x142261,a909))),x142262),f179(f918(x142261,a909)))),
% 109.25/108.94 inference(rename_variables,[],[3753])).
% 109.25/108.94 cnf(14227,plain,
% 109.25/108.94 (P1(f318(f55(x142271),f179(f918(x142271,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14230,plain,
% 109.25/108.94 (E(f318(f318(f3(f918(x142301,a909)),f179(f918(x142301,a909))),x142302),f179(f918(x142301,a909)))),
% 109.25/108.94 inference(rename_variables,[],[3753])).
% 109.25/108.94 cnf(14231,plain,
% 109.25/108.94 (P1(f318(f55(x142311),f179(f918(x142311,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14234,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x142341),x142342),f179(f918(x142341,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14238,plain,
% 109.25/108.94 (P1(f318(f318(f320(x142381),x142382),f233(f918(x142381,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(14239,plain,
% 109.25/108.94 (P1(f318(f318(f320(x142391),x142392),f233(f918(x142391,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3640])).
% 109.25/108.94 cnf(14242,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x142421,a909)),x142422),x142422))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(14261,plain,
% 109.25/108.94 (P1(f318(f55(a1),f294(a1,x142611,x142612)))),
% 109.25/108.94 inference(rename_variables,[],[3697])).
% 109.25/108.94 cnf(14264,plain,
% 109.25/108.94 (P1(f318(f55(a1),f294(a1,x142641,x142642)))),
% 109.25/108.94 inference(rename_variables,[],[3697])).
% 109.25/108.94 cnf(14267,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x142671),x142672),f179(f918(x142671,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14268,plain,
% 109.25/108.94 (P1(f318(f55(x142681),f179(f918(x142681,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14271,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x142711),x142712),f179(f918(x142711,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14272,plain,
% 109.25/108.94 (P1(f318(f55(x142721),f179(f918(x142721,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14275,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x142751),x142752),f179(f918(x142751,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14276,plain,
% 109.25/108.94 (P1(f318(f55(x142761),f179(f918(x142761,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14279,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x142791),x142792),f179(f918(x142791,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14280,plain,
% 109.25/108.94 (P1(f318(f55(x142801),f179(f918(x142801,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14283,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x142831),x142832),f179(f918(x142831,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14286,plain,
% 109.25/108.94 (E(f318(f318(f18(x142861,x142862),x142863),x142864),x142863)),
% 109.25/108.94 inference(rename_variables,[],[3482])).
% 109.25/108.94 cnf(14289,plain,
% 109.25/108.94 (E(f318(f318(f3(f918(x142891,a909)),f179(f918(x142891,a909))),x142892),f179(f918(x142891,a909)))),
% 109.25/108.94 inference(rename_variables,[],[3753])).
% 109.25/108.94 cnf(14290,plain,
% 109.25/108.94 (P1(f318(f55(x142901),f179(f918(x142901,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14294,plain,
% 109.25/108.94 (P1(f318(f55(x142941),f179(f918(x142941,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14297,plain,
% 109.25/108.94 (P25(x142971,x142971,f7(x142971),x142972)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(14300,plain,
% 109.25/108.94 (P25(x143001,x143001,f7(x143001),x143002)),
% 109.25/108.94 inference(rename_variables,[],[3723])).
% 109.25/108.94 cnf(14304,plain,
% 109.25/108.94 (P1(f318(f318(f320(x143041),f318(x143042,x143043)),f318(f301(x143044,x143041,x143042),f233(f918(x143044,a909)))))),
% 109.25/108.94 inference(rename_variables,[],[4076])).
% 109.25/108.94 cnf(14308,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x143081),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(14309,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x143091),x143091))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(14313,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x143131),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(14314,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x143141),x143141))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(14317,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x143171,a909)),f318(f301(x143172,x143171,x143173),f318(f302(x143172,x143171,x143173),x143174))),x143174))),
% 109.25/108.94 inference(rename_variables,[],[4337])).
% 109.25/108.94 cnf(14327,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x143271),x143272),f179(f918(x143271,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14328,plain,
% 109.25/108.94 (P1(f318(f55(x143281),f179(f918(x143281,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14331,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x143311),x143312),f179(f918(x143311,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14332,plain,
% 109.25/108.94 (P1(f318(f55(x143321),f179(f918(x143321,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14335,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x143351),x143352),f179(f918(x143351,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14336,plain,
% 109.25/108.94 (P1(f318(f55(x143361),f179(f918(x143361,a909))))),
% 109.25/108.94 inference(rename_variables,[],[3566])).
% 109.25/108.94 cnf(14343,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x143431,a909)),f179(f918(x143431,a909))),x143432))),
% 109.25/108.94 inference(rename_variables,[],[3926])).
% 109.25/108.94 cnf(14344,plain,
% 109.25/108.94 (~P1(f318(f318(f320(x143441),x143442),f179(f918(x143441,a909))))),
% 109.25/108.94 inference(rename_variables,[],[4678])).
% 109.25/108.94 cnf(14348,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x143481),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(14349,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x143491),x143491))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(14353,plain,
% 109.25/108.94 (~P1(f318(f318(f226(a911),x143531),f2(a911)))),
% 109.25/108.94 inference(rename_variables,[],[4670])).
% 109.25/108.94 cnf(14354,plain,
% 109.25/108.94 (P1(f318(f318(f225(a1),x143541),x143541))),
% 109.25/108.94 inference(rename_variables,[],[3492])).
% 109.25/108.94 cnf(14361,plain,
% 109.25/108.94 (P1(f318(f318(f225(f918(x143611,a909)),x143612),x143612))),
% 109.25/108.94 inference(rename_variables,[],[3781])).
% 109.25/108.94 cnf(14364,plain,
% 109.25/108.95 (P1(f318(f318(f225(f918(x143641,a909)),x143642),f233(f918(x143641,a909))))),
% 109.25/108.95 inference(rename_variables,[],[3867])).
% 109.25/108.95 cnf(14367,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),f2(a911)),x143671))),
% 109.25/108.95 inference(rename_variables,[],[3511])).
% 109.25/108.95 cnf(14368,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),f2(a911)),x143681))),
% 109.25/108.95 inference(rename_variables,[],[3512])).
% 109.25/108.95 cnf(14369,plain,
% 109.25/108.95 (~P1(f318(f318(f226(a911),x143691),f2(a911)))),
% 109.25/108.95 inference(rename_variables,[],[4670])).
% 109.25/108.95 cnf(14380,plain,
% 109.25/108.95 (~E(f318(f318(f142(x143801),x143802),x143803),x143803)),
% 109.25/108.95 inference(rename_variables,[],[4647])).
% 109.25/108.95 cnf(14383,plain,
% 109.25/108.95 (P1(f318(f318(f320(x143831),x143832),f233(f918(x143831,a909))))),
% 109.25/108.95 inference(rename_variables,[],[3640])).
% 109.25/108.95 cnf(14385,plain,
% 109.25/108.95 (E(f164(x143851,x143852,f104(x143851)),x143852)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14388,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),x143881),x143881))),
% 109.25/108.95 inference(rename_variables,[],[3491])).
% 109.25/108.95 cnf(14389,plain,
% 109.25/108.95 (E(f164(x143891,x143892,f104(x143891)),x143892)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14393,plain,
% 109.25/108.95 (P1(f318(f318(f320(x143931),x143932),f233(f918(x143931,a909))))),
% 109.25/108.95 inference(rename_variables,[],[3640])).
% 109.25/108.95 cnf(14398,plain,
% 109.25/108.95 (~E(f318(f318(f142(x143981),x143982),x143983),x143983)),
% 109.25/108.95 inference(rename_variables,[],[4647])).
% 109.25/108.95 cnf(14408,plain,
% 109.25/108.95 (~E(f318(a103,x144081),x144081)),
% 109.25/108.95 inference(rename_variables,[],[4635])).
% 109.25/108.95 cnf(14411,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),x144111),x144111))),
% 109.25/108.95 inference(rename_variables,[],[3491])).
% 109.25/108.95 cnf(14412,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),x144121),f318(a103,x144121)))),
% 109.25/108.95 inference(rename_variables,[],[3559])).
% 109.25/108.95 cnf(14413,plain,
% 109.25/108.95 (E(f164(x144131,x144132,f104(x144131)),x144132)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14414,plain,
% 109.25/108.95 (~E(f318(a103,x144141),x144141)),
% 109.25/108.95 inference(rename_variables,[],[4635])).
% 109.25/108.95 cnf(14417,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),x144171),f318(a103,x144171)))),
% 109.25/108.95 inference(rename_variables,[],[3559])).
% 109.25/108.95 cnf(14418,plain,
% 109.25/108.95 (E(f164(x144181,x144182,f104(x144181)),x144182)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14419,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),x144191),x144191))),
% 109.25/108.95 inference(rename_variables,[],[3491])).
% 109.25/108.95 cnf(14420,plain,
% 109.25/108.95 (~E(f318(a103,x144201),x144201)),
% 109.25/108.95 inference(rename_variables,[],[4635])).
% 109.25/108.95 cnf(14423,plain,
% 109.25/108.95 (P1(f318(f318(f225(f918(x144231,a909)),f179(f918(x144231,a909))),x144232))),
% 109.25/108.95 inference(rename_variables,[],[3926])).
% 109.25/108.95 cnf(14426,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),x144261),f318(a103,f318(f318(f73(a911),x144262),x144261))))),
% 109.25/108.95 inference(rename_variables,[],[3927])).
% 109.25/108.95 cnf(14427,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),x144271),f318(a103,x144271)))),
% 109.25/108.95 inference(rename_variables,[],[3559])).
% 109.25/108.95 cnf(14430,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),x144301),f318(a103,x144301)))),
% 109.25/108.95 inference(rename_variables,[],[3559])).
% 109.25/108.95 cnf(14431,plain,
% 109.25/108.95 (~E(f318(a103,x144311),x144311)),
% 109.25/108.95 inference(rename_variables,[],[4635])).
% 109.25/108.95 cnf(14434,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),x144341),f318(a103,x144341)))),
% 109.25/108.95 inference(rename_variables,[],[3559])).
% 109.25/108.95 cnf(14437,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),x144371),f318(a103,x144371)))),
% 109.25/108.95 inference(rename_variables,[],[3559])).
% 109.25/108.95 cnf(14438,plain,
% 109.25/108.95 (~E(f318(a103,x144381),x144381)),
% 109.25/108.95 inference(rename_variables,[],[4635])).
% 109.25/108.95 cnf(14441,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x144411),x144412),f179(f918(x144411,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14444,plain,
% 109.25/108.95 (~E(f318(a103,x144441),f2(a911))),
% 109.25/108.95 inference(rename_variables,[],[4637])).
% 109.25/108.95 cnf(14447,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),f2(a911)),x144471))),
% 109.25/108.95 inference(rename_variables,[],[3512])).
% 109.25/108.95 cnf(14451,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),f2(a911)),x144511))),
% 109.25/108.95 inference(rename_variables,[],[3512])).
% 109.25/108.95 cnf(14452,plain,
% 109.25/108.95 (E(f164(x144521,x144522,f104(x144521)),x144522)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14455,plain,
% 109.25/108.95 (P1(f318(f318(f225(f918(x144551,a909)),f318(f301(x144552,x144551,x144553),f318(f302(x144552,x144551,x144553),x144554))),x144554))),
% 109.25/108.95 inference(rename_variables,[],[4337])).
% 109.25/108.95 cnf(14456,plain,
% 109.25/108.95 (P25(x144561,x144561,f7(x144561),x144562)),
% 109.25/108.95 inference(rename_variables,[],[3723])).
% 109.25/108.95 cnf(14459,plain,
% 109.25/108.95 (P1(f318(f318(f278(a911),f318(a103,f2(a911))),x144591))),
% 109.25/108.95 inference(rename_variables,[],[3642])).
% 109.25/108.95 cnf(14460,plain,
% 109.25/108.95 (E(f164(x144601,x144602,f104(x144601)),x144602)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14461,plain,
% 109.25/108.95 (~E(f318(a103,x144611),x144611)),
% 109.25/108.95 inference(rename_variables,[],[4635])).
% 109.25/108.95 cnf(14464,plain,
% 109.25/108.95 (P1(f318(f318(f278(a911),x144641),x144641))),
% 109.25/108.95 inference(rename_variables,[],[3493])).
% 109.25/108.95 cnf(14466,plain,
% 109.25/108.95 (~E(f318(a103,x144661),x144661)),
% 109.25/108.95 inference(rename_variables,[],[4635])).
% 109.25/108.95 cnf(14469,plain,
% 109.25/108.95 (P1(f318(f318(f225(f918(x144691,a909)),f179(f918(x144691,a909))),x144692))),
% 109.25/108.95 inference(rename_variables,[],[3926])).
% 109.25/108.95 cnf(14470,plain,
% 109.25/108.95 (E(f318(f318(f18(x144701,x144702),x144703),x144704),x144703)),
% 109.25/108.95 inference(rename_variables,[],[3482])).
% 109.25/108.95 cnf(14473,plain,
% 109.25/108.95 (P1(f318(f318(f225(f918(x144731,a909)),f318(f301(x144732,x144731,x144733),f318(f302(x144732,x144731,x144733),x144734))),x144734))),
% 109.25/108.95 inference(rename_variables,[],[4337])).
% 109.25/108.95 cnf(14474,plain,
% 109.25/108.95 (E(f318(f318(f18(x144741,x144742),x144743),x144744),x144743)),
% 109.25/108.95 inference(rename_variables,[],[3482])).
% 109.25/108.95 cnf(14477,plain,
% 109.25/108.95 (P1(f318(f318(f225(f918(x144771,a909)),f179(f918(x144771,a909))),x144772))),
% 109.25/108.95 inference(rename_variables,[],[3926])).
% 109.25/108.95 cnf(14478,plain,
% 109.25/108.95 (E(f318(f318(f18(x144781,x144782),x144783),x144784),x144783)),
% 109.25/108.95 inference(rename_variables,[],[3482])).
% 109.25/108.95 cnf(14481,plain,
% 109.25/108.95 (P1(f318(f318(f225(f918(x144811,a909)),f318(f301(x144812,x144811,x144813),f318(f302(x144812,x144811,x144813),x144814))),x144814))),
% 109.25/108.95 inference(rename_variables,[],[4337])).
% 109.25/108.95 cnf(14482,plain,
% 109.25/108.95 (E(f318(f318(f18(x144821,x144822),x144823),x144824),x144823)),
% 109.25/108.95 inference(rename_variables,[],[3482])).
% 109.25/108.95 cnf(14485,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),f2(a911)),x144851))),
% 109.25/108.95 inference(rename_variables,[],[3512])).
% 109.25/108.95 cnf(14489,plain,
% 109.25/108.95 (E(f164(x144891,x144892,f104(x144891)),x144892)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14494,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),f2(a911)),x144941))),
% 109.25/108.95 inference(rename_variables,[],[3512])).
% 109.25/108.95 cnf(14497,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x144971),x144972),f179(f918(x144971,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14498,plain,
% 109.25/108.95 (E(f164(x144981,x144982,f104(x144981)),x144982)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14499,plain,
% 109.25/108.95 (P25(x144991,x144991,f7(x144991),x144992)),
% 109.25/108.95 inference(rename_variables,[],[3723])).
% 109.25/108.95 cnf(14502,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x145021),x145022),f179(f918(x145021,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14503,plain,
% 109.25/108.95 (E(f164(x145031,x145032,f104(x145031)),x145032)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14504,plain,
% 109.25/108.95 (P25(x145041,x145041,f7(x145041),x145042)),
% 109.25/108.95 inference(rename_variables,[],[3723])).
% 109.25/108.95 cnf(14515,plain,
% 109.25/108.95 (P1(f318(f55(a1),f294(a1,x145151,x145152)))),
% 109.25/108.95 inference(rename_variables,[],[3697])).
% 109.25/108.95 cnf(14518,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x145181),x145182),f179(f918(x145181,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14519,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x145191),x145192),f179(f918(x145191,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14522,plain,
% 109.25/108.95 (P1(f318(f55(x145221),f179(f918(x145221,a909))))),
% 109.25/108.95 inference(rename_variables,[],[3566])).
% 109.25/108.95 cnf(14523,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x145231),x145232),f179(f918(x145231,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14527,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x145271),x145272),f179(f918(x145271,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14528,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x145281),x145282),f179(f918(x145281,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14529,plain,
% 109.25/108.95 (P1(f318(f55(x145291),f179(f918(x145291,a909))))),
% 109.25/108.95 inference(rename_variables,[],[3566])).
% 109.25/108.95 cnf(14538,plain,
% 109.25/108.95 (P1(f318(f318(f320(x145381),x145382),f233(f918(x145381,a909))))),
% 109.25/108.95 inference(rename_variables,[],[3640])).
% 109.25/108.95 cnf(14539,plain,
% 109.25/108.95 (P1(f318(f318(f320(x145391),x145392),f233(f918(x145391,a909))))),
% 109.25/108.95 inference(rename_variables,[],[3640])).
% 109.25/108.95 cnf(14542,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x145421),x145422),f179(f918(x145421,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14546,plain,
% 109.25/108.95 (P1(f318(f55(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),x145461)),f318(f318(f9(a911,a911,a909),f226(a911)),x145462)))))),
% 109.25/108.95 inference(rename_variables,[],[4499])).
% 109.25/108.95 cnf(14547,plain,
% 109.25/108.95 (E(f318(f318(f224(a911),f318(a103,x145471)),f318(a103,x145472)),f318(a103,f318(f318(f224(a911),x145471),x145472)))),
% 109.25/108.95 inference(rename_variables,[],[3660])).
% 109.25/108.95 cnf(14550,plain,
% 109.25/108.95 (P1(f318(f55(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),x145501)),f318(f318(f9(a911,a911,a909),f226(a911)),x145502)))))),
% 109.25/108.95 inference(rename_variables,[],[4499])).
% 109.25/108.95 cnf(14551,plain,
% 109.25/108.95 (E(f318(f318(f223(a911),f318(a103,x145511)),f318(a103,x145512)),f318(a103,f318(f318(f223(a911),x145511),x145512)))),
% 109.25/108.95 inference(rename_variables,[],[3659])).
% 109.25/108.95 cnf(14554,plain,
% 109.25/108.95 (P1(f318(f318(f320(x145541),x145542),f233(f918(x145541,a909))))),
% 109.25/108.95 inference(rename_variables,[],[3640])).
% 109.25/108.95 cnf(14555,plain,
% 109.25/108.95 (P1(f318(f318(f320(x145551),x145552),f233(f918(x145551,a909))))),
% 109.25/108.95 inference(rename_variables,[],[3640])).
% 109.25/108.95 cnf(14558,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x145581),x145582),f179(f918(x145581,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14559,plain,
% 109.25/108.95 (~P1(f318(f318(f320(x145591),x145592),f179(f918(x145591,a909))))),
% 109.25/108.95 inference(rename_variables,[],[4678])).
% 109.25/108.95 cnf(14562,plain,
% 109.25/108.95 (P1(f318(f55(a911),f318(f253(a911),f318(f318(f20(a911,a909,a909),f318(f318(f10(a909,f918(a909,a909),a911),a316),x145621)),f318(f318(f9(a911,a911,a909),f226(a911)),x145622)))))),
% 109.25/108.95 inference(rename_variables,[],[4499])).
% 109.25/108.95 cnf(14575,plain,
% 109.25/108.95 (E(f164(x145751,x145752,f104(x145751)),x145752)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14578,plain,
% 109.25/108.95 (E(f164(x145781,x145782,f104(x145781)),x145782)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14585,plain,
% 109.25/108.95 (E(f164(x145851,x145852,f104(x145851)),x145852)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14588,plain,
% 109.25/108.95 (E(f164(x145881,x145882,f104(x145881)),x145882)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14594,plain,
% 109.25/108.95 (E(f164(x145941,x145942,f104(x145941)),x145942)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14597,plain,
% 109.25/108.95 (E(f164(x145971,x145972,f104(x145971)),x145972)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14600,plain,
% 109.25/108.95 (E(f164(x146001,x146002,f104(x146001)),x146002)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14603,plain,
% 109.25/108.95 (E(f164(x146031,x146032,f104(x146031)),x146032)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14606,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),x146061),f318(a103,x146061)))),
% 109.25/108.95 inference(rename_variables,[],[3559])).
% 109.25/108.95 cnf(14607,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),f2(a911)),x146071))),
% 109.25/108.95 inference(rename_variables,[],[3512])).
% 109.25/108.95 cnf(14608,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),f2(a911)),f318(a103,x146081)))),
% 109.25/108.95 inference(rename_variables,[],[3571])).
% 109.25/108.95 cnf(14609,plain,
% 109.25/108.95 (E(f164(x146091,x146092,f104(x146091)),x146092)),
% 109.25/108.95 inference(rename_variables,[],[3429])).
% 109.25/108.95 cnf(14613,plain,
% 109.25/108.95 (P1(f318(f318(f226(a911),x146131),f318(a103,f318(f318(f73(a911),x146132),x146131))))),
% 109.25/108.95 inference(rename_variables,[],[3927])).
% 109.25/108.95 cnf(14614,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),f2(a911)),x146141))),
% 109.25/108.95 inference(rename_variables,[],[3512])).
% 109.25/108.95 cnf(14621,plain,
% 109.25/108.95 (P1(f318(f318(f225(a911),f2(a911)),x146211))),
% 109.25/108.95 inference(rename_variables,[],[3512])).
% 109.25/108.95 cnf(14701,plain,
% 109.25/108.95 ($false),
% 109.25/108.95 inference(scs_inference,[],[3535,3305,4631,3692,4646,3101,3102,3103,3105,3106,3107,3109,3110,3111,3112,3113,3114,3115,3116,3117,3118,3121,3122,3124,3126,3127,3128,3129,3130,3133,3134,3138,3142,3144,3148,3150,3151,3152,3153,3155,3157,3160,3163,3165,3166,3168,3169,3172,3174,3175,3177,3178,3180,3181,3185,3186,3187,3189,3190,3192,3195,3197,3198,3199,3200,3201,3202,3204,3206,3209,3212,3214,3215,3217,3218,3220,3221,3223,3224,3226,3228,3231,3233,3234,3236,3238,3240,3242,3245,3247,3248,3249,3250,3253,3256,3258,3259,3260,3261,3263,3264,3265,3266,3269,3272,3274,3282,3283,3284,3286,3302,3383,4633,3097,3098,3294,3288,3292,4634,4145,4148,3385,4644,3782,3796,3759,3315,3309,3368,4660,4663,4664,3468,3471,3472,4661,4662,3469,3470,4643,3631,3331,3332,3494,4669,4674,4673,3375,3463,3382,3519,3518,3520,3814,3602,3995,3584,3610,4266,4514,4588,4512,4135,13373,13376,3723,12701,12981,13151,13154,13198,13269,13298,13369,13457,13959,13963,14054,14057,14148,14210,14297,14300,14456,14499,14504,3724,3461,3462,3428,4654,4655,3361,3362,3363,3364,3365,4635,10469,10476,10479,10498,10509,10512,10525,10777,10832,11127,11130,11164,11335,11338,11443,11523,11745,12125,12138,12141,12188,12296,12446,12456,12501,12728,12732,12736,12821,12824,12996,13000,13012,13022,13034,13057,13229,13233,13391,13503,13507,13583,13593,13648,13936,14209,14408,14414,14420,14431,14438,14461,14466,3360,3732,12764,4403,4404,3465,3783,3510,4637,10528,10761,11052,11643,12331,14444,3429,10690,10826,10829,11329,11332,11742,12032,12064,12083,12100,12123,12196,12199,12299,12304,12308,12490,12704,13301,13335,13341,13347,13350,13386,13524,13580,14197,14385,14389,14413,14418,14452,14460,14489,14498,14503,14575,14578,14585,14588,14594,14597,14600,14603,14609,3430,10693,13338,3327,13958,3328,10663,4305,3324,3740,3547,3940,3545,3544,3548,11649,11739,13058,13297,13535,13662,3550,4647,10451,10460,10780,10787,11133,12207,12210,12214,12449,12504,13517,13521,13532,13988,14380,14398,3482,13288,13291,14095,14286,14470,14474,14478,14482,3374,12719,3595,3587,3378,3379,3407,3475,3597,3694,12202,3695,3697,12973,14135,14138,14141,14144,14261,14264,14515,3491,10533,10567,10598,10723,10741,10808,10992,11252,11260,11269,11286,11399,11405,11571,11621,11660,11811,11900,12178,12283,12307,12353,12385,12484,12735,12782,12788,12794,12800,12853,12859,12865,12871,13040,13204,13379,13428,13445,13606,13613,13647,13683,13925,13947,13999,14019,14060,14069,14076,14079,14082,14186,14189,14201,14215,14388,14411,14419,3492,10882,10919,11367,12322,12388,12487,12785,12791,12797,12803,12856,12862,12868,12874,12883,13634,13640,13686,13807,13817,14181,14309,14314,14349,14354,3493,12770,12773,14464,4667,10495,10613,10754,10766,10813,10821,10909,10916,11257,11386,11609,11736,11796,11881,12238,12265,12286,12289,12325,12345,12348,12360,12573,12657,12710,12716,12727,12731,12748,12753,12835,12840,12845,12848,12888,12894,12900,12903,13033,13201,13228,13232,13266,13272,13275,13329,13332,13431,13448,13643,13672,13721,13724,13767,13944,13998,14072,4668,3552,10941,10944,10953,11412,11419,11820,13021,13614,13644,13849,13852,13856,3700,13790,13814,3423,13516,13520,3558,13179,13693,3388,3389,3391,12602,3351,4037,3422,3447,11315,4650,11646,3400,3386,3387,11448,11665,3828,3559,10559,10589,10628,10704,10726,10733,10736,10980,11249,11356,11478,12377,12461,12517,12711,12776,12779,13091,13380,13425,13928,13935,13943,13994,14000,14066,14073,14412,14417,14427,14430,14434,14437,14606,4670,11297,11508,11602,12682,12685,12987,13090,13265,13673,13891,13897,13900,13903,13908,13918,14049,14308,14313,14348,14353,14369,3530,13280,13283,13499,13658,14025,14031,4675,10835,10840,11017,11023,11300,11436,11516,11612,11670,11721,12495,3566,12423,13122,13408,14219,14223,14227,14231,14268,14272,14276,14280,14290,14294,14328,14332,14336,14522,14529,3512,10879,10947,12269,13011,13208,13421,13880,13884,13980,13983,14003,14007,14213,14368,14447,14451,14485,14494,14607,14614,14621,3938,10486,12547,12616,4676,10660,10860,10863,10968,10973,12181,12455,12593,12906,12911,12916,12919,12986,13451,3511,14004,14008,14214,14367,4383,4687,11020,11026,3781,11475,11615,11638,11779,11808,11835,11838,11932,11954,12698,13065,13133,13394,13476,13479,13555,13558,13562,13565,13610,13617,13623,13631,13661,13704,13718,14092,14147,14208,14242,14361,3438,13525,3370,4677,10868,11462,11903,3457,3808,3426,3408,3668,3536,12213,3829,3571,12548,12576,12579,12582,12585,12707,14608,3807,3640,10522,10554,10564,11150,11156,11370,11379,11537,11540,11543,11582,11585,11677,11700,11706,11752,11793,11799,11802,11846,11872,11875,11878,11889,12129,12330,12978,12995,13083,13142,13173,13186,13192,13213,13219,13257,13372,13399,13436,13454,13486,13552,13605,13652,13692,13738,13743,13746,13762,13932,13987,14012,14104,14239,14383,14393,14538,14554,14238,14539,14555,13986,14011,4678,10687,11159,11171,11344,11481,11505,11511,11548,11554,11560,11618,11630,11652,11655,11682,11690,11757,11772,11782,11805,11814,11823,11829,11832,11841,11856,11859,11862,11886,11892,11914,11917,11920,11923,11937,11957,11960,132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% 109.25/108.95 ['proof']).
% 109.25/108.95 % SZS output end Proof
% 109.25/108.95 % Total time :105.360000s
%------------------------------------------------------------------------------