TSTP Solution File: SWW311+1 by CSE---1.7
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%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : SWW311+1 : TPTP v8.2.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 18:07:07 EDT 2024
% Result : Theorem 22.40s 22.28s
% Output : CNFRefutation 22.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW311+1 : TPTP v8.2.0. Released v5.2.0.
% 0.03/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33 % Computer : n024.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 07:45:23 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.19/0.54 start to proof:theBenchmark
% 22.04/22.14 %-------------------------------------------
% 22.04/22.14 % File :CSE---1.7
% 22.04/22.14 % Problem :theBenchmark
% 22.04/22.14 % Transform :cnf
% 22.04/22.14 % Format :tptp:raw
% 22.04/22.14 % Command :java -jar mcs_scs.jar %d %s
% 22.04/22.14
% 22.04/22.14 % Result :Theorem 8.130000s
% 22.04/22.14 % Output :CNFRefutation 8.130000s
% 22.04/22.14 %-------------------------------------------
% 22.04/22.14 %------------------------------------------------------------------------------
% 22.04/22.14 % File : SWW311+1 : TPTP v8.2.0. Released v5.2.0.
% 22.04/22.14 % Domain : Software Verification
% 22.04/22.14 % Problem : Hoare's Logic with Procedures 434956, 5000 axioms selected
% 22.04/22.14 % Version : Especial.
% 22.04/22.14 % English :
% 22.04/22.14
% 22.04/22.14 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 22.04/22.14 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 22.04/22.14 % Source : [Bla11]
% 22.04/22.14 % Names : hoare_434956.5000.p [Bla11]
% 22.04/22.14
% 22.04/22.14 % Status : Theorem
% 22.04/22.14 % Rating : 0.47 v8.2.0, 0.44 v8.1.0, 0.53 v7.4.0, 0.67 v7.3.0, 0.62 v7.2.0, 0.59 v7.1.0, 0.65 v7.0.0, 0.67 v6.4.0, 0.62 v6.3.0, 0.67 v6.2.0, 0.80 v6.1.0, 0.83 v5.5.0, 0.78 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0
% 22.04/22.14 % Syntax : Number of formulae : 5223 (1633 unt; 0 def)
% 22.04/22.14 % Number of atoms : 12848 (4402 equ)
% 22.04/22.14 % Maximal formula atoms : 13 ( 2 avg)
% 22.04/22.15 % Number of connectives : 8615 ( 990 ~; 147 |; 732 &)
% 22.04/22.15 % ( 889 <=>;5857 =>; 0 <=; 0 <~>)
% 22.04/22.15 % Maximal formula depth : 22 ( 6 avg)
% 22.04/22.15 % Maximal term depth : 19 ( 2 avg)
% 22.04/22.15 % Number of predicates : 148 ( 147 usr; 0 prp; 1-6 aty)
% 22.04/22.15 % Number of functors : 375 ( 375 usr; 46 con; 0-7 aty)
% 22.04/22.15 % Number of variables : 16614 (16461 !; 153 ?)
% 22.04/22.15 % SPC : FOF_THM_RFO_SEQ
% 22.04/22.15
% 22.04/22.15 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 22.04/22.15 % 2011-03-01 11:40:13
% 22.04/22.15 %------------------------------------------------------------------------------
% 22.04/22.15 %----Relevant facts (4985)
% 22.04/22.15 fof(fact_ext,axiom,
% 22.04/22.15 ! [V_g_2,V_f_2] :
% 22.04/22.15 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x)
% 22.04/22.15 => V_f_2 = V_g_2 ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_asm,axiom,
% 22.04/22.15 ! [V_G_2,V_tsa_2,T_b] :
% 22.04/22.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_tsa_2),V_G_2))
% 22.04/22.15 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_weaken,axiom,
% 22.04/22.15 ! [V_tsa_2,V_ts_H_2,V_G_2,T_b] :
% 22.04/22.15 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_ts_H_2)
% 22.04/22.15 => ( 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))
% 22.04/22.15 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_cut,axiom,
% 22.04/22.15 ! [V_G_2,V_tsa_2,V_G_Ha_2,T_b] :
% 22.04/22.15 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_Ha_2,V_tsa_2)
% 22.04/22.15 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_G_Ha_2)
% 22.04/22.15 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_equalityI,axiom,
% 22.04/22.15 ! [V_B_2,V_A_2,T_b] :
% 22.04/22.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.04/22.15 => V_A_2 = V_B_2 ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_order__refl,axiom,
% 22.04/22.15 ! [V_x,T_a] :
% 22.04/22.15 ( class_Orderings_Opreorder(T_a)
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_le__fun__def,axiom,
% 22.04/22.15 ! [V_g_2,V_f_2,T_b,T_c] :
% 22.04/22.15 ( class_Orderings_Oord(T_c)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 22.04/22.15 <=> ! [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))) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_le__funD,axiom,
% 22.04/22.15 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 22.04/22.15 ( class_Orderings_Oord(T_c)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 22.04/22.15 => 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))) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_le__funE,axiom,
% 22.04/22.15 ! [V_x_2,V_g_2,V_f_2,T_b,T_c] :
% 22.04/22.15 ( class_Orderings_Oord(T_c)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 22.04/22.15 => 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))) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_subset__refl,axiom,
% 22.04/22.15 ! [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)) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_set__eq__subset,axiom,
% 22.04/22.15 ! [T_b,V_B_2,V_A_2] :
% 22.04/22.15 ( V_A_2 = V_B_2
% 22.04/22.15 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.04/22.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_rev__predicate1D,axiom,
% 22.04/22.15 ! [V_Q_2,T_b,V_x_2,V_P_2] :
% 22.04/22.15 ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 22.04/22.15 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_equalityD1,axiom,
% 22.04/22.15 ! [T_b,V_B_2,V_A_2] :
% 22.04/22.15 ( V_A_2 = V_B_2
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_equalityD2,axiom,
% 22.04/22.15 ! [T_b,V_B_2,V_A_2] :
% 22.04/22.15 ( V_A_2 = V_B_2
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_predicate1D,axiom,
% 22.04/22.15 ! [V_x_2,V_Q_2,V_P_2,T_b] :
% 22.04/22.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_P_2),V_Q_2))
% 22.04/22.15 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.04/22.15 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_subset__trans,axiom,
% 22.04/22.15 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 22.04/22.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_linorder__le__cases,axiom,
% 22.04/22.15 ! [V_y,V_x,T_a] :
% 22.04/22.15 ( class_Orderings_Olinorder(T_a)
% 22.04/22.15 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_xt1_I6_J,axiom,
% 22.04/22.15 ! [V_z,V_x,V_y,T_a] :
% 22.04/22.15 ( class_Orderings_Oorder(T_a)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_xt1_I5_J,axiom,
% 22.04/22.15 ! [V_x,V_y,T_a] :
% 22.04/22.15 ( class_Orderings_Oorder(T_a)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.04/22.15 => V_x = V_y ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_order__trans,axiom,
% 22.04/22.15 ! [V_z,V_y,V_x,T_a] :
% 22.04/22.15 ( class_Orderings_Opreorder(T_a)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_order__antisym,axiom,
% 22.04/22.15 ! [V_y,V_x,T_a] :
% 22.04/22.15 ( class_Orderings_Oorder(T_a)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.04/22.15 => V_x = V_y ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_xt1_I4_J,axiom,
% 22.04/22.15 ! [V_c,V_a,V_b,T_a] :
% 22.04/22.15 ( class_Orderings_Oorder(T_a)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 22.04/22.15 => ( V_b = V_c
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_ord__le__eq__trans,axiom,
% 22.04/22.15 ! [V_c,V_b,V_a,T_a] :
% 22.04/22.15 ( class_Orderings_Oord(T_a)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.04/22.15 => ( V_b = V_c
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_xt1_I3_J,axiom,
% 22.04/22.15 ! [V_c,V_b,V_a,T_a] :
% 22.04/22.15 ( class_Orderings_Oorder(T_a)
% 22.04/22.15 => ( V_a = V_b
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b))
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_ord__eq__le__trans,axiom,
% 22.04/22.15 ! [V_c,V_b,V_a,T_a] :
% 22.04/22.15 ( class_Orderings_Oord(T_a)
% 22.04/22.15 => ( V_a = V_b
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_order__antisym__conv,axiom,
% 22.04/22.15 ! [V_x_2,V_y_2,T_b] :
% 22.04/22.15 ( class_Orderings_Oorder(T_b)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2))
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.04/22.15 <=> V_x_2 = V_y_2 ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_order__eq__refl,axiom,
% 22.04/22.15 ! [V_y,V_x,T_a] :
% 22.04/22.15 ( class_Orderings_Opreorder(T_a)
% 22.04/22.15 => ( V_x = V_y
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_order__eq__iff,axiom,
% 22.04/22.15 ! [V_y_2,V_x_2,T_b] :
% 22.04/22.15 ( class_Orderings_Oorder(T_b)
% 22.04/22.15 => ( V_x_2 = V_y_2
% 22.04/22.15 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.04/22.15 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_linorder__linear,axiom,
% 22.04/22.15 ! [V_y,V_x,T_a] :
% 22.04/22.15 ( class_Orderings_Olinorder(T_a)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.04/22.15 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_equalityE,axiom,
% 22.04/22.15 ! [T_b,V_B_2,V_A_2] :
% 22.04/22.15 ( V_A_2 = V_B_2
% 22.04/22.15 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.04/22.15 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_Powp__mono,axiom,
% 22.04/22.15 ! [V_B_2,V_A_2,T_b] :
% 22.04/22.15 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.04/22.15 => 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))) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_le__funI,axiom,
% 22.04/22.15 ! [T_b,V_g_2,V_f_2,T_c] :
% 22.04/22.15 ( class_Orderings_Oord(T_c)
% 22.04/22.15 => ( ! [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)))
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_strict__mono__less__eq,axiom,
% 22.04/22.15 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 22.04/22.15 ( ( class_Orderings_Oorder(T_c)
% 22.04/22.15 & class_Orderings_Olinorder(T_b) )
% 22.04/22.15 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 22.04/22.15 => ( 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)))
% 22.04/22.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_greaterThan__subset__iff,axiom,
% 22.04/22.15 ! [V_y_2,V_x_2,T_b] :
% 22.04/22.15 ( class_Orderings_Olinorder(T_b)
% 22.04/22.15 => ( 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)))
% 22.04/22.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_lessThan__subset__iff,axiom,
% 22.04/22.15 ! [V_y_2,V_x_2,T_b] :
% 22.04/22.15 ( class_Orderings_Olinorder(T_b)
% 22.04/22.15 => ( 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)))
% 22.04/22.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_atLeast__subset__iff,axiom,
% 22.04/22.15 ! [V_y_2,V_x_2,T_b] :
% 22.04/22.15 ( class_Orderings_Oorder(T_b)
% 22.04/22.15 => ( 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)))
% 22.04/22.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_atMost__subset__iff,axiom,
% 22.04/22.15 ! [V_y_2,V_x_2,T_b] :
% 22.04/22.15 ( class_Orderings_Oorder(T_b)
% 22.04/22.15 => ( 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)))
% 22.04/22.15 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_SUP__subset,axiom,
% 22.04/22.15 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 22.04/22.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.04/22.15 => 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))) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_INF__subset,axiom,
% 22.04/22.15 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 22.04/22.15 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.04/22.15 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.04/22.15 => 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))) ) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_top__greatest,axiom,
% 22.04/22.15 ! [V_x,T_a] :
% 22.04/22.15 ( class_Orderings_Otop(T_a)
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_bot__least,axiom,
% 22.04/22.15 ! [V_x,T_a] :
% 22.04/22.15 ( class_Orderings_Obot(T_a)
% 22.04/22.15 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_empty__subsetI,axiom,
% 22.04/22.15 ! [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)) ).
% 22.04/22.15
% 22.04/22.15 fof(fact_UNIV__not__empty,axiom,
% 22.04/22.15 ! [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)) ).
% 22.04/22.15
% 22.04/22.16 fof(fact_bot__apply,axiom,
% 22.04/22.16 ! [V_x_2,T_c,T_b] :
% 22.04/22.16 ( class_Orderings_Obot(T_b)
% 22.04/22.16 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_top__apply,axiom,
% 22.04/22.16 ! [V_x_2,T_c,T_b] :
% 22.04/22.16 ( class_Orderings_Otop(T_b)
% 22.04/22.16 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Otop__class_Otop(T_b) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_greaterThan__eq__iff,axiom,
% 22.04/22.16 ! [V_y_2,V_x_2,T_b] :
% 22.04/22.16 ( class_Orderings_Olinorder(T_b)
% 22.04/22.16 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
% 22.04/22.16 <=> V_x_2 = V_y_2 ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_lessThan__eq__iff,axiom,
% 22.04/22.16 ! [V_y_2,V_x_2,T_b] :
% 22.04/22.16 ( class_Orderings_Olinorder(T_b)
% 22.04/22.16 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_y_2)
% 22.04/22.16 <=> V_x_2 = V_y_2 ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_atLeast__eq__iff,axiom,
% 22.04/22.16 ! [V_y_2,V_x_2,T_b] :
% 22.04/22.16 ( class_Orderings_Olinorder(T_b)
% 22.04/22.16 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_y_2)
% 22.04/22.16 <=> V_x_2 = V_y_2 ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_atMost__eq__iff,axiom,
% 22.04/22.16 ! [V_y_2,V_x_2,T_b] :
% 22.04/22.16 ( class_Orderings_Olinorder(T_b)
% 22.04/22.16 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_y_2)
% 22.04/22.16 <=> V_x_2 = V_y_2 ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_strict__mono__eq,axiom,
% 22.04/22.16 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 22.04/22.16 ( ( class_Orderings_Oorder(T_c)
% 22.04/22.16 & class_Orderings_Olinorder(T_b) )
% 22.04/22.16 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 22.04/22.16 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 22.04/22.16 <=> V_x_2 = V_y_2 ) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_subset__UNIV,axiom,
% 22.04/22.16 ! [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)))) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_subset__empty,axiom,
% 22.04/22.16 ! [V_A_2,T_b] :
% 22.04/22.16 ( 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))))
% 22.04/22.16 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_empty,axiom,
% 22.04/22.16 ! [V_G_2,T_b] : c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_hoare__derivs_Oequations_I1_J,axiom,
% 22.04/22.16 ! [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))) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Inf__empty,axiom,
% 22.04/22.16 ! [T_b] :
% 22.04/22.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.04/22.16 => 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) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Sup__empty,axiom,
% 22.04/22.16 ! [T_b] :
% 22.04/22.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.04/22.16 => 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) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Pow__mono,axiom,
% 22.04/22.16 ! [V_B_2,V_A_2,T_b] :
% 22.04/22.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.04/22.16 => 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))) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_greaterThanLessThan__empty,axiom,
% 22.04/22.16 ! [V_k_2,V_l_2,T_b] :
% 22.04/22.16 ( class_Orderings_Oorder(T_b)
% 22.04/22.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 22.04/22.16 => 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)) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_greaterThanAtMost__empty,axiom,
% 22.04/22.16 ! [V_k_2,V_l_2,T_b] :
% 22.04/22.16 ( class_Orderings_Oorder(T_b)
% 22.04/22.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
% 22.04/22.16 => 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)) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Inter__anti__mono,axiom,
% 22.04/22.16 ! [V_A_2,V_B_2,T_b] :
% 22.04/22.16 ( 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))
% 22.04/22.16 => 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))) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_atLeastLessThan__subset__iff,axiom,
% 22.04/22.16 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.04/22.16 ( class_Orderings_Olinorder(T_b)
% 22.04/22.16 => ( 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)))
% 22.04/22.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 22.04/22.16 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 22.04/22.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Compl__greaterThan,axiom,
% 22.04/22.16 ! [V_k_2,T_b] :
% 22.04/22.16 ( class_Orderings_Olinorder(T_b)
% 22.04/22.16 => 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) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Compl__atMost,axiom,
% 22.04/22.16 ! [V_k_2,T_b] :
% 22.04/22.16 ( class_Orderings_Olinorder(T_b)
% 22.04/22.16 => 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) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_atLeastLessThan__empty,axiom,
% 22.04/22.16 ! [V_a_2,V_b_2,T_b] :
% 22.04/22.16 ( class_Orderings_Oorder(T_b)
% 22.04/22.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
% 22.04/22.16 => 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)) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_atLeastatMost__subset__iff,axiom,
% 22.04/22.16 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.04/22.16 ( class_Orderings_Oorder(T_b)
% 22.04/22.16 => ( 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)))
% 22.04/22.16 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 22.04/22.16 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 22.04/22.16 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2)) ) ) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Compl__lessThan,axiom,
% 22.04/22.16 ! [V_k_2,T_b] :
% 22.04/22.16 ( class_Orderings_Olinorder(T_b)
% 22.04/22.16 => 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) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_top1I,axiom,
% 22.04/22.16 ! [V_x_2,T_b] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_x_2)) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Pow__not__empty,axiom,
% 22.04/22.16 ! [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)) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Pow__UNIV,axiom,
% 22.04/22.16 ! [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)) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Union__Pow__eq,axiom,
% 22.04/22.16 ! [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 ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Union__UNIV,axiom,
% 22.04/22.16 ! [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)) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Inter__empty,axiom,
% 22.04/22.16 ! [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)) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Compl__eq__Compl__iff,axiom,
% 22.04/22.16 ! [V_B_2,V_A_2,T_b] :
% 22.04/22.16 ( 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)
% 22.04/22.16 <=> V_A_2 = V_B_2 ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_double__complement,axiom,
% 22.04/22.16 ! [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 ).
% 22.04/22.16
% 22.04/22.16 fof(fact_subset__Pow__Union,axiom,
% 22.04/22.16 ! [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)))) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Compl__UNIV__eq,axiom,
% 22.04/22.16 ! [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)) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Compl__empty__eq,axiom,
% 22.04/22.16 ! [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)) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Union__empty,axiom,
% 22.04/22.16 ! [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)) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Compl__anti__mono,axiom,
% 22.04/22.16 ! [V_B_2,V_A_2,T_b] :
% 22.04/22.16 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.04/22.16 => 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))) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Compl__subset__Compl__iff,axiom,
% 22.04/22.16 ! [V_B_2,V_A_2,T_b] :
% 22.04/22.16 ( 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)))
% 22.04/22.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Inter__UNIV,axiom,
% 22.04/22.16 ! [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)) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Sup__le__iff,axiom,
% 22.04/22.16 ! [V_b_2,V_A_2,T_b] :
% 22.04/22.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.04/22.16 => ( 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))
% 22.04/22.16 <=> ! [B_x] :
% 22.04/22.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.04/22.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_le__Inf__iff,axiom,
% 22.04/22.16 ! [V_A_2,V_b_2,T_b] :
% 22.04/22.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.04/22.16 => ( 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)))
% 22.04/22.16 <=> ! [B_x] :
% 22.04/22.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.04/22.16 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) ) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Inf__UNIV,axiom,
% 22.04/22.16 ! [T_b] :
% 22.04/22.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.04/22.16 => 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) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Sup__UNIV,axiom,
% 22.04/22.16 ! [T_b] :
% 22.04/22.16 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.04/22.16 => 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) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_subset__Compl__self__eq,axiom,
% 22.04/22.16 ! [V_A_2,T_b] :
% 22.04/22.16 ( 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)))
% 22.04/22.16 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Union__mono,axiom,
% 22.04/22.16 ! [V_B_2,V_A_2,T_b] :
% 22.04/22.16 ( 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))
% 22.04/22.16 => 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))) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_atLeastatMost__empty__iff,axiom,
% 22.04/22.16 ! [V_b_2,V_a_2,T_b] :
% 22.04/22.16 ( class_Orderings_Oorder(T_b)
% 22.04/22.16 => ( 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))
% 22.04/22.16 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_atLeastatMost__empty__iff2,axiom,
% 22.04/22.16 ! [V_b_2,V_a_2,T_b] :
% 22.04/22.16 ( class_Orderings_Oorder(T_b)
% 22.04/22.16 => ( 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)
% 22.04/22.16 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_Compl__atLeast,axiom,
% 22.04/22.16 ! [V_k_2,T_b] :
% 22.04/22.16 ( class_Orderings_Olinorder(T_b)
% 22.04/22.16 => 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) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_compl__bot__eq,axiom,
% 22.04/22.16 ! [T_a] :
% 22.04/22.16 ( class_Lattices_Oboolean__algebra(T_a)
% 22.04/22.16 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ).
% 22.04/22.16
% 22.04/22.16 fof(fact_compl__top__eq,axiom,
% 22.12/22.16 ! [T_a] :
% 22.12/22.16 ( class_Lattices_Oboolean__algebra(T_a)
% 22.12/22.16 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_uminus__apply,axiom,
% 22.12/22.16 ! [V_x_2,V_A_2,T_c,T_b] :
% 22.12/22.16 ( class_Groups_Ouminus(T_b)
% 22.12/22.16 => 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)) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_compl__mono,axiom,
% 22.12/22.16 ! [V_y,V_x,T_a] :
% 22.12/22.16 ( class_Lattices_Oboolean__algebra(T_a)
% 22.12/22.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.12/22.16 => 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))) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_le__imp__neg__le,axiom,
% 22.12/22.16 ! [V_b,V_a,T_a] :
% 22.12/22.16 ( class_Groups_Oordered__ab__group__add(T_a)
% 22.12/22.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.12/22.16 => 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))) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_compl__le__compl__iff,axiom,
% 22.12/22.16 ! [V_y_2,V_x_2,T_b] :
% 22.12/22.16 ( class_Lattices_Oboolean__algebra(T_b)
% 22.12/22.16 => ( 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)))
% 22.12/22.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_neg__le__iff__le,axiom,
% 22.12/22.16 ! [V_a_2,V_b_2,T_b] :
% 22.12/22.16 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.12/22.16 => ( 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)))
% 22.12/22.16 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_minus__le__iff,axiom,
% 22.12/22.16 ! [V_b_2,V_a_2,T_b] :
% 22.12/22.16 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.12/22.16 => ( 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))
% 22.12/22.16 <=> 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)) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_le__minus__iff,axiom,
% 22.12/22.16 ! [V_b_2,V_a_2,T_b] :
% 22.12/22.16 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.12/22.16 => ( 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)))
% 22.12/22.16 <=> 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))) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_ivl__disj__un_I13_J,axiom,
% 22.12/22.16 ! [V_u_2,V_l_2,T_b] :
% 22.12/22.16 ( class_Orderings_Olinorder(T_b)
% 22.12/22.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 22.12/22.16 => 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) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_ivl__disj__un_I10_J,axiom,
% 22.12/22.16 ! [V_u_2,V_l_2,T_b] :
% 22.12/22.16 ( class_Orderings_Olinorder(T_b)
% 22.12/22.16 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 22.12/22.16 => 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) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_ivl__disj__int_I5_J,axiom,
% 22.12/22.16 ! [V_u_2,V_l_2,T_b] :
% 22.12/22.16 ( class_Orderings_Oorder(T_b)
% 22.12/22.16 => 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)) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_sup1E,axiom,
% 22.12/22.16 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 22.12/22.16 ( 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))
% 22.12/22.16 => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
% 22.12/22.16 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_sup1CI,axiom,
% 22.12/22.16 ! [T_b,V_A_2,V_x_2,V_B_2] :
% 22.12/22.16 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
% 22.12/22.16 => hBOOL(hAPP(V_A_2,V_x_2)) )
% 22.12/22.16 => 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)) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_inf1I,axiom,
% 22.12/22.16 ! [T_b,V_B_2,V_x_2,V_A_2] :
% 22.12/22.16 ( hBOOL(hAPP(V_A_2,V_x_2))
% 22.12/22.16 => ( hBOOL(hAPP(V_B_2,V_x_2))
% 22.12/22.16 => 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)) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_inf1E,axiom,
% 22.12/22.16 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 22.12/22.16 ( 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))
% 22.12/22.16 => ~ ( hBOOL(hAPP(V_A_2,V_x_2))
% 22.12/22.16 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Union__Un__distrib,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_compl__inf,axiom,
% 22.12/22.16 ! [V_y,V_x,T_a] :
% 22.12/22.16 ( class_Lattices_Oboolean__algebra(T_a)
% 22.12/22.16 => 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)) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_compl__sup,axiom,
% 22.12/22.16 ! [V_y,V_x,T_a] :
% 22.12/22.16 ( class_Lattices_Oboolean__algebra(T_a)
% 22.12/22.16 => 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)) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Int__absorb,axiom,
% 22.12/22.16 ! [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 ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Un__absorb,axiom,
% 22.12/22.16 ! [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 ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Int__commute,axiom,
% 22.12/22.16 ! [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) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Un__commute,axiom,
% 22.12/22.16 ! [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) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Int__left__absorb,axiom,
% 22.12/22.16 ! [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) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Un__left__absorb,axiom,
% 22.12/22.16 ! [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) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Int__left__commute,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Un__left__commute,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Int__Un__distrib,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Un__Int__distrib,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Int__assoc,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Un__assoc,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Int__Un__distrib2,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Un__Int__distrib2,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_bex__Un,axiom,
% 22.12/22.16 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 22.12/22.16 ( ? [B_x] :
% 22.12/22.16 ( 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)))
% 22.12/22.16 & hBOOL(hAPP(V_P_2,B_x)) )
% 22.12/22.16 <=> ( ? [B_x] :
% 22.12/22.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.12/22.16 & hBOOL(hAPP(V_P_2,B_x)) )
% 22.12/22.16 | ? [B_x] :
% 22.12/22.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 22.12/22.16 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_ball__Un,axiom,
% 22.12/22.16 ! [V_P_2,V_B_2,V_A_2,T_b] :
% 22.12/22.16 ( ! [B_x] :
% 22.12/22.16 ( 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)))
% 22.12/22.16 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.12/22.16 <=> ( ! [B_x] :
% 22.12/22.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.12/22.16 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.12/22.16 & ! [B_x] :
% 22.12/22.16 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 22.12/22.16 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_Un__Int__crazy,axiom,
% 22.12/22.16 ! [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)) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_sup1I1,axiom,
% 22.12/22.16 ! [V_B_2,T_b,V_x_2,V_A_2] :
% 22.12/22.16 ( hBOOL(hAPP(V_A_2,V_x_2))
% 22.12/22.16 => 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)) ) ).
% 22.12/22.16
% 22.12/22.16 fof(fact_sup1I2,axiom,
% 22.12/22.16 ! [V_A_2,T_b,V_x_2,V_B_2] :
% 22.12/22.16 ( hBOOL(hAPP(V_B_2,V_x_2))
% 22.12/22.17 => 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)) ) ).
% 22.12/22.17
% 22.12/22.17 fof(fact_inf1D1,axiom,
% 22.12/22.17 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 22.12/22.17 ( 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))
% 22.12/22.17 => hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 22.12/22.17
% 22.12/22.17 fof(fact_inf1D2,axiom,
% 22.12/22.17 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 22.14/22.17 ( 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))
% 22.14/22.17 => hBOOL(hAPP(V_B_2,V_x_2)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__apply,axiom,
% 22.14/22.17 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 22.14/22.17 ( class_Lattices_Olattice(T_b)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__apply,axiom,
% 22.14/22.17 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 22.14/22.17 ( class_Lattices_Olattice(T_b)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__inf__distrib2,axiom,
% 22.14/22.17 ! [V_x,V_z,V_y,T_a] :
% 22.14/22.17 ( class_Lattices_Odistrib__lattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__distrib2,axiom,
% 22.14/22.17 ! [V_x,V_z,V_y,T_a] :
% 22.14/22.17 ( class_Lattices_Odistrib__lattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__assoc,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__aci_I6_J,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup_Oassoc,axiom,
% 22.14/22.17 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__assoc,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__aci_I2_J,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf_Oassoc,axiom,
% 22.14/22.17 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__inf__distrib1,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Odistrib__lattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__distrib1,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Odistrib__lattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__left__commute,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__aci_I7_J,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup_Oleft__commute,axiom,
% 22.14/22.17 ! [V_c,V_a,V_b,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__left__commute,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__aci_I3_J,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf_Oleft__commute,axiom,
% 22.14/22.17 ! [V_c,V_a,V_b,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__left__idem,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__aci_I8_J,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup_Oleft__idem,axiom,
% 22.14/22.17 ! [V_b,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__left__idem,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__aci_I4_J,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf_Oleft__idem,axiom,
% 22.14/22.17 ! [V_b,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__inf__absorb,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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 ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__absorb,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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 ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__commute,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__aci_I5_J,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup_Ocommute,axiom,
% 22.14/22.17 ! [V_b,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__commute,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__aci_I1_J,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf_Ocommute,axiom,
% 22.14/22.17 ! [V_b,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__idem,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup_Oidem,axiom,
% 22.14/22.17 ! [V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__idem,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf_Oidem,axiom,
% 22.14/22.17 ! [V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_distrib__inf__le,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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)))) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_distrib__sup__le,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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)))) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__Int__assoc__eq,axiom,
% 22.14/22.17 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 22.14/22.17 ( 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))
% 22.14/22.17 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Union__Int__subset,axiom,
% 22.14/22.17 ! [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)))) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__ord_I3_J,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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))) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__ge1,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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))) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__ord_I4_J,axiom,
% 22.14/22.17 ! [V_x,V_y,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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))) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__ge2,axiom,
% 22.14/22.17 ! [V_x,V_y,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => 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))) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__ord_I1_J,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__le1,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__sup__ord_I2_J,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Olattice(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__le2,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__iff__inf,axiom,
% 22.14/22.17 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_b)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.17 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__iff__sup,axiom,
% 22.14/22.17 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_b)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.17 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__inf__iff,axiom,
% 22.14/22.17 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_b)
% 22.14/22.17 => ( 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)))
% 22.14/22.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__sup__iff,axiom,
% 22.14/22.17 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_b)
% 22.14/22.17 => ( 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))
% 22.14/22.17 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 22.14/22.17 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__supI1,axiom,
% 22.14/22.17 ! [V_b,V_a,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 22.14/22.17 => 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))) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__supI2,axiom,
% 22.14/22.17 ! [V_a,V_b,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 22.14/22.17 => 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))) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__infI1,axiom,
% 22.14/22.17 ! [V_b,V_x,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 22.14/22.17 => 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)) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__infI2,axiom,
% 22.14/22.17 ! [V_a,V_x,V_b,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 22.14/22.17 => 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)) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__absorb1,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__absorb2,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__absorb2,axiom,
% 22.14/22.17 ! [V_x,V_y,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__absorb1,axiom,
% 22.14/22.17 ! [V_x,V_y,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__infI,axiom,
% 22.14/22.17 ! [V_b,V_a,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 22.14/22.17 => 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))) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__greatest,axiom,
% 22.14/22.17 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 22.14/22.17 => 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))) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__supI,axiom,
% 22.14/22.17 ! [V_b,V_x,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 22.14/22.17 => 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)) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__least,axiom,
% 22.14/22.17 ! [V_z,V_x,V_y,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 22.14/22.17 => 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)) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__mono,axiom,
% 22.14/22.17 ! [V_d,V_b,V_c,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 22.14/22.17 => 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))) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__mono,axiom,
% 22.14/22.17 ! [V_d,V_b,V_c,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 22.14/22.17 => 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))) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__infE,axiom,
% 22.14/22.17 ! [V_b,V_a,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.17 => ( 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)))
% 22.14/22.17 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 22.14/22.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_le__supE,axiom,
% 22.14/22.17 ! [V_x,V_b,V_a,T_a] :
% 22.14/22.17 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.17 => ( 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))
% 22.14/22.17 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 22.14/22.17 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__eq__bot__iff,axiom,
% 22.14/22.17 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__bot(T_b)
% 22.14/22.17 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_b)
% 22.14/22.17 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_b)
% 22.14/22.17 & V_y_2 = c_Orderings_Obot__class_Obot(T_b) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__bot__right,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__bot(T_a)
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__bot__right,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__bot(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__bot__left,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__bot(T_a)
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__bot__left,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__bot(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Compl__Int,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Compl__Un,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__eq__top__iff,axiom,
% 22.14/22.17 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__top(T_b)
% 22.14/22.17 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_b)
% 22.14/22.17 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_b)
% 22.14/22.17 & V_y_2 = c_Orderings_Otop__class_Otop(T_b) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__top__right,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__top(T_a)
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__top__right,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__top(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__top__left,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__top(T_a)
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__top__left,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Obounded__lattice__top(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Pow__Int__eq,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Inter__Un__distrib,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_compl__unique,axiom,
% 22.14/22.17 ! [V_y,V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Oboolean__algebra(T_a)
% 22.14/22.17 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
% 22.14/22.17 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
% 22.14/22.17 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Inter__Un__subset,axiom,
% 22.14/22.17 ! [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)))) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__empty__left,axiom,
% 22.14/22.17 ! [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 ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__empty__right,axiom,
% 22.14/22.17 ! [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 ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__empty,axiom,
% 22.14/22.17 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.17 ( 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))
% 22.14/22.17 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.17 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__empty__left,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__empty__right,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_disjoint__iff__not__equal,axiom,
% 22.14/22.17 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.17 ( 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))
% 22.14/22.17 <=> ! [B_x] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.17 => ! [B_xa] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_B_2))
% 22.14/22.17 => B_x != B_xa ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Union__disjoint,axiom,
% 22.14/22.17 ! [V_A_2,V_C_2,T_b] :
% 22.14/22.17 ( 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))
% 22.14/22.17 <=> ! [B_x] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
% 22.14/22.17 => 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)) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__upper1,axiom,
% 22.14/22.17 ! [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))) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__upper2,axiom,
% 22.14/22.17 ! [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))) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_subset__Un__eq,axiom,
% 22.14/22.17 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.17 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__absorb1,axiom,
% 22.14/22.17 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__absorb2,axiom,
% 22.14/22.17 ! [V_A_2,V_B_2,T_b] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__least,axiom,
% 22.14/22.17 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 22.14/22.17 => 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)) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__mono,axiom,
% 22.14/22.17 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 22.14/22.17 => 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))) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__UNIV__right,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__UNIV__left,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__lower1,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__lower2,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__absorb2,axiom,
% 22.14/22.17 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__absorb1,axiom,
% 22.14/22.17 ! [V_A_2,V_B_2,T_b] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.17 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__greatest,axiom,
% 22.14/22.17 ! [V_B_2,V_A_2,V_C_2,T_b] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2))
% 22.14/22.17 => 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))) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__mono,axiom,
% 22.14/22.17 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_b] :
% 22.14/22.17 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_D_2))
% 22.14/22.17 => 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))) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__UNIV__right,axiom,
% 22.14/22.17 ! [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 ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Int__UNIV__left,axiom,
% 22.14/22.17 ! [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 ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Un__Pow__subset,axiom,
% 22.14/22.17 ! [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)))) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_inf__compl__bot,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Oboolean__algebra(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_compl__inf__bot,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Oboolean__algebra(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_sup__compl__top,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Oboolean__algebra(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_compl__sup__top,axiom,
% 22.14/22.17 ! [V_x,T_a] :
% 22.14/22.17 ( class_Lattices_Oboolean__algebra(T_a)
% 22.14/22.17 => 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) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__un_I17_J,axiom,
% 22.14/22.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Olinorder(T_b)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 22.14/22.17 => 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) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__int_I11_J,axiom,
% 22.14/22.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Oorder(T_b)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Compl__disjoint,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Compl__disjoint2,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Compl__partition2,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_Compl__partition,axiom,
% 22.14/22.17 ! [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)) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__un_I20_J,axiom,
% 22.14/22.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Olinorder(T_b)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 22.14/22.17 => 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) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__int_I14_J,axiom,
% 22.14/22.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Oorder(T_b)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__un_I21_J,axiom,
% 22.14/22.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Olinorder(T_b)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 22.14/22.17 => 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) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_disjoint__eq__subset__Compl,axiom,
% 22.14/22.17 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.17 ( 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))
% 22.14/22.17 <=> 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))) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__int_I15_J,axiom,
% 22.14/22.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Oorder(T_b)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__un_I8_J,axiom,
% 22.14/22.17 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Olinorder(T_b)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 22.14/22.17 => 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) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__un_I22_J,axiom,
% 22.14/22.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Olinorder(T_b)
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 22.14/22.17 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 22.14/22.17 => 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) ) ) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__int_I4_J,axiom,
% 22.14/22.17 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Oorder(T_b)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__int_I2_J,axiom,
% 22.14/22.17 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Oorder(T_b)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__int_I16_J,axiom,
% 22.14/22.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Oorder(T_b)
% 22.14/22.17 => 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)) ) ).
% 22.14/22.17
% 22.14/22.17 fof(fact_ivl__disj__int_I12_J,axiom,
% 22.14/22.17 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.17 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__int_I13_J,axiom,
% 22.14/22.18 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I14_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 22.14/22.18 => 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) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__int_I9_J,axiom,
% 22.14/22.18 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__int_I8_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__int_I7_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I9_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 22.14/22.18 => 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) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__int_I3_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__int_I1_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__int_I10_J,axiom,
% 22.14/22.18 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_compl__eq__compl__iff,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Lattices_Oboolean__algebra(T_b)
% 22.14/22.18 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)
% 22.14/22.18 <=> V_x_2 = V_y_2 ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_neg__equal__iff__equal,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Groups_Ogroup__add(T_b)
% 22.14/22.18 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 22.14/22.18 <=> V_a_2 = V_b_2 ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_minus__equation__iff,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Groups_Ogroup__add(T_b)
% 22.14/22.18 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_b_2
% 22.14/22.18 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) = V_a_2 ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_equation__minus__iff,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Groups_Ogroup__add(T_b)
% 22.14/22.18 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 22.14/22.18 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_double__compl,axiom,
% 22.14/22.18 ! [V_x,T_a] :
% 22.14/22.18 ( class_Lattices_Oboolean__algebra(T_a)
% 22.14/22.18 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_minus__minus,axiom,
% 22.14/22.18 ! [V_a,T_a] :
% 22.14/22.18 ( class_Groups_Ogroup__add(T_a)
% 22.14/22.18 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I11_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 22.14/22.18 => 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) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__int_I6_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I19_J,axiom,
% 22.14/22.18 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 22.14/22.18 => 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) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I18_J,axiom,
% 22.14/22.18 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 22.14/22.18 => 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) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I5_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 22.14/22.18 => 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) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I6_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_u_2))
% 22.14/22.18 => 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) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I12_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 22.14/22.18 => 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) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I7_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 22.14/22.18 => 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) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I1_J,axiom,
% 22.14/22.18 ! [V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I16_J,axiom,
% 22.14/22.18 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_u_2))
% 22.14/22.18 => 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) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atMost__Int__atLeast,axiom,
% 22.14/22.18 ! [V_n_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I2_J,axiom,
% 22.14/22.18 ! [V_u_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I15_J,axiom,
% 22.14/22.18 ! [V_u_2,V_m_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_m_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
% 22.14/22.18 => 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) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__cases,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => ( V_x != V_y
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__asym,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_xt1_I10_J,axiom,
% 22.14/22.18 ! [V_z,V_x,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__trans,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_xt1_I2_J,axiom,
% 22.14/22.18 ! [V_c,V_a,V_b,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 22.14/22.18 => ( V_b = V_c
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ord__less__eq__trans,axiom,
% 22.14/22.18 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Oord(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.14/22.18 => ( V_b = V_c
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_xt1_I1_J,axiom,
% 22.14/22.18 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( V_a = V_b
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ord__eq__less__trans,axiom,
% 22.14/22.18 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Oord(T_a)
% 22.14/22.18 => ( V_a = V_b
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_xt1_I9_J,axiom,
% 22.14/22.18 ! [V_a,V_b,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 22.14/22.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__asym_H,axiom,
% 22.14/22.18 ! [V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.14/22.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__imp__not__eq2,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => V_y != V_x ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__imp__not__eq,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => V_x != V_y ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__imp__not__less,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__not__sym,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__imp__neq,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => V_x != V_y ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__neqE,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( V_x != V_y
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__antisym__conv3,axiom,
% 22.14/22.18 ! [V_x_2,V_y_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> V_x_2 = V_y_2 ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_insert__code,axiom,
% 22.14/22.18 ! [V_x_2,V_A_2,V_y_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),V_A_2),V_x_2))
% 22.14/22.18 <=> ( V_y_2 = V_x_2
% 22.14/22.18 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_insert__commute,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_insert__absorb2,axiom,
% 22.14/22.18 ! [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) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__less__linear,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 | V_x = V_y
% 22.14/22.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_not__less__iff__gr__or__eq,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2))
% 22.14/22.18 | V_x_2 = V_y_2 ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__neq__iff,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( V_x_2 != V_y_2
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__irrefl,axiom,
% 22.14/22.18 ! [V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_a)
% 22.14/22.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_lessThan__strict__subset__iff,axiom,
% 22.14/22.18 ! [V_n_2,V_m_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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)))
% 22.14/22.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_m_2),V_n_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastatMost__psubset__iff,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( 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)))
% 22.14/22.18 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 22.14/22.18 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2))
% 22.14/22.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
% 22.14/22.18 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2))
% 22.14/22.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2)) ) ) )
% 22.14/22.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__fun__def,axiom,
% 22.14/22.18 ! [V_g_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( class_Orderings_Oord(T_c)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 22.14/22.18 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_g_2),V_f_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_xt1_I8_J,axiom,
% 22.14/22.18 ! [V_z,V_x,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__le__less__trans,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_xt1_I7_J,axiom,
% 22.14/22.18 ! [V_z,V_x,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__le__trans,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_xt1_I11_J,axiom,
% 22.14/22.18 ! [V_a,V_b,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 22.14/22.18 => ( V_a != V_b
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__le__neq__trans,axiom,
% 22.14/22.18 ! [V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.14/22.18 => ( V_a != V_b
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__le__imp__less__or__eq,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 | V_x = V_y ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__antisym__conv2,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> V_x_2 = V_y_2 ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__imp__le,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_leD,axiom,
% 22.14/22.18 ! [V_x,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.14/22.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_xt1_I12_J,axiom,
% 22.14/22.18 ! [V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( V_a != V_b
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__neq__le__trans,axiom,
% 22.14/22.18 ! [V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Oorder(T_a)
% 22.14/22.18 => ( V_a != V_b
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__antisym__conv1,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> V_x_2 = V_y_2 ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_not__leE,axiom,
% 22.14/22.18 ! [V_x,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_leI,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__le__less,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 | V_x_2 = V_y_2 ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__le__not__le,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Opreorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_order__less__le,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 & V_x_2 != V_y_2 ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__le__less__linear,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.14/22.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__not__le,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_x_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__not__less,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_singleton__inject,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( 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)))
% 22.14/22.18 => V_a_2 = V_b_2 ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_doubleton__eq__iff,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( 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))))
% 22.14/22.18 <=> ( ( V_a_2 = V_c_2
% 22.14/22.18 & V_b_2 = V_d_2 )
% 22.14/22.18 | ( V_a_2 = V_d_2
% 22.14/22.18 & V_b_2 = V_c_2 ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_insert__not__empty,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_empty__not__insert,axiom,
% 22.14/22.18 ! [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) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_insert__mono,axiom,
% 22.14/22.18 ! [V_a_2,V_D_2,V_C_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
% 22.14/22.18 => 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))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_subset__insertI2,axiom,
% 22.14/22.18 ! [V_b_2,V_B_2,V_A_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 => 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))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_subset__insertI,axiom,
% 22.14/22.18 ! [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))) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_not__psubset__empty,axiom,
% 22.14/22.18 ! [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)))) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Un__insert__left,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Un__insert__right,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_insert__inter__insert,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__supI1,axiom,
% 22.14/22.18 ! [V_b,V_a,V_x,T_a] :
% 22.14/22.18 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 22.14/22.18 => 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))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__supI2,axiom,
% 22.14/22.18 ! [V_a,V_b,V_x,T_a] :
% 22.14/22.18 ( class_Lattices_Osemilattice__sup(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 22.14/22.18 => 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))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__infI1,axiom,
% 22.14/22.18 ! [V_b,V_x,V_a,T_a] :
% 22.14/22.18 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 22.14/22.18 => 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)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__infI2,axiom,
% 22.14/22.18 ! [V_a,V_x,V_b,T_a] :
% 22.14/22.18 ( class_Lattices_Osemilattice__inf(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 22.14/22.18 => 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)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__minus__iff,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)))
% 22.14/22.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_minus__less__iff,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2))
% 22.14/22.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)),V_a_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_neg__less__iff__less,axiom,
% 22.14/22.18 ! [V_a_2,V_b_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => ( 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)))
% 22.14/22.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_subset__psubset__trans,axiom,
% 22.14/22.18 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_psubset__subset__trans,axiom,
% 22.14/22.18 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_psubset__imp__subset,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_subset__iff__psubset__eq,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 | V_A_2 = V_B_2 ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_psubset__eq,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 & V_A_2 != V_B_2 ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastLessThan__inj_I2_J,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 22.14/22.18 => V_b_2 = V_d_2 ) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastLessThan__inj_I1_J,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 22.14/22.18 => V_a_2 = V_c_2 ) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastLessThan__eq__iff,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
% 22.14/22.18 => ( 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)
% 22.14/22.18 <=> ( V_a_2 = V_c_2
% 22.14/22.18 & V_b_2 = V_d_2 ) ) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__Sup__iff,axiom,
% 22.14/22.18 ! [V_S_2,V_a_2,T_b] :
% 22.14/22.18 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.18 & class_Orderings_Olinorder(T_b) )
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_b,V_S_2)))
% 22.14/22.18 <=> ? [B_x] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 22.14/22.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),B_x)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Inf__less__iff,axiom,
% 22.14/22.18 ! [V_a_2,V_S_2,T_b] :
% 22.14/22.18 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.18 & class_Orderings_Olinorder(T_b) )
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Complete__Lattice_OInf__class_OInf(T_b,V_S_2)),V_a_2))
% 22.14/22.18 <=> ? [B_x] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 22.14/22.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_a_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_strict__monoD,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Orderings_Oorder(T_c)
% 22.14/22.18 & class_Orderings_Oorder(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_strict__mono__less,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Orderings_Oorder(T_c)
% 22.14/22.18 & class_Orderings_Olinorder(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
% 22.14/22.18 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_y_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I3_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 22.14/22.18 => 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) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_subset__singletonD,axiom,
% 22.14/22.18 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.18 ( 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)))))
% 22.14/22.18 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.18 | 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))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_insert__is__Un,axiom,
% 22.14/22.18 ! [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) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_ivl__disj__un_I4_J,axiom,
% 22.14/22.18 ! [V_u_2,V_l_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_l_2),V_u_2))
% 22.14/22.18 => 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) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastAtMost__singleton,axiom,
% 22.14/22.18 ! [V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => 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))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastAtMost__singleton__iff,axiom,
% 22.14/22.18 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( 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)))
% 22.14/22.18 <=> ( V_a_2 = V_b_2
% 22.14/22.18 & V_b_2 = V_c_2 ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastAtMost__singleton_H,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( V_a_2 = V_b_2
% 22.14/22.18 => 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))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Sup__singleton,axiom,
% 22.14/22.18 ! [V_a_2,T_b] :
% 22.14/22.18 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.18 => 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 ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Sup__insert,axiom,
% 22.14/22.18 ! [V_A_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastatMost__empty,axiom,
% 22.14/22.18 ! [V_a_2,V_b_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2))
% 22.14/22.18 => 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)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastLessThan__empty__iff2,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( 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)
% 22.14/22.18 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_atLeastLessThan__empty__iff,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( 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))
% 22.14/22.18 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Inf__singleton,axiom,
% 22.14/22.18 ! [V_a_2,T_b] :
% 22.14/22.18 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.18 => 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 ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Inf__insert,axiom,
% 22.14/22.18 ! [V_A_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Union__insert,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_greaterThanAtMost__empty__iff2,axiom,
% 22.14/22.18 ! [V_l_2,V_k_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( 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)
% 22.14/22.18 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_greaterThanAtMost__empty__iff,axiom,
% 22.14/22.18 ! [V_l_2,V_k_2,T_b] :
% 22.14/22.18 ( class_Orderings_Oorder(T_b)
% 22.14/22.18 => ( 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))
% 22.14/22.18 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Inter__insert,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_hoare__derivs_Oinsert,axiom,
% 22.14/22.18 ! [V_tsa_2,V_t_2,V_G_2,T_b] :
% 22.14/22.18 ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_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))))
% 22.14/22.18 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,V_tsa_2)
% 22.14/22.18 => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_b)),V_t_2),V_tsa_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Sup__binary,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Inf__binary,axiom,
% 22.14/22.18 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Un__eq__Union,axiom,
% 22.14/22.18 ! [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))))) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Pow__empty,axiom,
% 22.14/22.18 ! [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))) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Int__eq__Inter,axiom,
% 22.14/22.18 ! [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))))) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_the__elem__eq,axiom,
% 22.14/22.18 ! [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 ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Pow__insert,axiom,
% 22.14/22.18 ! [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))) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Inf__fin_Oidem,axiom,
% 22.14/22.18 ! [V_x,T_a] :
% 22.14/22.18 ( class_Lattices_Olattice(T_a)
% 22.14/22.18 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Sup__fin_Oidem,axiom,
% 22.14/22.18 ! [V_x,T_a] :
% 22.14/22.18 ( class_Lattices_Olattice(T_a)
% 22.14/22.18 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_linorder__neqE__linordered__idom,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Rings_Olinordered__idom(T_a)
% 22.14/22.18 => ( V_x != V_y
% 22.14/22.18 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Int__atLeastAtMostL2,axiom,
% 22.14/22.18 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Int__atLeastAtMostR2,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__uminus__atMost,axiom,
% 22.14/22.18 ! [V_x_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__uminus__atLeast,axiom,
% 22.14/22.18 ! [V_x_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__uminus__lessThan,axiom,
% 22.14/22.18 ! [V_x_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_psubset__trans,axiom,
% 22.14/22.18 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Max_Oidem,axiom,
% 22.14/22.18 ! [V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup_Oidem,axiom,
% 22.14/22.18 ! [V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup_Ocommute,axiom,
% 22.14/22.18 ! [V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__commute,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup_Oleft__idem,axiom,
% 22.14/22.18 ! [V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__left__idem,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup_Oleft__commute,axiom,
% 22.14/22.18 ! [V_c,V_a,V_b,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__left__commute,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup_Oassoc,axiom,
% 22.14/22.18 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__assoc,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__Pow__surj,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_B_2
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_empty__is__image,axiom,
% 22.14/22.18 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.18 ( 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)
% 22.14/22.18 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__empty,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__is__empty,axiom,
% 22.14/22.18 ! [V_A_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( 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))
% 22.14/22.18 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__insert,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_le__maxI1,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_le__maxI2,axiom,
% 22.14/22.18 ! [V_x,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__iff__sup,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2) = V_y_2 ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__sup__iff,axiom,
% 22.14/22.18 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 22.14/22.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__supI1,axiom,
% 22.14/22.18 ! [V_b,V_a,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 22.14/22.18 => 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))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__supI2,axiom,
% 22.14/22.18 ! [V_a,V_b,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 22.14/22.18 => 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))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__absorb2,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.14/22.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__absorb1,axiom,
% 22.14/22.18 ! [V_x,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.14/22.18 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__supI,axiom,
% 22.14/22.18 ! [V_b,V_x,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 22.14/22.18 => 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)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__least,axiom,
% 22.14/22.18 ! [V_z,V_x,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x))
% 22.14/22.18 => 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)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__mono,axiom,
% 22.14/22.18 ! [V_d,V_b,V_c,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 22.14/22.18 => 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))) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__supE,axiom,
% 22.14/22.18 ! [V_x,V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( 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))
% 22.14/22.18 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 22.14/22.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_le__max__iff__disj,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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)))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_x_2))
% 22.14/22.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_z_2),V_y_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_less__max__iff__disj,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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)))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 22.14/22.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_max__less__iff__conj,axiom,
% 22.14/22.18 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 22.14/22.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oless__supI1,axiom,
% 22.14/22.18 ! [V_b,V_a,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 22.14/22.18 => 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))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oless__supI2,axiom,
% 22.14/22.18 ! [V_a,V_b,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
% 22.14/22.18 => 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))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_subset__image__iff,axiom,
% 22.14/22.18 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 22.14/22.18 ( 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)))
% 22.14/22.18 <=> ? [B_AA] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2))
% 22.14/22.18 & V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__mono,axiom,
% 22.14/22.18 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.18 => 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))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__Un,axiom,
% 22.14/22.18 ! [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)) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_sup__max,axiom,
% 22.14/22.18 ! [T_b] :
% 22.14/22.18 ( ( class_Lattices_Osemilattice__sup(T_b)
% 22.14/22.18 & class_Orderings_Olinorder(T_b) )
% 22.14/22.18 => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__Pow__mono,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.18 ( 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))
% 22.14/22.18 => 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))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__Int__subset,axiom,
% 22.14/22.18 ! [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)))) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__uminus__atLeastAtMost,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__uminus__greaterThanLessThan,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__uminus__atLeastLessThan,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__uminus__greaterThanAtMost,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_image__uminus__greaterThan,axiom,
% 22.14/22.18 ! [V_x_2,T_b] :
% 22.14/22.18 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_surj__Compl__image__subset,axiom,
% 22.14/22.18 ! [V_A_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( 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))
% 22.14/22.18 => 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)))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Cantors__paradox,axiom,
% 22.14/22.18 ! [V_A_2,T_b] :
% 22.14/22.18 ~ ? [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) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_max__ord__max,axiom,
% 22.14/22.18 ! [T_b] :
% 22.14/22.18 ( class_Orderings_Oord(T_b)
% 22.14/22.18 => c_Orderings_Oord__class_Omax(T_b) = c_Orderings_Oord_Omax(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Omono__sup,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Lattices_Osemilattice__sup(T_c)
% 22.14/22.18 & class_Orderings_Olinorder(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 22.14/22.18 => 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)))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_OSup__fin_Osingleton,axiom,
% 22.14/22.18 ! [V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => 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 ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Int__atLeastAtMostR1,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_b_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Int__atLeastAtMostL1,axiom,
% 22.14/22.18 ! [V_d_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Int__greaterThanLessThan,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_strict__monoI,axiom,
% 22.14/22.18 ! [V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Orderings_Oorder(T_c)
% 22.14/22.18 & class_Orderings_Oorder(T_b) )
% 22.14/22.18 => ( ! [B_x,B_y] :
% 22.14/22.18 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),B_y))
% 22.14/22.18 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
% 22.14/22.18 => c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Int__greaterThanAtMost,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Min_Oidem,axiom,
% 22.14/22.18 ! [V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__assoc,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf_Oassoc,axiom,
% 22.14/22.18 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__left__commute,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf_Oleft__commute,axiom,
% 22.14/22.18 ! [V_c,V_a,V_b,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__left__idem,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf_Oleft__idem,axiom,
% 22.14/22.18 ! [V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__commute,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf_Ocommute,axiom,
% 22.14/22.18 ! [V_b,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf_Oidem,axiom,
% 22.14/22.18 ! [V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__of__mono,axiom,
% 22.14/22.18 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Orderings_Olinorder(T_c)
% 22.14/22.18 & class_Orderings_Olinorder(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 22.14/22.18 => 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)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__le__iff__disj,axiom,
% 22.14/22.18 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
% 22.14/22.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__infE,axiom,
% 22.14/22.18 ! [V_b,V_a,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( 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)))
% 22.14/22.18 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 22.14/22.18 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__mono,axiom,
% 22.14/22.18 ! [V_d,V_b,V_c,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d))
% 22.14/22.18 => 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))) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__greatest,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z))
% 22.14/22.18 => 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))) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__infI,axiom,
% 22.14/22.18 ! [V_b,V_a,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
% 22.14/22.18 => 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))) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__absorb2,axiom,
% 22.14/22.18 ! [V_x,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
% 22.14/22.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__absorb1,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.14/22.18 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__infI2,axiom,
% 22.14/22.18 ! [V_a,V_x,V_b,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
% 22.14/22.18 => 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)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__infI1,axiom,
% 22.14/22.18 ! [V_b,V_x,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
% 22.14/22.18 => 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)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__inf__iff,axiom,
% 22.14/22.18 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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)))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Ole__iff__inf,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),V_y_2) = V_x_2 ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__le2,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__le1,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oless__infI2,axiom,
% 22.14/22.18 ! [V_a,V_x,V_b,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
% 22.14/22.18 => 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)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oless__infI1,axiom,
% 22.14/22.18 ! [V_b,V_x,V_a,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
% 22.14/22.18 => 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)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__less__iff__disj,axiom,
% 22.14/22.18 ! [V_z_2,V_y_2,V_x_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),V_z_2))
% 22.14/22.18 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_y_2),V_z_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__less__iff__conj,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,V_z_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.18 => ( 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)))
% 22.14/22.18 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_x_2))
% 22.14/22.18 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_z_2),V_y_2)) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Omono__inf,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Lattices_Osemilattice__inf(T_c)
% 22.14/22.18 & class_Orderings_Olinorder(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 22.14/22.18 => 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)))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_inf__min,axiom,
% 22.14/22.18 ! [T_b] :
% 22.14/22.18 ( ( class_Lattices_Osemilattice__inf(T_b)
% 22.14/22.18 & class_Orderings_Olinorder(T_b) )
% 22.14/22.18 => c_Lattices_Osemilattice__inf__class_Oinf(T_b) = c_Orderings_Oord__class_Omin(T_b) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__sup__distrib2,axiom,
% 22.14/22.18 ! [V_x,V_z,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__inf__distrib2,axiom,
% 22.14/22.18 ! [V_x,V_z,V_y,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__sup__distrib1,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__inf__distrib1,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Oinf__sup__absorb,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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 ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Osup__inf__absorb,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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 ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_monoD,axiom,
% 22.14/22.18 ! [V_y_2,V_x_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Orderings_Oorder(T_c)
% 22.14/22.18 & class_Orderings_Oorder(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 22.14/22.18 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.14/22.18 => 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))) ) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_max__of__mono,axiom,
% 22.14/22.18 ! [V_n_2,V_m_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Orderings_Olinorder(T_c)
% 22.14/22.18 & class_Orderings_Olinorder(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 22.14/22.18 => 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)) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Odistrib__inf__le,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_min__max_Odistrib__sup__le,axiom,
% 22.14/22.18 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_a)
% 22.14/22.18 => 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)))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_minus__max__eq__min,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Groups_Olinordered__ab__group__add(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_minus__min__eq__max,axiom,
% 22.14/22.18 ! [V_y,V_x,T_a] :
% 22.14/22.18 ( class_Groups_Olinordered__ab__group__add(T_a)
% 22.14/22.18 => 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)) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_strict__mono__mono,axiom,
% 22.14/22.18 ! [V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Orderings_Oorder(T_c)
% 22.14/22.18 & class_Orderings_Oorder(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 22.14/22.18 => c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_mono__Un,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.18 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 22.14/22.18 => 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)))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_mono__Int,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.18 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 22.14/22.18 => 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)))) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_mono__sup,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Lattices_Osemilattice__sup(T_c)
% 22.14/22.18 & class_Lattices_Osemilattice__sup(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 22.14/22.18 => 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)))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_mono__inf,axiom,
% 22.14/22.18 ! [V_B_2,V_A_2,V_f_2,T_b,T_c] :
% 22.14/22.18 ( ( class_Lattices_Osemilattice__inf(T_c)
% 22.14/22.18 & class_Lattices_Osemilattice__inf(T_b) )
% 22.14/22.18 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 22.14/22.18 => 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)))) ) ) ).
% 22.14/22.18
% 22.14/22.18 fof(fact_Int__atLeastAtMost,axiom,
% 22.14/22.18 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.18 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Int__atLeastLessThan,axiom,
% 22.14/22.19 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__ord__min,axiom,
% 22.14/22.19 ! [T_b] :
% 22.14/22.19 ( class_Orderings_Oord(T_b)
% 22.14/22.19 => c_Orderings_Oord__class_Omin(T_b) = c_Orderings_Oord_Omin(T_b,c_Orderings_Oord__class_Oless__eq(T_b)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Ounion__inter,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__image__Compl__subset,axiom,
% 22.14/22.19 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => 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)))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Osingleton,axiom,
% 22.14/22.19 ! [V_x_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => 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 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_single__Diff__lessThan,axiom,
% 22.14/22.19 ! [V_k_2,T_b] :
% 22.14/22.19 ( class_Orderings_Oorder(T_b)
% 22.14/22.19 => 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_override__on__emptyset,axiom,
% 22.14/22.19 ! [V_g_2,V_f_2,T_c,T_b] : c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_f_2 ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__empty,axiom,
% 22.14/22.19 ! [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))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__uminus,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.19 => c_Fun_Oinj__on(T_b,T_b,c_Groups_Ouminus__class_Ouminus(T_b),V_A_2) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__def,axiom,
% 22.14/22.19 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.19 <=> ! [B_x] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.19 => ! [B_xa] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 22.14/22.19 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa)
% 22.14/22.19 => B_x = B_xa ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__diff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__idemp,axiom,
% 22.14/22.19 ! [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) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_minus__apply,axiom,
% 22.14/22.19 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 22.14/22.19 ( class_Groups_Ominus(T_b)
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_diff__eq__diff__eq,axiom,
% 22.14/22.19 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.19 ( class_Groups_Oab__group__add(T_b)
% 22.14/22.19 => ( 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)
% 22.14/22.19 => ( V_a_2 = V_b_2
% 22.14/22.19 <=> V_c_2 = V_d_2 ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__image__set__diff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_image__set__diff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => 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 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_diff__eq__diff__less__eq,axiom,
% 22.14/22.19 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.19 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.19 => ( 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)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_diff__eq__diff__less,axiom,
% 22.14/22.19 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.19 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.14/22.19 => ( 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)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_subset__inj__on,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__eq,axiom,
% 22.14/22.19 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 22.14/22.19 <=> V_x_2 = V_y_2 ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_injD,axiom,
% 22.14/22.19 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 22.14/22.19 => V_x_2 = V_y_2 ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__Int,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.19 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 22.14/22.19 => 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)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_minus__diff__eq,axiom,
% 22.14/22.19 ! [V_b,V_a,T_a] :
% 22.14/22.19 ( class_Groups_Oab__group__add(T_a)
% 22.14/22.19 => 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) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__diff__distrib__left,axiom,
% 22.14/22.19 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.19 ( class_Groups_Oordered__ab__group__add(T_a)
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_max__diff__distrib__left,axiom,
% 22.14/22.19 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.19 ( class_Groups_Oordered__ab__group__add(T_a)
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_empty__Diff,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__empty,axiom,
% 22.14/22.19 ! [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 ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__cancel,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__subset,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__mono,axiom,
% 22.14/22.19 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_D_2),V_B_2))
% 22.14/22.19 => 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))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_double__diff,axiom,
% 22.14/22.19 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 22.14/22.19 => 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 ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Un__Diff__cancel,axiom,
% 22.14/22.19 ! [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) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Un__Diff__cancel2,axiom,
% 22.14/22.19 ! [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) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Un__Diff,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__Int__distrib,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Int__Diff,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__Int__distrib2,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__Int2,axiom,
% 22.14/22.19 ! [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) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_strict__mono__imp__inj__on,axiom,
% 22.14/22.19 ! [V_A_2,V_f_2,T_b,T_c] :
% 22.14/22.19 ( ( class_Orderings_Oorder(T_c)
% 22.14/22.19 & class_Orderings_Olinorder(T_b) )
% 22.14/22.19 => ( c_Orderings_Oorder__class_Ostrict__mono(T_b,T_c,V_f_2)
% 22.14/22.19 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__Un,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( 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))
% 22.14/22.19 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.19 & c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 22.14/22.19 & 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)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__image__eq__iff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => ( 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)
% 22.14/22.19 <=> V_A_2 = V_B_2 ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__Un__image__eq__iff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( 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))
% 22.14/22.19 => ( 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)
% 22.14/22.19 <=> V_A_2 = V_B_2 ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_diff__eq,axiom,
% 22.14/22.19 ! [V_y,V_x,T_a] :
% 22.14/22.19 ( class_Lattices_Oboolean__algebra(T_a)
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__insert,axiom,
% 22.14/22.19 ! [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)))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__insert2,axiom,
% 22.14/22.19 ! [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) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__Diff__single,axiom,
% 22.14/22.19 ! [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) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__strict__subset,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => 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))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => 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 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__UNIV,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__disjoint,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__triv,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( 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))
% 22.14/22.19 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_image__diff__subset,axiom,
% 22.14/22.19 ! [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)))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__partition,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => 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 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__subset__conv,axiom,
% 22.14/22.19 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( 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))
% 22.14/22.19 <=> 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__Int,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__Un,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Un__Diff__Int,axiom,
% 22.14/22.19 ! [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 ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ivl__diff,axiom,
% 22.14/22.19 ! [V_m_2,V_n_2,V_i_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
% 22.14/22.19 => 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) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Ounion__inter,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Compl__eq__Diff__UNIV,axiom,
% 22.14/22.19 ! [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) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Compl__Diff__eq,axiom,
% 22.14/22.19 ! [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) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__eq,axiom,
% 22.14/22.19 ! [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)) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__Compl,axiom,
% 22.14/22.19 ! [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) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__le__Sup,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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))) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__image__subset__iff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => ( 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)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__image__Int,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_image__Int,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Inter,axiom,
% 22.14/22.19 ! [V_M_2,T_b] :
% 22.14/22.19 ( ? [B_x] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_M_2))
% 22.14/22.19 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_b,tc_HOL_Obool),V_M_2))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Diff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Int,axiom,
% 22.14/22.19 ! [V_G_2,V_F_2,T_b] :
% 22.14/22.19 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.14/22.19 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) )
% 22.14/22.19 => 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_G_2))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__imageI,axiom,
% 22.14/22.19 ! [V_h_2,T_c,V_F_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_F_2))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite_OinsertI,axiom,
% 22.14/22.19 ! [V_a_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite_OemptyI,axiom,
% 22.14/22.19 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__UNIV__inj__surj,axiom,
% 22.14/22.19 ! [V_f_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 22.14/22.19 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => 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)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__UNIV__surj__inj,axiom,
% 22.14/22.19 ! [V_f_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => c_Fun_Oinj__on(T_b,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_endo__inj__surj,axiom,
% 22.14/22.19 ! [V_f_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => ( c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2)
% 22.14/22.19 => hAPP(c_Set_Oimage(T_b,T_b,V_f_2),V_A_2) = V_A_2 ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__UN,axiom,
% 22.14/22.19 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( 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)))
% 22.14/22.19 <=> ! [B_x] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Finite__Set_Ofinite(T_b)
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__code,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Finite__Set_Ofinite(T_b)
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite_Oequations_I1_J,axiom,
% 22.14/22.19 ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__insert,axiom,
% 22.14/22.19 ! [V_A_2,V_a_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
% 22.14/22.19 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__subset,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_rev__finite__subset,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__UNIV,axiom,
% 22.14/22.19 ! [T_b] :
% 22.14/22.19 ( class_Finite__Set_Ofinite(T_b)
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Prod__UNIV,axiom,
% 22.14/22.19 ! [T_c,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))
% 22.14/22.19 => 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)))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Plus__UNIV__iff,axiom,
% 22.14/22.19 ! [T_c,T_b] :
% 22.14/22.19 ( 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))))
% 22.14/22.19 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 22.14/22.19 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__option__UNIV,axiom,
% 22.14/22.19 ! [T_b] :
% 22.14/22.19 ( 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))))
% 22.14/22.19 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Un,axiom,
% 22.14/22.19 ! [V_G_2,V_F_2,T_b] :
% 22.14/22.19 ( 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_G_2)))
% 22.14/22.19 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.14/22.19 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__UnI,axiom,
% 22.14/22.19 ! [V_G_2,V_F_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_G_2))
% 22.14/22.19 => 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_G_2))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Diff2,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( 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)))
% 22.14/22.19 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__UnionD,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)))
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Pow__iff,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
% 22.14/22.19 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__surj,axiom,
% 22.14/22.19 ! [V_f_2,V_B_2,T_c,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( 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)))
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Diff__insert,axiom,
% 22.14/22.19 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 22.14/22.19 ( 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))))
% 22.14/22.19 <=> 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__imageD,axiom,
% 22.14/22.19 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 22.14/22.19 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2)
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__compl,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
% 22.14/22.19 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__fun__UNIVD2,axiom,
% 22.14/22.19 ! [T_c,T_b] :
% 22.14/22.19 ( 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))))
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__surj__inj,axiom,
% 22.14/22.19 ! [V_f_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( 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)))
% 22.14/22.19 => c_Fun_Oinj__on(T_b,T_b,V_f_2,V_A_2) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__iff__surj,axiom,
% 22.14/22.19 ! [V_A_H_2,T_c,T_b,V_A_2] :
% 22.14/22.19 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( ? [B_f] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 22.14/22.19 & 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)) )
% 22.14/22.19 <=> ? [B_g] : hAPP(c_Set_Oimage(T_c,T_b,B_g),V_A_H_2) = V_A_2 ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__one_Ounion__inter,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__one_Ounion__disjoint,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__image__simple_Ounion__disjoint,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__one_Oinsert__remove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__image__simple_Oinsert__remove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.14/22.19 => 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)))))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Ohom__commute,axiom,
% 22.14/22.19 ! [V_N_2,V_h_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( ! [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))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.14/22.19 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Ohom__commute,axiom,
% 22.14/22.19 ! [V_N_2,V_h_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( ! [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))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.14/22.19 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Oremove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_equalityCE,axiom,
% 22.14/22.19 ! [V_c_2,T_b,V_B_2,V_A_2] :
% 22.14/22.19 ( V_A_2 = V_B_2
% 22.14/22.19 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) )
% 22.14/22.19 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_emptyE,axiom,
% 22.14/22.19 ! [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)))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insertE,axiom,
% 22.14/22.19 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 22.14/22.19 => ( V_a_2 != V_b_2
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insertCI,axiom,
% 22.14/22.19 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 22.14/22.19 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 22.14/22.19 => V_a_2 = V_b_2 )
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_subsetD,axiom,
% 22.14/22.19 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_UNIV__I,axiom,
% 22.14/22.19 ! [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)))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_image__eqI,axiom,
% 22.14/22.19 ! [T_b,V_A_2,T_c,V_x_2,V_f_2,V_b_2] :
% 22.14/22.19 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_UnE,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_UnCI,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 22.14/22.19 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
% 22.14/22.19 => 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_IntI,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 22.14/22.19 => 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))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_IntE,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_DiffI,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 22.14/22.19 => 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))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_DiffE,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ComplI,axiom,
% 22.14/22.19 ! [V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_UnionI,axiom,
% 22.14/22.19 ! [V_A_2,V_C_2,V_X_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2))
% 22.14/22.19 => 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))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_InterD,axiom,
% 22.14/22.19 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_InterE,axiom,
% 22.14/22.19 ! [V_X_2,V_C_2,V_A_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),V_C_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),V_X_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_PowI,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_mem__def,axiom,
% 22.14/22.19 ! [V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_eq__mem,axiom,
% 22.14/22.19 ! [V_y_2,V_x_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_fequal,V_y_2)))
% 22.14/22.19 <=> V_x_2 = V_y_2 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_eqset__imp__iff,axiom,
% 22.14/22.19 ! [V_x_2,T_b,V_B_2,V_A_2] :
% 22.14/22.19 ( V_A_2 = V_B_2
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_eqelem__imp__iff,axiom,
% 22.14/22.19 ! [V_A_2,T_b,V_y_2,V_x_2] :
% 22.14/22.19 ( V_x_2 = V_y_2
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_eq__mem__trans,axiom,
% 22.14/22.19 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 22.14/22.19 ( V_a_2 = V_b_2
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ball__UN,axiom,
% 22.14/22.19 ! [V_P_2,V_B_2,V_A_2,T_c,T_b] :
% 22.14/22.19 ( ! [B_x] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.14/22.19 <=> ! [B_x] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.14/22.19 => ! [B_xa] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(V_B_2,B_x)))
% 22.14/22.19 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_all__not__in__conv,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.19 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ex__in__conv,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.19 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_empty__iff,axiom,
% 22.14/22.19 ! [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)))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_equals0D,axiom,
% 22.14/22.19 ! [V_a_2,T_b,V_A_2] :
% 22.14/22.19 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insertI1,axiom,
% 22.14/22.19 ! [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))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__iff,axiom,
% 22.14/22.19 ! [V_A_2,V_b_2,V_a_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_A_2)))
% 22.14/22.19 <=> ( V_a_2 = V_b_2
% 22.14/22.19 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__ident,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 22.14/22.19 => ( 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)
% 22.14/22.19 <=> V_A_2 = V_B_2 ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insertI2,axiom,
% 22.14/22.19 ! [V_b_2,V_B_2,V_a_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__absorb,axiom,
% 22.14/22.19 ! [V_A_2,V_a_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2) = V_A_2 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_in__mono,axiom,
% 22.14/22.19 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_set__rev__mp,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_set__mp,axiom,
% 22.14/22.19 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_image__iff,axiom,
% 22.14/22.19 ! [V_A_2,V_f_2,T_c,V_z_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 22.14/22.19 <=> ? [B_x] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.14/22.19 & V_z_2 = hAPP(V_f_2,B_x) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_imageI,axiom,
% 22.14/22.19 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_rev__image__eqI,axiom,
% 22.14/22.19 ! [T_c,V_f_2,V_b_2,V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( V_b_2 = hAPP(V_f_2,V_x_2)
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Un__iff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 | hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_UnI1,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_UnI2,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,V_c_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
% 22.14/22.19 => 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Int__iff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 & hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_IntD1,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_IntD2,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__iff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_DiffD1,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_DiffD2,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__contraD,axiom,
% 22.14/22.19 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.19 => ( V_x_2 != V_y_2
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 22.14/22.19 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__iff,axiom,
% 22.14/22.19 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 22.14/22.19 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 22.14/22.19 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__onD,axiom,
% 22.14/22.19 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.19 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 22.14/22.19 => V_x_2 = V_y_2 ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__image__simple_Oinsert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Compl__iff,axiom,
% 22.14/22.19 ! [V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ComplD,axiom,
% 22.14/22.19 ! [V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ComplE,axiom,
% 22.14/22.19 ! [V_A_2,V_c_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Pow__top,axiom,
% 22.14/22.19 ! [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))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_psubsetD,axiom,
% 22.14/22.19 ! [V_c_2,V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_override__on__apply__notin,axiom,
% 22.14/22.19 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 22.14/22.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_override__on__apply__in,axiom,
% 22.14/22.19 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__one_Oinsert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__image__simple_Oempty,axiom,
% 22.14/22.19 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.14/22.19 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_singleton__iff,axiom,
% 22.14/22.19 ! [V_a_2,V_b_2,T_b] :
% 22.14/22.19 ( 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)))))
% 22.14/22.19 <=> V_b_2 = V_a_2 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_singletonE,axiom,
% 22.14/22.19 ! [V_a_2,V_b_2,T_b] :
% 22.14/22.19 ( 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)))))
% 22.14/22.19 => V_b_2 = V_a_2 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_subset__insert,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( 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)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__subset,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( 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))
% 22.14/22.19 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 22.14/22.19 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__image,axiom,
% 22.14/22.19 ! [V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Int__insert__right,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 22.14/22.19 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => 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)) )
% 22.14/22.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => 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) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Int__insert__left,axiom,
% 22.14/22.19 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 22.14/22.19 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 22.14/22.19 => 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)) )
% 22.14/22.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 22.14/22.19 => 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) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Int__insert__right__if0,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 22.14/22.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => 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) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Int__insert__left__if0,axiom,
% 22.14/22.19 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 22.14/22.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 22.14/22.19 => 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) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Int__insert__right__if1,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_a_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Int__insert__left__if1,axiom,
% 22.14/22.19 ! [V_B_2,V_C_2,V_a_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_C_2))
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_range__eqI,axiom,
% 22.14/22.19 ! [T_c,T_b,V_x_2,V_f_2,V_b_2] :
% 22.14/22.19 ( V_b_2 = hAPP(V_f_2,V_x_2)
% 22.14/22.19 => 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))))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_rangeI,axiom,
% 22.14/22.19 ! [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))))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__Diff1,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 22.14/22.19 => 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) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__Diff__if,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,V_x_2,T_b] :
% 22.14/22.19 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 22.14/22.19 => 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) )
% 22.14/22.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 22.14/22.19 => 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)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__upper,axiom,
% 22.14/22.19 ! [V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__lower,axiom,
% 22.14/22.19 ! [V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_lessThan__iff,axiom,
% 22.14/22.19 ! [V_k_2,V_i_2,T_b] :
% 22.14/22.19 ( class_Orderings_Oord(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_b),V_k_2)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_i_2),V_k_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_atMost__iff,axiom,
% 22.14/22.19 ! [V_k_2,V_i_2,T_b] :
% 22.14/22.19 ( class_Orderings_Oord(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_k_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Union__upper,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.19 => 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))) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Pow__bottom,axiom,
% 22.14/22.19 ! [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))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_atLeast__iff,axiom,
% 22.14/22.19 ! [V_k_2,V_i_2,T_b] :
% 22.14/22.19 ( class_Orderings_Oord(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_k_2)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_k_2),V_i_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_PowD,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Pow__iff,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_b),V_B_2)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_greaterThan__iff,axiom,
% 22.14/22.19 ! [V_k_2,V_i_2,T_b] :
% 22.14/22.19 ( class_Orderings_Oord(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inter__lower,axiom,
% 22.14/22.19 ! [V_A_2,V_B_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.19 => 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)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__one_Oremove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => hAPP(V_F_2,V_A_2) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__image__simple_Oremove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 22.14/22.19 => 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)))))) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__Diff,axiom,
% 22.14/22.19 ! [V_A_2,V_a_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => 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 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Diff__insert__absorb,axiom,
% 22.14/22.19 ! [V_A_2,V_x_2,T_b] :
% 22.14/22.19 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_range__ex1__eq,axiom,
% 22.14/22.19 ! [V_b_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => ( 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)))))
% 22.14/22.19 <=> ? [B_x] :
% 22.14/22.19 ( V_b_2 = hAPP(V_f_2,B_x)
% 22.14/22.19 & ! [B_y] :
% 22.14/22.19 ( V_b_2 = hAPP(V_f_2,B_y)
% 22.14/22.19 => B_y = B_x ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__image__mem__iff,axiom,
% 22.14/22.19 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.19 => ( 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)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Oin__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Oin__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__one_Osingleton,axiom,
% 22.14/22.19 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 22.14/22.19 => 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 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_subset__insert__iff,axiom,
% 22.14/22.19 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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)) )
% 22.14/22.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_diff__single__insert,axiom,
% 22.14/22.19 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( 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))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_Osup__Inf__absorb,axiom,
% 22.14/22.19 ! [V_a_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => 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 ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_Oinf__Sup__absorb,axiom,
% 22.14/22.19 ! [V_a_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => 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 ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inj__on__insert,axiom,
% 22.14/22.19 ! [V_A_2,V_a_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2))
% 22.14/22.19 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.19 & ~ 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))))))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Oinsert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Oinsert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_psubset__insert__iff,axiom,
% 22.14/22.19 ! [V_B_2,V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
% 22.14/22.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2))
% 22.14/22.19 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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)) )
% 22.14/22.19 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__image__simple_Ounion__inter,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Oremove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OSup__fin_Oclosed,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( ! [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))))))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_min__max_OInf__fin_Oclosed,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( ! [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))))))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ord_OatMost__iff,axiom,
% 22.14/22.19 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatMost(T_b,V_less__eq_2,V_k_2)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ord_OatLeast__iff,axiom,
% 22.14/22.19 ! [V_k_2,V_less__eq_2,V_i_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OatLeast(T_b,V_less__eq_2,V_k_2)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ord_OlessThan__iff,axiom,
% 22.14/22.19 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OlessThan(T_b,V_less_2,V_k_2)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ord_OgreaterThan__iff,axiom,
% 22.14/22.19 ! [V_k_2,V_less_2,V_i_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),c_SetInterval_Oord_OgreaterThan(T_b,V_less_2,V_k_2)))
% 22.14/22.19 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ord_OatLeastAtMost__iff,axiom,
% 22.14/22.19 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 22.14/22.19 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ord_OgreaterThanLessThan__iff,axiom,
% 22.14/22.19 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 22.14/22.19 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ord_OatLeastLessThan__iff,axiom,
% 22.14/22.19 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2))
% 22.14/22.19 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_ord_OgreaterThanAtMost__iff,axiom,
% 22.14/22.19 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_b] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2))
% 22.14/22.19 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_finite__Union,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_A_2))
% 22.14/22.19 => ( ! [B_M] :
% 22.14/22.19 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_M),V_A_2))
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_M)) )
% 22.14/22.19 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2))) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Oremove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Oremove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max_Oremove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min_Oremove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_iso__tuple__UNIV__I,axiom,
% 22.14/22.19 ! [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)))) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_insert__partition,axiom,
% 22.14/22.19 ! [V_F_2,V_x_2,T_b] :
% 22.14/22.19 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),V_F_2))
% 22.14/22.19 => ( ! [B_x] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ! [B_xa] :
% 22.14/22.19 ( 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)))
% 22.14/22.19 => ( B_x != B_xa
% 22.14/22.19 => 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)) ) ) )
% 22.14/22.19 => 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)) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_folding__one_Oclosed,axiom,
% 22.14/22.19 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.19 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( ! [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))))))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__le__Sup,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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))) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_minus__Max__eq__Min,axiom,
% 22.14/22.19 ! [V_S_2,T_b] :
% 22.14/22.19 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.14/22.19 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_minus__Min__eq__Max,axiom,
% 22.14/22.19 ! [V_S_2,T_b] :
% 22.14/22.19 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.14/22.19 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max_Osingleton,axiom,
% 22.14/22.19 ! [V_x_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => 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 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min_Osingleton,axiom,
% 22.14/22.19 ! [V_x_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => 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 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Osingleton,axiom,
% 22.14/22.19 ! [V_x_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => 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 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Osingleton,axiom,
% 22.14/22.19 ! [V_x_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => 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 ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max__ge,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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))) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min__le,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min__in,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max__in,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_sup__Inf__absorb,axiom,
% 22.14/22.19 ! [V_a_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => 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 ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Oin__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_inf__Sup__absorb,axiom,
% 22.14/22.19 ! [V_a_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.19 => 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 ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Oin__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min_Oin__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max_Oin__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin__Sup,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin__Inf,axiom,
% 22.14/22.19 ! [V_A_2,T_b] :
% 22.14/22.19 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max__mono,axiom,
% 22.14/22.19 ! [V_N_2,V_M_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 22.14/22.19 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.14/22.19 => 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))) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min__antimono,axiom,
% 22.14/22.19 ! [V_N_2,V_M_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_M_2),V_N_2))
% 22.14/22.19 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.14/22.19 => 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))) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Oinsert__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Oinsert__idem,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min__insert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Osubset__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max__insert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Osubset__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min_Osubset__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Ounion__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max_Osubset__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.19 => 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) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Ounion__idem,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min__Un,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max__Un,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Oinsert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Oinsert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min_Oinsert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max_Oinsert,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Oinsert__remove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => 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 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Oinsert__remove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => 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 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min_Oinsert__remove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => c_Big__Operators_Olinorder__class_OMin(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Ounion__disjoint,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Sup__fin_Ounion__inter,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max_Oinsert__remove,axiom,
% 22.14/22.19 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( ( 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))
% 22.14/22.19 => c_Big__Operators_Olinorder__class_OMax(T_b,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 )
% 22.14/22.19 & ( 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))
% 22.14/22.19 => 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)))))) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Ounion__disjoint,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Inf__fin_Ounion__inter,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Lattices_Olattice(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min_Ounion__disjoint,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Min_Ounion__inter,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max_Ounion__disjoint,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.19 => ( 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))
% 22.14/22.19 => 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)) ) ) ) ) ) ) ).
% 22.14/22.19
% 22.14/22.19 fof(fact_Max_Ounion__inter,axiom,
% 22.14/22.19 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.19 ( class_Orderings_Olinorder(T_b)
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.19 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.19 => ( 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))
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Max_Oclosed,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( ! [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))))))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Min_Oclosed,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( ! [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))))))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Inf__fin_Oclosed,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Lattices_Olattice(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( ! [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))))))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Sup__fin_Oclosed,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Lattices_Olattice(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( ! [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))))))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_member(T_b),c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2)),V_A_2)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fun__upd__image,axiom,
% 22.14/22.20 ! [V_y_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 22.14/22.20 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => 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)))))) )
% 22.14/22.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_the__inv__into__into,axiom,
% 22.14/22.20 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Max_Ohom__commute,axiom,
% 22.14/22.20 ! [V_N_2,V_h_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( ! [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))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.14/22.20 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Min_Ohom__commute,axiom,
% 22.14/22.20 ! [V_N_2,V_h_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( ! [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))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.14/22.20 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fun__upd__triv,axiom,
% 22.14/22.20 ! [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 ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fun__upd__idem,axiom,
% 22.14/22.20 ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
% 22.14/22.20 ( hAPP(V_f_2,V_x_2) = V_y_2
% 22.14/22.20 => c_Fun_Ofun__upd(T_c,T_b,V_f_2,V_x_2,V_y_2) = V_f_2 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fun__upd__other,axiom,
% 22.14/22.20 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 22.14/22.20 ( V_z_2 != V_x_2
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fun__upd__twist,axiom,
% 22.14/22.20 ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
% 22.14/22.20 ( V_a_2 != V_c_2
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fun__upd__apply,axiom,
% 22.14/22.20 ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
% 22.14/22.20 ( ( V_z_2 = V_x_2
% 22.14/22.20 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2),V_z_2) = V_y_2 )
% 22.14/22.20 & ( V_z_2 != V_x_2
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fun__upd__same,axiom,
% 22.14/22.20 ! [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 ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fun__upd__upd,axiom,
% 22.14/22.20 ! [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) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fun__upd__idem__iff,axiom,
% 22.14/22.20 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_x_2,V_y_2) = V_f_2
% 22.14/22.20 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_the__inv__into__f__eq,axiom,
% 22.14/22.20 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.20 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => hAPP(c_Fun_Othe__inv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_the__inv__into__f__f,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => 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 ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_the__inv__f__f,axiom,
% 22.14/22.20 ! [V_x_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.14/22.20 => 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 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_the__inv__into__onto,axiom,
% 22.14/22.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.20 => 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 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_inj__on__the__inv__into,axiom,
% 22.14/22.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_inj__on__fun__updI,axiom,
% 22.14/22.20 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_f__the__inv__into__f,axiom,
% 22.14/22.20 ! [V_y_2,V_A_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 22.14/22.20 => 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 ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Inf__fin_Ohom__commute,axiom,
% 22.14/22.20 ! [V_N_2,V_h_2,T_b] :
% 22.14/22.20 ( class_Lattices_Olattice(T_b)
% 22.14/22.20 => ( ! [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))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.14/22.20 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Sup__fin_Ohom__commute,axiom,
% 22.14/22.20 ! [V_N_2,V_h_2,T_b] :
% 22.14/22.20 ( class_Lattices_Olattice(T_b)
% 22.14/22.20 => ( ! [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))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.14/22.20 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__empty__induct,axiom,
% 22.14/22.20 ! [V_P_2,V_A_2,T_b] :
% 22.14/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(V_P_2,V_A_2))
% 22.14/22.20 => ( ! [B_a,B_A] :
% 22.14/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_A))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
% 22.14/22.20 => ( hBOOL(hAPP(V_P_2,B_A))
% 22.14/22.20 => 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)))))) ) ) )
% 22.14/22.20 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_folding__one__idem_Ounion__idem,axiom,
% 22.14/22.20 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.20 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => 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)) ) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__subset__induct,axiom,
% 22.14/22.20 ! [V_P_2,V_A_2,V_F_2,T_b] :
% 22.14/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_F_2),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 22.14/22.20 => ( ! [B_a,B_F] :
% 22.14/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 22.14/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_F))
% 22.14/22.20 => ( hBOOL(hAPP(V_P_2,B_F))
% 22.14/22.20 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
% 22.14/22.20 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_folding__one__idem_Osubset__idem,axiom,
% 22.14/22.20 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.20 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.20 => 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) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_folding__one__idem_Oinsert__idem,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.20 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_inj__on__Inter,axiom,
% 22.14/22.20 ! [V_f_2,T_c,T_b,V_S_2] :
% 22.14/22.20 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 22.14/22.20 => ( ! [B_A] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_A),V_S_2))
% 22.14/22.20 => c_Fun_Oinj__on(T_b,T_c,V_f_2,B_A) )
% 22.14/22.20 => 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)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_folding__one__idem_Oidem,axiom,
% 22.14/22.20 ! [V_x_2,V_F_2,V_f_2,T_b] :
% 22.14/22.20 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 22.14/22.20 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_folding__one__idem_Oin__idem,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.20 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Inter__subset,axiom,
% 22.14/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.20 ( ! [B_X] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_A_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_X),V_B_2)) )
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))
% 22.14/22.20 => 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)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__antimono,axiom,
% 22.14/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.20 => 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))) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_folding__one__idem_Ohom__commute,axiom,
% 22.14/22.20 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_b] :
% 22.14/22.20 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 22.14/22.20 => ( ! [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))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.14/22.20 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom,
% 22.14/22.20 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.14/22.20 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.14/22.20 => ( ! [B_x] :
% 22.14/22.20 ( 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)))
% 22.14/22.20 => hAPP(V_g_2,B_x) = V_z_2 )
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__diff1,axiom,
% 22.14/22.20 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Oab__group__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.20 => 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)) )
% 22.14/22.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.20 => 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) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__diff1__ring,axiom,
% 22.14/22.20 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Rings_Oring(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_InterI,axiom,
% 22.14/22.20 ! [V_A_2,V_C_2,T_b] :
% 22.14/22.20 ( ! [B_X] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X)) )
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Min__eqI,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( ! [B_y] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_y)) )
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__diff__nat__ivl,axiom,
% 22.14/22.20 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 22.14/22.20 ( class_Groups_Oab__group__add(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__singleton__def,axiom,
% 22.14/22.20 ! [V_a_2,V_f_2,T_b,V_g_2] :
% 22.14/22.20 ( V_g_2 = c_Finite__Set_Ofold1(T_b,V_f_2)
% 22.14/22.20 => 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 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__singleton,axiom,
% 22.14/22.20 ! [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 ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__diff__nat,axiom,
% 22.14/22.20 ! [V_f_2,V_A_2,V_B_2,T_b] :
% 22.14/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.20 => 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)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_folding__one_Oeq__fold,axiom,
% 22.14/22.20 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.20 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Sup__fin_OF__eq,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Lattices_Olattice(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Inf__fin_OF__eq,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Lattices_Olattice(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__diff1__nat,axiom,
% 22.14/22.20 ! [V_f_2,V_A_2,V_a_2,T_b] :
% 22.14/22.20 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.20 => 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)) )
% 22.14/22.20 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__diff,axiom,
% 22.14/22.20 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Oab__group__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Min_OF__eq,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Max_OF__eq,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_min__max_OInf__fin_OF__eq,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_min__max_OSup__fin_OF__eq,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__belowI,axiom,
% 22.14/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Lattices_Osemilattice__inf(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_below__fold1__iff,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Lattices_Osemilattice__inf(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> ! [B_x] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_min__max_Ofold1__belowI,axiom,
% 22.14/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_min__max_Obelow__fold1__iff,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> ! [B_x] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__below__iff,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( 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))
% 22.14/22.20 <=> ? [B_x] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_strict__below__fold1__iff,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> ! [B_x] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__strict__below__iff,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( 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))
% 22.14/22.20 <=> ? [B_x] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.20 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2)) ) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_semilattice__big_OF__eq,axiom,
% 22.14/22.20 ! [V_A_2,V_F_2,V_f_2,T_b] :
% 22.14/22.20 ( c_Big__Operators_Osemilattice__big(T_b,V_f_2,V_F_2)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__strict__mono,axiom,
% 22.14/22.20 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 22.14/22.20 & class_Groups_Oordered__cancel__ab__semigroup__add(T_c) )
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( ! [B_x] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 22.14/22.20 => 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))) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum_Oremove,axiom,
% 22.14/22.20 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => 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)))))) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__diff1_H,axiom,
% 22.14/22.20 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.14/22.20 => 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)))))) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__Un,axiom,
% 22.14/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Groups_Oab__semigroup__mult(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( 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))
% 22.14/22.20 => 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)) ) ) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__insert,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Groups_Oab__semigroup__mult(T_b)
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Max__eqI,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Orderings_Olinorder(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( ! [B_y] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_y),V_x_2)) )
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = V_x_2 ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__reindex__cong,axiom,
% 22.14/22.20 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 22.14/22.20 ( class_Groups_Ocomm__monoid__add(T_d)
% 22.14/22.20 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.14/22.20 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 22.14/22.20 => ( ! [B_a] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 22.14/22.20 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) )
% 22.14/22.20 => 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) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__atLeastLessThan,axiom,
% 22.14/22.20 ! [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))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__add__nat__ivl,axiom,
% 22.14/22.20 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_b] :
% 22.14/22.20 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_eq__add__iff2,axiom,
% 22.14/22.20 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Rings_Oring(T_b)
% 22.14/22.20 => ( 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)
% 22.14/22.20 <=> 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_eq__add__iff1,axiom,
% 22.14/22.20 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Rings_Oring(T_b)
% 22.14/22.20 => ( 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)
% 22.14/22.20 <=> 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 ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_atLeastLessThan__add__Un,axiom,
% 22.14/22.20 ! [V_k_2,V_j_2,V_i_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_times_Oidem,axiom,
% 22.14/22.20 ! [V_a,T_a] :
% 22.14/22.20 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 22.14/22.20 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_mult__idem,axiom,
% 22.14/22.20 ! [V_x,T_a] :
% 22.14/22.20 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 22.14/22.20 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_mult__left__idem,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Lattices_Oab__semigroup__idem__mult(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oab__semigroup__add(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oab__semigroup__mult(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__left__cancel,axiom,
% 22.14/22.20 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Groups_Ocancel__semigroup__add(T_b)
% 22.14/22.20 => ( 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)
% 22.14/22.20 <=> V_b_2 = V_c_2 ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__right__cancel,axiom,
% 22.14/22.20 ! [V_c_2,V_a_2,V_b_2,T_b] :
% 22.14/22.20 ( class_Groups_Ocancel__semigroup__add(T_b)
% 22.14/22.20 => ( 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)
% 22.14/22.20 <=> V_b_2 = V_c_2 ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__left__imp__eq,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Ocancel__semigroup__add(T_a)
% 22.14/22.20 => ( 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)
% 22.14/22.20 => V_b = V_c ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__imp__eq,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Ocancel__ab__semigroup__add(T_a)
% 22.14/22.20 => ( 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)
% 22.14/22.20 => V_b = V_c ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__right__imp__eq,axiom,
% 22.14/22.20 ! [V_c,V_a,V_b,T_a] :
% 22.14/22.20 ( class_Groups_Ocancel__semigroup__add(T_a)
% 22.14/22.20 => ( 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)
% 22.14/22.20 => V_b = V_c ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__class_Odistrib,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_combine__common__factor,axiom,
% 22.14/22.20 ! [V_c,V_b,V_e,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Osemiring(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__nat__set__iff__bounded__le,axiom,
% 22.14/22.20 ! [V_N_2] :
% 22.14/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 22.14/22.20 <=> ? [B_m] :
% 22.14/22.20 ! [B_x] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__add__iff2,axiom,
% 22.14/22.20 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Rings_Oordered__ring(T_b)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__add__iff1,axiom,
% 22.14/22.20 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Rings_Oordered__ring(T_b)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> 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)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_less__add__iff1,axiom,
% 22.14/22.20 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Rings_Oordered__ring(T_b)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> 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)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_less__add__iff2,axiom,
% 22.14/22.20 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Rings_Oordered__ring(T_b)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__le__cancel__right,axiom,
% 22.14/22.20 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__le__cancel__left,axiom,
% 22.14/22.20 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__right__mono,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__left__mono,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__mono,axiom,
% 22.14/22.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add(T_a)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 22.14/22.20 => 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))) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__le__imp__le__right,axiom,
% 22.14/22.20 ! [V_b,V_c,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__le__imp__le__left,axiom,
% 22.14/22.20 ! [V_b,V_a,V_c,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__less__cancel__right,axiom,
% 22.14/22.20 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__less__cancel__left,axiom,
% 22.14/22.20 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_b)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__strict__right__mono,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__strict__left__mono,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__strict__mono,axiom,
% 22.14/22.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 22.14/22.20 => 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))) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__less__imp__less__right,axiom,
% 22.14/22.20 ! [V_b,V_c,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__less__imp__less__left,axiom,
% 22.14/22.20 ! [V_b,V_a,V_c,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 22.14/22.20 => ( 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)))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__add__cancel,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Ogroup__add(T_a)
% 22.14/22.20 => 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 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__diff__cancel,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Ogroup__add(T_a)
% 22.14/22.20 => 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 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_minus__add__cancel,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Ogroup__add(T_a)
% 22.14/22.20 => 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 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__minus__cancel,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Ogroup__add(T_a)
% 22.14/22.20 => 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 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_minus__add,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Ogroup__add(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_minus__add__distrib,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oab__group__add(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_square__eq__iff,axiom,
% 22.14/22.20 ! [V_b_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Rings_Oidom(T_b)
% 22.14/22.20 => ( 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)
% 22.14/22.20 <=> ( V_a_2 = V_b_2
% 22.14/22.20 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_minus__mult__minus,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Oring(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_minus__mult__commute,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Oring(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_minus__mult__left,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Oring(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_minus__mult__right,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Oring(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_min__add__distrib__left,axiom,
% 22.14/22.20 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_max__add__distrib__left,axiom,
% 22.14/22.20 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__le__less__mono,axiom,
% 22.14/22.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 22.14/22.20 => 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))) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__less__le__mono,axiom,
% 22.14/22.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a)
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 22.14/22.20 => 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))) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__minus__eq__add,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Ogroup__add(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_ab__diff__minus,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Oab__group__add(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__def,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Groups_Ogroup__add(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__Un__nat,axiom,
% 22.14/22.20 ! [V_f_2,V_B_2,V_A_2,T_b] :
% 22.14/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum_Oinsert,axiom,
% 22.14/22.20 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__insert,axiom,
% 22.14/22.20 ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.14/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__Un__Int,axiom,
% 22.14/22.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__insert__idem,axiom,
% 22.14/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => 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)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__Un2,axiom,
% 22.14/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.14/22.20 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.20 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => 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)) ) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum_Oinsert__remove,axiom,
% 22.14/22.20 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => 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)))))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__Un__disjoint,axiom,
% 22.14/22.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.20 => ( 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))
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_setsum__Un,axiom,
% 22.14/22.20 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 22.14/22.20 ( class_Groups_Oab__group__add(T_c)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.14/22.20 => 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))) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
% 22.14/22.20 ! [V_y,V_x,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__ring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_fold1__in,axiom,
% 22.14/22.20 ! [V_A_2,T_b] :
% 22.14/22.20 ( class_Groups_Oab__semigroup__mult(T_b)
% 22.14/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.14/22.20 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.14/22.20 => ( ! [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))))))
% 22.14/22.20 => 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)) ) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__diff__iff,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_k_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_Nat_Odiff__diff__eq,axiom,
% 22.14/22.20 ! [V_n,V_m,V_k] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 22.14/22.20 => 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) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_eq__diff__iff,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_k_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 22.14/22.20 => ( 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)
% 22.14/22.20 <=> V_m_2 = V_n_2 ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__le__add__iff1,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> 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)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__diff__add__eq1,axiom,
% 22.14/22.20 ! [V_n,V_m,V_u,V_i,V_j] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__eq__add__iff1,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 22.14/22.20 => ( 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)
% 22.14/22.20 <=> 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 ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__lessThan,axiom,
% 22.14/22.20 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__atMost,axiom,
% 22.14/22.20 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__atLeastAtMost,axiom,
% 22.14/22.20 ! [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))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__greaterThanAtMost,axiom,
% 22.14/22.20 ! [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))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__greaterThanLessThan,axiom,
% 22.14/22.20 ! [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))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_left__add__mult__distrib,axiom,
% 22.14/22.20 ! [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) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__add__right__cancel,axiom,
% 22.14/22.20 ! [V_n_2,V_k_2,V_m_2] :
% 22.14/22.20 ( 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)
% 22.14/22.20 <=> V_m_2 = V_n_2 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__add__left__cancel,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_k_2] :
% 22.14/22.20 ( 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)
% 22.14/22.20 <=> V_m_2 = V_n_2 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__mult__distrib,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__mult__assoc,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__add__assoc,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__mult__distrib2,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__add__left__commute,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__mult__commute,axiom,
% 22.14/22.20 ! [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) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__add__commute,axiom,
% 22.14/22.20 ! [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) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__lessD1,axiom,
% 22.14/22.20 ! [V_k,V_j,V_i] :
% 22.14/22.20 ( 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))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_less__add__eq__less,axiom,
% 22.14/22.20 ! [V_n,V_m,V_l,V_k] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 22.14/22.20 => ( 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)
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__less__mono,axiom,
% 22.14/22.20 ! [V_l,V_k,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__less__mono1,axiom,
% 22.14/22.20 ! [V_k,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_trans__less__add2,axiom,
% 22.14/22.20 ! [V_m,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_trans__less__add1,axiom,
% 22.14/22.20 ! [V_m,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__add__left__cancel__less,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_k_2] :
% 22.14/22.20 ( 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)))
% 22.14/22.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_not__add__less2,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_not__add__less1,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_infinite__UNIV__nat,axiom,
% 22.14/22.20 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_finite__nat__set__iff__bounded,axiom,
% 22.14/22.20 ! [V_N_2] :
% 22.14/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2))
% 22.14/22.20 <=> ? [B_m] :
% 22.14/22.20 ! [B_x] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 22.14/22.20 ! [V_c,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 22.14/22.20 ! [V_d,V_c,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 22.14/22.20 ! [V_d,V_c,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 22.14/22.20 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 22.14/22.20 ! [V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 22.14/22.20 ! [V_ry,V_rx,V_lx,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 22.14/22.20 ! [V_ry,V_rx,V_lx,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 22.14/22.20 ! [V_rx,V_ly,V_lx,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 22.14/22.20 ! [V_rx,V_ly,V_lx,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 22.14/22.20 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 22.14/22.20 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 22.14/22.20 ! [V_ry,V_rx,V_ly,V_lx,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__less__le,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 22.14/22.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.14/22.20 & V_m_2 != V_n_2 ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__eq__less__or__eq,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.14/22.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 22.14/22.20 | V_m_2 = V_n_2 ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_less__imp__le__nat,axiom,
% 22.14/22.20 ! [V_n,V_m] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__neq__implies__less,axiom,
% 22.14/22.20 ! [V_n,V_m] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.14/22.20 => ( V_m != V_n
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_less__or__eq__imp__le,axiom,
% 22.14/22.20 ! [V_n,V_m] :
% 22.14/22.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.14/22.20 | V_m = V_n )
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__refl,axiom,
% 22.14/22.20 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__square,axiom,
% 22.14/22.20 ! [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))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__add2,axiom,
% 22.14/22.20 ! [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))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__add1,axiom,
% 22.14/22.20 ! [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))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__cube,axiom,
% 22.14/22.20 ! [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)))) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__iff__add,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.14/22.20 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__le__linear,axiom,
% 22.14/22.20 ! [V_n,V_m] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.14/22.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__add__left__cancel__le,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_k_2] :
% 22.14/22.20 ( 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)))
% 22.14/22.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_eq__imp__le,axiom,
% 22.14/22.20 ! [V_n,V_m] :
% 22.14/22.20 ( V_m = V_n
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_trans__le__add1,axiom,
% 22.14/22.20 ! [V_m,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_trans__le__add2,axiom,
% 22.14/22.20 ! [V_m,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__le__mono1,axiom,
% 22.14/22.20 ! [V_k,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_mult__le__mono1,axiom,
% 22.14/22.20 ! [V_k,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_mult__le__mono2,axiom,
% 22.14/22.20 ! [V_k,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__trans,axiom,
% 22.14/22.20 ! [V_k,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__antisym,axiom,
% 22.14/22.20 ! [V_n,V_m] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.14/22.20 => V_m = V_n ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__le__mono,axiom,
% 22.14/22.20 ! [V_l,V_k,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_mult__le__mono,axiom,
% 22.14/22.20 ! [V_l,V_k,V_j,V_i] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__leD2,axiom,
% 22.14/22.20 ! [V_n,V_k,V_m] :
% 22.14/22.20 ( 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))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__leD1,axiom,
% 22.14/22.20 ! [V_n,V_k,V_m] :
% 22.14/22.20 ( 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))
% 22.14/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__leE,axiom,
% 22.14/22.20 ! [V_n,V_k,V_m] :
% 22.14/22.20 ( 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))
% 22.14/22.20 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.14/22.20 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_less__diff__conv,axiom,
% 22.14/22.20 ! [V_k_2,V_j_2,V_i_2] :
% 22.14/22.20 ( 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)))
% 22.14/22.20 <=> 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_add__diff__inverse,axiom,
% 22.14/22.20 ! [V_n,V_m] :
% 22.14/22.20 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.14/22.20 => 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 ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_less__imp__diff__less,axiom,
% 22.14/22.20 ! [V_n,V_k,V_j] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__less__mono2,axiom,
% 22.14/22.20 ! [V_l,V_n,V_m] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__minus__add__max,axiom,
% 22.14/22.20 ! [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) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__mult__distrib2,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__add__inverse2,axiom,
% 22.14/22.20 ! [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 ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__add__inverse,axiom,
% 22.14/22.20 ! [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 ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__diff__left,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__commute,axiom,
% 22.14/22.20 ! [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) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__mult__distrib,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__cancel,axiom,
% 22.14/22.20 ! [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) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__cancel2,axiom,
% 22.14/22.20 ! [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) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_min__diff,axiom,
% 22.14/22.20 ! [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) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 22.14/22.20 ! [V_z,V_y,V_x,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_crossproduct__noteq,axiom,
% 22.14/22.20 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
% 22.14/22.20 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 22.14/22.20 => ( ( V_a_2 != V_b_2
% 22.14/22.20 & V_c_2 != V_d_2 )
% 22.14/22.20 <=> 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)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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)) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 22.14/22.20 ! [V_b,V_m,V_a,T_a] :
% 22.14/22.20 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_crossproduct__eq,axiom,
% 22.14/22.20 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_b] :
% 22.14/22.20 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 22.14/22.20 => ( 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))
% 22.14/22.20 <=> ( V_w_2 = V_x_2
% 22.14/22.20 | V_y_2 = V_z_2 ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__less__add__iff2,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_nat__less__add__iff1,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> 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)) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__less__mono,axiom,
% 22.14/22.20 ! [V_c,V_b,V_a] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a))
% 22.14/22.20 => 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))) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_less__diff__iff,axiom,
% 22.14/22.20 ! [V_n_2,V_m_2,V_k_2] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2))
% 22.14/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2))
% 22.14/22.20 => ( 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)))
% 22.14/22.20 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__le__self,axiom,
% 22.14/22.20 ! [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)) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__diff__right,axiom,
% 22.14/22.20 ! [V_i,V_j,V_k] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 22.14/22.20 => 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) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__diff__conv,axiom,
% 22.14/22.20 ! [V_i_2,V_k_2,V_j_2] :
% 22.14/22.20 ( 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))
% 22.14/22.20 <=> 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_le__add__diff,axiom,
% 22.14/22.20 ! [V_m,V_n,V_k] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__le__mono2,axiom,
% 22.14/22.20 ! [V_l,V_n,V_m] :
% 22.14/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.14/22.20 => 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))) ) ).
% 22.14/22.20
% 22.14/22.20 fof(fact_diff__le__mono,axiom,
% 22.14/22.20 ! [V_l,V_n,V_m] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.27/22.20 => 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))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_diff__diff__cancel,axiom,
% 22.27/22.20 ! [V_n,V_i] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n))
% 22.27/22.20 => 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 ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_le__add__diff__inverse,axiom,
% 22.27/22.20 ! [V_m,V_n] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.27/22.20 => 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 ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_add__diff__assoc,axiom,
% 22.27/22.20 ! [V_i,V_j,V_k] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 22.27/22.20 => 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) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_le__diff__conv2,axiom,
% 22.27/22.20 ! [V_i_2,V_j_2,V_k_2] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
% 22.27/22.20 => ( 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)))
% 22.27/22.20 <=> 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)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_le__add__diff__inverse2,axiom,
% 22.27/22.20 ! [V_m,V_n] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.27/22.20 => 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 ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_le__imp__diff__is__add,axiom,
% 22.27/22.20 ! [V_k_2,V_j_2,V_i_2] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 22.27/22.20 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
% 22.27/22.20 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_diff__add__assoc,axiom,
% 22.27/22.20 ! [V_i,V_j,V_k] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 22.27/22.20 => 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)) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_add__diff__assoc2,axiom,
% 22.27/22.20 ! [V_i,V_j,V_k] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 22.27/22.20 => 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) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_diff__add__assoc2,axiom,
% 22.27/22.20 ! [V_i,V_j,V_k] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 22.27/22.20 => 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) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_nat__eq__add__iff2,axiom,
% 22.27/22.20 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 22.27/22.20 => ( 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)
% 22.27/22.20 <=> 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_nat__diff__add__eq2,axiom,
% 22.27/22.20 ! [V_n,V_m,V_u,V_j,V_i] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.27/22.20 => 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)) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_nat__le__add__iff2,axiom,
% 22.27/22.20 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
% 22.27/22.20 => ( 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)))
% 22.27/22.20 <=> 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))) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_termination__basic__simps_I3_J,axiom,
% 22.27/22.20 ! [V_z,V_y,V_x] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y))
% 22.27/22.20 => 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))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_termination__basic__simps_I4_J,axiom,
% 22.27/22.20 ! [V_y,V_z,V_x] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z))
% 22.27/22.20 => 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))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_hom__fold1__commute,axiom,
% 22.27/22.20 ! [V_N_2,V_h_2,T_b] :
% 22.27/22.20 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 22.27/22.20 => ( ! [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))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.27/22.20 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.27/22.20 => 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)) ) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__graph__permute__diff,axiom,
% 22.27/22.20 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_b] :
% 22.27/22.20 ( class_Groups_Oab__semigroup__mult(T_b)
% 22.27/22.20 => ( 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))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 22.27/22.20 => 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)) ) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_setprod_Oremove,axiom,
% 22.27/22.20 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 22.27/22.20 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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)))))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_setsum__ivl__cong,axiom,
% 22.27/22.20 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_b,T_c] :
% 22.27/22.20 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.20 & class_Orderings_Oord(T_b) )
% 22.27/22.20 => ( V_a_2 = V_c_2
% 22.27/22.20 => ( V_b_2 = V_d_2
% 22.27/22.20 => ( ! [B_x] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),B_x))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_d_2))
% 22.27/22.20 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) )
% 22.27/22.20 => 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)) ) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_sup__nat__def,axiom,
% 22.27/22.20 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_less__not__refl,axiom,
% 22.27/22.20 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_nat__neq__iff,axiom,
% 22.27/22.20 ! [V_n_2,V_m_2] :
% 22.27/22.20 ( V_m_2 != V_n_2
% 22.27/22.20 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.20 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_linorder__neqE__nat,axiom,
% 22.27/22.20 ! [V_y,V_x] :
% 22.27/22.20 ( V_x != V_y
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 22.27/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_less__irrefl__nat,axiom,
% 22.27/22.20 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_less__not__refl2,axiom,
% 22.27/22.20 ! [V_m,V_n] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 22.27/22.20 => V_m != V_n ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_less__not__refl3,axiom,
% 22.27/22.20 ! [V_t,V_s] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t))
% 22.27/22.20 => V_s != V_t ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_nat__less__cases,axiom,
% 22.27/22.20 ! [V_P_2,V_n_2,V_m_2] :
% 22.27/22.20 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.20 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 22.27/22.20 => ( ( V_m_2 = V_n_2
% 22.27/22.20 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 22.27/22.20 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 22.27/22.20 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) )
% 22.27/22.20 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_inf__nat__def,axiom,
% 22.27/22.20 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__empty,axiom,
% 22.27/22.20 ! [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 ).
% 22.27/22.20
% 22.27/22.20 fof(fact_empty__fold__graphE,axiom,
% 22.27/22.20 ! [V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( 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))
% 22.27/22.20 => V_x_2 = V_z_2 ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__graph_OemptyI,axiom,
% 22.27/22.20 ! [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)) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__graph_Oequations_I1_J,axiom,
% 22.27/22.20 ! [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)) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__graph__imp__finite,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 22.27/22.20 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__graph_OinsertI,axiom,
% 22.27/22.20 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 22.27/22.20 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 22.27/22.20 => 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))) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_union__fold__insert,axiom,
% 22.27/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__sup__insert,axiom,
% 22.27/22.20 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Lattices_Osemilattice__sup(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__inf__insert,axiom,
% 22.27/22.20 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Lattices_Osemilattice__inf(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_min__max_Ofold__inf__insert,axiom,
% 22.27/22.20 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_min__max_Ofold__sup__insert,axiom,
% 22.27/22.20 ! [V_a_2,V_b_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_sup__Sup__fold__sup,axiom,
% 22.27/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_inf__Inf__fold__inf,axiom,
% 22.27/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_termination__basic__simps_I1_J,axiom,
% 22.27/22.20 ! [V_z,V_y,V_x] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 22.27/22.20 => 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))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_termination__basic__simps_I2_J,axiom,
% 22.27/22.20 ! [V_y,V_z,V_x] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z))
% 22.27/22.20 => 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))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom,
% 22.27/22.20 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofolding__one__idem(T_b,V_f_2,V_F_2)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_termination__basic__simps_I5_J,axiom,
% 22.27/22.20 ! [V_y,V_x] :
% 22.27/22.20 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y))
% 22.27/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_setprod__insert,axiom,
% 22.27/22.20 ! [V_f_2,V_a_2,V_A_2,T_b,T_c] :
% 22.27/22.20 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.20 => 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)) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_setprod_Oinsert,axiom,
% 22.27/22.20 ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
% 22.27/22.20 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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)) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_setprod__Un__Int,axiom,
% 22.27/22.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.27/22.20 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => 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)) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_setprod_Ounion__inter,axiom,
% 22.27/22.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.27/22.20 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => 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)) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__graph__insert__swap,axiom,
% 22.27/22.20 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_b] :
% 22.27/22.20 ( class_Groups_Oab__semigroup__mult(T_b)
% 22.27/22.20 => ( 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))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 22.27/22.20 => 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))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_sup__le__fold__sup,axiom,
% 22.27/22.20 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Lattices_Osemilattice__sup(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.20 => 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))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold__inf__le__inf,axiom,
% 22.27/22.20 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Lattices_Osemilattice__inf(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.20 => 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))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_min__max_Ofold__inf__le__inf,axiom,
% 22.27/22.20 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.20 => 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))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_min__max_Osup__le__fold__sup,axiom,
% 22.27/22.20 ! [V_b_2,V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.20 => 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))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Sup__fold__sup,axiom,
% 22.27/22.20 ! [V_A_2,T_b] :
% 22.27/22.20 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Inf__fold__inf,axiom,
% 22.27/22.20 ! [V_A_2,T_b] :
% 22.27/22.20 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold1__eq__fold__idem,axiom,
% 22.27/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom,
% 22.27/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Lattices_Olattice(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom,
% 22.27/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Lattices_Olattice(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Min_Oeq__fold__idem_H,axiom,
% 22.27/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Max_Oeq__fold__idem_H,axiom,
% 22.27/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom,
% 22.27/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom,
% 22.27/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_folding__one_Oeq__fold_H,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofolding__one(T_b,V_f_2,V_F_2)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_setprod_Oinsert__remove,axiom,
% 22.27/22.20 ! [V_x_2,V_g_2,V_A_2,T_b,T_c] :
% 22.27/22.20 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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)))))) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_setprod_Ounion__disjoint,axiom,
% 22.27/22.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.27/22.20 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => ( 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))
% 22.27/22.20 => 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)) ) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_setprod__Un__disjoint,axiom,
% 22.27/22.20 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.27/22.20 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => ( 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))
% 22.27/22.20 => 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)) ) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Diff1__fold__graph,axiom,
% 22.27/22.20 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( 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))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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))) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold1__eq__fold,axiom,
% 22.27/22.20 ! [V_a_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Groups_Oab__semigroup__mult(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.20 => 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) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Sup__fin_Oeq__fold_H,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Lattices_Olattice(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Inf__fin_Oeq__fold_H,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Lattices_Olattice(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Min_Oeq__fold_H,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_Max_Oeq__fold_H,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( class_Orderings_Olinorder(T_b)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm_Ofold__rec,axiom,
% 22.27/22.20 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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)))))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold1Set_Ointros,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.20 => 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)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
% 22.27/22.20 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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)))))) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm_Ofold__insert,axiom,
% 22.27/22.20 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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)) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm_Ofold__insert2,axiom,
% 22.27/22.20 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__Diff1__less,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => 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))) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__Diff2__less,axiom,
% 22.27/22.20 ! [V_y_2,V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 22.27/22.20 => 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))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm_Ofun__left__comm,axiom,
% 22.27/22.20 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.20 => 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)) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__lessThan,axiom,
% 22.27/22.20 ! [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 ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm,axiom,
% 22.27/22.20 ! [T_b] :
% 22.27/22.20 ( class_Groups_Oab__semigroup__mult(T_b)
% 22.27/22.20 => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom,
% 22.27/22.20 ! [V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 22.27/22.20 => ( 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)))
% 22.27/22.20 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__image,axiom,
% 22.27/22.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.27/22.20 => 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) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
% 22.27/22.20 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 22.27/22.20 => V_y_2 = V_x_2 ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_empty__fold1SetE,axiom,
% 22.27/22.20 ! [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)) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold1Set__nonempty,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,V_f_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
% 22.27/22.20 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_subset__card__intvl__is__intvl,axiom,
% 22.27/22.20 ! [V_k_2,V_A_2] :
% 22.27/22.20 ( 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)))))
% 22.27/22.20 => 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))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__atLeastLessThan,axiom,
% 22.27/22.20 ! [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) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__greaterThanAtMost,axiom,
% 22.27/22.20 ! [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) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__insert__le,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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)))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__mono,axiom,
% 22.27/22.20 ! [V_A_2,V_B_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.27/22.20 => 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))) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__seteq,axiom,
% 22.27/22.20 ! [V_A_2,V_B_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.27/22.20 => ( 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)))
% 22.27/22.20 => V_A_2 = V_B_2 ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__image__le,axiom,
% 22.27/22.20 ! [V_f_2,T_c,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_inj__on__iff__eq__card,axiom,
% 22.27/22.20 ! [V_f_2,T_c,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.27/22.20 <=> 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_eq__card__imp__inj__on,axiom,
% 22.27/22.20 ! [V_f_2,T_c,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( 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)
% 22.27/22.20 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_pigeonhole,axiom,
% 22.27/22.20 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( 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)))
% 22.27/22.20 => ~ c_Fun_Oinj__on(T_c,T_b,V_f_2,V_A_2) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_psubset__card__mono,axiom,
% 22.27/22.20 ! [V_A_2,V_B_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.27/22.20 => 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))) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
% 22.27/22.20 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm_Ofold__equality,axiom,
% 22.27/22.20 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 22.27/22.20 => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fold1Set__sing,axiom,
% 22.27/22.20 ! [V_b_2,V_a_2,V_f_2,T_b] :
% 22.27/22.20 ( 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))
% 22.27/22.20 <=> V_a_2 = V_b_2 ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card_Ounion__inter,axiom,
% 22.27/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => 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)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__Un__Int,axiom,
% 22.27/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => 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))) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__bij__eq,axiom,
% 22.27/22.20 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.27/22.20 => ( 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))
% 22.27/22.20 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 22.27/22.20 => ( 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))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.27/22.20 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__Diff__subset,axiom,
% 22.27/22.20 ! [V_A_2,V_B_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.27/22.20 => 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)) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__Diff__subset__Int,axiom,
% 22.27/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.27/22.20 ( 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)))
% 22.27/22.20 => 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))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_diff__card__le__card__Diff,axiom,
% 22.27/22.20 ! [V_A_2,V_B_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => 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)))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__psubset,axiom,
% 22.27/22.20 ! [V_A_2,V_B_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.27/22.20 => ( 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)))
% 22.27/22.20 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__Un__disjoint,axiom,
% 22.27/22.20 ! [V_B_2,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.20 => ( 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))
% 22.27/22.20 => 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)) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__Diff1__le,axiom,
% 22.27/22.20 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => 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))) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_card__inj__on__le,axiom,
% 22.27/22.20 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.20 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.27/22.20 => ( 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))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.27/22.20 => 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))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_inj__on__iff__card__le,axiom,
% 22.27/22.20 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.27/22.20 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.20 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.27/22.20 => ( ? [B_f] :
% 22.27/22.20 ( c_Fun_Oinj__on(T_b,T_c,B_f,V_A_2)
% 22.27/22.20 & 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)) )
% 22.27/22.20 <=> 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))) ) ) ) ).
% 22.27/22.20
% 22.27/22.20 fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
% 22.27/22.20 ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.21 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
% 22.27/22.21 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.21 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.21 => ? [B_y_H] :
% 22.27/22.21 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H)
% 22.27/22.21 & 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)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__Diff__singleton,axiom,
% 22.27/22.21 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__Diff__singleton__if,axiom,
% 22.27/22.21 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.21 => 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)) )
% 22.27/22.21 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.21 => 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) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card_Oremove,axiom,
% 22.27/22.21 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.21 => 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)))))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card_Oinsert__remove,axiom,
% 22.27/22.21 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => 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)))))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__Diff__insert,axiom,
% 22.27/22.21 ! [V_B_2,V_a_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_B_2))
% 22.27/22.21 => 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)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__Suc__Diff1,axiom,
% 22.27/22.21 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.21 => 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) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_lessI,axiom,
% 22.27/22.21 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__mono,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__UNIV__unit,axiom,
% 22.27/22.21 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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__Suc__1,axiom,
% 22.27/22.21 ! [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 ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mono__Suc,axiom,
% 22.27/22.21 c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_inj__Suc,axiom,
% 22.27/22.21 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_n__not__Suc__n,axiom,
% 22.27/22.21 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__n__not__n,axiom,
% 22.27/22.21 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat_Oinject,axiom,
% 22.27/22.21 ! [V_nat_H_2,V_nat_2] :
% 22.27/22.21 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2)
% 22.27/22.21 <=> V_nat_2 = V_nat_H_2 ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__inject,axiom,
% 22.27/22.21 ! [V_y,V_x] :
% 22.27/22.21 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y)
% 22.27/22.21 => V_x = V_y ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeast__Suc__greaterThan,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_one__reorient,axiom,
% 22.27/22.21 ! [V_x_2,T_b] :
% 22.27/22.21 ( class_Groups_Oone(T_b)
% 22.27/22.21 => ( c_Groups_Oone__class_Oone(T_b) = V_x_2
% 22.27/22.21 <=> V_x_2 = c_Groups_Oone__class_Oone(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_greaterThan__Suc,axiom,
% 22.27/22.21 ! [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)))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeast__Suc,axiom,
% 22.27/22.21 ! [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)))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mono__iff__le__Suc,axiom,
% 22.27/22.21 ! [V_f_2,T_b] :
% 22.27/22.21 ( class_Orderings_Oorder(T_b)
% 22.27/22.21 => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_b,V_f_2)
% 22.27/22.21 <=> ! [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)))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__1__left,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__1,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__1__right,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult_Ocomm__neutral,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_not__less__eq,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__Suc__eq,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 22.27/22.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 | V_m_2 = V_n_2 ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__less__eq,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_not__less__less__Suc__eq,axiom,
% 22.27/22.21 ! [V_m_2,V_n_2] :
% 22.27/22.21 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 22.27/22.21 <=> V_n_2 = V_m_2 ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__antisym,axiom,
% 22.27/22.21 ! [V_m,V_n] :
% 22.27/22.21 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m)))
% 22.27/22.21 => V_m = V_n ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__SucI,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__lessI,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => ( hAPP(c_Nat_OSuc,V_m) != V_n
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__trans__Suc,axiom,
% 22.27/22.21 ! [V_k,V_j,V_i] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__SucE,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 22.27/22.21 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => V_m = V_n ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__lessD,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__less__SucD,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n)))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__Suc__right,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__Suc,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__Suc__shift,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__n__not__le__n,axiom,
% 22.27/22.21 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_not__less__eq__eq,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_le__Suc__eq,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 22.27/22.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__le__mono,axiom,
% 22.27/22.21 ! [V_m_2,V_n_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_le__SucI,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_le__SucE,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n)))
% 22.27/22.21 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__leD,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod__eq__1__iff,axiom,
% 22.27/22.21 ! [V_f_2,V_F_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.27/22.21 => ( 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)
% 22.27/22.21 <=> ! [B_x] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 22.27/22.21 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__Suc__Suc,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__diff__diff,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__mult__cancel1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( 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)
% 22.27/22.21 <=> V_m_2 = V_n_2 ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__mult__1,axiom,
% 22.27/22.21 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__1__eq__mult__iff,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)
% 22.27/22.21 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 22.27/22.21 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__mult__1__right,axiom,
% 22.27/22.21 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__mult__eq__1__iff,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 22.27/22.21 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 22.27/22.21 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_image__Suc__atLeastLessThan,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeastLessThan__singleton,axiom,
% 22.27/22.21 ! [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))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_image__Suc__atLeastAtMost,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_min__Suc__Suc,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_lessThan__Suc,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_max__Suc__Suc,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atMost__Suc,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__atMost,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__add__one,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.21 => 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)))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__1__mult,axiom,
% 22.27/22.21 ! [V_n,V_m,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 22.27/22.21 ! [V_m,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 22.27/22.21 ! [V_a,V_m,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 22.27/22.21 ! [V_m,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_square__eq__1__iff,axiom,
% 22.27/22.21 ! [V_x_2,T_b] :
% 22.27/22.21 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 22.27/22.21 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_b)
% 22.27/22.21 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom,
% 22.27/22.21 ! [V_x,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__ring__1(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__add__Suc1,axiom,
% 22.27/22.21 ! [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)))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__add__Suc2,axiom,
% 22.27/22.21 ! [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)))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__iff__Suc__add,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__eq__Suc__le,axiom,
% 22.27/22.21 ! [V_m_2,V_n_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__Suc__eq__le,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__le__eq,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_le__imp__less__Suc,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__leI,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_le__less__Suc__eq,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2)))
% 22.27/22.21 <=> V_n_2 = V_m_2 ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__le__lessD,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__less__Suc,axiom,
% 22.27/22.21 ! [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))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__mult__less__cancel1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__Suc__right,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__Suc,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__diff__le,axiom,
% 22.27/22.21 ! [V_m,V_n] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.27/22.21 => 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)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__mult__le__cancel1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod_Oempty,axiom,
% 22.27/22.21 ! [V_g_2,T_c,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_b)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod__empty,axiom,
% 22.27/22.21 ! [V_f_2,T_c,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_b)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod_Oinfinite,axiom,
% 22.27/22.21 ! [V_g_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.21 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => 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) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod__infinite,axiom,
% 22.27/22.21 ! [V_f_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.21 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => 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) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeastLessThanSuc,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 => 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)) )
% 22.27/22.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeastAtMostSuc__conv,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 22.27/22.21 => 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)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__atLeastAtMost,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_lessThan__Suc__atMost,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__greaterThanLessThan,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__Suc__diff__eq2,axiom,
% 22.27/22.21 ! [V_m,V_j,V_k] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 22.27/22.21 => 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)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__Suc__diff__eq1,axiom,
% 22.27/22.21 ! [V_m,V_j,V_k] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
% 22.27/22.21 => 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)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__insert__disjoint,axiom,
% 22.27/22.21 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__insert__if,axiom,
% 22.27/22.21 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.21 => 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) )
% 22.27/22.21 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.21 => 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)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__head__upt__Suc,axiom,
% 22.27/22.21 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__head__Suc,axiom,
% 22.27/22.21 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__insert,axiom,
% 22.27/22.21 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => 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)))))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card_Oinsert,axiom,
% 22.27/22.21 ! [V_x_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__ub__add__nat,axiom,
% 22.27/22.21 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.27/22.21 => ( 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))))
% 22.27/22.21 => 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)))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__Suc__eq__diff__pred,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__eq__plus1,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__eq__plus1__left,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod__Un__one,axiom,
% 22.27/22.21 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 22.27/22.21 => ( ! [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 22.27/22.21 => 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)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod_Ounion__inter__neutral,axiom,
% 22.27/22.21 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.21 => ( ! [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 22.27/22.21 => 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)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_finite__fun__UNIVD1,axiom,
% 22.27/22.21 ! [T_c,T_b] :
% 22.27/22.21 ( 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))))
% 22.27/22.21 => ( 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))
% 22.27/22.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__zeroE,axiom,
% 22.27/22.21 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_le0,axiom,
% 22.27/22.21 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__less__Suc,axiom,
% 22.27/22.21 ! [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))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__reorient,axiom,
% 22.27/22.21 ! [V_x_2,T_b] :
% 22.27/22.21 ( class_Groups_Ozero(T_b)
% 22.27/22.21 => ( c_Groups_Ozero__class_Ozero(T_b) = V_x_2
% 22.27/22.21 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_bot__nat__def,axiom,
% 22.27/22.21 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__0__iff,axiom,
% 22.27/22.21 ! [V_a_2,V_b_2,T_b] :
% 22.27/22.21 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_b)
% 22.27/22.21 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_b_2),V_a_2)
% 22.27/22.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add_Ocomm__neutral,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__0__right,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Omonoid__add(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_double__zero__sym,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2)
% 22.27/22.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__0,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__0__left,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Omonoid__add(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_divisors__zero,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Ono__zero__divisors(T_a)
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_no__zero__divisors,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Ono__zero__divisors(T_a)
% 22.27/22.21 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__eq__0__iff,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Oring__no__zero__divisors(T_b)
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 | V_b_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__zero__right,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Omult__zero(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__zero__left,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Omult__zero(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_right__minus__eq,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_b)
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 <=> V_a_2 = V_b_2 ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_eq__iff__diff__eq__0,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Oab__group__add(T_b)
% 22.27/22.21 => ( V_a_2 = V_b_2
% 22.27/22.21 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__self,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__0__right,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__neq__one,axiom,
% 22.27/22.21 ! [T_a] :
% 22.27/22.21 ( class_Rings_Ozero__neq__one(T_a)
% 22.27/22.21 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_one__neq__zero,axiom,
% 22.27/22.21 ! [T_a] :
% 22.27/22.21 ( class_Rings_Ozero__neq__one(T_a)
% 22.27/22.21 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_minus__zero,axiom,
% 22.27/22.21 ! [T_a] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_a)
% 22.27/22.21 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_neg__0__equal__iff__equal,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_b)
% 22.27/22.21 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 22.27/22.21 <=> c_Groups_Ozero__class_Ozero(T_b) = V_a_2 ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_equal__neg__zero,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)
% 22.27/22.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_neg__equal__0__iff__equal,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_b)
% 22.27/22.21 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_neg__equal__zero,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2) = V_a_2
% 22.27/22.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__neq__Zero,axiom,
% 22.27/22.21 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Zero__neq__Suc,axiom,
% 22.27/22.21 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat_Osimps_I3_J,axiom,
% 22.27/22.21 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__not__Zero,axiom,
% 22.27/22.21 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat_Osimps_I2_J,axiom,
% 22.27/22.21 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Zero__not__Suc,axiom,
% 22.27/22.21 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_gr0I,axiom,
% 22.27/22.21 ! [V_n] :
% 22.27/22.21 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_gr__implies__not0,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__nat__zero__code,axiom,
% 22.27/22.21 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_neq0__conv,axiom,
% 22.27/22.21 ! [V_n_2] :
% 22.27/22.21 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_not__less0,axiom,
% 22.27/22.21 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__eq__self__zero,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m
% 22.27/22.21 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__is__0,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Nat_Oadd__0__right,axiom,
% 22.27/22.21 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 22.27/22.21
% 22.27/22.21 fof(fact_plus__nat_Oadd__0,axiom,
% 22.27/22.21 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 22.27/22.21
% 22.27/22.21 fof(fact_le__0__eq,axiom,
% 22.27/22.21 ! [V_n_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 22.27/22.21 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__eq__nat_Osimps_I1_J,axiom,
% 22.27/22.21 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diffs0__imp__equal,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 => V_m = V_n ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__self__eq__0,axiom,
% 22.27/22.21 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_minus__nat_Odiff__0,axiom,
% 22.27/22.21 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__0__eq__0,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__cancel2,axiom,
% 22.27/22.21 ! [V_n_2,V_k_2,V_m_2] :
% 22.27/22.21 ( 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)
% 22.27/22.21 <=> ( V_m_2 = V_n_2
% 22.27/22.21 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__cancel1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( 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)
% 22.27/22.21 <=> ( V_m_2 = V_n_2
% 22.27/22.21 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__mult__eq__cancel__disj,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( 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)
% 22.27/22.21 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 | V_m_2 = V_n_2 ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__is__0,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__0__right,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__0,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_sum__squares__eq__zero__iff,axiom,
% 22.27/22.21 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( 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)
% 22.27/22.21 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeastLessThan0,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeast__0,axiom,
% 22.27/22.21 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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_min__0L,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_min__0R,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_lessThan__0,axiom,
% 22.27/22.21 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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_max__0L,axiom,
% 22.27/22.21 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ).
% 22.27/22.21
% 22.27/22.21 fof(fact_max__0R,axiom,
% 22.27/22.21 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atMost__0,axiom,
% 22.27/22.21 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))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom,
% 22.27/22.21 ! [V_k_2,V_f_2,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.27/22.21 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_sum__squares__ge__zero,axiom,
% 22.27/22.21 ! [V_y,V_x,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__ring(T_a)
% 22.27/22.21 => 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)))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_sum__squares__le__zero__iff,axiom,
% 22.27/22.21 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_not__sum__squares__lt__zero,axiom,
% 22.27/22.21 ! [V_y,V_x,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__ring(T_a)
% 22.27/22.21 => ~ 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))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_sum__squares__gt__zero__iff,axiom,
% 22.27/22.21 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( 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))))
% 22.27/22.21 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__nonpos__nonpos,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__increasing2,axiom,
% 22.27/22.21 ! [V_a,V_b,V_c,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__increasing,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__nonneg__eq__0__iff,axiom,
% 22.27/22.21 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_x_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_y_2))
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__nonneg__nonneg,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_split__mult__neg__le,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__cancel__semiring(T_a)
% 22.27/22.21 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) )
% 22.27/22.21 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) )
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_split__mult__pos__le,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__ring(T_a)
% 22.27/22.21 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) )
% 22.27/22.21 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__mono,axiom,
% 22.27/22.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__semiring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__mono_H,axiom,
% 22.27/22.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__semiring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__left__mono__neg,axiom,
% 22.27/22.21 ! [V_c,V_a,V_b,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__ring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__right__mono__neg,axiom,
% 22.27/22.21 ! [V_c,V_a,V_b,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__ring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__mult__left__mono,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__comm__semiring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__left__mono,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__semiring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__right__mono,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__semiring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__nonpos__nonpos,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__ring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__nonpos__nonneg,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__cancel__semiring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__nonneg__nonpos2,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__cancel__semiring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__nonneg__nonpos,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__cancel__semiring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__nonneg__nonneg,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Oordered__cancel__semiring(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__le__0__iff,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 22.27/22.21 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__le__mult__iff,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 22.27/22.21 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__le__square,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__ring(T_a)
% 22.27/22.21 => 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))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_pos__add__strict,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__pos__pos,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__neg__neg,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_not__square__less__zero,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__ring(T_a)
% 22.27/22.21 => ~ 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))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__cancel__right__disj,axiom,
% 22.27/22.21 ! [V_b_2,V_c_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 22.27/22.21 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__cancel__left__disj,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) )
% 22.27/22.21 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__cancel__left__pos,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__pos__pos,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__pos__neg,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__pos__neg2,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__less__mult__pos,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__less__mult__pos2,axiom,
% 22.27/22.21 ! [V_a,V_b,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__cancel__left__neg,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_a_2)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__neg__pos,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__neg__neg,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__strict__right__mono,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__strict__left__mono,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_comm__mult__strict__left__mono,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__comm__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__strict__right__mono__neg,axiom,
% 22.27/22.21 ! [V_c,V_a,V_b,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__strict__left__mono__neg,axiom,
% 22.27/22.21 ! [V_c,V_a,V_b,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_le__iff__diff__le__0,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 22.27/22.21 <=> 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__iff__diff__less__0,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 22.27/22.21 <=> 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__scale__eq__noteq,axiom,
% 22.27/22.21 ! [V_d,V_c,V_b,V_a,V_r,T_a] :
% 22.27/22.21 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a)
% 22.27/22.21 => ( V_r != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => ( ( V_a = V_b
% 22.27/22.21 & V_c != V_d )
% 22.27/22.21 => 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)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_not__one__le__zero,axiom,
% 22.27/22.21 ! [T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.21 => ~ 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))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__le__one,axiom,
% 22.27/22.21 ! [T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.21 => 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))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__less__one,axiom,
% 22.27/22.21 ! [T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_not__one__less__zero,axiom,
% 22.27/22.21 ! [T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.21 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_neg__0__le__iff__le,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_le__minus__self__iff,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_neg__le__0__iff__le,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_minus__le__self__iff,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_neg__less__nonneg,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_a_2))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_neg__less__0__iff__less,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_neg__0__less__iff__less,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Oordered__ab__group__add(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__minus__self__iff,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_right__minus,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_eq__neg__iff__add__eq__0,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_b)
% 22.27/22.21 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_b_2)
% 22.27/22.21 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_left__minus,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_ab__left__minus,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oab__group__add(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_minus__unique,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_a)
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__0,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Groups_Ogroup__add(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__empty,axiom,
% 22.27/22.21 ! [V_f_2,T_c,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum_Oempty,axiom,
% 22.27/22.21 ! [V_g_2,T_c,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum_Oinfinite,axiom,
% 22.27/22.21 ! [V_g_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.21 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => 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) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__infinite,axiom,
% 22.27/22.21 ! [V_f_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.21 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => 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) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod__pos__nat__iff,axiom,
% 22.27/22.21 ! [V_f_2,V_S_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> ! [B_x] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod__zero__iff,axiom,
% 22.27/22.21 ! [V_f_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( ( class_Rings_Ocomm__semiring__1(T_c)
% 22.27/22.21 & class_Rings_Ono__zero__divisors(T_c) )
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( 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)
% 22.27/22.21 <=> ? [B_x] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.21 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod__zero,axiom,
% 22.27/22.21 ! [V_f_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( class_Rings_Ocomm__semiring__1(T_c)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( ? [B_x] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.21 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 22.27/22.21 => 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) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_gr0__conv__Suc,axiom,
% 22.27/22.21 ! [V_n_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 22.27/22.21 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__Suc0,axiom,
% 22.27/22.21 ! [V_n_2] :
% 22.27/22.21 ( 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))))
% 22.27/22.21 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_less__Suc__eq__0__disj,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)))
% 22.27/22.21 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 | ? [B_j] :
% 22.27/22.21 ( V_m_2 = hAPP(c_Nat_OSuc,B_j)
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_one__is__add,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( 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)
% 22.27/22.21 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 22.27/22.21 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.27/22.21 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__is__1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( 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))
% 22.27/22.21 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 22.27/22.21 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.27/22.21 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__gr__0,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 22.27/22.21 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card_Oempty,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__infinite,axiom,
% 22.27/22.21 ! [V_A_2,T_b] :
% 22.27/22.21 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__eq__1__iff,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( 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))
% 22.27/22.21 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 22.27/22.21 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__less,axiom,
% 22.27/22.21 ! [V_m,V_n] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__less__diff,axiom,
% 22.27/22.21 ! [V_m_2,V_n_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__mono2,axiom,
% 22.27/22.21 ! [V_k,V_j,V_i] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__mono1,axiom,
% 22.27/22.21 ! [V_k,V_j,V_i] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__mult__less__cancel1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__mult__eq__cancel1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 22.27/22.21 => ( 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)
% 22.27/22.21 <=> V_m_2 = V_n_2 ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__cancel2,axiom,
% 22.27/22.21 ! [V_n_2,V_k_2,V_m_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__cancel1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__0__less__mult__iff,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
% 22.27/22.21 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__add__0,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__is__0__eq,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__is__0__eq_H,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.27/22.21 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_One__nat__def,axiom,
% 22.27/22.21 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__eq__self__implies__10,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n)
% 22.27/22.21 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 22.27/22.21 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__shift__lb__Suc0__0,axiom,
% 22.27/22.21 ! [V_k_2,V_f_2] :
% 22.27/22.21 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 => 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)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__eq__0__iff,axiom,
% 22.27/22.21 ! [V_f_2,V_F_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.27/22.21 => ( 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)
% 22.27/22.21 <=> ! [B_x] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_F_2))
% 22.27/22.21 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_greaterThan__0,axiom,
% 22.27/22.21 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))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_lessThan__Suc__eq__insert__0,axiom,
% 22.27/22.21 ! [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))) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeast0LessThan,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_atLeast0AtMost,axiom,
% 22.27/22.21 ! [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) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__pred_H,axiom,
% 22.27/22.21 ! [V_n] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.21 => 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))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__eq__if,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n )
% 22.27/22.21 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__nonpos__neg,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__neg__nonpos,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__strict__increasing2,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__strict__increasing,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__nonneg__pos,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__pos__nonneg,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__le__cancel__left__pos,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__le__cancel__left__neg,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__ring__strict(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__strict__mono,axiom,
% 22.27/22.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__strict__mono_H,axiom,
% 22.27/22.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__le__imp__less,axiom,
% 22.27/22.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__le__less__imp__less,axiom,
% 22.27/22.21 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => 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))) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__right__less__imp__less,axiom,
% 22.27/22.21 ! [V_b,V_c,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring(T_a)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__imp__less__right,axiom,
% 22.27/22.21 ! [V_b,V_c,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__left__less__imp__less,axiom,
% 22.27/22.21 ! [V_b,V_a,V_c,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring(T_a)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__less__imp__less__left,axiom,
% 22.27/22.21 ! [V_b,V_a,V_c,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__right__le__imp__le,axiom,
% 22.27/22.21 ! [V_b,V_c,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__left__le__imp__le,axiom,
% 22.27/22.21 ! [V_b,V_a,V_c,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__strict(T_a)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__eq__if,axiom,
% 22.27/22.21 ! [V_n,V_m] :
% 22.27/22.21 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.27/22.21 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__left__le__one__le,axiom,
% 22.27/22.21 ! [V_y,V_x,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 22.27/22.21 => 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)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__right__le__one__le,axiom,
% 22.27/22.21 ! [V_y,V_x,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a)))
% 22.27/22.21 => 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)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_zero__less__two,axiom,
% 22.27/22.21 ! [T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.21 => 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)))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__eq__0__iff,axiom,
% 22.27/22.21 ! [V_A_2,T_b] :
% 22.27/22.21 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.27/22.21 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__ge__0__finite,axiom,
% 22.27/22.21 ! [V_A_2,T_b] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__pred,axiom,
% 22.27/22.21 ! [V_n] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.21 => 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 ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__Suc__less,axiom,
% 22.27/22.21 ! [V_i,V_n] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.21 => 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)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_n__less__m__mult__n,axiom,
% 22.27/22.21 ! [V_m,V_n] :
% 22.27/22.21 ( 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))
% 22.27/22.21 => ( 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))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_n__less__n__mult__m,axiom,
% 22.27/22.21 ! [V_m,V_n] :
% 22.27/22.21 ( 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))
% 22.27/22.21 => ( 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))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_one__less__mult,axiom,
% 22.27/22.21 ! [V_m,V_n] :
% 22.27/22.21 ( 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))
% 22.27/22.21 => ( 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))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__diff__split,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,V_P_2] :
% 22.27/22.21 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 22.27/22.21 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 22.27/22.21 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 22.27/22.21 & ! [B_d] :
% 22.27/22.21 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 22.27/22.21 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__diff__split__asm,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,V_P_2] :
% 22.27/22.21 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
% 22.27/22.21 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 22.27/22.21 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 22.27/22.21 | ? [B_d] :
% 22.27/22.21 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d)
% 22.27/22.21 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_one__le__mult__iff,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> ( 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))
% 22.27/22.21 & 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nat__mult__le__cancel1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__le__cancel2,axiom,
% 22.27/22.21 ! [V_n_2,V_k_2,V_m_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_mult__le__cancel1,axiom,
% 22.27/22.21 ! [V_n_2,V_m_2,V_k_2] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__eq__Suc0__iff,axiom,
% 22.27/22.21 ! [V_f_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( 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))
% 22.27/22.21 <=> ? [B_x] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.21 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 22.27/22.21 & ! [B_xa] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 22.27/22.21 => ( B_x != B_xa
% 22.27/22.21 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__eq__1__iff,axiom,
% 22.27/22.21 ! [V_f_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( 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)
% 22.27/22.21 <=> ? [B_x] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.21 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
% 22.27/22.21 & ! [B_xa] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 22.27/22.21 => ( B_x != B_xa
% 22.27/22.21 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_convex__bound__le,axiom,
% 22.27/22.21 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__1(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 22.27/22.21 => 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)) ) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__gt__0__iff,axiom,
% 22.27/22.21 ! [V_A_2,T_b] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.27/22.21 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_finite__UNIV__card__ge__0,axiom,
% 22.27/22.21 ! [T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 22.27/22.21 => 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))))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Suc__diff__1,axiom,
% 22.27/22.21 ! [V_n] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.21 => 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 ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_convex__bound__lt,axiom,
% 22.27/22.21 ! [V_v,V_u,V_y,V_a,V_x,T_a] :
% 22.27/22.21 ( class_Rings_Olinordered__semiring__1__strict(T_a)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v))
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a)
% 22.27/22.21 => 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)) ) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__op__ivl__Suc,axiom,
% 22.27/22.21 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.27/22.21 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 22.27/22.21 => 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) )
% 22.27/22.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
% 22.27/22.21 => 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)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__cl__ivl__Suc,axiom,
% 22.27/22.21 ! [V_f_2,V_m_2,V_n_2,T_b] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.27/22.21 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 22.27/22.21 => 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) )
% 22.27/22.21 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_ex__nat__less,axiom,
% 22.27/22.21 ! [V_P_2,V_n_2] :
% 22.27/22.21 ( ? [B_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 22.27/22.21 & hBOOL(hAPP(V_P_2,B_m)) )
% 22.27/22.21 <=> ? [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_all__nat__less,axiom,
% 22.27/22.21 ! [V_P_2,V_n_2] :
% 22.27/22.21 ( ! [B_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2))
% 22.27/22.21 => hBOOL(hAPP(V_P_2,B_m)) )
% 22.27/22.21 <=> ! [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_all__nat__less__eq,axiom,
% 22.27/22.21 ! [V_P_2,V_n_2] :
% 22.27/22.21 ( ! [B_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 22.27/22.21 => hBOOL(hAPP(V_P_2,B_m)) )
% 22.27/22.21 <=> ! [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_ex__nat__less__eq,axiom,
% 22.27/22.21 ! [V_P_2,V_n_2] :
% 22.27/22.21 ( ? [B_m] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2))
% 22.27/22.21 & hBOOL(hAPP(V_P_2,B_m)) )
% 22.27/22.21 <=> ? [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_even__less__0__iff,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card_Ounion__inter__neutral,axiom,
% 22.27/22.21 ! [V_B_2,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.21 => ( ( ? [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)))
% 22.27/22.21 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.27/22.21 => 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)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__mono2,axiom,
% 22.27/22.21 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Oordered__comm__monoid__add(T_c)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.27/22.21 => ( ! [B_b] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_b))) )
% 22.27/22.21 => 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))) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_double__eq__0__iff,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Groups_Olinordered__ab__group__add(T_b)
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum_Ounion__inter__neutral,axiom,
% 22.27/22.21 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.21 => ( ! [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 22.27/22.21 => 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)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__Un__zero,axiom,
% 22.27/22.21 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 22.27/22.21 => ( ! [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 22.27/22.21 => 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)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__Suc__eq,axiom,
% 22.27/22.21 ! [V_k_2,V_A_2,T_b] :
% 22.27/22.21 ( hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Nat_OSuc,V_k_2)
% 22.27/22.21 <=> ? [B_b,B_B] :
% 22.27/22.21 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_b),B_b),B_B)
% 22.27/22.21 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_b),B_B))
% 22.27/22.21 & hAPP(c_Finite__Set_Ocard(T_b),B_B) = V_k_2
% 22.27/22.21 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.21 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setsum__mono3,axiom,
% 22.27/22.21 ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
% 22.27/22.21 ( ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.21 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.27/22.21 => ( ! [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 22.27/22.21 => 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))) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Ints__odd__less__0,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => ( 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)))
% 22.27/22.21 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__Plus__conv__if,axiom,
% 22.27/22.21 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.27/22.21 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 22.27/22.21 => 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)) )
% 22.27/22.21 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) )
% 22.27/22.21 => 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) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Ints__0,axiom,
% 22.27/22.21 ! [T_b] :
% 22.27/22.21 ( class_Rings_Oring__1(T_b)
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Ints__add,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Oring__1(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Ints__mult,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Oring__1(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Ints__diff,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Oring__1(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => 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))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Ints__1,axiom,
% 22.27/22.21 ! [T_b] :
% 22.27/22.21 ( class_Rings_Oring__1(T_b)
% 22.27/22.21 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Int_Oring__1__class_OInts(T_b))) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Ints__minus,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Rings_Oring__1(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Ints__double__eq__0__iff,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Int_Oring__char__0(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_finite__Plus__iff,axiom,
% 22.27/22.21 ! [V_B_2,V_A_2,T_c,T_b] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_finite__Plus,axiom,
% 22.27/22.21 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.27/22.21 => 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))) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_finite__PlusD_I1_J,axiom,
% 22.27/22.21 ! [V_B_2,V_A_2,T_c,T_b] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_finite__PlusD_I2_J,axiom,
% 22.27/22.21 ! [V_B_2,V_A_2,T_c,T_b] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_card__Plus,axiom,
% 22.27/22.21 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.27/22.21 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Ints__odd__nonzero,axiom,
% 22.27/22.21 ! [V_a_2,T_b] :
% 22.27/22.21 ( class_Int_Oring__char__0(T_b)
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.21 => 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) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_UNIV__Plus__UNIV,axiom,
% 22.27/22.21 ! [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)) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_Plus__eq__empty__conv,axiom,
% 22.27/22.21 ! [V_B_2,V_A_2,T_c,T_b] :
% 22.27/22.21 ( 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))
% 22.27/22.21 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.27/22.21 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod__diff1,axiom,
% 22.27/22.21 ! [V_a_2,V_f_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( class_Fields_Ofield(T_c)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_c)
% 22.27/22.21 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.21 => 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)) )
% 22.27/22.21 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.21 => 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) ) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_fold__Un__disjoint,axiom,
% 22.27/22.21 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.21 => ( 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))
% 22.27/22.21 => 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)) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_ex__least__nat__less,axiom,
% 22.27/22.21 ! [V_n_2,V_P_2] :
% 22.27/22.21 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 22.27/22.21 => ( hBOOL(hAPP(V_P_2,V_n_2))
% 22.27/22.21 => ? [B_k] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2))
% 22.27/22.21 & ! [B_i] :
% 22.27/22.21 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k))
% 22.27/22.21 => ~ hBOOL(hAPP(V_P_2,B_i)) )
% 22.27/22.21 & 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)))) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_setprod__mono__one__right,axiom,
% 22.27/22.21 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 22.27/22.21 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 22.27/22.21 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 22.27/22.21 => ( ! [B_x] :
% 22.27/22.21 ( 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)))
% 22.27/22.21 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 22.27/22.21 => 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) ) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_divide__zero__left,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_divide__zero,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_add__divide__distrib,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => 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)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_times__divide__eq__right,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_diff__divide__distrib,axiom,
% 22.27/22.21 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => 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)) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_divide__1,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_minus__divide__left,axiom,
% 22.27/22.21 ! [V_b,V_a,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => 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) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_fold__image__empty,axiom,
% 22.27/22.21 ! [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 ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nonzero__eq__divide__eq,axiom,
% 22.27/22.21 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_b)
% 22.27/22.21 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 22.27/22.21 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nonzero__divide__eq__eq,axiom,
% 22.27/22.21 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_b)
% 22.27/22.21 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 22.27/22.21 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_divide__eq__imp,axiom,
% 22.27/22.21 ! [V_a,V_b,V_c,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)
% 22.27/22.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_eq__divide__imp,axiom,
% 22.27/22.21 ! [V_b,V_a,V_c,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b
% 22.27/22.21 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_right__inverse__eq,axiom,
% 22.27/22.21 ! [V_a_2,V_b_2,T_b] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_b)
% 22.27/22.21 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.21 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
% 22.27/22.21 <=> V_a_2 = V_b_2 ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_divide__self,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_divide__self__if,axiom,
% 22.27/22.21 ! [V_a,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring__inverse__zero(T_a)
% 22.27/22.21 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) )
% 22.27/22.21 & ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nonzero__minus__divide__right,axiom,
% 22.27/22.21 ! [V_a,V_b,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => 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)) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_nonzero__minus__divide__divide,axiom,
% 22.27/22.21 ! [V_a,V_b,T_a] :
% 22.27/22.21 ( class_Rings_Odivision__ring(T_a)
% 22.27/22.21 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.21 => 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) ) ) ).
% 22.27/22.21
% 22.27/22.21 fof(fact_folding__image__simple_Oeq__fold__g,axiom,
% 22.27/22.21 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.21 ( c_Finite__Set_Ofolding__image__simple(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.27/22.21 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__image__insert,axiom,
% 22.27/22.22 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Oab__semigroup__mult(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.27/22.22 => 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setsum_Oeq__fold,axiom,
% 22.27/22.22 ! [V_g_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setsum_OF__eq,axiom,
% 22.27/22.22 ! [V_g_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.22 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setprod_OF__eq,axiom,
% 22.27/22.22 ! [V_g_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.22 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setprod_Oeq__fold,axiom,
% 22.27/22.22 ! [V_g_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__image__Un__Int,axiom,
% 22.27/22.22 ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__left__mono__neg,axiom,
% 22.27/22.22 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__left__mono,axiom,
% 22.27/22.22 ! [V_c,V_a,V_b,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_neg__divide__le__eq,axiom,
% 22.27/22.22 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_neg__le__divide__eq,axiom,
% 22.27/22.22 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_mult__imp__le__div__pos,axiom,
% 22.27/22.22 ! [V_x,V_z,V_y,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.22 => ( 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))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_mult__imp__div__pos__le,axiom,
% 22.27/22.22 ! [V_z,V_x,V_y,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_times__divide__times__eq,axiom,
% 22.27/22.22 ! [V_w,V_z,V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_minus__divide__divide,axiom,
% 22.27/22.22 ! [V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_minus__divide__right,axiom,
% 22.27/22.22 ! [V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zero__le__divide__iff,axiom,
% 22.27/22.22 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 22.27/22.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 22.27/22.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__le__0__iff,axiom,
% 22.27/22.22 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 22.27/22.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 22.27/22.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__right__mono,axiom,
% 22.27/22.22 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__right__mono__neg,axiom,
% 22.27/22.22 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__strict__right__mono__neg,axiom,
% 22.27/22.22 ! [V_c,V_a,V_b,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__strict__right__mono,axiom,
% 22.27/22.22 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__neg__neg,axiom,
% 22.27/22.22 ! [V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__neg__pos,axiom,
% 22.27/22.22 ! [V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__pos__neg,axiom,
% 22.27/22.22 ! [V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__pos__pos,axiom,
% 22.27/22.22 ! [V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__less__0__iff,axiom,
% 22.27/22.22 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 22.27/22.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) )
% 22.27/22.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zero__less__divide__iff,axiom,
% 22.27/22.22 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2))
% 22.27/22.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2)) )
% 22.27/22.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_eq__divide__eq,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_b)
% 22.27/22.22 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
% 22.27/22.22 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 )
% 22.27/22.22 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__eq__eq,axiom,
% 22.27/22.22 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_b)
% 22.27/22.22 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
% 22.27/22.22 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) )
% 22.27/22.22 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_mult__divide__mult__cancel__right,axiom,
% 22.27/22.22 ! [V_b,V_a,V_c,T_a] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.22 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_mult__divide__mult__cancel__left,axiom,
% 22.27/22.22 ! [V_b,V_a,V_c,T_a] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.22 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_frac__eq__eq,axiom,
% 22.27/22.22 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
% 22.27/22.22 ( class_Fields_Ofield(T_b)
% 22.27/22.22 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => ( 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)
% 22.27/22.22 <=> 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) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__nonneg__pos,axiom,
% 22.27/22.22 ! [V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__nonneg__neg,axiom,
% 22.27/22.22 ! [V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_frac__less2,axiom,
% 22.27/22.22 ! [V_z,V_w,V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z))
% 22.27/22.22 => 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))) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_frac__less,axiom,
% 22.27/22.22 ! [V_z,V_w,V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 22.27/22.22 => 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))) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_frac__le,axiom,
% 22.27/22.22 ! [V_z,V_w,V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z))
% 22.27/22.22 => 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))) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__nonpos__pos,axiom,
% 22.27/22.22 ! [V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__nonpos__neg,axiom,
% 22.27/22.22 ! [V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__strict__left__mono__neg,axiom,
% 22.27/22.22 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__strict__left__mono,axiom,
% 22.27/22.22 ! [V_c,V_a,V_b,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_neg__divide__less__eq,axiom,
% 22.27/22.22 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_neg__less__divide__eq,axiom,
% 22.27/22.22 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_mult__imp__less__div__pos,axiom,
% 22.27/22.22 ! [V_x,V_z,V_y,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.22 => ( 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))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_mult__imp__div__pos__less,axiom,
% 22.27/22.22 ! [V_z,V_x,V_y,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_pos__divide__less__eq,axiom,
% 22.27/22.22 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_pos__less__divide__eq,axiom,
% 22.27/22.22 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__less__eq,axiom,
% 22.27/22.22 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => 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))) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_less__divide__eq,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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))) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__num__frac,axiom,
% 22.27/22.22 ! [V_x,V_z,V_y,T_a] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.22 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__divide__eq__iff,axiom,
% 22.27/22.22 ! [V_y,V_x,V_z,T_a] :
% 22.27/22.22 ( class_Fields_Ofield(T_a)
% 22.27/22.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__frac__num,axiom,
% 22.27/22.22 ! [V_z,V_x,V_y,T_a] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.22 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__add__eq__iff,axiom,
% 22.27/22.22 ! [V_y,V_x,V_z,T_a] :
% 22.27/22.22 ( class_Fields_Ofield(T_a)
% 22.27/22.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__frac__eq,axiom,
% 22.27/22.22 ! [V_w,V_x,V_z,V_y,T_a] :
% 22.27/22.22 ( class_Fields_Ofield(T_a)
% 22.27/22.22 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_diff__divide__eq__iff,axiom,
% 22.27/22.22 ! [V_y,V_x,V_z,T_a] :
% 22.27/22.22 ( class_Fields_Ofield(T_a)
% 22.27/22.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__diff__eq__iff,axiom,
% 22.27/22.22 ! [V_y,V_x,V_z,T_a] :
% 22.27/22.22 ( class_Fields_Ofield(T_a)
% 22.27/22.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_diff__frac__eq,axiom,
% 22.27/22.22 ! [V_w,V_x,V_z,V_y,T_a] :
% 22.27/22.22 ( class_Fields_Ofield(T_a)
% 22.27/22.22 => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_gt__half__sum,axiom,
% 22.27/22.22 ! [V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.22 => 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)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_less__half__sum,axiom,
% 22.27/22.22 ! [V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.22 => 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))))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_le__divide__eq,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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))) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__le__eq,axiom,
% 22.27/22.22 ! [V_a_2,V_c_2,V_b_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => 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))) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_pos__le__divide__eq,axiom,
% 22.27/22.22 ! [V_b_2,V_a_2,V_c_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_pos__divide__le__eq,axiom,
% 22.27/22.22 ! [V_a_2,V_b_2,V_c_2,T_b] :
% 22.27/22.22 ( class_Fields_Olinordered__field(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__monoid__big_OF__eq,axiom,
% 22.27/22.22 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 22.27/22.22 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.27/22.22 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setprod__Un,axiom,
% 22.27/22.22 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Fields_Ofield(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c) )
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__image__Un__one,axiom,
% 22.27/22.22 ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 22.27/22.22 => 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)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setprod__mono__one__left,axiom,
% 22.27/22.22 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 22.27/22.22 => 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) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setsum__mono__zero__right,axiom,
% 22.27/22.22 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 22.27/22.22 => 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) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setsum__mono__zero__left,axiom,
% 22.27/22.22 ! [V_f_2,V_S_2,V_T_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
% 22.27/22.22 => 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) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__monoid__big_Oinfinite,axiom,
% 22.27/22.22 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Big__Operators_Ocomm__monoid__big(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 22.27/22.22 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.27/22.22 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_field__le__mult__one__interval,axiom,
% 22.27/22.22 ! [V_y,V_x,T_a] :
% 22.27/22.22 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 22.27/22.22 => ( ! [B_z] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a)))
% 22.27/22.22 => 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)) ) )
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__neg,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.22 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__1__neg,axiom,
% 22.27/22.22 ! [V_a_2,T_b] :
% 22.27/22.22 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__if,axiom,
% 22.27/22.22 ! [V_x,T_a] :
% 22.27/22.22 ( class_Groups_Osgn__if(T_a)
% 22.27/22.22 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) )
% 22.27/22.22 & ( V_x != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.22 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.22 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold1Set_Oequations,axiom,
% 22.27/22.22 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
% 22.27/22.22 ( 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))
% 22.27/22.22 <=> ? [B_a,B_A] :
% 22.27/22.22 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 22.27/22.22 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
% 22.27/22.22 & ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_insert__fold1SetE,axiom,
% 22.27/22.22 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
% 22.27/22.22 ( 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))
% 22.27/22.22 => ~ ! [B_a,B_A] :
% 22.27/22.22 ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__sgn,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__0__0,axiom,
% 22.27/22.22 ! [V_a_2,T_b] :
% 22.27/22.22 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.22 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn0,axiom,
% 22.27/22.22 ! [T_a] :
% 22.27/22.22 ( class_Groups_Osgn__if(T_a)
% 22.27/22.22 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__times,axiom,
% 22.27/22.22 ! [V_b,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__less,axiom,
% 22.27/22.22 ! [V_a_2,T_b] :
% 22.27/22.22 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__greater,axiom,
% 22.27/22.22 ! [V_a_2,T_b] :
% 22.27/22.22 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__pos,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_sgn__1__pos,axiom,
% 22.27/22.22 ! [V_a_2,T_b] :
% 22.27/22.22 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.22 => ( c_Groups_Osgn__class_Osgn(T_b,V_a_2) = c_Groups_Oone__class_Oone(T_b)
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setprod__pos__nat,axiom,
% 22.27/22.22 ! [V_f_2,V_S_2,T_b] :
% 22.27/22.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 22.27/22.22 => 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))) )
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom,
% 22.27/22.22 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.27/22.22 => ( 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))
% 22.27/22.22 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.22 => ~ ! [B_y] :
% 22.27/22.22 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y)
% 22.27/22.22 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom,
% 22.27/22.22 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => 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)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom,
% 22.27/22.22 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setsum__SucD,axiom,
% 22.27/22.22 ! [V_n_2,V_A_2,V_f_2,T_b] :
% 22.27/22.22 ( 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)
% 22.27/22.22 => ? [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.22 & 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_card__partition,axiom,
% 22.27/22.22 ! [V_k_2,V_C_2,T_b] :
% 22.27/22.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_C_2))
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)))
% 22.27/22.22 => ( ! [B_c] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c),V_C_2))
% 22.27/22.22 => hAPP(c_Finite__Set_Ocard(T_b),B_c) = V_k_2 )
% 22.27/22.22 => ( ! [B_c1] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c1),V_C_2))
% 22.27/22.22 => ! [B_c2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_c2),V_C_2))
% 22.27/22.22 => ( B_c1 != B_c2
% 22.27/22.22 => 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)) ) ) )
% 22.27/22.22 => 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)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom,
% 22.27/22.22 ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fun__left__comm__idem__insert,axiom,
% 22.27/22.22 ! [T_b] : c_Finite__Set_Ofun__left__comm__idem(T_b,tc_fun(T_b,tc_HOL_Obool),c_Set_Oinsert(T_b)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fun__left__comm__idem,axiom,
% 22.27/22.22 ! [T_b] :
% 22.27/22.22 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 22.27/22.22 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fun__left__comm__idem__sup,axiom,
% 22.27/22.22 ! [T_b] :
% 22.27/22.22 ( class_Lattices_Osemilattice__sup(T_b)
% 22.27/22.22 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fun__left__comm__idem__inf,axiom,
% 22.27/22.22 ! [T_b] :
% 22.27/22.22 ( class_Lattices_Osemilattice__inf(T_b)
% 22.27/22.22 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom,
% 22.27/22.22 ! [T_b] :
% 22.27/22.22 ( class_Orderings_Olinorder(T_b)
% 22.27/22.22 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omin(T_b)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom,
% 22.27/22.22 ! [T_b] :
% 22.27/22.22 ( class_Orderings_Olinorder(T_b)
% 22.27/22.22 => c_Finite__Set_Ofun__left__comm__idem(T_b,T_b,c_Orderings_Oord__class_Omax(T_b)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_card__Pow,axiom,
% 22.27/22.22 ! [V_A_2,T_b] :
% 22.27/22.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__image__1,axiom,
% 22.27/22.22 ! [V_f_2,V_S_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 22.27/22.22 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_c) )
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_card_Oneutral,axiom,
% 22.27/22.22 ! [V_A_2,T_b] :
% 22.27/22.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.22 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.27/22.22 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_min__max_Ofold__sup__le__sup,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 22.27/22.22 ( class_Orderings_Olinorder(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_min__max_Oinf__le__fold__inf,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 22.27/22.22 ( class_Orderings_Olinorder(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__image__cong,axiom,
% 22.27/22.22 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Groups_Oab__semigroup__mult(T_c)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.22 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 22.27/22.22 ! [V_q,V_y,V_x,T_a] :
% 22.27/22.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 22.27/22.22 ! [V_q,V_p,V_x,T_a] :
% 22.27/22.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 22.27/22.22 ! [V_x,T_a] :
% 22.27/22.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.22 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom,
% 22.27/22.22 ! [V_q,V_x,T_a] :
% 22.27/22.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom,
% 22.27/22.22 ! [V_q,V_x,T_a] :
% 22.27/22.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom,
% 22.27/22.22 ! [V_q,V_x,T_a] :
% 22.27/22.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 22.27/22.22 ! [V_x,T_a] :
% 22.27/22.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 22.27/22.22 ! [V_q,V_p,V_x,T_a] :
% 22.27/22.22 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Ints__power,axiom,
% 22.27/22.22 ! [V_n_2,V_a_2,T_b] :
% 22.27/22.22 ( class_Rings_Oring__1(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Int_Oring__1__class_OInts(T_b)))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__eq__if,axiom,
% 22.27/22.22 ! [V_p,V_m] :
% 22.27/22.22 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.22 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 22.27/22.22 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.22 => 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)))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__strict__mono,axiom,
% 22.27/22.22 ! [V_n,V_b,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__diff,axiom,
% 22.27/22.22 ! [V_m,V_n,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Ofield(T_a)
% 22.27/22.22 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.27/22.22 => 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_one__less__power,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__le__imp__le__exp,axiom,
% 22.27/22.22 ! [V_n,V_m,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__increasing__iff,axiom,
% 22.27/22.22 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__decreasing,axiom,
% 22.27/22.22 ! [V_a,V_N,V_n,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zpower__zadd__distrib,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zpower__zpower,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_field__power__not__zero,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Oring__1__no__zero__divisors(T_a)
% 22.27/22.22 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__mult__distrib,axiom,
% 22.27/22.22 ! [V_n,V_b,V_a,T_a] :
% 22.27/22.22 ( class_Groups_Ocomm__monoid__mult(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__commutes,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__one,axiom,
% 22.27/22.22 ! [V_n,T_a] :
% 22.27/22.22 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__mult,axiom,
% 22.27/22.22 ! [V_n,V_m,V_a,T_a] :
% 22.27/22.22 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__divide,axiom,
% 22.27/22.22 ! [V_n,V_b,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__one__right,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.22 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__mono,axiom,
% 22.27/22.22 ! [V_n,V_b,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zero__le__power,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zero__less__power,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__eq__0__iff,axiom,
% 22.27/22.22 ! [V_n_2,V_a_2,T_b] :
% 22.27/22.22 ( ( class_Power_Opower(T_b)
% 22.27/22.22 & class_Rings_Omult__zero(T_b)
% 22.27/22.22 & class_Rings_Ono__zero__divisors(T_b)
% 22.27/22.22 & class_Rings_Ozero__neq__one(T_b) )
% 22.27/22.22 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_one__le__power,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__0__Suc,axiom,
% 22.27/22.22 ! [V_n,T_a] :
% 22.27/22.22 ( ( class_Power_Opower(T_a)
% 22.27/22.22 & class_Rings_Osemiring__0(T_a) )
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__inject__exp,axiom,
% 22.27/22.22 ! [V_n_2,V_m_2,V_a_2,T_b] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
% 22.27/22.22 => ( 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)
% 22.27/22.22 <=> V_m_2 = V_n_2 ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__Suc2,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__Suc,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Power_Opower(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__0,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Power_Opower(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__add,axiom,
% 22.27/22.22 ! [V_n,V_m,V_a,T_a] :
% 22.27/22.22 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_nonzero__power__divide,axiom,
% 22.27/22.22 ! [V_n,V_a,V_b,T_a] :
% 22.27/22.22 ( class_Fields_Ofield(T_a)
% 22.27/22.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__one__over,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__Suc__0,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_nat__power__eq__Suc__0__iff,axiom,
% 22.27/22.22 ! [V_m_2,V_x_2] :
% 22.27/22.22 ( 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))
% 22.27/22.22 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.22 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_nat__zero__less__power__iff,axiom,
% 22.27/22.22 ! [V_n_2,V_x_2] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2))
% 22.27/22.22 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_nat__power__less__imp__less,axiom,
% 22.27/22.22 ! [V_n,V_m,V_i] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__less__imp__less__base,axiom,
% 22.27/22.22 ! [V_b,V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__inject__base,axiom,
% 22.27/22.22 ! [V_b,V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( 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))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.22 => V_a = V_b ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__le__imp__le__base,axiom,
% 22.27/22.22 ! [V_b,V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( 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))))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__gt1__lemma,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 22.27/22.22 => 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)))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__less__power__Suc,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 22.27/22.22 => 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)))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__0__left,axiom,
% 22.27/22.22 ! [V_n,T_a] :
% 22.27/22.22 ( ( class_Power_Opower(T_a)
% 22.27/22.22 & class_Rings_Osemiring__0(T_a) )
% 22.27/22.22 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__gt1,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 22.27/22.22 => 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)))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__strict__increasing__iff,axiom,
% 22.27/22.22 ! [V_y_2,V_x_2,V_b_2,T_b] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__less__imp__less__exp,axiom,
% 22.27/22.22 ! [V_n,V_m,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__strict__increasing,axiom,
% 22.27/22.22 ! [V_a,V_N,V_n,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__increasing,axiom,
% 22.27/22.22 ! [V_a,V_N,V_n,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__minus,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Oring__1(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_nat__one__le__power,axiom,
% 22.27/22.22 ! [V_n,V_i] :
% 22.27/22.22 ( 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))
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__Suc__less,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__eq__imp__eq__base,axiom,
% 22.27/22.22 ! [V_b,V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( 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)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.22 => V_a = V_b ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__Suc__less__one,axiom,
% 22.27/22.22 ! [V_n,V_a,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__strict__decreasing,axiom,
% 22.27/22.22 ! [V_a,V_N,V_n,T_a] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power__power__power,axiom,
% 22.27/22.22 ! [T_b] :
% 22.27/22.22 ( class_Power_Opower(T_b)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_inf__le__fold__inf,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 22.27/22.22 ( class_Lattices_Osemilattice__inf(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),B_x)) )
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__sup__le__sup,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_A_2,T_b] :
% 22.27/22.22 ( class_Lattices_Osemilattice__sup(T_b)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) )
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_expand__Suc,axiom,
% 22.27/22.22 ! [V_v] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_folding__image__simple__idem_Ounion__idem,axiom,
% 22.27/22.22 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.27/22.22 => 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_UnionE,axiom,
% 22.27/22.22 ! [V_C_2,V_A_2,T_b] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ~ ! [B_X] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_A_2),B_X))
% 22.27/22.22 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_X),V_C_2)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zmult__1__right,axiom,
% 22.27/22.22 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zmult__1,axiom,
% 22.27/22.22 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ).
% 22.27/22.22
% 22.27/22.22 fof(fact_pos__zmult__eq__1__iff,axiom,
% 22.27/22.22 ! [V_n_2,V_m_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2))
% 22.27/22.22 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 22.27/22.22 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 22.27/22.22 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zmult__zless__mono2,axiom,
% 22.27/22.22 ! [V_k,V_j,V_i] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zdiff__zmult__distrib2,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zdiff__zmult__distrib,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__zmult__distrib,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zmult__assoc,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__zmult__distrib2,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zmult__commute,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zmult__zminus,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_eq__number__of,axiom,
% 22.27/22.22 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.22 & class_Int_Oring__char__0(T_b) )
% 22.27/22.22 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 22.27/22.22 <=> V_x_2 = V_y_2 ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_number__of__reorient,axiom,
% 22.27/22.22 ! [V_x_2,V_w_2,T_b] :
% 22.27/22.22 ( class_Int_Onumber(T_b)
% 22.27/22.22 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = V_x_2
% 22.27/22.22 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_folding__image__simple__idem_Oidem,axiom,
% 22.27/22.22 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.27/22.22 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_le__number__of,axiom,
% 22.27/22.22 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.22 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_less__number__of,axiom,
% 22.27/22.22 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.22 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_number__of__add,axiom,
% 22.27/22.22 ! [V_w,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__number__of__eq,axiom,
% 22.27/22.22 ! [V_w,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__number__of__left,axiom,
% 22.27/22.22 ! [V_z,V_w,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_number__of__mult,axiom,
% 22.27/22.22 ! [V_w,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_arith__simps_I32_J,axiom,
% 22.27/22.22 ! [V_w,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_mult__number__of__left,axiom,
% 22.27/22.22 ! [V_z,V_w,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_diff__number__of__eq,axiom,
% 22.27/22.22 ! [V_w,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_number__of__diff,axiom,
% 22.27/22.22 ! [V_w,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_number__of__minus,axiom,
% 22.27/22.22 ! [V_w,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_arith__simps_I30_J,axiom,
% 22.27/22.22 ! [V_w,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_le__number__of__eq__not__less,axiom,
% 22.27/22.22 ! [V_w_2,V_v_2,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber(T_b)
% 22.27/22.22 & class_Orderings_Olinorder(T_b) )
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ~ 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_right__distrib__number__of,axiom,
% 22.27/22.22 ! [V_c,V_b,V_v,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber(T_b)
% 22.27/22.22 & class_Rings_Osemiring(T_b) )
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_left__distrib__number__of,axiom,
% 22.27/22.22 ! [V_v,V_b,V_a,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber(T_b)
% 22.27/22.22 & class_Rings_Osemiring(T_b) )
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__number__of__diff2,axiom,
% 22.27/22.22 ! [V_w,V_c,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__number__of__diff1,axiom,
% 22.27/22.22 ! [V_c,V_w,V_v,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_right__diff__distrib__number__of,axiom,
% 22.27/22.22 ! [V_c,V_b,V_v,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber(T_b)
% 22.27/22.22 & class_Rings_Oring(T_b) )
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_left__diff__distrib__number__of,axiom,
% 22.27/22.22 ! [V_v,V_b,V_a,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber(T_b)
% 22.27/22.22 & class_Rings_Oring(T_b) )
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_minus__number__of__mult,axiom,
% 22.27/22.22 ! [V_z,V_w,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_min__number__of,axiom,
% 22.27/22.22 ! [V_v,V_u,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber(T_b)
% 22.27/22.22 & class_Orderings_Oord(T_b) )
% 22.27/22.22 => ( ( 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)))
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_max__number__of,axiom,
% 22.27/22.22 ! [V_v,V_u,T_b] :
% 22.27/22.22 ( ( class_Int_Onumber(T_b)
% 22.27/22.22 & class_Orderings_Oord(T_b) )
% 22.27/22.22 => ( ( 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)))
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Ints__number__of,axiom,
% 22.27/22.22 ! [V_w_2,T_b] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_b)
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_eq__divide__eq__number__of1,axiom,
% 22.27/22.22 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => 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 )
% 22.27/22.22 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_eq__divide__eq__number__of,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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)
% 22.27/22.22 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => 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 )
% 22.27/22.22 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__eq__eq__number__of,axiom,
% 22.27/22.22 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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)
% 22.27/22.22 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__eq__eq__number__of1,axiom,
% 22.27/22.22 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Ofield__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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
% 22.27/22.22 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.22 => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power_Opower_Opower__0,axiom,
% 22.27/22.22 ! [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 ).
% 22.27/22.22
% 22.27/22.22 fof(fact_power_Opower_Opower__Suc,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__less__eq__number__of1,axiom,
% 22.27/22.22 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> ( ( 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)))
% 22.27/22.22 => 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)))) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => ( ( 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)))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__less__eq__number__of,axiom,
% 22.27/22.22 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => 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))) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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))) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_less__divide__eq__number__of,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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))) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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))) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_less__divide__eq__number__of1,axiom,
% 22.27/22.22 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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))))
% 22.27/22.22 <=> ( ( 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)))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => ( ( 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)))
% 22.27/22.22 => 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)))) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_le__divide__eq__number__of1,axiom,
% 22.27/22.22 ! [V_w_2,V_b_2,V_a_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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))))
% 22.27/22.22 <=> ( ( 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)))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => ( ( 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)))
% 22.27/22.22 => 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)))) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_le__divide__eq__number__of,axiom,
% 22.27/22.22 ! [V_c_2,V_b_2,V_w_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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))) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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))) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__le__eq__number__of,axiom,
% 22.27/22.22 ! [V_w_2,V_c_2,V_b_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => 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))) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_c_2))
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),c_Groups_Ozero__class_Ozero(T_b)))
% 22.27/22.22 => 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))) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_divide__le__eq__number__of1,axiom,
% 22.27/22.22 ! [V_a_2,V_w_2,V_b_2,T_b] :
% 22.27/22.22 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.22 & class_Int_Onumber(T_b) )
% 22.27/22.22 => ( 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))
% 22.27/22.22 <=> ( ( 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)))
% 22.27/22.22 => 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)))) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => ( ( 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)))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ 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)))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_folding__image__simple__idem_Oin__idem,axiom,
% 22.27/22.22 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom,
% 22.27/22.22 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.27/22.22 => 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)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_folding__image__simple__idem_Osubset__idem,axiom,
% 22.27/22.22 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_c,T_b] :
% 22.27/22.22 ( c_Finite__Set_Ofolding__image__simple__idem(T_b,T_c,V_f_2,V_z_2,V_g_2,V_F_2)
% 22.27/22.22 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_number__of__pred,axiom,
% 22.27/22.22 ! [V_w,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setprod__pos,axiom,
% 22.27/22.22 ! [V_f_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_c)
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_setprod__nonneg,axiom,
% 22.27/22.22 ! [V_f_2,V_A_2,T_b,T_c] :
% 22.27/22.22 ( class_Rings_Olinordered__semidom(T_c)
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_finite__induct,axiom,
% 22.27/22.22 ! [V_P_2,V_F_2,T_b] :
% 22.27/22.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.27/22.22 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 22.27/22.22 => ( ! [B_x,B_F] :
% 22.27/22.22 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_F))
% 22.27/22.22 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_F))
% 22.27/22.22 => ( hBOOL(hAPP(V_P_2,B_F))
% 22.27/22.22 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_x),B_F))) ) ) )
% 22.27/22.22 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__graph_H_Ointros_I2_J,axiom,
% 22.27/22.22 ! [V_y_2,V_z_2,V_f_2,T_c,V_A_2,V_x_2,T_b] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.27/22.22 => ( 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)
% 22.27/22.22 => 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)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_number__of__succ,axiom,
% 22.27/22.22 ! [V_k,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_minus__numeral__code_I6_J,axiom,
% 22.27/22.22 ! [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))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_plus__numeral__code_I9_J,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_minus__numeral__code_I5_J,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_less__number__of__int__code,axiom,
% 22.27/22.22 ! [V_l_2,V_k_2] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_less__eq__number__of__int__code,axiom,
% 22.27/22.22 ! [V_l_2,V_k_2] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zsgn__def,axiom,
% 22.27/22.22 ! [V_i] :
% 22.27/22.22 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.27/22.22 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 22.27/22.22 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.27/22.22 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 22.27/22.22 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i))
% 22.27/22.22 => 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)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__left__mono,axiom,
% 22.27/22.22 ! [V_k,V_j,V_i] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zle__refl,axiom,
% 22.27/22.22 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zle__linear,axiom,
% 22.27/22.22 ! [V_w,V_z] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 22.27/22.22 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zle__trans,axiom,
% 22.27/22.22 ! [V_k,V_j,V_i] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zle__antisym,axiom,
% 22.27/22.22 ! [V_w,V_z] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z))
% 22.27/22.22 => V_z = V_w ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zless__le,axiom,
% 22.27/22.22 ! [V_w_2,V_z_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2))
% 22.27/22.22 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2))
% 22.27/22.22 & V_z_2 != V_w_2 ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_le__iff__pred__less,axiom,
% 22.27/22.22 ! [V_l_2,V_k_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__zless__mono,axiom,
% 22.27/22.22 ! [V_z,V_z_H,V_w,V_w_H] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__strict__right__mono,axiom,
% 22.27/22.22 ! [V_k,V_j,V_i] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zless__linear,axiom,
% 22.27/22.22 ! [V_y,V_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y))
% 22.27/22.22 | V_x = V_y
% 22.27/22.22 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zminus__zminus,axiom,
% 22.27/22.22 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ).
% 22.27/22.22
% 22.27/22.22 fof(fact_succ__pred,axiom,
% 22.27/22.22 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zminus__zadd__distrib,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__commute,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__left__commute,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__assoc,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_diff__int__def__symmetric,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_diff__int__def,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__0__right,axiom,
% 22.27/22.22 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__0,axiom,
% 22.27/22.22 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zadd__zminus__inverse2,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_finite__atLeastZeroLessThan__int,axiom,
% 22.27/22.22 ! [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))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zminus__0,axiom,
% 22.27/22.22 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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_less__bin__lemma,axiom,
% 22.27/22.22 ! [V_l_2,V_k_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
% 22.27/22.22 <=> 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_odd__less__0,axiom,
% 22.27/22.22 ! [V_z_2] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zless__add1__eq,axiom,
% 22.27/22.22 ! [V_z_2,V_w_2] :
% 22.27/22.22 ( 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))))
% 22.27/22.22 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 22.27/22.22 | V_w_2 = V_z_2 ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zless__imp__add1__zle,axiom,
% 22.27/22.22 ! [V_z,V_w] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z))
% 22.27/22.22 => 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)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_le__imp__0__less,axiom,
% 22.27/22.22 ! [V_z] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add1__zle__eq,axiom,
% 22.27/22.22 ! [V_z_2,V_w_2] :
% 22.27/22.22 ( 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))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zle__add1__eq__le,axiom,
% 22.27/22.22 ! [V_z_2,V_w_2] :
% 22.27/22.22 ( 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))))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_int__0__less__1,axiom,
% 22.27/22.22 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))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_int__one__le__iff__zero__less,axiom,
% 22.27/22.22 ! [V_z_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zle__diff1__eq,axiom,
% 22.27/22.22 ! [V_z_2,V_w_2] :
% 22.27/22.22 ( 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))))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_pred__def,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_int__0__neq__1,axiom,
% 22.27/22.22 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_odd__nonzero,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_succ__def,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__graph_H_Ointros_I1_J,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__graph_H_Oequations_I1_J,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_times__numeral__code_I5_J,axiom,
% 22.27/22.22 ! [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)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_self__quotient__aux1,axiom,
% 22.27/22.22 ! [V_q,V_r,V_a] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.27/22.22 => ( 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))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_self__quotient__aux2,axiom,
% 22.27/22.22 ! [V_q,V_r,V_a] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.27/22.22 => ( 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))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zdiv__mono2__neg__lemma,axiom,
% 22.27/22.22 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 22.27/22.22 ( 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)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_unique__quotient__lemma__neg,axiom,
% 22.27/22.22 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zdiv__mono2__lemma,axiom,
% 22.27/22.22 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] :
% 22.27/22.22 ( 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)
% 22.27/22.22 => ( 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)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_finite__atLeastAtMost__int,axiom,
% 22.27/22.22 ! [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))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_finite__atLeastLessThan__int,axiom,
% 22.27/22.22 ! [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))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_finite__greaterThanAtMost__int,axiom,
% 22.27/22.22 ! [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))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_finite__greaterThanLessThan__int,axiom,
% 22.27/22.22 ! [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))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_number__of__is__id,axiom,
% 22.27/22.22 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ).
% 22.27/22.22
% 22.27/22.22 fof(fact_infinite__UNIV__int,axiom,
% 22.27/22.22 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_q__pos__lemma,axiom,
% 22.27/22.22 ! [V_r_H,V_q_H,V_b_H] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_q__neg__lemma,axiom,
% 22.27/22.22 ! [V_r_H,V_q_H,V_b_H] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_unique__quotient__lemma,axiom,
% 22.27/22.22 ! [V_r,V_q,V_r_H,V_q_H,V_b] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 22.27/22.22 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_simp__from__to,axiom,
% 22.27/22.22 ! [V_i_2,V_j_2] :
% 22.27/22.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 22.27/22.22 => 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)) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
% 22.27/22.22 => 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)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 22.27/22.22 ! [V_n,V_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.22 => 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))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 22.27/22.22 ! [V_y,V_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 22.27/22.22 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))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 22.27/22.22 ! [V_y,V_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 22.27/22.22 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))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_bset_I8_J,axiom,
% 22.27/22.22 ! [V_B_2,V_t_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ( 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))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_aset_I6_J,axiom,
% 22.27/22.22 ! [V_A_2,V_t_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ( 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))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 22.27/22.22 => 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)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_aset_I8_J,axiom,
% 22.27/22.22 ! [V_t_2,V_A_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_bset_I6_J,axiom,
% 22.27/22.22 ! [V_t_2,V_B_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
% 22.27/22.22 => 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_periodic__finite__ex,axiom,
% 22.27/22.22 ! [V_P_2,V_d_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 22.27/22.22 => ( ! [B_x,B_k] :
% 22.27/22.22 ( hBOOL(hAPP(V_P_2,B_x))
% 22.27/22.22 <=> 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)))) )
% 22.27/22.22 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 22.27/22.22 <=> ? [B_x] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_bset_I3_J,axiom,
% 22.27/22.22 ! [V_B_2,V_t_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ( 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))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xa] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2))
% 22.27/22.22 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) )
% 22.27/22.22 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_aset_I3_J,axiom,
% 22.27/22.22 ! [V_A_2,V_t_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ( 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))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xa] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2))
% 22.27/22.22 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) )
% 22.27/22.22 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_aset_I5_J,axiom,
% 22.27/22.22 ! [V_A_2,V_t_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 22.27/22.22 => 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)) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_bset_I7_J,axiom,
% 22.27/22.22 ! [V_B_2,V_t_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 22.27/22.22 => 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))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_bset_I4_J,axiom,
% 22.27/22.22 ! [V_B_2,V_t_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( B_x != V_t_2
% 22.27/22.22 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_aset_I4_J,axiom,
% 22.27/22.22 ! [V_A_2,V_t_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( B_x != V_t_2
% 22.27/22.22 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_aset_I7_J,axiom,
% 22.27/22.22 ! [V_t_2,V_A_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
% 22.27/22.22 => 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))) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_bset_I5_J,axiom,
% 22.27/22.22 ! [V_t_2,V_B_2,V_D_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( ! [B_xa] :
% 22.27/22.22 ( 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)))
% 22.27/22.22 => ! [B_xb] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
% 22.27/22.22 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
% 22.27/22.22 => 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)) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Suc__nat__number__of__add,axiom,
% 22.27/22.22 ! [V_n,V_v] :
% 22.27/22.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_tsub__def,axiom,
% 22.27/22.22 ! [V_x,V_y] :
% 22.27/22.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 22.27/22.22 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 22.27/22.22 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_not__neg__0,axiom,
% 22.27/22.22 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_not__neg__1,axiom,
% 22.27/22.22 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_not__neg__eq__ge__0,axiom,
% 22.27/22.22 ! [V_x_2] :
% 22.27/22.22 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_neg__def,axiom,
% 22.27/22.22 ! [V_Z_2] :
% 22.27/22.22 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_neg__imp__number__of__eq__0,axiom,
% 22.27/22.22 ! [V_v] :
% 22.27/22.22 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.22 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_eq__nat__number__of,axiom,
% 22.27/22.22 ! [V_v_H_2,V_v_2] :
% 22.27/22.22 ( 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)
% 22.27/22.22 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 22.27/22.22 => 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))) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)))
% 22.27/22.22 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 22.27/22.22 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2)))
% 22.27/22.22 => V_v_2 = V_v_H_2 ) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_nat__number__of__add__left,axiom,
% 22.27/22.22 ! [V_k,V_v_H,V_v] :
% 22.27/22.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.22 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 22.27/22.22 => 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) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom,
% 22.27/22.22 ! [V_y,V_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_neg__number__of__pred__iff__0,axiom,
% 22.27/22.22 ! [V_v_2] :
% 22.27/22.22 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))))
% 22.27/22.22 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_tsub__eq,axiom,
% 22.27/22.22 ! [V_x,V_y] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
% 22.27/22.22 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Suc__nat__number__of,axiom,
% 22.27/22.22 ! [V_v] :
% 22.27/22.22 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.22 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.22 => 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)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_fold__graph_H_Oequations_I2_J,axiom,
% 22.27/22.22 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_c,T_b] :
% 22.27/22.22 ( 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))
% 22.27/22.22 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.27/22.22 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 )
% 22.27/22.22 | ? [B_x,B_y] :
% 22.27/22.22 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y)
% 22.27/22.22 & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a2_2))
% 22.27/22.22 & 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_int__power__div__base,axiom,
% 22.27/22.22 ! [V_k,V_m] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 22.27/22.22 => 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)))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_nat__number__of__diff__1,axiom,
% 22.27/22.22 ! [V_v] :
% 22.27/22.22 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.22 => 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)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_decr__mult__lemma,axiom,
% 22.27/22.22 ! [V_k_2,V_P_2,V_d_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(V_P_2,B_x))
% 22.27/22.22 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(V_P_2,B_x))
% 22.27/22.22 => 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)))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_incr__mult__lemma,axiom,
% 22.27/22.22 ! [V_k_2,V_P_2,V_d_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2))
% 22.27/22.22 => ( ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(V_P_2,B_x))
% 22.27/22.22 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) )
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 22.27/22.22 => ! [B_x] :
% 22.27/22.22 ( hBOOL(hAPP(V_P_2,B_x))
% 22.27/22.22 => 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)))) ) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zdiv__zero,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zdiv__zminus2,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zdiv__zminus__zminus,axiom,
% 22.27/22.22 ! [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) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Pls__def,axiom,
% 22.27/22.22 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_rel__simps_I19_J,axiom,
% 22.27/22.22 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_rel__simps_I2_J,axiom,
% 22.27/22.22 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__Pls,axiom,
% 22.27/22.22 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__Pls__right,axiom,
% 22.27/22.22 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__0,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__by__0,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.22 => 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) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_mult__Pls,axiom,
% 22.27/22.22 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ).
% 22.27/22.22
% 22.27/22.22 fof(fact_diff__bin__simps_I1_J,axiom,
% 22.27/22.22 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ).
% 22.27/22.22
% 22.27/22.22 fof(fact_minus__Pls,axiom,
% 22.27/22.22 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__by__1,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
% 22.27/22.22 ! [V_y,V_x] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_pos__imp__zdiv__neg__iff,axiom,
% 22.27/22.22 ! [V_a_2,V_b_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_neg__imp__zdiv__neg__iff,axiom,
% 22.27/22.22 ! [V_a_2,V_b_2] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.22 => ( 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)))
% 22.27/22.22 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__neg__pos__less0,axiom,
% 22.27/22.22 ! [V_b,V_a] :
% 22.27/22.22 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.22 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.27/22.22 => 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))) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zdiv__self,axiom,
% 22.27/22.22 ! [V_a] :
% 22.27/22.22 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.27/22.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_number__of__Pls,axiom,
% 22.27/22.22 ! [T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_semiring__norm_I112_J,axiom,
% 22.27/22.22 ! [T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__numeral__0__right,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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 ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_add__numeral__0,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Int_Onumber__ring(T_a)
% 22.27/22.22 => 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 ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_bin__less__0__simps_I1_J,axiom,
% 22.27/22.22 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_nat__number__of__Pls,axiom,
% 22.27/22.22 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_semiring__norm_I113_J,axiom,
% 22.27/22.22 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zero__is__num__zero,axiom,
% 22.27/22.22 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__mult__mult1,axiom,
% 22.27/22.22 ! [V_b,V_a,V_c,T_a] :
% 22.27/22.22 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.22 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__mult__mult2,axiom,
% 22.27/22.22 ! [V_b,V_a,V_c,T_a] :
% 22.27/22.22 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.22 => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__mult__self1__is__id,axiom,
% 22.27/22.22 ! [V_a,V_b,T_a] :
% 22.27/22.22 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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 ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__mult__self2__is__id,axiom,
% 22.27/22.22 ! [V_a,V_b,T_a] :
% 22.27/22.22 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.22 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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 ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__mult__mult1__if,axiom,
% 22.27/22.22 ! [V_b,V_a,V_c,T_a] :
% 22.27/22.22 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.22 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) )
% 22.27/22.22 & ( V_c != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => 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) ) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_div__self,axiom,
% 22.27/22.22 ! [V_a,T_a] :
% 22.27/22.22 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.22 => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.22 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_not__neg__number__of__Pls,axiom,
% 22.27/22.22 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ).
% 22.27/22.22
% 22.27/22.22 fof(fact_zdiv__eq__0__iff,axiom,
% 22.27/22.22 ! [V_k_2,V_i_2] :
% 22.27/22.22 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.27/22.22 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.27/22.22 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2))
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) )
% 22.27/22.23 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_pos__imp__zdiv__nonneg__iff,axiom,
% 22.27/22.23 ! [V_a_2,V_b_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_pos__imp__zdiv__pos__iff,axiom,
% 22.27/22.23 ! [V_i_2,V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom,
% 22.27/22.23 ! [V_b_2,V_a_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2))
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2))
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiv__mono2,axiom,
% 22.27/22.23 ! [V_b,V_b_H,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 22.27/22.23 => 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))) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__nonneg__neg__le0,axiom,
% 22.27/22.23 ! [V_b,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__pos__pos__trivial,axiom,
% 22.27/22.23 ! [V_b,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 22.27/22.23 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_neg__imp__zdiv__nonneg__iff,axiom,
% 22.27/22.23 ! [V_a_2,V_b_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__nonpos__pos__le0,axiom,
% 22.27/22.23 ! [V_b,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiv__mono2__neg,axiom,
% 22.27/22.23 ! [V_b,V_b_H,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b))
% 22.27/22.23 => 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))) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__neg__neg__trivial,axiom,
% 22.27/22.23 ! [V_b,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 22.27/22.23 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiv__mono1,axiom,
% 22.27/22.23 ! [V_b,V_a_H,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiv__mono1__neg,axiom,
% 22.27/22.23 ! [V_b,V_a_H,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__div__less__self,axiom,
% 22.27/22.23 ! [V_k,V_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiv__zmult2__eq,axiom,
% 22.27/22.23 ! [V_b,V_a,V_c] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_divide__Numeral0,axiom,
% 22.27/22.23 ! [V_x,T_a] :
% 22.27/22.23 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 22.27/22.23 & class_Int_Onumber__ring(T_a) )
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_eq__number__of__0,axiom,
% 22.27/22.23 ! [V_v_2] :
% 22.27/22.23 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_eq__0__number__of,axiom,
% 22.27/22.23 ! [V_v_2] :
% 22.27/22.23 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_number__of2,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__nat__number__of,axiom,
% 22.27/22.23 ! [V_v_H_2,V_v_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2))
% 22.27/22.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) )
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_le__nat__number__of,axiom,
% 22.27/22.23 ! [V_v_H_2,V_v_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2))
% 22.27/22.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__mult__self2,axiom,
% 22.27/22.23 ! [V_c,V_a,V_b,T_a] :
% 22.27/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.23 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__mult__self1,axiom,
% 22.27/22.23 ! [V_c,V_a,V_b,T_a] :
% 22.27/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.23 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__add__self2,axiom,
% 22.27/22.23 ! [V_a,V_b,T_a] :
% 22.27/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.23 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__add__self1,axiom,
% 22.27/22.23 ! [V_a,V_b,T_a] :
% 22.27/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.23 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_le__special_I3_J,axiom,
% 22.27/22.23 ! [V_x_2,T_b] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_le__special_I1_J,axiom,
% 22.27/22.23 ! [V_y_2,T_b] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__special_I1_J,axiom,
% 22.27/22.23 ! [V_y_2,T_b] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__special_I3_J,axiom,
% 22.27/22.23 ! [V_x_2,T_b] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__0__number__of,axiom,
% 22.27/22.23 ! [V_v_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__nat__number__of,axiom,
% 22.27/22.23 ! [V_v_H,V_v] :
% 22.27/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls))
% 22.27/22.23 => 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)) ) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_split__zdiv,axiom,
% 22.27/22.23 ! [V_k_2,V_n_2,V_P_2] :
% 22.27/22.23 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
% 22.27/22.23 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.27/22.23 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.27/22.23 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 22.27/22.23 => ! [B_i] :
% 22.27/22.23 ( ? [B_j] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 22.27/22.23 & 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) )
% 22.27/22.23 => hBOOL(hAPP(V_P_2,B_i)) ) )
% 22.27/22.23 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => ! [B_i] :
% 22.27/22.23 ( ? [B_j] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 & 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) )
% 22.27/22.23 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_divmod__int__rel__div__eq,axiom,
% 22.27/22.23 ! [V_r_1,V_y,V_b_1,V_a_1] :
% 22.27/22.23 ( 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)
% 22.27/22.23 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1))
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1))
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 22.27/22.23 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.27/22.23 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__number__of__mult__left,axiom,
% 22.27/22.23 ! [V_k,V_v_H,V_v] :
% 22.27/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => 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) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mult__nat__number__of,axiom,
% 22.27/22.23 ! [V_v_H,V_v] :
% 22.27/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Suc__diff__number__of,axiom,
% 22.27/22.23 ! [V_m,V_v] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v))
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__1__add__number__of,axiom,
% 22.27/22.23 ! [V_v] :
% 22.27/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__number__of__add__1,axiom,
% 22.27/22.23 ! [V_v] :
% 22.27/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_z3div__def,axiom,
% 22.27/22.23 ! [V_k,V_l] :
% 22.27/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 22.27/22.23 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_eq__special_I3_J,axiom,
% 22.27/22.23 ! [V_x_2,T_b] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.23 <=> 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)))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_eq__special_I1_J,axiom,
% 22.27/22.23 ! [V_y_2,T_b] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 22.27/22.23 <=> 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)))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nats__number__of,axiom,
% 22.27/22.23 ! [V_w_2,T_b] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power__nat__number__of__number__of,axiom,
% 22.27/22.23 ! [V_w,V_v] :
% 22.27/22.23 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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)) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__le__mono,axiom,
% 22.27/22.23 ! [V_k,V_n,V_m] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__le__dividend,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__mult2__eq,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__div__distrib,axiom,
% 22.27/22.23 ! [V_y,V_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom,
% 22.27/22.23 ! [V_y,V_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_iszero__0,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_iszero__def,axiom,
% 22.27/22.23 ! [V_z_2,T_b] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_b)
% 22.27/22.23 => ( c_Int_Oiszero(T_b,V_z_2)
% 22.27/22.23 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__1,axiom,
% 22.27/22.23 ! [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 ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__less,axiom,
% 22.27/22.23 ! [V_n,V_m] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.23 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__mult__div__cancel__disj,axiom,
% 22.27/22.23 ! [V_n,V_m,V_k] :
% 22.27/22.23 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 => 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) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__0,axiom,
% 22.27/22.23 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__numerals_I1_J,axiom,
% 22.27/22.23 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_not__iszero__1,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_eq__nat__nat__iff,axiom,
% 22.27/22.23 ! [V_z_H_2,V_z_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2))
% 22.27/22.23 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2)
% 22.27/22.23 <=> V_z_2 = V_z_H_2 ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_ex__nat,axiom,
% 22.27/22.23 ! [V_P_2] :
% 22.27/22.23 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 22.27/22.23 <=> ? [B_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 22.27/22.23 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_all__nat,axiom,
% 22.27/22.23 ! [V_P_2] :
% 22.27/22.23 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 22.27/22.23 <=> ! [B_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 22.27/22.23 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__relations_I1_J,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 22.27/22.23 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2)
% 22.27/22.23 <=> V_x_2 = V_y_2 ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__number__of__def,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__number__of,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__numerals_I2_J,axiom,
% 22.27/22.23 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_neg__nat,axiom,
% 22.27/22.23 ! [V_z] :
% 22.27/22.23 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 22.27/22.23 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_card__atLeastZeroLessThan__int,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__nat__number__of,axiom,
% 22.27/22.23 ! [V_v_H,V_v] :
% 22.27/22.23 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_card__atLeastLessThan__int,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_card__greaterThanAtMost__int,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_one__div__nat__number__of,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__le__mono2,axiom,
% 22.27/22.23 ! [V_k,V_n,V_m] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__mult__self1__is__m,axiom,
% 22.27/22.23 ! [V_m,V_n] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.23 => 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 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__mult__self__is__m,axiom,
% 22.27/22.23 ! [V_m,V_n] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.23 => 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 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__mult__div__cancel1,axiom,
% 22.27/22.23 ! [V_n,V_m,V_k] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__less__dividend,axiom,
% 22.27/22.23 ! [V_m,V_n] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__le__0,axiom,
% 22.27/22.23 ! [V_z] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__0__iff,axiom,
% 22.27/22.23 ! [V_i_2] :
% 22.27/22.23 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zless__nat__conj,axiom,
% 22.27/22.23 ! [V_z_2,V_w_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__mono__iff,axiom,
% 22.27/22.23 ! [V_w_2,V_z_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2))
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__relations_I3_J,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__1,axiom,
% 22.27/22.23 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_iszero__Numeral0,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nats__0,axiom,
% 22.27/22.23 ! [T_b] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_b)
% 22.27/22.23 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Ozero__class_Ozero(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nats__add,axiom,
% 22.27/22.23 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_b)
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 22.27/22.23 => 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))) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nats__mult,axiom,
% 22.27/22.23 ! [V_b_2,V_a_2,T_b] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_b)
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Nat_Osemiring__1__class_ONats(T_b)))
% 22.27/22.23 => 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))) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nats__1,axiom,
% 22.27/22.23 ! [T_b] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_b)
% 22.27/22.23 => hBOOL(hAPP(hAPP(c_member(T_b),c_Groups_Oone__class_Oone(T_b)),c_Nat_Osemiring__1__class_ONats(T_b))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__if,axiom,
% 22.27/22.23 ! [V_m,V_n] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.23 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.23 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.23 => 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)) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__geq,axiom,
% 22.27/22.23 ! [V_m,V_n] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.23 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_split__div,axiom,
% 22.27/22.23 ! [V_k_2,V_n_2,V_P_2] :
% 22.27/22.23 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
% 22.27/22.23 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 22.27/22.23 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 => ! [B_i,B_j] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 22.27/22.23 => ( 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)
% 22.27/22.23 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zero__less__nat__eq,axiom,
% 22.27/22.23 ! [V_z_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__less__eq__zless,axiom,
% 22.27/22.23 ! [V_z_2,V_w_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__relations_I2_J,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__le__eq__zle,axiom,
% 22.27/22.23 ! [V_z_2,V_w_2] :
% 22.27/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 22.27/22.23 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) )
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__add__distrib,axiom,
% 22.27/22.23 ! [V_z_H,V_z] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 22.27/22.23 ! [V_y,V_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__mult__distrib,axiom,
% 22.27/22.23 ! [V_z_H,V_z] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 22.27/22.23 ! [V_y,V_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__diff__distrib,axiom,
% 22.27/22.23 ! [V_z,V_z_H] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_card__atLeastAtMost__int,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 22.27/22.23 ! [V_n,V_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__power__eq,axiom,
% 22.27/22.23 ! [V_n,V_z] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom,
% 22.27/22.23 ! [V_y,V_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_card__greaterThanLessThan__int,axiom,
% 22.27/22.23 ! [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)))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_le__div__geq,axiom,
% 22.27/22.23 ! [V_m,V_n] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_split__div__lemma,axiom,
% 22.27/22.23 ! [V_m_2,V_q_2,V_n_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 22.27/22.23 => ( ( 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))
% 22.27/22.23 & 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)))) )
% 22.27/22.23 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_split__div_H,axiom,
% 22.27/22.23 ! [V_n_2,V_m_2,V_P_2] :
% 22.27/22.23 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
% 22.27/22.23 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) )
% 22.27/22.23 | ? [B_q] :
% 22.27/22.23 ( 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))
% 22.27/22.23 & 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))))
% 22.27/22.23 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_one__less__nat__eq,axiom,
% 22.27/22.23 ! [V_z_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Suc__nat__eq__nat__zadd1,axiom,
% 22.27/22.23 ! [V_z] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__mult__distrib__neg,axiom,
% 22.27/22.23 ! [V_z_H,V_z] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_eq__number__of__eq,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 22.27/22.23 <=> 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)))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power__nat__number__of,axiom,
% 22.27/22.23 ! [V_n,V_v] :
% 22.27/22.23 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__aux__def,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__morphism__nat__int,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_eq__special_I2_J,axiom,
% 22.27/22.23 ! [V_y_2,T_b] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 => ( c_Groups_Oone__class_Oone(T_b) = hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)
% 22.27/22.23 <=> 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)))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_eq__special_I4_J,axiom,
% 22.27/22.23 ! [V_x_2,T_b] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2) = c_Groups_Oone__class_Oone(T_b)
% 22.27/22.23 <=> 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))))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__number__of__lemma,axiom,
% 22.27/22.23 ! [V_v,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => ( ( 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)))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ 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)))
% 22.27/22.23 => 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) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_negative__zle,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_negative__zless,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__set__return__embed,axiom,
% 22.27/22.23 ! [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 ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__int,axiom,
% 22.27/22.23 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I46_J,axiom,
% 22.27/22.23 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I39_J,axiom,
% 22.27/22.23 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__eq__iff,axiom,
% 22.27/22.23 ! [V_n_2,V_m_2,T_b] :
% 22.27/22.23 ( class_Nat_Osemiring__char__0(T_b)
% 22.27/22.23 => ( 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)
% 22.27/22.23 <=> V_m_2 = V_n_2 ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I51_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
% 22.27/22.23 <=> V_k_2 = V_l_2 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I17_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__int__code_I16_J,axiom,
% 22.27/22.23 ! [V_k2_2,V_k1_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__eq__int__code_I16_J,axiom,
% 22.27/22.23 ! [V_k2_2,V_k1_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I34_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiv__int,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_not__neg__int,axiom,
% 22.27/22.23 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_inj__int,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__set__relations_I2_J,axiom,
% 22.27/22.23 ! [V_A_2,V_x_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2))
% 22.27/22.23 <=> 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__numerals_I4_J,axiom,
% 22.27/22.23 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)))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__set__relations_I5_J,axiom,
% 22.27/22.23 ! [V_B_2,V_A_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.27/22.23 <=> 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__numerals_I1_J,axiom,
% 22.27/22.23 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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__0,axiom,
% 22.27/22.23 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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__eq__0__conv,axiom,
% 22.27/22.23 ! [V_n_2] :
% 22.27/22.23 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.27/22.23 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
% 22.27/22.23 ! [V_P_2] :
% 22.27/22.23 ( ! [B_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 22.27/22.23 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.27/22.23 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
% 22.27/22.23 ! [V_P_2] :
% 22.27/22.23 ( ? [B_x] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 22.27/22.23 & hBOOL(hAPP(V_P_2,B_x)) )
% 22.27/22.23 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zero__zle__int,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__less__0__conv,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__relations_I2_J,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zless__int,axiom,
% 22.27/22.23 ! [V_n_2,V_m_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_bin__less__0__simps_I4_J,axiom,
% 22.27/22.23 ! [V_w_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__relations_I3_J,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zle__int,axiom,
% 22.27/22.23 ! [V_n_2,V_m_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zadd__int__left,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zadd__int,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zle__iff__zadd,axiom,
% 22.27/22.23 ! [V_z_2,V_w_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2))
% 22.27/22.23 <=> ? [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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I22_J,axiom,
% 22.27/22.23 ! [V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I12_J,axiom,
% 22.27/22.23 ! [V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zero__le__imp__of__nat,axiom,
% 22.27/22.23 ! [V_m,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__0__le__iff,axiom,
% 22.27/22.23 ! [V_n,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_negative__eq__positive,axiom,
% 22.27/22.23 ! [V_m_2,V_n_2] :
% 22.27/22.23 ( 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)
% 22.27/22.23 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__less__0__iff,axiom,
% 22.27/22.23 ! [V_m,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.23 => ~ 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Bit1__def,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_not__int__zless__negative,axiom,
% 22.27/22.23 ! [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)))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zmult__int,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__mult,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__0,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__less__iff,axiom,
% 22.27/22.23 ! [V_n_2,V_m_2,T_b] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_b)
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__imp__of__nat__less,axiom,
% 22.27/22.23 ! [V_n,V_m,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__less__imp__less,axiom,
% 22.27/22.23 ! [V_n,V_m,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.23 => ( 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)))
% 22.27/22.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__numerals_I2_J,axiom,
% 22.27/22.23 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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__1,axiom,
% 22.27/22.23 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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__le__iff,axiom,
% 22.27/22.23 ! [V_n_2,V_m_2,T_b] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_b)
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__add,axiom,
% 22.27/22.23 ! [V_n,V_m,T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__mult,axiom,
% 22.27/22.23 ! [V_n,V_m,T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_neg__number__of__Bit1,axiom,
% 22.27/22.23 ! [V_w_2] :
% 22.27/22.23 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2))))
% 22.27/22.23 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_not__neg__nat,axiom,
% 22.27/22.23 ! [V_z] :
% 22.27/22.23 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z))
% 22.27/22.23 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__1,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_minus__Bit1,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_iszero__number__of__Bit1,axiom,
% 22.27/22.23 ! [V_w,T_a] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 & class_Int_Oring__char__0(T_a) )
% 22.27/22.23 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Ints__of__nat,axiom,
% 22.27/22.23 ! [V_n_2,T_b] :
% 22.27/22.23 ( class_Rings_Oring__1(T_b)
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_succ__Pls,axiom,
% 22.27/22.23 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__power,axiom,
% 22.27/22.23 ! [V_n,V_m,T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zpower__int,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__power,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__in__Nats,axiom,
% 22.27/22.23 ! [V_n_2,T_b] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_b)
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__set__relations_I1_J,axiom,
% 22.27/22.23 ! [V_A_2] :
% 22.27/22.23 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2))
% 22.27/22.23 <=> 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_inj__of__nat,axiom,
% 22.27/22.23 ! [T_b] :
% 22.27/22.23 ( class_Nat_Osemiring__char__0(T_b)
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_number__of__Bit1,axiom,
% 22.27/22.23 ! [V_w,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mult__numeral__1,axiom,
% 22.27/22.23 ! [V_a,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mult__numeral__1__right,axiom,
% 22.27/22.23 ! [V_a,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__le__0__conv,axiom,
% 22.27/22.23 ! [V_n_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_numeral__1__eq__1,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_semiring__norm_I110_J,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__Suc0__eq__1,axiom,
% 22.27/22.23 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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zless__iff__Suc__zadd,axiom,
% 22.27/22.23 ! [V_z_2,V_w_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2))
% 22.27/22.23 <=> ? [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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__nat__eq,axiom,
% 22.27/22.23 ! [V_z] :
% 22.27/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 22.27/22.23 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 22.27/22.23 => 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) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__eq__iff,axiom,
% 22.27/22.23 ! [V_z_2,V_m_2] :
% 22.27/22.23 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2
% 22.27/22.23 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2)
% 22.27/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__0__le,axiom,
% 22.27/22.23 ! [V_z] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 22.27/22.23 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zless__nat__eq__int__zless,axiom,
% 22.27/22.23 ! [V_z_2,V_m_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2)))
% 22.27/22.23 <=> 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I5_J,axiom,
% 22.27/22.23 ! [V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I29_J,axiom,
% 22.27/22.23 ! [V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__zle__neg,axiom,
% 22.27/22.23 ! [V_m_2,V_n_2] :
% 22.27/22.23 ( 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))))
% 22.27/22.23 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__Suc,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_divide__numeral__1,axiom,
% 22.27/22.23 ! [V_a,T_a] :
% 22.27/22.23 ( ( class_Fields_Ofield(T_a)
% 22.27/22.23 & class_Int_Onumber__ring(T_a) )
% 22.27/22.23 => 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 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_divide__Numeral1,axiom,
% 22.27/22.23 ! [V_x,T_a] :
% 22.27/22.23 ( ( class_Fields_Ofield(T_a)
% 22.27/22.23 & class_Int_Onumber__ring(T_a) )
% 22.27/22.23 => 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 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_negative__zle__0,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__zminus__int,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_one__is__num__one,axiom,
% 22.27/22.23 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiff__int,axiom,
% 22.27/22.23 ! [V_m,V_n] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Numeral1__eq1__nat,axiom,
% 22.27/22.23 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__numeral__1__eq__1,axiom,
% 22.27/22.23 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__Suc,axiom,
% 22.27/22.23 ! [V_m,T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_neg__zminus__int,axiom,
% 22.27/22.23 ! [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))))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__diff,axiom,
% 22.27/22.23 ! [V_m,V_n,T_a] :
% 22.27/22.23 ( class_Rings_Oring__1(T_a)
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_not__iszero__Numeral1,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zero__less__int__conv,axiom,
% 22.27/22.23 ! [V_n_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__eq__iff,axiom,
% 22.27/22.23 ! [V_m_2,V_w_2] :
% 22.27/22.23 ( hAPP(c_Int_Onat,V_w_2) = V_m_2
% 22.27/22.23 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 22.27/22.23 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 22.27/22.23 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__eq__iff2,axiom,
% 22.27/22.23 ! [V_w_2,V_m_2] :
% 22.27/22.23 ( V_m_2 = hAPP(c_Int_Onat,V_w_2)
% 22.27/22.23 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 22.27/22.23 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 22.27/22.23 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_split__nat,axiom,
% 22.27/22.23 ! [V_i_2,V_P_2] :
% 22.27/22.23 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2)))
% 22.27/22.23 <=> ( ! [B_n] :
% 22.27/22.23 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n)
% 22.27/22.23 => hBOOL(hAPP(V_P_2,B_n)) )
% 22.27/22.23 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zmult__zless__mono2__lemma,axiom,
% 22.27/22.23 ! [V_k,V_j,V_i] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_numeral__1__eq__Suc__0,axiom,
% 22.27/22.23 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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_numeral__3__eq__3,axiom,
% 22.27/22.23 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)))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_not__zle__0__negative,axiom,
% 22.27/22.23 ! [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))))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_negative__zless__0,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power3__eq__cube,axiom,
% 22.27/22.23 ! [V_a,T_a] :
% 22.27/22.23 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 22.27/22.23 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))))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Suc3__eq__add__3,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Suc__div__eq__add3__div__number__of,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Suc__div__eq__add3__div,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__Suc__eq__div__add3,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__eq__iff__number__of,axiom,
% 22.27/22.23 ! [V_v_2,V_m_2] :
% 22.27/22.23 ( 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)
% 22.27/22.23 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))
% 22.27/22.23 & 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__numerals_I4_J,axiom,
% 22.27/22.23 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)))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__0__less__iff,axiom,
% 22.27/22.23 ! [V_n_2,T_b] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_b)
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__nat__number__of,axiom,
% 22.27/22.23 ! [V_v] :
% 22.27/22.23 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_le__special_I4_J,axiom,
% 22.27/22.23 ! [V_x_2,T_b] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_le__special_I2_J,axiom,
% 22.27/22.23 ! [V_y_2,T_b] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__special_I4_J,axiom,
% 22.27/22.23 ! [V_x_2,T_b] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__special_I2_J,axiom,
% 22.27/22.23 ! [V_y_2,T_b] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 & class_Rings_Olinordered__idom(T_b) )
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__special_I2_J,axiom,
% 22.27/22.23 ! [V_w,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__special_I3_J,axiom,
% 22.27/22.23 ! [V_v,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__less__iff,axiom,
% 22.27/22.23 ! [V_m_2,V_w_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2))
% 22.27/22.23 <=> 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Suc__diff__eq__diff__pred,axiom,
% 22.27/22.23 ! [V_m,V_n] :
% 22.27/22.23 ( 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))
% 22.27/22.23 => 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)))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiff__int__split,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2,V_P_2] :
% 22.27/22.23 ( 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))))
% 22.27/22.23 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2))
% 22.27/22.23 => 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)))) )
% 22.27/22.23 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 22.27/22.23 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__number__of__eq,axiom,
% 22.27/22.23 ! [V_v,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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) )
% 22.27/22.23 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.27/22.23 => 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) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_image__atLeastZeroLessThan__int,axiom,
% 22.27/22.23 ! [V_u_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2))
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_diff__special_I1_J,axiom,
% 22.27/22.23 ! [V_w,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_diff__special_I2_J,axiom,
% 22.27/22.23 ! [V_v,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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)))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_pos__zdiv__mult__2,axiom,
% 22.27/22.23 ! [V_b,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_neg__zdiv__mult__2,axiom,
% 22.27/22.23 ! [V_b,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_of__nat__double,axiom,
% 22.27/22.23 ! [V_x,T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Suc__n__div__2__gt__zero,axiom,
% 22.27/22.23 ! [V_n] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.27/22.23 => 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)))))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power__minus1__odd,axiom,
% 22.27/22.23 ! [V_n,T_a] :
% 22.27/22.23 ( class_Rings_Oring__1(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I49_J,axiom,
% 22.27/22.23 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I50_J,axiom,
% 22.27/22.23 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_int__int__eq,axiom,
% 22.27/22.23 ! [V_n_2,V_m_2] :
% 22.27/22.23 ( 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)
% 22.27/22.23 <=> V_m_2 = V_n_2 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__set__relations_I4_J,axiom,
% 22.27/22.23 ! [V_B_2,V_A_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.27/22.23 <=> 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__relations_I1_J,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2] :
% 22.27/22.23 ( 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)
% 22.27/22.23 <=> V_x_2 = V_y_2 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__set__relations_I3_J,axiom,
% 22.27/22.23 ! [V_B_2,V_A_2] :
% 22.27/22.23 ( V_A_2 = V_B_2
% 22.27/22.23 <=> 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Bit0__Pls,axiom,
% 22.27/22.23 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I38_J,axiom,
% 22.27/22.23 ! [V_l_2] :
% 22.27/22.23 ( c_Int_OPls = c_Int_OBit0(V_l_2)
% 22.27/22.23 <=> c_Int_OPls = V_l_2 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I44_J,axiom,
% 22.27/22.23 ! [V_k_2] :
% 22.27/22.23 ( c_Int_OBit0(V_k_2) = c_Int_OPls
% 22.27/22.23 <=> V_k_2 = c_Int_OPls ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Bit0__def,axiom,
% 22.27/22.23 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__Bit0__Bit0,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I31_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__eq__int__code_I13_J,axiom,
% 22.27/22.23 ! [V_k2_2,V_k1_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__int__code_I13_J,axiom,
% 22.27/22.23 ! [V_k2_2,V_k1_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I14_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I48_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
% 22.27/22.23 <=> V_k_2 = V_l_2 ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_minus__Bit0,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_diff__bin__simps_I7_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mult__Bit0,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_bin__less__0__simps_I3_J,axiom,
% 22.27/22.23 ! [V_w_2] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I21_J,axiom,
% 22.27/22.23 ! [V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I27_J,axiom,
% 22.27/22.23 ! [V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I32_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__eq__int__code_I14_J,axiom,
% 22.27/22.23 ! [V_k2_2,V_k1_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I10_J,axiom,
% 22.27/22.23 ! [V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I4_J,axiom,
% 22.27/22.23 ! [V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__int__code_I15_J,axiom,
% 22.27/22.23 ! [V_k2_2,V_k1_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I16_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__Bit0__Bit1,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__Bit1__Bit0,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_diff__bin__simps_I3_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_diff__bin__simps_I9_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_diff__bin__simps_I10_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiv__number__of__Bit0,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_neg__number__of__Bit0,axiom,
% 22.27/22.23 ! [V_w_2] :
% 22.27/22.23 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2))))
% 22.27/22.23 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_pred__Bit1,axiom,
% 22.27/22.23 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_pred__Bit0,axiom,
% 22.27/22.23 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_iszero__number__of__Bit0,axiom,
% 22.27/22.23 ! [V_w_2,T_b] :
% 22.27/22.23 ( ( class_Int_Onumber__ring(T_b)
% 22.27/22.23 & class_Int_Oring__char__0(T_b) )
% 22.27/22.23 => ( c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),c_Int_OBit0(V_w_2)))
% 22.27/22.23 <=> c_Int_Oiszero(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_succ__Bit0,axiom,
% 22.27/22.23 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_succ__Bit1,axiom,
% 22.27/22.23 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_number__of__Bit0,axiom,
% 22.27/22.23 ! [V_w,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__eq__int__code_I15_J,axiom,
% 22.27/22.23 ! [V_k2_2,V_k1_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I33_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__int__code_I14_J,axiom,
% 22.27/22.23 ! [V_k2_2,V_k1_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_rel__simps_I15_J,axiom,
% 22.27/22.23 ! [V_l_2,V_k_2] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_card__UNIV__bool,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mult__Bit1,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_diff__bin__simps_I8_J,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__Bit1__Bit1,axiom,
% 22.27/22.23 ! [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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_double__number__of__Bit0,axiom,
% 22.27/22.23 ! [V_w,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_number__of1,axiom,
% 22.27/22.23 ! [V_n] :
% 22.27/22.23 ( 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)))
% 22.27/22.23 => ( 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))))
% 22.27/22.23 & 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)))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__int__nat__numerals_I3_J,axiom,
% 22.27/22.23 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)))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mult__2__right,axiom,
% 22.27/22.23 ! [V_z,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mult__2,axiom,
% 22.27/22.23 ! [V_z,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_one__add__one__is__two,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zero__eq__power2,axiom,
% 22.27/22.23 ! [V_a_2,T_b] :
% 22.27/22.23 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 22.27/22.23 => ( 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)
% 22.27/22.23 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zero__power2,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_semiring__norm_I115_J,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_numeral__2__eq__2,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__eq__square,axiom,
% 22.27/22.23 ! [V_a,T_a] :
% 22.27/22.23 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 22.27/22.23 ! [V_x,T_a] :
% 22.27/22.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.23 => 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)))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 22.27/22.23 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))))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__2__eq__Suc,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__2__eq__Suc_H,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_one__power2,axiom,
% 22.27/22.23 ! [T_a] :
% 22.27/22.23 ( class_Rings_Osemiring__1(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__minus,axiom,
% 22.27/22.23 ! [V_a,T_a] :
% 22.27/22.23 ( class_Rings_Oring__1(T_a)
% 22.27/22.23 => 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)))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__mult__2__right,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__mult__2,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power__even__eq,axiom,
% 22.27/22.23 ! [V_n,V_a,T_a] :
% 22.27/22.23 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.23 => 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)))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_transfer__nat__int__numerals_I3_J,axiom,
% 22.27/22.23 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)))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__1__add__1,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div2__Suc__Suc,axiom,
% 22.27/22.23 ! [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))))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_add__self__div__2,axiom,
% 22.27/22.23 ! [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 ).
% 22.27/22.23
% 22.27/22.23 fof(fact_half__gt__zero__iff,axiom,
% 22.27/22.23 ! [V_r_2,T_b] :
% 22.27/22.23 ( ( class_Fields_Olinordered__field__inverse__zero(T_b)
% 22.27/22.23 & class_Int_Onumber__ring(T_b) )
% 22.27/22.23 => ( 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))))))
% 22.27/22.23 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_r_2)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_half__gt__zero,axiom,
% 22.27/22.23 ! [V_r,T_a] :
% 22.27/22.23 ( ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 22.27/22.23 & class_Int_Onumber__ring(T_a) )
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r))
% 22.27/22.23 => 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)))))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zero__le__power2,axiom,
% 22.27/22.23 ! [V_a,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.23 => 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)))))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__le__imp__le,axiom,
% 22.27/22.23 ! [V_y,V_x,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.23 => ( 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))))))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__eq__imp__eq,axiom,
% 22.27/22.23 ! [V_y,V_x,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.23 => ( 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))))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.23 => V_x = V_y ) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zero__less__power2,axiom,
% 22.27/22.23 ! [V_a_2,T_b] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.23 => ( 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))))))
% 22.27/22.23 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__less__0,axiom,
% 22.27/22.23 ! [V_a,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.23 => ~ 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_sum__power2__eq__zero__iff,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.23 => ( 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)
% 22.27/22.23 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.23 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__eq__square__number__of,axiom,
% 22.27/22.23 ! [V_w,T_b] :
% 22.27/22.23 ( ( class_Groups_Omonoid__mult(T_b)
% 22.27/22.23 & class_Int_Onumber(T_b) )
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_less__2__cases,axiom,
% 22.27/22.23 ! [V_n] :
% 22.27/22.23 ( 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)))))
% 22.27/22.23 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.27/22.23 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_nat__2,axiom,
% 22.27/22.23 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))) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__eq__1__iff,axiom,
% 22.27/22.23 ! [V_a_2,T_b] :
% 22.27/22.23 ( class_Rings_Oring__1__no__zero__divisors(T_b)
% 22.27/22.23 => ( 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)
% 22.27/22.23 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_b)
% 22.27/22.23 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b)) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 22.27/22.23 ! [V_n,V_x,T_a] :
% 22.27/22.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power__minus__even,axiom,
% 22.27/22.23 ! [V_n,V_a,T_a] :
% 22.27/22.23 ( class_Rings_Oring__1(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__less__imp__less,axiom,
% 22.27/22.23 ! [V_y,V_x,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__semidom(T_a)
% 22.27/22.23 => ( 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))))))
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.27/22.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_sum__power2__le__zero__iff,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.23 => ( 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)))
% 22.27/22.23 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.23 & V_y_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_sum__power2__ge__zero,axiom,
% 22.27/22.23 ! [V_y,V_x,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.23 => 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))))))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_sum__power2__gt__zero__iff,axiom,
% 22.27/22.23 ! [V_y_2,V_x_2,T_b] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_b)
% 22.27/22.23 => ( 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)))))))
% 22.27/22.23 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_b)
% 22.27/22.23 | V_y_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_not__sum__power2__lt__zero,axiom,
% 22.27/22.23 ! [V_y,V_x,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.23 => ~ 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__sum,axiom,
% 22.27/22.23 ! [V_y,V_x,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zero__le__even__power_H,axiom,
% 22.27/22.23 ! [V_n,V_a,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.23 => 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)))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom,
% 22.27/22.23 ! [V_n,V_x,T_a] :
% 22.27/22.23 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power__odd__eq,axiom,
% 22.27/22.23 ! [V_n,V_a,T_a] :
% 22.27/22.23 ( class_Groups_Omonoid__mult(T_a)
% 22.27/22.23 => 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))))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power__minus1__even,axiom,
% 22.27/22.23 ! [V_n,T_a] :
% 22.27/22.23 ( class_Rings_Oring__1(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiv__number__of__Bit1,axiom,
% 22.27/22.23 ! [V_v,V_w] :
% 22.27/22.23 ( ( 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)))
% 22.27/22.23 => 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)) )
% 22.27/22.23 & ( ~ 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)))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_div__2__gt__zero,axiom,
% 22.27/22.23 ! [V_n] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n))
% 22.27/22.23 => 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)))))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_power2__diff,axiom,
% 22.27/22.23 ! [V_y,V_x,T_a] :
% 22.27/22.23 ( class_Int_Onumber__ring(T_a)
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_odd__0__le__power__imp__0__le,axiom,
% 22.27/22.23 ! [V_n,V_a,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.23 => ( 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)))))
% 22.27/22.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_odd__power__less__zero,axiom,
% 22.27/22.23 ! [V_n,V_a,T_a] :
% 22.27/22.23 ( class_Rings_Olinordered__idom(T_a)
% 22.27/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom,
% 22.27/22.23 ! [V_B_2,V_A_2] :
% 22.27/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.27/22.23 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom,
% 22.27/22.23 ! [V_B_2,V_A_2] :
% 22.27/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.27/22.23 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 22.27/22.23 => 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))) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zmod__number__of__Bit1,axiom,
% 22.27/22.23 ! [V_v,V_w] :
% 22.27/22.23 ( ( 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)))
% 22.27/22.23 => 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)) )
% 22.27/22.23 & ( ~ 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)))
% 22.27/22.23 => 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)) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_neg__zmod__mult__2,axiom,
% 22.27/22.23 ! [V_b,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.27/22.23 => 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)) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_pos__zmod__mult__2,axiom,
% 22.27/22.23 ! [V_b,V_a] :
% 22.27/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.27/22.23 => 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))) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zmod__simps_I3_J,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zmod__zmult1__eq,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiff__zmod__left,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zdiff__zmod__right,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zminus__zmod,axiom,
% 22.27/22.23 ! [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) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zmod__zminus__zminus,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zmod__zminus2,axiom,
% 22.27/22.23 ! [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)) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mod__diff__cong,axiom,
% 22.27/22.23 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 22.27/22.23 ( class_Divides_Oring__div(T_a)
% 22.27/22.23 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 22.27/22.23 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 22.27/22.23 => 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) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mod__diff__eq,axiom,
% 22.27/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.23 ( class_Divides_Oring__div(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mod__diff__left__eq,axiom,
% 22.27/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.23 ( class_Divides_Oring__div(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mod__diff__right__eq,axiom,
% 22.27/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.23 ( class_Divides_Oring__div(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_mod__add__cong,axiom,
% 22.27/22.23 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 22.27/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.23 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 22.27/22.23 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 22.27/22.23 => 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) ) ) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zmod__simps_I1_J,axiom,
% 22.27/22.23 ! [V_b,V_c,V_a,T_a] :
% 22.27/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.27/22.23 => 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) ) ).
% 22.27/22.23
% 22.27/22.23 fof(fact_zmod__simps_I2_J,axiom,
% 22.27/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.27/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__add__eq,axiom,
% 22.40/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__add__left__eq,axiom,
% 22.40/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__add__right__eq,axiom,
% 22.40/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__add__self1,axiom,
% 22.40/22.23 ! [V_a,V_b,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__add__self2,axiom,
% 22.40/22.23 ! [V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__minus__eq,axiom,
% 22.40/22.23 ! [V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Oring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__minus__cong,axiom,
% 22.40/22.23 ! [V_a_H,V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Oring__div(T_a)
% 22.40/22.23 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b)
% 22.40/22.23 => 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) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__self,axiom,
% 22.40/22.23 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__self,axiom,
% 22.40/22.23 ! [V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__by__0,axiom,
% 22.40/22.23 ! [V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__zero,axiom,
% 22.40/22.23 ! [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) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__0,axiom,
% 22.40/22.23 ! [V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mod__trivial,axiom,
% 22.40/22.23 ! [V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__cong,axiom,
% 22.40/22.23 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c)
% 22.40/22.23 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c)
% 22.40/22.23 => 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) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__simps_I4_J,axiom,
% 22.40/22.23 ! [V_b,V_c,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__mult2,axiom,
% 22.40/22.23 ! [V_b,V_c,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__mult1,axiom,
% 22.40/22.23 ! [V_b,V_a,V_c,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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)) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__eq,axiom,
% 22.40/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__left__eq,axiom,
% 22.40/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__right__eq,axiom,
% 22.40/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zpower__zmod,axiom,
% 22.40/22.23 ! [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) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__self1__is__0,axiom,
% 22.40/22.23 ! [V_a,V_b,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__self2__is__0,axiom,
% 22.40/22.23 ! [V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__self1,axiom,
% 22.40/22.23 ! [V_b,V_c,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__self2,axiom,
% 22.40/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__by__1,axiom,
% 22.40/22.23 ! [V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__div__trivial,axiom,
% 22.40/22.23 ! [V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 22.40/22.23 ! [V_y,V_x] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.40/22.23 => 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))) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__le__nonneg__dividend,axiom,
% 22.40/22.23 ! [V_k,V_m] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m))
% 22.40/22.23 => 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)) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_pos__mod__bound,axiom,
% 22.40/22.23 ! [V_a,V_b] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.23 => 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)) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_neg__mod__bound,axiom,
% 22.40/22.23 ! [V_a,V_b] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 => 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))) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__eq__0__iff,axiom,
% 22.40/22.23 ! [V_d_2,V_m_2] :
% 22.40/22.23 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__zminus1__not__zero,axiom,
% 22.40/22.23 ! [V_l,V_k] :
% 22.40/22.23 ( 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)
% 22.40/22.23 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__zminus2__not__zero,axiom,
% 22.40/22.23 ! [V_l,V_k] :
% 22.40/22.23 ( 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)
% 22.40/22.23 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__zdiv__trivial,axiom,
% 22.40/22.23 ! [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) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_DIVISION__BY__ZERO,axiom,
% 22.40/22.23 ! [V_a] :
% 22.40/22.23 ( 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)
% 22.40/22.23 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zdiv__zadd1__eq,axiom,
% 22.40/22.23 ! [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)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom,
% 22.40/22.23 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom,
% 22.40/22.23 ! [V_B_2,V_A_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.23 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 22.40/22.23 => 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)) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom,
% 22.40/22.23 ! [V_B_2,V_A_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.23 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 22.40/22.23 => 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)) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_nat__set__def,axiom,
% 22.40/22.23 ! [V_S_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_S_2)
% 22.40/22.23 <=> ! [B_x] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2))
% 22.40/22.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_semiring__div__class_Omod__div__equality_H,axiom,
% 22.40/22.23 ! [V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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 ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__div__equality2,axiom,
% 22.40/22.23 ! [V_a,V_b,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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 ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__div__equality,axiom,
% 22.40/22.23 ! [V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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 ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_div__mod__equality2,axiom,
% 22.40/22.23 ! [V_c,V_a,V_b,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_div__mod__equality,axiom,
% 22.40/22.23 ! [V_c,V_b,V_a,T_a] :
% 22.40/22.23 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_pos__mod__sign,axiom,
% 22.40/22.23 ! [V_a,V_b] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.23 => 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))) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_pos__mod__conj,axiom,
% 22.40/22.23 ! [V_a,V_b] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.23 => ( 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)))
% 22.40/22.23 & 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)) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__pos__pos__trivial,axiom,
% 22.40/22.23 ! [V_b,V_a] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 22.40/22.23 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_neg__mod__sign,axiom,
% 22.40/22.23 ! [V_a,V_b] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 => 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))) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_neg__mod__conj,axiom,
% 22.40/22.23 ! [V_a,V_b] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 => ( 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)))
% 22.40/22.23 & 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))) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__neg__neg__trivial,axiom,
% 22.40/22.23 ! [V_b,V_a] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a))
% 22.40/22.23 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom,
% 22.40/22.23 ! [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)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_transfer__int__nat__set__relations_I4_J,axiom,
% 22.40/22.23 ! [V_B_2,V_A_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.23 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.40/22.23 <=> 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))) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_transfer__int__nat__set__relations_I3_J,axiom,
% 22.40/22.23 ! [V_B_2,V_A_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.23 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 22.40/22.23 => ( V_A_2 = V_B_2
% 22.40/22.23 <=> 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) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__zminus2__eq__if,axiom,
% 22.40/22.23 ! [V_b,V_a] :
% 22.40/22.23 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => 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) )
% 22.40/22.23 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => 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) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__zminus1__eq__if,axiom,
% 22.40/22.23 ! [V_b,V_a] :
% 22.40/22.23 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => 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) )
% 22.40/22.23 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => 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)) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__zdiv__equality,axiom,
% 22.40/22.23 ! [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)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zdiv__zmult1__eq,axiom,
% 22.40/22.23 ! [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)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zdiv__zmod__equality,axiom,
% 22.40/22.23 ! [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) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zdiv__zmod__equality2,axiom,
% 22.40/22.23 ! [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) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmult__div__cancel,axiom,
% 22.40/22.23 ! [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)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__zdiv__equality_H,axiom,
% 22.40/22.23 ! [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)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__pos__neg__trivial,axiom,
% 22.40/22.23 ! [V_b,V_a] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.23 => ( 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)))
% 22.40/22.23 => 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) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
% 22.40/22.23 ! [V_y_2,V_x_2] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
% 22.40/22.23 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom,
% 22.40/22.23 ! [V_x_2,V_A_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 22.40/22.23 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_split__zmod,axiom,
% 22.40/22.23 ! [V_k_2,V_n_2,V_P_2] :
% 22.40/22.23 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
% 22.40/22.23 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 22.40/22.23 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 22.40/22.23 => ! [B_i,B_j] :
% 22.40/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 22.40/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 22.40/22.23 & 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) )
% 22.40/22.23 => hBOOL(hAPP(V_P_2,B_j)) ) )
% 22.40/22.23 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 => ! [B_i,B_j] :
% 22.40/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 22.40/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 & 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) )
% 22.40/22.23 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmult2__lemma__aux3,axiom,
% 22.40/22.23 ! [V_q,V_b,V_r,V_c] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 22.40/22.23 => 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))) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmult2__lemma__aux4,axiom,
% 22.40/22.23 ! [V_q,V_b,V_r,V_c] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
% 22.40/22.23 => 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))) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmult2__lemma__aux1,axiom,
% 22.40/22.23 ! [V_q,V_r,V_b,V_c] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 => 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))) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmult2__lemma__aux2,axiom,
% 22.40/22.23 ! [V_q,V_r,V_b,V_c] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 => 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))) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_divmod__int__rel__mod__eq,axiom,
% 22.40/22.23 ! [V_y,V_q_1,V_b_1,V_a_1] :
% 22.40/22.23 ( 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)
% 22.40/22.23 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.40/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) )
% 22.40/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1))
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y))
% 22.40/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 22.40/22.23 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__number__of__Bit0,axiom,
% 22.40/22.23 ! [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))) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zmod__zmult2__eq,axiom,
% 22.40/22.23 ! [V_b,V_a,V_c] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 22.40/22.23 => 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)) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zdiv__zminus1__eq__if,axiom,
% 22.40/22.23 ! [V_a,V_b] :
% 22.40/22.23 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => 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)) )
% 22.40/22.23 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => 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)) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_zdiv__zminus2__eq__if,axiom,
% 22.40/22.23 ! [V_a,V_b] :
% 22.40/22.23 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => 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)) )
% 22.40/22.23 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.23 => 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)) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_transfer__nat__int__set__return__embed,axiom,
% 22.40/22.23 ! [V_A_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.23 => 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 ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_split__pos__lemma,axiom,
% 22.40/22.23 ! [V_n_2,V_P_2,V_k_2] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))
% 22.40/22.23 => ( 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)))
% 22.40/22.23 <=> ! [B_i,B_j] :
% 22.40/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j))
% 22.40/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2))
% 22.40/22.23 & 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) )
% 22.40/22.23 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_split__neg__lemma,axiom,
% 22.40/22.23 ! [V_n_2,V_P_2,V_k_2] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 => ( 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)))
% 22.40/22.23 <=> ! [B_i,B_j] :
% 22.40/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j))
% 22.40/22.23 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.23 & 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) )
% 22.40/22.23 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_transfer__int__nat__set__relations_I1_J,axiom,
% 22.40/22.23 ! [V_A_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.23 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2))
% 22.40/22.23 <=> 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))) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom,
% 22.40/22.23 ! [V_A_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.23 => 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)) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
% 22.40/22.23 ! [V_B_2,V_A_2] :
% 22.40/22.23 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.23 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 22.40/22.23 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.40/22.23 <=> 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))) ) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_z3mod__def,axiom,
% 22.40/22.23 ! [V_k,V_l] :
% 22.40/22.23 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 22.40/22.23 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) )
% 22.40/22.23 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 22.40/22.23 => 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)) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_power__m1__odd,axiom,
% 22.40/22.23 ! [V_n,T_a] :
% 22.40/22.23 ( class_Int_Onumber__ring(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_power__m1__even,axiom,
% 22.40/22.23 ! [V_n,T_a] :
% 22.40/22.23 ( class_Int_Onumber__ring(T_a)
% 22.40/22.23 => 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) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_one__mod__nat__number__of,axiom,
% 22.40/22.23 ! [V_v_H] :
% 22.40/22.23 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 22.40/22.23 => 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)) )
% 22.40/22.23 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 22.40/22.23 => 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))) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__less__eq__dividend,axiom,
% 22.40/22.23 ! [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)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_rel__simps_I7_J,axiom,
% 22.40/22.23 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__less,axiom,
% 22.40/22.23 ! [V_n,V_m] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.40/22.23 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__Suc__eq__Suc__mod,axiom,
% 22.40/22.23 ! [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) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__distrib,axiom,
% 22.40/22.23 ! [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)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__mult__distrib2,axiom,
% 22.40/22.23 ! [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)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_Bit1__Min,axiom,
% 22.40/22.23 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ).
% 22.40/22.23
% 22.40/22.23 fof(fact_rel__simps_I43_J,axiom,
% 22.40/22.23 ! [V_l_2] :
% 22.40/22.23 ( c_Int_OMin = c_Int_OBit1(V_l_2)
% 22.40/22.23 <=> c_Int_OMin = V_l_2 ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_rel__simps_I47_J,axiom,
% 22.40/22.23 ! [V_k_2] :
% 22.40/22.23 ( c_Int_OBit1(V_k_2) = c_Int_OMin
% 22.40/22.23 <=> V_k_2 = c_Int_OMin ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_rel__simps_I40_J,axiom,
% 22.40/22.23 c_Int_OMin != c_Int_OPls ).
% 22.40/22.23
% 22.40/22.23 fof(fact_rel__simps_I37_J,axiom,
% 22.40/22.23 c_Int_OPls != c_Int_OMin ).
% 22.40/22.23
% 22.40/22.23 fof(fact_rel__simps_I24_J,axiom,
% 22.40/22.23 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_rel__simps_I42_J,axiom,
% 22.40/22.23 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_rel__simps_I45_J,axiom,
% 22.40/22.23 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__Suc,axiom,
% 22.40/22.23 ! [V_n,V_m] :
% 22.40/22.23 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
% 22.40/22.23 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.40/22.23 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
% 22.40/22.23 => 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)) ) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__1,axiom,
% 22.40/22.23 ! [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) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__less__divisor,axiom,
% 22.40/22.23 ! [V_m,V_n] :
% 22.40/22.23 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.40/22.23 => 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)) ) ).
% 22.40/22.23
% 22.40/22.23 fof(fact_mod__eq__0__iff,axiom,
% 22.40/22.23 ! [V_d_2,V_m_2] :
% 22.40/22.24 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.24 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__geq,axiom,
% 22.40/22.24 ! [V_n,V_m] :
% 22.40/22.24 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__if,axiom,
% 22.40/22.24 ! [V_n,V_m] :
% 22.40/22.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.40/22.24 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__mult__self3,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_le__mod__geq,axiom,
% 22.40/22.24 ! [V_m,V_n] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_bin__less__0__simps_I2_J,axiom,
% 22.40/22.24 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I23_J,axiom,
% 22.40/22.24 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I20_J,axiom,
% 22.40/22.24 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I26_J,axiom,
% 22.40/22.24 ! [V_k_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I30_J,axiom,
% 22.40/22.24 ! [V_k_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I3_J,axiom,
% 22.40/22.24 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I6_J,axiom,
% 22.40/22.24 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I13_J,axiom,
% 22.40/22.24 ! [V_k_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I9_J,axiom,
% 22.40/22.24 ! [V_k_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I28_J,axiom,
% 22.40/22.24 ! [V_k_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I8_J,axiom,
% 22.40/22.24 ! [V_k_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zmod__int,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_eq__number__of__Pls__Min,axiom,
% 22.40/22.24 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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_div__add1__eq,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Int_OMin__def,axiom,
% 22.40/22.24 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mult__Min,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_neg__number__of__Min,axiom,
% 22.40/22.24 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pred__Pls,axiom,
% 22.40/22.24 c_Int_Opred(c_Int_OPls) = c_Int_OMin ).
% 22.40/22.24
% 22.40/22.24 fof(fact_add__Min__right,axiom,
% 22.40/22.24 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_add__Min,axiom,
% 22.40/22.24 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pred__Min,axiom,
% 22.40/22.24 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nonzero__number__of__Min,axiom,
% 22.40/22.24 ! [T_a] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_succ__Min,axiom,
% 22.40/22.24 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ).
% 22.40/22.24
% 22.40/22.24 fof(fact_diff__bin__simps_I2_J,axiom,
% 22.40/22.24 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__le__divisor,axiom,
% 22.40/22.24 ! [V_m,V_n] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__mult__self4,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mult__minus1,axiom,
% 22.40/22.24 ! [V_z,T_a] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mult__minus1__right,axiom,
% 22.40/22.24 ! [V_z,T_a] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_number__of__Min,axiom,
% 22.40/22.24 ! [T_a] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_arith__simps_I31_J,axiom,
% 22.40/22.24 ! [T_a] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_divide__minus1,axiom,
% 22.40/22.24 ! [V_x,T_a] :
% 22.40/22.24 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 22.40/22.24 & class_Int_Onumber__ring(T_a) )
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I11_J,axiom,
% 22.40/22.24 ! [V_k_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rel__simps_I25_J,axiom,
% 22.40/22.24 ! [V_k_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__mult2__eq,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_div__mult1__eq,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_div__mod__equality_H,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mult__div__cancel,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Divides_Omod__div__equality_H,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zmod__minus1__right,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_diff__bin__simps_I4_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_minus__Min,axiom,
% 22.40/22.24 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zmult__eq__1__iff,axiom,
% 22.40/22.24 ! [V_n_2,V_m_2] :
% 22.40/22.24 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 22.40/22.24 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 22.40/22.24 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
% 22.40/22.24 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
% 22.40/22.24 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pos__zmult__eq__1__iff__lemma,axiom,
% 22.40/22.24 ! [V_n,V_m] :
% 22.40/22.24 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 22.40/22.24 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint)
% 22.40/22.24 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_diff__bin__simps_I6_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_diff__bin__simps_I5_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zdiv__minus1__right,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_split__mod,axiom,
% 22.40/22.24 ! [V_k_2,V_n_2,V_P_2] :
% 22.40/22.24 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
% 22.40/22.24 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.24 => hBOOL(hAPP(V_P_2,V_n_2)) )
% 22.40/22.24 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.24 => ! [B_i,B_j] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2))
% 22.40/22.24 => ( 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)
% 22.40/22.24 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__lemma,axiom,
% 22.40/22.24 ! [V_q,V_b,V_r,V_c] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b))
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Suc__times__mod__eq,axiom,
% 22.40/22.24 ! [V_m,V_k] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__mod__distrib,axiom,
% 22.40/22.24 ! [V_y,V_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom,
% 22.40/22.24 ! [V_y,V_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_minus1__divide,axiom,
% 22.40/22.24 ! [V_x,T_a] :
% 22.40/22.24 ( ( class_Fields_Ofield__inverse__zero(T_a)
% 22.40/22.24 & class_Int_Onumber__ring(T_a) )
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_div__eq__minus1,axiom,
% 22.40/22.24 ! [V_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__Suc__eq__mod__add3,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Suc__mod__eq__add3__mod,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod2__Suc__Suc,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__nat__number__of,axiom,
% 22.40/22.24 ! [V_v_H,V_v] :
% 22.40/22.24 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)))
% 22.40/22.24 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H)))
% 22.40/22.24 => 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))) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_div__pos__neg__trivial,axiom,
% 22.40/22.24 ! [V_b,V_a] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.24 => ( 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)))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zmod__minus1,axiom,
% 22.40/22.24 ! [V_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod2__gr__0,axiom,
% 22.40/22.24 ! [V_m_2] :
% 22.40/22.24 ( 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))))))
% 22.40/22.24 <=> 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_int__of__code,axiom,
% 22.40/22.24 ! [V_k] :
% 22.40/22.24 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.24 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 22.40/22.24 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.24 => ( ( 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)
% 22.40/22.24 => 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)))))) )
% 22.40/22.24 & ( 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)
% 22.40/22.24 => 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)) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
% 22.40/22.24 ! [V_A_2,V_x_2] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 22.40/22.24 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 22.40/22.24 <=> 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))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__bounded,axiom,
% 22.40/22.24 ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
% 22.40/22.24 & class_Rings_Osemiring__1(T_c) )
% 22.40/22.24 => ( ! [B_i] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom,
% 22.40/22.24 ! [V_n_2,V_m_2] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_m_2)
% 22.40/22.24 => ( c_Nat__Transfer_Ois__nat(V_n_2)
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral__zero__minus__one,axiom,
% 22.40/22.24 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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom,
% 22.40/22.24 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom,
% 22.40/22.24 ! [V_y,V_x] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_x)
% 22.40/22.24 => ( c_Nat__Transfer_Ois__nat(V_y)
% 22.40/22.24 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom,
% 22.40/22.24 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom,
% 22.40/22.24 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom,
% 22.40/22.24 ! [V_y,V_x] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_x)
% 22.40/22.24 => ( c_Nat__Transfer_Ois__nat(V_y)
% 22.40/22.24 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom,
% 22.40/22.24 ! [V_y,V_x] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_x)
% 22.40/22.24 => ( c_Nat__Transfer_Ois__nat(V_y)
% 22.40/22.24 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom,
% 22.40/22.24 ! [V_y,V_x] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_x)
% 22.40/22.24 => ( c_Nat__Transfer_Ois__nat(V_y)
% 22.40/22.24 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom,
% 22.40/22.24 ! [V_n,V_x] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_x)
% 22.40/22.24 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom,
% 22.40/22.24 ! [V_y,V_x] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_x)
% 22.40/22.24 => ( c_Nat__Transfer_Ois__nat(V_y)
% 22.40/22.24 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_is__nat__def,axiom,
% 22.40/22.24 ! [V_x_2] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2] :
% 22.40/22.24 ( c_Nat__Transfer_Ois__nat(V_x_2)
% 22.40/22.24 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom,
% 22.40/22.24 ! [V_x_2,V_A_2] :
% 22.40/22.24 ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
% 22.40/22.24 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zero__code__numeral__code,axiom,
% 22.40/22.24 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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom,
% 22.40/22.24 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom,
% 22.40/22.24 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_one__code__numeral__code,axiom,
% 22.40/22.24 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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral_Osize_I1_J,axiom,
% 22.40/22.24 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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__of__nat,axiom,
% 22.40/22.24 ! [V_k,T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => 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)))) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => 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)) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__of__aux__code,axiom,
% 22.40/22.24 ! [V_n,V_i] :
% 22.40/22.24 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.24 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n )
% 22.40/22.24 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_negD,axiom,
% 22.40/22.24 ! [V_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => ? [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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_number__of__eq,axiom,
% 22.40/22.24 ! [V_k,T_a] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_int__number__of__def,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__int__eq,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__eq__iff,axiom,
% 22.40/22.24 ! [V_z_2,V_w_2,T_b] :
% 22.40/22.24 ( class_Int_Oring__char__0(T_b)
% 22.40/22.24 => ( 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)
% 22.40/22.24 <=> V_w_2 = V_z_2 ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__eq__0__iff,axiom,
% 22.40/22.24 ! [V_z_2,T_b] :
% 22.40/22.24 ( class_Int_Oring__char__0(T_b)
% 22.40/22.24 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.40/22.24 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__0__eq__iff,axiom,
% 22.40/22.24 ! [V_z_2,T_b] :
% 22.40/22.24 ( class_Int_Oring__char__0(T_b)
% 22.40/22.24 => ( c_Groups_Ozero__class_Ozero(T_b) = hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_z_2)
% 22.40/22.24 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__0,axiom,
% 22.40/22.24 ! [T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__le__iff,axiom,
% 22.40/22.24 ! [V_z_2,V_w_2,T_b] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_b)
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__less__iff,axiom,
% 22.40/22.24 ! [V_z_2,V_w_2,T_b] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_b)
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__add,axiom,
% 22.40/22.24 ! [V_z,V_w,T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__number__of__eq,axiom,
% 22.40/22.24 ! [V_v,T_a] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__mult,axiom,
% 22.40/22.24 ! [V_z,V_w,T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__1,axiom,
% 22.40/22.24 ! [T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__diff,axiom,
% 22.40/22.24 ! [V_z,V_w,T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__of__nat__eq,axiom,
% 22.40/22.24 ! [V_n,T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__minus,axiom,
% 22.40/22.24 ! [V_z,T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Ints__of__int,axiom,
% 22.40/22.24 ! [V_z_2,T_b] :
% 22.40/22.24 ( class_Rings_Oring__1(T_b)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__power,axiom,
% 22.40/22.24 ! [V_n,V_z,T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__m1,axiom,
% 22.40/22.24 ! [T_a] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__0__le__iff,axiom,
% 22.40/22.24 ! [V_z_2,T_b] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_b)
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__le__0__iff,axiom,
% 22.40/22.24 ! [V_z_2,T_b] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_b)
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__less__0__iff,axiom,
% 22.40/22.24 ! [V_z_2,T_b] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_b)
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__0__less__iff,axiom,
% 22.40/22.24 ! [V_z_2,T_b] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_b)
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__nat__nat,axiom,
% 22.40/22.24 ! [V_z,T_a] :
% 22.40/22.24 ( class_Rings_Oring__1(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral_Osize_I2_J,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral_Osize_I3_J,axiom,
% 22.40/22.24 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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zero__less__imp__eq__int,axiom,
% 22.40/22.24 ! [V_k] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 22.40/22.24 => ? [B_n] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 22.40/22.24 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_decr__lemma,axiom,
% 22.40/22.24 ! [V_z,V_x,V_d] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__minus__commute,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__one,axiom,
% 22.40/22.24 ! [T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__of__nat,axiom,
% 22.40/22.24 ! [V_n,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__int__eq,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__le__D1,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__ge__self,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__divide,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__mult__self,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__mult,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__idempotent,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_power__abs,axiom,
% 22.40/22.24 ! [V_n,V_a,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__minus__cancel,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__add__abs,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__eq__0,axiom,
% 22.40/22.24 ! [V_a_2,T_b] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 22.40/22.24 => ( hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2) = c_Groups_Ozero__class_Ozero(T_b)
% 22.40/22.24 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__zero,axiom,
% 22.40/22.24 ! [T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral_Oinject,axiom,
% 22.40/22.24 ! [V_code__numeral_H_2,V_code__numeral_2] :
% 22.40/22.24 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2)
% 22.40/22.24 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__ge__zero,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__le__zero__iff,axiom,
% 22.40/22.24 ! [V_a_2,T_b] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__of__nonneg,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__of__pos,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zero__less__abs__iff,axiom,
% 22.40/22.24 ! [V_a_2,T_b] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__not__less__zero,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => ~ 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__triangle__ineq,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__mult__less,axiom,
% 22.40/22.24 ! [V_d,V_b,V_c,V_a,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
% 22.40/22.24 => 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))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__triangle__ineq3,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__triangle__ineq2,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__triangle__ineq2__sym,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__le__D2,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b))
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__leI,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b))
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__le__iff,axiom,
% 22.40/22.24 ! [V_b_2,V_a_2,T_b] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 22.40/22.24 => ( 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))
% 22.40/22.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2))
% 22.40/22.24 & 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)) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__ge__minus__self,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__less__iff,axiom,
% 22.40/22.24 ! [V_b_2,V_a_2,T_b] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_b)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)),V_b_2))
% 22.40/22.24 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
% 22.40/22.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_a_2)),V_b_2)) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nonzero__abs__divide,axiom,
% 22.40/22.24 ! [V_a,V_b,T_a] :
% 22.40/22.24 ( class_Fields_Olinordered__field(T_a)
% 22.40/22.24 => ( V_b != c_Groups_Ozero__class_Ozero(T_a)
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__power__minus,axiom,
% 22.40/22.24 ! [V_n,V_a,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__zmult__eq__1,axiom,
% 22.40/22.24 ! [V_n,V_m] :
% 22.40/22.24 ( 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)
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__sgn,axiom,
% 22.40/22.24 ! [V_k,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mult__sgn__abs,axiom,
% 22.40/22.24 ! [V_x,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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 ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral_Osimps_I2_J,axiom,
% 22.40/22.24 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral_Osimps_I3_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__mult__pos,axiom,
% 22.40/22.24 ! [V_y,V_x,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__eq__mult,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Rings_Oordered__ring__abs(T_a)
% 22.40/22.24 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) )
% 22.40/22.24 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) )
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__triangle__ineq4,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__diff__triangle__ineq,axiom,
% 22.40/22.24 ! [V_d,V_c,V_b,V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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))))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__of__nonpos,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__minus__le__zero,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__of__neg,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__if,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Groups_Oabs__if(T_a)
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)))
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zero__le__power__abs,axiom,
% 22.40/22.24 ! [V_n,V_a,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__div__pos,axiom,
% 22.40/22.24 ! [V_x,V_y,T_a] :
% 22.40/22.24 ( class_Fields_Olinordered__field__inverse__zero(T_a)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__minus__one,axiom,
% 22.40/22.24 ! [T_a] :
% 22.40/22.24 ( ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 & class_Rings_Olinordered__idom(T_a) )
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zabs__less__one__iff,axiom,
% 22.40/22.24 ! [V_z_2] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zabs__def,axiom,
% 22.40/22.24 ! [V_i] :
% 22.40/22.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__abs__mult__distrib,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral_Osize_I4_J,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zero__le__zpower__abs,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__number__of,axiom,
% 22.40/22.24 ! [V_x,T_a] :
% 22.40/22.24 ( ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 & class_Rings_Olinordered__idom(T_a) )
% 22.40/22.24 => ( ( 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)))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( ~ 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)))
% 22.40/22.24 => 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) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__power__minus__one,axiom,
% 22.40/22.24 ! [V_n,T_a] :
% 22.40/22.24 ( ( class_Int_Onumber__ring(T_a)
% 22.40/22.24 & class_Rings_Olinordered__idom(T_a) )
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zero__less__zpower__abs__iff,axiom,
% 22.40/22.24 ! [V_n_2,V_x_2] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Suc__code__numeral__minus__one,axiom,
% 22.40/22.24 ! [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 ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__power2,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_power2__abs,axiom,
% 22.40/22.24 ! [V_a,T_a] :
% 22.40/22.24 ( class_Rings_Olinordered__idom(T_a)
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_incr__lemma,axiom,
% 22.40/22.24 ! [V_x,V_z,V_d] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d))
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nitpick_Oint__lcm__def,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral_Osimps_I5_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat0__intermed__int__val,axiom,
% 22.40/22.24 ! [V_k_2,V_f_2,V_n_2] :
% 22.40/22.24 ( ! [B_i] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 22.40/22.24 => 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))) )
% 22.40/22.24 => ( 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))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 22.40/22.24 => ? [B_i] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 22.40/22.24 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_int__val__lemma,axiom,
% 22.40/22.24 ! [V_k_2,V_f_2,V_n_2] :
% 22.40/22.24 ( ! [B_i] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 22.40/22.24 => 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))) )
% 22.40/22.24 => ( 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))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 22.40/22.24 => ? [B_i] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 22.40/22.24 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_code__numeral_Osimps_I4_J,axiom,
% 22.40/22.24 ! [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 ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nitpick_Onat__lcm__def,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__mod__eq__lemma,axiom,
% 22.40/22.24 ! [V_y,V_n,V_x] :
% 22.40/22.24 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x))
% 22.40/22.24 => ? [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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__induct__0,axiom,
% 22.40/22.24 ! [V_i_2,V_P_2,V_p_2] :
% 22.40/22.24 ( ! [B_i] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2))
% 22.40/22.24 => ( hBOOL(hAPP(V_P_2,B_i))
% 22.40/22.24 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
% 22.40/22.24 => ( hBOOL(hAPP(V_P_2,V_i_2))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
% 22.40/22.24 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__intermed__int__val,axiom,
% 22.40/22.24 ! [V_k_2,V_f_2,V_n_2,V_m_2] :
% 22.40/22.24 ( ! [B_i] :
% 22.40/22.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 22.40/22.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) )
% 22.40/22.24 => 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))) )
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2)))
% 22.40/22.24 => ? [B_i] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i))
% 22.40/22.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2))
% 22.40/22.24 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__gcd_Osimps,axiom,
% 22.40/22.24 ! [V_x,V_y] :
% 22.40/22.24 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.24 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x )
% 22.40/22.24 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nitpick_Oint__gcd__def,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_log_Osimps,axiom,
% 22.40/22.24 ! [V_i,V_b] :
% 22.40/22.24 ( ( ( 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)))
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 22.40/22.24 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 22.40/22.24 & ( ~ ( 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)))
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) )
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mod__div__decomp,axiom,
% 22.40/22.24 ! [V_b,V_a,T_a] :
% 22.40/22.24 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_field__le__epsilon,axiom,
% 22.40/22.24 ! [V_y,V_x,T_a] :
% 22.40/22.24 ( class_Fields_Olinordered__field(T_a)
% 22.40/22.24 => ( ! [B_e] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e))
% 22.40/22.24 => 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))) )
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_minus__shift__def,axiom,
% 22.40/22.24 ! [V_r,V_l,V_k] :
% 22.40/22.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inc__shift__def,axiom,
% 22.40/22.24 ! [V_k,V_v] :
% 22.40/22.24 ( ( V_v = V_k
% 22.40/22.24 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) )
% 22.40/22.24 & ( V_v != V_k
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_subtract__code__numeral__def,axiom,
% 22.40/22.24 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_minus__code__numeral__code,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pair__box_Osize_I1_J,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_arith__series__int,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_negDivAlg__eqn__1__number__of,axiom,
% 22.40/22.24 ! [V_w] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 => ( ( 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))))
% 22.40/22.24 => 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))) )
% 22.40/22.24 & ( ~ 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))))
% 22.40/22.24 => 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)))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fold__image__reindex,axiom,
% 22.40/22.24 ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
% 22.40/22.24 ( class_Groups_Oab__semigroup__mult(T_d)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
% 22.40/22.24 => 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) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUP2__I,axiom,
% 22.40/22.24 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF1__D,axiom,
% 22.40/22.24 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF1__E,axiom,
% 22.40/22.24 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 22.40/22.24 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF2__D,axiom,
% 22.40/22.24 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF2__E,axiom,
% 22.40/22.24 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
% 22.40/22.24 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__E,axiom,
% 22.40/22.24 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
% 22.40/22.24 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__D,axiom,
% 22.40/22.24 ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_finite__INT,axiom,
% 22.40/22.24 ! [V_A_2,T_c,V_I_2,T_b] :
% 22.40/22.24 ( ? [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 22.40/22.24 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__I,axiom,
% 22.40/22.24 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUP1__I,axiom,
% 22.40/22.24 ! [T_c,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__abs,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__abs__ge__zero,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__setprod,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 22.40/22.24 & class_Rings_Oring__1(T_b) )
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__setsum,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Rings_Oring__1(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__0,axiom,
% 22.40/22.24 ! [V_A_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__nat__setsum,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Rings_Osemiring__1(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__shift__bounds__Suc__ivl,axiom,
% 22.40/22.24 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_range__composition,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inj__fun,axiom,
% 22.40/22.24 ! [T_d,V_f_2,T_c,T_b] :
% 22.40/22.24 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF__INT__eq,axiom,
% 22.40/22.24 ! [V_x_2,V_r_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF__INT__eq2,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUP__UN__eq2,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_r_2,T_d,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__atLeast__UNIV,axiom,
% 22.40/22.24 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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__lessThan__UNIV,axiom,
% 22.40/22.24 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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__empty,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__constant,axiom,
% 22.40/22.24 ! [V_c_2,T_c,T_b,V_A_2] :
% 22.40/22.24 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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 ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INTER__UNIV__conv_I2_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INTER__UNIV__conv_I1_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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)
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__atMost__UNIV,axiom,
% 22.40/22.24 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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom,
% 22.40/22.24 ! [V_x_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inj__singleton,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__insert__distrib,axiom,
% 22.40/22.24 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__constant__conv,axiom,
% 22.40/22.24 ! [V_c_2,T_c,T_b,V_A_2] :
% 22.40/22.24 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUP__UN__eq,axiom,
% 22.40/22.24 ! [V_x_2,V_r_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_finite__range__imageI,axiom,
% 22.40/22.24 ! [V_f_2,T_d,V_g_2,T_c,T_b] :
% 22.40/22.24 ( 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)))))
% 22.40/22.24 => 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))))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__absorb,axiom,
% 22.40/22.24 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I2_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I1_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I1_J,axiom,
% 22.40/22.24 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__singleton,axiom,
% 22.40/22.24 ! [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 ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I1_J,axiom,
% 22.40/22.24 ! [V_B_2,V_a_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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))) )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod_Odistrib,axiom,
% 22.40/22.24 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I2_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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 )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I3_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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 )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I2_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I3_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__insert,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I5_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I5_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_bot__fun__def,axiom,
% 22.40/22.24 ! [V_x_2,T_c,T_b] :
% 22.40/22.24 ( class_Orderings_Obot(T_b)
% 22.40/22.24 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_c,T_b)),V_x_2) = c_Orderings_Obot__class_Obot(T_b) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUP__const,axiom,
% 22.40/22.24 ! [V_M_2,T_b,V_A_2,T_c] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.40/22.24 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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 ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UNION__empty__conv_I1_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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)
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__empty2,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__constant,axiom,
% 22.40/22.24 ! [V_c_2,T_c,T_b,V_A_2] :
% 22.40/22.24 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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 ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UNION__empty__conv_I2_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF__const,axiom,
% 22.40/22.24 ! [V_M_2,T_b,V_A_2,T_c] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.40/22.24 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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 ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pair__box_Oinject,axiom,
% 22.40/22.24 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.24 ( 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)
% 22.40/22.24 <=> ( V_a_2 = V_a_H_2
% 22.40/22.24 & V_b_2 = V_b_H_2 ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Compl__INT,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Compl__UN,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fun__Compl__def,axiom,
% 22.40/22.24 ! [V_x_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Ouminus(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__negf,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Oab__group__add(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fold__image__def,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__divide__distrib,axiom,
% 22.40/22.24 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Fields_Ofield(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I8_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I8_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__commute,axiom,
% 22.40/22.24 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUPR__apply,axiom,
% 22.40/22.24 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_comp__cong,axiom,
% 22.40/22.24 ! [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] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_o__eq__dest__lhs,axiom,
% 22.40/22.24 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 22.40/22.24 ( hAPP(c_Fun_Ocomp(T_d,T_c,T_b,V_a_2),V_b_2) = V_c_2
% 22.40/22.24 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_K__record__comp,axiom,
% 22.40/22.24 ! [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 ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUP__commute,axiom,
% 22.40/22.24 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I9_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I9_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I9_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I9_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__UN__flatten,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUP1__iff,axiom,
% 22.40/22.24 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> ? [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.24 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Union__def,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I8_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I8_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INFI__apply,axiom,
% 22.40/22.24 ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF__commute,axiom,
% 22.40/22.24 ! [V_f_2,V_B_2,T_d,V_A_2,T_c,T_b] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Inter__def,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Pow__INT__eq,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_o__eq__elim,axiom,
% 22.40/22.24 ! [V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 22.40/22.24 ( 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)
% 22.40/22.24 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_o__eq__dest,axiom,
% 22.40/22.24 ! [V_v_2,V_d_2,V_c_2,T_e,V_b_2,V_a_2,T_b,T_c,T_d] :
% 22.40/22.24 ( 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)
% 22.40/22.24 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_o__apply,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_o__assoc,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_o__def,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fun__upd__def,axiom,
% 22.40/22.24 ! [V_b_2,V_f_2,T_c,T_b,V_a_2,V_x_2] :
% 22.40/22.24 ( ( V_x_2 = V_a_2
% 22.40/22.24 => hAPP(c_Fun_Ofun__upd(T_b,T_c,V_f_2,V_a_2,V_b_2),V_x_2) = V_b_2 )
% 22.40/22.24 & ( V_x_2 != V_a_2
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
% 22.40/22.24 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 22.40/22.24 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom,
% 22.40/22.24 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 22.40/22.24 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod__timesf,axiom,
% 22.40/22.24 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__right__distrib,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
% 22.40/22.24 ( class_Rings_Osemiring__0(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__left__distrib,axiom,
% 22.40/22.24 ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Rings_Osemiring__0(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__product,axiom,
% 22.40/22.24 ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Rings_Osemiring__0(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fun__upd__comp,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__insert__distrib,axiom,
% 22.40/22.24 ! [V_B_2,V_a_2,T_c,V_A_2,V_u_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_u_2),V_A_2))
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_bot__empty__eq2,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_bot__empty__eq,axiom,
% 22.40/22.24 ! [V_x_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),V_x_2))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_sup__Un__eq,axiom,
% 22.40/22.24 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inf__Int__eq,axiom,
% 22.40/22.24 ! [V_x_2,V_S_2,V_R_2,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__absorb,axiom,
% 22.40/22.24 ! [V_A_2,T_c,V_I_2,V_k_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_k_2),V_I_2))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__iff,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> ? [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__iff,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,V_b_2,T_b] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,B_x))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pred__equals__eq,axiom,
% 22.40/22.24 ! [V_S_2,V_R_2,T_b] :
% 22.40/22.24 ( 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)
% 22.40/22.24 <=> V_R_2 = V_S_2 ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pred__equals__eq2,axiom,
% 22.40/22.24 ! [V_S_2,V_R_2,T_c,T_b] :
% 22.40/22.24 ( 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)
% 22.40/22.24 <=> V_R_2 = V_S_2 ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_sup__Un__eq2,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inf__Int__eq2,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Un__Inter,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inj__on__id2,axiom,
% 22.40/22.24 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_COMBI(T_b),V_A_2) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__Int__distrib,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Un__INT__distrib2,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I6_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Un__INT__distrib,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I7_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I6_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I7_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Int__Union,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Int__Union2,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I5_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I4_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I5_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Int__UN__distrib,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I4_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Int__UN__distrib2,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__Un__distrib,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__Un,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__Un,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inf__fun__def,axiom,
% 22.40/22.24 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Lattices_Olattice(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_sup__fun__def,axiom,
% 22.40/22.24 ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Lattices_Olattice(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inj__on__imageI2,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,V_f_H_2,T_d,T_c,T_b] :
% 22.40/22.24 ( 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)
% 22.40/22.24 => c_Fun_Oinj__on(T_b,T_d,V_f_2,V_A_2) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I2_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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 )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I1_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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 )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__insert,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_override__on__def,axiom,
% 22.40/22.24 ! [V_g_2,V_f_2,T_c,V_A_2,V_a_2,T_b] :
% 22.40/22.24 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.24 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_g_2,V_a_2) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.24 => hAPP(c_Fun_Ooverride__on(T_b,T_c,V_f_2,V_g_2,V_A_2),V_a_2) = hAPP(V_f_2,V_a_2) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_int__setprod,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_int__setsum,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I10_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__UN,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I10_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__Union,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__image,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__ident,axiom,
% 22.40/22.24 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I10_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I10_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__compose,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INTER__eq__Inter__image,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Inter__image__eq,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod__dividef,axiom,
% 22.40/22.24 ! [V_g_2,V_f_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Fields_Ofield__inverse__zero(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_b] :
% 22.40/22.24 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 & class_Groups_Ocomm__monoid__mult(T_b) )
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom,
% 22.40/22.24 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__UN__finite__eq,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_card__eq__setsum,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__subtractf,axiom,
% 22.40/22.24 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Oab__group__add(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fun__diff__def,axiom,
% 22.40/22.24 ! [V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Ominus(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod__1,axiom,
% 22.40/22.24 ! [V_A_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I7_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__simps_I6_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I7_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__extend__simps_I6_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I4_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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 )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__extend__simps_I3_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I3_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Union__image__eq,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UNION__eq__Union__image,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__setsum__abs,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_abs__setprod,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Fields_Olinordered__field(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom,
% 22.40/22.24 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__subset__iff,axiom,
% 22.40/22.24 ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__subset__iff,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,V_I_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_le__INF__iff,axiom,
% 22.40/22.24 ! [V_M_2,V_A_2,T_c,V_u_2,T_b] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUP__le__iff,axiom,
% 22.40/22.24 ! [V_u_2,V_M_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.24 => ( 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))
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__lower,axiom,
% 22.40/22.24 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pred__subset__eq,axiom,
% 22.40/22.24 ! [V_S_2,V_R_2,T_b] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_R_2),V_S_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pred__subset__eq2,axiom,
% 22.40/22.24 ! [V_S_2,V_R_2,T_c,T_b] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inj__on__add__nat,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__addf,axiom,
% 22.40/22.24 ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_less__eq__Suc__le__raw,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__upper,axiom,
% 22.40/22.24 ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum_Odistrib,axiom,
% 22.40/22.24 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF__leI,axiom,
% 22.40/22.24 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_le__SUPI,axiom,
% 22.40/22.24 ! [V_M_2,V_A_2,V_i_2,T_b,T_c] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_A_2))
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF__less__iff,axiom,
% 22.40/22.24 ! [V_a_2,V_f_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.24 & class_Orderings_Olinorder(T_b) )
% 22.40/22.24 => ( 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))
% 22.40/22.24 <=> ? [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_less__SUP__iff,axiom,
% 22.40/22.24 ! [V_f_2,V_A_2,T_c,V_a_2,T_b] :
% 22.40/22.24 ( ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.24 & class_Orderings_Olinorder(T_b) )
% 22.40/22.24 => ( 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)))
% 22.40/22.24 <=> ? [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.24 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__shift__bounds__nat__ivl,axiom,
% 22.40/22.24 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__number__of__Bit0,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Int__Inter__image,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__le__add__shift,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__Pow__subset,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__nat__setprod,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( ( class_Groups_Ocomm__monoid__mult(T_b)
% 22.40/22.24 & class_Rings_Osemiring__1(T_b) )
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__add__atLeastLessThan,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__add__atLeastAtMost,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__delta_H,axiom,
% 22.40/22.24 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__delta,axiom,
% 22.40/22.24 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__constant,axiom,
% 22.40/22.24 ! [V_c_2,T_c,V_A_2,V_x_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__greaterThan__UNIV,axiom,
% 22.40/22.24 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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod__delta,axiom,
% 22.40/22.24 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod__delta_H,axiom,
% 22.40/22.24 ! [V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__eq__UN,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INT__simps_I4_J,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
% 22.40/22.24 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__constant,axiom,
% 22.40/22.24 ! [V_A_2,V_y_2,T_c,T_b] :
% 22.40/22.24 ( class_Rings_Osemiring__1(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_power__number__of__even,axiom,
% 22.40/22.24 ! [V_w_2,V_z_2,T_b] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_b)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fold__image__distrib,axiom,
% 22.40/22.24 ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_dual__max,axiom,
% 22.40/22.24 ! [T_b] :
% 22.40/22.24 ( class_Orderings_Olinorder(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_dual__min,axiom,
% 22.40/22.24 ! [T_b] :
% 22.40/22.24 ( class_Orderings_Olinorder(T_b)
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod__constant,axiom,
% 22.40/22.24 ! [V_y_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_sup__SUPR__fold__sup,axiom,
% 22.40/22.24 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inf__INFI__fold__inf,axiom,
% 22.40/22.24 ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zpower__number__of__even,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_comp__surj,axiom,
% 22.40/22.24 ! [V_g_2,T_d,V_f_2,T_b,T_c] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => ( 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))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__lessThan__Suc,axiom,
% 22.40/22.24 ! [V_n_2,V_f_2,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__o,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inj__comp,axiom,
% 22.40/22.24 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 22.40/22.24 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.24 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_d,tc_HOL_Obool)))
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_comp__inj__on__iff,axiom,
% 22.40/22.24 ! [V_f_H_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.24 => ( 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))
% 22.40/22.24 <=> 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_comp__inj__on,axiom,
% 22.40/22.24 ! [V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.24 => ( 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))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inj__on__imageI,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,V_g_2,T_d,T_c,T_b] :
% 22.40/22.24 ( 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)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__atMost__Suc,axiom,
% 22.40/22.24 ! [V_n_2,V_f_2,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom,
% 22.40/22.24 ! [V_A_2,V_f_2,T_b] :
% 22.40/22.24 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 & class_Groups_Ocomm__monoid__mult(T_b) )
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Un__Union__image,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__add__int__atLeastLessThan,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom,
% 22.40/22.24 ! [V_f_2,V_A_2,T_b] :
% 22.40/22.24 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 & class_Groups_Ocomm__monoid__mult(T_b) )
% 22.40/22.24 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Powp__Pow__eq,axiom,
% 22.40/22.24 ! [V_x_2,V_A_2,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_b),V_A_2))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__restrict__set,axiom,
% 22.40/22.24 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__eq__fold__image,axiom,
% 22.40/22.24 ! [V_f_2,T_c,V_A_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_power__number__of__even__number__of,axiom,
% 22.40/22.24 ! [V_w_2,V_v_2,T_b] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_b)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUPR__fold__sup,axiom,
% 22.40/22.24 ! [V_f_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_card__def,axiom,
% 22.40/22.24 ! [V_A_2,T_b] :
% 22.40/22.24 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_card_Oeq__fold__g,axiom,
% 22.40/22.24 ! [V_A_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_fun__left__comm__idem__remove,axiom,
% 22.40/22.24 ! [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))))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INFI__fold__inf,axiom,
% 22.40/22.24 ! [V_f_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Complete__Lattice_Ocomplete__lattice(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_diff__nat__eq__if,axiom,
% 22.40/22.24 ! [V_z_2,V_z_H_2] :
% 22.40/22.24 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_negDivAlg__div__mod,axiom,
% 22.40/22.24 ! [V_l,V_k] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_negDivAlg__minus1,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_UN__le__eq__Un0,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom,
% 22.40/22.24 ! [V_f_2,V_A_2,T_b] :
% 22.40/22.24 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 & class_Groups_Ocomm__monoid__mult(T_b) )
% 22.40/22.24 => ( c_Nat__Transfer_Onat__set(V_A_2)
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_adjust__eq,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__head,axiom,
% 22.40/22.24 ! [V_P_2,V_n_2,V_m_2,T_b] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_minus__fold__remove,axiom,
% 22.40/22.24 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__reindex,axiom,
% 22.40/22.24 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_d)
% 22.40/22.24 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_eq__number__of__Suc,axiom,
% 22.40/22.24 ! [V_n_2,V_v_2] :
% 22.40/22.24 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
% 22.40/22.24 <=> 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))))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Suc__eq__number__of,axiom,
% 22.40/22.24 ! [V_v_2,V_n_2] :
% 22.40/22.24 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
% 22.40/22.24 <=> 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))))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod__reindex,axiom,
% 22.40/22.24 ! [V_h_2,V_B_2,V_f_2,T_c,T_b,T_d] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_d)
% 22.40/22.24 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod__reindex__cong,axiom,
% 22.40/22.24 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_d)
% 22.40/22.24 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.24 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 22.40/22.24 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)
% 22.40/22.24 => 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) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__number__of__Bit1,axiom,
% 22.40/22.24 ! [V_w_2] :
% 22.40/22.24 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 22.40/22.24 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
% 22.40/22.24 => 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)))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_geometric__sum,axiom,
% 22.40/22.24 ! [V_n_2,V_x_2,T_b] :
% 22.40/22.24 ( class_Fields_Ofield(T_b)
% 22.40/22.24 => ( V_x_2 != c_Groups_Oone__class_Oone(T_b)
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_gauss__sum,axiom,
% 22.40/22.24 ! [V_n_2,T_b] :
% 22.40/22.24 ( class_Rings_Ocomm__semiring__1(T_b)
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum__natinterval__difff,axiom,
% 22.40/22.24 ! [V_f_2,V_n_2,V_m_2,T_b] :
% 22.40/22.24 ( class_Groups_Oab__group__add(T_b)
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.40/22.24 => 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)))) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.40/22.24 => 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) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_less__number__of__Suc,axiom,
% 22.40/22.24 ! [V_n_2,V_v_2] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_less__Suc__number__of,axiom,
% 22.40/22.24 ! [V_v_2,V_n_2] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> 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))))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_le__number__of__Suc,axiom,
% 22.40/22.24 ! [V_n_2,V_v_2] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_le__Suc__number__of,axiom,
% 22.40/22.24 ! [V_v_2,V_n_2] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 <=> 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))))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_max__number__of__Suc,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_max__Suc__number__of,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_power__number__of__odd,axiom,
% 22.40/22.24 ! [V_z_2,V_w_2,T_b] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_b)
% 22.40/22.24 => ( ( 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)))
% 22.40/22.24 => 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))) )
% 22.40/22.24 & ( ~ 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)))
% 22.40/22.24 => 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) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod__gen__delta,axiom,
% 22.40/22.24 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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)))) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_S_2))
% 22.40/22.24 => 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)) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
% 22.40/22.24 ! [V_x_2,V_y_2,V_c_2] :
% 22.40/22.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 22.40/22.24 => 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))) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
% 22.40/22.24 => 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)) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setsum_Oreindex,axiom,
% 22.40/22.24 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 22.40/22.24 => 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) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_zpower__number__of__odd,axiom,
% 22.40/22.24 ! [V_z_2,V_w_2] :
% 22.40/22.24 ( ( 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)))
% 22.40/22.24 => 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))) )
% 22.40/22.24 & ( ~ 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)))
% 22.40/22.24 => 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) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_setprod_Oreindex,axiom,
% 22.40/22.24 ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
% 22.40/22.24 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.40/22.24 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.24 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
% 22.40/22.24 => 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) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_arith__series__general,axiom,
% 22.40/22.24 ! [V_n_2,V_d_2,V_a_2,T_b] :
% 22.40/22.24 ( class_Rings_Ocomm__semiring__1(T_b)
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_negDivAlg_Osimps,axiom,
% 22.40/22.24 ! [V_b,V_a] :
% 22.40/22.24 ( ( ( 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)))
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( ~ ( 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)))
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_min__number__of__Suc,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_min__Suc__number__of,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_arith__series__nat,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_the__inv__into__comp,axiom,
% 22.40/22.24 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 22.40/22.24 => ( 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))))
% 22.40/22.24 => 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) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_power__number__of__odd__number__of,axiom,
% 22.40/22.24 ! [V_v_2,V_w_2,T_b] :
% 22.40/22.24 ( class_Int_Onumber__ring(T_b)
% 22.40/22.24 => ( ( 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)))
% 22.40/22.24 => 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))) )
% 22.40/22.24 & ( ~ 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)))
% 22.40/22.24 => 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) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_negDivAlg__eqn,axiom,
% 22.40/22.24 ! [V_a,V_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.24 => ( ( 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)))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( ~ 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)))
% 22.40/22.24 => 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))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_negDivAlg__eqn__number__of,axiom,
% 22.40/22.24 ! [V_w,V_v] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 => ( ( 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))))
% 22.40/22.24 => 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))) )
% 22.40/22.24 & ( ~ 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))))
% 22.40/22.24 => 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)))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_diff__nat__number__of,axiom,
% 22.40/22.24 ! [V_v_2,V_v_H_2] :
% 22.40/22.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_norm__frac_Osimps,axiom,
% 22.40/22.24 ! [V_a_2,V_b_2] :
% 22.40/22.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 22.40/22.24 => 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))) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__case__add__eq__if,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_posDivAlg__eqn__1__number__of,axiom,
% 22.40/22.24 ! [V_w] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 => ( ( 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)))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( ~ 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)))
% 22.40/22.24 => 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)))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_posDivAlg_Osimps,axiom,
% 22.40/22.24 ! [V_b,V_a] :
% 22.40/22.24 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.24 => 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))) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_sup2CI,axiom,
% 22.40/22.24 ! [T_c,T_b,V_A_2,V_y_2,V_x_2,V_B_2] :
% 22.40/22.24 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) )
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_sup2E,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inf2I,axiom,
% 22.40/22.24 ! [T_c,T_b,V_B_2,V_y_2,V_x_2,V_A_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inf2E,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 22.40/22.24 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_bot2E,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_SUP2__iff,axiom,
% 22.40/22.24 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> ? [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.24 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF1__iff,axiom,
% 22.40/22.24 ! [V_b_2,V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_INF2__iff,axiom,
% 22.40/22.24 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 <=> ! [B_x] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_predicate2D,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 22.40/22.24 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_rev__predicate2D,axiom,
% 22.40/22.24 ! [V_Q_2,T_c,T_b,V_y_2,V_x_2,V_P_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 22.40/22.24 => ( 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))
% 22.40/22.24 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_less__by__empty,axiom,
% 22.40/22.24 ! [V_B_2,T_b,V_A_2] :
% 22.40/22.24 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_sup2I2,axiom,
% 22.40/22.24 ! [V_A_2,T_c,T_b,V_y_2,V_x_2,V_B_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2))
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_sup2I1,axiom,
% 22.40/22.24 ! [V_B_2,T_c,T_b,V_y_2,V_x_2,V_A_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2))
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inf2D1,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_inf2D2,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__case__0,axiom,
% 22.40/22.24 ! [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 ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__case__Suc,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_posDivAlg__0,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_max__Suc1,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_max__Suc2,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_less__eq__nat_Osimps_I2_J,axiom,
% 22.40/22.24 ! [V_n_2,V_m_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
% 22.40/22.24 <=> 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_diff__Suc,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_min__Suc1,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_min__Suc2,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_posDivAlg__div__mod,axiom,
% 22.40/22.24 ! [V_l,V_k] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__case__number__of,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_posDivAlg__eqn,axiom,
% 22.40/22.24 ! [V_a,V_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
% 22.40/22.24 => 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))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_posDivAlg__eqn__number__of,axiom,
% 22.40/22.24 ! [V_w,V_v] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 => ( ( 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)))
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( ~ 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)))
% 22.40/22.24 => 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)))) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_in__rel__def,axiom,
% 22.40/22.24 ! [V_y_2,V_x_2,V_R_2,T_c,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_b,T_c,V_R_2),V_x_2),V_y_2))
% 22.40/22.24 <=> 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_div__mod__code__numeral__def,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nitpick_Orefl_H__def,axiom,
% 22.40/22.24 ! [V_r_2,T_b] :
% 22.40/22.24 ( c_Nitpick_Orefl_H(T_b,V_r_2)
% 22.40/22.24 <=> ! [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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_adjust__def,axiom,
% 22.40/22.24 ! [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))))))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_divmod__nat__step,axiom,
% 22.40/22.24 ! [V_m,V_n] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.40/22.24 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__rec__add__eq__if,axiom,
% 22.40/22.24 ! [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))))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__rec__0,axiom,
% 22.40/22.24 ! [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 ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__rec__Suc,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_divmod__nat__zero,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_divmod__nat__base,axiom,
% 22.40/22.24 ! [V_n,V_m] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_divmod__nat__div__mod,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_nat__rec__number__of,axiom,
% 22.40/22.24 ! [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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pair__imageI,axiom,
% 22.40/22.24 ! [V_f_2,T_d,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__int__num,axiom,
% 22.40/22.24 ! [V_k_2,T_b] :
% 22.40/22.24 ( class_Rings_Oring__1(T_b)
% 22.40/22.24 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 => hAPP(c_Int_Oring__1__class_Oof__int(T_b),V_k_2) = c_Groups_Ozero__class_Ozero(T_b) )
% 22.40/22.24 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => 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))) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.24 => 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))))) ) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_semiring__1__class_Oof__nat__code,axiom,
% 22.40/22.24 ! [V_n_2,T_b] :
% 22.40/22.24 ( class_Rings_Osemiring__1(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_splitI,axiom,
% 22.40/22.24 ! [T_c,T_b,V_b_2,V_a_2,V_f_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2))
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_prod__caseI,axiom,
% 22.40/22.24 ! [T_c,T_b,V_b_2,V_a_2,V_f1_2] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2))
% 22.40/22.24 => 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))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_mem__splitI,axiom,
% 22.40/22.24 ! [T_d,T_c,V_b_2,V_a_2,V_c_2,V_z_2,T_b] :
% 22.40/22.24 ( hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2)))
% 22.40/22.24 => 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)))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_splitD,axiom,
% 22.40/22.24 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 22.40/22.24 ( 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)))
% 22.40/22.24 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_splitD_H,axiom,
% 22.40/22.24 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
% 22.40/22.24 ( 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))
% 22.40/22.24 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__nat__aux_Osimps_I1_J,axiom,
% 22.40/22.24 ! [V_i_2,V_inc_2,T_b] :
% 22.40/22.24 ( class_Rings_Osemiring__1(T_b)
% 22.40/22.24 => 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 ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_of__nat__aux_Osimps_I2_J,axiom,
% 22.40/22.24 ! [V_i_2,V_n_2,V_inc_2,T_b] :
% 22.40/22.24 ( class_Rings_Osemiring__1(T_b)
% 22.40/22.24 => 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)) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_split__paired__All,axiom,
% 22.40/22.24 ! [T_c,T_b,V_P_2] :
% 22.40/22.24 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 22.40/22.24 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Pair__eq,axiom,
% 22.40/22.24 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.24 ( 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)
% 22.40/22.24 <=> ( V_a_2 = V_a_H_2
% 22.40/22.24 & V_b_2 = V_b_H_2 ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Pair__inject,axiom,
% 22.40/22.24 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] :
% 22.40/22.24 ( 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)
% 22.40/22.24 => ~ ( V_a = V_a_H
% 22.40/22.24 => V_b != V_b_H ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_split__weak__cong,axiom,
% 22.40/22.24 ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
% 22.40/22.24 ( V_p_2 = V_q_2
% 22.40/22.24 => 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) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_divmod__int__mod__div,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_prod_Osimps_I2_J,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_split__conv,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_divmod__nat__if,axiom,
% 22.40/22.24 ! [V_m_2,V_n_2] :
% 22.40/22.24 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.24 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) )
% 22.40/22.24 => 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)) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_split__eta,axiom,
% 22.40/22.24 ! [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 ).
% 22.40/22.24
% 22.40/22.24 fof(fact_swap__inj__on,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_split__twice,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_Nitpick_OFrac__def,axiom,
% 22.40/22.24 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)))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_divmod__int__def,axiom,
% 22.40/22.24 ! [V_b,V_a] :
% 22.40/22.24 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.24 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.24 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 => 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))) ) ) ) ) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.24 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.24 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) )
% 22.40/22.24 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.24 => 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))) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_divmod__int__pdivmod,axiom,
% 22.40/22.24 ! [V_l_2,V_k_2] :
% 22.40/22.24 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 => 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)) )
% 22.40/22.24 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 => 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) )
% 22.40/22.24 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 => 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)))) ) ) ) ) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_apsnd__conv,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_negateSnd__def,axiom,
% 22.40/22.24 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_apsnd__compose,axiom,
% 22.40/22.24 ! [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) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_negateSnd__eq,axiom,
% 22.40/22.24 ! [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)) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pdivmod__def,axiom,
% 22.40/22.24 ! [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))) ).
% 22.40/22.24
% 22.40/22.24 fof(fact_pdivmod__posDivAlg,axiom,
% 22.40/22.24 ! [V_k,V_l] :
% 22.40/22.24 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.24 => 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)) )
% 22.40/22.25 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__int__code,axiom,
% 22.40/22.25 ! [V_l_2,V_k_2] :
% 22.40/22.25 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => 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)) )
% 22.40/22.25 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => 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) )
% 22.40/22.25 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => 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)))) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__nat__rel__mult1__eq,axiom,
% 22.40/22.25 ! [V_a,V_r,V_q,V_c,V_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 22.40/22.25 => 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)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__nat__rel__mult2__eq,axiom,
% 22.40/22.25 ! [V_c,V_r,V_q,V_b,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 22.40/22.25 => 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)))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pair__box_Osize_I2_J,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__nat__rel__unique,axiom,
% 22.40/22.25 ! [V_qr_H,V_qr,V_n,V_m] :
% 22.40/22.25 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 22.40/22.25 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
% 22.40/22.25 => V_qr = V_qr_H ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__nat__eq,axiom,
% 22.40/22.25 ! [V_qr,V_n,V_m] :
% 22.40/22.25 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
% 22.40/22.25 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__nat__rel__divmod__nat,axiom,
% 22.40/22.25 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mod__eq,axiom,
% 22.40/22.25 ! [V_r,V_q,V_n,V_m] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_div__eq,axiom,
% 22.40/22.25 ! [V_r,V_q,V_n,V_m] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__nat__rel,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__nat__rel__add1__eq,axiom,
% 22.40/22.25 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c))
% 22.40/22.25 => 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)))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pair__box_Osimps_I2_J,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pair__box_Orecs,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_negDivAlg_Opsimps,axiom,
% 22.40/22.25 ! [V_b_2,V_a_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ( ( 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)))
% 22.40/22.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.25 => 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)) )
% 22.40/22.25 & ( ~ ( 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)))
% 22.40/22.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.25 => 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))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_posDivAlg_Opsimps,axiom,
% 22.40/22.25 ! [V_b_2,V_a_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 22.40/22.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.25 => 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) )
% 22.40/22.25 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2))
% 22.40/22.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.25 => 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))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_norm__frac_Opsimps,axiom,
% 22.40/22.25 ! [V_b_2,V_a_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => 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)) )
% 22.40/22.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 22.40/22.25 => 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)) )
% 22.40/22.25 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
% 22.40/22.25 => 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))) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_negDivAlg_Opinduct,axiom,
% 22.40/22.25 ! [V_P_2,V_a1_2,V_a0_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ! [B_a,B_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ( ~ ( 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)))
% 22.40/22.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.25 => 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))) )
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_posDivAlg_Opinduct,axiom,
% 22.40/22.25 ! [V_P_2,V_a1_2,V_a0_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ! [B_a,B_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b))
% 22.40/22.25 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
% 22.40/22.25 => 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))) )
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_accp__subset,axiom,
% 22.40/22.25 ! [V_R2_2,V_R1_2,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_zmult2__lemma,axiom,
% 22.40/22.25 ! [V_c,V_r,V_q,V_b,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
% 22.40/22.25 => 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)))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__int__rel__0,axiom,
% 22.40/22.25 ! [V_b] :
% 22.40/22.25 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => 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)))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_self__remainder,axiom,
% 22.40/22.25 ! [V_r,V_q,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_unique__quotient,axiom,
% 22.40/22.25 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => V_q = V_q_H ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_unique__remainder,axiom,
% 22.40/22.25 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => V_r = V_r_H ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__int__rel__neg,axiom,
% 22.40/22.25 ! [V_qr,V_b,V_a] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__int__correct,axiom,
% 22.40/22.25 ! [V_a,V_b] :
% 22.40/22.25 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_accp__downward,axiom,
% 22.40/22.25 ! [V_a_2,V_b_2,V_r_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 22.40/22.25 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_accp_Oequations,axiom,
% 22.40/22.25 ! [V_a_2,V_r_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 22.40/22.25 <=> ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 22.40/22.25 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_accp_Osimps,axiom,
% 22.40/22.25 ! [V_a_2,V_r_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
% 22.40/22.25 <=> ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
% 22.40/22.25 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_self__quotient,axiom,
% 22.40/22.25 ! [V_r,V_q,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__int__rel__mod,axiom,
% 22.40/22.25 ! [V_r,V_q,V_b,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__int__rel__div,axiom,
% 22.40/22.25 ! [V_r,V_q,V_b,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_negDivAlg__correct,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.25 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__int__rel__div__mod,axiom,
% 22.40/22.25 ! [V_a,V_b] :
% 22.40/22.25 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => 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)))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_posDivAlg__correct,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.25 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_zadd1__lemma,axiom,
% 22.40/22.25 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => 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)))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_zminus1__lemma,axiom,
% 22.40/22.25 ! [V_r_2,V_q_2,V_b_2,V_a_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => 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))))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__int__relI,axiom,
% 22.40/22.25 ! [V_r,V_q,V_b,V_a] :
% 22.40/22.25 ( 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)
% 22.40/22.25 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
% 22.40/22.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) )
% 22.40/22.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r))
% 22.40/22.25 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) )
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_zmult1__lemma,axiom,
% 22.40/22.25 ! [V_a,V_r,V_q,V_c,V_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
% 22.40/22.25 => 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)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__int__rel__def,axiom,
% 22.40/22.25 ! [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))))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat__gcd_Opsimps,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.25 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 )
% 22.40/22.25 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat_Osize_I2_J,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_coinduct3__mono__lemma,axiom,
% 22.40/22.25 ! [V_B_2,V_X_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( class_Orderings_Oorder(T_b)
% 22.40/22.25 => ( c_Orderings_Oorder__class_Omono(T_b,tc_fun(T_c,tc_HOL_Obool),V_f_2)
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat_Osize_I1_J,axiom,
% 22.40/22.25 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom,
% 22.40/22.25 ! [V_f_2,V_A_2,T_b] :
% 22.40/22.25 ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mod__pos__neg__1__number__of,axiom,
% 22.40/22.25 ! [V_w] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => 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))))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_in__measure,axiom,
% 22.40/22.25 ! [V_f_2,V_y_2,V_x_2,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 <=> 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_snd__apsnd,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apsnd__eq__conv,axiom,
% 22.40/22.25 ! [V_g_2,V_x_2,V_f_2,T_b,T_c,T_d] :
% 22.40/22.25 ( 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)
% 22.40/22.25 <=> 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_snd__conv,axiom,
% 22.40/22.25 ! [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 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_snd__eqD,axiom,
% 22.40/22.25 ! [V_a,V_y,V_x,T_a,T_b] :
% 22.40/22.25 ( 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
% 22.40/22.25 => V_y = V_a ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_snd__def,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mod__int__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mod__neg__pos,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mod__pos__pos,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mod__pos__pos__1__number__of,axiom,
% 22.40/22.25 ! [V_w] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mod__pos__neg,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => 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)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mod__neg__neg,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => 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)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom,
% 22.40/22.25 ! [V_f_2,V_A_2,T_b] :
% 22.40/22.25 ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) )
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Oremove,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_norm__frac_Opinduct,axiom,
% 22.40/22.25 ! [V_P_2,V_a1_2,V_a0_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ! [B_a,B_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => 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))) )
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) )
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Ocommute__left__comp,axiom,
% 22.40/22.25 ! [V_g_2,V_x_2,V_y_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Ocommute__comp,axiom,
% 22.40/22.25 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Ocommute__comps_I1_J,axiom,
% 22.40/22.25 ! [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] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_fa_2,V_F_2)
% 22.40/22.25 => 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) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mod__nat__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Ocommute__left__comp_H_H,axiom,
% 22.40/22.25 ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Ocommute__comp_H_H,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Ocommute__left__comp_H,axiom,
% 22.40/22.25 ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Ocommute__comp_H,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Oeq__fold,axiom,
% 22.40/22.25 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => 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) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Oinsert,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Ounion__inter,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Oinsert__remove,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Ounion,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_div__pos__neg__1__number__of,axiom,
% 22.40/22.25 ! [V_w] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => 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))))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat__def,axiom,
% 22.40/22.25 ! [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)))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UN__finite2__subset,axiom,
% 22.40/22.25 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 22.40/22.25 ( ! [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)))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Pair__fst__snd__eq,axiom,
% 22.40/22.25 ! [T_c,T_b,V_t_2,V_s_2] :
% 22.40/22.25 ( V_s_2 = V_t_2
% 22.40/22.25 <=> ( hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2)
% 22.40/22.25 & hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_prod__eqI,axiom,
% 22.40/22.25 ! [V_q,V_p,T_b,T_a] :
% 22.40/22.25 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q)
% 22.40/22.25 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q)
% 22.40/22.25 => V_p = V_q ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fst__apsnd,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fst__conv,axiom,
% 22.40/22.25 ! [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 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fst__eqD,axiom,
% 22.40/22.25 ! [V_a,V_y,V_x,T_b,T_a] :
% 22.40/22.25 ( 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
% 22.40/22.25 => V_x = V_a ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Rep__Integ__inject,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2] :
% 22.40/22.25 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2)
% 22.40/22.25 <=> V_x_2 = V_y_2 ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fst__def,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_surjective__pairing,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pair__collapse,axiom,
% 22.40/22.25 ! [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 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_prod__case__beta,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_div__int__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_split__beta,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_split__comp__eq,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_split__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_split__comp,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_div__neg__pos,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_div__pos__pos,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_div__pos__pos__1__number__of,axiom,
% 22.40/22.25 ! [V_w] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_div__pos__neg,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => 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)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_div__neg__neg,axiom,
% 22.40/22.25 ! [V_b,V_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
% 22.40/22.25 => 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)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_prod__size__simp,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_exI__realizer,axiom,
% 22.40/22.25 ! [T_b,T_c,V_x_2,V_y_2,V_P_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2))
% 22.40/22.25 => 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)))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_conjI__realizer,axiom,
% 22.40/22.25 ! [T_c,T_b,V_q_2,V_Q_2,V_p_2,V_P_2] :
% 22.40/22.25 ( hBOOL(hAPP(V_P_2,V_p_2))
% 22.40/22.25 => ( hBOOL(hAPP(V_Q_2,V_q_2))
% 22.40/22.25 => ( 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))))
% 22.40/22.25 & 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)))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_div__nat__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__nat__rel__def,axiom,
% 22.40/22.25 ! [V_qr_2,V_n_2,V_m_2] :
% 22.40/22.25 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2))
% 22.40/22.25 <=> ( 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))
% 22.40/22.25 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.25 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.40/22.25 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.25 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 & 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)) ) )
% 22.40/22.25 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 & 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))) ) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat__gcd_Opinduct,axiom,
% 22.40/22.25 ! [V_P_2,V_a1_2,V_a0_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ! [B_x,B_y] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) )
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_range,axiom,
% 22.40/22.25 ! [V_s,V_k] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mlex__leq,axiom,
% 22.40/22.25 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mlex__less,axiom,
% 22.40/22.25 ! [V_R_2,T_b,V_y_2,V_x_2,V_f_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Least__mono,axiom,
% 22.40/22.25 ! [V_S_2,V_f_2,T_b,T_c] :
% 22.40/22.25 ( ( class_Orderings_Oorder(T_c)
% 22.40/22.25 & class_Orderings_Oorder(T_b) )
% 22.40/22.25 => ( c_Orderings_Oorder__class_Omono(T_b,T_c,V_f_2)
% 22.40/22.25 => ( ? [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 22.40/22.25 & ! [B_xa] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_S_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) )
% 22.40/22.25 => 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))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding__image_Oreindex,axiom,
% 22.40/22.25 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.40/22.25 => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
% 22.40/22.25 => 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) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat_Osize_I4_J,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat__size,axiom,
% 22.40/22.25 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ).
% 22.40/22.25
% 22.40/22.25 fof(fact_LeastI__ex,axiom,
% 22.40/22.25 ! [V_P_2,T_b] :
% 22.40/22.25 ( class_Orderings_Owellorder(T_b)
% 22.40/22.25 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 22.40/22.25 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_LeastI,axiom,
% 22.40/22.25 ! [V_k_2,V_P_2,T_b] :
% 22.40/22.25 ( class_Orderings_Owellorder(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 22.40/22.25 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_b,V_P_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Least__le,axiom,
% 22.40/22.25 ! [V_k_2,V_P_2,T_b] :
% 22.40/22.25 ( class_Orderings_Owellorder(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(V_P_2,V_k_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Orderings_Oord__class_OLeast(T_b,V_P_2)),V_k_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_not__less__Least,axiom,
% 22.40/22.25 ! [V_P_2,V_k_2,T_b] :
% 22.40/22.25 ( class_Orderings_Owellorder(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),c_Orderings_Oord__class_OLeast(T_b,V_P_2)))
% 22.40/22.25 => ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding__image_Odistrib,axiom,
% 22.40/22.25 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat_Osize_I3_J,axiom,
% 22.40/22.25 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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Least__Suc,axiom,
% 22.40/22.25 ! [V_n_2,V_P_2] :
% 22.40/22.25 ( hBOOL(hAPP(V_P_2,V_n_2))
% 22.40/22.25 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding__image_Oeq__fold,axiom,
% 22.40/22.25 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.40/22.25 => 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) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_prod_Orecs,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__reindex__nonzero,axiom,
% 22.40/22.25 ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__add(T_d)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 22.40/22.25 => ! [B_y] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
% 22.40/22.25 => ( B_x != B_y
% 22.40/22.25 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 22.40/22.25 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
% 22.40/22.25 => 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) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UN__finite2__eq,axiom,
% 22.40/22.25 ! [V_B_2,V_k_2,V_A_2,T_b] :
% 22.40/22.25 ( ! [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)
% 22.40/22.25 => 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) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UN__finite__subset,axiom,
% 22.40/22.25 ! [V_C_2,V_A_2,T_b] :
% 22.40/22.25 ( ! [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))
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_image__INT,axiom,
% 22.40/22.25 ! [V_j_2,V_B_2,V_A_2,T_d,V_C_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_C_2)
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_d),B_x),V_A_2))
% 22.40/22.25 => 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)) )
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_d),V_j_2),V_A_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_in__lex__prod,axiom,
% 22.40/22.25 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 <=> ( 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))
% 22.40/22.25 | ( V_a_2 = V_a_H_2
% 22.40/22.25 & 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_same__fstI,axiom,
% 22.40/22.25 ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_P_2] :
% 22.40/22.25 ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_in__finite__psubset,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.40/22.25 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding__idem_Ounion__idem,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding__idem_Oidem__comp,axiom,
% 22.40/22.25 ! [V_x_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => 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) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding__idem_Oidem__left__comp,axiom,
% 22.40/22.25 ! [V_g_2,V_x_2,T_d,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => 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) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding__idem_Oin__comp__idem,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.25 => 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) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding__idem_Oinsert__idem,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding__idem_Osubset__comp__idem,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.40/22.25 => 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) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__nonneg__leq__bound,axiom,
% 22.40/22.25 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_b,T_c] :
% 22.40/22.25 ( class_Groups_Oordered__ab__group__add(T_c)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 22.40/22.25 => ( ! [B_i] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 22.40/22.25 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_s_2) = V_B_2
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__nonneg__0,axiom,
% 22.40/22.25 ! [V_i_2,V_f_2,V_s_2,T_b,T_c] :
% 22.40/22.25 ( class_Groups_Oordered__ab__group__add(T_c)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 22.40/22.25 => ( ! [B_i] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_s_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_i))) )
% 22.40/22.25 => ( 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)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),V_s_2))
% 22.40/22.25 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_sum__diff__distrib,axiom,
% 22.40/22.25 ! [V_n_2,V_P_2,V_Q_2] :
% 22.40/22.25 ( ! [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)))
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apsnd__apfst,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apfst__apsnd,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pair__lessI2,axiom,
% 22.40/22.25 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apfst__eq__conv,axiom,
% 22.40/22.25 ! [V_g_2,V_x_2,V_f_2,T_c,T_b,T_d] :
% 22.40/22.25 ( 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)
% 22.40/22.25 <=> 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fst__apfst,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apfst__compose,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apfst__conv,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_snd__apfst,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apsnd__apfst__commute,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pair__lessI1,axiom,
% 22.40/22.25 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pair__leqI2,axiom,
% 22.40/22.25 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_smin__insertI,axiom,
% 22.40/22.25 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_smax__insertI,axiom,
% 22.40/22.25 ! [V_X_2,V_x_2,V_Y_2,V_y_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_smin__emptyI,axiom,
% 22.40/22.25 ! [V_X_2] :
% 22.40/22.25 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_smax__emptyI,axiom,
% 22.40/22.25 ! [V_Y_2] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2))
% 22.40/22.25 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pair__leqI1,axiom,
% 22.40/22.25 ! [V_t_2,V_s_2,V_b_2,V_a_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wmax__insertI,axiom,
% 22.40/22.25 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wmin__insertI,axiom,
% 22.40/22.25 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wmin__emptyI,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wmax__emptyI,axiom,
% 22.40/22.25 ! [V_X_2] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2))
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_min__weak__def,axiom,
% 22.40/22.25 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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_max__weak__def,axiom,
% 22.40/22.25 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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_min__rpair__set,axiom,
% 22.40/22.25 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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_max__strict__def,axiom,
% 22.40/22.25 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_max__ext__additive,axiom,
% 22.40/22.25 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_min__strict__def,axiom,
% 22.40/22.25 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_max__rpair__set,axiom,
% 22.40/22.25 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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_max__extp__max__ext__eq,axiom,
% 22.40/22.25 ! [V_xa_2,V_x_2,V_R_2,T_b] :
% 22.40/22.25 ( 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)
% 22.40/22.25 <=> 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_less__than__iff,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2] :
% 22.40/22.25 ( 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))
% 22.40/22.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_intrel__iff,axiom,
% 22.40/22.25 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 22.40/22.25 ( 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))
% 22.40/22.25 <=> 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) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pair__less__def,axiom,
% 22.40/22.25 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mlex__prod__def,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rp__inv__image__rp,axiom,
% 22.40/22.25 ! [V_f_2,T_c,V_P_2,T_b] :
% 22.40/22.25 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 22.40/22.25 => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_P_2),V_f_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_strong__setprod__reindex__cong,axiom,
% 22.40/22.25 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__mult(T_d)
% 22.40/22.25 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.25 => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => 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) )
% 22.40/22.25 => 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) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rp__inv__image__def,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_in__inv__image,axiom,
% 22.40/22.25 ! [V_f_2,V_r_2,T_c,V_y_2,V_x_2,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 <=> 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equiv__intrel__iff,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 <=> 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom,
% 22.40/22.25 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.25 & class_Groups_Ocomm__monoid__mult(T_b) )
% 22.40/22.25 => ( V_A_2 = V_B_2
% 22.40/22.25 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 22.40/22.25 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 22.40/22.25 => 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) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__empty,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Un__Image,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__Un,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__UN,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__INT__subset,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__Int__subset,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__mono,axiom,
% 22.40/22.25 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_H_2),V_A_2))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__iff,axiom,
% 22.40/22.25 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 22.40/22.25 <=> ? [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.25 & 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rev__ImageI,axiom,
% 22.40/22.25 ! [V_r_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_OImage(T_b,T_c,V_r_2),V_A_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__eq__UN,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__singleton__iff,axiom,
% 22.40/22.25 ! [V_a_2,V_r_2,T_c,V_b_2,T_b] :
% 22.40/22.25 ( 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))))))
% 22.40/22.25 <=> 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_measure__def,axiom,
% 22.40/22.25 ! [T_b] : c_Wellfounded_Omeasure(T_b) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_b),c_Wellfounded_Oless__than) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_of__int,axiom,
% 22.40/22.25 ! [V_j_2,V_i_2,T_b] :
% 22.40/22.25 ( class_Rings_Oring__1(T_b)
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_One__int__def,axiom,
% 22.40/22.25 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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mult,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Rep__Integ__inverse,axiom,
% 22.40/22.25 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_minus,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Zero__int__def,axiom,
% 22.40/22.25 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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_int__def,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_add,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_minus__int__def,axiom,
% 22.40/22.25 ! [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))))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_less,axiom,
% 22.40/22.25 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 22.40/22.25 ( 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)))))))
% 22.40/22.25 <=> 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_le,axiom,
% 22.40/22.25 ! [V_v_2,V_u_2,V_y_2,V_x_2] :
% 22.40/22.25 ( 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)))))))
% 22.40/22.25 <=> 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_irrefl__def,axiom,
% 22.40/22.25 ! [V_r_2,T_b] :
% 22.40/22.25 ( c_Relation_Oirrefl(T_b,V_r_2)
% 22.40/22.25 <=> ! [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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_eq__Abs__Integ,axiom,
% 22.40/22.25 ! [V_z_2] :
% 22.40/22.25 ~ ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Field__insert,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Field__Union,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Field__empty,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mono__Field,axiom,
% 22.40/22.25 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Field__Un,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__Field,axiom,
% 22.40/22.25 ! [V_r_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_OField(T_b),V_r_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Id__on__def,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotient__def,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_ImageE,axiom,
% 22.40/22.25 ! [V_A_2,V_r_2,T_c,V_b_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),V_A_2)))
% 22.40/22.25 => ~ ! [B_x] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => ~ hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotient__empty,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotient__is__empty2,axiom,
% 22.40/22.25 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( 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)
% 22.40/22.25 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotient__is__empty,axiom,
% 22.40/22.25 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Id__on__def_H,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Id__on__empty,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__Id__on,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotient__diff1,axiom,
% 22.40/22.25 ! [V_a_2,V_A_2,V_r_2,T_b] :
% 22.40/22.25 ( 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)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotientI,axiom,
% 22.40/22.25 ! [V_r_2,V_A_2,V_x_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Id__on__eqI,axiom,
% 22.40/22.25 ! [V_A_2,T_b,V_b_2,V_a_2] :
% 22.40/22.25 ( V_a_2 = V_b_2
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Id__on__iff,axiom,
% 22.40/22.25 ! [V_A_2,V_y_2,V_x_2,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 <=> ( V_x_2 = V_y_2
% 22.40/22.25 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_singleton__quotient,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_card__quotient__disjoint,axiom,
% 22.40/22.25 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( 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)
% 22.40/22.25 => 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) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equiv__class__nondisjoint,axiom,
% 22.40/22.25 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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)))))))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_subset__equiv__class,axiom,
% 22.40/22.25 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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))))))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotientE,axiom,
% 22.40/22.25 ! [V_r_2,V_A_2,V_X_2,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ~ ! [B_x] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equiv__intrel,axiom,
% 22.40/22.25 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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Union__quotient,axiom,
% 22.40/22.25 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => 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 ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equiv__class__self,axiom,
% 22.40/22.25 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 => 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)))))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotient__disj,axiom,
% 22.40/22.25 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( V_X_2 = V_Y_2
% 22.40/22.25 | 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)) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equiv__class__eq,axiom,
% 22.40/22.25 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotient__eq__iff,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 22.40/22.25 => ( V_X_2 = V_Y_2
% 22.40/22.25 <=> 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)) ) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_quotient__eqI,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_X_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_Y_2))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equiv__class__eq__iff,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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))
% 22.40/22.25 <=> ( 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))))
% 22.40/22.25 & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.25 & hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_eq__equiv__class,axiom,
% 22.40/22.25 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_eq__equiv__class__iff,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 22.40/22.25 => ( 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))))
% 22.40/22.25 <=> 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)) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equiv__class__subset,axiom,
% 22.40/22.25 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)))))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_eq__equiv__class__iff2,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
% 22.40/22.25 => ( 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)
% 22.40/22.25 <=> 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)) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UN__equiv__class2,axiom,
% 22.40/22.25 ! [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] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 22.40/22.25 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 22.40/22.25 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a1_2),V_A1_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a2_2),V_A2_2))
% 22.40/22.25 => 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) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UN__equiv__class,axiom,
% 22.40/22.25 ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 => 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) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equivp__equiv,axiom,
% 22.40/22.25 ! [V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_A_2)
% 22.40/22.25 <=> 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equivp__transp,axiom,
% 22.40/22.25 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equivp__symp,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equivp__reflp,axiom,
% 22.40/22.25 ! [V_x_2,V_R_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equivp__def,axiom,
% 22.40/22.25 ! [V_R_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.25 <=> ! [B_x,B_y] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 22.40/22.25 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_identity__equivp,axiom,
% 22.40/22.25 ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_congruent2__implies__congruent,axiom,
% 22.40/22.25 ! [V_a_2,V_f_2,V_r2_2,T_d,T_c,V_r1_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r1_2)
% 22.40/22.25 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 => c_Equiv__Relations_Ocongruent(T_c,T_d,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_congruent2D,axiom,
% 22.40/22.25 ! [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] :
% 22.40/22.25 ( c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2)
% 22.40/22.25 => ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_congruentD,axiom,
% 22.40/22.25 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_c,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 22.40/22.25 => ( 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))
% 22.40/22.25 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_congruent2__implies__congruent__UN,axiom,
% 22.40/22.25 ! [V_a_2,V_f_2,T_d,V_r2_2,V_A2_2,T_c,V_r1_2,V_A1_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 22.40/22.25 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 22.40/22.25 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A2_2))
% 22.40/22.25 => 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)) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UN__equiv__class__inject,axiom,
% 22.40/22.25 ! [V_Y_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 22.40/22.25 => ( 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)
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => ! [B_y] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_A_2))
% 22.40/22.25 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
% 22.40/22.25 => 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)) ) ) )
% 22.40/22.25 => V_X_2 = V_Y_2 ) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UN__equiv__class__type2,axiom,
% 22.40/22.25 ! [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] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A1_2,V_r1_2)
% 22.40/22.25 => ( c_Equiv__Relations_Oequiv(T_c,V_A2_2,V_r2_2)
% 22.40/22.25 => ( c_Equiv__Relations_Ocongruent2(T_b,T_c,tc_fun(T_d,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2)
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( ! [B_x1] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x1),V_A1_2))
% 22.40/22.25 => ! [B_x2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x2),V_A2_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) )
% 22.40/22.25 => 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)) ) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UN__equiv__class__type,axiom,
% 22.40/22.25 ! [V_B_2,V_X_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) )
% 22.40/22.25 => 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)) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Integ__def,axiom,
% 22.40/22.25 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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Id__onE,axiom,
% 22.40/22.25 ! [V_A_2,V_c_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_c_2),c_Relation_OId__on(T_b,V_A_2)))
% 22.40/22.25 => ~ ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom,
% 22.40/22.25 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.25 & class_Groups_Ocomm__monoid__mult(T_b) )
% 22.40/22.25 => ( V_A_2 = V_B_2
% 22.40/22.25 => ( c_Nat__Transfer_Onat__set(V_B_2)
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 22.40/22.25 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) )
% 22.40/22.25 => 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) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Rep__Integ,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_type__definition__Integ,axiom,
% 22.40/22.25 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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_accp__acc__eq,axiom,
% 22.40/22.25 ! [V_x_2,V_r_2,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_max__extp_Oequations,axiom,
% 22.40/22.25 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 22.40/22.25 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 22.40/22.25 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 22.40/22.25 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 22.40/22.25 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 & ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 22.40/22.25 => ? [B_xa] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 22.40/22.25 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_acc__subset,axiom,
% 22.40/22.25 ! [V_R2_2,V_R1_2,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_acc__downward,axiom,
% 22.40/22.25 ! [V_a_2,V_r_2,V_b_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_acc_Osimps,axiom,
% 22.40/22.25 ! [V_r_2,V_a_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 22.40/22.25 <=> ! [B_x] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_type__definition_ORep__range,axiom,
% 22.40/22.25 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 22.40/22.25 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 22.40/22.25 => 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 ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_type__definition_OAbs__image,axiom,
% 22.40/22.25 ! [V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 22.40/22.25 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_type__definition_OAbs__inject,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 22.40/22.25 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 22.40/22.25 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2)
% 22.40/22.25 <=> V_x_2 = V_y_2 ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_type__definition_ORep__inverse,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 22.40/22.25 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 22.40/22.25 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_type__definition_ORep__inject,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 22.40/22.25 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 22.40/22.25 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2)
% 22.40/22.25 <=> V_x_2 = V_y_2 ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_type__definition_ORep,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 22.40/22.25 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_type__definition_OAbs__inverse,axiom,
% 22.40/22.25 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_c,T_b] :
% 22.40/22.25 ( c_Typedef_Otype__definition(T_b,T_c,V_Rep_2,V_Abs_2,V_A_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),V_A_2))
% 22.40/22.25 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_max__ext_Ointros,axiom,
% 22.40/22.25 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 22.40/22.25 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 22.40/22.25 => ? [B_xa] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 22.40/22.25 & 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)) ) )
% 22.40/22.25 => 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))) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Nitpick_Ozero__frac__def,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_the__elem__def,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_The__split__eq,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_split__paired__The,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_the__inv__into__def,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fold__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_divmod__nat__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fold1__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_The__split,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Nitpick_Oone__frac__def,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Nitpick_Onumber__of__frac__def,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Nitpick_Ofrac__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_flat__lub__def,axiom,
% 22.40/22.25 ! [V_b_2,V_A_2,T_b] :
% 22.40/22.25 ( ( 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)))))
% 22.40/22.25 => c_Partial__Function_Oflat__lub(T_b,V_b_2,V_A_2) = V_b_2 )
% 22.40/22.25 & ( ~ 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)))))
% 22.40/22.25 => 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)))))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_inj__vimage__singleton,axiom,
% 22.40/22.25 ! [V_a_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.25 => 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))))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Rep__Integ__cases,axiom,
% 22.40/22.25 ! [V_y_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 22.40/22.25 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimageI,axiom,
% 22.40/22.25 ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
% 22.40/22.25 ( hAPP(V_f_2,V_a_2) = V_b_2
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__UNIV,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__empty,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__Un,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__INT,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__compose,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__ident,axiom,
% 22.40/22.25 ! [V_Y_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_COMBI(T_b)),V_Y_2) = V_Y_2 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__Compl,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__code,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2),V_x_2))
% 22.40/22.25 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__Int,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__mono,axiom,
% 22.40/22.25 ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__UN,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__Diff,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimageI2,axiom,
% 22.40/22.25 ! [T_c,V_A_2,V_a_2,V_f_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_A_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimageD,axiom,
% 22.40/22.25 ! [V_A_2,V_f_2,T_c,V_a_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_A_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__eq,axiom,
% 22.40/22.25 ! [V_B_2,V_f_2,T_c,V_a_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)))
% 22.40/22.25 <=> hBOOL(hAPP(hAPP(c_member(T_c),hAPP(V_f_2,V_a_2)),V_B_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_image__vimage__subset,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_surj__image__vimage__eq,axiom,
% 22.40/22.25 ! [V_A_2,V_f_2,T_b,T_c] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => 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 ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__Union,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__singleton__eq,axiom,
% 22.40/22.25 ! [V_b_2,V_f_2,T_c,V_a_2,T_b] :
% 22.40/22.25 ( 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))))))
% 22.40/22.25 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__insert,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__vimageD,axiom,
% 22.40/22.25 ! [V_F_2,V_h_2,T_c,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__subsetD,axiom,
% 22.40/22.25 ! [V_A_2,V_B_2,V_f_2,T_b,T_c] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_image__vimage__eq,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__vimageI,axiom,
% 22.40/22.25 ! [V_h_2,T_c,V_F_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
% 22.40/22.25 => ( c_Fun_Oinj__on(T_c,T_b,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Ovimage(T_c,T_b,V_h_2),V_F_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_inj__vimage__image__eq,axiom,
% 22.40/22.25 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.25 => 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 ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__const,axiom,
% 22.40/22.25 ! [T_c,V_A_2,V_c_2,T_b] :
% 22.40/22.25 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.40/22.25 => 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)) )
% 22.40/22.25 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__eq__UN,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__subsetI,axiom,
% 22.40/22.25 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__if,axiom,
% 22.40/22.25 ! [V_B_2,T_c,V_d_2,V_A_2,V_c_2,T_b] :
% 22.40/22.25 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.40/22.25 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 22.40/22.25 => 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)) )
% 22.40/22.25 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 22.40/22.25 => 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 ) ) )
% 22.40/22.25 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
% 22.40/22.25 => ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 22.40/22.25 => 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) )
% 22.40/22.25 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_d_2),V_A_2))
% 22.40/22.25 => 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)) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_image__split__eq__Sigma,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Rep__Integ__induct,axiom,
% 22.40/22.25 ! [V_P_2,V_y_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg))
% 22.40/22.25 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x)))
% 22.40/22.25 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_inj__on__INTER,axiom,
% 22.40/22.25 ! [V_A_2,V_f_2,T_d,T_c,T_b,V_I_2] :
% 22.40/22.25 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => ( ! [B_i] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_I_2))
% 22.40/22.25 => c_Fun_Oinj__on(T_c,T_d,V_f_2,hAPP(V_A_2,B_i)) )
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_SigmaI,axiom,
% 22.40/22.25 ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Times__eq__cancel2,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 22.40/22.25 => ( 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))
% 22.40/22.25 <=> V_A_2 = V_B_2 ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__Diff__distrib2,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Times__Diff__distrib1,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__Diff__distrib1,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__empty1,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__Union,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_card__cartesian__product,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__cartesian__product,axiom,
% 22.40/22.25 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Times__empty,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__empty2,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Compl__Times__UNIV2,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Compl__Times__UNIV1,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setprod__cartesian__product,axiom,
% 22.40/22.25 ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__mult(T_b)
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__Un__distrib1,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Times__Un__distrib1,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__Un__distrib2,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_swap__product,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__cartesian__product,axiom,
% 22.40/22.25 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.40/22.25 => 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)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_equiv__type,axiom,
% 22.40/22.25 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.25 => 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)))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__Int__distrib2,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Times__Int__distrib1,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__Int__distrib1,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Id__on__subset__Times,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UNIV__Times__UNIV,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_SigmaE2,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_SigmaD2,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_SigmaD1,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mem__Sigma__iff,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 & hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_card__cartesian__product__singleton,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Times__subset__cancel2,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_c,V_C_2,V_x_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_C_2))
% 22.40/22.25 => ( 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))))
% 22.40/22.25 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__subset,axiom,
% 22.40/22.25 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 => 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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__cartesian__productD1,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__cartesian__productD2,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_c,T_b] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fst__image__times,axiom,
% 22.40/22.25 ! [V_A_2,T_c,T_b,V_B_2] :
% 22.40/22.25 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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)) )
% 22.40/22.25 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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 ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_snd__image__times,axiom,
% 22.40/22.25 ! [V_B_2,T_c,T_b,V_A_2] :
% 22.40/22.25 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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)) )
% 22.40/22.25 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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 ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_insert__times__insert,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__equiv__class,axiom,
% 22.40/22.25 ! [V_X_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( 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))))
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__Times,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UN__Times__distrib,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Sigma__def,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__quotient,axiom,
% 22.40/22.25 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( 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))))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Ex__inj__on__UNION__Sigma,axiom,
% 22.40/22.25 ! [V_A_2,V_I_2,T_c,T_b] :
% 22.40/22.25 ? [B_f] :
% 22.40/22.25 ( 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))
% 22.40/22.25 & 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fold__image__Sigma,axiom,
% 22.40/22.25 ! [V_g_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__mult(T_d)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__SigmaI,axiom,
% 22.40/22.25 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( ! [B_a] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setprod__Sigma,axiom,
% 22.40/22.25 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__mult(T_d)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__Sigma,axiom,
% 22.40/22.25 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_d] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__add(T_d)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_card__SigmaI,axiom,
% 22.40/22.25 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_x))) )
% 22.40/22.25 => 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) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_SigmaE,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_c_2,T_c,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ~ ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => ! [B_y] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_c),B_y),hAPP(V_B_2,B_x)))
% 22.40/22.25 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair__surj,axiom,
% 22.40/22.25 ! [V_g_2,T_d,T_e,V_f_2,T_b,T_c] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair__inj__on,axiom,
% 22.40/22.25 ! [V_B_2,V_g_2,T_e,T_d,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.25 => ( c_Fun_Oinj__on(T_d,T_e,V_g_2,V_B_2)
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair__imageI,axiom,
% 22.40/22.25 ! [V_g_2,V_f_2,T_e,T_d,V_R_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair__ident,axiom,
% 22.40/22.25 ! [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 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_snd__prod__fun,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fst__map__pair,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair__simp,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_fst__comp__map__pair,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair_Ocomp,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair__compose,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair_Ocompositionality,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_snd__comp__map__pair,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair__surj__on,axiom,
% 22.40/22.25 ! [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] :
% 22.40/22.25 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 22.40/22.25 => ( hAPP(c_Set_Oimage(T_e,T_d,V_g_2),V_B_2) = V_B_H_2
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_prod__fun__imageE,axiom,
% 22.40/22.25 ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => ~ ! [B_x,B_y] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => ~ 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_refl__on__def,axiom,
% 22.40/22.25 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.25 <=> ( 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))))
% 22.40/22.25 & ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_card__less__Suc2,axiom,
% 22.40/22.25 ! [V_i_2,V_M_2] :
% 22.40/22.25 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 22.40/22.25 => 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))))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_CollectI,axiom,
% 22.40/22.25 ! [T_b,V_a_2,V_P_2] :
% 22.40/22.25 ( hBOOL(hAPP(V_P_2,V_a_2))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__Collect__conjI,axiom,
% 22.40/22.25 ! [V_Q_2,V_P_2,T_b] :
% 22.40/22.25 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 22.40/22.25 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) )
% 22.40/22.25 => 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)))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__Collect__less__nat,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__Collect__le__nat,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__split,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_SetCompr__Sigma__eq,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__neg__eq,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__Collect__eq,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_CollectE,axiom,
% 22.40/22.25 ! [V_P_2,V_a_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 22.40/22.25 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_CollectD,axiom,
% 22.40/22.25 ! [V_P_2,V_a_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 22.40/22.25 => hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_mem__Collect__eq,axiom,
% 22.40/22.25 ! [V_P_2,V_a_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 22.40/22.25 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__mem__eq,axiom,
% 22.40/22.25 ! [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 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_insert__Collect,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__Collect__disjI,axiom,
% 22.40/22.25 ! [V_Q_2,V_P_2,T_b] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 22.40/22.25 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Q_2))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__def,axiom,
% 22.40/22.25 ! [V_P_2,T_b] : hAPP(c_Set_OCollect(T_b),V_P_2) = V_P_2 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__conj__eq,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__disj__eq,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_empty__Collect__eq,axiom,
% 22.40/22.25 ! [V_P_2,T_b] :
% 22.40/22.25 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_P_2)
% 22.40/22.25 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__empty__eq,axiom,
% 22.40/22.25 ! [V_P_2,T_b] :
% 22.40/22.25 ( hAPP(c_Set_OCollect(T_b),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_empty__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_refl__on__Id__on,axiom,
% 22.40/22.25 ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_UNIV__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_insert__compr__raw,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_insert__compr,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Un__def,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Int__def,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Int__Collect,axiom,
% 22.40/22.25 ! [V_P_2,V_A_2,V_x_2,T_b] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.25 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__conv__if,axiom,
% 22.40/22.25 ! [T_b,V_a_2,V_P_2] :
% 22.40/22.25 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 22.40/22.25 => 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))) )
% 22.40/22.25 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__conv__if2,axiom,
% 22.40/22.25 ! [T_b,V_a_2,V_P_2] :
% 22.40/22.25 ( ( hBOOL(hAPP(V_P_2,V_a_2))
% 22.40/22.25 => 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))) )
% 22.40/22.25 & ( ~ hBOOL(hAPP(V_P_2,V_a_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_singleton__conv,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_singleton__conv2,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_set__diff__eq,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__Collect__not,axiom,
% 22.40/22.25 ! [V_P_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 22.40/22.25 => ( 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))))
% 22.40/22.25 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_insert__def,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Compl__eq,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Collect__imp__eq,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__M__bounded__by__nat,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_refl__on__empty,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_refl__on__Un,axiom,
% 22.40/22.25 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_refl__on__Int,axiom,
% 22.40/22.25 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__setsum__restrict,axiom,
% 22.40/22.25 ! [V_R_2,V_f_2,V_T_2,T_c,V_S_2,T_b,T_d] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__add(T_d)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 22.40/22.25 => 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) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_if__image__distrib,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_nat__seg__image__imp__finite,axiom,
% 22.40/22.25 ! [V_n_2,V_f_2,T_b,V_A_2] :
% 22.40/22.25 ( 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)))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_refl__onD,axiom,
% 22.40/22.25 ! [V_a_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_refl__onD1,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_refl__onD2,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
% 22.40/22.25 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.25 => ( 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))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__restrict__set_H,axiom,
% 22.40/22.25 ! [V_B_2,V_f_2,V_A_2,T_b,T_c] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => 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) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__image__gen,axiom,
% 22.40/22.25 ! [V_f_2,T_d,V_g_2,V_S_2,T_b,T_c] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Image__singleton,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__cases,axiom,
% 22.40/22.25 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_b,T_c] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => 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))))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_card__less__Suc,axiom,
% 22.40/22.25 ! [V_i_2,V_M_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 22.40/22.25 => 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))))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_card__less,axiom,
% 22.40/22.25 ! [V_i_2,V_M_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
% 22.40/22.25 => 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) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_refl__onI,axiom,
% 22.40/22.25 ! [V_A_2,V_r_2,T_b] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.25 => 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)) )
% 22.40/22.25 => c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__multicount,axiom,
% 22.40/22.25 ! [V_k_2,V_R_2,V_T_2,T_c,V_S_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_T_2))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_T_2))
% 22.40/22.25 => 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 )
% 22.40/22.25 => 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)) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_min__max_Osup__Inf1__distrib,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,T_b] :
% 22.40/22.25 ( class_Orderings_Olinorder(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__Collect__subsets,axiom,
% 22.40/22.25 ! [V_A_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => 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)))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Pow__Compl,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Pow__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__Collect__bounded__ex,axiom,
% 22.40/22.25 ! [V_Q_2,T_c,V_P_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 22.40/22.25 => ( 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)))))
% 22.40/22.25 <=> ! [B_y] :
% 22.40/22.25 ( hBOOL(hAPP(V_P_2,B_y))
% 22.40/22.25 => 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)))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__image__set,axiom,
% 22.40/22.25 ! [V_f_2,T_c,V_P_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_P_2)))
% 22.40/22.25 => 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))))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_inj__graph,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__psubset__def,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_inv__image__def,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_add__Min__commute,axiom,
% 22.40/22.25 ! [V_k_2,V_N_2,T_b] :
% 22.40/22.25 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.40/22.25 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_add__Max__commute,axiom,
% 22.40/22.25 ! [V_k_2,V_N_2,T_b] :
% 22.40/22.25 ( class_Groups_Olinordered__ab__semigroup__add(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_N_2))
% 22.40/22.25 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_sup__Inf1__distrib,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,T_b] :
% 22.40/22.25 ( class_Lattices_Odistrib__lattice(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_sup__Inf2__distrib,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( class_Lattices_Odistrib__lattice(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.40/22.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))))) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_inf__Sup1__distrib,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,T_b] :
% 22.40/22.25 ( class_Lattices_Odistrib__lattice(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_inf__Sup2__distrib,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( class_Lattices_Odistrib__lattice(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.40/22.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))))) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_min__max_Oinf__Sup1__distrib,axiom,
% 22.40/22.25 ! [V_x_2,V_A_2,T_b] :
% 22.40/22.25 ( class_Orderings_Olinorder(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_min__max_Oinf__Sup2__distrib,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( class_Orderings_Olinorder(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.40/22.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))))) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_min__max_Osup__Inf2__distrib,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( class_Orderings_Olinorder(T_b)
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
% 22.40/22.25 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 => 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))))))) ) ) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Nitpick_Oprod__def,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_int__ge__less__than__def,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_int__ge__less__than2__def,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_reflp__def,axiom,
% 22.40/22.25 ! [V_r_2,T_b] :
% 22.40/22.25 ( c_Predicate_Oreflp(T_b,V_r_2)
% 22.40/22.25 <=> 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__mult__setsum__if__inj,axiom,
% 22.40/22.25 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] :
% 22.40/22.25 ( class_Rings_Osemiring__0(T_d)
% 22.40/22.25 => ( 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)))
% 22.40/22.25 => 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))))))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__multicount__gen,axiom,
% 22.40/22.25 ! [V_k_2,V_R_2,V_t_2,T_c,V_s_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_s_2))
% 22.40/22.25 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_t_2))
% 22.40/22.25 => ( ! [B_x] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_t_2))
% 22.40/22.25 => 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) )
% 22.40/22.25 => 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) ) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_inj__on__id,axiom,
% 22.40/22.25 ! [V_A_2,T_b] : c_Fun_Oinj__on(T_b,T_b,c_Fun_Oid(T_b),V_A_2) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_of__int__eq__id,axiom,
% 22.40/22.25 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_o__eq__id__dest,axiom,
% 22.40/22.25 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_b,T_c,T_d] :
% 22.40/22.25 ( 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)
% 22.40/22.25 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_o__id,axiom,
% 22.40/22.25 ! [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 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_id__o,axiom,
% 22.40/22.25 ! [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 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_id__def,axiom,
% 22.40/22.25 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apsnd__id,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_reflpE,axiom,
% 22.40/22.25 ! [V_x_2,V_r_2,T_b] :
% 22.40/22.25 ( c_Predicate_Oreflp(T_b,V_r_2)
% 22.40/22.25 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_id__apply,axiom,
% 22.40/22.25 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apfst__id,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_vimage__id,axiom,
% 22.40/22.25 ! [V_A_2,T_b] : hAPP(c_Set_Ovimage(T_b,T_b,c_Fun_Oid(T_b)),V_A_2) = V_A_2 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair_Oid,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_map__pair_Oidentity,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_image__id,axiom,
% 22.40/22.25 ! [V_Y_2,T_b] : hAPP(c_Set_Oimage(T_b,T_b,c_Fun_Oid(T_b)),V_Y_2) = V_Y_2 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_surj__id,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_folding_Oempty,axiom,
% 22.40/22.25 ! [V_F_2,V_f_2,T_c,T_b] :
% 22.40/22.25 ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
% 22.40/22.25 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apsnd__def,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_apfst__def,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_split__Pair,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setsum__reindex__id,axiom,
% 22.40/22.25 ! [V_B_2,V_f_2,T_b,T_c] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.25 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_setprod__reindex__id,axiom,
% 22.40/22.25 ! [V_B_2,V_f_2,T_b,T_c] :
% 22.40/22.25 ( class_Groups_Ocomm__monoid__mult(T_c)
% 22.40/22.25 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_B_2)
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__conv__nat__seg__image,axiom,
% 22.40/22.25 ! [V_A_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.25 <=> ? [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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__comp__def,axiom,
% 22.40/22.25 ! [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))))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__Collect__split,axiom,
% 22.40/22.25 ! [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))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__compI,axiom,
% 22.40/22.25 ! [V_s_2,V_c_2,T_d,V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_RangeI,axiom,
% 22.40/22.25 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__comp__UNION__distrib2,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__comp__UNION__distrib,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__comp__empty2,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__comp__empty1,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__comp__distrib,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__comp__distrib2,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_O__assoc,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__comp__mono,axiom,
% 22.40/22.25 ! [V_s_2,V_s_H_2,T_d,V_r_2,V_r_H_2,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__Id__on,axiom,
% 22.40/22.25 ! [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 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_union__comp__emptyR,axiom,
% 22.40/22.25 ! [V_C_2,V_B_2,V_A_2,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_union__comp__emptyL,axiom,
% 22.40/22.25 ! [V_B_2,V_C_2,V_A_2,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__Union,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__empty,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__empty__iff,axiom,
% 22.40/22.25 ! [V_r_2,T_b,T_c] :
% 22.40/22.25 ( hAPP(c_Relation_ORange(T_c,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.25 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_c,T_b),tc_HOL_Obool)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_rel__comp__subset__Sigma,axiom,
% 22.40/22.25 ! [V_C_2,V_s_2,T_d,V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 22.40/22.25 ( 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))))
% 22.40/22.25 => ( 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))))
% 22.40/22.25 => 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)))) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__Un__eq,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_finite__Range,axiom,
% 22.40/22.25 ! [V_r_2,T_c,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 22.40/22.25 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_snd__eq__Range,axiom,
% 22.40/22.25 ! [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) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__iff,axiom,
% 22.40/22.25 ! [V_r_2,T_c,V_a_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 22.40/22.25 <=> ? [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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__insert,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__Int__subset,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Range__Diff__subset,axiom,
% 22.40/22.25 ! [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)))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_max__ext__compat,axiom,
% 22.40/22.25 ! [V_S_2,V_R_2,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_min__ext__compat,axiom,
% 22.40/22.25 ! [V_S_2,V_R_2,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_RangeP__Range__eq,axiom,
% 22.40/22.25 ! [V_x_2,V_r_2,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Relation_ORange(T_b,T_c),V_r_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_RangeE,axiom,
% 22.40/22.25 ! [V_r_2,T_c,V_b_2,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_c,T_b),V_r_2)))
% 22.40/22.25 => ~ ! [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)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pred__comp__rel__comp__eq,axiom,
% 22.40/22.25 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 <=> 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))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pred__comp_Ointros,axiom,
% 22.40/22.25 ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 22.40/22.25 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_RangeP_Ointros,axiom,
% 22.40/22.25 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 22.40/22.25 => hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_b_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_pred__comp_Oequations,axiom,
% 22.40/22.25 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 <=> ? [B_b] :
% 22.40/22.25 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b))
% 22.40/22.25 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_RangeP_Oequations,axiom,
% 22.40/22.25 ! [V_a2_2,V_r_2,T_c,T_b] :
% 22.40/22.25 ( hBOOL(hAPP(c_Predicate_ORangeP(T_b,T_c,V_r_2),V_a2_2))
% 22.40/22.25 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_reduction__pairI,axiom,
% 22.40/22.25 ! [V_S_2,V_R_2,T_b] :
% 22.40/22.25 ( c_Wellfounded_Owf(T_b,V_R_2)
% 22.40/22.25 => ( 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))
% 22.40/22.25 => 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)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_Domain__Collect__split,axiom,
% 22.40/22.25 ! [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)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_the__eq__trivial,axiom,
% 22.40/22.25 ! [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 ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wf__less__than,axiom,
% 22.40/22.25 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wf__empty,axiom,
% 22.40/22.25 ! [T_b] : c_Wellfounded_Owf(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wf__inv__image,axiom,
% 22.40/22.25 ! [V_f_2,T_c,V_r_2,T_b] :
% 22.40/22.25 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.25 => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wf__lex__prod,axiom,
% 22.40/22.25 ! [V_rb_2,T_c,V_ra_2,T_b] :
% 22.40/22.25 ( c_Wellfounded_Owf(T_b,V_ra_2)
% 22.40/22.25 => ( c_Wellfounded_Owf(T_c,V_rb_2)
% 22.40/22.25 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wf__measure,axiom,
% 22.40/22.25 ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_DomainI,axiom,
% 22.40/22.25 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.25 ( 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))
% 22.40/22.25 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 22.40/22.25
% 22.40/22.25 fof(fact_wf__comp__self,axiom,
% 22.40/22.26 ! [V_R_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_R_2)
% 22.40/22.26 <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_min__ext__wf,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_b,V_r_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__subset,axiom,
% 22.40/22.26 ! [V_p_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => c_Wellfounded_Owf(T_b,V_p_2) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__irrefl,axiom,
% 22.40/22.26 ! [V_a_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => ~ 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__asym,axiom,
% 22.40/22.26 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => ~ 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__not__sym,axiom,
% 22.40/22.26 ! [V_x_2,V_a_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => ~ 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__not__refl,axiom,
% 22.40/22.26 ! [V_a_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => ~ 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_max__ext__wf,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_b,V_r_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__pair__less,axiom,
% 22.40/22.26 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__finite__psubset,axiom,
% 22.40/22.26 ! [T_b] : c_Wellfounded_Owf(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__mlex,axiom,
% 22.40/22.26 ! [V_f_2,V_R_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_R_2)
% 22.40/22.26 => c_Wellfounded_Owf(T_b,c_Wellfounded_Omlex__prod(T_b,V_f_2,V_R_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__Int1,axiom,
% 22.40/22.26 ! [V_r_H_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__Int2,axiom,
% 22.40/22.26 ! [V_r_H_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__Id__on,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__less,axiom,
% 22.40/22.26 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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__int__ge__less__than2,axiom,
% 22.40/22.26 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__int__ge__less__than,axiom,
% 22.40/22.26 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__Un,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => ( c_Wellfounded_Owf(T_b,V_s_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__acc__iff,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_acc__wfD,axiom,
% 22.40/22.26 ! [V_x_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__no__loop,axiom,
% 22.40/22.26 ! [V_R_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__union__merge,axiom,
% 22.40/22.26 ! [V_S_2,V_R_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 <=> 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__empty,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__empty__iff,axiom,
% 22.40/22.26 ! [V_r_2,T_c,T_b] :
% 22.40/22.26 ( hAPP(c_Relation_ODomain(T_b,T_c),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.26 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__mono,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,T_c,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__Un__eq,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__Domain,axiom,
% 22.40/22.26 ! [V_r_2,T_c,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),V_r_2))
% 22.40/22.26 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_fst__eq__Domain,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__iff__no__infinite__down__chain,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 <=> ~ ? [B_f] :
% 22.40/22.26 ! [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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wfE__pf,axiom,
% 22.40/22.26 ! [V_A_2,V_R_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_R_2)
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__union__compatible,axiom,
% 22.40/22.26 ! [V_S_2,V_R_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_R_2)
% 22.40/22.26 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__iff,axiom,
% 22.40/22.26 ! [V_r_2,T_c,V_a_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 22.40/22.26 <=> ? [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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf,axiom,
% 22.40/22.26 ! [T_b] :
% 22.40/22.26 ( class_Orderings_Owellorder(T_b)
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__insert,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_reduction__pair__def,axiom,
% 22.40/22.26 ! [V_P_2,T_b] :
% 22.40/22.26 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 22.40/22.26 <=> ( 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))
% 22.40/22.26 & 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_reduction__pair__lemma,axiom,
% 22.40/22.26 ! [V_S_2,V_R_2,V_P_2,T_b] :
% 22.40/22.26 ( c_FunDef_Oreduction__pair(T_b,V_P_2)
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => ( c_Wellfounded_Owf(T_b,V_S_2)
% 22.40/22.26 => 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)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__Int__subset,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__Diff__subset,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Field__def,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__map__pair__image,axiom,
% 22.40/22.26 ! [V_f_2,T_c,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__Union,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_the__sym__eq__trivial,axiom,
% 22.40/22.26 ! [V_x_2,T_b] : c_HOL_OThe(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_DomainP__Domain__eq,axiom,
% 22.40/22.26 ! [V_x_2,V_r_2,T_c,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__lenlex,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olenlex(T_b,V_r_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_DomainE,axiom,
% 22.40/22.26 ! [V_r_2,T_c,V_a_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Relation_ODomain(T_b,T_c),V_r_2)))
% 22.40/22.26 => ~ ! [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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_DomainP_Ointros,axiom,
% 22.40/22.26 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 22.40/22.26 => hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_DomainP_Oequations,axiom,
% 22.40/22.26 ! [V_a1_2,V_r_2,T_c,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Predicate_ODomainP(T_b,T_c,V_r_2),V_a1_2))
% 22.40/22.26 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_pred__nat__def,axiom,
% 22.40/22.26 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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__lex,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => c_Wellfounded_Owf(tc_List_Olist(T_b),c_List_Olex(T_b,V_r_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__lexn,axiom,
% 22.40/22.26 ! [V_n_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => c_Wellfounded_Owf(tc_List_Olist(T_b),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lex__def,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexn_Osimps_I1_J,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__pred__nat,axiom,
% 22.40/22.26 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__same__fst,axiom,
% 22.40/22.26 ! [T_b,V_R_2,T_c,V_P_2] :
% 22.40/22.26 ( ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(V_P_2,B_x))
% 22.40/22.26 => c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x)) )
% 22.40/22.26 => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_P_2,V_R_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__if__measure,axiom,
% 22.40/22.26 ! [T_b,V_g_2,V_f_2,V_P_2] :
% 22.40/22.26 ( ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(V_P_2,B_x))
% 22.40/22.26 => 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))) )
% 22.40/22.26 => 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))))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wfP__def,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 22.40/22.26 <=> 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wfP__empty,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_accp__wfPD,axiom,
% 22.40/22.26 ! [V_x_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 22.40/22.26 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_x_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wfP__accp__iff,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 22.40/22.26 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x1)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wfP__subset,axiom,
% 22.40/22.26 ! [V_p_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => c_Wellfounded_OwfP(T_b,V_p_2) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__in__rel,axiom,
% 22.40/22.26 ! [V_R_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_R_2)
% 22.40/22.26 => c_Wellfounded_OwfP(T_b,c_FunDef_Oin__rel(T_b,T_b,V_R_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wfP__wf__eq,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 <=> c_Wellfounded_Owf(T_b,V_r_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wfP__acyclicP,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_OwfP(T_b,V_r_2)
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_pigeonhole__infinite,axiom,
% 22.40/22.26 ! [V_f_2,T_c,V_A_2,T_b] :
% 22.40/22.26 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 22.40/22.26 => ? [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.26 & ~ 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)))))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_refl__on__def_H,axiom,
% 22.40/22.26 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.26 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.26 <=> ( ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 22.40/22.26 => 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)) )
% 22.40/22.26 & ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.26 => 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)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_ball__empty,axiom,
% 22.40/22.26 ! [V_P_2,T_b,B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 22.40/22.26 => hBOOL(hAPP(V_P_2,B_x)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__acyclic,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_acyclic__subset,axiom,
% 22.40/22.26 ! [V_r_2,V_s_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Oacyclic(T_b,V_s_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_INFI__bool__eq,axiom,
% 22.40/22.26 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Powp__def,axiom,
% 22.40/22.26 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Predicate_OPowp(T_b,V_A_2),V_B_2))
% 22.40/22.26 <=> ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
% 22.40/22.26 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Collect__ball__eq,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_congruent__def,axiom,
% 22.40/22.26 ! [V_f_2,V_r_2,T_c,T_b] :
% 22.40/22.26 ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
% 22.40/22.26 <=> ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_INTER__def,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__iff__acyclic__if__finite,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 22.40/22.26 => ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__acyclic__wf,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 22.40/22.26 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 22.40/22.26 => c_Wellfounded_Owf(T_b,V_r_2) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Sup__Inf,axiom,
% 22.40/22.26 ! [V_A_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => 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)))))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Inf__Sup,axiom,
% 22.40/22.26 ! [V_A_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => 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))))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Owf_H__def,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Nitpick_Owf_H(T_b,V_r_2)
% 22.40/22.26 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 22.40/22.26 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 22.40/22.26 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Abs__Integ__induct,axiom,
% 22.40/22.26 ! [V_x_2,V_P_2] :
% 22.40/22.26 ( ! [B_y] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg))
% 22.40/22.26 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) )
% 22.40/22.26 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Abs__Integ__cases,axiom,
% 22.40/22.26 ! [V_x_2] :
% 22.40/22.26 ~ ! [B_y] :
% 22.40/22.26 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
% 22.40/22.26 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Inter__eq,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__UN__I,axiom,
% 22.40/22.26 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.26 => ( ! [B_a] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 22.40/22.26 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_B_2,B_a))) )
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_inj__on__diff__nat,axiom,
% 22.40/22.26 ! [V_k_2,V_N_2] :
% 22.40/22.26 ( ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) )
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wfP__SUP,axiom,
% 22.40/22.26 ! [T_b,V_r_2,T_c] :
% 22.40/22.26 ( ! [B_i] : c_Wellfounded_OwfP(T_c,hAPP(V_r_2,B_i))
% 22.40/22.26 => ( ! [B_i,B_j] :
% 22.40/22.26 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j)
% 22.40/22.26 => 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)) )
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_mem__splitI2,axiom,
% 22.40/22.26 ! [V_c_2,V_z_2,T_d,T_c,T_b,V_p_2] :
% 22.40/22.26 ( ! [B_a,B_b] :
% 22.40/22.26 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_d),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) )
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_mem__splitE,axiom,
% 22.40/22.26 ! [V_p_2,V_c_2,T_d,T_c,V_z_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ~ ! [B_x,B_y] :
% 22.40/22.26 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_c,T_d),B_x),B_y)
% 22.40/22.26 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Eps__split,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_exE__some,axiom,
% 22.40/22.26 ! [T_b,V_c_2,V_P_2] :
% 22.40/22.26 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 22.40/22.26 => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_P_2)
% 22.40/22.26 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_some__sym__eq__trivial,axiom,
% 22.40/22.26 ! [V_x_2,T_b] : c_Hilbert__Choice_OEps(T_b,hAPP(c_fequal,V_x_2)) = V_x_2 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_some__eq__trivial,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_some__eq__ex,axiom,
% 22.40/22.26 ! [T_b,V_P_2] :
% 22.40/22.26 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2)))
% 22.40/22.26 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_someI__ex,axiom,
% 22.40/22.26 ! [T_b,V_P_2] :
% 22.40/22.26 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 22.40/22.26 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_tfl__some,axiom,
% 22.40/22.26 ! [T_b,B_P] :
% 22.40/22.26 ( ? [B_x] : hBOOL(hAPP(B_P,B_x))
% 22.40/22.26 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_b,B_P))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_someI,axiom,
% 22.40/22.26 ! [T_b,V_x_2,V_P_2] :
% 22.40/22.26 ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.26 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_b,V_P_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_split__paired__Eps,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Eps__split__eq,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wfI__pf,axiom,
% 22.40/22.26 ! [V_R_2,T_b] :
% 22.40/22.26 ( ! [B_A] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
% 22.40/22.26 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Sigma__mono,axiom,
% 22.40/22.26 ! [V_D_2,V_B_2,T_c,V_C_2,V_A_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2))
% 22.40/22.26 => ( ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.26 => 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))) )
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_not__acc__down,axiom,
% 22.40/22.26 ! [V_R_2,V_x_2,T_b] :
% 22.40/22.26 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_R_2)))
% 22.40/22.26 => ~ ! [B_z] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),B_z),c_Wellfounded_Oacc(T_b,V_R_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_acc_OaccI,axiom,
% 22.40/22.26 ! [V_r_2,V_x_2,T_b] :
% 22.40/22.26 ( ! [B_y] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),B_y),c_Wellfounded_Oacc(T_b,V_r_2))) )
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_max__ext_Osimps,axiom,
% 22.40/22.26 ! [V_R_2,V_a2_2,V_a1_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 22.40/22.26 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 22.40/22.26 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.26 & ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 22.40/22.26 => ? [B_xa] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 22.40/22.26 & 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)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_def__coinduct__set,axiom,
% 22.40/22.26 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 22.40/22.26 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 22.40/22.26 => ( 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))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_def__gfp__unfold,axiom,
% 22.40/22.26 ! [V_f_2,V_A_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => V_A_2 = hAPP(V_f_2,V_A_2) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_gfp__unfold,axiom,
% 22.40/22.26 ! [V_f_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_gfp__upperbound,axiom,
% 22.40/22.26 ! [V_f_2,V_X_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),hAPP(V_f_2,V_X_2)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_weak__coinduct,axiom,
% 22.40/22.26 ! [V_f_2,V_X_2,V_a_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_gfp__lemma3,axiom,
% 22.40/22.26 ! [V_f_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_gfp__lemma2,axiom,
% 22.40/22.26 ! [V_f_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => 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)))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_weak__coinduct__image,axiom,
% 22.40/22.26 ! [V_f_2,V_g_2,T_c,V_X_2,V_a_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 22.40/22.26 => ( 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))))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_gfp__fun__UnI2,axiom,
% 22.40/22.26 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 22.40/22.26 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_def__coinduct,axiom,
% 22.40/22.26 ! [V_X_2,V_f_2,V_A_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_b,V_f_2)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => ( 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))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_X_2),V_A_2)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_coinduct__lemma,axiom,
% 22.40/22.26 ! [V_f_2,V_X_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( 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)))))
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => 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))))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_coinduct,axiom,
% 22.40/22.26 ! [V_X_2,V_f_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => ( 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)))))
% 22.40/22.26 => 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_coinduct__set,axiom,
% 22.40/22.26 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 22.40/22.26 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 22.40/22.26 => ( 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)))))
% 22.40/22.26 => 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_coinduct3,axiom,
% 22.40/22.26 ! [V_X_2,V_a_2,V_f_2,T_b] :
% 22.40/22.26 ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 22.40/22.26 => ( 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))))))
% 22.40/22.26 => 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_def__coinduct3,axiom,
% 22.40/22.26 ! [V_X_2,V_a_2,V_f_2,T_b,V_A_2] :
% 22.40/22.26 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 22.40/22.26 => ( 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)))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_def__Collect__coinduct,axiom,
% 22.40/22.26 ! [V_X_2,V_a_2,V_P_2,T_b,V_A_2] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_X_2))
% 22.40/22.26 => ( ! [B_z] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_z),V_X_2))
% 22.40/22.26 => 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)) )
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lfp__lowerbound,axiom,
% 22.40/22.26 ! [V_A_2,V_f_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_A_2)),V_A_2))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lfp__unfold,axiom,
% 22.40/22.26 ! [V_f_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_def__lfp__unfold,axiom,
% 22.40/22.26 ! [V_f_2,V_h_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => V_h_2 = hAPP(V_f_2,V_h_2) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lfp__const,axiom,
% 22.40/22.26 ! [V_t_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => c_Inductive_Ocomplete__lattice__class_Olfp(T_b,hAPP(c_COMBK(T_b,T_b),V_t_2)) = V_t_2 ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lfp__lemma3,axiom,
% 22.40/22.26 ! [V_f_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => 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)))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lfp__lemma2,axiom,
% 22.40/22.26 ! [V_f_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lfp__induct,axiom,
% 22.40/22.26 ! [V_P_2,V_f_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_def__lfp__induct,axiom,
% 22.40/22.26 ! [V_P_2,V_f_2,V_A_2,T_b] :
% 22.40/22.26 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.26 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_b,V_f_2)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(T_b,T_b,V_f_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_A_2),V_P_2)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_coinduct3__lemma,axiom,
% 22.40/22.26 ! [V_f_2,V_X_2,T_b] :
% 22.40/22.26 ( 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))))))
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => 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)))))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_def__lfp__induct__set,axiom,
% 22.40/22.26 ! [V_P_2,V_a_2,V_f_2,T_b,V_A_2] :
% 22.40/22.26 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.26 => ( ! [B_x] :
% 22.40/22.26 ( 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)))))
% 22.40/22.26 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.26 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lfp__induct__set,axiom,
% 22.40/22.26 ! [V_P_2,V_f_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2)
% 22.40/22.26 => ( ! [B_x] :
% 22.40/22.26 ( 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)))))
% 22.40/22.26 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.26 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lfp__induct2,axiom,
% 22.40/22.26 ! [V_P_2,V_f_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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)
% 22.40/22.26 => ( ! [B_a,B_b] :
% 22.40/22.26 ( 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))))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) )
% 22.40/22.26 => hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__no__infinite__down__chainE,axiom,
% 22.40/22.26 ! [V_f_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => ~ ! [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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_iterate_Osimps,axiom,
% 22.40/22.26 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 22.40/22.26 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_scomp__unfold,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_scomp__scomp,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_scomp__Pair,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Pair__scomp,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_scomp__apply,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_scomp__def,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_less__eq,axiom,
% 22.40/22.26 ! [V_n_2,V_m_2] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__eq__minimal,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 <=> ! [B_Q] :
% 22.40/22.26 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 22.40/22.26 => ? [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_Q))
% 22.40/22.26 & ! [B_y] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_y),B_Q)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__trancl,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 => c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_less__than__def,axiom,
% 22.40/22.26 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_acyclic__def,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 22.40/22.26 <=> ! [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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl_Or__into__trancl,axiom,
% 22.40/22.26 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__subset__Field2,axiom,
% 22.40/22.26 ! [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))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_r__into__trancl_H,axiom,
% 22.40/22.26 ! [V_r_2,V_p_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__empty,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__domain,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__range,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__trancl,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 22.40/22.26 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__trans,axiom,
% 22.40/22.26 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
% 22.40/22.26 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__into__trancl2,axiom,
% 22.40/22.26 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_r__r__into__trancl,axiom,
% 22.40/22.26 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__mono,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,V_p_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_s_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__unfold,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__subset__Sigma,axiom,
% 22.40/22.26 ! [V_A_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__Int__subset,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__insert,axiom,
% 22.40/22.26 ! [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)))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_reflcl__set__eq,axiom,
% 22.40/22.26 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 <=> 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_r__into__rtrancl,axiom,
% 22.40/22.26 ! [V_r_2,V_p_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),V_r_2))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl_Ortrancl__refl,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_IdI,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__into__rtrancl,axiom,
% 22.40/22.26 ! [V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__unfold__left,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__unfold__right,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__reflcl,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_reflcl__trancl,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__trancl__absorb,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__rtrancl__absorb,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__rtrancl,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Range__rtrancl,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_refl__rtrancl,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__idemp,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__trans,axiom,
% 22.40/22.26 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
% 22.40/22.26 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__rtrancl__into__rtrancl,axiom,
% 22.40/22.26 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__r__diff__Id,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__rtrancl__UnI,axiom,
% 22.40/22.26 ! [V_S_2,V_R_2,V_x_2,T_b] :
% 22.40/22.26 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 22.40/22.26 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_x_2),c_Transitive__Closure_Ortrancl(T_b,V_S_2))) )
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__mono,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__subset,axiom,
% 22.40/22.26 ! [V_S_2,V_R_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => c_Transitive__Closure_Ortrancl(T_b,V_S_2) = c_Transitive__Closure_Ortrancl(T_b,V_R_2) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__subset__rtrancl,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__reflcl__absorb,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__Un__rtrancl,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__reflcl,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__Un__subset,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Image__closed__trancl,axiom,
% 22.40/22.26 ! [V_X_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => hAPP(c_Relation_OImage(T_b,T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_X_2) = V_X_2 ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__unfold,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__idemp__self__comp,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_r__comp__rtrancl__eq,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__Int__subset,axiom,
% 22.40/22.26 ! [V_r_2,V_s_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__empty,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_R__O__Id,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Id__O__R,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Image__Id,axiom,
% 22.40/22.26 ! [V_A_2,T_b] : hAPP(c_Relation_OImage(T_b,T_b,c_Relation_OId(T_b)),V_A_2) = V_A_2 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_pair__in__Id__conv,axiom,
% 22.40/22.26 ! [V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> V_a_2 = V_b_2 ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__trancl__trancl,axiom,
% 22.40/22.26 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__rtrancl__trancl,axiom,
% 22.40/22.26 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__into__trancl1,axiom,
% 22.40/22.26 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtranclD,axiom,
% 22.40/22.26 ! [V_R_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( V_a_2 = V_b_2
% 22.40/22.26 | ( V_a_2 != V_b_2
% 22.40/22.26 & 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__into__trancl2,axiom,
% 22.40/22.26 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__eq__or__trancl,axiom,
% 22.40/22.26 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( V_x_2 = V_y_2
% 22.40/22.26 | ( V_x_2 != V_y_2
% 22.40/22.26 & 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__Id,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Range__Id,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_refl__Id,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_pair__leq__def,axiom,
% 22.40/22.26 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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Not__Domain__rtrancl,axiom,
% 22.40/22.26 ! [V_y_2,V_R_2,V_x_2,T_b] :
% 22.40/22.26 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ODomain(T_b,T_b),V_R_2)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 <=> V_x_2 = V_y_2 ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_acc__downwards,axiom,
% 22.40/22.26 ! [V_b_2,V_r_2,V_a_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_acc__downwards__aux,axiom,
% 22.40/22.26 ! [V_r_2,V_a_2,V_b_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__insert,axiom,
% 22.40/22.26 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 <=> ( c_Wellfounded_Owf(T_b,V_r_2)
% 22.40/22.26 & ~ 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_acyclic__insert,axiom,
% 22.40/22.26 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 <=> ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 22.40/22.26 & ~ 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_refl__reflcl,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Id__def,axiom,
% 22.40/22.26 ! [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))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_irrefl__diff__Id,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_pred__nat__trancl__eq__le,axiom,
% 22.40/22.26 ! [V_n_2,V_m_2] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__subset__Sigma__aux,axiom,
% 22.40/22.26 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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))))
% 22.40/22.26 => ( V_a_2 = V_b_2
% 22.40/22.26 | hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_irrefl__tranclI,axiom,
% 22.40/22.26 ! [V_x_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ~ 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_sequence__trans,axiom,
% 22.40/22.26 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_b] :
% 22.40/22.26 ( ! [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)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__converse,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__Id,axiom,
% 22.40/22.26 ! [T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),c_Relation_OId(T_b)) = c_Relation_OId(T_b) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_acyclic__converse,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Oacyclic(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 22.40/22.26 <=> c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_refl__on__converse,axiom,
% 22.40/22.26 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.26 ( c_Relation_Orefl__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 22.40/22.26 <=> c_Relation_Orefl__on(T_b,V_A_2,V_r_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__Id__on,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__inv__image,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__converse,axiom,
% 22.40/22.26 ! [V_r_2,T_c,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_c)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
% 22.40/22.26 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_c,T_b)),V_r_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__Int,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__converse,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Field__converse,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__iff,axiom,
% 22.40/22.26 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converseI,axiom,
% 22.40/22.26 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converseD,axiom,
% 22.40/22.26 ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__Un,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__rel__comp,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__UNION,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__INTER,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__converse,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__converse__trancl,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 22.40/22.26 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_equiv__comp__eq,axiom,
% 22.40/22.26 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.26 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.26 => 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 ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Range__def,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Domain__converse,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Range__converse,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__converseI,axiom,
% 22.40/22.26 ! [V_r_2,V_x_2,V_y_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__converseD,axiom,
% 22.40/22.26 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__converseI,axiom,
% 22.40/22.26 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__converseD,axiom,
% 22.40/22.26 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Image__subset__eq,axiom,
% 22.40/22.26 ! [V_B_2,V_A_2,V_r_2,T_c,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 <=> 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))))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_refl__on__comp__subset,axiom,
% 22.40/22.26 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.26 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_comp__equivI,axiom,
% 22.40/22.26 ! [V_A_2,V_r_2,T_b] :
% 22.40/22.26 ( 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
% 22.40/22.26 => ( hAPP(c_Relation_ODomain(T_b,T_b),V_r_2) = V_A_2
% 22.40/22.26 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__acyclic__wf__converse,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_b)),V_r_2))
% 22.40/22.26 => ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 22.40/22.26 => c_Wellfounded_Owf(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converse__def,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Image__INT__eq,axiom,
% 22.40/22.26 ! [V_B_2,T_d,V_A_2,V_r_2,T_c,T_b] :
% 22.40/22.26 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2))
% 22.40/22.26 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_d,tc_HOL_Obool))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_total__on__diff__Id,axiom,
% 22.40/22.26 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_single__valued__Id,axiom,
% 22.40/22.26 ! [T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId(T_b)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_single__valued__subset,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,T_c,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2)
% 22.40/22.26 => c_Relation_Osingle__valued(T_b,T_c,V_r_2) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_single__valued__rel__comp,axiom,
% 22.40/22.26 ! [V_s_2,T_d,V_r_2,T_c,T_b] :
% 22.40/22.26 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 22.40/22.26 => ( c_Relation_Osingle__valued(T_c,T_d,V_s_2)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_single__valued__Id__on,axiom,
% 22.40/22.26 ! [V_A_2,T_b] : c_Relation_Osingle__valued(T_b,T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_total__on__empty,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_total__on__converse,axiom,
% 22.40/22.26 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.26 ( c_Relation_Ototal__on(T_b,V_A_2,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 22.40/22.26 <=> c_Relation_Ototal__on(T_b,V_A_2,V_r_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_single__valuedD,axiom,
% 22.40/22.26 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 22.40/22.26 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => V_y_2 = V_z_2 ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_single__valued__def,axiom,
% 22.40/22.26 ! [V_r_2,T_c,T_b] :
% 22.40/22.26 ( c_Relation_Osingle__valued(T_b,T_c,V_r_2)
% 22.40/22.26 <=> ! [B_x,B_y] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ! [B_z] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => B_y = B_z ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_total__on__def,axiom,
% 22.40/22.26 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.26 ( c_Relation_Ototal__on(T_b,V_A_2,V_r_2)
% 22.40/22.26 <=> ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.26 => ! [B_xa] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_A_2))
% 22.40/22.26 => ( B_x != B_xa
% 22.40/22.26 => ( 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))
% 22.40/22.26 | 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)) ) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_single__valued__confluent,axiom,
% 22.40/22.26 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 22.40/22.26 ( c_Relation_Osingle__valued(T_b,T_b,V_r_2)
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 | 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))) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Image__Int__eq,axiom,
% 22.40/22.26 ! [V_B_2,V_A_2,V_R_2,T_c,T_b] :
% 22.40/22.26 ( c_Relation_Osingle__valued(T_b,T_c,hAPP(c_Relation_Oconverse(T_c,T_b),V_R_2))
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__imp__UN__rel__pow,axiom,
% 22.40/22.26 ! [V_R_2,V_p_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_acyclicI,axiom,
% 22.40/22.26 ! [V_r_2,T_b] :
% 22.40/22.26 ( ! [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)))
% 22.40/22.26 => c_Wellfounded_Oacyclic(T_b,V_r_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_single__valued__rel__pow,axiom,
% 22.40/22.26 ! [V_n_2,V_R_2,T_b] :
% 22.40/22.26 ( c_Relation_Osingle__valued(T_b,T_b,V_R_2)
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_comp__funpow,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_funpow__swap1,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_funpow__mult,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_wf__exp,axiom,
% 22.40/22.26 ! [V_R_2,V_n_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => c_Wellfounded_Owf(T_b,V_R_2) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__commute,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__1,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__power,axiom,
% 22.40/22.26 ! [V_R_2,V_p_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
% 22.40/22.26 <=> ? [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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__imp__rtrancl,axiom,
% 22.40/22.26 ! [V_R_2,V_n_2,V_p_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_relpow_Osimps_I2_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__add,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_relpow_Osimps_I1_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__0__E,axiom,
% 22.40/22.26 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => V_x_2 = V_y_2 ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__0__I,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__Suc__I2,axiom,
% 22.40/22.26 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__Suc__I,axiom,
% 22.40/22.26 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_funpow_Osimps_I2_J,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_funpow__add,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_funpow_Osimps_I1_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_trancl__power,axiom,
% 22.40/22.26 ! [V_R_2,V_p_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
% 22.40/22.26 <=> ? [B_n] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n))
% 22.40/22.26 & 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__is__UN__rel__pow,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_funpow__code__def,axiom,
% 22.40/22.26 ! [T_b] : c_Nat_Ofunpow(T_b) = c_Nat_Ocompow(T_b,T_b) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__E2,axiom,
% 22.40/22.26 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => V_x_2 != V_z_2 )
% 22.40/22.26 => ~ ! [B_y,B_m] :
% 22.40/22.26 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => ~ 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))) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__E,axiom,
% 22.40/22.26 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => V_x_2 != V_z_2 )
% 22.40/22.26 => ~ ! [B_y,B_m] :
% 22.40/22.26 ( V_n_2 = hAPP(c_Nat_OSuc,B_m)
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => ~ 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)) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__Un__separatorE,axiom,
% 22.40/22.26 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => ( ! [B_x] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ! [B_y] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => B_x = B_y ) )
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__Un__separator__converseE,axiom,
% 22.40/22.26 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => ( ! [B_x] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ! [B_y] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => B_y = B_x ) )
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__Suc__E,axiom,
% 22.40/22.26 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ~ ! [B_y] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ~ 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__Suc__D2,axiom,
% 22.40/22.26 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ? [B_y] :
% 22.40/22.26 ( 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))
% 22.40/22.26 & 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__pow__Suc__E2,axiom,
% 22.40/22.26 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ~ ! [B_y] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ~ 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_tranclD2,axiom,
% 22.40/22.26 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ? [B_z] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 & 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_tranclD,axiom,
% 22.40/22.26 ! [V_R_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ? [B_z] :
% 22.40/22.26 ( 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))
% 22.40/22.26 & 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_IdE,axiom,
% 22.40/22.26 ! [V_p_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Relation_OId(T_b)))
% 22.40/22.26 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_transfer__nat__int__set__cong,axiom,
% 22.40/22.26 ! [V_P_H_2,V_P_2] :
% 22.40/22.26 ( ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x))
% 22.40/22.26 => ( hBOOL(hAPP(V_P_2,B_x))
% 22.40/22.26 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) )
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Int__Collect__mono,axiom,
% 22.40/22.26 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.40/22.26 => ( ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.26 => ( hBOOL(hAPP(V_P_2,B_x))
% 22.40/22.26 => hBOOL(hAPP(V_Q_2,B_x)) ) )
% 22.40/22.26 => 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)))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_converseE,axiom,
% 22.40/22.26 ! [V_r_2,V_yx_2,T_c,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ~ ! [B_x,B_y] :
% 22.40/22.26 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_y),B_x)
% 22.40/22.26 => ~ 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rel__compE,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,T_d,V_xz_2,T_c,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ~ ! [B_x,B_y,B_z] :
% 22.40/22.26 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_z)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => ~ 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)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Oplus__frac__def,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Otimes__frac__def,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Oof__frac__def,axiom,
% 22.40/22.26 ! [V_q,T_a,T_b] :
% 22.40/22.26 ( ( class_Rings_Oinverse(T_b)
% 22.40/22.26 & class_Rings_Oring__1(T_b) )
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Oinverse__frac__def,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Ouminus__frac__def,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Oless__frac__def,axiom,
% 22.40/22.26 ! [V_r_2,V_q_2,T_b] :
% 22.40/22.26 ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
% 22.40/22.26 <=> 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Oless__eq__frac__def,axiom,
% 22.40/22.26 ! [V_r_2,V_q_2,T_b] :
% 22.40/22.26 ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
% 22.40/22.26 <=> 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Odenom__def,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Onum__def,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_internal__split__def,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_bool_Osize_I1_J,axiom,
% 22.40/22.26 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_internal__split__conv,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_bool_Osize_I2_J,axiom,
% 22.40/22.26 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__less__ub,axiom,
% 22.40/22.26 ! [V_u_2,V_f_2] :
% 22.40/22.26 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n)))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lenlex__def,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexn__length,axiom,
% 22.40/22.26 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2
% 22.40/22.26 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_neq__if__length__neq,axiom,
% 22.40/22.26 ! [V_ys,V_xs,T_a] :
% 22.40/22.26 ( 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)
% 22.40/22.26 => V_xs != V_ys ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lenlex__conv,axiom,
% 22.40/22.26 ! [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)))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__sublist,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexn_Osimps_I2_J,axiom,
% 22.40/22.26 ! [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)))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_impossible__Cons,axiom,
% 22.40/22.26 ! [V_x,V_ys,V_xs,T_a] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list_Oinject,axiom,
% 22.40/22.26 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)
% 22.40/22.26 <=> ( V_a_2 = V_a_H_2
% 22.40/22.26 & V_list_2 = V_list_H_2 ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_not__Cons__self2,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ).
% 22.40/22.26
% 22.40/22.26 fof(fact_not__Cons__self,axiom,
% 22.40/22.26 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list_Osize_I4_J,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Cons__in__lex,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( ( 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))
% 22.40/22.26 & 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) )
% 22.40/22.26 | ( V_x_2 = V_y_2
% 22.40/22.26 & 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__Cons__def,axiom,
% 22.40/22.26 ! [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)))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_pick_Osimps,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_a,V_i] :
% 22.40/22.26 ( ( 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)))
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( ~ 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_select__weight__cons__zero,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexord__cons__cons,axiom,
% 22.40/22.26 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( 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))
% 22.40/22.26 | ( V_a_2 = V_b_2
% 22.40/22.26 & 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexord__lex,axiom,
% 22.40/22.26 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( 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)))
% 22.40/22.26 & 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) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__listrel1__ConsI2,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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))))
% 22.40/22.26 => 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)))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list_Osize_I2_J,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Cons__acc__listrel1I,axiom,
% 22.40/22.26 ! [V_xs_2,V_r_2,V_x_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
% 22.40/22.26 => ( 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))))
% 22.40/22.26 => 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)))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1__mono,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1__converse,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__listrel1__ConsI1,axiom,
% 22.40/22.26 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1I2,axiom,
% 22.40/22.26 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__listrel1__eq__len,axiom,
% 22.40/22.26 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1__eq__len,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__listrel1__converse,axiom,
% 22.40/22.26 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 <=> 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1I1,axiom,
% 22.40/22.26 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Cons__listrel1__Cons,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( ( 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))
% 22.40/22.26 & V_xs_2 = V_ys_2 )
% 22.40/22.26 | ( V_x_2 = V_y_2
% 22.40/22.26 & 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__Cons,axiom,
% 22.40/22.26 ! [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))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexord__irreflexive,axiom,
% 22.40/22.26 ! [V_y_2,V_r_2,T_b] :
% 22.40/22.26 ( ! [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))
% 22.40/22.26 => ~ 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__rtrancl__refl,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__mono,axiom,
% 22.40/22.26 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__subset__rtrancl__listrel1,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__eq__len,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__rtrancl__trans,axiom,
% 22.40/22.26 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => ( 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))))
% 22.40/22.26 => 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)))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__reflcl__if__listrel1,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1__subset__listrel,axiom,
% 22.40/22.26 ! [V_r_H_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rtrancl__listrel1__if__listrel,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel_OCons,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrelp__listrel__eq,axiom,
% 22.40/22.26 ! [V_xa_2,V_x_2,V_r_2,T_b] :
% 22.40/22.26 ( 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)
% 22.40/22.26 <=> 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__Cons2,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ~ ! [B_x,B_xs] :
% 22.40/22.26 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => ~ 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrelp_Oequations_I2_J,axiom,
% 22.40/22.26 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
% 22.40/22.26 & c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrelp_OCons,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 22.40/22.26 => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__Cons1,axiom,
% 22.40/22.26 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ~ ! [B_y,B_ys] :
% 22.40/22.26 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
% 22.40/22.26 => ( 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))
% 22.40/22.26 => ~ 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__subset,axiom,
% 22.40/22.26 ! [V_A_2,V_r_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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))))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lists__UNIV,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lists__mono,axiom,
% 22.40/22.26 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_equiv__listrel,axiom,
% 22.40/22.26 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.26 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__refl__on,axiom,
% 22.40/22.26 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.26 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Cons__in__lists__iff,axiom,
% 22.40/22.26 ! [V_A_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.26 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lists__accI,axiom,
% 22.40/22.26 ! [V_r_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lists__accD,axiom,
% 22.40/22.26 ! [V_r_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__iff__nth,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( 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)
% 22.40/22.26 & ! [B_n] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexord__linear,axiom,
% 22.40/22.26 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 22.40/22.26 ( ! [B_a,B_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 | B_a = B_b
% 22.40/22.26 | 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)) )
% 22.40/22.26 => ( 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)))
% 22.40/22.26 | V_x_2 = V_y_2
% 22.40/22.26 | 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_infinite__UNIV__listI,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__eq__iff__nth__eq,axiom,
% 22.40/22.26 ! [T_b,V_ys_2,V_xs_2] :
% 22.40/22.26 ( V_xs_2 = V_ys_2
% 22.40/22.26 <=> ( 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)
% 22.40/22.26 & ! [B_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_b),V_ys_2),B_i) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__Cons__Suc,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__Cons__0,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth_Osimps,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__Cons_H,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_a,V_n] :
% 22.40/22.26 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x )
% 22.40/22.26 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__Cons__number__of,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_a,V_v] :
% 22.40/22.26 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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 )
% 22.40/22.26 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexord__take__index__conv,axiom,
% 22.40/22.26 ! [V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( ( 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)))
% 22.40/22.26 & 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 )
% 22.40/22.26 | ? [B_i] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 & hAPP(hAPP(c_List_Otake(T_b),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_b),B_i),V_y_2)
% 22.40/22.26 & 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)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__sublist,axiom,
% 22.40/22.26 ! [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))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__set,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_List_Oset(T_b),V_xs_2))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__subset__Cons,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__all,axiom,
% 22.40/22.26 ! [V_n,V_xs,T_a] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__take__subset,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__take__subset__set__take,axiom,
% 22.40/22.26 ! [V_xs_2,T_b,V_n_2,V_m_2] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__sublist__subset,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__take,axiom,
% 22.40/22.26 ! [V_xs,T_a,V_n,V_i] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__ConsD,axiom,
% 22.40/22.26 ! [V_xs_2,V_x_2,V_y_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => ( V_y_2 = V_x_2
% 22.40/22.26 | hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__set__sublistD,axiom,
% 22.40/22.26 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__set__takeD,axiom,
% 22.40/22.26 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_notin__set__sublistI,axiom,
% 22.40/22.26 ! [V_I_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => ~ 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__Suc__Cons,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__take,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__take,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_List_Oset_Osimps_I2_J,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_sublist__upt__eq__take,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_card__length,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_all__set__conv__all__nth,axiom,
% 22.40/22.26 ! [V_P_2,V_xs_2,T_b] :
% 22.40/22.26 ( ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.26 <=> ! [B_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__size__estimation,axiom,
% 22.40/22.26 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__size__estimation_H,axiom,
% 22.40/22.26 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__lists__conv__set,axiom,
% 22.40/22.26 ! [V_A_2,V_xs_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 22.40/22.26 <=> ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__pos__if__in__set,axiom,
% 22.40/22.26 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__mem,axiom,
% 22.40/22.26 ! [V_xs_2,T_b,V_n_2] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__set__conv__nth,axiom,
% 22.40/22.26 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 <=> ? [B_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 & hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) = V_x_2 ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lists__eq__set,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__conv__nth,axiom,
% 22.40/22.26 ! [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))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__lists__length__eq,axiom,
% 22.40/22.26 ! [V_n_2,V_A_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.26 => 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))))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_finite__lists__length__le,axiom,
% 22.40/22.26 ! [V_n_2,V_A_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.26 => 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))))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__iff__zip,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( 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)
% 22.40/22.26 & ! [B_x] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => 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)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__zip,axiom,
% 22.40/22.26 ! [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)))))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__zip,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__zip,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_zip__Cons__Cons,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__eq__iff__zip__eq,axiom,
% 22.40/22.26 ! [T_b,V_ys_2,V_xs_2] :
% 22.40/22.26 ( V_xs_2 = V_ys_2
% 22.40/22.26 <=> ( 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)
% 22.40/22.26 & ! [B_x] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_zip__same,axiom,
% 22.40/22.26 ! [V_xs_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 & V_a_2 = V_b_2 ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__zip__leftD,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__zip__rightD,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__set__zipE,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__zip,axiom,
% 22.40/22.26 ! [V_ys,T_b,V_xs,T_a,V_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_greaterThanLessThan__upto,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listsum__setsum__nth,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listsum__eq__0__nat__iff__nat,axiom,
% 22.40/22.26 ! [V_ns_2] :
% 22.40/22.26 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 <=> ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 22.40/22.26 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__upto,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_atLeastAtMost__upto,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_elem__le__listsum__nat,axiom,
% 22.40/22.26 ! [V_ns,V_k] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listsum__simps_I2_J,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_a] :
% 22.40/22.26 ( class_Groups_Omonoid__add(T_a)
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_atLeastLessThan__upto,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_greaterThanAtMost__upto,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nat__list__def,axiom,
% 22.40/22.26 ! [V_l_2] :
% 22.40/22.26 ( c_List_Onat__list(V_l_2)
% 22.40/22.26 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__size__pointwise,axiom,
% 22.40/22.26 ! [V_g_2,V_f_2,V_xs_2,T_b] :
% 22.40/22.26 ( ! [B_x] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listsum__update__nat,axiom,
% 22.40/22.26 ! [V_n,V_ns,V_k] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_butlast__take,axiom,
% 22.40/22.26 ! [V_xs,T_a,V_n] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__beyond,axiom,
% 22.40/22.26 ! [V_x,V_i,V_xs,T_a] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__id,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__list__update__neq,axiom,
% 22.40/22.26 ! [V_x,V_xs,T_a,V_j,V_i] :
% 22.40/22.26 ( V_i != V_j
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__list__update,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_butlast__list__update,axiom,
% 22.40/22.26 ! [V_x,V_xs,T_a,V_k] :
% 22.40/22.26 ( ( 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))
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( 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))
% 22.40/22.26 => 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) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_zip__update,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_update__zip,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__swap,axiom,
% 22.40/22.26 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
% 22.40/22.26 ( V_i != V_i_H
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__overwrite,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update_Osimps_I2_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__code_I3_J,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__code_I2_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__set__butlastD,axiom,
% 22.40/22.26 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__update__subsetI,axiom,
% 22.40/22.26 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__update__subset__insert,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__list__update,axiom,
% 22.40/22.26 ! [V_x,V_j,V_xs,T_a,V_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( ( V_i = V_j
% 22.40/22.26 => 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 )
% 22.40/22.26 & ( V_i != V_j
% 22.40/22.26 => 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) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__same__conv,axiom,
% 22.40/22.26 ! [V_x_2,V_xs_2,T_b,V_i_2] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
% 22.40/22.26 <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__list__update__eq,axiom,
% 22.40/22.26 ! [V_x,V_xs,T_a,V_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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 ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__butlast,axiom,
% 22.40/22.26 ! [V_xs,T_a,V_n] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__butlast,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__update__memI,axiom,
% 22.40/22.26 ! [V_x_2,V_xs_2,T_b,V_n_2] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_butlast__conv__take,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1__iff__update,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ? [B_y,B_n] :
% 22.40/22.26 ( 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))
% 22.40/22.26 & 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)))
% 22.40/22.26 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__list__update,axiom,
% 22.40/22.26 ! [V_i_2,V_a_2,V_xs_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.26 => ( ~ 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))))))
% 22.40/22.26 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__upto,axiom,
% 22.40/22.26 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__take,axiom,
% 22.40/22.26 ! [V_i,V_xs,T_a] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.26 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__sublistI,axiom,
% 22.40/22.26 ! [V_I_2,V_xs_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.26 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__zipI2,axiom,
% 22.40/22.26 ! [V_xs,T_b,V_ys,T_a] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys))
% 22.40/22.26 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__zipI1,axiom,
% 22.40/22.26 ! [V_ys,T_b,V_xs,T_a] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.26 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct_Osimps_I2_J,axiom,
% 22.40/22.26 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
% 22.40/22.26 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__card,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_card__distinct,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( 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)
% 22.40/22.26 => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__conv__nth,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.26 <=> ! [B_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ! [B_j] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( B_i != B_j
% 22.40/22.26 => hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j) ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__eq__iff__index__eq,axiom,
% 22.40/22.26 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => ( 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)
% 22.40/22.26 <=> V_i_2 = V_j_2 ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__listsum__conv__Setsum,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.26 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nitpick_Ocard_H__def,axiom,
% 22.40/22.26 ! [V_A_2,T_b] :
% 22.40/22.26 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.26 => 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)))) )
% 22.40/22.26 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.26 => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__take__lemma,axiom,
% 22.40/22.26 ! [V_ys,V_xs,T_a,V_k] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( 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)))
% 22.40/22.26 => ( ! [B_i] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
% 22.40/22.26 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
% 22.40/22.26 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__remove1__eq,axiom,
% 22.40/22.26 ! [V_x_2,V_xs_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__Cons__number__of,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_a,V_v] :
% 22.40/22.26 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lists_ONil,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__Nil1,axiom,
% 22.40/22.26 ! [V_r_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__Nil2,axiom,
% 22.40/22.26 ! [V_r_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__butlast,axiom,
% 22.40/22.26 ! [T_a,V_xs] :
% 22.40/22.26 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.26 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.26 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct_Osimps_I1_J,axiom,
% 22.40/22.26 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__remove1,axiom,
% 22.40/22.26 ! [V_x,V_xs,T_a] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.26 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_butlast_Osimps_I1_J,axiom,
% 22.40/22.26 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_butlast_Osimps_I2_J,axiom,
% 22.40/22.26 ! [V_x,T_a,V_xs] :
% 22.40/22.26 ( ( V_xs = c_List_Olist_ONil(T_a)
% 22.40/22.26 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) )
% 22.40/22.26 & ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_remove1_Osimps_I2_J,axiom,
% 22.40/22.26 ! [V_xs,T_a,V_y,V_x] :
% 22.40/22.26 ( ( V_x = V_y
% 22.40/22.26 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs )
% 22.40/22.26 & ( V_x != V_y
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list_Osimps_I3_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list_Osimps_I2_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_upto__empty,axiom,
% 22.40/22.26 ! [V_i,V_j] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i))
% 22.40/22.26 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__Nil,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__eq__Nil,axiom,
% 22.40/22.26 ! [V_xs_2,V_n_2,T_b] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 22.40/22.26 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 | V_xs_2 = c_List_Olist_ONil(T_b) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__0,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_sublist__nil,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_remove1_Osimps_I1_J,axiom,
% 22.40/22.26 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_remove1__commute,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrelp_ONil,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrelp_Oequations_I1_J,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_zip_Osimps_I1_J,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_zip__Nil,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list_Osize_I1_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listsum__simps_I1_J,axiom,
% 22.40/22.26 ! [T_a] :
% 22.40/22.26 ( class_Groups_Omonoid__add(T_a)
% 22.40/22.26 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__0__conv,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list_Osize_I3_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_List_Oset_Osimps_I1_J,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__empty2,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
% 22.40/22.26 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__empty,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.26 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__nonempty,axiom,
% 22.40/22.26 ! [V_x_2,V_k_2,V_xs_2,T_b] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
% 22.40/22.26 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update_Osimps_I1_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__code_I1_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__set__remove1,axiom,
% 22.40/22.26 ! [V_xs_2,T_b,V_b_2,V_a_2] :
% 22.40/22.26 ( V_a_2 != V_b_2
% 22.40/22.26 => ( 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))))
% 22.40/22.26 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_notin__set__remove1,axiom,
% 22.40/22.26 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => ~ 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_remove1__idem,axiom,
% 22.40/22.26 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_sublist__empty,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__remove1__subset,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__greater__0__conv,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> V_xs_2 != c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__1__Cons,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_not__Nil__listrel1,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_not__listrel1__Nil,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel_ONil,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexord__Nil__right,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nil__notin__lex,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nil2__notin__lex,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__Cons,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_upto_Osimps,axiom,
% 22.40/22.26 ! [V_j,V_i] :
% 22.40/22.26 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 22.40/22.26 => 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)) )
% 22.40/22.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
% 22.40/22.26 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_sublist__singleton,axiom,
% 22.40/22.26 ! [V_x_2,T_b,V_A_2] :
% 22.40/22.26 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 22.40/22.26 => 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)) )
% 22.40/22.26 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
% 22.40/22.26 => 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) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lists__empty,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__Cons_H,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_a,V_n] :
% 22.40/22.26 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_upto__rec__number__of,axiom,
% 22.40/22.26 ! [V_n,V_m] :
% 22.40/22.26 ( ( 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)))
% 22.40/22.26 => 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))) )
% 22.40/22.26 & ( ~ 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)))
% 22.40/22.26 => 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) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel__Nil,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__Cons__sing__Nil,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__remove1,axiom,
% 22.40/22.26 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => 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)) )
% 22.40/22.26 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => 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) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_upto_Opsimps,axiom,
% 22.40/22.26 ! [V_j_2,V_i_2] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 22.40/22.26 => 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)) )
% 22.40/22.26 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
% 22.40/22.26 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_select,axiom,
% 22.40/22.26 ! [V_s_2,T_b,V_xs_2] :
% 22.40/22.26 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listset_Osimps_I1_J,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_zip__Cons1,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list_Osimps_I5_J,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list_Osimps_I4_J,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listset_Osimps_I2_J,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_zip__Cons,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_sorted__list__of__set__remove,axiom,
% 22.40/22.26 ! [V_x_2,V_A_2,T_b] :
% 22.40/22.26 ( class_Orderings_Olinorder(T_b)
% 22.40/22.26 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_upto_Opinduct,axiom,
% 22.40/22.26 ! [V_P_2,V_a1_2,V_a0_2] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( ! [B_i,B_j] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j))
% 22.40/22.26 => 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)) )
% 22.40/22.26 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) )
% 22.40/22.26 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_sorted__list__of__set__empty,axiom,
% 22.40/22.26 ! [T_b] :
% 22.40/22.26 ( class_Orderings_Olinorder(T_b)
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_anamorph_Osimps,axiom,
% 22.40/22.26 ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
% 22.40/22.26 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_sublist__Cons,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append1__eq__conv,axiom,
% 22.40/22.26 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( V_xs_2 = V_ys_2
% 22.40/22.26 & V_x_2 = V_y_2 ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Cons__eq__append__conv,axiom,
% 22.40/22.26 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)
% 22.40/22.26 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 22.40/22.26 & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2 )
% 22.40/22.26 | ? [B_ys_H] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2
% 22.40/22.26 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__eq__Cons__conv,axiom,
% 22.40/22.26 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
% 22.40/22.26 ( 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)
% 22.40/22.26 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_b)
% 22.40/22.26 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
% 22.40/22.26 | ? [B_ys_H] :
% 22.40/22.26 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H)
% 22.40/22.26 & hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Cons__eq__appendI,axiom,
% 22.40/22.26 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
% 22.40/22.26 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
% 22.40/22.26 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__Cons,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__in__lists__conv,axiom,
% 22.40/22.26 ! [V_A_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
% 22.40/22.26 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__assoc,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__eq__append__conv2,axiom,
% 22.40/22.26 ! [V_tsa_2,V_zs_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)
% 22.40/22.26 <=> ? [B_us] :
% 22.40/22.26 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_zs_2),B_us)
% 22.40/22.26 & hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ys_2) = V_tsa_2 )
% 22.40/22.26 | ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),B_us) = V_zs_2
% 22.40/22.26 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_tsa_2) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_same__append__eq,axiom,
% 22.40/22.26 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)
% 22.40/22.26 <=> V_ys_2 = V_zs_2 ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__same__eq,axiom,
% 22.40/22.26 ! [V_zs_2,V_xs_2,V_ys_2,T_b] :
% 22.40/22.26 ( 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)
% 22.40/22.26 <=> V_ys_2 = V_zs_2 ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__eq__appendI,axiom,
% 22.40/22.26 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs
% 22.40/22.26 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us)
% 22.40/22.26 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listsum__append,axiom,
% 22.40/22.26 ! [V_ys,V_xs,T_a] :
% 22.40/22.26 ( class_Groups_Omonoid__add(T_a)
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__append,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_zip__append,axiom,
% 22.40/22.26 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
% 22.40/22.26 ( 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)
% 22.40/22.26 => ( 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)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__append,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_eq__Nil__appendI,axiom,
% 22.40/22.26 ! [T_a,V_ys,V_xs] :
% 22.40/22.26 ( V_xs = V_ys
% 22.40/22.26 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__self__conv2,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
% 22.40/22.26 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__self__conv,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
% 22.40/22.26 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__is__Nil__conv,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
% 22.40/22.26 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 22.40/22.26 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_self__append__conv2,axiom,
% 22.40/22.26 ! [V_xs_2,T_b,V_ys_2] :
% 22.40/22.26 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 22.40/22.26 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_self__append__conv,axiom,
% 22.40/22.26 ! [V_ys_2,T_b,V_xs_2] :
% 22.40/22.26 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 22.40/22.26 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__Nil2,axiom,
% 22.40/22.26 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ).
% 22.40/22.26
% 22.40/22.26 fof(fact_Nil__is__append__conv,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
% 22.40/22.26 <=> ( V_xs_2 = c_List_Olist_ONil(T_b)
% 22.40/22.26 & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__Nil,axiom,
% 22.40/22.26 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ).
% 22.40/22.26
% 22.40/22.26 fof(fact_butlast__append,axiom,
% 22.40/22.26 ! [V_xs,T_a,V_ys] :
% 22.40/22.26 ( ( V_ys = c_List_Olist_ONil(T_a)
% 22.40/22.26 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) )
% 22.40/22.26 & ( V_ys != c_List_Olist_ONil(T_a)
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__append__length,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__append__length__plus,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__append,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__append1,axiom,
% 22.40/22.26 ! [V_x,V_ys,V_xs,T_a,V_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__length,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_remove1__append,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__set__butlast__appendI,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.26 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
% 22.40/22.26 | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2)))) )
% 22.40/22.26 => 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))))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_butlast__snoc,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__listrel1I,axiom,
% 22.40/22.26 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( ( ( 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)))
% 22.40/22.26 & V_us_2 = V_vs_2 )
% 22.40/22.26 | ( V_xs_2 = V_ys_2
% 22.40/22.26 & 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))) ) )
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexord__append__leftI,axiom,
% 22.40/22.26 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__append,axiom,
% 22.40/22.26 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 22.40/22.26 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.26 & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 22.40/22.26 & 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__append,axiom,
% 22.40/22.26 ! [V_ys,V_xs,T_a,V_n] :
% 22.40/22.26 ( ( 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)))
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( ~ 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)))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_list__update__append,axiom,
% 22.40/22.26 ! [V_x,V_ys,V_xs,T_a,V_n] :
% 22.40/22.26 ( ( 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)))
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( ~ 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)))
% 22.40/22.26 => 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)) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_sublist__append,axiom,
% 22.40/22.26 ! [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)))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1I,axiom,
% 22.40/22.26 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => ( 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))
% 22.40/22.26 => 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))) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexord__append__left__rightI,axiom,
% 22.40/22.26 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__Suc__conv__app__nth,axiom,
% 22.40/22.26 ! [V_xs,T_a,V_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_snoc__listrel1__snoc__iff,axiom,
% 22.40/22.26 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 <=> ( ( 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)))
% 22.40/22.26 & V_x_2 = V_y_2 )
% 22.40/22.26 | ( V_xs_2 = V_ys_2
% 22.40/22.26 & 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)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_listrel1E,axiom,
% 22.40/22.26 ! [V_r_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ~ ! [B_x,B_y] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => ! [B_us,B_vs] :
% 22.40/22.26 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
% 22.40/22.26 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_lexord__append__leftD,axiom,
% 22.40/22.26 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => ( ! [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))
% 22.40/22.26 => 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))) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rotate1__def,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_upd__conv__take__nth__drop,axiom,
% 22.40/22.26 ! [V_a,V_xs,T_a,V_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__take__drop__id,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__Suc__Cons,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__1__Cons,axiom,
% 22.40/22.26 ! [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 ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__via__drop,axiom,
% 22.40/22.26 ! [V_ys,V_y,V_xs,V_n,T_a] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)
% 22.40/22.26 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct1__rotate,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
% 22.40/22.26 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_distinct__drop,axiom,
% 22.40/22.26 ! [V_i,V_xs,T_a] :
% 22.40/22.26 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.26 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__butlast,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_butlast__drop,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_take__drop,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__take,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__drop,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__0,axiom,
% 22.40/22.26 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__zip,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__drop,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_length__rotate1,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__rotate1,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_in__set__dropD,axiom,
% 22.40/22.26 ! [V_xs_2,V_n_2,V_x_2,T_b] :
% 22.40/22.26 ( 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))))
% 22.40/22.26 => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__drop__subset,axiom,
% 22.40/22.26 ! [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))) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rotate1__is__Nil__conv,axiom,
% 22.40/22.26 ! [V_xs_2,T_b] :
% 22.40/22.26 ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 22.40/22.26 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__Nil,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_set__drop__subset__set__drop,axiom,
% 22.40/22.26 ! [V_xs_2,T_b,V_m_2,V_n_2] :
% 22.40/22.26 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
% 22.40/22.26 => 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)))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__all,axiom,
% 22.40/22.26 ! [V_n,V_xs,T_a] :
% 22.40/22.26 ( 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))
% 22.40/22.26 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__eq__Nil,axiom,
% 22.40/22.26 ! [V_xs_2,V_n_2,T_b] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 22.40/22.26 <=> 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__append,axiom,
% 22.40/22.26 ! [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)) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__eq__conv__conj,axiom,
% 22.40/22.26 ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
% 22.40/22.26 ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
% 22.40/22.26 <=> ( 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)
% 22.40/22.26 & 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) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__Cons,axiom,
% 22.40/22.26 ! [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) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__Cons_H,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_a,V_n] :
% 22.40/22.26 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__drop,axiom,
% 22.40/22.26 ! [V_xs,T_a,V_i,V_n] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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)) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_append__eq__append__conv__if,axiom,
% 22.40/22.26 ! [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] :
% 22.40/22.26 ( 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)
% 22.40/22.26 <=> ( ( 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)))
% 22.40/22.26 => ( 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)
% 22.40/22.26 & 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) ) )
% 22.40/22.26 & ( ~ 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)))
% 22.40/22.26 => ( 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
% 22.40/22.26 & 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 ) ) ) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_nth__drop_H,axiom,
% 22.40/22.26 ! [V_xs,T_a,V_i] :
% 22.40/22.26 ( 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)))
% 22.40/22.26 => 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) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_rotate__simps,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_b,T_a] :
% 22.40/22.26 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a)
% 22.40/22.26 & 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))) ) ).
% 22.40/22.26
% 22.40/22.26 fof(fact_drop__Cons__number__of,axiom,
% 22.40/22.26 ! [V_xs,V_x,T_a,V_v] :
% 22.40/22.26 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.26 => 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) )
% 22.40/22.26 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_take__add,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_j,V_i] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate1__length01,axiom,
% 22.40/22.27 ! [V_xs,T_a] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__append2,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__append1,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_id__take__nth__drop,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_i] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_take__hd__drop,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_n] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__drop__conv__nth,axiom,
% 22.40/22.27 ! [V_n,T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd_Osimps,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__append,axiom,
% 22.40/22.27 ! [V_ys,T_a,V_xs] :
% 22.40/22.27 ( ( V_xs = c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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) )
% 22.40/22.27 & ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__append2,axiom,
% 22.40/22.27 ! [V_ys,T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__in__set,axiom,
% 22.40/22.27 ! [T_b,V_xs_2] :
% 22.40/22.27 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__conv__nth,axiom,
% 22.40/22.27 ! [T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate1__hd__tl,axiom,
% 22.40/22.27 ! [T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__rotate__conv__nth,axiom,
% 22.40/22.27 ! [V_n,T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_tl__drop,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_drop__tl,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_tl_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__rotate,axiom,
% 22.40/22.27 ! [V_xs_2,V_n_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
% 22.40/22.27 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__tl,axiom,
% 22.40/22.27 ! [V_xs,T_a] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate0,axiom,
% 22.40/22.27 ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__rotate,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__add,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__rotate,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__rotate,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__is__Nil__conv,axiom,
% 22.40/22.27 ! [V_xs_2,V_n_2,T_b] :
% 22.40/22.27 ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 22.40/22.27 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_tl_Osimps_I1_J,axiom,
% 22.40/22.27 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate1__rotate__swap,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_tl__append2,axiom,
% 22.40/22.27 ! [V_ys,T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_take__tl,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__conv__mod,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_drop__Suc,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__Suc,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_tl__append,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__id,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_n] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__length01,axiom,
% 22.40/22.27 ! [V_n,V_xs,T_a] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__tl,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_tl__take,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_take__Suc,axiom,
% 22.40/22.27 ! [V_n,T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__drop__take,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_fold1__set,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( class_Lattices_Oab__semigroup__idem__mult(T_b)
% 22.40/22.27 => ( V_xs_2 != c_List_Olist_ONil(T_b)
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lexord__append__rightI,axiom,
% 22.40/22.27 ! [V_r_2,V_x_2,T_b,V_y_2] :
% 22.40/22.27 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__Nil,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_start__le__sum,axiom,
% 22.40/22.27 ! [V_ns_2,V_n_2,V_m_2] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__assoc,axiom,
% 22.40/22.27 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Groups_Osemigroup__add(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__absorb0,axiom,
% 22.40/22.27 ! [V_zs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Groups_Omonoid__add(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__Cons,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__append,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__foldl,axiom,
% 22.40/22.27 ! [T_b] :
% 22.40/22.27 ( class_Groups_Omonoid__add(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sum__eq__0__conv,axiom,
% 22.40/22.27 ! [V_ns_2,V_m_2] :
% 22.40/22.27 ( 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)
% 22.40/22.27 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 & ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 22.40/22.27 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_fun__left__comm__idem_Ofold__set,axiom,
% 22.40/22.27 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Sup__set__fold,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Inf__set__fold,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Sup__fin__set__fold,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Lattices_Olattice(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Inf__fin__set__fold,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Lattices_Olattice(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Min__fin__set__fold,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Max__fin__set__fold,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_min__max_OInf__fin__set__fold,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_min__max_OSup__fin__set__fold,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_SUPR__set__fold,axiom,
% 22.40/22.27 ! [V_f_2,V_xs_2,T_c,T_b] :
% 22.40/22.27 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_INFI__set__fold,axiom,
% 22.40/22.27 ! [V_f_2,V_xs_2,T_c,T_b] :
% 22.40/22.27 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_elem__le__sum,axiom,
% 22.40/22.27 ! [V_ns_2,V_n_2] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__list__of__set__insert,axiom,
% 22.40/22.27 ! [V_x_2,V_A_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.27 => 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)))))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lexord__Nil__left,axiom,
% 22.40/22.27 ! [V_r_2,V_y_2,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__key_Osimps_I1_J,axiom,
% 22.40/22.27 ! [V_x_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__key_Osimps_I2_J,axiom,
% 22.40/22.27 ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( ( 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)))
% 22.40/22.27 => 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)) )
% 22.40/22.27 & ( ~ 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)))
% 22.40/22.27 => 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)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__insort,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__insort,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__left__comm,axiom,
% 22.40/22.27 ! [V_xs_2,V_y_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_fun__left__comm__insort,axiom,
% 22.40/22.27 ! [T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__key__left__comm,axiom,
% 22.40/22.27 ! [V_xs_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2)
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remove1__insort,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__not__Nil,axiom,
% 22.40/22.27 ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__insort,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => ( 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)))
% 22.40/22.27 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__insert__insort__key,axiom,
% 22.40/22.27 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( ~ 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))))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__insert__insort,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__insort__insert,axiom,
% 22.40/22.27 ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__insert__triv,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__insort__insert,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__insert__key__triv,axiom,
% 22.40/22.27 ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( 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))))
% 22.40/22.27 => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__list__update,axiom,
% 22.40/22.27 ! [V_x,V_k,T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => ( ( 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))
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x )
% 22.40/22.27 & ( 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))
% 22.40/22.27 => 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) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__conv__nth,axiom,
% 22.40/22.27 ! [T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__ConsL,axiom,
% 22.40/22.27 ! [V_x,T_a,V_xs] :
% 22.40/22.27 ( V_xs = c_List_Olist_ONil(T_a)
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__ConsR,axiom,
% 22.40/22.27 ! [V_x,T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last_Osimps,axiom,
% 22.40/22.27 ! [V_x,T_a,V_xs] :
% 22.40/22.27 ( ( V_xs = c_List_Olist_ONil(T_a)
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x )
% 22.40/22.27 & ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__appendL,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_ys] :
% 22.40/22.27 ( V_ys = c_List_Olist_ONil(T_a)
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__appendR,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_ys] :
% 22.40/22.27 ( V_ys != c_List_Olist_ONil(T_a)
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__append,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_ys] :
% 22.40/22.27 ( ( V_ys = c_List_Olist_ONil(T_a)
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) )
% 22.40/22.27 & ( V_ys != c_List_Olist_ONil(T_a)
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__in__set,axiom,
% 22.40/22.27 ! [T_b,V_as_2] :
% 22.40/22.27 ( V_as_2 != c_List_Olist_ONil(T_b)
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__snoc,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__drop,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_n] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_snoc__eq__iff__butlast,axiom,
% 22.40/22.27 ! [V_ys_2,V_x_2,V_xs_2,T_b] :
% 22.40/22.27 ( 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
% 22.40/22.27 <=> ( V_ys_2 != c_List_Olist_ONil(T_b)
% 22.40/22.27 & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
% 22.40/22.27 & c_List_Olast(T_b,V_ys_2) = V_x_2 ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_append__butlast__last__id,axiom,
% 22.40/22.27 ! [T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => 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 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lists_Osimps,axiom,
% 22.40/22.27 ! [V_A_2,V_a_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
% 22.40/22.27 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 22.40/22.27 | ? [B_a,B_l] :
% 22.40/22.27 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l)
% 22.40/22.27 & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
% 22.40/22.27 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2))) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_select__weigth__select,axiom,
% 22.40/22.27 ! [T_b,V_xs_2] :
% 22.40/22.27 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_inj__mapI,axiom,
% 22.40/22.27 ! [V_f_2,T_c,T_b] :
% 22.40/22.27 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__map,axiom,
% 22.40/22.27 ! [V_f_2,T_c,T_b,V_xs_2] :
% 22.40/22.27 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__map,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__tl,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__same__conv__map,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__map__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__map1,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__zip__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__zip__map2,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__map2,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Nil__is__map__conv,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
% 22.40/22.27 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__is__Nil__conv,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 22.40/22.27 <=> V_xs_2 = c_List_Olist_ONil(T_c) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__update,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__eq__conv,axiom,
% 22.40/22.27 ! [V_g_2,V_xs_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( 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)
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),hAPP(c_List_Oset(T_c),V_xs_2)))
% 22.40/22.27 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__eq__imp__length__eq,axiom,
% 22.40/22.27 ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__map,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__subtractf,axiom,
% 22.40/22.27 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Groups_Oab__group__add(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__0,axiom,
% 22.40/22.27 ! [V_xs_2,T_c,T_b] :
% 22.40/22.27 ( class_Groups_Omonoid__add(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__const__mult,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
% 22.40/22.27 ( class_Rings_Osemiring__0(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__mult__const,axiom,
% 22.40/22.27 ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Rings_Osemiring__0(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__addf,axiom,
% 22.40/22.27 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_inj__map__eq__map,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.27 => ( 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)
% 22.40/22.27 <=> V_xs_2 = V_ys_2 ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__injective,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => ( c_Fun_Oinj__on(T_c,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))
% 22.40/22.27 => V_xs_2 = V_ys_2 ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__ident,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)),V_xs_2) = V_xs_2 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_take__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__butlast,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__append,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__map,axiom,
% 22.40/22.27 ! [V_f_2,T_c,T_b,V_xs_2] :
% 22.40/22.27 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_drop__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_List_Omap_Oidentity,axiom,
% 22.40/22.27 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_COMBI(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_List_Omap_Oid,axiom,
% 22.40/22.27 ! [T_b] : hAPP(c_List_Omap(T_b,T_b),c_Fun_Oid(T_b)) = c_Fun_Oid(tc_List_Olist(T_b)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__map,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_List_Omap_Ocompositionality,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__comp__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_List_Omap_Ocomp,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__size__map,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__inj__on,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => V_xs_2 = V_ys_2 ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_inj__on__map__eq__map,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( 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)
% 22.40/22.27 <=> V_xs_2 = V_ys_2 ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nth__map,axiom,
% 22.40/22.27 ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__fun__upd,axiom,
% 22.40/22.27 ! [V_v_2,V_f_2,T_c,V_xs_2,V_y_2,T_b] :
% 22.40/22.27 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__map,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
% 22.40/22.27 <=> ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
% 22.40/22.27 & c_Fun_Oinj__on(T_c,T_b,V_f_2,hAPP(c_List_Oset(T_c),V_xs_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__abs,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( class_Groups_Oordered__ab__group__add__abs(T_b)
% 22.40/22.27 => 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)))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_uminus__listsum__map,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Groups_Oab__group__add(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_inj__on__mapI,axiom,
% 22.40/22.27 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_inj__mapD,axiom,
% 22.40/22.27 ! [V_f_2,T_c,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_inj__map,axiom,
% 22.40/22.27 ! [V_f_2,T_c,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 <=> c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__distinct__conv__setsum__set,axiom,
% 22.40/22.27 ! [V_f_2,V_xs_2,T_b,T_c] :
% 22.40/22.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__triv,axiom,
% 22.40/22.27 ! [V_xs_2,V_r_2,T_c,T_b] :
% 22.40/22.27 ( class_Rings_Osemiring__1(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__map__remove1,axiom,
% 22.40/22.27 ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
% 22.40/22.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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)))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Nitpick_Osetsum_H__def,axiom,
% 22.40/22.27 ! [V_f_2,V_A_2,T_b,T_c] :
% 22.40/22.27 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.27 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.27 => 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))))) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.27 => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_pick__same,axiom,
% 22.40/22.27 ! [V_xs_2,T_b,V_l_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zero__code__numeral__def,axiom,
% 22.40/22.27 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Code__Numeral_Oof__nat__inject,axiom,
% 22.40/22.27 ! [V_m_2,V_n_2] :
% 22.40/22.27 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2)
% 22.40/22.27 <=> V_n_2 = V_m_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_times__code__numeral__code,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Code__Numeral_Oof__nat__code,axiom,
% 22.40/22.27 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_one__code__numeral__def,axiom,
% 22.40/22.27 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_less__code__numeral__code,axiom,
% 22.40/22.27 ! [V_m_2,V_n_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_code__numeral_Oof__nat__inject,axiom,
% 22.40/22.27 ! [V_y_2,V_x_2] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 22.40/22.27 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2)
% 22.40/22.27 <=> V_x_2 = V_y_2 ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__fst__zip,axiom,
% 22.40/22.27 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => 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 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__snd__zip,axiom,
% 22.40/22.27 ! [V_ys_2,T_c,V_xs_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => 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 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_number__of__code__numeral__def,axiom,
% 22.40/22.27 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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__map__fst__snd,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_plus__code__numeral__code,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_less__eq__code__numeral__code,axiom,
% 22.40/22.27 ! [V_m_2,V_n_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_subtract__code__numeral__code,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_pick__member,axiom,
% 22.40/22.27 ! [V_xs_2,T_b,V_i_2] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => 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)))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__eq__conv,axiom,
% 22.40/22.27 ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
% 22.40/22.27 <=> ( 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
% 22.40/22.27 & 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 ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__size__conv__listsum,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_code__numeral__not__eq__zero,axiom,
% 22.40/22.27 ! [V_i_2] :
% 22.40/22.27 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 22.40/22.27 <=> 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_setsum__set__upto__conv__listsum__int,axiom,
% 22.40/22.27 ! [V_j_2,V_i_2,V_f_2,T_b] :
% 22.40/22.27 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_interv__listsum__conv__setsum__set__int,axiom,
% 22.40/22.27 ! [V_l_2,V_k_2,V_f_2,T_b] :
% 22.40/22.27 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_select__weight__member,axiom,
% 22.40/22.27 ! [V_s_2,V_xs_2,T_b] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => 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)))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_select__weight__def,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_select__def,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__mono,axiom,
% 22.40/22.27 ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
% 22.40/22.27 ( ( class_Groups_Omonoid__add(T_c)
% 22.40/22.27 & class_Groups_Oordered__ab__semigroup__add(T_c) )
% 22.40/22.27 => ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
% 22.40/22.27 => 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)))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nat__of__of__nat,axiom,
% 22.40/22.27 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ).
% 22.40/22.27
% 22.40/22.27 fof(fact_of__nat__nat__of,axiom,
% 22.40/22.27 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nat__of__inverse,axiom,
% 22.40/22.27 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ).
% 22.40/22.27
% 22.40/22.27 fof(fact_times__code__numeral__def,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_code__numeral_Onat__of__inject,axiom,
% 22.40/22.27 ! [V_y_2,V_x_2] :
% 22.40/22.27 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2)
% 22.40/22.27 <=> V_x_2 = V_y_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Code__Numeral_Onat__of__inject,axiom,
% 22.40/22.27 ! [V_l_2,V_k_2] :
% 22.40/22.27 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
% 22.40/22.27 <=> V_k_2 = V_l_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_type__definition__code__numeral,axiom,
% 22.40/22.27 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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_less__code__numeral__def,axiom,
% 22.40/22.27 ! [V_m_2,V_n_2] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 22.40/22.27 <=> 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nat__of,axiom,
% 22.40/22.27 ! [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)))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nat__of__number,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_int__of__def,axiom,
% 22.40/22.27 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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_less__eq__code__numeral__def,axiom,
% 22.40/22.27 ! [V_m_2,V_n_2] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2))
% 22.40/22.27 <=> 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nat__of__code,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nat__of__aux__def,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Suc__code__numeral__def,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_minus__code__numeral__def,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_of__nat__inverse,axiom,
% 22.40/22.27 ! [V_y_2] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 22.40/22.27 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_plus__code__numeral__def,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_div__code__numeral__def,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_mod__code__numeral__def,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_code__numeral__decr,axiom,
% 22.40/22.27 ! [V_k] :
% 22.40/22.27 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__DSequence_Opos__not__seq__def,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_partition__set,axiom,
% 22.40/22.27 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_partition__P,axiom,
% 22.40/22.27 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_yes_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 & ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_no_2)))
% 22.40/22.27 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_partition_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_partition_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lists__Int__eq,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lists__IntI,axiom,
% 22.40/22.27 ! [V_B_2,V_A_2,V_l_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_A_2)))
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_l_2),c_List_Olists(T_b,V_B_2)))
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsp_ONil,axiom,
% 22.40/22.27 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsp_Oequations_I1_J,axiom,
% 22.40/22.27 ! [V_A_2,T_b] : hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),c_List_Olist_ONil(T_b))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_in__listsp__conv__set,axiom,
% 22.40/22.27 ! [V_xs_2,V_A_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_A_2,B_x)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsp__conj__eq,axiom,
% 22.40/22.27 ! [V_x_2,V_B_2,V_A_2,T_b] :
% 22.40/22.27 ( 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))
% 22.40/22.27 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_x_2))
% 22.40/22.27 & hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_x_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsp__infI,axiom,
% 22.40/22.27 ! [V_B_2,V_l_2,V_A_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_l_2))
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Olistsp(T_b,V_B_2),V_l_2))
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsp__inf__eq,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsp_Oequations_I2_J,axiom,
% 22.40/22.27 ! [V_a2_2,V_a1_2,V_A_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a2_2)))
% 22.40/22.27 <=> ( hBOOL(hAPP(V_A_2,V_a1_2))
% 22.40/22.27 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_a2_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_append__in__listsp__conv,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_A_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
% 22.40/22.27 <=> ( hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_xs_2))
% 22.40/22.27 & hBOOL(hAPP(c_List_Olistsp(T_b,V_A_2),V_ys_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsp__mono,axiom,
% 22.40/22.27 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsp__lists__eq,axiom,
% 22.40/22.27 ! [V_x_2,V_A_2,T_b] :
% 22.40/22.27 ( 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))
% 22.40/22.27 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_x_2),c_List_Olists(T_b,V_A_2))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_product_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__def,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 22.40/22.27 <=> ( 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)
% 22.40/22.27 & ! [B_x] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__map1,axiom,
% 22.40/22.27 ! [V_bs_2,V_as_2,V_f_2,T_d,V_P_2,T_c,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 <=> 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__map2,axiom,
% 22.40/22.27 ! [V_bs_2,V_f_2,T_d,V_as_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( 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))
% 22.40/22.27 <=> 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__dropI,axiom,
% 22.40/22.27 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_as_2,V_bs_2)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__appendI,axiom,
% 22.40/22.27 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2)
% 22.40/22.27 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_c_2,V_d_2)
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__append,axiom,
% 22.40/22.27 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => ( 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))
% 22.40/22.27 <=> ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 22.40/22.27 & c_List_Olist__all2(T_b,T_c,V_P_2,V_us_2,V_vs_2) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__Cons,axiom,
% 22.40/22.27 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( 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))
% 22.40/22.27 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 22.40/22.27 & c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__takeI,axiom,
% 22.40/22.27 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__eq,axiom,
% 22.40/22.27 ! [T_b,V_ys_2,V_xs_2] :
% 22.40/22.27 ( V_xs_2 = V_ys_2
% 22.40/22.27 <=> c_List_Olist__all2(T_b,T_b,c_fequal,V_xs_2,V_ys_2) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__lengthD,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__Nil2,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,c_List_Olist_ONil(T_c))
% 22.40/22.27 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__Nil,axiom,
% 22.40/22.27 ! [V_ys_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,c_List_Olist_ONil(T_b),V_ys_2)
% 22.40/22.27 <=> V_ys_2 = c_List_Olist_ONil(T_c) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_product_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__conv__all__nth,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 22.40/22.27 <=> ( 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)
% 22.40/22.27 & ! [B_i] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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))) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__nthD,axiom,
% 22.40/22.27 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__nthD2,axiom,
% 22.40/22.27 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__update__cong,axiom,
% 22.40/22.27 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_c,V_xs_2,T_b,V_i_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 22.40/22.27 => 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)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__update__cong2,axiom,
% 22.40/22.27 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2)
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2))
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__product,axiom,
% 22.40/22.27 ! [V_ys,T_b,V_xs,T_a] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys))
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_product__list__set,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sublists__powset,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__sublists,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sublists_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sublists_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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))))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__set__sublists,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => 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)))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__n__lists,axiom,
% 22.40/22.27 ! [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)))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_enum__the__def,axiom,
% 22.40/22.27 ! [V_P_2,T_b] : c_Enum_Oenum__the(T_b,V_P_2) = c_HOL_OThe(T_b,V_P_2) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__n__lists,axiom,
% 22.40/22.27 ! [V_n,V_xs,T_a] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_n__lists_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_n__lists__Nil,axiom,
% 22.40/22.27 ! [T_a,V_n] :
% 22.40/22.27 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => 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))) )
% 22.40/22.27 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__n__lists,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__n__lists__elem,axiom,
% 22.40/22.27 ! [V_xs_2,V_n_2,V_ys_2,T_b] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2I,axiom,
% 22.40/22.27 ! [V_P_2,V_b_2,V_a_2,T_c,T_b] :
% 22.40/22.27 ( ! [B_x] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_HOL_Obool),V_P_2),B_x)) )
% 22.40/22.27 => ( 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)
% 22.40/22.27 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_all__nth__imp__all__set,axiom,
% 22.40/22.27 ! [V_x_2,V_P_2,V_xs_2,T_b] :
% 22.40/22.27 ( ! [B_i] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
% 22.40/22.27 ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__removeAll__inj__on,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__remdups,axiom,
% 22.40/22.27 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__remdups__leq,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remdups__id__iff__distinct,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
% 22.40/22.27 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__removeAll,axiom,
% 22.40/22.27 ! [V_x,V_xs,T_a] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__remdups__id,axiom,
% 22.40/22.27 ! [V_xs,T_a] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.27 => c_List_Oremdups(T_a,V_xs) = V_xs ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__remdups,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__remdups__eq,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remdups__remdups,axiom,
% 22.40/22.27 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remdups_Osimps_I1_J,axiom,
% 22.40/22.27 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remdups__eq__nil__right__iff,axiom,
% 22.40/22.27 ! [V_x_2,T_b] :
% 22.40/22.27 ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
% 22.40/22.27 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_removeAll_Osimps_I1_J,axiom,
% 22.40/22.27 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remdups__eq__nil__iff,axiom,
% 22.40/22.27 ! [V_x_2,T_b] :
% 22.40/22.27 ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
% 22.40/22.27 <=> V_x_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_removeAll_Osimps_I2_J,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_y,V_x] :
% 22.40/22.27 ( ( V_x = V_y
% 22.40/22.27 => 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) )
% 22.40/22.27 & ( V_x != V_y
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_removeAll__append,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remdups__map__remdups,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remove1__remdups,axiom,
% 22.40/22.27 ! [V_x,V_xs,T_a] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_removeAll__id,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hAPP(c_List_OremoveAll(T_b,V_x_2),V_xs_2) = V_xs_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__remove1__removeAll,axiom,
% 22.40/22.27 ! [V_x,V_xs,T_a] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.27 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remdups_Osimps_I2_J,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__remdups__card__conv,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__removeAll__inj,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__removeAll,axiom,
% 22.40/22.27 ! [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)))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__remdups__concat,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__list__of__set__sort__remdups,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sort__key__simps_I1_J,axiom,
% 22.40/22.27 ! [V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__conv__concat,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat__conv__foldl,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__sort,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__sort,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__sort,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osort__key(T_b,T_c,V_f_2,V_xs_2)))
% 22.40/22.27 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat_Osimps_I1_J,axiom,
% 22.40/22.27 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Nil__eq__concat__conv,axiom,
% 22.40/22.27 ! [V_xss_2,T_b] :
% 22.40/22.27 ( c_List_Olist_ONil(T_b) = c_List_Oconcat(T_b,V_xss_2)
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 22.40/22.27 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat__eq__Nil__conv,axiom,
% 22.40/22.27 ! [V_xss_2,T_b] :
% 22.40/22.27 ( c_List_Oconcat(T_b,V_xss_2) = c_List_Olist_ONil(T_b)
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)))
% 22.40/22.27 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__concat,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__concat,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__concat,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sort__key__simps_I2_J,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat__append,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sort__foldl__insort,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat__eq__concat__iff,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.27 ( ! [B_x] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => 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)) )
% 22.40/22.27 => ( 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)
% 22.40/22.27 => ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 22.40/22.27 <=> V_xs_2 = V_ys_2 ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat__injective,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.27 ( c_List_Oconcat(T_b,V_xs_2) = c_List_Oconcat(T_b,V_ys_2)
% 22.40/22.27 => ( 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)
% 22.40/22.27 => ( ! [B_x] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => 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)) )
% 22.40/22.27 => V_xs_2 = V_ys_2 ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat__map__singleton,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_n__lists_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose_Osimps_I3_J,axiom,
% 22.40/22.27 ! [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))))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__aux__filter__head,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__concat,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__sort,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,V_P_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__filter,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__is__subset,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__id__conv,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = V_xs_2
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sum__length__filter__compl,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__filter__le,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__filter,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remove1__filter__not,axiom,
% 22.40/22.27 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 22.40/22.27 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__remove1,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__insort__triv,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,T_b,V_x_2,V_P_2,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_partition__filter1,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_partition__filter2,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_partition__filter__conv,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter_Osimps_I2_J,axiom,
% 22.40/22.27 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 22.40/22.27 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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)) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__append,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__empty__conv,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) = c_List_Olist_ONil(T_b)
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__filter__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_removeAll__filter__not,axiom,
% 22.40/22.27 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 22.40/22.27 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_remdups__filter,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_removeAll__filter__not__eq,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nth__transpose,axiom,
% 22.40/22.27 ! [V_xs_2,T_b,V_i_2] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__map__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__filter,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__filter__less,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__minus__filter__out,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__in__sublist,axiom,
% 22.40/22.27 ! [V_s_2,V_xs_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__empty,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( c_List_Otranspose(T_b,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_b))
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 22.40/22.27 => B_x = c_List_Olist_ONil(T_b) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__filter__conv__card,axiom,
% 22.40/22.27 ! [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))))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__aux__filter__tail,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose_Opsimps_I3_J,axiom,
% 22.40/22.27 ! [V_xss_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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))))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose_Opsimps_I2_J,axiom,
% 22.40/22.27 ! [V_xss_2,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sublist__shift__lemma__Suc,axiom,
% 22.40/22.27 ! [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)))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_select__weigth__drop__zero,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_pick__drop__zero,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose_Opsimps_I1_J,axiom,
% 22.40/22.27 ! [T_b] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__max__length,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__aux__max,axiom,
% 22.40/22.27 ! [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)))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldr_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldr_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldr__append,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldr__conv__foldl,axiom,
% 22.40/22.27 ! [V_a_2,V_xs_2,T_b] :
% 22.40/22.27 ( class_Groups_Oab__semigroup__add(T_b)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldr__map,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__foldr1__lemma,axiom,
% 22.40/22.27 ! [V_xs_2,V_a_2,T_b] :
% 22.40/22.27 ( class_Groups_Omonoid__add(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__foldr1,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( class_Groups_Omonoid__add(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__transpose,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sublist__def,axiom,
% 22.40/22.27 ! [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))))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sublist__shift__lemma,axiom,
% 22.40/22.27 ! [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))))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__upt,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_atLeastLessThan__upt,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__Suc,axiom,
% 22.40/22.27 ! [V_j,V_i] :
% 22.40/22.27 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => 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))) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__Suc__append,axiom,
% 22.40/22.27 ! [V_j,V_i] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__add__eq__append,axiom,
% 22.40/22.27 ! [V_k,V_j,V_i] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__rec,axiom,
% 22.40/22.27 ! [V_j,V_i] :
% 22.40/22.27 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => 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)) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__conv__Cons,axiom,
% 22.40/22.27 ! [V_j,V_i] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__conv__Nil,axiom,
% 22.40/22.27 ! [V_i,V_j] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i))
% 22.40/22.27 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__eq__Nil__conv,axiom,
% 22.40/22.27 ! [V_j_2,V_i_2] :
% 22.40/22.27 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
% 22.40/22.27 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__0,axiom,
% 22.40/22.27 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_take__upt,axiom,
% 22.40/22.27 ! [V_n,V_m,V_i] :
% 22.40/22.27 ( 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))
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__list__of__set__range,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__upt,axiom,
% 22.40/22.27 ! [V_j,V_i] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_drop__upt,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__upt,axiom,
% 22.40/22.27 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__upt,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__rec__number__of,axiom,
% 22.40/22.27 ! [V_n,V_m] :
% 22.40/22.27 ( ( 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)))
% 22.40/22.27 => 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))) )
% 22.40/22.27 & ( ~ 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)))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_upt__eq__Cons__conv,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_j_2,V_i_2] :
% 22.40/22.27 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2)
% 22.40/22.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2))
% 22.40/22.27 & V_i_2 = V_x_2
% 22.40/22.27 & 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 ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__upt,axiom,
% 22.40/22.27 ! [V_j,V_i] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__Suc__upt,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_atLeastAtMost__upt,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_atLeast__upt,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nth__upt,axiom,
% 22.40/22.27 ! [V_j,V_k,V_i] :
% 22.40/22.27 ( 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))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_greaterThanAtMost__upt,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_greaterThanLessThan__upt,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_atMost__upto,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__nth,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
% 22.40/22.27 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 22.40/22.27 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
% 22.40/22.27 ! [V_n_2,V_m_2,V_f_2,T_b] :
% 22.40/22.27 ( class_Groups_Ocomm__monoid__add(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nth__map__upt,axiom,
% 22.40/22.27 ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__rectangle,axiom,
% 22.40/22.27 ! [V_n_2,T_b,V_xs_2] :
% 22.40/22.27 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 22.40/22.27 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
% 22.40/22.27 => ( ! [B_i] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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 )
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__key__remove1,axiom,
% 22.40/22.27 ! [V_f_2,V_xs_2,V_a_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 22.40/22.27 => ( 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
% 22.40/22.27 => 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 ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted_ONil,axiom,
% 22.40/22.27 ! [T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__single,axiom,
% 22.40/22.27 ! [V_x,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__upt,axiom,
% 22.40/22.27 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__sort,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osort__key(T_b,T_b,c_COMBI(T_b),V_xs_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__insort__insert,axiom,
% 22.40/22.27 ! [V_x_2,V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__drop,axiom,
% 22.40/22.27 ! [V_n,V_xs,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__upto,axiom,
% 22.40/22.27 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__take,axiom,
% 22.40/22.27 ! [V_n,V_xs,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__remove1,axiom,
% 22.40/22.27 ! [V_a,V_xs,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__tl,axiom,
% 22.40/22.27 ! [V_xs,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__insort,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( 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))
% 22.40/22.27 <=> c_List_Olinorder__class_Osorted(T_b,V_xs_2) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__butlast,axiom,
% 22.40/22.27 ! [V_xs,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted_Oequations_I1_J,axiom,
% 22.40/22.27 ! [T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__many,axiom,
% 22.40/22.27 ! [V_zs,V_y,V_x,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
% 22.40/22.27 => 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))) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__many__eq,axiom,
% 22.40/22.27 ! [V_zs_2,V_y_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( 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)))
% 22.40/22.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2))
% 22.40/22.27 & c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__remdups,axiom,
% 22.40/22.27 ! [V_l,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_a,V_l)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__distinct__set__unique,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
% 22.40/22.27 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 22.40/22.27 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__sort__key,axiom,
% 22.40/22.27 ! [V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__insort__insert__key,axiom,
% 22.40/22.27 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__map__remove1,axiom,
% 22.40/22.27 ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__insort__key,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( 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)))
% 22.40/22.27 <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__filter,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__map__same,axiom,
% 22.40/22.27 ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__same,axiom,
% 22.40/22.27 ! [V_xs_2,V_g_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__Cons,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 22.40/22.27 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 22.40/22.27 & ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__append,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 22.40/22.27 <=> ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 22.40/22.27 & c_List_Olinorder__class_Osorted(T_b,V_ys_2)
% 22.40/22.27 & ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => ! [B_xa] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),V_ys_2)))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) ) ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__insort,axiom,
% 22.40/22.27 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
% 22.40/22.27 => ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted_Oequations_I2_J,axiom,
% 22.40/22.27 ! [V_a1_2,V_a2_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
% 22.40/22.27 <=> ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) )
% 22.40/22.27 & c_List_Olinorder__class_Osorted(T_b,V_a1_2) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__list__of__set,axiom,
% 22.40/22.27 ! [V_A_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.27 => ( hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2
% 22.40/22.27 & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
% 22.40/22.27 & hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__remove1,axiom,
% 22.40/22.27 ! [V_xs_2,V_a_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 22.40/22.27 => 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 ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__equals__nth__mono,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 22.40/22.27 <=> ! [B_j] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ! [B_i] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 22.40/22.27 => 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))) ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__nth__mono,axiom,
% 22.40/22.27 ! [V_j,V_i,V_xs,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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))) ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__sorted__distinct__set__unique,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
% 22.40/22.27 => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
% 22.40/22.27 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__column,axiom,
% 22.40/22.27 ! [V_i_2,V_xs_2,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nth__nth__transpose__sorted,axiom,
% 22.40/22.27 ! [V_j_2,V_i_2,V_xs_2,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( 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))))
% 22.40/22.27 => ( 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))))
% 22.40/22.27 => 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) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_inj__on__rev,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__rev,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
% 22.40/22.27 <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev_Osimps_I1_J,axiom,
% 22.40/22.27 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Nil__is__rev__conv,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( c_List_Olist_ONil(T_b) = hAPP(c_List_Orev(T_b),V_xs_2)
% 22.40/22.27 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__is__Nil__conv,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( hAPP(c_List_Orev(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
% 22.40/22.27 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__singleton__conv,axiom,
% 22.40/22.27 ! [V_x_2,V_xs_2,T_b] :
% 22.40/22.27 ( 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))
% 22.40/22.27 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_singleton__rev__conv,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__append,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__concat,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__filter,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__rev,axiom,
% 22.40/22.27 ! [V_ys,T_b,V_xs,T_a] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__rev,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__rev1,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( c_List_Olist__all2(T_b,T_c,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2),V_ys_2)
% 22.40/22.27 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,hAPP(c_List_Orev(T_c),V_ys_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__rev,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_P_2,T_c,T_b] :
% 22.40/22.27 ( 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))
% 22.40/22.27 <=> c_List_Olist__all2(T_b,T_c,V_P_2,V_xs_2,V_ys_2) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__is__rev__conv,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.27 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
% 22.40/22.27 <=> V_xs_2 = V_ys_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__swap,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,T_b] :
% 22.40/22.27 ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
% 22.40/22.27 <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__rev__ident,axiom,
% 22.40/22.27 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__rev,axiom,
% 22.40/22.27 ! [V_xs,T_a] :
% 22.40/22.27 ( class_Groups_Ocomm__monoid__add(T_a)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__rev,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldr__foldl,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__foldr,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__eq__Cons__iff,axiom,
% 22.40/22.27 ! [V_ys_2,V_y_2,V_xs_2,T_b] :
% 22.40/22.27 ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
% 22.40/22.27 <=> 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__rev,axiom,
% 22.40/22.27 ! [T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__rev,axiom,
% 22.40/22.27 ! [T_a,V_xs] :
% 22.40/22.27 ( V_xs != c_List_Olist_ONil(T_a)
% 22.40/22.27 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__transpose,axiom,
% 22.40/22.27 ! [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)))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__foldl__cons,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__drop,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__take,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rotate__rev,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__nth,axiom,
% 22.40/22.27 ! [V_xs,T_a,V_n] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__update,axiom,
% 22.40/22.27 ! [V_y,V_xs,T_a,V_k] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__rev__nth__mono,axiom,
% 22.40/22.27 ! [V_j,V_i,V_xs,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs))
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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))) ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldr__max__sorted,axiom,
% 22.40/22.27 ! [V_y_2,V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),V_xs_2))
% 22.40/22.27 => ( ( V_xs_2 = c_List_Olist_ONil(T_b)
% 22.40/22.27 => c_List_Ofoldr(T_b,T_b,c_Orderings_Oord__class_Omax(T_b),V_xs_2,V_y_2) = V_y_2 )
% 22.40/22.27 & ( V_xs_2 != c_List_Olist_ONil(T_b)
% 22.40/22.27 => 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) ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__transpose__sorted,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
% 22.40/22.27 => 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) )
% 22.40/22.27 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_b))
% 22.40/22.27 => 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))) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__column__length,axiom,
% 22.40/22.27 ! [V_i_2,V_xs_2,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transpose__transpose,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
% 22.40/22.27 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__takeWhile,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__takeWhile__le,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__eq__all__conv,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = V_xs_2
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__takeWhileD,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,V_x_2,T_b] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__takeWhile__snd,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__takeWhile__fst,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__tail,axiom,
% 22.40/22.27 ! [V_l_2,V_xs_2,T_b,V_x_2,V_P_2] :
% 22.40/22.27 ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile_Osimps_I2_J,axiom,
% 22.40/22.27 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 22.40/22.27 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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)) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__eq__take,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__takeWhile,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_P_2,V_xs_2))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_return__list__def,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__append1,axiom,
% 22.40/22.27 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__nth,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nth__length__takeWhile,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ~ 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))))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__not__last,axiom,
% 22.40/22.27 ! [T_b,V_xs_2] :
% 22.40/22.27 ( V_xs_2 != c_List_Olist_ONil(T_b)
% 22.40/22.27 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
% 22.40/22.27 ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transfer__nat__int__list__return__embed,axiom,
% 22.40/22.27 ! [V_l] :
% 22.40/22.27 ( c_List_Onat__list(V_l)
% 22.40/22.27 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_embed__list__def,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__neq__rev,axiom,
% 22.40/22.27 ! [V_x_2,V_xs_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile__neq__rev,axiom,
% 22.40/22.27 ! [V_x_2,V_xs_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__dropWhile__id,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__dropWhile,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_P_2,V_xs_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__dropWhile__le,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile__eq__Nil__conv,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) = c_List_Olist_ONil(T_b)
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile_Osimps_I2_J,axiom,
% 22.40/22.27 ! [V_xs_2,T_b,V_x_2,V_P_2] :
% 22.40/22.27 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile_Osimps_I1_J,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__dropWhile,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__dropWhile,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_OdropWhile(T_b,V_P_2,V_xs_2) != c_List_Olist_ONil(T_b)
% 22.40/22.27 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_P_2,V_xs_2)))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile__map,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile__append1,axiom,
% 22.40/22.27 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile__eq__Cons__conv,axiom,
% 22.40/22.27 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 <=> ( 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))
% 22.40/22.27 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile__eq__drop,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile__nth,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b,V_j_2] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => 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)))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_listsum__map__filter,axiom,
% 22.40/22.27 ! [V_f_2,V_P_2,V_xs_2,T_b,T_c] :
% 22.40/22.27 ( class_Groups_Omonoid__add(T_c)
% 22.40/22.27 => ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => ( ~ hBOOL(hAPP(V_P_2,B_x))
% 22.40/22.27 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted__nth__monoI,axiom,
% 22.40/22.27 ! [V_xs,T_a] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_a)
% 22.40/22.27 => ( ! [B_i,B_j] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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))) ) )
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__eq__filter,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( ! [B_x] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_b,V_P_2),V_xs_2) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__eq__take__P__nth,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 22.40/22.27 ( ! [B_i] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2))
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) ) )
% 22.40/22.27 => ( ( 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)))
% 22.40/22.27 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) )
% 22.40/22.27 => c_List_OtakeWhile(T_b,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),V_n_2),V_xs_2) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__takeWhile__less__P__nth,axiom,
% 22.40/22.27 ! [V_xs_2,T_b,V_P_2,V_j_2] :
% 22.40/22.27 ( ! [B_i] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i))) )
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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)))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted_Osimps,axiom,
% 22.40/22.27 ! [V_a_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,V_a_2)
% 22.40/22.27 <=> ( V_a_2 = c_List_Olist_ONil(T_b)
% 22.40/22.27 | ? [B_xs,B_x] :
% 22.40/22.27 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
% 22.40/22.27 & ! [B_xa] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),hAPP(c_List_Oset(T_b),B_xs)))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),B_xa)) )
% 22.40/22.27 & c_List_Olinorder__class_Osorted(T_b,B_xs) ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_not__in__set__insert,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_List_Oinsert__def,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 )
% 22.40/22.27 & ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insert__remdups,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__insert,axiom,
% 22.40/22.27 ! [V_x,V_xs,T_a] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_in__set__insert,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => c_List_Oinsert(T_b,V_x_2,V_xs_2) = V_xs_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_List_Oset__insert,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insert__Nil,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat__map__maps,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_maps__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_maps__simps_I2_J,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_maps__simps_I1_J,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_distinct__concat,axiom,
% 22.40/22.27 ! [V_xs_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_b)),V_xs_2))
% 22.40/22.27 => ( ! [B_ys] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(T_b),B_ys)) )
% 22.40/22.27 => ( ! [B_ys] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 22.40/22.27 => ! [B_zs] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)))
% 22.40/22.27 => ( B_ys != B_zs
% 22.40/22.27 => 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)) ) ) )
% 22.40/22.27 => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Oconcat(T_b,V_xs_2))) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_measures__lesseq,axiom,
% 22.40/22.27 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( 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)))
% 22.40/22.27 => 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)))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_wf__measures,axiom,
% 22.40/22.27 ! [V_fs_2,T_b] : c_Wellfounded_Owf(T_b,c_List_Omeasures(T_b,V_fs_2)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_in__measures_I1_J,axiom,
% 22.40/22.27 ! [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))))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_measures__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_measures__less,axiom,
% 22.40/22.27 ! [V_fs_2,T_b,V_y_2,V_x_2,V_f_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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)))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_in__measures_I2_J,axiom,
% 22.40/22.27 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_b] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 <=> ( 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)))
% 22.40/22.27 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
% 22.40/22.27 & 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))) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_foldl__apply,axiom,
% 22.40/22.27 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_c,T_d,V_xs_2,T_b] :
% 22.40/22.27 ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => 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)) )
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_order__fun_I2_J,axiom,
% 22.40/22.27 ! [V_g_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( ( class_Orderings_Oorder(T_c)
% 22.40/22.27 & class_Enum_Oenum(T_b) )
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 22.40/22.27 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 22.40/22.27 & 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)))) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_enum__ex__prod__def,axiom,
% 22.40/22.27 ! [V_P_2,T_b,T_c] :
% 22.40/22.27 ( ( class_Enum_Oenum(T_c)
% 22.40/22.27 & class_Enum_Oenum(T_b) )
% 22.40/22.27 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_b,T_c)),V_P_2))
% 22.40/22.27 <=> 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))))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_exists__code,axiom,
% 22.40/22.27 ! [V_P_2,T_b] :
% 22.40/22.27 ( class_Enum_Oenum(T_b)
% 22.40/22.27 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 22.40/22.27 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_enum__ex,axiom,
% 22.40/22.27 ! [V_P_2,T_b] :
% 22.40/22.27 ( class_Enum_Oenum(T_b)
% 22.40/22.27 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_b),V_P_2))
% 22.40/22.27 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__obtain__same__length,axiom,
% 22.40/22.27 ! [V_P_2,V_ys_2,T_c,V_xs_2,T_b] :
% 22.40/22.27 ( ( 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))
% 22.40/22.27 => 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)))) )
% 22.40/22.27 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_pos__not__random__dseq__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_dropWhile__append2,axiom,
% 22.40/22.27 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 22.40/22.27 ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all2__all__nthI,axiom,
% 22.40/22.27 ! [V_P_2,V_b_2,T_c,V_a_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 => ( ! [B_n] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => 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))) )
% 22.40/22.27 => c_List_Olist__all2(T_b,T_c,V_P_2,V_a_2,V_b_2) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_finite__sorted__distinct__unique,axiom,
% 22.40/22.27 ! [V_A_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.27 => ? [B_x] :
% 22.40/22.27 ( hAPP(c_List_Oset(T_b),B_x) = V_A_2
% 22.40/22.27 & c_List_Olinorder__class_Osorted(T_b,B_x)
% 22.40/22.27 & hBOOL(hAPP(c_List_Odistinct(T_b),B_x))
% 22.40/22.27 & ! [B_y] :
% 22.40/22.27 ( ( hAPP(c_List_Oset(T_b),B_y) = V_A_2
% 22.40/22.27 & c_List_Olinorder__class_Osorted(T_b,B_y)
% 22.40/22.27 & hBOOL(hAPP(c_List_Odistinct(T_b),B_y)) )
% 22.40/22.27 => B_y = B_x ) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_takeWhile__append2,axiom,
% 22.40/22.27 ! [V_ys_2,V_P_2,V_xs_2,T_b] :
% 22.40/22.27 ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_insort__is__Cons,axiom,
% 22.40/22.27 ! [V_a_2,V_f_2,V_xs_2,T_b,T_c] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_c)
% 22.40/22.27 => ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) )
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__eq__Cons__iff,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 <=> ? [B_us,B_vs] :
% 22.40/22.27 ( 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))
% 22.40/22.27 & ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 22.40/22.27 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 & hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Cons__eq__filter__iff,axiom,
% 22.40/22.27 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 <=> ? [B_us,B_vs] :
% 22.40/22.27 ( 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))
% 22.40/22.27 & ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),B_us)))
% 22.40/22.27 => ~ hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 & hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 & V_xs_2 = hAPP(c_List_Ofilter(T_b,V_P_2),B_vs) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_order__fun_I1_J,axiom,
% 22.40/22.27 ! [V_g_2,V_f_2,T_b,T_c] :
% 22.40/22.27 ( ( class_Orderings_Oorder(T_c)
% 22.40/22.27 & class_Enum_Oenum(T_b) )
% 22.40/22.27 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,T_c)),V_f_2),V_g_2))
% 22.40/22.27 <=> 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_enum__all,axiom,
% 22.40/22.27 ! [V_P_2,T_b] :
% 22.40/22.27 ( class_Enum_Oenum(T_b)
% 22.40/22.27 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2))
% 22.40/22.27 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_all__code,axiom,
% 22.40/22.27 ! [V_P_2,T_b] :
% 22.40/22.27 ( class_Enum_Oenum(T_b)
% 22.40/22.27 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1))
% 22.40/22.27 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_b),V_P_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_enum__all__prod__def,axiom,
% 22.40/22.27 ! [V_P_2,T_b,T_c] :
% 22.40/22.27 ( ( class_Enum_Oenum(T_c)
% 22.40/22.27 & class_Enum_Oenum(T_b) )
% 22.40/22.27 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_b,T_c)),V_P_2))
% 22.40/22.27 <=> 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))))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ball__nth,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,T_b,V_n_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_sorted_OCons,axiom,
% 22.40/22.27 ! [V_x_2,V_xs_2,T_b] :
% 22.40/22.27 ( class_Orderings_Olinorder(T_b)
% 22.40/22.27 => ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) )
% 22.40/22.27 => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
% 22.40/22.27 => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ex__length,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 22.40/22.27 <=> ? [B_n] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_in__set__conv__decomp__first,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 <=> ? [B_ys] :
% 22.40/22.27 ( ? [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))
% 22.40/22.27 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_ys))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ex__simps_I2_J,axiom,
% 22.40/22.27 ! [V_P_2,T_b] : ~ c_List_Olist__ex(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ex__append,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 22.40/22.27 <=> ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 22.40/22.27 | c_List_Olist__ex(T_b,V_P_2,V_ys_2) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ex__iff,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 22.40/22.27 <=> ? [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ex__rev,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__ex(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 22.40/22.27 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ex__simps_I1_J,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__ex(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 22.40/22.27 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 | c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_in__set__conv__decomp,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 <=> ? [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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_in__set__conv__decomp__last,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 <=> ? [B_ys,B_zs] :
% 22.40/22.27 ( 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))
% 22.40/22.27 & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),B_zs))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all__length,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 22.40/22.27 <=> ! [B_n] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_measure__function__int,axiom,
% 22.40/22.27 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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all__simps_I2_J,axiom,
% 22.40/22.27 ! [V_P_2,T_b] : c_List_Olist__all(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all__append,axiom,
% 22.40/22.27 ! [V_ys_2,V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))
% 22.40/22.27 <=> ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 22.40/22.27 & c_List_Olist__all(T_b,V_P_2,V_ys_2) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_measure__size,axiom,
% 22.40/22.27 ! [T_b] :
% 22.40/22.27 ( class_Nat_Osize(T_b)
% 22.40/22.27 => c_FunDef_Ois__measure(T_b,c_Nat_Osize__class_Osize(T_b)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_is__measure_Ointros,axiom,
% 22.40/22.27 ! [V_f_2,T_b] : c_FunDef_Ois__measure(T_b,V_f_2) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_is__measure_Oequations,axiom,
% 22.40/22.27 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_is__measure_Osimps,axiom,
% 22.40/22.27 ! [V_a_2,T_b] : c_FunDef_Ois__measure(T_b,V_a_2) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all__iff,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_measure__fst,axiom,
% 22.40/22.27 ! [T_c,V_f_2,T_b] :
% 22.40/22.27 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_measure__snd,axiom,
% 22.40/22.27 ! [T_c,V_f_2,T_b] :
% 22.40/22.27 ( c_FunDef_Ois__measure(T_b,V_f_2)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all__rev,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__all(T_b,V_P_2,hAPP(c_List_Orev(T_b),V_xs_2))
% 22.40/22.27 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all__simps_I1_J,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__all(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 22.40/22.27 <=> ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 & c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Ball__set__list__all,axiom,
% 22.40/22.27 ! [V_P_2,V_xs_2,T_b] :
% 22.40/22.27 ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 <=> c_List_Olist__all(T_b,V_P_2,V_xs_2) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__all__iff__raw,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__all(T_b,V_P_2,V_xs_2)
% 22.40/22.27 <=> ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ex1__simps_I2_J,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__ex1(T_b,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))
% 22.40/22.27 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => c_List_Olist__ex1(T_b,V_P_2,V_xs_2) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_transfer__morphism__int__nat,axiom,
% 22.40/22.27 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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ex1__simps_I1_J,axiom,
% 22.40/22.27 ! [V_P_2,T_b] : ~ c_List_Olist__ex1(T_b,V_P_2,c_List_Olist_ONil(T_b)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_bool_Osize_I4_J,axiom,
% 22.40/22.27 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_bool_Osize_I3_J,axiom,
% 22.40/22.27 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_list__ex1__iff,axiom,
% 22.40/22.27 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.27 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 22.40/22.27 <=> ? [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 & hBOOL(hAPP(V_P_2,B_x))
% 22.40/22.27 & ! [B_y] :
% 22.40/22.27 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 & hBOOL(hAPP(V_P_2,B_y)) )
% 22.40/22.27 => B_y = B_x ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
% 22.40/22.27 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 22.40/22.27 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.27 => 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) )
% 22.40/22.27 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
% 22.40/22.27 ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
% 22.40/22.27 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.27 => 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) )
% 22.40/22.27 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
% 22.40/22.27 => 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)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__DSequence_Oneg__bind__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__DSequence_Opos__empty__def,axiom,
% 22.40/22.27 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_pos__empty__def,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_neg__bind__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__DSequence_Opos__bind__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_neg__map__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_neg__single__def,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_pos__bind__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__DSequence_Oneg__single__def,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_pos__map__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_pos__single__def,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__splice,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_splice_Osimps_I3_J,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_splice__Nil2,axiom,
% 22.40/22.27 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ).
% 22.40/22.27
% 22.40/22.27 fof(fact_splice_Osimps_I1_J,axiom,
% 22.40/22.27 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ).
% 22.40/22.27
% 22.40/22.27 fof(fact_splice_Osimps_I2_J,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__DSequence_Opos__single__def,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_acyclicP__converse,axiom,
% 22.40/22.27 ! [V_r_2,T_b] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 <=> 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_converse__meet,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_conversep__noteq,axiom,
% 22.40/22.27 ! [V_y_2,V_x_2,T_b] :
% 22.40/22.27 ( 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))
% 22.40/22.27 <=> V_x_2 != V_y_2 ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_conversep__eq,axiom,
% 22.40/22.27 ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal ).
% 22.40/22.27
% 22.40/22.27 fof(fact_conversep__conversep,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_conversep__iff,axiom,
% 22.40/22.27 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 22.40/22.27 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_conversep_Oequations,axiom,
% 22.40/22.27 ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
% 22.40/22.27 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_conversep_Ointros,axiom,
% 22.40/22.27 ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
% 22.40/22.27 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_conversepD,axiom,
% 22.40/22.27 ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
% 22.40/22.27 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_converse__pred__comp,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_converse__join,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_conversep__converse__eq,axiom,
% 22.40/22.27 ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
% 22.40/22.27 ( 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))
% 22.40/22.27 <=> 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_,axiom,
% 22.40/22.27 ! [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)))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_tl__replicate,axiom,
% 22.40/22.27 ! [V_x,T_a,V_n] :
% 22.40/22.27 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => 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) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_replicate__length__filter,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_length__replicate,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__replicate__const,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_replicate__app__Cons__same,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_replicate__Suc,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_rev__replicate,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_take__replicate,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_drop__replicate,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_hd__replicate,axiom,
% 22.40/22.27 ! [V_x,T_a,V_n] :
% 22.40/22.27 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_last__replicate,axiom,
% 22.40/22.27 ! [V_x,T_a,V_n] :
% 22.40/22.27 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_zip__replicate,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Bex__set__replicate,axiom,
% 22.40/22.27 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 22.40/22.27 ( ? [B_x] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 & hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 22.40/22.27 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_Ball__set__replicate,axiom,
% 22.40/22.27 ! [V_P_2,V_a_2,V_n_2,T_b] :
% 22.40/22.27 ( ! [B_x] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.27 <=> ( hBOOL(hAPP(V_P_2,V_a_2))
% 22.40/22.27 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_replicate__eq__replicate,axiom,
% 22.40/22.27 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_b] :
% 22.40/22.27 ( c_List_Oreplicate(T_b,V_m_2,V_x_2) = c_List_Oreplicate(T_b,V_n_2,V_y_2)
% 22.40/22.27 <=> ( V_m_2 = V_n_2
% 22.40/22.27 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => V_x_2 = V_y_2 ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_nth__replicate,axiom,
% 22.40/22.27 ! [V_x,T_a,V_n,V_i] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n))
% 22.40/22.27 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_replicate__add,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_append__replicate__commute,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_filter__replicate,axiom,
% 22.40/22.27 ! [V_n_2,T_b,V_x_2,V_P_2] :
% 22.40/22.27 ( ( hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(V_P_2,V_x_2))
% 22.40/22.27 => 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) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_concat__replicate__trivial,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_replicate__0,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_empty__replicate,axiom,
% 22.40/22.27 ! [V_x_2,V_n_2,T_b] :
% 22.40/22.27 ( c_List_Olist_ONil(T_b) = c_List_Oreplicate(T_b,V_n_2,V_x_2)
% 22.40/22.27 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_replicate__empty,axiom,
% 22.40/22.27 ! [V_x_2,V_n_2,T_b] :
% 22.40/22.27 ( c_List_Oreplicate(T_b,V_n_2,V_x_2) = c_List_Olist_ONil(T_b)
% 22.40/22.27 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__replicate,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_in__set__replicate,axiom,
% 22.40/22.27 ! [V_y_2,V_n_2,V_x_2,T_b] :
% 22.40/22.27 ( 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))))
% 22.40/22.27 <=> ( V_x_2 = V_y_2
% 22.40/22.27 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_replicate__append__same,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_map__replicate__trivial,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__replicate__conv__if,axiom,
% 22.40/22.27 ! [V_x_2,T_b,V_n_2] :
% 22.40/22.27 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => 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)) )
% 22.40/22.27 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => 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))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__replicate,axiom,
% 22.40/22.27 ! [V_x_2,T_b,V_n_2] :
% 22.40/22.27 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
% 22.40/22.27 => 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))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_set__replicate__Suc,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_small__lazy__list_Osimps,axiom,
% 22.40/22.27 ! [V_d_2,T_b] :
% 22.40/22.27 ( class_Lazy__Sequence_Osmall__lazy(T_b)
% 22.40/22.27 => 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)))) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_eq__comp__r,axiom,
% 22.40/22.27 ! [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 ).
% 22.40/22.27
% 22.40/22.27 fof(fact_small__lazy__prod__def,axiom,
% 22.40/22.27 ! [V_d,T_b,T_a] :
% 22.40/22.27 ( ( class_Lazy__Sequence_Osmall__lazy(T_a)
% 22.40/22.27 & class_Lazy__Sequence_Osmall__lazy(T_b) )
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_New__DSequence_Opos__union__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lazy__sequence_Osize_I4_J,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact__01,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lazy__sequence_Oinject,axiom,
% 22.40/22.27 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_b] :
% 22.40/22.27 ( 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)
% 22.40/22.27 <=> ( V_a_2 = V_a_H_2
% 22.40/22.27 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_pos__union__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lazy__sequence_Osize_I2_J,axiom,
% 22.40/22.27 ! [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))) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_small__lazy_H_Osimps,axiom,
% 22.40/22.27 ! [V_i,V_d] :
% 22.40/22.27 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 22.40/22.27 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i))
% 22.40/22.27 => 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)))) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_small__lazy_H_Opsimps,axiom,
% 22.40/22.27 ! [V_i_2,V_d_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 22.40/22.27 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) )
% 22.40/22.27 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2))
% 22.40/22.27 => 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)))) ) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_small__lazy__int__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_small__lazy_H_Opinduct,axiom,
% 22.40/22.27 ! [V_P_2,V_a1_2,V_a0_2] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( ! [B_d,B_i] :
% 22.40/22.27 ( 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)))
% 22.40/22.27 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i))
% 22.40/22.27 => 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)))) )
% 22.40/22.27 => hBOOL(hAPP(hAPP(V_P_2,B_d),B_i)) ) )
% 22.40/22.27 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_size__code,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lazy__sequence__size__code,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_seq__case,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_yieldn__def,axiom,
% 22.40/22.27 ! [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)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_lazy__sequence_Osimps_I5_J,axiom,
% 22.40/22.27 ! [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) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_refl__on__INTER,axiom,
% 22.40/22.27 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 22.40/22.27 ( ! [B_x] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 22.40/22.27 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 22.40/22.27 => 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)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_in__set__member,axiom,
% 22.40/22.27 ! [V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.27 <=> hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2)) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_member__rec_I2_J,axiom,
% 22.40/22.27 ! [V_y,T_a] : ~ hBOOL(hAPP(hAPP(c_List_Omember(T_a),c_List_Olist_ONil(T_a)),V_y)) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_member__set,axiom,
% 22.40/22.27 ! [T_b] : c_List_Omember(T_b) = c_List_Oset(T_b) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_member__rec_I1_J,axiom,
% 22.40/22.27 ! [V_y_2,V_xs_2,V_x_2,T_b] :
% 22.40/22.27 ( 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))
% 22.40/22.27 <=> ( V_x_2 = V_y_2
% 22.40/22.27 | hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_y_2)) ) ) ).
% 22.40/22.27
% 22.40/22.27 fof(fact_List_Omember__def,axiom,
% 22.40/22.28 ! [V_x_2,V_xs_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_List_Omember(T_b),V_xs_2),V_x_2))
% 22.40/22.28 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_list__ex1__iff__raw,axiom,
% 22.40/22.28 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.28 ( c_List_Olist__ex1(T_b,V_P_2,V_xs_2)
% 22.40/22.28 <=> ? [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.28 & hBOOL(hAPP(V_P_2,B_x))
% 22.40/22.28 & ! [B_y] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.28 & hBOOL(hAPP(V_P_2,B_y)) )
% 22.40/22.28 => B_y = B_x ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_setsum__UNION__zero,axiom,
% 22.40/22.28 ! [V_f_2,V_S_2,T_b,T_c] :
% 22.40/22.28 ( class_Groups_Ocomm__monoid__add(T_c)
% 22.40/22.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),V_S_2))
% 22.40/22.28 => ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_S_2))
% 22.40/22.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),B_x)) )
% 22.40/22.28 => ( ! [B_T1] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T1),V_S_2))
% 22.40/22.28 => ! [B_T2] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_T2),V_S_2))
% 22.40/22.28 => ( B_T1 != B_T2
% 22.40/22.28 => ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T1))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),B_T2))
% 22.40/22.28 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) )
% 22.40/22.28 => 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) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_THE__default__def,axiom,
% 22.40/22.28 ! [V_d_2,T_b,V_P_2] :
% 22.40/22.28 ( ( ? [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(V_P_2,B_x))
% 22.40/22.28 & ! [B_y] :
% 22.40/22.28 ( hBOOL(hAPP(V_P_2,B_y))
% 22.40/22.28 => B_y = B_x ) )
% 22.40/22.28 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = c_HOL_OThe(T_b,V_P_2) )
% 22.40/22.28 & ( ~ ? [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(V_P_2,B_x))
% 22.40/22.28 & ! [B_y] :
% 22.40/22.28 ( hBOOL(hAPP(V_P_2,B_y))
% 22.40/22.28 => B_y = B_x ) )
% 22.40/22.28 => c_FunDef_OTHE__default(T_b,V_d_2,V_P_2) = V_d_2 ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_INF2__I,axiom,
% 22.40/22.28 ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,T_b] :
% 22.40/22.28 ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.28 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) )
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_SUP2__E,axiom,
% 22.40/22.28 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_d,T_c,T_b] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ~ ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.28 => ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_finite__maxlen,axiom,
% 22.40/22.28 ! [V_M_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),V_M_2))
% 22.40/22.28 => ? [B_n] :
% 22.40/22.28 ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_x),V_M_2))
% 22.40/22.28 => 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)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_lazy__sequence_Osize_I3_J,axiom,
% 22.40/22.28 ! [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) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_lazy__sequence_Osize_I1_J,axiom,
% 22.40/22.28 ! [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) ).
% 22.40/22.28
% 22.40/22.28 fof(fact__02,axiom,
% 22.40/22.28 ! [V_yq,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OEmpty(T_a),V_yq) = V_yq ).
% 22.40/22.28
% 22.40/22.28 fof(fact_lazy__sequence_Osimps_I3_J,axiom,
% 22.40/22.28 ! [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) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_lazy__sequence_Osimps_I2_J,axiom,
% 22.40/22.28 ! [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) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_lazy__sequence_Osimps_I4_J,axiom,
% 22.40/22.28 ! [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 ).
% 22.40/22.28
% 22.40/22.28 fof(fact_list__all__iff__all__interval__int,axiom,
% 22.40/22.28 ! [V_j_2,V_i_2,V_P_2] :
% 22.40/22.28 ( c_List_Olist__all(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 22.40/22.28 <=> c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_list__ex__iff__not__all__inverval__int,axiom,
% 22.40/22.28 ! [V_j_2,V_i_2,V_P_2] :
% 22.40/22.28 ( c_List_Olist__ex(tc_Int_Oint,V_P_2,c_List_Oupto(V_i_2,V_j_2))
% 22.40/22.28 <=> ~ 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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_all__interval__int__def,axiom,
% 22.40/22.28 ! [V_j_2,V_i_2,V_P_2] :
% 22.40/22.28 ( c_List_Oall__interval__int(V_P_2,V_i_2,V_j_2)
% 22.40/22.28 <=> ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2)))
% 22.40/22.28 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_code__numeral_Orecs_I2_J,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Random_Osimps,axiom,
% 22.40/22.28 ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
% 22.40/22.28 ( ( 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)))
% 22.40/22.28 => 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)) )
% 22.40/22.28 & ( ~ 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)))
% 22.40/22.28 => 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))))))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_code__numeral_Orecs_I1_J,axiom,
% 22.40/22.28 ! [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 ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Random__Sequence_Oempty__def,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Random__Sequence_Osingle__def,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Random__Sequence_Omap__def,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_exE__realizer,axiom,
% 22.40/22.28 ! [T_d,V_f_2,V_Q_2,V_p_2,T_b,T_c,V_P_2] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( ! [B_x,B_y] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(V_P_2,B_y),B_x))
% 22.40/22.28 => hBOOL(hAPP(V_Q_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
% 22.40/22.28 => 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))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Image__Collect__split,axiom,
% 22.40/22.28 ! [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)))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_lexord__trans,axiom,
% 22.40/22.28 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( 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)))
% 22.40/22.28 => ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => 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))) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__less__than,axiom,
% 22.40/22.28 c_Relation_Otrans(tc_Nat_Onat,c_Wellfounded_Oless__than) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__lex__prod,axiom,
% 22.40/22.28 ! [V_R2_2,T_c,V_R1_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_R1_2)
% 22.40/22.28 => ( c_Relation_Otrans(T_c,V_R2_2)
% 22.40/22.28 => c_Relation_Otrans(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_R1_2,V_R2_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_transD,axiom,
% 22.40/22.28 ! [V_c_2,V_b_2,V_a_2,V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => ( 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))
% 22.40/22.28 => ( 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))
% 22.40/22.28 => 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)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__def,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 <=> ! [B_x,B_y] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ! [B_z] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => 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)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__rtrancl,axiom,
% 22.40/22.28 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__Id,axiom,
% 22.40/22.28 ! [T_b] : c_Relation_Otrans(T_b,c_Relation_OId(T_b)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__trancl,axiom,
% 22.40/22.28 ! [V_r_2,T_b] : c_Relation_Otrans(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trancl__id,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => c_Transitive__Closure_Otrancl(T_b,V_r_2) = V_r_2 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__Id__on,axiom,
% 22.40/22.28 ! [V_A_2,T_b] : c_Relation_Otrans(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__finite__psubset,axiom,
% 22.40/22.28 ! [T_b] : c_Relation_Otrans(tc_fun(T_b,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_b)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_lexord__transI,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olexord(T_b,V_r_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_listrel__trans,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => c_Relation_Otrans(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bex__empty,axiom,
% 22.40/22.28 ! [V_P_2,T_b] :
% 22.40/22.28 ~ ? [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
% 22.40/22.28 & hBOOL(hAPP(V_P_2,B_x)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__converse,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 22.40/22.28 <=> c_Relation_Otrans(T_b,V_r_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_finite__Collect__bex,axiom,
% 22.40/22.28 ! [V_Q_2,T_c,V_A_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.28 => ( 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)))))
% 22.40/22.28 <=> ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.28 => 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)))) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bex__UNIV,axiom,
% 22.40/22.28 ! [V_P_2,T_b] :
% 22.40/22.28 ( ? [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))))
% 22.40/22.28 & hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.28 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__Int,axiom,
% 22.40/22.28 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => ( c_Relation_Otrans(T_b,V_s_2)
% 22.40/22.28 => 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)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_SUPR__bool__eq,axiom,
% 22.40/22.28 ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_HOL_Obool) = c_Set_OBex(T_b) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__O__subset,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__reflclI,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => 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))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__inv__image,axiom,
% 22.40/22.28 ! [V_f_2,T_c,V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => c_Relation_Otrans(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Union__eq,axiom,
% 22.40/22.28 ! [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)))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Bex__set__list__ex,axiom,
% 22.40/22.28 ! [V_P_2,V_xs_2,T_b] :
% 22.40/22.28 ( ? [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.28 & hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.28 <=> c_List_Olist__ex(T_b,V_P_2,V_xs_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_list__ex__iff__raw,axiom,
% 22.40/22.28 ! [V_xs_2,V_P_2,T_b] :
% 22.40/22.28 ( c_List_Olist__ex(T_b,V_P_2,V_xs_2)
% 22.40/22.28 <=> ? [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
% 22.40/22.28 & hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_UN__eq,axiom,
% 22.40/22.28 ! [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))))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_INT__eq,axiom,
% 22.40/22.28 ! [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))))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Sup__fun__def,axiom,
% 22.40/22.28 ! [V_x_2,V_A_2,T_c,T_b] :
% 22.40/22.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.28 => 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)))))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Sup__apply,axiom,
% 22.40/22.28 ! [V_x_2,V_A_2,T_c,T_b] :
% 22.40/22.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.28 => 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)))))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Inf__fun__def,axiom,
% 22.40/22.28 ! [V_x_2,V_A_2,T_c,T_b] :
% 22.40/22.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.28 => 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)))))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Inf__apply,axiom,
% 22.40/22.28 ! [V_x_2,V_A_2,T_c,T_b] :
% 22.40/22.28 ( class_Complete__Lattice_Ocomplete__lattice(T_b)
% 22.40/22.28 => 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)))))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_max__extp_Ointros,axiom,
% 22.40/22.28 ! [V_R_2,V_Y_2,V_X_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2))
% 22.40/22.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_Y_2))
% 22.40/22.28 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.28 => ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_X_2))
% 22.40/22.28 => ? [B_xa] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_Y_2))
% 22.40/22.28 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) )
% 22.40/22.28 => c_Wellfounded_Omax__extp(T_b,V_R_2,V_X_2,V_Y_2) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_transp__def,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Predicate_Otransp(T_b,V_r_2)
% 22.40/22.28 <=> 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))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_transpE,axiom,
% 22.40/22.28 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b] :
% 22.40/22.28 ( c_Predicate_Otransp(T_b,V_r_2)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_z_2))
% 22.40/22.28 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_z_2)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_equivp__reflp__symp__transp,axiom,
% 22.40/22.28 ! [V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.28 <=> ( c_Predicate_Oreflp(T_b,V_R_2)
% 22.40/22.28 & c_Predicate_Osymp(T_b,V_R_2)
% 22.40/22.28 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_equivpI,axiom,
% 22.40/22.28 ! [V_R_2,T_b] :
% 22.40/22.28 ( c_Predicate_Oreflp(T_b,V_R_2)
% 22.40/22.28 => ( c_Predicate_Osymp(T_b,V_R_2)
% 22.40/22.28 => ( c_Predicate_Otransp(T_b,V_R_2)
% 22.40/22.28 => c_Equiv__Relations_Oequivp(T_b,V_R_2) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sympE,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2,V_r_2,T_b] :
% 22.40/22.28 ( c_Predicate_Osymp(T_b,V_r_2)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
% 22.40/22.28 => hBOOL(hAPP(hAPP(V_r_2,V_y_2),V_x_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_equivpE,axiom,
% 22.40/22.28 ! [V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.28 => ~ ( c_Predicate_Oreflp(T_b,V_R_2)
% 22.40/22.28 => ( c_Predicate_Osymp(T_b,V_R_2)
% 22.40/22.28 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_max__extp_Osimps,axiom,
% 22.40/22.28 ! [V_a2_2,V_a1_2,V_R_2,T_b] :
% 22.40/22.28 ( c_Wellfounded_Omax__extp(T_b,V_R_2,V_a1_2,V_a2_2)
% 22.40/22.28 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a1_2))
% 22.40/22.28 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_a2_2))
% 22.40/22.28 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.28 & ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_a1_2))
% 22.40/22.28 => ? [B_xa] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_a2_2))
% 22.40/22.28 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_trans__diff__Id,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => ( c_Relation_Oantisym(T_b,V_r_2)
% 22.40/22.28 => 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))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_antisym__Id__on,axiom,
% 22.40/22.28 ! [V_A_2,T_b] : c_Relation_Oantisym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_antisym__converse,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Oantisym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 22.40/22.28 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_antisym__empty,axiom,
% 22.40/22.28 ! [T_b] : c_Relation_Oantisym(T_b,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_antisym__Id,axiom,
% 22.40/22.28 ! [T_b] : c_Relation_Oantisym(T_b,c_Relation_OId(T_b)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_antisym__subset,axiom,
% 22.40/22.28 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ( c_Relation_Oantisym(T_b,V_s_2)
% 22.40/22.28 => c_Relation_Oantisym(T_b,V_r_2) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_antisym__def,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Oantisym(T_b,V_r_2)
% 22.40/22.28 <=> ! [B_x,B_y] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ( 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))
% 22.40/22.28 => B_x = B_y ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_antisymD,axiom,
% 22.40/22.28 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Oantisym(T_b,V_r_2)
% 22.40/22.28 => ( 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))
% 22.40/22.28 => ( 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))
% 22.40/22.28 => V_a_2 = V_b_2 ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_antisym__reflcl,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 <=> c_Relation_Oantisym(T_b,V_r_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_acyclic__impl__antisym__rtrancl,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Wellfounded_Oacyclic(T_b,V_r_2)
% 22.40/22.28 => c_Relation_Oantisym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_fun__lub__def,axiom,
% 22.40/22.28 ! [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)))))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__trans__comp__subset,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => 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)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_symD,axiom,
% 22.40/22.28 ! [V_b_2,V_a_2,V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => ( 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))
% 22.40/22.28 => 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)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__def,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 <=> ! [B_x,B_y] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => 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)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__rtrancl,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => c_Relation_Osym(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__Id,axiom,
% 22.40/22.28 ! [T_b] : c_Relation_Osym(T_b,c_Relation_OId(T_b)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__Un,axiom,
% 22.40/22.28 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => ( c_Relation_Osym(T_b,V_s_2)
% 22.40/22.28 => 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)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__trancl,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => c_Relation_Osym(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__Id__on,axiom,
% 22.40/22.28 ! [V_A_2,T_b] : c_Relation_Osym(T_b,c_Relation_OId__on(T_b,V_A_2)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_listrel__sym,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => c_Relation_Osym(tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__converse,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))
% 22.40/22.28 <=> c_Relation_Osym(T_b,V_r_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__conv__converse__eq,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 <=> hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2) = V_r_2 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__Int,axiom,
% 22.40/22.28 ! [V_s_2,V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => ( c_Relation_Osym(T_b,V_s_2)
% 22.40/22.28 => 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)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__Un__converse,axiom,
% 22.40/22.28 ! [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))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__inv__image,axiom,
% 22.40/22.28 ! [V_f_2,T_c,V_r_2,T_b] :
% 22.40/22.28 ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => c_Relation_Osym(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_sym__Int__converse,axiom,
% 22.40/22.28 ! [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))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_equivE,axiom,
% 22.40/22.28 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.28 => ~ ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.28 => ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => ~ c_Relation_Otrans(T_b,V_r_2) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_equivI,axiom,
% 22.40/22.28 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.28 ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.28 => ( c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 => ( c_Relation_Otrans(T_b,V_r_2)
% 22.40/22.28 => c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_equiv__def,axiom,
% 22.40/22.28 ! [V_r_2,V_A_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
% 22.40/22.28 <=> ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
% 22.40/22.28 & c_Relation_Osym(T_b,V_r_2)
% 22.40/22.28 & c_Relation_Otrans(T_b,V_r_2) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_symp__def,axiom,
% 22.40/22.28 ! [V_r_2,T_b] :
% 22.40/22.28 ( c_Predicate_Osymp(T_b,V_r_2)
% 22.40/22.28 <=> 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))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_part__equivp__refl__symp__transp,axiom,
% 22.40/22.28 ! [V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 22.40/22.28 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 22.40/22.28 & c_Predicate_Osymp(T_b,V_R_2)
% 22.40/22.28 & c_Predicate_Otransp(T_b,V_R_2) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_part__equivpI,axiom,
% 22.40/22.28 ! [T_b,V_R_2] :
% 22.40/22.28 ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 22.40/22.28 => ( c_Predicate_Osymp(T_b,V_R_2)
% 22.40/22.28 => ( c_Predicate_Otransp(T_b,V_R_2)
% 22.40/22.28 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_part__equivp__def,axiom,
% 22.40/22.28 ! [V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 22.40/22.28 <=> ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 22.40/22.28 & ! [B_x,B_y] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
% 22.40/22.28 <=> ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 22.40/22.28 & hBOOL(hAPP(hAPP(V_R_2,B_y),B_y))
% 22.40/22.28 & hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_part__equivp__symp,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2,V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 22.40/22.28 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_part__equivp__transp,axiom,
% 22.40/22.28 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
% 22.40/22.28 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_equivp__implies__part__equivp,axiom,
% 22.40/22.28 ! [V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.28 => c_Equiv__Relations_Opart__equivp(T_b,V_R_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_part__equivpE,axiom,
% 22.40/22.28 ! [V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 22.40/22.28 => ~ ( ? [B_x] : hBOOL(hAPP(hAPP(V_R_2,B_x),B_x))
% 22.40/22.28 => ( c_Predicate_Osymp(T_b,V_R_2)
% 22.40/22.28 => ~ c_Predicate_Otransp(T_b,V_R_2) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_part__equivp__typedef,axiom,
% 22.40/22.28 ! [V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Opart__equivp(T_b,V_R_2)
% 22.40/22.28 => ? [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))))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inj__iff,axiom,
% 22.40/22.28 ! [V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 <=> 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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__o__cancel,axiom,
% 22.40/22.28 ! [V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 => 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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__id,axiom,
% 22.40/22.28 ! [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) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__f__eq,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 22.40/22.28 => 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 ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__f__f,axiom,
% 22.40/22.28 ! [V_x_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 => 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 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__into__f__f,axiom,
% 22.40/22.28 ! [V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.28 => 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 ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__into__f__eq,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
% 22.40/22.28 => ( hAPP(V_f_2,V_x_2) = V_y_2
% 22.40/22.28 => hAPP(c_Hilbert__Choice_Oinv__into(T_b,T_c,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_f__inv__into__f,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,V_y_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 22.40/22.28 => 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 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__into__into,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,V_x_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__into__injective,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2,V_f_2,V_A_2,T_c,T_b] :
% 22.40/22.28 ( 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)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)))
% 22.40/22.28 => V_x_2 = V_y_2 ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_image__surj__f__inv__f,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_b,T_c] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => 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 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_surj__f__inv__f,axiom,
% 22.40/22.28 ! [V_y_2,V_f_2,T_b,T_c] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => 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 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_surj__iff__all,axiom,
% 22.40/22.28 ! [V_f_2,T_b,T_c] :
% 22.40/22.28 ( 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))
% 22.40/22.28 <=> ! [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 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_image__inv__into__cancel,axiom,
% 22.40/22.28 ! [V_B_H_2,V_A_H_2,V_A_2,V_f_2,T_b,T_c] :
% 22.40/22.28 ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = V_A_H_2
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_H_2),V_A_H_2))
% 22.40/22.28 => 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 ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__into__def,axiom,
% 22.40/22.28 ! [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))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__def,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_o__inv__o__cancel,axiom,
% 22.40/22.28 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 => 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 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_surj__imp__inj__inv,axiom,
% 22.40/22.28 ! [V_f_2,T_b,T_c] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => 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))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__image__comp,axiom,
% 22.40/22.28 ! [V_X_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 => 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 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_image__inv__f__f,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 => 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 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inj__imp__surj__inv,axiom,
% 22.40/22.28 ! [V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__into__image__cancel,axiom,
% 22.40/22.28 ! [V_S_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_A_2))
% 22.40/22.28 => 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 ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inj__on__inv__into,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => 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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__into__comp,axiom,
% 22.40/22.28 ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
% 22.40/22.28 => ( 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))))
% 22.40/22.28 => 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) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_surj__iff,axiom,
% 22.40/22.28 ! [V_f_2,T_b,T_c] :
% 22.40/22.28 ( 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))
% 22.40/22.28 <=> 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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inj__transfer,axiom,
% 22.40/22.28 ! [V_x_2,V_P_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 => ( ! [B_y] :
% 22.40/22.28 ( 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)))))
% 22.40/22.28 => 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))) )
% 22.40/22.28 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_fold__image__UN__disjoint,axiom,
% 22.40/22.28 ! [V_g_2,V_A_2,T_c,V_I_2,T_b,T_d] :
% 22.40/22.28 ( class_Groups_Ocomm__monoid__mult(T_d)
% 22.40/22.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_I_2))
% 22.40/22.28 => ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 22.40/22.28 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),hAPP(V_A_2,B_x))) )
% 22.40/22.28 => ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2))
% 22.40/22.28 => ! [B_xa] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_xa),V_I_2))
% 22.40/22.28 => ( B_x != B_xa
% 22.40/22.28 => 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)) ) ) )
% 22.40/22.28 => 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) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_nat__of__induct,axiom,
% 22.40/22.28 ! [V_P_2,V_y_2] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 22.40/22.28 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Onat__of,B_x)))
% 22.40/22.28 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_nat__of__cases,axiom,
% 22.40/22.28 ! [V_y_2] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 22.40/22.28 => ~ ! [B_x] : V_y_2 != hAPP(c_Code__Numeral_Onat__of,B_x) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_of__nat__induct,axiom,
% 22.40/22.28 ! [V_x_2,V_P_2] :
% 22.40/22.28 ( ! [B_y] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
% 22.40/22.28 => hBOOL(hAPP(V_P_2,hAPP(c_Code__Numeral_Oof__nat,B_y))) )
% 22.40/22.28 => hBOOL(hAPP(V_P_2,V_x_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_of__nat__cases,axiom,
% 22.40/22.28 ! [V_x_2] :
% 22.40/22.28 ~ ! [B_y] :
% 22.40/22.28 ( V_x_2 = hAPP(c_Code__Numeral_Oof__nat,B_y)
% 22.40/22.28 => ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_y),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_lazy__sequence_Orecs_I1_J,axiom,
% 22.40/22.28 ! [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 ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Least__Suc2,axiom,
% 22.40/22.28 ! [V_m_2,V_Q_2,V_n_2,V_P_2] :
% 22.40/22.28 ( hBOOL(hAPP(V_P_2,V_n_2))
% 22.40/22.28 => ( hBOOL(hAPP(V_Q_2,V_m_2))
% 22.40/22.28 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
% 22.40/22.28 => ( ! [B_k] :
% 22.40/22.28 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k)))
% 22.40/22.28 <=> hBOOL(hAPP(V_Q_2,B_k)) )
% 22.40/22.28 => 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)) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_lazy__sequence_Orecs_I2_J,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_beyond__def,axiom,
% 22.40/22.28 ! [V_l,V_k] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 22.40/22.28 => c_Quickcheck_Obeyond(V_k,V_l) = V_l )
% 22.40/22.28 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
% 22.40/22.28 => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__image__Collect__eq,axiom,
% 22.40/22.28 ! [V_P_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => 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))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__id,axiom,
% 22.40/22.28 ! [V_A_2,T_b] : c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_A_2) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__inv__into,axiom,
% 22.40/22.28 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 22.40/22.28 => 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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__into__inv__into__eq,axiom,
% 22.40/22.28 ! [V_a_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
% 22.40/22.28 => 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) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__imp__bij__inv,axiom,
% 22.40/22.28 ! [V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => 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))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inv__inv__eq,axiom,
% 22.40/22.28 ! [V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => 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 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_o__inv__distrib,axiom,
% 22.40/22.28 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( 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)))
% 22.40/22.28 => 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)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__image__INT,axiom,
% 22.40/22.28 ! [V_B_2,V_A_2,T_d,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__comp__iff2,axiom,
% 22.40/22.28 ! [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] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 22.40/22.28 => ( 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))
% 22.40/22.28 => ( c_Fun_Obij__betw(T_d,T_b,V_f_2,V_A_2,V_A_H_2)
% 22.40/22.28 <=> 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) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__comp__iff,axiom,
% 22.40/22.28 ! [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] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 22.40/22.28 => ( c_Fun_Obij__betw(T_c,T_d,V_f_H_2,V_A_H_2,V_A_H_H_2)
% 22.40/22.28 <=> 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) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__trans,axiom,
% 22.40/22.28 ! [V_C_2,V_g_2,T_d,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 22.40/22.28 => ( c_Fun_Obij__betw(T_c,T_d,V_g_2,V_B_2,V_C_2)
% 22.40/22.28 => 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) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__comp,axiom,
% 22.40/22.28 ! [V_g_2,T_d,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( 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)))
% 22.40/22.28 => 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))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_finite__vimage__iff,axiom,
% 22.40/22.28 ! [V_F_2,V_h_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_c,V_h_2),V_F_2)))
% 22.40/22.28 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_F_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__image__Compl__eq,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__def,axiom,
% 22.40/22.28 ! [V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 & 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)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bijI,axiom,
% 22.40/22.28 ! [V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
% 22.40/22.28 => ( 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))
% 22.40/22.28 => 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))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__combine,axiom,
% 22.40/22.28 ! [V_D_2,V_C_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 22.40/22.28 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_C_2,V_D_2)
% 22.40/22.28 => ( 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))
% 22.40/22.28 => 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)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__Disj__Un,axiom,
% 22.40/22.28 ! [V_f_2,V_B_H_2,V_A_H_2,T_c,V_B_2,V_A_2,T_b] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ( 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))
% 22.40/22.28 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 22.40/22.28 => ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2)
% 22.40/22.28 => 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)) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__subset,axiom,
% 22.40/22.28 ! [V_B_H_2,V_B_2,V_A_H_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_A_H_2)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.40/22.28 => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2) = V_B_H_2
% 22.40/22.28 => c_Fun_Obij__betw(T_b,T_c,V_f_2,V_B_2,V_B_H_2) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__is__surj,axiom,
% 22.40/22.28 ! [V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__imp__surj,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_inj__on__imp__bij__betw,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__def,axiom,
% 22.40/22.28 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 22.40/22.28 <=> ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.28 & hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = V_B_2 ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__imp__inj__on,axiom,
% 22.40/22.28 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 22.40/22.28 => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__is__inj,axiom,
% 22.40/22.28 ! [V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__same__card,axiom,
% 22.40/22.28 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 22.40/22.28 => hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_beyond__zero,axiom,
% 22.40/22.28 ! [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) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__the__inv__into,axiom,
% 22.40/22.28 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 22.40/22.28 => 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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__empty1,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)
% 22.40/22.28 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__empty2,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__finite,axiom,
% 22.40/22.28 ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_c,V_f_2,V_A_2,V_B_2)
% 22.40/22.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.28 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_BIJ,axiom,
% 22.40/22.28 ! [V_B_2,T_c,V_A_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
% 22.40/22.28 => ( ? [B_f] : c_Fun_Obij__betw(T_b,T_c,B_f,V_A_2,V_B_2)
% 22.40/22.28 <=> hAPP(c_Finite__Set_Ocard(T_b),V_A_2) = hAPP(c_Finite__Set_Ocard(T_c),V_B_2) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__betw__id__iff,axiom,
% 22.40/22.28 ! [V_B_2,V_A_2,T_b] :
% 22.40/22.28 ( c_Fun_Obij__betw(T_b,T_b,c_Fun_Oid(T_b),V_A_2,V_B_2)
% 22.40/22.28 <=> V_A_2 = V_B_2 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__id,axiom,
% 22.40/22.28 ! [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))) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_vimage__subset__eq,axiom,
% 22.40/22.28 ! [V_A_2,V_B_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( 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))
% 22.40/22.28 <=> 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))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bij__vimage__eq__inv__image,axiom,
% 22.40/22.28 ! [V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => 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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_ex__bij__betw__nat__finite__1,axiom,
% 22.40/22.28 ! [V_M_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 22.40/22.28 => ? [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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Cantor__Bernstein,axiom,
% 22.40/22.28 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
% 22.40/22.28 => ( 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))
% 22.40/22.28 => ( c_Fun_Oinj__on(T_c,T_b,V_g_2,V_B_2)
% 22.40/22.28 => ( 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))
% 22.40/22.28 => ? [B_h] : c_Fun_Obij__betw(T_b,T_c,B_h,V_A_2,V_B_2) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_ex__bij__betw__nat__finite,axiom,
% 22.40/22.28 ! [V_M_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 22.40/22.28 => ? [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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_ex__bij__betw__finite__nat,axiom,
% 22.40/22.28 ! [V_M_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_M_2))
% 22.40/22.28 => ? [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))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_curry__def,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_refl__on__UNION,axiom,
% 22.40/22.28 ! [V_r_2,V_A_2,T_c,V_S_2,T_b] :
% 22.40/22.28 ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
% 22.40/22.28 => c_Relation_Orefl__on(T_c,hAPP(V_A_2,B_x),hAPP(V_r_2,B_x)) )
% 22.40/22.28 => 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)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_curryI,axiom,
% 22.40/22.28 ! [V_b_2,V_a_2,T_c,T_b,V_f_2] :
% 22.40/22.28 ( hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_split__curry,axiom,
% 22.40/22.28 ! [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 ).
% 22.40/22.28
% 22.40/22.28 fof(fact_curry__split,axiom,
% 22.40/22.28 ! [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 ).
% 22.40/22.28
% 22.40/22.28 fof(fact_curry__conv,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_curryD,axiom,
% 22.40/22.28 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 22.40/22.28 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_curryE,axiom,
% 22.40/22.28 ! [V_b_2,V_a_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(T_b,T_c,tc_HOL_Obool,V_f_2),V_a_2),V_b_2))
% 22.40/22.28 => hBOOL(hAPP(V_f_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bex__reg__eqv,axiom,
% 22.40/22.28 ! [V_P_2,V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.28 => ( ? [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 22.40/22.28 & hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.28 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_wf__weak__decr__stable,axiom,
% 22.40/22.28 ! [V_r_2,V_f_2,T_b] :
% 22.40/22.28 ( ! [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)))
% 22.40/22.28 => ( c_Wellfounded_Owf(T_b,c_Transitive__Closure_Otrancl(T_b,V_r_2))
% 22.40/22.28 => ? [B_i] :
% 22.40/22.28 ! [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) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Respects__def,axiom,
% 22.40/22.28 ! [V_x_2,V_R_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(c_Quotient_ORespects(T_b,V_R_2),V_x_2))
% 22.40/22.28 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_in__respects,axiom,
% 22.40/22.28 ! [V_R_2,V_x_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Quotient_ORespects(T_b,V_R_2)))
% 22.40/22.28 <=> hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_bex__reg__right,axiom,
% 22.40/22.28 ! [V_P_2,V_Q_2,V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.28 => ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(V_Q_2,B_x))
% 22.40/22.28 => hBOOL(hAPP(V_P_2,B_x)) )
% 22.40/22.28 => ( ? [B_x1] : hBOOL(hAPP(V_Q_2,B_x1))
% 22.40/22.28 => ? [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Quotient_ORespects(T_b,V_R_2)))
% 22.40/22.28 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_babs__reg__eqv,axiom,
% 22.40/22.28 ! [V_P_2,T_c,V_R_2,T_b] :
% 22.40/22.28 ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
% 22.40/22.28 => c_Quotient_OBabs(T_b,T_c,c_Quotient_ORespects(T_b,V_R_2),V_P_2) = V_P_2 ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_Babs__def,axiom,
% 22.40/22.28 ! [V_m_2,T_c,V_p_2,V_x_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_p_2))
% 22.40/22.28 => hAPP(c_Quotient_OBabs(T_b,T_c,V_p_2,V_m_2),V_x_2) = hAPP(V_m_2,V_x_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_INT__anti__mono,axiom,
% 22.40/22.28 ! [V_g_2,V_f_2,T_c,V_A_2,V_B_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
% 22.40/22.28 => ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.28 => 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))) )
% 22.40/22.28 => 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))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_INT__greatest,axiom,
% 22.40/22.28 ! [V_B_2,V_C_2,T_c,V_A_2,T_b] :
% 22.40/22.28 ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
% 22.40/22.28 => 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))) )
% 22.40/22.28 => 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))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_converse__rtranclE2,axiom,
% 22.40/22.28 ! [V_r_2,V_zb_2,V_za_2,V_xb_2,V_xa_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( 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)
% 22.40/22.28 => ~ ! [B_a,B_b] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ~ 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))) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_converse__rtrancl__induct2,axiom,
% 22.40/22.28 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2))
% 22.40/22.28 => ( ! [B_a,B_b,B_aa,B_ba] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ( 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)))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba))
% 22.40/22.28 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) )
% 22.40/22.28 => hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_rtrancl__induct2,axiom,
% 22.40/22.28 ! [V_P_2,V_r_2,V_by_2,V_bx_2,V_ay_2,V_ax_2,T_c,T_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_P_2,V_ax_2),V_ay_2))
% 22.40/22.28 => ( ! [B_a,B_b] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ! [B_aa,B_ba] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(V_P_2,B_a),B_b))
% 22.40/22.28 => hBOOL(hAPP(hAPP(V_P_2,B_aa),B_ba)) ) ) )
% 22.40/22.28 => hBOOL(hAPP(hAPP(V_P_2,V_bx_2),V_by_2)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_congruentI,axiom,
% 22.40/22.28 ! [T_c,V_f_2,V_r_2,T_b] :
% 22.40/22.28 ( ! [B_y,B_z] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => hAPP(V_f_2,B_y) = hAPP(V_f_2,B_z) )
% 22.40/22.28 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_congruent2I_H,axiom,
% 22.40/22.28 ! [T_d,V_f_2,V_r2_2,T_c,V_r1_2,T_b] :
% 22.40/22.28 ( ! [B_y1,B_z1] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => ! [B_y2,B_z2] :
% 22.40/22.28 ( 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))
% 22.40/22.28 => hAPP(hAPP(V_f_2,B_y1),B_y2) = hAPP(hAPP(V_f_2,B_z1),B_z2) ) )
% 22.40/22.28 => c_Equiv__Relations_Ocongruent2(T_b,T_c,T_d,V_r1_2,V_r2_2,V_f_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact__03,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact__04,axiom,
% 22.40/22.28 ! [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) ).
% 22.40/22.28
% 22.40/22.28 fof(fact__05,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_list__all__iff__all__interval__nat,axiom,
% 22.40/22.28 ! [V_j_2,V_i_2,V_P_2] :
% 22.40/22.28 ( c_List_Olist__all(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 22.40/22.28 <=> c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact__06,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact__07,axiom,
% 22.40/22.28 ! [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) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_all__interval__nat__def,axiom,
% 22.40/22.28 ! [V_j_2,V_i_2,V_P_2] :
% 22.40/22.28 ( c_List_Oall__interval__nat(V_P_2,V_i_2,V_j_2)
% 22.40/22.28 <=> ! [B_x] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => hBOOL(hAPP(V_P_2,B_x)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_list__ex__iff__not__all__inverval__nat,axiom,
% 22.40/22.28 ! [V_j_2,V_i_2,V_P_2] :
% 22.40/22.28 ( c_List_Olist__ex(tc_Nat_Onat,V_P_2,c_List_Oupt(V_i_2,V_j_2))
% 22.40/22.28 <=> ~ 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) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_New__DSequence_Opos__map__def,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_folding__image_Ocong,axiom,
% 22.40/22.28 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
% 22.40/22.28 ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
% 22.40/22.28 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
% 22.40/22.28 => ( ! [B_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2))
% 22.40/22.28 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) )
% 22.40/22.28 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(V_F_2,V_h_2),V_A_2) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_power__dvd__imp__le,axiom,
% 22.40/22.28 ! [V_n,V_m,V_i] :
% 22.40/22.28 ( 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)))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_finite__nonempty__imp__fold1Set,axiom,
% 22.40/22.28 ! [V_f_2,V_A_2,T_b] :
% 22.40/22.28 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
% 22.40/22.28 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
% 22.40/22.28 => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),B_x1)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oorder__refl,axiom,
% 22.40/22.28 ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__0__right,axiom,
% 22.40/22.28 ! [V_a,T_a] :
% 22.40/22.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__1__left,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__imp__le,axiom,
% 22.40/22.28 ! [V_n,V_k] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2,T_b] :
% 22.40/22.28 ( ( class_Divides_Osemiring__div(T_b)
% 22.40/22.28 & class_Int_Onumber(T_b) )
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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)))
% 22.40/22.28 <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_le__imp__power__dvd,axiom,
% 22.40/22.28 ! [V_a,V_n,V_m,T_a] :
% 22.40/22.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__power__le,axiom,
% 22.40/22.28 ! [V_m,V_n,V_y,V_x,T_a] :
% 22.40/22.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_y),V_m))) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_power__le__dvd,axiom,
% 22.40/22.28 ! [V_m,V_b,V_n,V_a,T_a] :
% 22.40/22.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_OatLeastatMost__subset__iff,axiom,
% 22.40/22.28 ! [V_d_2,V_c_2,V_b_2,V_a_2] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2,V_d_2)))
% 22.40/22.28 <=> ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2))
% 22.40/22.28 | ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c_2),V_a_2))
% 22.40/22.28 & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_d_2)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__diffD,axiom,
% 22.40/22.28 ! [V_n,V_m,V_k] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__diffD1,axiom,
% 22.40/22.28 ! [V_n,V_m,V_k] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_OlessThan__iff,axiom,
% 22.40/22.28 ! [V_k_2,V_i_2] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OlessThan(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)))
% 22.40/22.28 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_OgreaterThan__iff,axiom,
% 22.40/22.28 ! [V_k_2,V_i_2] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OgreaterThan(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)))
% 22.40/22.28 <=> ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_OatLeast__iff,axiom,
% 22.40/22.28 ! [V_k_2,V_i_2] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
% 22.40/22.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_i_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_OatMost__iff,axiom,
% 22.40/22.28 ! [V_k_2,V_i_2] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_i_2),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2)))
% 22.40/22.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_i_2),V_k_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__1__iff__1,axiom,
% 22.40/22.28 ! [V_m_2] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
% 22.40/22.28 <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_nat__dvd__not__less,axiom,
% 22.40/22.28 ! [V_n,V_m] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
% 22.40/22.28 => ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__div__neg,axiom,
% 22.40/22.28 ! [V_x,V_y,T_a] :
% 22.40/22.28 ( class_Divides_Oring__div(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 22.40/22.28 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__neg__div,axiom,
% 22.40/22.28 ! [V_x,V_y,T_a] :
% 22.40/22.28 ( class_Divides_Oring__div(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 22.40/22.28 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)),V_y) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__minus__iff,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2,T_b] :
% 22.40/22.28 ( class_Rings_Ocomm__ring__1(T_b)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_y_2)))
% 22.40/22.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_minus__dvd__iff,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2,T_b] :
% 22.40/22.28 ( class_Rings_Ocomm__ring__1(T_b)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
% 22.40/22.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__diff__nat,axiom,
% 22.40/22.28 ! [V_n,V_m,V_k] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__diff,axiom,
% 22.40/22.28 ! [V_z,V_y,V_x,T_a] :
% 22.40/22.28 ( class_Rings_Ocomm__ring__1(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_z))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_y),V_z))) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_div__power,axiom,
% 22.40/22.28 ! [V_n,V_x,V_y,T_a] :
% 22.40/22.28 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
% 22.40/22.28 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(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_y),V_n)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__imp__mod__0,axiom,
% 22.40/22.28 ! [V_b,V_a,T_a] :
% 22.40/22.28 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 22.40/22.28 => c_Divides_Odiv__class_Omod(T_a,V_b,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__eq__mod__eq__0,axiom,
% 22.40/22.28 ! [V_b_2,V_a_2,T_b] :
% 22.40/22.28 ( class_Divides_Osemiring__div(T_b)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 22.40/22.28 <=> c_Divides_Odiv__class_Omod(T_b,V_b_2,V_a_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__mod__iff,axiom,
% 22.40/22.28 ! [V_m_2,V_n_2,V_k_2,T_b] :
% 22.40/22.28 ( class_Divides_Osemiring__div(T_b)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_n_2))
% 22.40/22.28 => ( 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)))
% 22.40/22.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_k_2),V_m_2)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_mod__mod__cancel,axiom,
% 22.40/22.28 ! [V_a,V_b,V_c,T_a] :
% 22.40/22.28 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_c),V_b))
% 22.40/22.28 => 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) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__mod,axiom,
% 22.40/22.28 ! [V_n,V_m,V_k,T_a] :
% 22.40/22.28 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n))) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__mod__imp__dvd,axiom,
% 22.40/22.28 ! [V_n,V_m,V_k,T_a] :
% 22.40/22.28 ( class_Divides_Osemiring__div(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),c_Divides_Odiv__class_Omod(T_a,V_m,V_n)))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_n))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_k),V_m)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__0__left,axiom,
% 22.40/22.28 ! [V_a,T_a] :
% 22.40/22.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
% 22.40/22.28 => V_a = c_Groups_Ozero__class_Ozero(T_a) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_div__dvd__div,axiom,
% 22.40/22.28 ! [V_c_2,V_b_2,V_a_2,T_b] :
% 22.40/22.28 ( class_Divides_Osemiring__div(T_b)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_b_2))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_a_2),V_c_2))
% 22.40/22.28 => ( 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)))
% 22.40/22.28 <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_b_2),V_c_2)) ) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__power__same,axiom,
% 22.40/22.28 ! [V_n,V_y,V_x,T_a] :
% 22.40/22.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(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_y),V_n))) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__trans,axiom,
% 22.40/22.28 ! [V_c,V_b,V_a,T_a] :
% 22.40/22.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_b))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_b),V_c))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_c)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__refl,axiom,
% 22.40/22.28 ! [V_a,T_a] :
% 22.40/22.28 ( class_Rings_Ocomm__semiring__1(T_a)
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),V_a)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__asym,axiom,
% 22.40/22.28 ! [V_y,V_x] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__trans,axiom,
% 22.40/22.28 ! [V_z,V_y,V_x] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__asym_H,axiom,
% 22.40/22.28 ! [V_b,V_a] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 22.40/22.28 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__le__trans,axiom,
% 22.40/22.28 ! [V_z,V_y,V_x] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oord__less__eq__trans,axiom,
% 22.40/22.28 ! [V_c,V_b,V_a] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) )
% 22.40/22.28 => ( V_b = V_c
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__imp__not__eq2,axiom,
% 22.40/22.28 ! [V_y,V_x] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 => V_y != V_x ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__imp__not__eq,axiom,
% 22.40/22.28 ! [V_y,V_x] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 => V_x != V_y ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__imp__not__less,axiom,
% 22.40/22.28 ! [V_y,V_x] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__imp__le,axiom,
% 22.40/22.28 ! [V_y,V_x] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__not__sym,axiom,
% 22.40/22.28 ! [V_y,V_x] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 => ~ ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oless__imp__neq,axiom,
% 22.40/22.28 ! [V_y,V_x] :
% 22.40/22.28 ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 => V_x != V_y ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Ole__less__trans,axiom,
% 22.40/22.28 ! [V_z,V_y,V_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_y)) )
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_z),V_x)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oord__eq__less__trans,axiom,
% 22.40/22.28 ! [V_c,V_b,V_a] :
% 22.40/22.28 ( V_a = V_b
% 22.40/22.28 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_b)) )
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_c),V_a)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oorder__trans,axiom,
% 22.40/22.28 ! [V_z,V_y,V_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_z))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_z)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oantisym,axiom,
% 22.40/22.28 ! [V_y,V_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x))
% 22.40/22.28 => V_x = V_y ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd__antisym,axiom,
% 22.40/22.28 ! [V_n,V_m] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m),V_n))
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_n),V_m))
% 22.40/22.28 => V_m = V_n ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oord__le__eq__trans,axiom,
% 22.40/22.28 ! [V_c,V_b,V_a] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 22.40/22.28 => ( V_b = V_c
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Oord__eq__le__trans,axiom,
% 22.40/22.28 ! [V_c,V_b,V_a] :
% 22.40/22.28 ( V_a = V_b
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_c))
% 22.40/22.28 => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_c)) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Ole__neq__trans,axiom,
% 22.40/22.28 ! [V_b,V_a] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 22.40/22.28 => ( V_a != V_b
% 22.40/22.28 => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a),V_b))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b),V_a)) ) ) ) ).
% 22.40/22.28
% 22.40/22.28 fof(fact_dvd_Ole__imp__less__or__eq,axiom,
% 22.40/22.28 ! [V_y,V_x] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 => ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_y))
% 22.40/22.28 & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_y),V_x)) )
% 22.40/22.28 | V_x = V_y ) ) ).
% 22.40/22.28
% 22.40/22.28 %----Arity declarations (216)
% 22.40/22.28 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom,
% 22.40/22.28 class_Lattices_Obounded__lattice(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Lattices_Obounded__lattice,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Lattices_Obounded__lattice(T_1)
% 22.40/22.28 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Complete__Lattice_Ocomplete__lattice(T_1)
% 22.40/22.28 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Lattices_Obounded__lattice__top,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Lattices_Obounded__lattice(T_1)
% 22.40/22.28 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Lattices_Obounded__lattice(T_1)
% 22.40/22.28 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Lattices_Osemilattice__sup,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Lattices_Olattice(T_1)
% 22.40/22.28 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Lattices_Osemilattice__inf,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Lattices_Olattice(T_1)
% 22.40/22.28 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Lattices_Odistrib__lattice,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Lattices_Odistrib__lattice(T_1)
% 22.40/22.28 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Lattices_Oboolean__algebra,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Lattices_Oboolean__algebra(T_1)
% 22.40/22.28 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Orderings_Opreorder,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Orderings_Opreorder(T_1)
% 22.40/22.28 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Finite__Set_Ofinite,axiom,
% 22.40/22.28 ! [T_1,T_2] :
% 22.40/22.28 ( ( class_Finite__Set_Ofinite(T_2)
% 22.40/22.28 & class_Finite__Set_Ofinite(T_1) )
% 22.40/22.28 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Lattices_Olattice,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Lattices_Olattice(T_1)
% 22.40/22.28 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Orderings_Oorder,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Orderings_Oorder(T_1)
% 22.40/22.28 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Orderings_Otop,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Orderings_Otop(T_1)
% 22.40/22.28 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Orderings_Oord,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Orderings_Oord(T_1)
% 22.40/22.28 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Orderings_Obot,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Orderings_Obot(T_1)
% 22.40/22.28 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Groups_Ouminus,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Groups_Ouminus(T_1)
% 22.40/22.28 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Groups_Ominus,axiom,
% 22.40/22.28 ! [T_2,T_1] :
% 22.40/22.28 ( class_Groups_Ominus(T_1)
% 22.40/22.28 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_fun__Enum_Oenum,axiom,
% 22.40/22.28 ! [T_1,T_2] :
% 22.40/22.28 ( ( class_Enum_Oenum(T_2)
% 22.40/22.28 & class_Enum_Oenum(T_1) )
% 22.40/22.28 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 22.40/22.28 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 22.40/22.28 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom,
% 22.40/22.28 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom,
% 22.40/22.28 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom,
% 22.40/22.28 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom,
% 22.40/22.28 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom,
% 22.40/22.28 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom,
% 22.40/22.28 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom,
% 22.40/22.28 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom,
% 22.40/22.28 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom,
% 22.40/22.28 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom,
% 22.40/22.28 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom,
% 22.40/22.28 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom,
% 22.40/22.28 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom,
% 22.40/22.28 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom,
% 22.40/22.28 class_Rings_Olinordered__semiring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom,
% 22.40/22.28 class_Rings_Olinordered__semidom(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom,
% 22.40/22.28 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom,
% 22.40/22.28 class_Lattices_Osemilattice__sup(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom,
% 22.40/22.28 class_Lattices_Osemilattice__inf(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom,
% 22.40/22.28 class_Lattices_Odistrib__lattice(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom,
% 22.40/22.28 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom,
% 22.40/22.28 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Oab__semigroup__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom,
% 22.40/22.28 class_Rings_Oordered__semiring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom,
% 22.40/22.28 class_Rings_Oordered__ring__abs(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom,
% 22.40/22.28 class_Rings_Ono__zero__divisors(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom,
% 22.40/22.28 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom,
% 22.40/22.28 class_Rings_Olinordered__ring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom,
% 22.40/22.28 class_Rings_Olinordered__idom(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom,
% 22.40/22.28 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom,
% 22.40/22.28 class_Groups_Osemigroup__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Divides_Osemiring__div,axiom,
% 22.40/22.28 class_Divides_Osemiring__div(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom,
% 22.40/22.28 class_Rings_Ocomm__semiring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom,
% 22.40/22.28 class_Nat_Osemiring__char__0(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oab__group__add,axiom,
% 22.40/22.28 class_Groups_Oab__group__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom,
% 22.40/22.28 class_Rings_Ozero__neq__one(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oordered__ring,axiom,
% 22.40/22.28 class_Rings_Oordered__ring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Orderings_Opreorder,axiom,
% 22.40/22.28 class_Orderings_Opreorder(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Orderings_Olinorder,axiom,
% 22.40/22.28 class_Orderings_Olinorder(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom,
% 22.40/22.28 class_Groups_Omonoid__mult(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom,
% 22.40/22.28 class_Rings_Ocomm__ring__1(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Omonoid__add,axiom,
% 22.40/22.28 class_Groups_Omonoid__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Osemiring__1,axiom,
% 22.40/22.28 class_Rings_Osemiring__1(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Osemiring__0,axiom,
% 22.40/22.28 class_Rings_Osemiring__0(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Lattices_Olattice,axiom,
% 22.40/22.28 class_Lattices_Olattice(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Ogroup__add,axiom,
% 22.40/22.28 class_Groups_Ogroup__add(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Divides_Oring__div,axiom,
% 22.40/22.28 class_Divides_Oring__div(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Omult__zero,axiom,
% 22.40/22.28 class_Rings_Omult__zero(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Orderings_Oorder,axiom,
% 22.40/22.28 class_Orderings_Oorder(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Int_Oring__char__0,axiom,
% 22.40/22.28 class_Int_Oring__char__0(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Int_Onumber__ring,axiom,
% 22.40/22.28 class_Int_Onumber__ring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Osemiring,axiom,
% 22.40/22.28 class_Rings_Osemiring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Orderings_Oord,axiom,
% 22.40/22.28 class_Orderings_Oord(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Ouminus,axiom,
% 22.40/22.28 class_Groups_Ouminus(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Osgn__if,axiom,
% 22.40/22.28 class_Groups_Osgn__if(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oabs__if,axiom,
% 22.40/22.28 class_Groups_Oabs__if(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oring__1,axiom,
% 22.40/22.28 class_Rings_Oring__1(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Ominus,axiom,
% 22.40/22.28 class_Groups_Ominus(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Power_Opower,axiom,
% 22.40/22.28 class_Power_Opower(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Ozero,axiom,
% 22.40/22.28 class_Groups_Ozero(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oring,axiom,
% 22.40/22.28 class_Rings_Oring(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Rings_Oidom,axiom,
% 22.40/22.28 class_Rings_Oidom(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Int_Onumber,axiom,
% 22.40/22.28 class_Int_Onumber(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Int__Oint__Groups_Oone,axiom,
% 22.40/22.28 class_Groups_Oone(tc_Int_Oint) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 22.40/22.28 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 22.40/22.28 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom,
% 22.40/22.28 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom,
% 22.40/22.28 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom,
% 22.40/22.28 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom,
% 22.40/22.28 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom,
% 22.40/22.28 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom,
% 22.40/22.28 class_Rings_Olinordered__semiring(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom,
% 22.40/22.28 class_Rings_Olinordered__semidom(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom,
% 22.40/22.28 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom,
% 22.40/22.28 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom,
% 22.40/22.28 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom,
% 22.40/22.28 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom,
% 22.40/22.28 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom,
% 22.40/22.28 class_Rings_Oordered__semiring(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom,
% 22.40/22.28 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom,
% 22.40/22.28 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom,
% 22.40/22.28 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom,
% 22.40/22.28 class_Groups_Osemigroup__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom,
% 22.40/22.28 class_Divides_Osemiring__div(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom,
% 22.40/22.28 class_Rings_Ocomm__semiring(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Orderings_Owellorder,axiom,
% 22.40/22.28 class_Orderings_Owellorder(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom,
% 22.40/22.28 class_Nat_Osemiring__char__0(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom,
% 22.40/22.28 class_Rings_Ozero__neq__one(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Orderings_Opreorder,axiom,
% 22.40/22.28 class_Orderings_Opreorder(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Orderings_Olinorder,axiom,
% 22.40/22.28 class_Orderings_Olinorder(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom,
% 22.40/22.28 class_Groups_Omonoid__mult(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom,
% 22.40/22.28 class_Groups_Omonoid__add(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom,
% 22.40/22.28 class_Rings_Osemiring__1(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom,
% 22.40/22.28 class_Rings_Osemiring__0(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Lattices_Olattice,axiom,
% 22.40/22.28 class_Lattices_Olattice(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Omult__zero,axiom,
% 22.40/22.28 class_Rings_Omult__zero(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Orderings_Oorder,axiom,
% 22.40/22.28 class_Orderings_Oorder(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Rings_Osemiring,axiom,
% 22.40/22.28 class_Rings_Osemiring(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Orderings_Oord,axiom,
% 22.40/22.28 class_Orderings_Oord(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Orderings_Obot,axiom,
% 22.40/22.28 class_Orderings_Obot(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Ominus,axiom,
% 22.40/22.28 class_Groups_Ominus(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Power_Opower,axiom,
% 22.40/22.28 class_Power_Opower(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Ozero,axiom,
% 22.40/22.28 class_Groups_Ozero(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Int_Onumber,axiom,
% 22.40/22.28 class_Int_Onumber(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Groups_Oone,axiom,
% 22.40/22.28 class_Groups_Oone(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nat__Onat__Nat_Osize,axiom,
% 22.40/22.28 class_Nat_Osize(tc_Nat_Onat) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom,
% 22.40/22.28 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom,
% 22.40/22.28 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom,
% 22.40/22.28 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom,
% 22.40/22.28 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom,
% 22.40/22.28 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom,
% 22.40/22.28 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom,
% 22.40/22.28 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Orderings_Opreorder,axiom,
% 22.40/22.28 class_Orderings_Opreorder(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom,
% 22.40/22.28 class_Finite__Set_Ofinite(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Lattices_Olattice,axiom,
% 22.40/22.28 class_Lattices_Olattice(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Orderings_Oorder,axiom,
% 22.40/22.28 class_Orderings_Oorder(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Orderings_Otop,axiom,
% 22.40/22.28 class_Orderings_Otop(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Orderings_Oord,axiom,
% 22.40/22.28 class_Orderings_Oord(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Orderings_Obot,axiom,
% 22.40/22.28 class_Orderings_Obot(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Groups_Ouminus,axiom,
% 22.40/22.28 class_Groups_Ouminus(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Groups_Ominus,axiom,
% 22.40/22.28 class_Groups_Ominus(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Enum_Oenum,axiom,
% 22.40/22.28 class_Enum_Oenum(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_HOL__Obool__Nat_Osize,axiom,
% 22.40/22.28 class_Nat_Osize(tc_HOL_Obool) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom,
% 22.40/22.28 ! [T_1] :
% 22.40/22.28 ( class_Lazy__Sequence_Osmall__lazy(T_1)
% 22.40/22.28 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_List__Olist__Nat_Osize,axiom,
% 22.40/22.28 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_sum__Finite__Set_Ofinite,axiom,
% 22.40/22.28 ! [T_1,T_2] :
% 22.40/22.28 ( ( class_Finite__Set_Ofinite(T_2)
% 22.40/22.28 & class_Finite__Set_Ofinite(T_1) )
% 22.40/22.28 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_sum__Enum_Oenum,axiom,
% 22.40/22.28 ! [T_1,T_2] :
% 22.40/22.28 ( ( class_Enum_Oenum(T_2)
% 22.40/22.28 & class_Enum_Oenum(T_1) )
% 22.40/22.28 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_sum__Nat_Osize,axiom,
% 22.40/22.28 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom,
% 22.40/22.28 ! [T_1] :
% 22.40/22.28 ( class_Finite__Set_Ofinite(T_1)
% 22.40/22.28 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Option__Ooption__Enum_Oenum,axiom,
% 22.40/22.28 ! [T_1] :
% 22.40/22.28 ( class_Enum_Oenum(T_1)
% 22.40/22.28 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Option__Ooption__Nat_Osize,axiom,
% 22.40/22.28 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Nitpick__Opair____box__Nat_Osize,axiom,
% 22.40/22.28 ! [T_1,T_2] : class_Nat_Osize(tc_Nitpick_Opair__box(T_2,T_1)) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom,
% 22.40/22.28 ! [T_1,T_2] :
% 22.40/22.28 ( ( class_Lazy__Sequence_Osmall__lazy(T_2)
% 22.40/22.28 & class_Lazy__Sequence_Osmall__lazy(T_1) )
% 22.40/22.28 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_prod__Finite__Set_Ofinite,axiom,
% 22.40/22.28 ! [T_1,T_2] :
% 22.40/22.28 ( ( class_Finite__Set_Ofinite(T_2)
% 22.40/22.28 & class_Finite__Set_Ofinite(T_1) )
% 22.40/22.28 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_prod__Enum_Oenum,axiom,
% 22.40/22.28 ! [T_1,T_2] :
% 22.40/22.28 ( ( class_Enum_Oenum(T_2)
% 22.40/22.28 & class_Enum_Oenum(T_1) )
% 22.40/22.28 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_prod__Nat_Osize,axiom,
% 22.40/22.28 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom,
% 22.40/22.28 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom,
% 22.40/22.28 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom,
% 22.40/22.28 class_Enum_Oenum(tc_Product__Type_Ounit) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Product____Type__Ounit__Nat_Osize,axiom,
% 22.40/22.28 class_Nat_Osize(tc_Product__Type_Ounit) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom,
% 22.40/22.28 class_Nat_Osize(tc_Code__Evaluation_Oterm) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom,
% 22.40/22.28 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom,
% 22.40/22.28 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom,
% 22.40/22.28 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom,
% 22.40/22.28 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom,
% 22.40/22.28 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom,
% 22.40/22.28 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom,
% 22.40/22.28 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom,
% 22.40/22.28 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom,
% 22.40/22.28 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom,
% 22.40/22.28 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom,
% 22.40/22.28 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom,
% 22.40/22.28 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom,
% 22.40/22.28 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom,
% 22.40/22.28 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom,
% 22.40/22.28 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom,
% 22.40/22.28 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom,
% 22.40/22.28 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom,
% 22.40/22.28 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom,
% 22.40/22.28 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom,
% 22.40/22.28 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom,
% 22.40/22.28 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom,
% 22.40/22.28 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom,
% 22.40/22.28 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom,
% 22.40/22.28 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom,
% 22.40/22.28 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom,
% 22.40/22.28 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom,
% 22.40/22.28 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom,
% 22.40/22.28 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom,
% 22.40/22.28 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom,
% 22.40/22.28 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom,
% 22.40/22.28 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom,
% 22.40/22.28 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom,
% 22.40/22.28 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom,
% 22.40/22.28 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom,
% 22.40/22.28 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom,
% 22.40/22.28 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom,
% 22.40/22.28 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ).
% 22.40/22.28
% 22.40/22.28 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom,
% 22.40/22.28 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ).
% 22.40/22.28
% 22.40/22.28 %----Helper facts (20)
% 22.40/22.28 fof(help_c__COMBI__1,axiom,
% 22.40/22.28 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__COMBK__1,axiom,
% 22.40/22.28 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__COMBB__1,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__COMBC__1,axiom,
% 22.40/22.28 ! [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) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__COMBS__1,axiom,
% 22.40/22.28 ! [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)) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fequal__1,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2] :
% 22.40/22.28 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
% 22.40/22.28 | V_x_2 = V_y_2 ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fequal__2,axiom,
% 22.40/22.28 ! [V_y_2,V_x_2] :
% 22.40/22.28 ( V_x_2 != V_y_2
% 22.40/22.28 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fFalse__1,axiom,
% 22.40/22.28 ~ hBOOL(c_fFalse) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fTrue__1,axiom,
% 22.40/22.28 hBOOL(c_fTrue) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fNot__1,axiom,
% 22.40/22.28 ! [V_P_2] :
% 22.40/22.28 ( ~ hBOOL(hAPP(c_fNot,V_P_2))
% 22.40/22.28 | ~ hBOOL(V_P_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fNot__2,axiom,
% 22.40/22.28 ! [V_P_2] :
% 22.40/22.28 ( ~ ~ hBOOL(V_P_2)
% 22.40/22.28 | hBOOL(hAPP(c_fNot,V_P_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fconj__1,axiom,
% 22.40/22.28 ! [V_Q_2,V_P_2] :
% 22.40/22.28 ( ~ hBOOL(V_P_2)
% 22.40/22.28 | ~ hBOOL(V_Q_2)
% 22.40/22.28 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fconj__2,axiom,
% 22.40/22.28 ! [V_Q_2,V_P_2] :
% 22.40/22.28 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 22.40/22.28 | hBOOL(V_P_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fconj__3,axiom,
% 22.40/22.28 ! [V_Q_2,V_P_2] :
% 22.40/22.28 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2))
% 22.40/22.28 | hBOOL(V_Q_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fdisj__1,axiom,
% 22.40/22.28 ! [V_Q_2,V_P_2] :
% 22.40/22.28 ( ~ hBOOL(V_P_2)
% 22.40/22.28 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fdisj__2,axiom,
% 22.40/22.28 ! [V_P_2,V_Q_2] :
% 22.40/22.28 ( ~ hBOOL(V_Q_2)
% 22.40/22.28 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fdisj__3,axiom,
% 22.40/22.28 ! [V_Q_2,V_P_2] :
% 22.40/22.28 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2))
% 22.40/22.28 | hBOOL(V_P_2)
% 22.40/22.28 | hBOOL(V_Q_2) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fimplies__1,axiom,
% 22.40/22.28 ! [V_Q_2,V_P_2] :
% 22.40/22.28 ( hBOOL(V_P_2)
% 22.40/22.28 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fimplies__2,axiom,
% 22.40/22.28 ! [V_P_2,V_Q_2] :
% 22.40/22.28 ( ~ hBOOL(V_Q_2)
% 22.40/22.28 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ).
% 22.40/22.28
% 22.40/22.28 fof(help_c__fimplies__3,axiom,
% 22.40/22.28 ! [V_Q_2,V_P_2] :
% 22.40/22.28 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2))
% 22.40/22.28 | ~ hBOOL(V_P_2)
% 22.40/22.28 | hBOOL(V_Q_2) ) ).
% 22.40/22.28
% 22.40/22.28 %----Conjectures (2)
% 22.40/22.28 fof(conj_0,hypothesis,
% 22.40/22.28 c_Hoare__Mirabelle_Ohoare__derivs(t_a,v_G_H,v_ts) ).
% 22.40/22.28
% 22.40/22.28 fof(conj_1,conjecture,
% 22.40/22.28 ! [B_G] :
% 22.40/22.28 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_HOL_Obool)),v_G_H),B_G))
% 22.40/22.28 => c_Hoare__Mirabelle_Ohoare__derivs(t_a,B_G,v_ts) ) ).
% 22.40/22.28
% 22.40/22.28 %------------------------------------------------------------------------------
% 22.40/22.28 %-------------------------------------------
% 22.40/22.28 % Proof found
% 22.40/22.28 % SZS status Theorem for theBenchmark
% 22.40/22.28 % SZS output start Proof
% 22.40/22.29 %ClaNum:10398(EqnAxiom:3078)
% 22.40/22.29 %VarNum:71131(SingletonVarNum:20420)
% 22.40/22.29 %MaxLitNum:8
% 22.40/22.29 %MaxfuncDepth:15
% 22.40/22.29 %SharedTerms:999
% 22.40/22.29 %goalClause: 3792 4624
% 22.40/22.29 %singleGoalClaCount:2
% 22.40/22.29 [3082]P1(a179)
% 22.40/22.29 [3083]P2(a904)
% 22.40/22.29 [3084]P2(a906)
% 22.40/22.29 [3085]P2(a1)
% 22.40/22.29 [3086]P2(a91)
% 22.40/22.29 [3087]P3(a904)
% 22.40/22.29 [3088]P3(a906)
% 22.40/22.29 [3089]P3(a1)
% 22.40/22.29 [3090]P3(a91)
% 22.40/22.29 [3091]P4(a906)
% 22.40/22.29 [3092]P4(a1)
% 22.40/22.29 [3093]P4(a91)
% 22.40/22.29 [3094]P111(a904)
% 22.40/22.29 [3095]P111(a906)
% 22.40/22.29 [3096]P111(a1)
% 22.40/22.29 [3097]P111(a91)
% 22.40/22.29 [3098]P5(a904)
% 22.40/22.29 [3099]P112(a904)
% 22.40/22.29 [3100]P62(a904)
% 22.40/22.29 [3101]P62(a906)
% 22.40/22.29 [3102]P63(a904)
% 22.40/22.29 [3103]P64(a904)
% 22.40/22.29 [3104]P64(a1)
% 22.40/22.29 [3105]P65(a1)
% 22.40/22.29 [3106]P101(a904)
% 22.40/22.29 [3107]P101(a906)
% 22.40/22.29 [3108]P101(a1)
% 22.40/22.29 [3109]P102(a904)
% 22.40/22.29 [3110]P102(a906)
% 22.40/22.29 [3111]P102(a1)
% 22.40/22.29 [3112]P106(a904)
% 22.40/22.29 [3113]P106(a906)
% 22.40/22.29 [3114]P106(a1)
% 22.40/22.29 [3115]P107(a904)
% 22.40/22.29 [3116]P107(a906)
% 22.40/22.29 [3117]P107(a1)
% 22.40/22.29 [3118]P103(a904)
% 22.40/22.29 [3119]P105(a904)
% 22.40/22.29 [3120]P66(a1)
% 22.40/22.29 [3121]P113(a1)
% 22.40/22.29 [3122]P83(a1)
% 22.40/22.29 [3123]P84(a904)
% 22.40/22.29 [3124]P84(a906)
% 22.40/22.29 [3125]P84(a1)
% 22.40/22.29 [3126]P84(a91)
% 22.40/22.29 [3127]P67(a1)
% 22.40/22.29 [3128]P68(a904)
% 22.40/22.29 [3129]P68(a909)
% 22.40/22.29 [3130]P124(a1)
% 22.40/22.29 [3131]P76(a906)
% 22.40/22.29 [3132]P76(a1)
% 22.40/22.29 [3133]P76(a91)
% 22.40/22.29 [3134]P89(a906)
% 22.40/22.29 [3135]P89(a1)
% 22.40/22.29 [3136]P89(a91)
% 22.40/22.29 [3137]P77(a906)
% 22.40/22.29 [3138]P77(a1)
% 22.40/22.29 [3139]P77(a91)
% 22.40/22.29 [3140]P78(a906)
% 22.40/22.29 [3141]P78(a1)
% 22.40/22.29 [3142]P78(a91)
% 22.40/22.29 [3143]P79(a906)
% 22.40/22.29 [3144]P79(a1)
% 22.40/22.29 [3145]P79(a91)
% 22.40/22.29 [3146]P80(a906)
% 22.40/22.29 [3147]P80(a1)
% 22.40/22.29 [3148]P80(a91)
% 22.40/22.29 [3149]P114(a906)
% 22.40/22.29 [3150]P114(a1)
% 22.40/22.29 [3151]P114(a91)
% 22.40/22.29 [3152]P139(a906)
% 22.40/22.29 [3153]P139(a1)
% 22.40/22.29 [3154]P139(a91)
% 22.40/22.29 [3155]P125(a1)
% 22.40/22.29 [3156]P90(a906)
% 22.40/22.29 [3157]P90(a1)
% 22.40/22.29 [3158]P90(a91)
% 22.40/22.29 [3159]P91(a906)
% 22.40/22.29 [3160]P91(a1)
% 22.40/22.29 [3161]P91(a91)
% 22.40/22.29 [3162]P118(a1)
% 22.40/22.29 [3163]P115(a1)
% 22.40/22.29 [3164]P119(a906)
% 22.40/22.29 [3165]P119(a1)
% 22.40/22.29 [3166]P119(a91)
% 22.40/22.29 [3167]P143(a906)
% 22.40/22.29 [3168]P143(a1)
% 22.40/22.29 [3169]P82(a906)
% 22.40/22.29 [3170]P82(a1)
% 22.40/22.29 [3171]P82(a91)
% 22.40/22.29 [3172]P86(a906)
% 22.40/22.29 [3173]P86(a1)
% 22.40/22.29 [3174]P86(a91)
% 22.40/22.29 [3175]P87(a906)
% 22.40/22.29 [3176]P87(a1)
% 22.40/22.29 [3177]P87(a91)
% 22.40/22.29 [3178]P126(a906)
% 22.40/22.29 [3179]P126(a1)
% 22.40/22.29 [3180]P126(a91)
% 22.40/22.29 [3181]P140(a1)
% 22.40/22.29 [3182]P96(a906)
% 22.40/22.29 [3183]P96(a1)
% 22.40/22.29 [3184]P96(a91)
% 22.40/22.29 [3185]P88(a906)
% 22.40/22.29 [3186]P88(a1)
% 22.40/22.29 [3187]P88(a91)
% 22.40/22.29 [3188]P129(a906)
% 22.40/22.29 [3189]P129(a1)
% 22.40/22.29 [3190]P129(a91)
% 22.40/22.29 [3191]P142(a1)
% 22.40/22.29 [3192]P130(a906)
% 22.40/22.29 [3193]P130(a1)
% 22.40/22.29 [3194]P130(a91)
% 22.40/22.29 [3195]P144(a906)
% 22.40/22.29 [3196]P144(a1)
% 22.40/22.29 [3197]P144(a91)
% 22.40/22.29 [3198]P127(a1)
% 22.40/22.29 [3199]P128(a1)
% 22.40/22.29 [3200]P93(a906)
% 22.40/22.29 [3201]P93(a1)
% 22.40/22.29 [3202]P93(a91)
% 22.40/22.29 [3203]P135(a906)
% 22.40/22.29 [3204]P135(a1)
% 22.40/22.29 [3205]P135(a91)
% 22.40/22.29 [3206]P137(a906)
% 22.40/22.29 [3207]P137(a1)
% 22.40/22.29 [3208]P137(a91)
% 22.40/22.29 [3209]P136(a906)
% 22.40/22.29 [3210]P136(a1)
% 22.40/22.29 [3211]P136(a91)
% 22.40/22.29 [3212]P131(a906)
% 22.40/22.29 [3213]P131(a1)
% 22.40/22.29 [3214]P131(a91)
% 22.40/22.29 [3215]P122(a906)
% 22.40/22.29 [3216]P122(a1)
% 22.40/22.29 [3217]P122(a91)
% 22.40/22.29 [3218]P132(a906)
% 22.40/22.29 [3219]P132(a1)
% 22.40/22.29 [3220]P132(a91)
% 22.40/22.29 [3221]P133(a1)
% 22.40/22.29 [3222]P134(a1)
% 22.40/22.29 [3223]P141(a1)
% 22.40/22.29 [3224]P97(a1)
% 22.40/22.29 [3225]P94(a1)
% 22.40/22.29 [3226]P116(a906)
% 22.40/22.29 [3227]P116(a1)
% 22.40/22.29 [3228]P116(a91)
% 22.40/22.29 [3229]P145(a906)
% 22.40/22.29 [3230]P145(a1)
% 22.40/22.29 [3231]P145(a91)
% 22.40/22.29 [3232]P98(a1)
% 22.40/22.29 [3233]P99(a906)
% 22.40/22.29 [3234]P99(a1)
% 22.40/22.29 [3235]P99(a91)
% 22.40/22.29 [3236]P69(a906)
% 22.40/22.29 [3237]P69(a1)
% 22.40/22.29 [3238]P69(a91)
% 22.40/22.29 [3239]P146(a906)
% 22.40/22.29 [3240]P146(a1)
% 22.40/22.29 [3241]P146(a91)
% 22.40/22.29 [3242]P108(a906)
% 22.40/22.29 [3243]P108(a1)
% 22.40/22.29 [3244]P108(a91)
% 22.40/22.29 [3245]P70(a1)
% 22.40/22.29 [3246]P92(a1)
% 22.40/22.29 [3247]P138(a1)
% 22.40/22.29 [3248]P81(a1)
% 22.40/22.29 [3249]P117(a906)
% 22.40/22.29 [3250]P85(a906)
% 22.40/22.29 [3251]P85(a1)
% 22.40/22.29 [3252]P85(a91)
% 22.40/22.29 [3253]P95(a906)
% 22.40/22.29 [3254]P95(a1)
% 22.40/22.29 [3255]P95(a91)
% 22.40/22.29 [3256]P71(a904)
% 22.40/22.29 [3257]P71(a909)
% 22.40/22.29 [3258]P110(a904)
% 22.40/22.29 [3259]P110(a906)
% 22.40/22.29 [3260]P110(a909)
% 22.40/22.29 [3261]P110(a91)
% 22.40/22.29 [3262]P110(a315)
% 22.40/22.29 [3263]P109(a909)
% 22.40/22.29 [3264]P109(a1)
% 22.40/22.29 [3265]P104(a904)
% 22.40/22.29 [3280]P37(a906,a232)
% 22.40/22.29 [3281]P37(a906,a309)
% 22.40/22.29 [3282]P38(a906,a232)
% 22.40/22.29 [3361]P14(a903,a915,a916)
% 22.40/22.29 [3362]P40(a906,a906,a104)
% 22.40/22.29 [4610]~E(a89,a77)
% 22.40/22.29 [4611]~P1(a231)
% 22.40/22.29 [4624]~P14(a903,a808,a916)
% 22.40/22.29 [3079]E(f2(a1),a77)
% 22.40/22.29 [3080]E(f3(a91),a4)
% 22.40/22.29 [3081]E(f92(a91),a5)
% 22.40/22.29 [3266]E(f93(a906),f180(a906))
% 22.40/22.29 [3267]E(f94(a906),f230(a906))
% 22.40/22.29 [3268]E(f181(a906),f2(a906))
% 22.40/22.29 [3269]E(f95(a1),f25(a1))
% 22.40/22.29 [3270]E(f78(a231),f2(a906))
% 22.40/22.29 [3271]E(f78(a179),f2(a906))
% 22.40/22.29 [3272]P6(f72(a1))
% 22.40/22.29 [3273]P6(f2(a1))
% 22.40/22.29 [3328]P37(f912(a906,a906),a26)
% 22.40/22.29 [3669]E(f312(a906,a906,a232,a232),a26)
% 22.40/22.29 [4612]~E(f72(a1),f2(a1))
% 22.40/22.29 [3274]E(f6(f2(a91)),f2(a906))
% 22.40/22.29 [3275]E(f103(f2(a906)),f2(a906))
% 22.40/22.29 [3284]E(f319(f73(a1),a77),a77)
% 22.40/22.29 [3287]E(f319(a104,f2(a906)),f72(a906))
% 22.40/22.29 [3288]E(f319(a97,f72(a1)),f72(a906))
% 22.40/22.29 [3289]E(f319(a5,f72(a906)),f72(a91))
% 22.40/22.29 [3291]E(f319(a5,f2(a906)),f2(a91))
% 22.40/22.29 [3293]E(f319(f96(a1),a77),f2(a1))
% 22.40/22.29 [3294]E(f319(f96(a91),a77),f2(a91))
% 22.40/22.29 [3295]E(f319(a97,f2(a1)),f2(a906))
% 22.40/22.29 [3296]E(f319(f96(a906),a77),f2(a906))
% 22.40/22.29 [3297]E(f319(f182(a904),a231),f2(a906))
% 22.40/22.29 [3298]E(f319(f182(a904),a179),f2(a906))
% 22.40/22.29 [3304]E(f319(f73(a1),f72(a1)),a89)
% 22.40/22.29 [3311]E(f319(f73(a1),f2(a1)),f2(a1))
% 22.40/22.29 [3312]E(f319(f92(a1),f72(a906)),f72(a1))
% 22.40/22.29 [3313]E(f319(f92(a1),f2(a906)),f2(a1))
% 22.40/22.29 [3315]E(f319(f182(a91),f2(a91)),f2(a906))
% 22.40/22.29 [3325]E(f319(a97,f72(a1)),f319(a104,f2(a906)))
% 22.40/22.29 [3326]E(f310(f912(a906,a906),a26),a27)
% 22.40/22.29 [3327]E(f311(f912(a906,a906),a26),a28)
% 22.40/22.29 [3353]E(f319(f274(a906),f2(a906)),f181(f913(a906,a904)))
% 22.40/22.29 [3354]E(f319(f275(a906),f2(a906)),f234(f913(a906,a904)))
% 22.40/22.29 [3364]P41(f181(f913(a1,a904)))
% 22.40/22.29 [3398]E(f319(f319(f3(a91),f2(a91)),f72(a91)),f2(a91))
% 22.40/22.29 [3473]P1(f319(f319(f226(a1),a89),f2(a1)))
% 22.40/22.29 [3497]P1(f319(f319(f225(a1),f2(a1)),f72(a1)))
% 22.40/22.29 [3499]P1(f319(f319(f226(a1),f2(a1)),f72(a1)))
% 22.40/22.29 [3699]E(f319(f319(f281(a906,a906,a906),a309),f299(a906,a309)),a232)
% 22.40/22.29 [3737]P42(a1,a906,a97,f319(f225(a1),f2(a1)))
% 22.40/22.29 [3741]E(f319(f319(f33(a906,f913(a906,a904)),f234(f913(a906,a904))),f274(a906)),f234(f913(a906,a904)))
% 22.40/22.29 [3742]E(f319(f319(f33(a906,f913(a906,a904)),f234(f913(a906,a904))),f275(a906)),f234(f913(a906,a904)))
% 22.40/22.29 [3743]E(f319(f319(f33(a906,f913(a906,a904)),f234(f913(a906,a904))),f293(a906)),f234(f913(a906,a904)))
% 22.40/22.29 [3744]E(f319(f319(f34(a906,f913(a906,a904)),f234(f913(a906,a904))),f296(a906)),f181(f913(a906,a904)))
% 22.40/22.29 [3760]P25(a906,a1,f92(a1),f234(f913(a906,a904)))
% 22.40/22.29 [3774]P42(a906,a1,f92(a1),f319(f18(a904,a906),a179))
% 22.40/22.29 [3902]E(f319(f66(a906,a91,a1,a5),a97),f96(a91))
% 22.40/22.29 [4122]P58(a91,a906,a22,a5,f234(f913(a906,a904)))
% 22.40/22.29 [4126]P58(a1,f913(f912(a906,a906),a904),a99,a83,a90)
% 22.40/22.29 [4376]E(f250(a1,a1,a1,a1,f25(a1),f73(a1)),a45)
% 22.40/22.29 [4621]~E(f319(f96(a1),a89),f319(f96(a1),a77))
% 22.40/22.29 [4622]~P1(f319(a186,f72(a1)))
% 22.40/22.29 [4623]~P1(f319(a186,f2(a1)))
% 22.40/22.29 [4647]~P1(f319(f319(f226(a1),a77),f2(a1)))
% 22.40/22.29 [3346]E(f319(f319(f3(a1),a89),a89),a77)
% 22.40/22.29 [3360]E(f319(f92(a1),f319(a104,f2(a906))),f72(a1))
% 22.40/22.29 [3427]E(f319(f29(a909),f234(f913(a909,a904))),f72(a906))
% 22.40/22.29 [3447]P1(f319(a186,f319(f96(a1),a89)))
% 22.40/22.29 [3449]P1(f319(f319(f225(a1),a89),a77))
% 22.40/22.29 [3451]P1(f319(f319(f226(a1),a89),a77))
% 22.40/22.29 [3507]E(f319(f319(f301(a906),f2(a906)),f181(f913(a906,a904))),f319(f293(a906),f2(a906)))
% 22.40/22.29 [3562]P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),a77)))
% 22.40/22.29 [3574]E(f319(f302(a906,a906,a104),f234(f913(a906,a904))),f319(f296(a906),f2(a906)))
% 22.40/22.29 [3609]P8(f912(a906,a906),f234(f913(f912(a906,a906),a904)),a101)
% 22.40/22.29 [3909]E(f319(f66(a906,a1,a91,f92(a1)),a22),a24)
% 22.40/22.29 [3972]P37(a906,f319(f254(f912(a906,a906)),f319(f249(a906,a906,a904),f226(a906))))
% 22.40/22.29 [4638]~P1(f319(a186,f319(f96(a1),a77)))
% 22.40/22.29 [4639]~P1(f319(f319(f225(a1),a77),a89))
% 22.40/22.29 [4640]~P1(f319(f319(f226(a1),a77),a77))
% 22.40/22.29 [4641]~P1(f319(f319(f226(a1),a77),a89))
% 22.40/22.29 [4642]~P1(f319(f319(f226(a1),a89),a89))
% 22.40/22.29 [4651]~P1(f319(f55(a906),f234(f913(a906,a904))))
% 22.40/22.29 [4652]~P1(f319(f55(a1),f234(f913(a1,a904))))
% 22.40/22.29 [4551]E(f319(f249(a1,a1,a904),f319(f319(f10(f913(a1,a904),f913(a1,a904),a1),f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f226(a1),f2(a1))))),f319(f319(f9(a1,a1,f913(a1,a904)),f319(f319(f10(f913(a1,f913(a1,a904)),f913(a1,f913(a1,a904)),a1),f9(a1,a1,a904)),f319(f319(f10(f913(a1,a1),f913(a1,f913(a1,a904)),a1),f319(f10(a1,f913(a1,a904),a1),a316)),a210))),f72(a1)))),a206)
% 22.40/22.29 [3671]E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a89)),a89),a89)
% 22.40/22.29 [3709]E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77),f319(f73(a1),a89))
% 22.40/22.29 [3746]E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77),f319(f319(f3(a1),a77),a89))
% 22.40/22.29 [3792]P1(f319(f319(f225(f913(f905(a903),a904)),a915),a808))
% 22.40/22.29 [3843]E(f319(f319(f54(f912(a906,a906)),f234(f913(f912(a906,a906),a904))),a101),a90)
% 22.40/22.29 [3911]E(f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),f72(a1))
% 22.40/22.29 [3912]E(f319(f96(a91),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),f72(a91))
% 22.40/22.29 [3913]E(f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),f72(a906))
% 22.40/22.29 [3920]E(f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),f319(a104,f2(a906)))
% 22.40/22.29 [4244]E(f319(f319(f93(f913(f912(f912(a906,a906),f912(a906,a906)),a904)),a26),f299(f912(a906,a906),f181(f913(f912(f912(a906,a906),f912(a906,a906)),a904)))),a64)
% 22.40/22.29 [4304]E(f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),f72(a906)),f2(a906))),f181(f913(f912(a906,a906),a904))))),f72(a1))
% 22.40/22.29 [4305]E(f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),f2(a906)),f2(a906))),f181(f913(f912(a906,a906),a904))))),f2(a1))
% 22.40/22.29 [4318]E(f319(f254(f912(a906,a906)),f319(f249(a906,a906,a904),f319(f319(f10(a906,f913(a906,a904),a906),f319(f9(a906,a906,a904),a316)),a104))),a309)
% 22.40/22.29 [4072]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),a89),a77)
% 22.40/22.29 [4369]E(f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(a104,f319(a104,f319(a104,f2(a906)))))
% 22.40/22.29 [4434]P27(f913(f912(a906,a906),a904),f319(f319(f244(f913(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),a904),f913(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),a904)),a27),a65))
% 22.40/22.29 [4435]P27(f913(f912(a906,a906),a904),f319(f319(f244(f913(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),a904),f913(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),a904)),a28),a63))
% 22.40/22.29 [4445]P6(f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))))
% 22.40/22.29 [4472]E(f319(f319(f93(f913(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),a904)),f311(f912(a906,a906),a64)),f319(f319(f301(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),f181(f913(f912(a906,a906),a904))),f181(f913(f912(a906,a906),a904)))),f181(f913(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),a904)))),a63)
% 22.40/22.29 [4473]E(f319(f319(f93(f913(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),a904)),f310(f912(a906,a906),a64)),f319(f319(f301(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),f181(f913(f912(a906,a906),a904))),f181(f913(f912(a906,a906),a904)))),f181(f913(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),a904)))),a65)
% 22.40/22.29 [4479]E(f319(f92(a1),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))))
% 22.40/22.29 [4492]P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))))
% 22.40/22.29 [4489]E(f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)),f319(a104,f319(a104,f2(a906))))
% 22.40/22.29 [4490]E(f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)),f319(f319(f74(a906),f72(a906)),f72(a906)))
% 22.40/22.29 [4491]E(f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)),f319(f29(a904),f234(f913(a904,a904))))
% 22.40/22.29 [4531]P6(f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))
% 22.40/22.29 [4532]E(f319(a97,f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(a104,f319(a104,f2(a906))))
% 22.40/22.29 [4553]E(f319(f92(a1),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))
% 22.40/22.29 [4566]P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.29 [3283]P7(x32831,a316)
% 22.40/22.29 [3670]P25(a906,a906,a104,x36701)
% 22.40/22.29 [3276]P110(f905(x32761))
% 22.40/22.29 [3277]P110(f910(x32771))
% 22.40/22.29 [3278]P110(f907(x32781))
% 22.40/22.29 [3279]P110(f908(x32791))
% 22.40/22.29 [3299]P37(a1,f98(x32991))
% 22.40/22.29 [3300]P37(a1,f100(x33001))
% 22.40/22.29 [3349]P37(f913(x33491,a904),f306(x33491))
% 22.40/22.29 [3350]P38(f913(x33501,a904),f306(x33501))
% 22.40/22.29 [3376]E(f235(x33761,x33761,a316),a316)
% 22.40/22.29 [3391]E(f39(a1,x33911,x33911),f2(a1))
% 22.40/22.29 [3444]P15(x34441,f913(x34441,a904),f301(x34441))
% 22.40/22.29 [4614]~E(f319(a104,x46141),x46141)
% 22.40/22.29 [4620]~E(f319(a104,x46201),f2(a906))
% 22.40/22.29 [3285]E(f319(f96(a1),x32851),x32851)
% 22.40/22.29 [3286]E(f319(f182(a906),x32861),x32861)
% 22.40/22.29 [3301]E(f319(a83,f320(x33011)),x33011)
% 22.40/22.29 [3302]E(f319(a5,f572(x33021)),x33021)
% 22.40/22.29 [3303]E(f233(x33031,f2(a91)),f2(a91))
% 22.40/22.29 [3316]E(f106(x33161,f105(x33161)),f105(x33161))
% 22.40/22.29 [3317]E(f144(x33171,f105(x33171)),f105(x33171))
% 22.40/22.29 [3322]E(f319(f159(x33221),f105(x33221)),f105(x33221))
% 22.40/22.29 [3323]E(f319(f163(x33231),f105(x33231)),f105(x33231))
% 22.40/22.29 [3324]E(f319(f160(x33241),f105(x33241)),f105(x33241))
% 22.40/22.29 [3329]E(f319(f96(a1),x33291),f319(f95(a1),x33291))
% 22.40/22.29 [3330]E(f319(a83,f319(a99,x33301)),x33301)
% 22.40/22.29 [3332]E(f319(a5,f319(a22,x33321)),x33321)
% 22.40/22.29 [3333]E(f319(a22,f319(a5,x33331)),x33331)
% 22.40/22.29 [3335]P6(f319(f92(a1),x33351))
% 22.40/22.29 [3344]E(f319(f182(f907(x33441)),f105(x33441)),f2(a906))
% 22.40/22.29 [3345]E(f319(f182(f908(x33451)),f111(x33451)),f2(a906))
% 22.40/22.29 [3367]E(f319(f319(f180(a906),x33671),f2(a906)),x33671)
% 22.40/22.29 [3368]E(f319(f319(f3(a906),x33681),f2(a906)),x33681)
% 22.40/22.29 [3369]E(f319(f319(f74(a906),x33691),f2(a906)),x33691)
% 22.40/22.29 [3370]E(f319(f319(f74(a1),x33701),f2(a1)),x33701)
% 22.40/22.29 [3371]E(f319(f319(f75(a906),x33711),f72(a906)),x33711)
% 22.40/22.29 [3372]E(f319(f319(f75(a1),x33721),f72(a1)),x33721)
% 22.40/22.29 [3373]E(f319(f319(f230(a906),x33731),f2(a906)),f2(a906))
% 22.40/22.29 [3374]E(f319(f319(f75(a906),x33741),f2(a906)),f2(a906))
% 22.40/22.29 [3375]E(f319(f319(f30(a1),x33751),f2(a1)),f2(a1))
% 22.40/22.29 [3382]E(f319(f164(x33821),f105(x33821)),f181(f913(x33821,a904)))
% 22.40/22.29 [3386]P1(f319(f129(x33861),f105(x33861)))
% 22.40/22.29 [3392]E(f319(f146(x33921,x33921),f7(x33921)),f25(f907(x33921)))
% 22.40/22.29 [3393]E(f319(f146(x33931,x33931),f25(x33931)),f25(f907(x33931)))
% 22.40/22.29 [3394]E(f39(a1,x33941,f2(a1)),x33941)
% 22.40/22.29 [3395]E(f319(f225(a906),f319(a104,x33951)),f319(f226(a906),x33951))
% 22.40/22.29 [3396]E(f319(f274(a906),f319(a104,x33961)),f319(f293(a906),x33961))
% 22.40/22.29 [3397]E(f319(f275(a906),f319(a104,x33971)),f319(f296(a906),x33971))
% 22.40/22.29 [3399]E(f39(a1,f2(a1),x33991),f2(a1))
% 22.40/22.29 [3412]E(f319(f319(f74(a906),x34121),f72(a906)),f319(a104,x34121))
% 22.40/22.29 [3421]E(f319(f294(a906,x34211),f2(a906)),f181(f913(a906,a904)))
% 22.40/22.29 [3433]E(f295(a906,f2(a906),x34331),f319(f293(a906),x34331))
% 22.40/22.29 [3476]E(f319(f319(f3(a906),f319(a104,x34761)),f72(a906)),x34761)
% 22.40/22.29 [3488]E(f41(f2(a1),x34881),f319(f319(f244(a1,a1),f2(a1)),f2(a1)))
% 22.40/22.29 [3537]P1(f319(f319(f226(a906),x35371),f319(a104,x35371)))
% 22.40/22.29 [3549]P1(f319(f319(f226(a906),f2(a906)),f319(a104,x35491)))
% 22.40/22.29 [3773]E(f85(x37731,x37731,f234(f913(x37731,a904)),f25(x37731)),f25(x37731))
% 22.40/22.29 [3830]E(f319(f319(f3(a91),f319(a5,f319(a104,f319(a22,x38301)))),f72(a91)),x38301)
% 22.40/22.29 [3893]P1(f319(f319(f225(a1),f319(f73(a1),f319(f92(a1),x38931))),f2(a1)))
% 22.40/22.29 [4035]P1(f319(f319(f226(a1),f319(f73(a1),f319(f92(a1),f319(a104,x40351)))),f2(a1)))
% 22.40/22.29 [4627]~E(f234(f913(x46271,a904)),f181(f913(x46271,a904)))
% 22.40/22.29 [4650]~P1(f319(f319(f226(a906),x46501),f2(a906)))
% 22.40/22.29 [4659]~P1(f319(f319(f226(a1),f319(f92(a1),x46591)),f2(a1)))
% 22.40/22.29 [3334]E(f112(x33341,f111(f908(x33341))),f111(x33341))
% 22.40/22.29 [3348]E(f171(x33481,f105(f907(x33481))),f105(f907(x33481)))
% 22.40/22.29 [3351]E(f319(f319(f75(a1),a77),x33511),a77)
% 22.40/22.29 [3352]E(f319(f319(f74(a1),a77),x33521),x33521)
% 22.40/22.29 [3355]E(f319(a97,f319(f92(a1),x33551)),x33551)
% 22.40/22.29 [3356]E(f319(f319(f3(a1),x33561),a77),x33561)
% 22.40/22.29 [3357]E(f319(f319(f74(a1),x33571),a77),x33571)
% 22.40/22.29 [3359]E(f319(f319(f3(a906),x33591),x33591),f2(a906))
% 22.40/22.29 [3365]E(f319(f73(a1),f319(f73(a1),x33651)),x33651)
% 22.40/22.29 [3366]E(f319(f29(a906),f319(f274(a906),x33661)),x33661)
% 22.40/22.29 [3377]E(f319(f319(f180(a906),f2(a906)),x33771),x33771)
% 22.40/22.29 [3378]E(f319(f319(f74(a906),f2(a906)),x33781),x33781)
% 22.40/22.29 [3379]E(f319(f319(f74(a1),f2(a1)),x33791),x33791)
% 22.40/22.29 [3380]E(f319(f319(f75(a906),f72(a906)),x33801),x33801)
% 22.40/22.29 [3381]E(f319(f319(f75(a1),f72(a1)),x33811),x33811)
% 22.40/22.29 [3387]E(f319(f319(f230(a906),f2(a906)),x33871),f2(a906))
% 22.40/22.29 [3388]E(f319(f319(f3(a906),f2(a906)),x33881),f2(a906))
% 22.40/22.29 [3389]E(f319(f319(f75(a906),f2(a906)),x33891),f2(a906))
% 22.40/22.29 [3390]E(f319(f319(f30(a1),f2(a1)),x33901),f2(a1))
% 22.40/22.29 [3400]E(f120(x34001,f319(f73(a1),x34001)),f124(a1,x34001))
% 22.40/22.29 [3405]E(f319(f294(a906,f2(a906)),x34051),f319(f274(a906),x34051))
% 22.40/22.29 [3406]E(f319(f319(f75(a1),a89),x34061),f319(f73(a1),x34061))
% 22.40/22.29 [3414]E(f319(a97,f319(f96(a1),x34141)),f319(f96(a906),x34141))
% 22.40/22.29 [3415]E(f319(a22,f319(f96(a91),x34151)),f319(f96(a906),x34151))
% 22.40/22.29 [3416]E(f319(f29(a906),f319(f293(a906),x34161)),f319(a104,x34161))
% 22.40/22.29 [3425]E(f319(f319(f74(a906),f72(a906)),x34251),f319(a104,x34251))
% 22.40/22.29 [3429]E(f319(f95(a1),f319(f92(a1),x34291)),f319(f92(a1),x34291))
% 22.40/22.29 [3430]E(f319(f69(a1),f319(f92(a1),x34301)),f319(f92(a1),x34301))
% 22.40/22.29 [3434]E(f319(f29(x34341),f181(f913(x34341,a904))),f2(a906))
% 22.40/22.29 [3436]E(f319(f319(f30(a906),x34361),f319(a104,f2(a906))),x34361)
% 22.40/22.29 [3445]E(f39(a906,x34451,f319(a104,f2(a906))),f2(a906))
% 22.40/22.29 [3446]E(f39(a1,x34461,f319(f96(a1),a89)),f2(a1))
% 22.40/22.29 [3460]E(f319(f319(f30(a1),x34601),f319(f96(a1),a89)),f319(f73(a1),x34601))
% 22.40/22.29 [3464]E(f131(a906,f319(f294(a906,x34641),f2(a906))),f105(a906))
% 22.40/22.29 [3465]E(f319(f319(f74(a1),x34651),f72(a1)),f319(f319(f3(a1),x34651),a89))
% 22.40/22.29 [3466]E(f319(f319(f3(a1),x34661),f72(a1)),f319(f319(f74(a1),x34661),a89))
% 22.40/22.29 [3470]P1(f319(f319(f225(a906),x34701),x34701))
% 22.40/22.29 [3471]P1(f319(f319(f225(a1),x34711),x34711))
% 22.40/22.29 [3472]P1(f319(f319(f279(a906),x34721),x34721))
% 22.40/22.29 [3477]E(f319(f73(a1),f319(f96(a1),x34771)),f319(f96(a1),f319(f73(a1),x34771)))
% 22.40/22.29 [3478]P1(f319(f55(a906),f319(f274(a906),x34781)))
% 22.40/22.29 [3479]P1(f319(f55(a906),f319(f293(a906),x34791)))
% 22.40/22.29 [3486]E(f153(x34861,f234(f913(x34861,a904))),f234(f913(f907(x34861),a904)))
% 22.40/22.29 [3491]P1(f319(f319(f225(a906),f2(a906)),x34911))
% 22.40/22.29 [3501]E(f319(f319(f74(a906),f103(x35011)),f319(a104,f2(a906))),f103(f319(a104,x35011)))
% 22.40/22.29 [3502]E(f319(f254(x35021),f319(f18(a904,x35021),a179)),f234(f913(x35021,a904)))
% 22.40/22.29 [3503]E(f319(f254(x35031),f319(f18(a904,x35031),a231)),f181(f913(x35031,a904)))
% 22.40/22.29 [3506]E(f319(f319(f301(a906),x35061),f319(f274(a906),x35061)),f319(f274(a906),f319(a104,x35061)))
% 22.40/22.29 [3518]E(f319(f319(f74(a1),f72(a1)),f319(f92(a1),x35181)),f319(f92(a1),f319(a104,x35181)))
% 22.40/22.29 [3520]E(f319(f319(f143(f907(x35201)),f105(x35201)),f105(f907(x35201))),f48(x35201,f105(x35201)))
% 22.40/22.29 [3540]E(f181(f913(f912(x35401,x35401),a904)),f255(x35401,f181(f913(x35401,a904))))
% 22.40/22.29 [3541]E(f319(f300(x35411),f234(f913(x35411,a904))),f234(f913(f913(x35411,a904),a904)))
% 22.40/22.29 [3542]E(f319(f73(f913(x35421,a904)),f234(f913(x35421,a904))),f181(f913(x35421,a904)))
% 22.40/22.29 [3543]E(f319(f73(f913(x35431,a904)),f181(f913(x35431,a904))),f234(f913(x35431,a904)))
% 22.40/22.29 [3545]P1(f319(f55(x35451),f181(f913(x35451,a904))))
% 22.40/22.29 [3547]E(f319(f294(a906,x35471),f319(a104,x35471)),f319(f319(f301(a906),x35471),f181(f913(a906,a904))))
% 22.40/22.29 [3548]E(f79(f912(a906,a906),f42(x35481,f2(a906))),f319(f319(f244(a906,a906),f2(a906)),x35481))
% 22.40/22.29 [3561]E(f319(f319(f301(a906),f319(a104,x35611)),f319(f293(a906),x35611)),f319(f293(a906),f319(a104,x35611)))
% 22.40/22.29 [3565]P37(x35651,f181(f913(f912(x35651,x35651),a904)))
% 22.40/22.29 [3566]P39(x35661,f181(f913(f912(x35661,x35661),a904)))
% 22.40/22.29 [3569]P1(f319(f319(f225(a1),f2(a1)),f319(f92(a1),x35691)))
% 22.40/22.29 [3576]E(f319(f319(f74(a906),f319(f182(a906),x35761)),f319(a104,f2(a906))),f319(f182(a906),f319(a104,x35761)))
% 22.40/22.29 [3678]P41(f319(f302(a906,a1,f92(a1)),x36781))
% 22.40/22.29 [3715]P54(x37151,f181(f913(x37151,a904)),f181(f913(f912(x37151,x37151),a904)))
% 22.40/22.29 [3733]E(f319(f319(f244(a1,a1),f319(f96(a1),a89)),f319(f319(f3(a1),x37331),f72(a1))),f44(f319(f96(a1),a89),x37331))
% 22.40/22.29 [3786]P61(x37861,f319(f18(f913(x37861,a904),x37861),f319(f18(a904,x37861),a231)))
% 22.40/22.29 [3984]P1(f319(f319(f321(f913(f912(a906,a906),a904)),f320(x39841)),a90))
% 22.40/22.29 [4007]P1(f319(f319(f321(f913(f912(a906,a906),a904)),f319(a99,x40071)),a90))
% 22.40/22.29 [4135]P25(x41351,f913(x41351,a904),f319(f319(f9(x41351,f913(x41351,a904),f913(x41351,a904)),f301(x41351)),f181(f913(x41351,a904))),f234(f913(x41351,a904)))
% 22.40/22.29 [4637]~E(f319(a5,f319(a104,f319(a22,x46371))),f2(a91))
% 22.40/22.29 [4643]~P1(f319(a186,f319(f92(a1),x46431)))
% 22.40/22.29 [4646]~P1(f319(f319(f226(a906),x46461),x46461))
% 22.40/22.29 [4654]~P1(f319(f319(f225(a906),f319(a104,x46541)),x46541))
% 22.40/22.29 [3493]E(f319(a97,f319(f73(a1),f319(f92(a1),x34931))),f2(a906))
% 22.40/22.29 [3496]E(f319(f319(f74(a1),f319(f73(a1),x34961)),x34961),f2(a1))
% 22.40/22.29 [3500]E(f319(f29(a1),f319(f294(a1,f2(a1)),x35001)),f319(a97,x35001))
% 22.40/22.29 [3511]E(f319(f319(f236(a906),f319(a104,f2(a906))),x35111),f319(a104,f2(a906)))
% 22.40/22.29 [3606]E(f319(f273(x36061),f181(f913(f912(x36061,x36061),a904))),f181(f913(x36061,a904)))
% 22.40/22.29 [3613]E(f32(f913(x36131,a904),f234(f913(f913(x36131,a904),a904))),f181(f913(x36131,a904)))
% 22.40/22.29 [3614]E(f32(f913(x36141,a904),f181(f913(f913(x36141,a904),a904))),f234(f913(x36141,a904)))
% 22.40/22.29 [3615]E(f31(f913(x36151,a904),f234(f913(f913(x36151,a904),a904))),f234(f913(x36151,a904)))
% 22.40/22.29 [3616]E(f31(f913(x36161,a904),f181(f913(f913(x36161,a904),a904))),f181(f913(x36161,a904)))
% 22.40/22.29 [3620]P1(f319(f319(f279(a906),f319(a104,f2(a906))),x36201))
% 22.40/22.29 [3660]E(f319(f319(f301(f907(x36601)),f105(x36601)),f181(f913(f907(x36601),a904))),f153(x36601,f181(f913(x36601,a904))))
% 22.40/22.29 [3661]E(f319(f319(f301(f907(x36611)),f105(x36611)),f181(f913(f907(x36611),a904))),f154(x36611,f105(f913(x36611,a904))))
% 22.40/22.29 [3698]E(f319(f319(f74(a906),f6(x36981)),f319(a104,f2(a906))),f6(f319(a5,f319(a104,f319(a22,x36981)))))
% 22.40/22.29 [3724]E(f319(f29(a1),f319(f302(a906,a1,f92(a1)),x37241)),f319(f29(a906),x37241))
% 22.40/22.29 [3727]P1(f319(f319(f225(a906),x37271),f319(f319(f75(a906),x37271),x37271)))
% 22.40/22.29 [3764]E(f319(f302(a1,a906,a97),f295(a1,f2(a1),f319(f92(a1),x37641))),f319(f293(a906),x37641))
% 22.40/22.29 [3781]E(f319(f319(f30(a906),f319(a104,f2(a906))),f319(f96(a906),x37811)),f319(a97,f319(f319(f30(a1),f72(a1)),f319(f96(a1),x37811))))
% 22.40/22.29 [3783]E(f319(f164(a906),f131(a906,f319(f294(a906,f2(a906)),f319(a104,x37831)))),f319(f293(a906),x37831))
% 22.40/22.29 [3784]E(f319(f319(f74(a906),f319(f182(a91),x37841)),f319(a104,f2(a906))),f319(f182(a91),f319(a5,f319(a104,f319(a22,x37841)))))
% 22.40/22.29 [3804]P39(x38041,f299(x38041,f181(f913(f912(x38041,x38041),a904))))
% 22.40/22.29 [3805]P53(x38051,f299(x38051,f181(f913(f912(x38051,x38051),a904))))
% 22.40/22.29 [3806]E(f319(f302(a1,a906,a97),f319(f302(a906,a1,f92(a1)),x38061)),x38061)
% 22.40/22.29 [3836]E(f319(f319(f301(a906),f2(a906)),f319(f302(a906,a906,a104),f319(f274(a906),x38361))),f319(f274(a906),f319(a104,x38361)))
% 22.40/22.29 [3842]P56(x38421,x38421,f299(x38421,f181(f913(f912(x38421,x38421),a904))))
% 22.40/22.29 [3848]P1(f319(a186,f319(f73(a1),f319(f92(a1),f319(a104,x38481)))))
% 22.40/22.29 [3858]E(f319(f319(f3(f913(a906,a904)),f319(f275(a906),x38581)),f319(f319(f301(a906),x38581),f181(f913(a906,a904)))),f319(f275(a906),f319(a104,x38581)))
% 22.40/22.29 [3883]E(f319(f319(f301(f913(x38831,a904)),f181(f913(x38831,a904))),f181(f913(f913(x38831,a904),a904))),f319(f300(x38831),f181(f913(x38831,a904))))
% 22.40/22.29 [3914]E(f319(f319(f3(f913(a906,a904)),f319(f296(a906),x39141)),f319(f319(f301(a906),f319(a104,x39141)),f181(f913(a906,a904)))),f319(f296(a906),f319(a104,x39141)))
% 22.40/22.29 [4384]P15(x43841,f913(x43841,a904),f319(f319(f10(f913(x43841,a904),f913(f913(x43841,a904),f913(x43841,a904)),x43841),f319(f9(f913(x43841,a904),f913(x43841,a904),f913(x43841,a904)),f3(f913(x43841,a904)))),f319(f319(f9(x43841,f913(x43841,a904),f913(x43841,a904)),f301(x43841)),f181(f913(x43841,a904)))))
% 22.40/22.29 [4471]E(f319(f254(f912(a1,a1)),f319(f249(a1,a1,a904),f319(f319(f10(f913(a1,a904),f913(a1,a904),a1),f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),x44711)))),f226(a1)))),f100(x44711))
% 22.40/22.29 [4510]E(f319(f254(f912(a1,a1)),f319(f249(a1,a1,a904),f319(f319(f20(a1,f913(a1,a904),f913(a1,a904)),f319(f319(f10(f913(a904,a904),f913(f913(a1,a904),f913(a1,a904)),a1),f10(a904,a904,a1)),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),x45101)))),f226(a1)))),f98(x45101))
% 22.40/22.29 [4573]E(f319(f254(f912(f913(x45731,a904),f913(x45731,a904))),f319(f249(f913(x45731,a904),f913(x45731,a904),a904),f319(f319(f9(f913(x45731,a904),f913(f913(x45731,a904),a904),f913(f913(x45731,a904),a904)),f319(f319(f10(f913(f913(x45731,a904),f913(a904,a904)),f913(f913(f913(x45731,a904),a904),f913(f913(x45731,a904),a904)),f913(x45731,a904)),f20(f913(x45731,a904),a904,a904)),f319(f319(f10(f913(f913(x45731,a904),a904),f913(f913(x45731,a904),f913(a904,a904)),f913(x45731,a904)),f319(f10(a904,f913(a904,a904),f913(x45731,a904)),a317)),f226(f913(x45731,a904))))),f55(x45731)))),f306(x45731))
% 22.40/22.29 [4658]~P1(f319(f55(f907(x46581)),f234(f913(f907(x46581),a904))))
% 22.40/22.29 [4668]~P1(f319(f319(f225(a1),f2(a1)),f319(f73(a1),f319(f92(a1),f319(a104,x46681)))))
% 22.40/22.29 [3640]E(f319(f319(f3(a1),f319(f319(f74(a1),x36401),a89)),a89),x36401)
% 22.40/22.29 [3653]E(f319(f164(a906),f131(a906,f319(f294(a906,f2(a906)),x36531))),f319(f274(a906),x36531))
% 22.40/22.29 [3941]E(f319(f278(x39411,x39411),f299(x39411,f181(f913(f912(x39411,x39411),a904)))),f299(x39411,f181(f913(f912(x39411,x39411),a904))))
% 22.40/22.29 [3985]P1(f319(f319(f225(a906),x39851),f319(f319(f75(a906),x39851),f319(f319(f75(a906),x39851),x39851))))
% 22.40/22.29 [4248]P1(f319(f55(a906),f319(f254(a906),f319(f319(f9(a906,a906,a904),f225(a906)),x42481))))
% 22.40/22.29 [4249]P1(f319(f55(a906),f319(f254(a906),f319(f319(f9(a906,a906,a904),f226(a906)),x42491))))
% 22.40/22.29 [4524]E(f319(f254(f912(x45241,x45241)),f319(f319(f10(f913(x45241,a904),a904,f912(x45241,x45241)),f80(x45241)),f319(f319(f9(f912(x45241,x45241),f913(x45241,f912(x45241,x45241)),f913(x45241,a904)),f319(f319(f10(f913(f912(x45241,x45241),a904),f913(f913(x45241,f912(x45241,x45241)),f913(x45241,a904)),f912(x45241,x45241)),f10(f912(x45241,x45241),a904,x45241)),a316)),f319(f319(f20(x45241,x45241,f912(x45241,x45241)),f244(x45241,x45241)),f7(x45241))))),f299(x45241,f181(f913(f912(x45241,x45241),a904))))
% 22.40/22.29 [4661]~E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x46611)),x46611),a77)
% 22.40/22.29 [4662]~E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x46621)),x46621),f2(a1))
% 22.40/22.29 [4114]E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f3(a1),a89),x41141))),f319(f319(f3(a1),a89),x41141)),f319(f319(f3(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x41141)),x41141)))
% 22.40/22.29 [4229]E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f73(a1),x42291)),a89))),f319(f319(f74(a1),f319(f73(a1),x42291)),a89)),f319(f73(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x42291)),x42291)))
% 22.40/22.29 [4299]E(f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x42991),f2(a906))),f181(f913(f912(a906,a906),a904))))),f319(f92(a1),x42991))
% 22.40/22.29 [4310]E(f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),f324(x43101)),f509(x43101))),f181(f913(f912(a906,a906),a904))))),x43101)
% 22.40/22.29 [4316]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f3(a1),a89),x43161))),f319(f319(f3(a1),a89),x43161))),a89),f319(f319(f3(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43161)),x43161)))
% 22.40/22.29 [4348]E(f319(f254(a1),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),x43481)),f319(f302(a906,a1,f92(a1)),f319(f254(a906),f319(f319(f10(a1,a904,a906),x43481),f92(a1)))))
% 22.40/22.29 [4392]P41(f319(f254(a1),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),x43921)))
% 22.40/22.29 [4413]P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),x44131),f181(f913(f912(a906,a906),a904)))),a65))
% 22.40/22.29 [4418]E(f319(f302(a1,a906,a97),f319(f254(a1),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),f319(f319(f10(a906,a904,a1),x44181),a97)))),f319(f254(a906),x44181))
% 22.40/22.29 [4587]E(f304(a906,f319(f319(f33(f912(a906,a906),f913(a906,a904)),f319(a99,x45871)),f319(f249(a906,a906,f913(a906,a904)),f319(f319(f9(a906,f913(a906,a904),f913(a906,f913(a906,a904))),f319(f319(f10(f913(a906,f913(f913(a906,a904),f913(a906,a904))),f913(f913(a906,a904),f913(a906,f913(a906,a904))),a906),f9(a906,f913(a906,a904),f913(a906,a904))),f319(f319(f10(f913(a906,a906),f913(a906,f913(f913(a906,a904),f913(a906,a904))),a906),f319(f10(a906,f913(f913(a906,a904),f913(a906,a904)),a906),f301(a906))),f3(a906)))),f181(f913(a906,a904)))))),f319(a97,x45871))
% 22.40/22.29 [4087]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x40871)),x40871)),a89),f319(f319(f74(a1),x40871),x40871))
% 22.40/22.29 [4333]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f3(a1),x43331),a89))),f319(f319(f3(a1),x43331),a89))),a89),f319(f319(f3(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43331)),x43331)),a89))
% 22.40/22.29 [4671]~E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x46711)),x46711)),a89),a89)
% 22.40/22.29 [4295]E(f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x42951)),x42951)),a89)),f319(f319(f82(a906,a906),f319(f96(a906),x42951)),f319(f319(f20(a906,a906,a906),f74(a906)),f7(a906))))
% 22.40/22.29 [4301]E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f3(a1),a89),x43011))),f319(f319(f3(a1),a89),x43011)),f319(f319(f3(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43011)),x43011)),a89)))
% 22.40/22.29 [4331]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f73(a1),x43311))),f319(f73(a1),x43311))),a89),f319(f73(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43311)),x43311)),a89)))
% 22.40/22.29 [4357]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f3(a1),a77),x43571))),f319(f319(f3(a1),a77),x43571))),a89),f319(f319(f3(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43571)),x43571)),a89)))
% 22.40/22.29 [4601]E(f319(a83,f319(f319(f33(f912(a906,a906),f913(f912(a906,a906),a904)),f319(a99,x46011)),f319(f249(a906,a906,f913(f912(a906,a906),a904)),f319(f319(f10(f913(a906,f913(f912(a906,a906),a904)),f913(a906,f913(f912(a906,a906),a904)),a906),f319(f10(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904),a906),f277(f912(a906,a906),f912(a906,a906),a101))),f319(f319(f9(a906,f913(f912(a906,a906),a904),f913(a906,f913(f912(a906,a906),a904))),f319(f319(f10(f913(a906,f913(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f913(f913(f912(a906,a906),a904),f913(a906,f913(f912(a906,a906),a904))),a906),f9(a906,f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f10(f913(a906,f912(a906,a906)),f913(a906,f913(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),a906),f319(f10(f912(a906,a906),f913(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),a906),f301(f912(a906,a906)))),f319(f9(a906,a906,f912(a906,a906)),f244(a906,a906))))),f181(f913(f912(a906,a906),a904))))))),f319(f73(a1),x46011))
% 22.40/22.29 [4360]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43601)),x43601)),a89)),a89),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),x43601),a89))),f319(f319(f74(a1),x43601),a89)))
% 22.40/22.29 [4493]E(f319(f319(f74(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))),x44931),f319(a104,f319(a104,f319(a104,x44931))))
% 22.40/22.29 [4533]E(f319(f319(f74(a906),x45331),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(a104,f319(a104,x45331)))
% 22.40/22.29 [4534]E(f319(f319(f75(a906),x45341),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(f319(f74(a906),x45341),x45341))
% 22.40/22.29 [4535]E(f319(f319(f30(a906),f319(f319(f74(a906),x45351),x45351)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x45351)
% 22.40/22.29 [4567]E(f39(a906,f319(a104,f319(a104,x45671)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f39(a906,x45671,f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.29 [4564]E(f319(f319(f74(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x45641),f319(a104,f319(a104,x45641)))
% 22.40/22.29 [4565]E(f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x45651),f319(f319(f74(a906),x45651),x45651))
% 22.40/22.29 [4577]E(f319(f319(f30(a906),f319(a104,f319(a104,x45771))),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(a104,f319(f319(f30(a906),x45771),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.29 [4608]E(f319(f249(a1,a1,f912(a1,a1)),f319(f319(f20(a1,f913(a1,f912(a1,a1)),f913(a1,f912(a1,a1))),f319(f319(f10(f913(a1,f913(f912(a1,a1),f912(a1,a1))),f913(f913(a1,f912(a1,a1)),f913(a1,f912(a1,a1))),a1),f20(a1,f912(a1,a1),f912(a1,a1))),f319(f319(f10(f913(a1,f912(a1,a1)),f913(a1,f913(f912(a1,a1),f912(a1,a1))),a1),f319(f20(a1,f912(a1,a1),f913(f912(a1,a1),f912(a1,a1))),f319(f319(f10(a904,f913(f912(a1,a1),f913(f912(a1,a1),f912(a1,a1))),a1),f86(f912(a1,a1))),f319(f319(f10(a1,a904,a1),f319(f225(a1),f2(a1))),f319(f319(f9(a1,a1,a1),f3(a1)),x46081))))),f319(f319(f9(a1,f913(a1,a1),f913(a1,f912(a1,a1))),f319(f319(f10(f913(a1,f912(a1,a1)),f913(f913(a1,a1),f913(a1,f912(a1,a1))),a1),f10(a1,f912(a1,a1),a1)),f319(f319(f10(a1,f913(a1,f912(a1,a1)),a1),f244(a1,a1)),f319(f319(f9(a1,a1,a1),f319(f319(f10(a1,f913(a1,a1),a1),f74(a1)),f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))),f72(a1))))),f319(f319(f9(a1,a1,a1),f3(a1)),x46081))))),f319(f319(f10(a1,f913(a1,f912(a1,a1)),a1),f244(a1,a1)),f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))),f37(x46081))
% 22.40/22.29 [3319]P110(f912(x33191,x33192))
% 22.40/22.29 [3320]P110(f914(x33201,x33202))
% 22.40/22.29 [3321]P110(f911(x33211,x33212))
% 22.40/22.29 [3338]P13(a1,f170(x33381,x33382))
% 22.40/22.29 [3339]P37(x33391,f145(x33391,x33392))
% 22.40/22.29 [3340]P38(x33401,f255(x33401,x33402))
% 22.40/22.29 [3341]P38(x33411,f299(x33411,x33412))
% 22.40/22.29 [3342]P39(x33421,f255(x33421,x33422))
% 22.40/22.29 [3343]P53(x33431,f255(x33431,x33432))
% 22.40/22.29 [3407]P31(x34071,x34072,f105(x34071))
% 22.40/22.29 [3440]P54(x34401,x34402,f255(x34401,x34402))
% 22.40/22.29 [3441]P56(x34411,x34411,f255(x34411,x34412))
% 22.40/22.29 [3701]P25(x37011,x37011,f7(x37011),x37012)
% 22.40/22.29 [3702]P25(x37021,x37021,f25(x37021),x37022)
% 22.40/22.29 [3711]P32(x37111,x37112,f105(x37111),f105(x37111))
% 22.40/22.29 [3718]P25(f907(x37181),f907(x37181),f160(x37181),x37182)
% 22.40/22.29 [4112]P26(x41121,x41121,f25(x41121),x41122,x41122)
% 22.40/22.29 [4632]~P33(x46321,x46322,f105(x46321))
% 22.40/22.29 [4633]~P35(x46331,x46332,f105(x46331))
% 22.40/22.29 [3305]E(f319(f7(x33051),x33052),x33052)
% 22.40/22.29 [3306]E(f319(f254(x33061),x33062),x33062)
% 22.40/22.29 [3308]E(f319(f25(x33081),x33082),x33082)
% 22.40/22.29 [3318]E(f319(f184(x33181),x33182),f107(x33181))
% 22.40/22.29 [3336]E(f79(x33361,f319(a316,x33362)),x33362)
% 22.40/22.29 [3337]E(f84(x33371,f319(a316,x33372)),x33372)
% 22.40/22.29 [3358]E(f319(f117(x33581,x33582),f111(x33581)),f2(a906))
% 22.40/22.29 [3363]E(f319(f128(x33631,x33632),f105(x33631)),f105(x33631))
% 22.40/22.29 [3383]E(f299(x33831,f299(x33831,x33832)),f299(x33831,x33832))
% 22.40/22.29 [3384]E(f144(x33841,f144(x33841,x33842)),f144(x33841,x33842))
% 22.40/22.29 [3402]E(f319(f319(f126(x34021),x34022),f105(x34021)),x34022)
% 22.40/22.29 [3408]E(f165(x34081,x34082,f105(x34081)),x34082)
% 22.40/22.29 [3409]E(f165(x34091,f105(x34091),x34092),x34092)
% 22.40/22.29 [3410]E(f108(x34101,f111(x34101),x34102),x34102)
% 22.40/22.29 [3411]E(f161(x34111,f2(a906),x34112),f105(x34111))
% 22.40/22.29 [3417]E(f319(f319(f167(x34171),x34172),f105(x34171)),f105(x34171))
% 22.40/22.29 [3418]E(f319(f319(f130(x34181),x34182),f105(x34181)),f105(x34181))
% 22.40/22.29 [3420]E(f147(x34201,x34202,f105(x34201)),f2(a906))
% 22.40/22.29 [3422]E(f162(x34221,x34222,f105(x34221)),f105(x34221))
% 22.40/22.29 [3423]E(f169(x34231,x34232,f105(x34231)),f105(x34231))
% 22.40/22.29 [3424]E(f168(x34241,f105(x34241),x34242),f105(x34241))
% 22.40/22.29 [3428]E(f319(f164(x34281),f144(x34281,x34282)),f319(f164(x34281),x34282))
% 22.40/22.29 [3431]E(f319(f276(x34311,x34311),f255(x34311,x34312)),x34312)
% 22.40/22.29 [3432]E(f319(f256(x34321,x34321),f255(x34321,x34322)),x34322)
% 22.40/22.29 [3439]E(f319(f278(x34391,x34391),f255(x34391,x34392)),f255(x34391,x34392))
% 22.40/22.29 [3452]E(f299(f907(x34521),f149(x34521,x34522)),f150(x34521,f299(x34521,x34522)))
% 22.40/22.29 [3454]P1(f319(f129(a1),f170(x34541,x34542)))
% 22.40/22.29 [3462]E(f319(f276(x34621,x34621),f299(x34621,x34622)),f234(f913(x34621,a904)))
% 22.40/22.29 [3463]E(f319(f256(x34631,x34631),f299(x34631,x34632)),f234(f913(x34631,a904)))
% 22.40/22.29 [3467]P1(f319(f129(x34671),f144(x34671,x34672)))
% 22.40/22.29 [3469]P1(f319(f152(x34691,x34692),f105(x34691)))
% 22.40/22.29 [3475]E(f319(f164(a1),f170(x34751,x34752)),f295(a1,x34751,x34752))
% 22.40/22.29 [3489]P57(x34891,f181(f913(x34891,a904)),x34892)
% 22.40/22.29 [3494]E(f319(f248(a1,a1),f40(x34941,x34942)),f39(a1,x34941,x34942))
% 22.40/22.29 [3495]E(f319(f294(a906,x34951),f319(a104,x34952)),f295(a906,x34951,x34952))
% 22.40/22.29 [3510]E(f319(f319(f143(x35101),x35102),f105(x35101)),f132(x35101,x35102,f105(x35101)))
% 22.40/22.29 [3522]E(f295(a906,f319(a104,x35221),x35222),f297(a906,x35221,x35222))
% 22.40/22.29 [3525]P54(x35251,f234(f913(x35251,a904)),f299(x35251,x35252))
% 22.40/22.29 [3587]E(f319(f319(f3(a906),x35871),f319(a104,x35872)),f319(f29(a906),f298(a906,x35872,x35871)))
% 22.40/22.29 [3641]E(f158(x36411,x36412,f105(x36411)),f319(f319(f244(f907(x36411),f907(x36411)),f105(x36411)),f105(x36411)))
% 22.40/22.29 [3658]E(f319(f249(x36581,x36582,f912(x36581,x36582)),f244(x36581,x36582)),f25(f912(x36581,x36582)))
% 22.40/22.29 [3662]P1(f319(f319(f321(f907(x36621)),f105(x36621)),f153(x36621,x36622)))
% 22.40/22.29 [3663]E(f319(f182(f907(x36631)),f106(x36631,x36632)),f319(f319(f3(a906),f319(f182(f907(x36631)),x36632)),f72(a906)))
% 22.40/22.29 [3672]P1(f319(f55(a906),f298(a906,x36721,x36722)))
% 22.40/22.29 [3673]P1(f319(f55(a906),f297(a906,x36731,x36732)))
% 22.40/22.29 [3674]P1(f319(f55(a906),f295(a906,x36741,x36742)))
% 22.40/22.29 [3675]P1(f319(f55(a1),f298(a1,x36751,x36752)))
% 22.40/22.29 [3676]P1(f319(f55(a1),f297(a1,x36761,x36762)))
% 22.40/22.29 [3677]P1(f319(f55(a1),f295(a1,x36771,x36772)))
% 22.40/22.29 [3780]E(f319(f302(a906,a906,a104),f295(a906,x37801,x37802)),f295(a906,f319(a104,x37801),f319(a104,x37802)))
% 22.40/22.29 [3800]E(f319(f319(f281(x38001,x38001,x38001),f299(x38001,x38002)),f299(x38001,x38002)),f299(x38001,x38002))
% 22.40/22.29 [3834]E(f319(f319(f244(a91,a91),f319(f319(f30(a91),x38341),x38342)),f39(a91,x38341,x38342)),f23(x38341,x38342))
% 22.40/22.29 [3835]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),x38351),x38352)),f39(a1,x38351,x38352)),f40(x38351,x38352))
% 22.40/22.29 [3862]E(f319(f319(f244(a906,a906),f319(f319(f30(a906),x38621),x38622)),f39(a906,x38621,x38622)),f79(f912(a906,a906),f42(x38621,x38622)))
% 22.40/22.29 [3906]P1(f319(f319(f226(a906),f319(f319(f3(a906),x39061),x39062)),f319(a104,x39061)))
% 22.40/22.29 [3958]P38(x39581,f319(f319(f281(x39581,x39581,x39581),x39582),f299(x39581,x39582)))
% 22.40/22.29 [4006]E(f319(f319(f74(a1),f319(f319(f75(a1),x40061),f319(f319(f30(a1),x40062),x40061))),f39(a1,x40062,x40061)),x40062)
% 22.40/22.29 [4010]E(f319(f319(f33(a906,f913(f912(f907(x40101),f907(x40101)),a904)),f234(f913(a906,a904))),f135(x40101,x40102)),f137(x40101,x40102))
% 22.40/22.29 [4225]P1(f319(f319(f321(f912(f907(x42251),f907(x42251))),f319(f319(f244(f907(x42251),f907(x42251)),f105(x42251)),f105(x42251))),f150(x42251,x42252)))
% 22.40/22.29 [4328]E(f245(x43281,x43281,x43281,a316,f245(x43281,x43281,x43281,x43282,a316)),x43282)
% 22.40/22.29 [4378]E(f250(x43781,x43781,x43782,x43782,f7(x43781),f7(x43782)),f25(f912(x43781,x43782)))
% 22.40/22.29 [4380]E(f250(x43801,x43801,x43802,x43802,f25(x43801),f25(x43802)),f25(f912(x43801,x43802)))
% 22.40/22.29 [3401]E(f319(f160(x34011),f319(f160(x34011),x34012)),x34012)
% 22.40/22.29 [3403]E(f319(f319(f130(x34031),f2(a906)),x34032),x34032)
% 22.40/22.29 [3419]E(f319(f319(f167(x34191),f2(a906)),x34192),f105(x34191))
% 22.40/22.29 [3426]E(f319(f319(f126(x34261),f105(x34261)),x34262),x34262)
% 22.40/22.29 [3435]E(f31(f913(x34351,a904),f319(f300(x34351),x34352)),x34352)
% 22.40/22.29 [3437]E(f319(f164(x34371),f319(f159(x34371),x34372)),f319(f164(x34371),x34372))
% 22.40/22.29 [3438]E(f319(f164(x34381),f319(f160(x34381),x34382)),f319(f164(x34381),x34382))
% 22.40/22.29 [3443]E(f319(f319(f3(a91),x34431),x34432),f319(f319(a4,x34431),x34432))
% 22.40/22.29 [3456]E(f319(f319(f74(a906),x34561),x34562),f319(f319(f74(a906),x34562),x34561))
% 22.40/22.29 [3457]E(f319(f319(f74(a1),x34571),x34572),f319(f319(f74(a1),x34572),x34571))
% 22.40/22.29 [3458]E(f319(f319(f75(a906),x34581),x34582),f319(f319(f75(a906),x34582),x34581))
% 22.40/22.29 [3459]E(f319(f319(f75(a1),x34591),x34592),f319(f319(f75(a1),x34592),x34591))
% 22.40/22.29 [3481]E(f319(f319(f175(x34811,x34811),f2(a906)),x34812),f25(x34811))
% 22.40/22.29 [3482]E(f319(f182(f907(x34821)),f319(f159(x34821),x34822)),f319(f182(f907(x34821)),x34822))
% 22.40/22.29 [3483]E(f319(f182(f907(x34831)),f319(f160(x34831),x34832)),f319(f182(f907(x34831)),x34832))
% 22.40/22.29 [3484]E(f168(x34841,x34842,f181(f913(a906,a904))),f105(x34841))
% 22.40/22.29 [3485]E(f319(f319(f146(x34851,x34851),f7(x34851)),x34852),x34852)
% 22.40/22.29 [3487]E(f319(f243(a1,a1),f40(x34871,x34872)),f319(f319(f30(a1),x34871),x34872))
% 22.40/22.29 [3504]E(f319(f182(f907(x35041)),f144(x35041,x35042)),f319(f29(x35041),f319(f164(x35041),x35042)))
% 22.40/22.29 [3505]E(f319(f273(x35051),f319(f278(x35051,x35051),x35052)),f319(f273(x35051),x35052))
% 22.40/22.29 [3509]P1(f319(f55(x35091),f319(f164(x35091),x35092)))
% 22.40/22.29 [3517]E(f319(f319(f74(a1),x35171),f319(f73(a1),x35172)),f319(f319(f3(a1),x35171),x35172))
% 22.40/22.29 [3524]P14(x35241,x35242,f181(f913(f905(x35241),a904)))
% 22.40/22.29 [3526]E(f319(f302(x35261,x35261,f7(x35261)),x35262),x35262)
% 22.40/22.29 [3527]E(f319(f302(x35271,x35271,f25(x35271)),x35272),x35272)
% 22.40/22.29 [3528]E(f319(f303(x35281,x35281,f7(x35281)),x35282),x35282)
% 22.40/22.29 [3529]E(f319(f303(x35291,x35291,f25(x35291)),x35292),x35292)
% 22.40/22.29 [3530]P1(f319(f234(f913(x35301,a904)),x35302))
% 22.40/22.29 [3532]E(f319(f29(a906),f319(f294(a906,x35321),x35322)),f319(f319(f3(a906),x35322),x35321))
% 22.40/22.29 [3533]E(f319(f294(a906,f319(a104,x35331)),x35332),f298(a906,x35331,x35332))
% 22.40/22.29 [3546]E(f319(f319(f301(x35461),x35462),f181(f913(x35461,a904))),f319(f254(x35461),f319(a316,x35462)))
% 22.40/22.29 [3551]E(f299(x35511,f319(f278(x35511,x35511),x35512)),f319(f278(x35511,x35511),f299(x35511,x35512)))
% 22.40/22.29 [3556]E(f319(f319(f74(a906),f319(a104,x35561)),x35562),f319(f319(f74(a906),x35561),f319(a104,x35562)))
% 22.40/22.29 [3557]E(f319(f319(f3(a906),f319(a104,x35571)),f319(a104,x35572)),f319(f319(f3(a906),x35571),x35572))
% 22.40/22.29 [3563]E(f49(x35631,f2(a906),x35632),f319(f319(f143(f907(x35631)),f105(x35631)),f105(f907(x35631))))
% 22.40/22.29 [3564]E(f319(f29(a906),f297(a906,x35641,x35642)),f319(f319(f3(a906),x35642),x35641))
% 22.40/22.29 [3573]P37(x35731,f319(f319(f280(a906,x35731),a232),x35732))
% 22.40/22.29 [3575]P13(a906,f131(a906,f319(f294(a906,x35751),x35752)))
% 22.40/22.29 [3577]P1(f319(f55(a906),f319(f294(a906,x35771),x35772)))
% 22.40/22.29 [3578]P1(f319(f55(a1),f319(f294(a1,x35781),x35782)))
% 22.40/22.29 [3581]E(f319(f278(f907(x35811),f907(x35811)),f149(x35811,x35812)),f149(x35811,f319(f278(x35811,x35811),x35812)))
% 22.40/22.29 [3583]E(f319(f294(a1,x35831),f319(f319(f74(a1),x35832),f72(a1))),f295(a1,x35831,x35832))
% 22.40/22.29 [3586]E(f319(f319(f30(a1),f319(f73(a1),x35861)),f319(f73(a1),x35862)),f319(f319(f30(a1),x35861),x35862))
% 22.40/22.29 [3594]E(f319(f319(f175(f912(x35941,x35941),a904),f72(a906)),x35942),x35942)
% 22.40/22.29 [3596]E(f319(f319(f93(f913(x35961,a904)),x35962),f181(f913(x35961,a904))),x35962)
% 22.40/22.29 [3597]E(f319(f319(f94(f913(x35971,a904)),x35972),f234(f913(x35971,a904))),x35972)
% 22.40/22.29 [3598]E(f319(f319(f3(f913(x35981,a904)),x35982),f181(f913(x35981,a904))),x35982)
% 22.40/22.29 [3599]E(f319(f243(a906,a906),f79(f912(a906,a906),f42(x35991,x35992))),f319(f319(f30(a906),x35991),x35992))
% 22.40/22.29 [3605]E(f295(a1,f319(f319(f74(a1),x36051),f72(a1)),x36052),f297(a1,x36051,x36052))
% 22.40/22.29 [3610]E(f319(f248(a906,a906),f79(f912(a906,a906),f42(x36101,x36102))),f39(a906,x36101,x36102))
% 22.40/22.29 [3619]P1(f319(f319(f321(x36191),x36192),f234(f913(x36191,a904))))
% 22.40/22.29 [3624]E(f319(f319(f3(a906),f319(a104,x36241)),x36242),f319(f29(a906),f295(a906,x36242,x36241)))
% 22.40/22.29 [3649]E(f319(f319(f93(f913(x36491,a904)),x36492),f234(f913(x36491,a904))),f234(f913(x36491,a904)))
% 22.40/22.29 [3650]E(f319(f319(f94(f913(x36501,a904)),x36502),f181(f913(x36501,a904))),f181(f913(x36501,a904)))
% 22.40/22.29 [3651]E(f319(f319(f3(f913(x36511,a904)),x36512),f234(f913(x36511,a904))),f181(f913(x36511,a904)))
% 22.40/22.29 [3666]E(f39(a1,f319(f73(a1),x36661),f319(f73(a1),x36662)),f319(f73(a1),f39(a1,x36661,x36662)))
% 22.40/22.29 [3667]E(f39(a1,f319(f92(a1),x36671),f319(f92(a1),x36672)),f319(f92(a1),f39(a906,x36671,x36672)))
% 22.40/22.29 [3679]E(f319(f182(f907(x36791)),f319(f163(x36791),x36792)),f319(f319(f3(a906),f319(f182(f907(x36791)),x36792)),f72(a906)))
% 22.40/22.29 [3703]E(f319(f319(f30(a1),f39(a1,x37031,x37032)),x37032),f2(a1))
% 22.40/22.29 [3713]E(f319(a5,f39(a906,f319(a22,x37131),f319(a22,x37132))),f39(a91,x37131,x37132))
% 22.40/22.29 [3747]E(f319(a5,f319(f319(f3(a906),f319(a22,x37471)),f319(a22,x37472))),f319(f319(f3(a91),x37471),x37472))
% 22.40/22.29 [3748]E(f319(a5,f319(f319(f74(a906),f319(a22,x37481)),f319(a22,x37482))),f319(f319(f74(a91),x37481),x37482))
% 22.40/22.29 [3749]E(f319(a5,f319(f319(f75(a906),f319(a22,x37491)),f319(a22,x37492))),f319(f319(f75(a91),x37491),x37492))
% 22.40/22.29 [3750]E(f319(a5,f319(f319(f30(a906),f319(a22,x37501)),f319(a22,x37502))),f319(f319(f30(a91),x37501),x37502))
% 22.40/22.29 [3758]E(f319(f302(a906,a906,a104),f319(f294(a906,x37581),x37582)),f319(f294(a906,f319(a104,x37581)),f319(a104,x37582)))
% 22.40/22.29 [3785]P1(f319(f42(x37851,x37852),f79(f912(a906,a906),f42(x37851,x37852))))
% 22.40/22.29 [3809]E(f39(a906,f319(a104,f39(a906,x38091,x38092)),x38092),f39(a906,f319(a104,x38091),x38092))
% 22.40/22.29 [3821]E(f319(f319(f34(f913(x38211,a904),f913(x38211,a904)),x38212),f7(f913(x38211,a904))),f32(f913(x38211,a904),x38212))
% 22.40/22.29 [3822]E(f319(f319(f33(f913(x38221,a904),f913(x38221,a904)),x38222),f7(f913(x38221,a904))),f31(f913(x38221,a904),x38222))
% 22.40/22.29 [3823]E(f319(f302(f907(x38231),f913(x38231,a904),f164(x38231)),f319(f164(f907(x38231)),f48(x38231,x38232))),f319(f300(x38231),f319(f164(x38231),x38232)))
% 22.40/22.29 [3827]P1(f319(f319(f321(f913(x38271,a904)),x38272),f319(f300(x38271),x38272)))
% 22.40/22.29 [3833]E(f39(a1,f319(f73(a1),f39(a1,x38331,x38332)),x38332),f39(a1,f319(f73(a1),x38331),x38332))
% 22.40/22.29 [3844]P1(f319(f319(f225(f913(x38441,a904)),x38442),f234(f913(x38441,a904))))
% 22.40/22.29 [3846]E(f319(f319(f281(x38461,x38461,x38461),f299(x38461,x38462)),f299(x38461,f299(x38461,x38462))),f299(x38461,x38462))
% 22.40/22.29 [3847]E(f319(f319(f93(f913(x38471,a904)),f319(f256(x38471,x38471),x38472)),f319(f276(x38471,x38471),x38472)),f319(f273(x38471),x38472))
% 22.40/22.29 [3868]E(f305(x38681,x38682,f234(f913(x38681,a904)),f234(f913(x38682,a904))),f234(f913(f914(x38681,x38682),a904)))
% 22.40/22.29 [3915]P1(f319(f319(f225(a906),f39(a906,x39151,x39152)),x39151))
% 22.40/22.29 [3939]P1(f319(f319(f225(a1),f319(f73(a1),f319(f92(a1),x39391))),f319(f92(a1),x39392)))
% 22.40/22.29 [3963]P1(f319(f319(f321(f913(x39631,a904)),f181(f913(x39631,a904))),f319(f300(x39631),x39632)))
% 22.40/22.29 [3968]E(f299(x39681,f319(f319(f281(x39681,x39681,x39681),x39682),f299(x39681,x39682))),f299(x39681,x39682))
% 22.40/22.29 [3971]E(f319(f319(f281(x39711,x39711,x39711),f299(x39711,x39712)),x39712),f319(f319(f281(x39711,x39711,x39711),x39712),f299(x39711,x39712)))
% 22.40/22.29 [3973]E(f319(a97,f319(f319(f74(a1),f319(f319(f3(a1),x39731),x39732)),f72(a1))),f319(f29(a1),f295(a1,x39732,x39731)))
% 22.40/22.29 [3986]E(f319(f276(x39861,x39861),f319(f319(f281(x39861,x39861,x39861),x39862),f299(x39861,x39862))),f319(f276(x39861,x39861),x39862))
% 22.40/22.29 [3987]E(f319(f256(x39871,x39871),f319(f319(f281(x39871,x39871,x39871),x39872),f299(x39871,x39872))),f319(f256(x39871,x39871),x39872))
% 22.40/22.29 [4005]E(f319(f134(f907(x40051),f907(x40051),f126(x40051),f105(x40051)),f161(f907(x40051),x40052,f105(x40051))),f105(x40051))
% 22.40/22.29 [4014]P25(a906,a906,f319(f319(f9(a906,a906,a906),f74(a906)),x40141),x40142)
% 22.40/22.29 [4016]P13(a906,f319(f160(a906),f319(f319(f146(f907(x40161),a906),f182(f907(x40161))),f171(x40161,x40162))))
% 22.40/22.29 [4043]P53(x40431,f319(f319(f93(f913(f912(x40431,x40431),a904)),x40432),f319(f278(x40431,x40431),x40432)))
% 22.40/22.29 [4044]P53(x40441,f319(f319(f94(f913(f912(x40441,x40441),a904)),x40442),f319(f278(x40441,x40441),x40442)))
% 22.40/22.29 [4055]P1(f319(f319(f226(a1),f319(f73(a1),f319(f92(a1),f319(a104,x40551)))),f319(f92(a1),x40552)))
% 22.40/22.29 [4101]E(f319(f134(f907(x41011),x41011,f319(f9(x41011,f907(x41011),f907(x41011)),f143(x41011)),f105(x41011)),x41012),f319(f160(x41011),x41012))
% 22.40/22.29 [4149]P1(f319(f319(f225(f913(f912(f907(x41491),f907(x41491)),a904)),f150(x41491,x41492)),f299(f907(x41491),f149(x41491,x41492))))
% 22.40/22.29 [4177]P1(f319(f42(x41771,x41772),f319(f319(f244(a906,a906),f319(f319(f30(a906),x41771),x41772)),f39(a906,x41771,x41772))))
% 22.40/22.29 [4189]P1(f319(f319(f225(f913(f912(f907(x41891),f907(x41891)),a904)),f149(x41891,f299(x41891,x41892))),f299(f907(x41891),f149(x41891,x41892))))
% 22.40/22.29 [4404]E(f319(f319(f251(f912(a91,a91),a91,f912(a91,a91),f912(x44041,f912(a91,a91))),f259(f319(f157(a91),f319(f319(f146(f912(a91,x44041),a91),f243(a91,x44041)),x44042)))),f319(f319(f10(x44041,f913(f912(a91,a91),f912(x44041,f912(a91,a91))),a91),f244(x44041,f912(a91,a91))),f260(x44041,x44042))),f258(x44041,x44042))
% 22.40/22.29 [4480]E(f216(a906,f912(x44801,f908(x44801)),f2(a906),f319(f249(x44801,f908(x44801),a906),f319(f18(f913(f908(x44801),a906),x44801),f319(f319(f9(f908(x44801),a906,a906),f319(f319(f10(a906,f913(a906,a906),f908(x44801)),f74(a906)),f182(f908(x44801)))),f72(a906)))),f319(f127(x44801),x44802)),f319(f182(f908(x44801)),x44802))
% 22.40/22.29 [4600]E(f319(f249(f913(f912(x46001,x46001),a904),f913(f912(x46001,x46001),a904),f913(f913(x46002,x46001),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904)))),f319(f319(f9(f913(f912(x46001,x46001),a904),f913(f913(f912(x46001,x46001),a904),f913(f913(x46002,x46001),f913(f912(x46002,x46002),a904))),f913(f913(f912(x46001,x46001),a904),f913(f913(x46002,x46001),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904))))),f319(f319(f10(f913(f913(f913(x46002,x46001),f913(f912(x46002,x46002),a904)),f913(f913(x46002,x46001),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904)))),f913(f913(f913(f912(x46001,x46001),a904),f913(f913(x46002,x46001),f913(f912(x46002,x46002),a904))),f913(f913(f912(x46001,x46001),a904),f913(f913(x46002,x46001),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904))))),f913(f912(x46001,x46001),a904)),f10(f913(f913(x46002,x46001),f913(f912(x46002,x46002),a904)),f913(f913(x46002,x46001),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904))),f913(f912(x46001,x46001),a904))),f319(f319(f10(f913(f913(x46002,x46001),f913(f913(f912(x46002,x46002),a904),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904)))),f913(f913(f913(x46002,x46001),f913(f912(x46002,x46002),a904)),f913(f913(x46002,x46001),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904)))),f913(f912(x46001,x46001),a904)),f20(f913(x46002,x46001),f913(f912(x46002,x46002),a904),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904)))),f319(f319(f10(f913(f913(x46002,x46001),f913(f912(x46002,x46002),a904)),f913(f913(x46002,x46001),f913(f913(f912(x46002,x46002),a904),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904)))),f913(f912(x46001,x46001),a904)),f319(f10(f913(f912(x46002,x46002),a904),f913(f913(f912(x46002,x46002),a904),f912(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904))),f913(x46002,x46001)),f244(f913(f912(x46002,x46002),a904),f913(f912(x46002,x46002),a904)))),f280(x46001,x46002))))),f280(x46001,x46002))),f67(x46001,x46002))
% 22.40/22.29 [4644]~E(f319(f300(x46441),x46442),f181(f913(f913(x46441,a904),a904)))
% 22.40/22.29 [4653]~P1(f319(f319(f164(x46531),f105(x46531)),x46532))
% 22.40/22.29 [4657]~P1(f319(f319(f321(x46571),x46572),f181(f913(x46571,a904))))
% 22.40/22.29 [4663]~P1(f319(f319(f226(f913(x46631,a904)),x46632),f181(f913(x46631,a904))))
% 22.40/22.29 [3535]E(f319(f319(f3(a906),x35351),f319(f319(f74(a906),x35351),x35352)),f2(a906))
% 22.40/22.29 [3538]E(f319(f319(f93(f913(x35381,a904)),x35382),x35382),x35382)
% 22.40/22.29 [3539]E(f319(f319(f94(f913(x35391,a904)),x35392),x35392),x35392)
% 22.40/22.29 [3567]E(f319(f319(f3(f913(x35671,a904)),x35672),x35672),f181(f913(x35671,a904)))
% 22.40/22.29 [3570]E(f319(f135(x35701,x35702),f2(a906)),f181(f913(f912(f907(x35701),f907(x35701)),a904)))
% 22.40/22.29 [3571]E(f319(f319(f74(a906),x35711),f319(a104,x35712)),f319(a104,f319(f319(f74(a906),x35711),x35712)))
% 22.40/22.29 [3582]E(f187(f319(f92(a1),x35821),f319(f92(a1),x35822)),f319(f92(a1),f319(f319(f3(a906),x35821),x35822)))
% 22.40/22.29 [3585]E(f319(f319(f30(a1),f319(f73(a1),x35851)),x35852),f319(f319(f30(a1),x35851),f319(f73(a1),x35852)))
% 22.40/22.29 [3589]E(f319(f29(a1),f319(f294(a1,x35891),x35892)),f319(a97,f319(f319(f3(a1),x35892),x35891)))
% 22.40/22.29 [3592]E(f319(f319(f74(a906),f319(a104,x35921)),x35922),f319(a104,f319(f319(f74(a906),x35921),x35922)))
% 22.40/22.29 [3595]E(f319(f73(f913(x35951,a904)),f319(f73(f913(x35951,a904)),x35952)),x35952)
% 22.40/22.29 [3607]E(f171(x36071,f319(f319(f143(f907(x36071)),f105(x36071)),x36072)),f171(x36071,x36072))
% 22.40/22.29 [3611]E(f319(f319(f74(a906),x36111),f319(f319(f75(a906),x36111),x36112)),f319(f319(f75(a906),x36111),f319(a104,x36112)))
% 22.40/22.29 [3617]E(f319(f319(a4,f319(a5,x36171)),f319(a5,x36172)),f319(a5,f319(f319(f3(a906),x36171),x36172)))
% 22.40/22.29 [3632]E(f319(f319(f75(a1),f319(f73(a1),x36321)),x36322),f319(f73(a1),f319(f319(f75(a1),x36321),x36322)))
% 22.40/22.29 [3634]E(f319(f319(f236(a1),f319(f92(a1),x36341)),x36342),f319(f92(a1),f319(f319(f236(a906),x36341),x36342)))
% 22.40/22.29 [3635]E(f319(f319(f180(a906),f319(a104,x36351)),f319(a104,x36352)),f319(a104,f319(f319(f180(a906),x36351),x36352)))
% 22.40/22.29 [3636]E(f319(f319(f230(a906),f319(a104,x36361)),f319(a104,x36362)),f319(a104,f319(f319(f230(a906),x36361),x36362)))
% 22.40/22.29 [3637]E(f319(f319(f74(a91),f319(a5,x36371)),f319(a5,x36372)),f319(a5,f319(f319(f74(a906),x36371),x36372)))
% 22.40/22.29 [3638]E(f319(f319(f75(a91),f319(a5,x36381)),f319(a5,x36382)),f319(a5,f319(f319(f75(a906),x36381),x36382)))
% 22.40/22.29 [3643]E(f319(f164(a906),f131(a906,f319(f294(a906,x36431),x36432))),f319(f294(a906,x36431),x36432))
% 22.40/22.29 [3644]E(f304(x36441,f319(f319(f301(x36441),x36442),f181(f913(x36441,a904)))),x36442)
% 22.40/22.29 [3647]E(f319(f276(x36471,x36472),f181(f913(f912(x36471,x36472),a904))),f181(f913(x36472,a904)))
% 22.40/22.29 [3648]E(f319(f256(x36481,x36482),f181(f913(f912(x36481,x36482),a904))),f181(f913(x36481,a904)))
% 22.40/22.29 [3652]E(f319(a97,f319(f319(f3(a1),x36521),x36522)),f319(f29(a1),f297(a1,x36522,x36521)))
% 22.40/22.29 [3657]E(f319(f319(f74(a906),x36571),f319(f319(f75(a906),x36572),x36571)),f319(f319(f75(a906),f319(a104,x36572)),x36571))
% 22.40/22.29 [3659]E(f319(f319(f54(x36591),f181(f913(x36591,a904))),x36592),f181(f913(f913(x36591,a904),a904)))
% 22.40/22.29 [3668]E(f319(f182(f907(a906)),f131(a906,f319(f294(a906,x36681),x36682))),f319(f319(f3(a906),x36682),x36681))
% 22.40/22.29 [3683]E(f319(f319(f93(f913(x36831,a904)),f181(f913(x36831,a904))),x36832),x36832)
% 22.40/22.29 [3684]E(f319(f319(f94(f913(x36841,a904)),f234(f913(x36841,a904))),x36842),x36842)
% 22.40/22.29 [3685]E(f319(f319(f74(a1),f319(f73(a1),x36851)),f319(f73(a1),x36852)),f319(f73(a1),f319(f319(f74(a1),x36851),x36852)))
% 22.40/22.29 [3688]E(f319(f319(f74(a1),f319(f96(a1),x36881)),f319(f96(a1),x36882)),f319(f96(a1),f319(f319(f74(a1),x36881),x36882)))
% 22.40/22.29 [3690]E(f319(f319(f74(a1),f319(f92(a1),x36901)),f319(f92(a1),x36902)),f319(f92(a1),f319(f319(f74(a906),x36901),x36902)))
% 22.40/22.29 [3691]E(f319(f319(f75(a1),f319(f96(a1),x36911)),f319(f96(a1),x36912)),f319(f96(a1),f319(f319(f75(a1),x36911),x36912)))
% 22.40/22.29 [3693]E(f319(f319(f75(a1),f319(f92(a1),x36931)),f319(f92(a1),x36932)),f319(f92(a1),f319(f319(f75(a906),x36931),x36932)))
% 22.40/22.29 [3694]E(f319(f319(f30(a1),f319(f92(a1),x36941)),f319(f92(a1),x36942)),f319(f92(a1),f319(f319(f30(a906),x36941),x36942)))
% 22.40/22.29 [3714]E(f319(f319(f8(x37141,a906),f319(f18(a906,x37141),f72(a906))),x37142),f319(f29(x37141),x37142))
% 22.40/22.29 [3719]E(f319(f73(a1),f39(a1,f319(f73(a1),x37191),x37192)),f39(a1,x37191,f319(f73(a1),x37192)))
% 22.40/22.29 [3721]E(f319(f164(a1),f170(x37211,f319(f319(f3(a1),x37212),f72(a1)))),f319(f294(a1,x37211),x37212))
% 22.40/22.29 [3725]P1(f319(f319(f225(a906),x37251),f319(f319(f74(a906),x37252),x37251)))
% 22.40/22.29 [3726]P1(f319(f319(f225(a906),x37261),f319(f319(f74(a906),x37261),x37262)))
% 22.40/22.29 [3729]E(f319(f319(f93(f913(x37291,a904)),f234(f913(x37291,a904))),x37292),f234(f913(x37291,a904)))
% 22.40/22.29 [3730]E(f319(f319(f94(f913(x37301,a904)),f181(f913(x37301,a904))),x37302),f181(f913(x37301,a904)))
% 22.40/22.29 [3731]E(f319(f319(f3(f913(x37311,a904)),f181(f913(x37311,a904))),x37312),f181(f913(x37311,a904)))
% 22.40/22.29 [3738]E(f319(f319(f244(a1,a1),x37381),f319(f73(a1),x37382)),f319(a45,f319(f319(f244(a1,a1),x37381),x37382)))
% 22.40/22.29 [3739]E(f319(f294(a1,f319(f319(f74(a1),x37391),f72(a1))),x37392),f298(a1,x37391,x37392))
% 22.40/22.29 [3751]E(f319(f319(f75(a906),x37511),f319(f319(f30(a906),x37512),x37511)),f319(f319(f3(a906),x37512),f39(a906,x37512,x37511)))
% 22.40/22.29 [3752]E(f319(f319(f75(a1),x37521),f319(f319(f30(a1),x37522),x37521)),f319(f319(f3(a1),x37522),f39(a1,x37522,x37521)))
% 22.40/22.29 [3755]E(f319(f164(a1),f170(f319(f319(f74(a1),x37551),f72(a1)),x37552)),f297(a1,x37551,x37552))
% 22.40/22.29 [3759]P1(f319(f319(f225(f913(x37591,a904)),x37592),x37592))
% 22.40/22.29 [3762]E(f319(f319(f93(f913(x37621,a904)),x37622),f319(f73(f913(x37621,a904)),x37622)),f234(f913(x37621,a904)))
% 22.40/22.29 [3763]E(f319(f319(f94(f913(x37631,a904)),x37632),f319(f73(f913(x37631,a904)),x37632)),f181(f913(x37631,a904)))
% 22.40/22.29 [3771]E(f319(f319(f3(a906),f319(f319(f3(a906),x37711),f72(a906))),x37712),f319(f319(f3(a906),x37711),f319(a104,x37712)))
% 22.40/22.29 [3777]E(f319(f319(f3(f913(x37771,a904)),f234(f913(x37771,a904))),x37772),f319(f73(f913(x37771,a904)),x37772))
% 22.40/22.29 [3778]E(f319(f319(f3(a1),f319(f96(a1),x37781)),f319(f96(a1),x37782)),f319(f96(a1),f319(f319(f74(a1),x37781),f319(f73(a1),x37782))))
% 22.40/22.29 [3791]E(f319(f164(a906),f131(a906,f319(f294(a906,x37911),f319(a104,x37912)))),f295(a906,x37911,x37912))
% 22.40/22.29 [3807]E(f319(f182(f907(f907(x38071))),f48(x38071,x38072)),f319(f319(f236(a906),f319(a104,f319(a104,f2(a906)))),f319(f182(f907(x38071)),x38072)))
% 22.40/22.29 [3825]E(f319(f319(f175(f912(x38251,x38251),a904),f2(a906)),x38252),f299(x38251,f181(f913(f912(x38251,x38251),a904))))
% 22.40/22.29 [3829]P1(f319(f129(a906),f131(a906,f319(f294(a906,x38291),x38292))))
% 22.40/22.29 [3845]E(f319(f302(a1,a906,a97),f295(a1,f319(f92(a1),x38451),f319(f92(a1),x38452))),f295(a906,x38451,x38452))
% 22.40/22.29 [3854]E(f177(a906,f2(a906),f7(a906),f319(f319(f3(a906),x38541),x38542)),f319(f319(f3(a906),x38541),f319(a104,x38542)))
% 22.40/22.29 [3855]E(f319(a97,f319(f319(f3(a1),x38551),f319(f319(f74(a1),x38552),f72(a1)))),f319(f29(a1),f298(a1,x38552,x38551)))
% 22.40/22.29 [3884]E(f319(f319(f146(a906,a906),a104),f131(a906,f319(f294(a906,x38841),x38842))),f131(a906,f319(f294(a906,f319(a104,x38841)),f319(a104,x38842))))
% 22.40/22.29 [3891]E(f319(f164(a1),f170(f319(f319(f74(a1),x38911),f72(a1)),f319(f319(f3(a1),x38912),f72(a1)))),f298(a1,x38911,x38912))
% 22.40/22.29 [3903]P1(f319(f319(f225(f913(x39031,a904)),f181(f913(x39031,a904))),x39032))
% 22.40/22.29 [3907]E(f79(x39071,f319(f319(f9(x39071,x39071,a904),a316),x39072)),x39072)
% 22.40/22.29 [3908]E(f84(x39081,f319(f319(f9(x39081,x39081,a904),a316),x39082)),x39082)
% 22.40/22.29 [3916]E(f319(f164(a906),f131(a906,f319(f294(a906,f319(a104,x39161)),f319(a104,x39162)))),f297(a906,x39161,x39162))
% 22.40/22.29 [3942]E(f319(f319(f246(x39421,x39422),f234(f913(x39421,a904))),f319(f18(f913(x39422,a904),x39421),f234(f913(x39422,a904)))),f234(f913(f912(x39421,x39422),a904)))
% 22.40/22.29 [3975]E(f319(f254(x39751),f319(f319(f10(a904,a904,x39751),a314),x39752)),f319(f73(f913(x39751,a904)),f319(f254(x39751),x39752)))
% 22.40/22.29 [3978]E(f319(f254(x39781),f319(f319(f9(x39781,x39781,a904),a316),x39782)),f319(f319(f301(x39781),x39782),f181(f913(x39781,a904))))
% 22.40/22.29 [4000]P1(f319(f319(f225(a906),f319(f29(x40001),f319(f164(x40001),x40002))),f319(f182(f907(x40001)),x40002)))
% 22.40/22.29 [4001]P1(f319(f319(f225(a906),f319(f182(f907(x40011)),f144(x40011,x40012))),f319(f182(f907(x40011)),x40012)))
% 22.40/22.29 [4011]E(f319(f254(x40111),f319(f319(f9(x40111,f913(x40111,a904),a904),f321(x40111)),x40112)),x40112)
% 22.40/22.29 [4024]E(f319(f319(f167(x40241),f319(f319(f3(a906),f319(f182(f907(x40241)),x40242)),f72(a906))),x40242),f106(x40241,x40242))
% 22.40/22.29 [4042]E(f177(a906,f2(a906),f319(f319(f10(a906,a906,a906),a104),f319(f230(a906),x40421)),x40422),f319(f319(f230(a906),f319(a104,x40421)),x40422))
% 22.40/22.29 [4047]E(f31(f913(x40471,a904),f319(f302(f913(f912(x40471,x40471),a904),f913(x40471,a904),f273(x40471)),x40472)),f319(f273(x40471),f31(f913(f912(x40471,x40471),a904),x40472)))
% 22.40/22.29 [4048]E(f177(a906,f319(a104,x40481),f319(f319(f10(a906,a906,a906),a104),f319(f180(a906),x40481)),x40482),f319(f319(f180(a906),f319(a104,x40481)),x40482))
% 22.40/22.29 [4050]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),f319(f69(a1),x40501)),f319(f69(a1),x40502))),f39(a1,f319(f69(a1),x40501),f319(f69(a1),x40502))),f47(x40501,x40502))
% 22.40/22.29 [4073]P1(f319(f319(f225(f913(f913(x40731,a904),a904)),x40732),f319(f300(x40731),f31(f913(x40731,a904),x40732))))
% 22.40/22.29 [4106]E(f319(f319(f33(x41061,f913(x41061,a904)),x41062),f319(f319(f9(x41061,f913(x41061,a904),f913(x41061,a904)),f301(x41061)),f181(f913(x41061,a904)))),x41062)
% 22.40/22.29 [4107]E(f319(f319(f281(x41071,x41071,x41071),f319(f278(x41071,x41071),x41072)),f299(x41071,f319(f278(x41071,x41071),x41072))),f319(f278(x41071,x41071),f319(f319(f281(x41071,x41071,x41071),x41072),f299(x41071,x41072))))
% 22.40/22.29 [4170]E(f319(f164(x41701),f319(f134(f907(x41701),f907(x41701),f126(x41701),f105(x41701)),x41702)),f319(f319(f33(f907(x41701),f913(x41701,a904)),f319(f164(f907(x41701)),x41702)),f164(x41701)))
% 22.40/22.29 [4200]E(f319(f319(f93(f913(f912(x42001,x42001),a904)),f299(x42001,f181(f913(f912(x42001,x42001),a904)))),f319(f319(f281(x42001,x42001,x42001),f299(x42001,x42002)),x42002)),f299(x42001,x42002))
% 22.40/22.29 [4235]E(f319(f319(f173(x42351,x42351),x42352),x42352),f319(f319(f146(x42351,f912(x42351,x42351)),f319(f319(f20(x42351,x42351,f912(x42351,x42351)),f244(x42351,x42351)),f7(x42351))),x42352))
% 22.40/22.29 [4343]E(f319(f134(a906,f907(x43431),f319(f9(f907(x43431),a906,a906),f319(f319(f10(a906,f913(a906,a906),f907(x43431)),f180(a906)),f182(f907(x43431)))),f2(a906)),f319(f160(f907(x43431)),x43432)),f319(f182(f907(f907(x43431))),f171(x43431,x43432)))
% 22.40/22.29 [4417]E(f319(f319(f280(f912(a906,f907(x44171)),f907(x44171)),f312(a906,f907(x44171),a232,f137(x44171,x44172))),f319(f319(f20(f907(x44171),f907(x44171),f912(a906,f907(x44171))),f319(f319(f10(a906,f913(f907(x44171),f912(a906,f907(x44171))),f907(x44171)),f244(a906,f907(x44171))),f182(f907(x44171)))),f7(f907(x44171)))),f138(x44171,x44172))
% 22.40/22.29 [4555]E(f319(f254(x45551),f319(f319(f10(f913(f913(x45551,a904),a904),a904,x45551),f81(f913(x45551,a904))),f319(f319(f10(f913(f913(x45551,a904),a904),f913(f913(x45551,a904),a904),x45551),f319(f20(f913(x45551,a904),a904,a904),f319(f319(f10(a904,f913(a904,a904),f913(x45551,a904)),a322),f319(f319(f9(f913(x45551,a904),f913(f913(x45551,a904),a904),a904),f321(f913(x45551,a904))),x45552)))),f321(x45551)))),f32(f913(x45551,a904),x45552))
% 22.40/22.29 [4556]E(f319(f254(x45561),f319(f319(f10(f913(f913(x45561,a904),a904),a904,x45561),f80(f913(x45561,a904))),f319(f319(f10(f913(f913(x45561,a904),a904),f913(f913(x45561,a904),a904),x45561),f319(f20(f913(x45561,a904),a904,a904),f319(f319(f10(a904,f913(a904,a904),f913(x45561,a904)),a317),f319(f319(f9(f913(x45561,a904),f913(f913(x45561,a904),a904),a904),f321(f913(x45561,a904))),x45562)))),f321(x45561)))),f31(f913(x45561,a904),x45562))
% 22.40/22.29 [4664]~P1(f319(f319(f226(a1),f319(f92(a1),x46641)),f319(f73(a1),f319(f92(a1),x46642))))
% 22.40/22.29 [3655]E(f319(f319(f3(a906),f319(f319(f74(a906),x36551),x36552)),x36552),x36551)
% 22.40/22.29 [3656]E(f319(f319(f3(a906),f319(f319(f74(a906),x36561),x36562)),x36561),x36562)
% 22.40/22.29 [3720]E(f319(f319(f74(a906),f319(f319(f3(a906),x37201),x37202)),x37202),f319(f319(f180(a906),x37201),x37202))
% 22.40/22.29 [3832]E(f319(f319(f75(a906),f319(f319(f30(a906),x38321),x38322)),x38322),f319(f319(f3(a906),x38321),f39(a906,x38321,x38322)))
% 22.40/22.29 [3859]E(f319(f164(a906),f131(a906,f319(f294(a906,f319(a104,x38591)),x38592))),f298(a906,x38591,x38592))
% 22.40/22.29 [3867]E(f319(f92(a1),f209(f319(a97,f319(f69(a1),x38671)),f319(a97,f319(f69(a1),x38672)))),f319(f319(a210,x38671),x38672))
% 22.40/22.29 [3869]E(f319(f319(f93(f913(x38691,a904)),f319(f73(f913(x38691,a904)),x38692)),x38692),f234(f913(x38691,a904)))
% 22.40/22.29 [3870]E(f319(f319(f94(f913(x38701,a904)),f319(f73(f913(x38701,a904)),x38702)),x38702),f181(f913(x38701,a904)))
% 22.40/22.29 [3880]P1(f319(f319(f225(a906),f319(f319(f3(a906),x38801),x38802)),x38801))
% 22.40/22.29 [3881]P1(f319(f319(f225(a906),f319(f319(f30(a906),x38811),x38812)),x38811))
% 22.40/22.29 [3904]P1(f319(f319(f226(a906),x39041),f319(a104,f319(f319(f74(a906),x39042),x39041))))
% 22.40/22.29 [3905]P1(f319(f319(f226(a906),x39051),f319(a104,f319(f319(f74(a906),x39051),x39052))))
% 22.40/22.29 [3927]E(f319(f319(f75(a906),f319(a97,f319(f69(a1),x39271))),f319(a97,f319(f69(a1),x39272))),f319(a97,f319(f69(a1),f319(f319(f75(a1),x39271),x39272))))
% 22.40/22.29 [3938]P1(f319(f319(f225(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x39381)),x39382)))
% 22.40/22.29 [4004]E(f319(f277(f907(x40041),f907(x40041),f150(x40041,x40042)),f319(f319(f301(f907(x40041)),f105(x40041)),f181(f913(f907(x40041),a904)))),f319(f319(f301(f907(x40041)),f105(x40041)),f181(f913(f907(x40041),a904))))
% 22.40/22.29 [4022]E(f319(f319(f93(f913(f912(x40221,x40221),a904)),f299(x40221,x40222)),f299(x40221,f181(f913(f912(x40221,x40221),a904)))),f299(x40221,x40222))
% 22.40/22.29 [4102]E(f319(f254(f913(x41021,a904)),f319(f319(f9(f913(x41021,a904),f913(x41021,a904),a904),f225(f913(x41021,a904))),x41022)),f319(f300(x41021),x41022))
% 22.40/22.29 [4119]E(f319(f319(f146(a1,a906),a97),f319(f319(f126(a1),f319(f319(f146(a906,a1),f92(a1)),x41191)),f319(f319(f146(a906,a1),f92(a1)),x41192))),f319(f319(f126(a906),x41191),x41192))
% 22.40/22.29 [4148]E(f319(f302(a1,a1,f319(f319(f9(a1,a1,a1),f74(a1)),x41481)),f319(f294(a1,f2(a1)),f319(f319(f3(a1),x41482),x41481))),f319(f294(a1,x41481),x41482))
% 22.40/22.29 [4150]P55(x41501,f319(f319(f3(f913(f912(x41501,x41501),a904)),x41502),f299(x41501,f181(f913(f912(x41501,x41501),a904)))))
% 22.40/22.29 [4168]E(f319(f182(f907(x41681)),f319(f134(f907(x41681),f907(x41681),f126(x41681),f105(x41681)),x41682)),f319(f157(a906),f319(f319(f146(f907(x41681),a906),f182(f907(x41681))),x41682)))
% 22.40/22.29 [4172]P54(x41721,f234(f913(x41721,a904)),f319(f319(f93(f913(f912(x41721,x41721),a904)),x41722),f299(x41721,f181(f913(f912(x41721,x41721),a904)))))
% 22.40/22.29 [4214]E(f177(a906,f2(a906),f319(f319(f10(a906,a906,a906),a104),f319(f319(f9(a906,a906,a906),f230(a906)),x42141)),x42142),f319(f319(f230(a906),x42142),f319(a104,x42141)))
% 22.40/22.29 [4217]E(f177(a906,f319(a104,x42171),f319(f319(f10(a906,a906,a906),a104),f319(f319(f9(a906,a906,a906),f180(a906)),x42171)),x42172),f319(f319(f180(a906),x42172),f319(a104,x42171)))
% 22.40/22.29 [4220]E(f319(f302(x42201,f907(x42201),f319(f319(f9(x42201,f907(x42201),f907(x42201)),f143(x42201)),f105(x42201))),x42202),f166(x42201,x42202,f319(f319(f301(f907(x42201)),f105(x42201)),f181(f913(f907(x42201),a904)))))
% 22.40/22.29 [4222]E(f319(f319(f93(f913(f912(x42221,x42221),a904)),f319(f319(f281(x42221,x42221,x42221),x42222),f299(x42221,x42222))),f299(x42221,f181(f913(f912(x42221,x42221),a904)))),f299(x42221,x42222))
% 22.40/22.29 [4230]P1(f319(f319(f225(f913(f912(x42301,x42301),a904)),f255(x42301,x42302)),f319(f319(f246(x42301,x42301),x42302),f319(f18(f913(x42301,a904),x42301),x42302))))
% 22.40/22.29 [4233]E(f319(f302(a1,a906,a97),f319(f319(f93(f913(a1,a904)),f319(f302(a906,a1,f92(a1)),x42331)),f319(f302(a906,a1,f92(a1)),x42332))),f319(f319(f93(f913(a906,a904)),x42331),x42332))
% 22.40/22.29 [4234]E(f319(f302(a1,a906,a97),f319(f319(f94(f913(a1,a904)),f319(f302(a906,a1,f92(a1)),x42341)),f319(f302(a906,a1,f92(a1)),x42342))),f319(f319(f94(f913(a906,a904)),x42341),x42342))
% 22.40/22.29 [4237]E(f319(f254(x42371),f319(f319(f10(a904,a904,x42371),a314),f319(f319(f9(x42371,f913(x42371,a904),a904),f321(x42371)),x42372))),f319(f73(f913(x42371,a904)),x42372))
% 22.40/22.29 [4263]E(f319(f134(f907(x42631),f907(x42631),f126(x42631),f105(x42631)),f319(f319(f146(f907(x42631),f907(x42631)),f160(x42631)),f319(f160(f907(x42631)),x42632))),f319(f160(x42631),f319(f134(f907(x42631),f907(x42631),f126(x42631),f105(x42631)),x42632)))
% 22.40/22.29 [4285]E(f319(f319(f33(a906,f913(f912(x42851,x42851),a904)),f234(f913(a906,a904))),f319(f319(f9(a906,f913(f912(x42851,x42851),a904),f913(f912(x42851,x42851),a904)),f175(f912(x42851,x42851),a904)),x42852)),f299(x42851,x42852))
% 22.40/22.29 [4300]E(f79(x43001,f319(f319(f10(f913(x43001,a904),a904,x43001),f319(a316,x43002)),f319(f319(f9(x43001,f913(x43001,a904),f913(x43001,a904)),f301(x43001)),f181(f913(x43001,a904))))),f304(x43001,x43002))
% 22.40/22.29 [4309]E(f319(f182(f907(x43091)),f144(x43091,f319(f134(f907(x43091),f907(x43091),f126(x43091),f105(x43091)),x43092))),f319(f29(x43091),f319(f319(f33(f907(x43091),f913(x43091,a904)),f319(f164(f907(x43091)),x43092)),f164(x43091))))
% 22.40/22.29 [4323]E(f319(f319(f93(f913(f912(x43231,x43231),a904)),x43232),f319(f319(f281(x43231,x43231,x43231),f319(f319(f281(x43231,x43231,x43231),x43232),f299(x43231,x43232))),x43232)),f319(f319(f281(x43231,x43231,x43231),x43232),f299(x43231,x43232)))
% 22.40/22.29 [4353]P1(f319(f319(f225(f913(f912(x43531,x43531),a904)),f319(f319(f281(x43531,x43531,x43531),x43532),f299(x43531,x43532))),f319(f319(f246(x43531,x43531),f319(f273(x43531),x43532)),f319(f18(f913(x43531,a904),x43531),f319(f273(x43531),x43532)))))
% 22.40/22.29 [4393]E(f319(f254(f907(x43931)),f319(f319(f9(f907(x43931),f913(x43931,a904),a904),f319(f319(f10(f913(x43931,a904),f913(f913(x43931,a904),a904),f907(x43931)),f225(f913(x43931,a904))),f164(x43931))),x43932)),f153(x43931,x43932))
% 22.40/22.29 [4406]E(f319(f148(f907(x44061),x44061,f105(x44061),f319(f319(f10(f907(x44061),f913(f907(x44061),f907(x44061)),x44061),f319(f9(f907(x44061),f907(x44061),f907(x44061)),f126(x44061))),f319(f319(f9(x44061,f907(x44061),f907(x44061)),f143(x44061)),f105(x44061)))),x44062),f319(f159(x44061),x44062))
% 22.40/22.29 [4443]P25(f913(x44431,x44432),f913(f912(x44431,x44432),a904),f319(f319(f10(f913(f912(x44431,x44432),a904),f913(f912(x44431,x44432),a904),f913(x44431,x44432)),f254(f912(x44431,x44432))),f319(f319(f10(f913(x44431,f913(x44432,a904)),f913(f912(x44431,x44432),a904),f913(x44431,x44432)),f249(x44431,x44432,a904)),f319(f10(x44432,f913(x44432,a904),x44431),f319(f9(x44432,x44432,a904),a316)))),f234(f913(f913(x44431,x44432),a904)))
% 22.40/22.29 [4499]E(f319(f319(f33(x44991,f913(f912(x44991,x44991),a904)),x44992),f319(f319(f9(x44991,f913(f912(x44991,x44991),a904),f913(f912(x44991,x44991),a904)),f319(f319(f10(f912(x44991,x44991),f913(f913(f912(x44991,x44991),a904),f913(f912(x44991,x44991),a904)),x44991),f301(f912(x44991,x44991))),f319(f319(f20(x44991,x44991,f912(x44991,x44991)),f244(x44991,x44991)),f7(x44991)))),f181(f913(f912(x44991,x44991),a904)))),f255(x44991,x44992))
% 22.40/22.29 [4507]E(f195(x45071,f319(f319(f244(a1,a1),f319(f73(a1),f319(f319(f66(f912(a1,a1),a1,x45071,f243(a1,a1)),f205(x45071)),x45072))),f319(f319(f66(f912(a1,a1),a1,x45071,f248(a1,a1)),f205(x45071)),x45072))),f220(x45071,x45072))
% 22.40/22.29 [4597]E(f319(f254(f913(x45971,a904)),f319(f319(f10(f913(f913(x45971,a904),a904),a904,f913(x45971,a904)),f80(f913(x45971,a904))),f319(f319(f9(f913(x45971,a904),f913(f913(x45971,a904),a904),f913(f913(x45971,a904),a904)),f319(f319(f10(f913(f913(x45971,a904),f913(a904,a904)),f913(f913(f913(x45971,a904),a904),f913(f913(x45971,a904),a904)),f913(x45971,a904)),f20(f913(x45971,a904),a904,a904)),f319(f319(f10(f913(f913(x45971,a904),a904),f913(f913(x45971,a904),f913(a904,a904)),f913(x45971,a904)),f319(f10(a904,f913(a904,a904),f913(x45971,a904)),a317)),f319(f319(f9(f913(x45971,a904),f913(f913(x45971,a904),f913(x45971,a904)),f913(f913(x45971,a904),a904)),f319(f319(f10(f913(f913(x45971,a904),a904),f913(f913(f913(x45971,a904),f913(x45971,a904)),f913(f913(x45971,a904),a904)),f913(x45971,a904)),f10(f913(x45971,a904),a904,f913(x45971,a904))),a316)),f73(f913(x45971,a904)))))),f319(f319(f10(f913(f913(x45971,a904),a904),a904,f913(x45971,a904)),f319(f321(f913(x45971,a904)),x45972)),f300(x45971))))),f319(f300(x45971),f319(f73(f913(x45971,a904)),x45972)))
% 22.40/22.29 [4666]~P1(f319(f319(f226(a906),f319(f319(f74(a906),x46661),x46662)),x46662))
% 22.40/22.29 [4667]~P1(f319(f319(f226(a906),f319(f319(f74(a906),x46671),x46672)),x46671))
% 22.40/22.29 [3943]E(f319(f319(f3(a906),x39431),f319(f319(f75(a906),f319(f319(f30(a906),x39431),x39432)),x39432)),f39(a906,x39431,x39432))
% 22.40/22.29 [3944]E(f319(f319(f3(a1),x39441),f319(f319(f75(a1),f319(f319(f30(a1),x39441),x39442)),x39442)),f39(a1,x39441,x39442))
% 22.40/22.29 [3976]E(f319(f319(f146(a906,x39761),f319(f156(x39761),x39762)),f131(a906,f319(f294(a906,f2(a906)),f319(f182(f907(x39761)),x39762)))),x39762)
% 22.40/22.29 [4029]E(f319(f277(x40291,x40291,f299(x40291,f181(f913(f912(x40291,x40291),a904)))),x40292),x40292)
% 22.40/22.29 [4153]E(f299(x41531,f319(f319(f93(f913(f912(x41531,x41531),a904)),x41532),f299(x41531,f181(f913(f912(x41531,x41531),a904))))),f299(x41531,x41532))
% 22.40/22.29 [4154]E(f299(x41541,f319(f319(f3(f913(f912(x41541,x41541),a904)),x41542),f299(x41541,f181(f913(f912(x41541,x41541),a904))))),f299(x41541,x41542))
% 22.40/22.29 [4320]E(f319(f92(a1),f319(f319(f30(a906),f319(f319(f75(a906),f319(a97,f319(f69(a1),x43201))),f319(a97,f319(f69(a1),x43202)))),f209(f319(a97,f319(f69(a1),x43201)),f319(a97,f319(f69(a1),x43202))))),f211(x43201,x43202))
% 22.40/22.29 [4345]E(f319(f319(f3(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43451)),x43451)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43452)),x43452)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f3(a1),x43451),x43452))),f319(f319(f3(a1),x43451),x43452))),a89))
% 22.40/22.29 [4368]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43681)),x43681)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43682)),x43682)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),x43681),x43682))),f319(f319(f74(a1),x43681),x43682)))
% 22.40/22.29 [4371]E(f319(f319(f251(f912(a91,a91),a91,f912(a91,a91),f912(x43711,f912(a91,a91))),f259(f319(a5,f319(f182(f907(x43711)),x43712)))),f319(f319(f10(x43711,f913(f912(a91,a91),f912(x43711,f912(a91,a91))),a91),f244(x43711,f912(a91,a91))),f319(f319(f10(a906,x43711,a91),f319(f156(x43711),x43712)),a22))),f267(x43711,x43712))
% 22.40/22.29 [4399]E(f319(f319(f3(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43991)),x43991)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43992)),x43992)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f3(a1),f319(f319(f74(a1),x43991),a89)),x43992))),f319(f319(f3(a1),f319(f319(f74(a1),x43991),a89)),x43992)))
% 22.40/22.29 [4448]E(f319(f134(a906,f907(x44481),f319(f9(f907(x44481),a906,a906),f319(f319(f10(a906,f913(a906,a906),f907(x44481)),f180(a906)),f182(f907(x44481)))),f2(a906)),f319(f160(f907(x44481)),f171(x44481,x44482))),f319(f182(f907(f907(x44481))),f319(f128(f907(x44481),f319(f319(f10(a904,a904,f907(x44481)),a314),f319(f319(f9(f907(x44481),f907(x44481),a904),a316),f105(x44481)))),x44482)))
% 22.40/22.29 [4454]E(f319(f319(f33(a906,f913(x44541,a904)),f234(f913(a906,a904))),f319(f319(f9(a906,f913(a906,f913(x44541,a904)),f913(x44541,a904)),f319(f319(f10(f913(a906,a904),f913(f913(a906,f913(x44541,a904)),f913(x44541,a904)),a906),f33(a906,f913(x44541,a904))),f294(a906,f2(a906)))),x44542)),f319(f319(f33(a906,f913(x44541,a904)),f234(f913(a906,a904))),x44542))
% 22.40/22.29 [4477]P1(f319(f55(a906),f319(f254(a906),f319(f319(f20(a906,a904,a904),f319(f319(f10(a904,f913(a904,a904),a906),a317),x44771)),f319(f319(f9(a906,a906,a904),f226(a906)),x44772)))))
% 22.40/22.29 [4604]E(f319(f254(f912(f907(x46041),f907(x46041))),f319(f249(f907(x46041),f907(x46041),a904),f319(f319(f20(f907(x46041),f913(f907(x46041),a904),f913(f907(x46041),a904)),f319(f319(f10(f913(f907(x46041),f913(a904,a904)),f913(f913(f907(x46041),a904),f913(f907(x46041),a904)),f907(x46041)),f20(f907(x46041),a904,a904)),f319(f319(f10(f913(f907(x46041),a904),f913(f907(x46041),f913(a904,a904)),f907(x46041)),f319(f10(a904,f913(a904,a904),f907(x46041)),a318)),f319(f319(f9(f907(x46041),f913(f907(x46041),a906),f913(f907(x46041),a904)),f319(f319(f10(f913(a906,a904),f913(f913(f907(x46041),a906),f913(f907(x46041),a904)),f907(x46041)),f10(a906,a904,f907(x46041))),f319(f319(f10(a906,f913(a906,a904),f907(x46041)),f226(a906)),f182(f907(x46041))))),f182(f907(x46041)))))),f319(f319(f20(f907(x46041),f913(f907(x46041),a904),f913(f907(x46041),a904)),f319(f319(f10(f913(f907(x46041),f913(a904,a904)),f913(f913(f907(x46041),a904),f913(f907(x46041),a904)),f907(x46041)),f20(f907(x46041),a904,a904)),f319(f319(f10(f913(f907(x46041),a904),f913(f907(x46041),f913(a904,a904)),f907(x46041)),f319(f10(a904,f913(a904,a904),f907(x46041)),a317)),f319(f319(f9(f907(x46041),f913(f907(x46041),a906),f913(f907(x46041),a904)),f319(f319(f10(f913(a906,a904),f913(f913(f907(x46041),a906),f913(f907(x46041),a904)),f907(x46041)),f10(a906,a904,f907(x46041))),f319(f319(f10(a906,f913(a906,a904),f907(x46041)),a316),f182(f907(x46041))))),f182(f907(x46041)))))),f319(f319(f9(f907(x46041),f913(f912(f907(x46041),f907(x46041)),a904),f913(f907(x46041),a904)),f319(f319(f10(f913(f907(x46041),f913(f913(f912(f907(x46041),f907(x46041)),a904),a904)),f913(f913(f912(f907(x46041),f907(x46041)),a904),f913(f907(x46041),a904)),f907(x46041)),f9(f907(x46041),f913(f912(f907(x46041),f907(x46041)),a904),a904)),f319(f319(f10(f913(f907(x46041),f912(f907(x46041),f907(x46041))),f913(f907(x46041),f913(f913(f912(f907(x46041),f907(x46041)),a904),a904)),f907(x46041)),f319(f10(f912(f907(x46041),f907(x46041)),f913(f913(f912(f907(x46041),f907(x46041)),a904),a904),f907(x46041)),f321(f912(f907(x46041),f907(x46041))))),f244(f907(x46041),f907(x46041))))),f137(x46041,x46042)))))),f138(x46041,x46042))
% 22.40/22.29 [4370]E(f319(a97,f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x43701),x43702)),f181(f913(f912(a906,a906),a904)))))),f319(f319(f3(a906),x43701),x43702))
% 22.40/22.29 [4374]E(f319(f319(f281(x43741,x43741,x43741),f319(f319(f93(f913(f912(x43741,x43741),a904)),x43742),f299(x43741,f181(f913(f912(x43741,x43741),a904))))),f299(x43741,f319(f319(f93(f913(f912(x43741,x43741),a904)),x43742),f299(x43741,f181(f913(f912(x43741,x43741),a904)))))),f299(x43741,x43742))
% 22.40/22.29 [4410]E(f260(x44101,f319(f128(f912(a91,x44101),f319(f249(a91,x44101,a904),f319(f319(f10(a904,f913(x44101,a904),a91),f18(a904,x44101)),f319(f226(a91),f2(a91))))),x44102)),f260(x44101,x44102))
% 22.40/22.29 [4411]E(f258(x44111,f319(f128(f912(a91,x44111),f319(f249(a91,x44111,a904),f319(f319(f10(a904,f913(x44111,a904),a91),f18(a904,x44111)),f319(f226(a91),f2(a91))))),x44112)),f258(x44111,x44112))
% 22.40/22.29 [4412]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),x44121),f319(f319(f3(a1),x44122),a89)))),f319(f319(f74(a1),x44121),f319(f319(f3(a1),x44122),a89)))),a89),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x44121)),x44121)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x44122)),x44122)))
% 22.40/22.29 [4414]E(f319(f73(a1),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x44141),x44142)),f181(f913(f912(a906,a906),a904)))))),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x44142),x44141)),f181(f913(f912(a906,a906),a904))))))
% 22.40/22.29 [4469]E(f319(f319(f280(f907(a906),x44691),f137(a906,a232)),f319(f319(f9(x44691,f907(f913(x44691,a906)),f907(a906)),f319(f319(f10(f913(f913(x44691,a906),a906),f913(f907(f913(x44691,a906)),f907(a906)),x44691),f146(f913(x44691,a906),a906)),f319(f9(f913(x44691,a906),x44691,a906),f7(f913(x44691,a906))))),x44692)),f145(x44691,x44692))
% 22.40/22.29 [4496]E(f319(f319(f82(a1,a906),f319(f96(a1),f319(f319(f74(a1),x44961),a89))),f319(f319(f20(a1,a906,a906),f319(f319(f9(a1,a906,f913(a906,a906)),f319(f319(f10(a904,f913(a906,f913(a906,a906)),a1),f86(a906)),a186)),f2(a906))),f319(f319(f10(a906,a906,a1),a104),f319(f319(f10(a906,a906,a1),f319(f230(a906),x44962)),a97)))),f319(f319(f230(a906),f319(a104,x44962)),f319(f96(a906),x44961)))
% 22.40/22.29 [4497]E(f319(f319(f82(a1,a906),f319(f96(a1),f319(f319(f74(a1),x44971),a89))),f319(f319(f20(a1,a906,a906),f319(f319(f9(a1,a906,f913(a906,a906)),f319(f319(f10(a904,f913(a906,f913(a906,a906)),a1),f86(a906)),a186)),f319(a104,x44972))),f319(f319(f10(a906,a906,a1),a104),f319(f319(f10(a906,a906,a1),f319(f180(a906),x44972)),a97)))),f319(f319(f180(a906),f319(a104,x44972)),f319(f96(a906),x44971)))
% 22.40/22.29 [4517]E(f319(f134(f907(x45171),f907(x45171),f126(x45171),f105(x45171)),f319(f319(f146(f907(x45171),f907(x45171)),f148(f907(x45171),x45171,f105(x45171),f319(f319(f10(f907(x45171),f913(f907(x45171),f907(x45171)),x45171),f18(f907(x45171),f907(x45171))),f319(f319(f9(x45171,f907(x45171),f907(x45171)),f143(x45171)),f105(x45171))))),x45172)),f319(f319(f146(f907(x45171),x45171),f133(x45171)),f319(f128(f907(x45171),f319(f319(f10(a904,a904,f907(x45171)),a314),f319(f319(f9(f907(x45171),f907(x45171),a904),a316),f105(x45171)))),x45172)))
% 22.40/22.29 [4588]E(f319(f249(a1,a1,a904),f319(f319(f9(a1,f913(a1,a904),f913(a1,a904)),f319(f319(f10(f913(a1,f913(a904,a904)),f913(f913(a1,a904),f913(a1,a904)),a1),f20(a1,a904,a904)),f319(f319(f10(f913(a1,a904),f913(a1,f913(a904,a904)),a1),f319(f10(a904,f913(a904,a904),a1),a317)),f319(f319(f10(f913(a1,a1),f913(a1,a904),a1),f319(f10(a1,a904,a1),f319(a316,x45881))),f319(f319(f10(a1,f913(a1,a1),a1),f74(a1)),f319(f75(a1),x45882)))))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f319(f10(a904,a904,a1),f319(a322,f319(f319(f226(a1),f2(a1)),x45882))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),f319(f319(f9(a1,a1,a904),f226(a1)),x45882))))),f319(f319(f10(a904,a904,a1),f319(a322,f319(a314,f319(f319(f226(a1),f2(a1)),x45882)))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f226(a1),x45882))),f319(f319(f9(a1,a1,a904),f225(a1)),f2(a1))))))),f43(x45881,x45882))
% 22.40/22.29 [4591]E(f319(f254(x45911),f319(f319(f10(f913(a906,a904),a904,x45911),f80(a906)),f319(f319(f9(x45911,f913(a906,a904),f913(a906,a904)),f319(f319(f10(f913(a906,f913(a904,a904)),f913(f913(a906,a904),f913(a906,a904)),x45911),f20(a906,a904,a904)),f319(f319(f10(f913(a906,a904),f913(a906,f913(a904,a904)),x45911),f319(f10(a904,f913(a904,a904),a906),a317)),f319(f319(f9(x45911,f913(a906,x45911),f913(a906,a904)),f319(f319(f10(f913(x45911,a904),f913(f913(a906,x45911),f913(a906,a904)),x45911),f10(x45911,a904,a906)),a316)),f319(f156(x45911),x45912))))),f319(f319(f9(a906,a906,a904),f226(a906)),f319(f182(f907(x45911)),x45912))))),f319(f164(x45911),x45912))
% 22.40/22.29 [4673]~E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x46731)),x46731)),a89),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x46732)),x46732))
% 22.40/22.29 [4334]E(f319(f319(f3(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43341)),x43341)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43342)),x43342)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f3(a1),x43341),x43342))),f319(f319(f3(a1),x43341),x43342)))
% 22.40/22.29 [4335]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43351)),x43351)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43352)),x43352)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),x43351),x43352))),f319(f319(f74(a1),x43351),x43352)))
% 22.40/22.29 [4422]E(f319(f319(f3(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x44221)),x44221)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x44222)),x44222)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f3(a1),x44221),x44222))),f319(f319(f3(a1),x44221),x44222))),a89))
% 22.40/22.29 [4423]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x44231)),x44231)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x44232)),x44232)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),x44231),x44232))),f319(f319(f74(a1),x44231),x44232))),a89))
% 22.40/22.29 [4455]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),x44551),x44552))),f319(f319(f75(a1),x44551),x44552))),a89)),x44552),f319(f319(f75(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x44551)),x44551)),x44552))
% 22.40/22.29 [4512]E(f319(f134(f907(f907(x45121)),f907(f907(x45121)),f126(f907(x45121)),f105(f907(x45121))),f319(f319(f146(f907(x45121),f907(f907(x45121))),f148(f907(f907(x45121)),x45121,f105(f907(x45121)),f319(f18(f913(f907(x45121),f907(f907(x45121))),x45121),f319(f319(f9(f907(x45121),f907(f907(x45121)),f907(f907(x45121))),f143(f907(x45121))),f105(f907(x45121)))))),x45122)),f319(f319(f146(f907(x45121),f907(x45121)),f163(x45121)),f319(f128(f907(x45121),f319(f319(f10(a904,a904,f907(x45121)),a314),f319(f319(f9(f907(x45121),f907(x45121),a904),a316),f105(x45121)))),x45122)))
% 22.40/22.29 [4520]E(f319(f319(f82(a1,a906),f319(f96(a1),f319(f319(f74(a1),x45201),a89))),f319(f319(f20(a1,a906,a906),f319(f319(f9(a1,a906,f913(a906,a906)),f319(f319(f10(a904,f913(a906,f913(a906,a906)),a1),f86(a906)),a186)),f2(a906))),f319(f319(f10(a906,a906,a1),a104),f319(f319(f9(a1,a906,a906),f319(f319(f10(a906,f913(a906,a906),a1),f230(a906)),a97)),x45202)))),f319(f319(f230(a906),f319(f96(a906),x45201)),f319(a104,x45202)))
% 22.40/22.29 [4521]E(f319(f319(f82(a1,a906),f319(f96(a1),f319(f319(f74(a1),x45211),a89))),f319(f319(f20(a1,a906,a906),f319(f319(f9(a1,a906,f913(a906,a906)),f319(f319(f10(a904,f913(a906,f913(a906,a906)),a1),f86(a906)),a186)),f319(a104,x45212))),f319(f319(f10(a906,a906,a1),a104),f319(f319(f9(a1,a906,a906),f319(f319(f10(a906,f913(a906,a906),a1),f180(a906)),a97)),x45212)))),f319(f319(f180(a906),f319(f96(a906),x45211)),f319(a104,x45212)))
% 22.40/22.29 [4363]E(f319(f319(f236(a1),x43631),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43632)),x43632)),a89))),f319(f319(f82(a1,a1),f319(f319(f236(a1),x43631),f319(f96(a906),x43632))),f319(f319(f20(a1,a1,a1),f75(a1)),f7(a1))))
% 22.40/22.29 [4398]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),x43981),x43982))),f319(f319(f75(a1),x43981),x43982))),a89),f319(f319(f75(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x43981)),x43981)),a89)),x43982))
% 22.40/22.29 [4457]E(f319(f319(f30(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x44571)),x44571)),a89))),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x44572)),x44572)),a89))),f319(f319(f30(a1),f319(f96(a1),x44571)),f319(f96(a1),x44572)))
% 22.40/22.29 [4511]E(f319(f249(x45111,x45111,a904),f319(f319(f20(x45111,a904,f913(x45111,a904)),f319(f319(f10(f913(x45111,f913(a904,a904)),f913(a904,f913(x45111,a904)),x45111),f9(x45111,a904,a904)),f319(f319(f10(f913(x45111,a904),f913(x45111,f913(a904,a904)),x45111),f319(f10(a904,f913(a904,a904),x45111),a317)),a316))),x45112)),f255(x45111,x45112))
% 22.40/22.29 [4570]E(f39(a1,f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x45701)),x45701)),a89)),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x45702)),x45702)),a89))),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f39(a1,f319(f96(a1),x45701),f319(f96(a1),x45702))))
% 22.40/22.29 [4536]E(f319(f319(f30(a906),x45361),f319(f319(f74(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))),x45362)),f319(f319(f30(a906),x45361),f319(a104,f319(a104,f319(a104,x45362)))))
% 22.40/22.29 [4537]E(f39(a906,x45371,f319(f319(f74(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))),x45372)),f39(a906,x45371,f319(a104,f319(a104,f319(a104,x45372)))))
% 22.40/22.29 [4538]E(f39(a906,f319(f319(f74(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))),x45381),x45382),f39(a906,f319(a104,f319(a104,f319(a104,x45381))),x45382))
% 22.40/22.29 [4563]E(f115(f319(x45631,f319(f319(f75(a91),f319(f96(a91),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))),x45632))),f319(f193(x45631),x45632))
% 22.40/22.29 [4568]E(f319(f319(f30(a906),f319(f319(f74(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))),x45681)),x45682),f319(f319(f30(a906),f319(a104,f319(a104,f319(a104,x45681)))),x45682))
% 22.40/22.29 [4631]~E(f118(x46311,x46312,x46313),f111(x46311))
% 22.40/22.29 [3385]E(f319(f185(x33851,x33852),x33853),f113(x33851,x33852))
% 22.40/22.29 [3404]E(f319(f192(x34041,x34042),x34043),f319(f121(x34041),x34042))
% 22.40/22.29 [3480]E(f319(f319(f146(x34801,x34802),x34803),f105(x34801)),f105(x34802))
% 22.40/22.29 [3519]E(f319(f176(x35191,x35192,x35193),f2(a906)),x35192)
% 22.40/22.29 [3521]E(f319(f319(f173(x35211,x35212),x35213),f105(x35212)),f105(f912(x35211,x35212)))
% 22.40/22.29 [3536]E(f319(f182(f907(x35361)),f161(x35361,x35362,x35363)),x35362)
% 22.40/22.29 [3555]E(f79(x35551,f56(x35551,x35552,x35553)),f319(f57(x35551,x35552),x35553))
% 22.40/22.29 [3559]E(f235(x35591,x35592,f235(x35592,x35591,x35593)),x35593)
% 22.40/22.29 [3579]E(f319(f160(x35791),f161(x35791,x35792,x35793)),f161(x35791,x35792,x35793))
% 22.40/22.29 [3604]E(f132(x36041,x36042,f144(x36041,x36043)),f144(x36041,f132(x36041,x36042,x36043)))
% 22.40/22.29 [3622]E(f319(f243(f907(x36221),f907(x36221)),f158(x36221,x36222,x36223)),f319(f128(x36221,x36222),x36223))
% 22.40/22.29 [3664]E(f319(f319(f143(x36641),x36642),f161(x36641,x36643,x36642)),f161(x36641,f319(a104,x36643),x36642))
% 22.40/22.29 [3695]E(f19(x36951,x36952,x36953,f2(a91)),x36952)
% 22.40/22.29 [3696]E(f177(x36961,x36962,x36963,f2(a906)),x36962)
% 22.40/22.29 [3697]E(f21(x36971,x36972,x36973,f2(a91)),x36972)
% 22.40/22.29 [3704]E(f155(x37041,x37042,x37043,f105(x37041)),f105(x37042))
% 22.40/22.29 [3705]E(f122(x37051,x37052,x37053,f111(x37051)),f111(x37052))
% 22.40/22.29 [3712]E(f319(f319(f156(x37121),f319(f319(f143(x37121),x37122),x37123)),f2(a906)),x37122)
% 22.40/22.29 [3740]E(f53(x37401,x37402,f105(x37401),x37403),f105(f912(x37401,x37402)))
% 22.40/22.29 [3761]P25(x37611,x37612,x37613,f181(f913(x37611,a904)))
% 22.40/22.29 [3863]E(f257(x38631,x38632,x38633),f319(f244(f913(a91,f913(a904,f910(f908(x38631)))),f912(a91,a91)),f35(x38631)))
% 22.40/22.29 [3917]E(f319(f66(x39171,x39172,x39171,x39173),f25(x39171)),x39173)
% 22.40/22.29 [4089]P1(f319(f319(f321(f912(x40891,x40891)),f319(f319(f244(x40891,x40891),x40892),x40892)),f299(x40891,x40893)))
% 22.40/22.29 [4675]~P1(f319(f319(f321(f912(f907(x46751),f907(x46751))),f319(f319(f244(f907(x46751),f907(x46751)),x46752),f105(x46751))),f137(x46751,x46753)))
% 22.40/22.29 [4676]~P1(f319(f319(f321(f912(f907(x46761),f907(x46761))),f319(f319(f244(f907(x46761),f907(x46761)),x46762),f105(x46761))),f139(x46761,x46763)))
% 22.40/22.29 [4677]~P1(f319(f319(f321(f912(f907(x46771),f907(x46771))),f319(f319(f244(f907(x46771),f907(x46771)),x46772),f105(x46771))),f149(x46771,x46773)))
% 22.40/22.29 [4678]~P1(f319(f319(f321(f912(f907(x46781),f907(x46781))),f319(f319(f244(f907(x46781),f907(x46781)),f105(x46781)),x46782)),f137(x46781,x46783)))
% 22.40/22.29 [4679]~P1(f319(f319(f321(f912(f907(x46791),f907(x46791))),f319(f319(f244(f907(x46791),f907(x46791)),f105(x46791)),x46792)),f149(x46791,x46793)))
% 22.40/22.29 [3455]E(f319(f319(f194(x34551),x34552),x34553),f195(x34551,f208(x34552,x34553)))
% 22.40/22.29 [3508]E(f319(f278(x35081,x35082),f319(f278(x35082,x35081),x35083)),x35083)
% 22.40/22.29 [3531]E(f319(f319(f173(x35311,x35312),f105(x35311)),x35313),f105(f912(x35311,x35312)))
% 22.40/22.29 [3534]E(f168(x35341,x35342,f319(f274(a906),x35343)),f319(f319(f167(x35341),x35343),x35342))
% 22.40/22.29 [3552]E(f144(x35521,f319(f128(x35521,x35522),x35523)),f319(f128(x35521,x35522),f144(x35521,x35523)))
% 22.40/22.29 [3553]E(f319(f276(x35531,x35532),f319(f278(x35532,x35531),x35533)),f319(f256(x35532,x35531),x35533))
% 22.40/22.29 [3554]E(f319(f256(x35541,x35542),f319(f278(x35542,x35541),x35543)),f319(f276(x35542,x35541),x35543))
% 22.40/22.29 [3572]E(f319(f128(x35721,x35722),f319(f160(x35721),x35723)),f319(f160(x35721),f319(f128(x35721,x35722),x35723)))
% 22.40/22.29 [3584]E(f319(f319(f130(x35841),x35842),f319(f163(x35841),x35843)),f319(f319(f130(x35841),f319(a104,x35842)),x35843))
% 22.40/22.29 [3600]E(f319(f302(x36001,x36002,x36003),f181(f913(x36001,a904))),f181(f913(x36002,a904)))
% 22.40/22.29 [3601]E(f319(f277(x36011,x36012,x36013),f181(f913(x36011,a904))),f181(f913(x36012,a904)))
% 22.40/22.29 [3602]E(f319(f303(x36021,x36022,x36023),f234(f913(x36022,a904))),f234(f913(x36021,a904)))
% 22.40/22.29 [3603]E(f319(f303(x36031,x36032,x36033),f181(f913(x36032,a904))),f181(f913(x36031,a904)))
% 22.40/22.29 [3628]E(f112(x36281,f118(f908(x36281),x36282,x36283)),f108(x36281,x36282,f112(x36281,x36283)))
% 22.40/22.29 [3630]E(f319(f319(f301(x36301),x36302),f319(f164(x36301),x36303)),f319(f164(x36301),f132(x36301,x36302,x36303)))
% 22.40/22.29 [3716]E(f319(f302(f912(x37161,x37162),x37162,f248(x37161,x37162)),x37163),f319(f276(x37161,x37162),x37163))
% 22.40/22.29 [3717]E(f319(f302(f912(x37171,x37172),x37171,f243(x37171,x37172)),x37173),f319(f256(x37171,x37172),x37173))
% 22.40/22.29 [3732]E(f319(f164(x37321),f161(x37321,f319(a104,x37322),x37323)),f319(f319(f301(x37321),x37323),f181(f913(x37321,a904))))
% 22.40/22.29 [3790]E(f319(f319(f244(x37901,x37902),f319(f243(x37901,x37902),x37903)),f319(f248(x37901,x37902),x37903)),x37903)
% 22.40/22.29 [3798]E(f319(f182(f908(x37981)),f118(x37981,x37982,x37983)),f319(f319(f74(a906),f319(f182(f908(x37981)),x37983)),f319(a104,f2(a906))))
% 22.40/22.29 [3799]E(f319(f319(f249(x37991,x37992,x37991),f18(x37991,x37992)),x37993),f319(f243(x37991,x37992),x37993))
% 22.40/22.29 [3923]E(f319(f66(x39231,x39231,x39232,f25(x39231)),x39233),x39233)
% 22.40/22.29 [3930]E(f319(f319(f126(x39301),f161(x39301,x39302,x39303)),f319(f319(f143(x39301),x39303),f105(x39301))),f319(f319(f143(x39301),x39303),f161(x39301,x39302,x39303)))
% 22.40/22.29 [4097]P1(f319(f319(f225(f913(x40971,a904)),f319(f164(x40971),f319(f128(x40971,x40972),x40973))),f319(f164(x40971),x40973)))
% 22.40/22.29 [4140]P1(f319(f319(f225(f913(x41401,a904)),f319(f164(x41401),f319(f319(f167(x41401),x41402),x41403))),f319(f164(x41401),x41403)))
% 22.40/22.29 [4141]P1(f319(f319(f225(f913(x41411,a904)),f319(f164(x41411),f319(f319(f130(x41411),x41412),x41413))),f319(f164(x41411),x41413)))
% 22.40/22.29 [4144]P1(f319(f319(f225(f913(x41441,a904)),f319(f164(x41441),f168(x41441,x41442,x41443))),f319(f164(x41441),x41442)))
% 22.40/22.29 [4145]P1(f319(f319(f225(f913(x41451,a904)),f319(f164(x41451),f162(x41451,x41452,x41453))),f319(f164(x41451),x41453)))
% 22.40/22.29 [4166]P25(f912(x41661,x41662),f912(x41662,x41661),f319(f249(x41661,x41662,f912(x41662,x41661)),f319(f9(x41662,x41661,f912(x41662,x41661)),f244(x41662,x41661))),x41663)
% 22.40/22.29 [4176]E(f319(f319(f319(f175(f907(x41761),f907(x41761)),f39(a906,x41762,f319(f182(f907(x41761)),x41763))),f159(x41761)),x41763),f319(f319(f319(f175(f907(x41761),f907(x41761)),x41762),f159(x41761)),x41763))
% 22.40/22.29 [4218]P1(f319(f319(f321(f912(f907(x42181),f907(x42181))),f319(f319(f244(f907(x42181),f907(x42181)),x42182),x42182)),f150(x42181,f299(x42181,x42183))))
% 22.40/22.29 [4358]E(f79(f912(x43581,x43582),f319(f319(f20(f912(x43581,x43582),x43582,a904),f319(f319(f10(x43581,f913(x43582,a904),f912(x43581,x43582)),x43583),f243(x43581,x43582))),f248(x43581,x43582))),f79(f912(x43581,x43582),f319(f249(x43581,x43582,a904),x43583)))
% 22.40/22.29 [4359]E(f84(f912(x43591,x43592),f319(f319(f20(f912(x43591,x43592),x43592,a904),f319(f319(f10(x43591,f913(x43592,a904),f912(x43591,x43592)),x43593),f243(x43591,x43592))),f248(x43591,x43592))),f84(f912(x43591,x43592),f319(f249(x43591,x43592,a904),x43593)))
% 22.40/22.29 [4390]E(f319(f319(f280(f912(a906,x43901),x43901),f312(a906,x43901,a232,x43902)),f319(f319(f20(x43901,x43901,f912(a906,x43901)),f319(f319(f10(a906,f913(x43901,f912(a906,x43901)),x43901),f244(a906,x43901)),x43903)),f7(x43901))),f313(x43901,x43903,x43902))
% 22.40/22.29 [4450]E(f319(f250(x44501,x44501,x44502,x44502,f7(x44501),f7(x44502)),x44503),x44503)
% 22.40/22.29 [4529]E(f319(f134(f907(f907(x45291)),f907(f907(x45291)),f126(f907(x45291)),f105(f907(x45291))),f319(f319(f146(f907(x45291),f907(f907(x45291))),f319(f319(f9(f907(x45291),f907(x45291),f907(f907(x45291))),f319(f319(f10(f913(x45291,f907(x45291)),f913(f907(x45291),f907(f907(x45291))),f907(x45291)),f146(x45291,f907(x45291))),f319(f9(x45291,f907(x45291),f907(x45291)),f143(x45291)))),x45292)),f49(x45291,x45293,x45292))),f49(x45291,f319(a104,x45293),x45292))
% 22.40/22.29 [4596]E(f216(a906,f912(x45961,f908(x45961)),f2(a906),f319(f249(x45961,f908(x45961),a906),f319(f319(f9(x45961,a906,f913(f908(x45961),a906)),f319(f319(f10(f913(f908(x45961),f913(a906,a906)),f913(a906,f913(f908(x45961),a906)),x45961),f9(f908(x45961),a906,a906)),f319(f319(f10(f913(f908(x45961),a906),f913(f908(x45961),f913(a906,a906)),x45961),f319(f10(a906,f913(a906,a906),f908(x45961)),f74(a906))),f319(f319(f9(x45961,f913(f908(x45961),a906),f913(f908(x45961),a906)),f319(f319(f10(f913(a906,a906),f913(f913(f908(x45961),a906),f913(f908(x45961),a906)),x45961),f10(a906,a906,f908(x45961))),f319(f319(f10(a906,f913(a906,a906),x45961),f74(a906)),x45962))),f117(x45961,x45962))))),f72(a906))),f319(f127(x45961),x45963)),f319(f117(x45961,x45962),x45963))
% 22.40/22.29 [4603]E(f319(f319(f82(a1,x46031),f211(f319(f319(f66(f912(a1,a1),a1,x46031,f248(a1,a1)),f205(x46031)),x46032),f319(f319(f66(f912(a1,a1),a1,x46031,f248(a1,a1)),f205(x46031)),x46033))),f319(f319(f20(a1,a1,x46031),f319(f319(f10(a1,f913(a1,x46031),a1),f194(x46031)),f319(f319(f20(a1,a1,a1),f319(f319(f10(a1,f913(a1,a1),a1),f74(a1)),f319(f319(f10(a1,a1,a1),f319(f75(a1),f319(f319(f66(f912(a1,a1),a1,x46031,f243(a1,a1)),f205(x46031)),x46032))),f319(f319(f9(a1,a1,a1),f30(a1)),f319(f319(f66(f912(a1,a1),a1,x46031,f248(a1,a1)),f205(x46031)),x46032))))),f319(f319(f10(a1,a1,a1),f319(f75(a1),f319(f319(f66(f912(a1,a1),a1,x46031,f243(a1,a1)),f205(x46031)),x46033))),f319(f319(f9(a1,a1,a1),f30(a1)),f319(f319(f66(f912(a1,a1),a1,x46031,f248(a1,a1)),f205(x46031)),x46033)))))),f7(a1))),f223(x46031,x46032,x46033))
% 22.40/22.29 [4626]~E(f319(f319(f143(x46261),x46262),x46263),x46263)
% 22.40/22.29 [4629]~E(f319(f319(f143(x46291),x46292),x46293),f105(x46291))
% 22.40/22.29 [4635]~E(f319(f319(f301(x46351),x46352),x46353),f181(f913(x46351,a904)))
% 22.40/22.29 [4655]~E(f319(f302(x46551,f913(x46551,a904),x46552),x46553),f319(f300(x46551),x46553))
% 22.40/22.29 [3513]E(f319(f319(f151(x35131,f105(x35131)),x35132),x35133),f105(x35131))
% 22.40/22.29 [3514]E(f319(f133(x35141),f319(f319(f143(x35141),x35142),x35143)),x35142)
% 22.40/22.29 [3515]E(f319(f163(x35151),f319(f319(f143(x35151),x35152),x35153)),x35153)
% 22.40/22.29 [3558]E(f319(f319(f130(x35581),f72(a906)),f319(f319(f143(x35581),x35582),x35583)),x35583)
% 22.40/22.29 [3591]E(f106(x35911,f319(f319(f130(x35911),x35912),x35913)),f319(f319(f130(x35911),x35912),f106(x35911,x35913)))
% 22.40/22.29 [3593]E(f319(f319(f151(x35931,x35932),x35933),f319(f319(f156(x35931),x35932),x35933)),x35932)
% 22.40/22.29 [3612]E(f319(f319(f301(x36121),x36122),f319(f319(f301(x36121),x36122),x36123)),f319(f319(f301(x36121),x36122),x36123))
% 22.40/22.29 [3625]E(f319(f319(f301(x36251),x36252),f319(f164(x36251),x36253)),f319(f164(x36251),f319(f319(f143(x36251),x36252),x36253)))
% 22.40/22.29 [3627]E(f319(f319(f130(x36271),x36272),f319(f163(x36271),x36273)),f319(f163(x36271),f319(f319(f130(x36271),x36272),x36273)))
% 22.40/22.29 [3639]E(f319(f319(f167(x36391),f72(a906)),f319(f319(f143(x36391),x36392),x36393)),f319(f319(f143(x36391),x36392),f105(x36391)))
% 22.40/22.29 [3682]E(f319(f57(x36821,x36822),f319(f319(f301(x36821),x36823),f181(f913(x36821,a904)))),x36823)
% 22.40/22.29 [3722]E(f319(f319(f74(a906),x37221),f319(f319(f74(a906),x37222),x37223)),f319(f319(f74(a906),x37222),f319(f319(f74(a906),x37221),x37223)))
% 22.40/22.29 [3723]E(f319(f319(f74(a1),x37231),f319(f319(f74(a1),x37232),x37233)),f319(f319(f74(a1),x37232),f319(f319(f74(a1),x37231),x37233)))
% 22.40/22.29 [3728]E(f319(f319(f246(x37281,x37282),f181(f913(x37281,a904))),x37283),f181(f913(f912(x37281,x37282),a904)))
% 22.40/22.29 [3753]E(f319(f319(f93(f913(x37531,a904)),x37532),x37533),f319(f319(f93(f913(x37531,a904)),x37533),x37532))
% 22.40/22.29 [3754]E(f319(f319(f94(f913(x37541,a904)),x37542),x37543),f319(f319(f94(f913(x37541,a904)),x37543),x37542))
% 22.40/22.29 [3756]E(f319(f319(f126(x37561),x37562),f319(f319(f143(x37561),x37563),f105(x37561))),f319(f159(x37561),f319(f319(f143(x37561),x37563),x37562)))
% 22.40/22.29 [3757]E(f319(f319(f126(x37571),f319(f160(x37571),x37572)),f319(f160(x37571),x37573)),f319(f160(x37571),f319(f319(f126(x37571),x37573),x37572)))
% 22.40/22.29 [3767]E(f319(f163(x37671),f319(f319(f167(x37671),f319(a104,x37672)),x37673)),f319(f319(f167(x37671),x37672),f319(f163(x37671),x37673)))
% 22.40/22.29 [3775]P1(f319(f319(f321(x37751),x37752),f319(f319(f301(x37751),x37752),x37753)))
% 22.40/22.29 [3779]E(f319(f319(f34(x37791,f913(x37792,a904)),f181(f913(x37791,a904))),x37793),f234(f913(x37792,a904)))
% 22.40/22.29 [3782]E(f319(f277(x37821,x37821,f255(x37821,x37822)),x37823),f319(f319(f94(f913(x37821,a904)),x37822),x37823))
% 22.40/22.29 [3797]E(f319(f182(f907(x37971)),f319(f319(f143(x37971),x37972),x37973)),f319(f319(f74(a906),f319(f182(f907(x37971)),x37973)),f319(a104,f2(a906))))
% 22.40/22.29 [3801]E(f106(x38011,f319(f319(f126(x38011),x38012),f319(f319(f143(x38011),x38013),f105(x38011)))),x38012)
% 22.40/22.29 [3802]E(f136(x38021,f319(f319(f126(x38021),x38022),f319(f319(f143(x38021),x38023),f105(x38021)))),x38023)
% 22.40/22.29 [3810]E(f319(f319(f126(x38101),f319(f319(f167(x38101),x38102),x38103)),f319(f319(f130(x38101),x38102),x38103)),x38103)
% 22.40/22.29 [3819]E(f319(f319(f3(a906),f319(f319(f74(a906),x38191),x38192)),f319(f319(f74(a906),x38193),x38192)),f319(f319(f3(a906),x38191),x38193))
% 22.40/22.29 [3820]E(f319(f319(f3(a906),f319(f319(f74(a906),x38201),x38202)),f319(f319(f74(a906),x38201),x38203)),f319(f319(f3(a906),x38202),x38203))
% 22.40/22.29 [3826]E(f319(f319(f126(x38261),f319(f160(x38261),x38262)),f319(f319(f143(x38261),x38263),f105(x38261))),f319(f160(x38261),f319(f319(f143(x38261),x38263),x38262)))
% 22.40/22.29 [3828]E(f319(f319(f74(a906),f319(f182(f907(x38281)),x38282)),f319(f182(f907(x38281)),x38283)),f319(f182(f907(x38281)),f319(f319(f126(x38281),x38282),x38283)))
% 22.40/22.29 [3831]E(f319(f319(f74(a906),f319(f182(f907(x38311)),x38312)),f319(f182(f907(x38311)),x38313)),f319(f182(f907(x38311)),f165(x38311,x38312,x38313)))
% 22.40/22.29 [3838]E(f319(f319(f93(f913(x38381,a904)),f319(f164(x38381),x38382)),f319(f164(x38381),x38383)),f319(f164(x38381),f319(f319(f126(x38381),x38382),x38383)))
% 22.40/22.29 [3839]E(f39(a906,f319(f319(f75(a906),x38391),x38392),f319(f319(f75(a906),x38391),x38393)),f319(f319(f75(a906),x38391),f39(a906,x38392,x38393)))
% 22.40/22.29 [3851]E(f319(f319(f167(x38511),f319(f319(f3(a906),x38512),f72(a906))),f319(f163(x38511),x38513)),f319(f163(x38511),f319(f319(f167(x38511),x38512),x38513)))
% 22.40/22.29 [3856]E(f319(f319(f94(f913(x38561,a904)),x38562),f319(f73(f913(x38561,a904)),x38563)),f319(f319(f3(f913(x38561,a904)),x38562),x38563))
% 22.40/22.29 [3857]E(f319(f319(f3(f913(x38571,a904)),x38572),f319(f73(f913(x38571,a904)),x38573)),f319(f319(f94(f913(x38571,a904)),x38572),x38573))
% 22.40/22.29 [3873]E(f319(f319(f246(x38731,x38732),x38733),f319(f18(f913(x38732,a904),x38731),f181(f913(x38732,a904)))),f181(f913(f912(x38731,x38732),a904)))
% 22.40/22.29 [3875]E(f319(f319(f3(a906),f319(f319(f75(a906),x38751),x38752)),f319(f319(f75(a906),x38751),x38753)),f319(f319(f75(a906),x38751),f319(f319(f3(a906),x38752),x38753)))
% 22.40/22.29 [3876]E(f319(f319(f74(a906),f319(f319(f75(a906),x38761),x38762)),f319(f319(f75(a906),x38761),x38763)),f319(f319(f75(a906),x38761),f319(f319(f74(a906),x38762),x38763)))
% 22.40/22.29 [3877]E(f319(f319(f3(a1),f319(f319(f75(a1),x38771),x38772)),f319(f319(f75(a1),x38771),x38773)),f319(f319(f75(a1),x38771),f319(f319(f3(a1),x38772),x38773)))
% 22.40/22.29 [3878]E(f319(f319(f74(a1),f319(f319(f75(a1),x38781),x38782)),f319(f319(f75(a1),x38781),x38783)),f319(f319(f75(a1),x38781),f319(f319(f74(a1),x38782),x38783)))
% 22.40/22.29 [3879]E(f319(f319(f75(a1),f319(f319(f236(a1),x38791),x38792)),f319(f319(f236(a1),x38791),x38793)),f319(f319(f236(a1),x38791),f319(f319(f74(a906),x38792),x38793)))
% 22.40/22.29 [3892]E(f319(f319(f33(x38921,f913(x38922,a904)),x38923),f319(f18(f913(x38922,a904),x38921),f181(f913(x38922,a904)))),f181(f913(x38922,a904)))
% 22.40/22.29 [3894]E(f39(a906,f319(f319(f75(a906),x38941),x38942),f319(f319(f75(a906),x38943),x38942)),f319(f319(f75(a906),f39(a906,x38941,x38943)),x38942))
% 22.40/22.29 [3899]E(f39(a1,f319(f319(f3(a1),x38991),f39(a1,x38992,x38993)),x38993),f39(a1,f319(f319(f3(a1),x38991),x38992),x38993))
% 22.40/22.29 [3900]E(f39(a1,f319(f319(f75(a1),x39001),f39(a1,x39002,x39003)),x39003),f39(a1,f319(f319(f75(a1),x39001),x39002),x39003))
% 22.40/22.29 [3901]P1(f319(f319(f225(f913(x39011,a904)),x39012),f319(f319(f301(x39011),x39013),x39012)))
% 22.40/22.29 [3980]E(f319(f319(f34(f913(x39801,a904),f913(x39801,a904)),x39802),f319(f93(f913(x39801,a904)),x39803)),f319(f319(f93(f913(x39801,a904)),x39803),f32(f913(x39801,a904),x39802)))
% 22.40/22.29 [3981]E(f319(f319(f33(f913(x39811,a904),f913(x39811,a904)),x39812),f319(f94(f913(x39811,a904)),x39813)),f319(f319(f94(f913(x39811,a904)),x39813),f31(f913(x39811,a904),x39812)))
% 22.40/22.29 [3991]E(f319(f164(x39911),f319(f319(f319(f175(f907(x39911),f907(x39911)),x39912),f159(x39911)),x39913)),f319(f164(x39911),x39913))
% 22.40/22.29 [3995]E(f319(f319(f167(x39951),f319(f182(f907(x39951)),f169(x39951,x39952,x39953))),x39953),f169(x39951,x39952,x39953))
% 22.40/22.29 [3999]E(f319(f182(f907(x39991)),f319(f319(f319(f175(f907(x39991),f907(x39991)),x39992),f159(x39991)),x39993)),f319(f182(f907(x39991)),x39993))
% 22.40/22.29 [4002]E(f319(f319(f249(x40021,x40022,x40022),f319(f18(f913(x40022,x40022),x40021),f7(x40022))),x40023),f319(f248(x40021,x40022),x40023))
% 22.40/22.29 [4008]E(f39(a1,f319(f319(f3(a1),f39(a1,x40081,x40082)),x40083),x40082),f39(a1,f319(f319(f3(a1),x40081),x40083),x40082))
% 22.40/22.29 [4009]E(f39(a1,f319(f319(f236(a1),f39(a1,x40091,x40092)),x40093),x40092),f39(a1,f319(f319(f236(a1),x40091),x40093),x40092))
% 22.40/22.29 [4012]E(f319(f319(f33(f913(f912(x40121,x40122),a904),f913(x40122,a904)),x40123),f276(x40121,x40122)),f319(f276(x40121,x40122),f31(f913(f912(x40121,x40122),a904),x40123)))
% 22.40/22.29 [4013]E(f319(f319(f33(f913(f912(x40131,x40132),a904),f913(x40131,a904)),x40133),f256(x40131,x40132)),f319(f256(x40131,x40132),f31(f913(f912(x40131,x40132),a904),x40133)))
% 22.40/22.29 [4033]E(f319(f66(x40331,x40331,x40331,x40332),f319(f319(f175(x40331,x40331),x40333),x40332)),f319(f319(f175(x40331,x40331),f319(a104,x40333)),x40332))
% 22.40/22.29 [4051]E(f319(f319(f130(x40511),f319(f319(f3(a906),f319(f182(f907(x40511)),x40512)),x40513)),f319(f160(x40511),x40512)),f319(f160(x40511),f319(f319(f167(x40511),x40513),x40512)))
% 22.40/22.29 [4052]E(f319(f319(f167(x40521),f319(f319(f3(a906),f319(f182(f907(x40521)),x40522)),x40523)),f319(f160(x40521),x40522)),f319(f160(x40521),f319(f319(f130(x40521),x40523),x40522)))
% 22.40/22.29 [4054]E(f319(f319(f74(a906),f319(f157(a906),f319(f319(f146(x40541,a906),x40542),x40543))),f319(f182(f907(x40541)),x40543)),f147(x40541,x40542,x40543))
% 22.40/22.29 [4074]E(f319(f159(x40741),f319(f319(f319(f175(f907(x40741),f907(x40741)),x40742),f159(x40741)),x40743)),f319(f319(f319(f175(f907(x40741),f907(x40741)),f319(a104,x40742)),f159(x40741)),x40743))
% 22.40/22.29 [4090]P1(f319(f319(f225(a906),f319(f182(f907(x40901)),f319(f128(x40901,x40902),x40903))),f319(f182(f907(x40901)),x40903)))
% 22.40/22.29 [4105]E(f319(f319(f93(f913(f913(x41051,a904),a904)),f319(f300(x41051),x41052)),f319(f302(f913(x41051,a904),f913(x41051,a904),f319(f301(x41051),x41053)),f319(f300(x41051),x41052))),f319(f300(x41051),f319(f319(f301(x41051),x41053),x41052)))
% 22.40/22.29 [4137]P1(f319(f319(f225(a906),f319(f182(f907(x41371)),f169(x41371,x41372,x41373))),f319(f182(f907(x41371)),x41373)))
% 22.40/22.29 [4143]E(f319(f256(x41431,x41432),f319(f254(f912(x41431,x41432)),f319(f249(x41431,x41432,a904),x41433))),f319(f254(x41431),f319(f319(f10(f913(x41432,a904),a904,x41431),f80(x41432)),x41433)))
% 22.40/22.29 [4155]E(f319(f302(a906,a906,f319(f319(f9(a906,a906,a906),f74(a906)),x41551)),f295(a906,x41552,x41553)),f295(a906,f319(f319(f74(a906),x41552),x41551),f319(f319(f74(a906),x41553),x41551)))
% 22.40/22.29 [4169]E(f319(f302(a906,a906,f319(f319(f9(a906,a906,a906),f74(a906)),x41691)),f319(f294(a906,x41692),x41693)),f319(f294(a906,f319(f319(f74(a906),x41692),x41691)),f319(f319(f74(a906),x41693),x41691)))
% 22.40/22.29 [4186]E(f319(f319(f173(x41861,x41862),f319(f319(f146(f912(x41861,x41862),x41861),f243(x41861,x41862)),x41863)),f319(f319(f146(f912(x41861,x41862),x41862),f248(x41861,x41862)),x41863)),x41863)
% 22.40/22.29 [4191]E(f319(f319(f74(a906),f319(f319(f75(a906),x41911),f39(a906,f319(f319(f30(a906),x41912),x41911),x41913))),f39(a906,x41912,x41911)),f39(a906,x41912,f319(f319(f75(a906),x41911),x41913)))
% 22.40/22.29 [4203]E(f319(f319(f126(x42031),x42032),f319(f134(f907(x42031),f907(x42031),f126(x42031),f105(x42031)),x42033)),f319(f134(f907(x42031),f907(x42031),f126(x42031),x42032),x42033))
% 22.40/22.29 [4223]P1(f319(f319(f321(f912(x42231,x42231)),f319(f319(f244(x42231,x42231),x42232),x42232)),f319(f319(f175(f912(x42231,x42231),a904),f2(a906)),x42233)))
% 22.40/22.29 [4228]E(f319(f254(x42281),f319(f319(f10(f913(x42282,a904),a904,x42281),f80(x42282)),f319(f9(x42282,x42281,a904),x42283))),f319(f276(x42282,x42281),f319(f254(f912(x42282,x42281)),f319(f249(x42282,x42281,a904),x42283))))
% 22.40/22.29 [4245]E(f319(f319(f93(f913(x42451,a904)),f319(f319(f33(a906,f913(x42451,a904)),f295(a906,f72(a906),x42452)),x42453)),f319(x42453,f2(a906))),f319(f319(f33(a906,f913(x42451,a904)),f319(f293(a906),x42452)),x42453))
% 22.40/22.29 [4260]E(f319(f134(f907(x42601),f907(x42601),f126(x42601),f105(x42601)),f319(f319(f146(f907(x42601),f907(x42601)),f128(x42601,x42602)),x42603)),f319(f128(x42601,x42602),f319(f134(f907(x42601),f907(x42601),f126(x42601),f105(x42601)),x42603)))
% 22.40/22.29 [4264]E(f319(f248(f907(x42641),f907(x42641)),f158(x42641,x42642,x42643)),f319(f128(x42641,f319(f66(a904,a904,x42641,a314),x42642)),x42643))
% 22.40/22.29 [4303]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f75(a1),x43031),f319(f319(f30(a1),x43032),x43031))),f39(a1,x43032,x43031))),x43033),f319(f319(f74(a1),x43032),x43033))
% 22.40/22.29 [4344]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f75(a1),f319(f319(f30(a1),x43441),x43442)),x43442)),f39(a1,x43441,x43442))),x43443),f319(f319(f74(a1),x43441),x43443))
% 22.40/22.29 [4372]E(f79(f912(x43721,x43722),f319(f249(x43721,x43722,a904),f319(f319(f10(f913(x43722,f912(x43721,x43722)),f913(x43722,a904),x43721),f319(f10(f912(x43721,x43722),a904,x43722),x43723)),f244(x43721,x43722)))),f79(f912(x43721,x43722),x43723))
% 22.40/22.29 [4373]E(f84(f912(x43731,x43732),f319(f249(x43731,x43732,a904),f319(f319(f10(f913(x43732,f912(x43731,x43732)),f913(x43732,a904),x43731),f319(f10(f912(x43731,x43732),a904,x43732),x43733)),f244(x43731,x43732)))),f84(f912(x43731,x43732),x43733))
% 22.40/22.29 [4401]P1(f319(f319(f225(f913(x44011,a904)),f31(f913(x44011,a904),f319(f319(f94(f913(f913(x44011,a904),a904)),x44012),x44013))),f319(f319(f94(f913(x44011,a904)),f31(f913(x44011,a904),x44012)),f31(f913(x44011,a904),x44013))))
% 22.40/22.29 [4402]E(f319(f160(x44021),f319(f319(f319(f175(f907(x44021),f907(x44021)),f319(f319(f3(a906),f319(f182(f907(x44021)),x44022)),f39(a906,x44023,f319(f182(f907(x44021)),x44022)))),f159(x44021)),x44022)),f319(f319(f319(f175(f907(x44021),f907(x44021)),x44023),f159(x44021)),f319(f160(x44021),x44022)))
% 22.40/22.29 [4440]P1(f319(f319(f225(a906),f319(f182(f907(x44401)),f319(f319(f130(x44401),f319(f182(f907(x44401)),f169(x44401,x44402,x44403))),x44403))),f319(f182(f907(x44401)),x44403)))
% 22.40/22.29 [4665]~P1(f319(f56(x46651,x46652,f181(f913(x46651,a904))),x46653))
% 22.40/22.29 [4674]~P1(f319(f319(f321(f912(x46741,x46741)),f319(f319(f244(x46741,x46741),x46742),x46743)),f145(x46741,f105(f913(x46741,a906)))))
% 22.40/22.29 [3768]E(f319(f182(f907(x37681)),f319(f319(f167(x37681),x37682),x37683)),f319(f319(f230(a906),f319(f182(f907(x37681)),x37683)),x37682))
% 22.40/22.29 [3769]E(f319(f182(f907(x37691)),f319(f319(f130(x37691),x37692),x37693)),f319(f319(f3(a906),f319(f182(f907(x37691)),x37693)),x37692))
% 22.40/22.29 [3796]E(f319(f182(f907(f907(x37961))),f49(x37961,x37962,x37963)),f319(f319(f236(a906),f319(f182(f907(x37961)),x37963)),x37962))
% 22.40/22.29 [3812]E(f319(f319(f30(a906),f319(f319(f30(a906),x38121),x38122)),x38123),f319(f319(f30(a906),x38121),f319(f319(f75(a906),x38122),x38123)))
% 22.40/22.29 [3813]E(f319(f319(f3(a906),f319(f319(f3(a906),x38131),x38132)),x38133),f319(f319(f3(a906),x38131),f319(f319(f74(a906),x38132),x38133)))
% 22.40/22.29 [3814]E(f319(f319(f74(a906),f319(f319(f74(a906),x38141),x38142)),x38143),f319(f319(f74(a906),x38141),f319(f319(f74(a906),x38142),x38143)))
% 22.40/22.29 [3815]E(f319(f319(f74(a1),f319(f319(f74(a1),x38151),x38152)),x38153),f319(f319(f74(a1),x38151),f319(f319(f74(a1),x38152),x38153)))
% 22.40/22.29 [3816]E(f319(f319(f75(a906),f319(f319(f75(a906),x38161),x38162)),x38163),f319(f319(f75(a906),x38161),f319(f319(f75(a906),x38162),x38163)))
% 22.40/22.29 [3817]E(f319(f319(f75(a1),f319(f319(f75(a1),x38171),x38172)),x38173),f319(f319(f75(a1),x38171),f319(f319(f75(a1),x38172),x38173)))
% 22.40/22.29 [3818]E(f319(f319(f236(a1),f319(f319(f236(a1),x38181),x38182)),x38183),f319(f319(f236(a1),x38181),f319(f319(f75(a906),x38182),x38183)))
% 22.40/22.29 [3837]E(f154(x38371,f319(f319(f143(f913(x38371,a904)),x38372),x38373)),f166(x38371,x38372,f154(x38371,x38373)))
% 22.40/22.29 [3874]E(f319(f319(f3(a906),f319(f319(f3(a906),x38741),x38742)),x38743),f319(f319(f3(a906),f319(f319(f3(a906),x38741),x38743)),x38742))
% 22.40/22.29 [3882]E(f319(f319(f94(f913(x38821,a904)),x38822),f319(f319(f3(f913(x38821,a904)),x38823),x38822)),f181(f913(x38821,a904)))
% 22.40/22.29 [3886]E(f319(f319(f146(a906,x38861),f319(f18(x38861,a906),x38862)),f131(a906,f319(f294(a906,f2(a906)),x38863))),f161(x38861,x38863,x38862))
% 22.40/22.29 [3928]E(f32(f913(x39281,a904),f319(f319(f301(f913(x39281,a904)),x39282),x39283)),f319(f319(f94(f913(x39281,a904)),x39282),f32(f913(x39281,a904),x39283)))
% 22.40/22.29 [3929]E(f31(f913(x39291,a904),f319(f319(f301(f913(x39291,a904)),x39292),x39293)),f319(f319(f93(f913(x39291,a904)),x39292),f31(f913(x39291,a904),x39293)))
% 22.40/22.29 [3931]E(f161(x39311,f319(f182(f907(x39311)),f319(f128(x39311,f319(a316,x39312)),x39313)),x39312),f319(f128(x39311,f319(a316,x39312)),x39313))
% 22.40/22.29 [3933]E(f319(f319(f3(a906),f319(f319(f75(a906),x39331),x39332)),f319(f319(f75(a906),x39333),x39332)),f319(f319(f75(a906),f319(f319(f3(a906),x39331),x39333)),x39332))
% 22.40/22.29 [3934]E(f319(f319(f74(a906),f319(f319(f75(a906),x39341),x39342)),f319(f319(f75(a906),x39343),x39342)),f319(f319(f75(a906),f319(f319(f74(a906),x39341),x39343)),x39342))
% 22.40/22.29 [3935]E(f319(f319(f3(a1),f319(f319(f75(a1),x39351),x39352)),f319(f319(f75(a1),x39353),x39352)),f319(f319(f75(a1),f319(f319(f3(a1),x39351),x39353)),x39352))
% 22.40/22.29 [3936]E(f319(f319(f74(a1),f319(f319(f75(a1),x39361),x39362)),f319(f319(f75(a1),x39363),x39362)),f319(f319(f75(a1),f319(f319(f74(a1),x39361),x39363)),x39362))
% 22.40/22.29 [3937]E(f319(f319(f230(a906),f319(f319(f3(a906),x39371),x39372)),f319(f319(f3(a906),x39373),x39372)),f319(f319(f3(a906),f319(f319(f230(a906),x39371),x39373)),x39372))
% 22.40/22.29 [3957]E(f319(f319(f94(f913(f907(x39571),a904)),f152(x39571,x39572)),f152(x39571,x39573)),f152(x39571,f319(f319(f94(f913(x39571,a904)),x39572),x39573)))
% 22.40/22.29 [3960]E(f319(f319(f93(f913(x39601,a904)),x39602),f319(f319(f93(f913(x39601,a904)),x39602),x39603)),f319(f319(f93(f913(x39601,a904)),x39602),x39603))
% 22.40/22.29 [3961]E(f319(f319(f93(f913(x39611,a904)),x39612),f319(f319(f3(f913(x39611,a904)),x39613),x39612)),f319(f319(f93(f913(x39611,a904)),x39612),x39613))
% 22.40/22.29 [3962]E(f319(f319(f94(f913(x39621,a904)),x39622),f319(f319(f94(f913(x39621,a904)),x39622),x39623)),f319(f319(f94(f913(x39621,a904)),x39622),x39623))
% 22.40/22.29 [3974]E(f319(f319(f281(x39741,x39742,x39742),x39743),f299(x39742,f181(f913(f912(x39742,x39742),a904)))),x39743)
% 22.40/22.29 [3977]E(f319(f319(f93(f913(x39771,a904)),f319(f319(f301(x39771),x39772),f181(f913(x39771,a904)))),x39773),f319(f319(f301(x39771),x39772),x39773))
% 22.40/22.29 [3994]E(f319(f319(f3(a906),f319(f319(f3(a906),f319(a104,x39941)),x39942)),f319(a104,x39943)),f319(f319(f3(a906),f319(f319(f3(a906),x39941),x39942)),x39943))
% 22.40/22.29 [4020]E(f319(f319(f94(f913(f913(x40201,a904),a904)),f319(f300(x40201),x40202)),f319(f300(x40201),x40203)),f319(f300(x40201),f319(f319(f94(f913(x40201,a904)),x40202),x40203)))
% 22.40/22.29 [4023]E(f319(f319(f93(f913(x40231,a904)),f319(f73(f913(x40231,a904)),x40232)),x40233),f319(f73(f913(x40231,a904)),f319(f319(f3(f913(x40231,a904)),x40232),x40233)))
% 22.40/22.29 [4031]E(f319(f319(f301(x40311),x40312),f319(f319(f3(f913(x40311,a904)),x40313),f319(f319(f301(x40311),x40312),f181(f913(x40311,a904))))),f319(f319(f301(x40311),x40312),x40313))
% 22.40/22.29 [4040]P1(f319(f319(f225(f913(x40401,a904)),x40402),f319(f319(f93(f913(x40401,a904)),x40403),x40402)))
% 22.40/22.29 [4041]P1(f319(f319(f225(f913(x40411,a904)),x40412),f319(f319(f93(f913(x40411,a904)),x40412),x40413)))
% 22.40/22.29 [4045]E(f319(f319(f94(f913(x40451,a904)),f319(f73(f913(x40451,a904)),x40452)),f319(f73(f913(x40451,a904)),x40453)),f319(f73(f913(x40451,a904)),f319(f319(f93(f913(x40451,a904)),x40452),x40453)))
% 22.40/22.29 [4046]E(f319(f319(f93(f913(x40461,a904)),f319(f73(f913(x40461,a904)),x40462)),f319(f73(f913(x40461,a904)),x40463)),f319(f73(f913(x40461,a904)),f319(f319(f94(f913(x40461,a904)),x40462),x40463)))
% 22.40/22.29 [4060]P1(f319(f319(f225(f913(x40601,a904)),f319(f164(x40601),x40602)),f319(f164(x40601),f319(f319(f143(x40601),x40603),x40602))))
% 22.40/22.29 [4071]E(f319(f319(f93(f913(x40711,a904)),f319(f319(f3(f913(x40711,a904)),x40712),x40713)),f319(f319(f94(f913(x40711,a904)),x40712),x40713)),x40712)
% 22.40/22.29 [4124]E(f319(f319(f8(x41241,a1),f319(f319(f10(a906,a1,x41241),f92(a1)),x41242)),x41243),f319(f92(a1),f319(f319(f8(x41241,a906),x41242),x41243)))
% 22.40/22.29 [4125]E(f319(f319(f11(x41251,a1),f319(f319(f10(a906,a1,x41251),f92(a1)),x41252)),x41253),f319(f92(a1),f319(f319(f11(x41251,a906),x41252),x41253)))
% 22.40/22.29 [4171]E(f319(f319(f126(x41711),f169(x41711,x41712,x41713)),f319(f319(f130(x41711),f319(f182(f907(x41711)),f169(x41711,x41712,x41713))),x41713)),x41713)
% 22.40/22.29 [4174]E(f319(f73(f913(f912(x41741,x41742),a904)),f319(f319(f246(x41741,x41742),x41743),f319(f18(f913(x41742,a904),x41741),f234(f913(x41742,a904))))),f319(f319(f246(x41741,x41742),f319(f73(f913(x41741,a904)),x41743)),f319(f18(f913(x41742,a904),x41741),f234(f913(x41742,a904)))))
% 22.40/22.29 [4175]E(f319(f73(f913(f912(x41751,x41752),a904)),f319(f319(f246(x41751,x41752),f234(f913(x41751,a904))),f319(f18(f913(x41752,a904),x41751),x41753))),f319(f319(f246(x41751,x41752),f234(f913(x41751,a904))),f319(f18(f913(x41752,a904),x41751),f319(f73(f913(x41752,a904)),x41753))))
% 22.40/22.29 [4224]E(f319(f319(f33(f913(x42241,a904),f913(x42241,a904)),x42242),f319(f319(f9(f913(x42241,a904),f913(x42241,a904),f913(x42241,a904)),f94(f913(x42241,a904))),x42243)),f319(f319(f94(f913(x42241,a904)),f31(f913(x42241,a904),x42242)),x42243))
% 22.40/22.29 [4231]E(f319(f134(f907(x42311),f907(x42311),f126(x42311),f105(x42311)),f319(f319(f143(f907(x42311)),x42312),x42313)),f319(f319(f126(x42311),x42312),f319(f134(f907(x42311),f907(x42311),f126(x42311),f105(x42311)),x42313)))
% 22.40/22.29 [4251]E(f319(f319(f301(f913(x42511,a904)),f319(f277(x42511,x42511,x42512),f319(f319(f301(x42511),x42513),f181(f913(x42511,a904))))),f181(f913(f913(x42511,a904),a904))),f319(f319(f54(x42511),f319(f319(f301(x42511),x42513),f181(f913(x42511,a904)))),x42512))
% 22.40/22.29 [4261]E(f319(f319(f74(a906),f319(f319(f75(a906),x42611),f319(f319(f30(a906),x42612),x42613))),f319(f319(f30(a906),f319(f319(f75(a906),x42611),f39(a906,x42612,x42613))),x42613)),f319(f319(f30(a906),f319(f319(f75(a906),x42611),x42612)),x42613))
% 22.40/22.29 [4262]E(f319(f319(f74(a1),f319(f319(f75(a1),x42621),f319(f319(f30(a1),x42622),x42623))),f319(f319(f30(a1),f319(f319(f75(a1),x42621),f39(a1,x42622,x42623))),x42623)),f319(f319(f30(a1),f319(f319(f75(a1),x42621),x42622)),x42623))
% 22.40/22.29 [4290]E(f319(f319(f3(f913(x42901,a904)),f319(f164(x42901),x42902)),f319(f319(f301(x42901),x42903),f181(f913(x42901,a904)))),f319(f164(x42901),f319(f128(x42901,f319(f319(f10(a904,a904,x42901),a314),f319(a316,x42903))),x42902)))
% 22.40/22.29 [4342]E(f319(f319(f126(x43421),f319(f134(f907(x43421),f907(x43421),f126(x43421),f105(x43421)),x43422)),f319(f134(f907(x43421),f907(x43421),f126(x43421),f105(x43421)),x43423)),f319(f134(f907(x43421),f907(x43421),f126(x43421),f105(x43421)),f319(f319(f126(f907(x43421)),x43422),x43423)))
% 22.40/22.29 [4346]E(f319(f319(f244(f907(x43461),f907(x43461)),f319(f128(x43461,x43462),x43463)),f319(f128(x43461,f319(f66(a904,a904,x43461,a314),x43462)),x43463)),f158(x43461,x43462,x43463))
% 22.40/22.29 [4350]E(f319(f319(f74(a906),f319(f319(f74(a906),f319(f319(f30(a906),x43501),x43502)),f319(f319(f30(a906),x43503),x43502))),f319(f319(f30(a906),f319(f319(f74(a906),f39(a906,x43501,x43502)),f39(a906,x43503,x43502))),x43502)),f319(f319(f30(a906),f319(f319(f74(a906),x43501),x43503)),x43502))
% 22.40/22.29 [4351]E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f30(a1),x43511),x43512)),f319(f319(f30(a1),x43513),x43512))),f319(f319(f30(a1),f319(f319(f74(a1),f39(a1,x43511,x43512)),f39(a1,x43513,x43512))),x43512)),f319(f319(f30(a1),f319(f319(f74(a1),x43511),x43513)),x43512))
% 22.40/22.29 [4405]E(f319(f319(f94(f913(f907(x44051),a904)),f319(f319(f9(f907(x44051),f913(f907(x44051),a904),a904),f321(f907(x44051))),f153(x44051,x44052))),f319(f319(f9(f907(x44051),f913(f907(x44051),a904),a904),f321(f907(x44051))),f153(x44051,x44053))),f152(x44051,f319(f319(f94(f913(x44051,a904)),f319(f319(f9(x44051,f913(x44051,a904),a904),f321(x44051)),x44052)),f319(f319(f9(x44051,f913(x44051,a904),a904),f321(x44051)),x44053))))
% 22.40/22.29 [4416]E(f319(f254(x44161),f319(f319(f20(x44161,a904,a904),f319(f319(f10(a904,f913(a904,a904),x44161),a318),f319(f319(f9(x44161,x44161,a904),a316),x44162))),f319(f319(f9(x44161,f913(x44161,a904),a904),f321(x44161)),x44163))),f319(f319(f301(x44161),x44162),x44163))
% 22.40/22.29 [4438]E(f319(f319(f82(f907(f907(x44381)),f907(f907(x44381))),f48(x44381,x44382)),f319(f319(f20(f907(f907(x44381)),f907(f907(x44381)),f907(f907(x44381))),f319(f319(f10(f907(f907(x44381)),f913(f907(f907(x44381)),f907(f907(x44381))),f907(f907(x44381))),f126(f907(x44381))),f319(f146(f907(x44381),f907(x44381)),f319(f143(x44381),x44383)))),f7(f907(f907(x44381))))),f48(x44381,f319(f319(f143(x44381),x44383),x44382)))
% 22.40/22.29 [4441]E(f319(f254(x44411),f319(f319(f20(x44411,a904,a904),f319(f319(f10(a904,f913(a904,a904),x44411),a318),f319(f319(f9(x44411,f913(x44411,a904),a904),f321(x44411)),x44412))),f319(f319(f9(x44411,f913(x44411,a904),a904),f321(x44411)),x44413))),f319(f319(f93(f913(x44411,a904)),x44412),x44413))
% 22.40/22.29 [4442]E(f319(f254(x44421),f319(f319(f20(x44421,a904,a904),f319(f319(f10(a904,f913(a904,a904),x44421),a317),f319(f319(f9(x44421,f913(x44421,a904),a904),f321(x44421)),x44422))),f319(f319(f9(x44421,f913(x44421,a904),a904),f321(x44421)),x44423))),f319(f319(f94(f913(x44421,a904)),x44422),x44423))
% 22.40/22.29 [4530]E(f319(f319(f33(x45301,f913(f913(x45301,a904),a904)),x45302),f319(f319(f9(x45301,f913(f913(x45301,a904),a904),f913(f913(x45301,a904),a904)),f319(f319(f10(f913(x45301,a904),f913(f913(f913(x45301,a904),a904),f913(f913(x45301,a904),a904)),x45301),f301(f913(x45301,a904))),f319(f319(f10(f913(x45301,a904),f913(x45301,a904),x45301),f277(x45301,x45301,x45303)),f319(f319(f9(x45301,f913(x45301,a904),f913(x45301,a904)),f301(x45301)),f181(f913(x45301,a904)))))),f181(f913(f913(x45301,a904),a904)))),f319(f319(f54(x45301),x45302),x45303))
% 22.40/22.29 [4539]E(f319(f319(f194(x45391),f319(f319(f75(a1),f319(f319(f66(f912(a1,a1),a1,x45391,f243(a1,a1)),f205(x45391)),x45392)),f319(f319(f66(f912(a1,a1),a1,x45391,f243(a1,a1)),f205(x45391)),x45393))),f319(f319(f75(a1),f319(f319(f66(f912(a1,a1),a1,x45391,f248(a1,a1)),f205(x45391)),x45392)),f319(f319(f66(f912(a1,a1),a1,x45391,f248(a1,a1)),f205(x45391)),x45393))),f221(x45391,x45392,x45393))
% 22.40/22.29 [4543]E(f319(f254(f907(x45431)),f319(f319(f20(f907(x45431),a904,a904),f319(f319(f10(a904,f913(a904,a904),f907(x45431)),a317),f319(f319(f9(f907(x45431),a906,a904),f319(f319(f10(a906,f913(a906,a904),f907(x45431)),a316),f182(f907(x45431)))),x45432))),f319(f319(f9(f907(x45431),f913(x45431,a904),a904),f319(f319(f10(f913(x45431,a904),f913(f913(x45431,a904),a904),f907(x45431)),f225(f913(x45431,a904))),f164(x45431))),f319(f164(x45431),x45433)))),f319(f164(f907(x45431)),f49(x45431,x45432,x45433)))
% 22.40/22.29 [3950]E(f39(a906,f319(f319(f74(a906),f319(f319(f75(a906),x39501),x39502)),x39503),x39502),f39(a906,x39503,x39502))
% 22.40/22.29 [3993]E(f131(a906,f319(f294(a906,f319(f319(f74(a906),x39931),x39932)),x39933)),f319(f319(f130(a906),x39932),f131(a906,f319(f294(a906,x39931),x39933))))
% 22.40/22.29 [4030]E(f319(f319(f74(a1),f319(f92(a1),x40301)),f319(f319(f74(a1),f319(f92(a1),x40302)),x40303)),f319(f319(f74(a1),f319(f92(a1),f319(f319(f74(a906),x40301),x40302))),x40303))
% 22.40/22.29 [4036]E(f319(f319(f93(f913(x40361,a904)),f319(f319(f3(f913(x40361,a904)),x40362),x40363)),x40363),f319(f319(f93(f913(x40361,a904)),x40362),x40363))
% 22.40/22.29 [4037]E(f319(f319(f3(f913(x40371,a904)),f319(f319(f3(f913(x40371,a904)),x40372),x40373)),x40373),f319(f319(f3(f913(x40371,a904)),x40372),x40373))
% 22.40/22.29 [4061]E(f319(f319(f281(x40611,x40611,x40612),f299(x40611,f181(f913(f912(x40611,x40611),a904)))),x40613),x40613)
% 22.40/22.29 [4069]E(f319(f319(f93(f913(x40691,a904)),f319(f273(x40691),x40692)),f319(f273(x40691),x40693)),f319(f273(x40691),f319(f319(f93(f913(f912(x40691,x40691),a904)),x40692),x40693)))
% 22.40/22.29 [4079]E(f258(x40791,f319(f319(f143(f912(a91,x40791)),f319(f319(f244(a91,x40791),f2(a91)),x40792)),x40793)),f258(x40791,x40793))
% 22.40/22.29 [4081]E(f319(f319(f94(f913(x40811,a904)),f32(f913(x40811,a904),x40812)),f32(f913(x40811,a904),x40813)),f32(f913(x40811,a904),f319(f319(f93(f913(f913(x40811,a904),a904)),x40812),x40813)))
% 22.40/22.29 [4082]E(f319(f319(f93(f913(x40821,a904)),f31(f913(x40821,a904),x40822)),f31(f913(x40821,a904),x40823)),f31(f913(x40821,a904),f319(f319(f93(f913(f913(x40821,a904),a904)),x40822),x40823)))
% 22.40/22.29 [4121]E(f319(f319(f281(x41211,x41211,x41211),f319(f319(f175(f912(x41211,x41211),a904),x41212),x41213)),x41213),f319(f319(f175(f912(x41211,x41211),a904),f319(a104,x41212)),x41213))
% 22.40/22.29 [4163]P1(f319(f319(f225(f913(x41631,a904)),f319(f319(f94(f913(x41631,a904)),x41632),x41633)),x41633))
% 22.40/22.29 [4164]P1(f319(f319(f225(f913(x41641,a904)),f319(f319(f94(f913(x41641,a904)),x41642),x41643)),x41642))
% 22.40/22.29 [4165]P1(f319(f319(f225(f913(x41651,a904)),f319(f319(f3(f913(x41651,a904)),x41652),x41653)),x41652))
% 22.40/22.29 [4188]E(f299(x41881,f319(f319(f93(f913(f912(x41881,x41881),a904)),f299(x41881,x41882)),f299(x41881,x41883))),f299(x41881,f319(f319(f93(f913(f912(x41881,x41881),a904)),x41882),x41883)))
% 22.40/22.29 [4192]E(f31(f913(x41921,a904),f319(f319(f301(f913(x41921,a904)),x41922),f319(f319(f301(f913(x41921,a904)),x41923),f181(f913(f913(x41921,a904),a904))))),f319(f319(f93(f913(x41921,a904)),x41922),x41923))
% 22.40/22.29 [4193]E(f32(f913(x41931,a904),f319(f319(f301(f913(x41931,a904)),x41932),f319(f319(f301(f913(x41931,a904)),x41933),f181(f913(f913(x41931,a904),a904))))),f319(f319(f94(f913(x41931,a904)),x41932),x41933))
% 22.40/22.29 [4198]E(f319(f319(f281(x41981,x41981,x41981),f319(f319(f175(f912(x41981,x41981),a904),x41982),x41983)),x41983),f319(f319(f281(x41981,x41981,x41981),x41983),f319(f319(f175(f912(x41981,x41981),a904),x41982),x41983)))
% 22.40/22.29 [4265]E(f319(f319(f93(f913(x42651,a904)),f319(f254(x42651),f319(f319(f9(x42651,x42651,a904),a316),x42652))),x42653),f319(f319(f301(x42651),x42652),x42653))
% 22.40/22.29 [4266]E(f319(a97,f319(f319(f8(x42661,a1),f319(f319(f10(a906,a1,x42661),f92(a1)),x42662)),x42663)),f319(f319(f8(x42661,a906),x42662),x42663))
% 22.40/22.29 [4267]E(f319(a97,f319(f319(f11(x42671,a1),f319(f319(f10(a906,a1,x42671),f92(a1)),x42672)),x42673)),f319(f319(f11(x42671,a906),x42672),x42673))
% 22.40/22.29 [4339]E(f319(f148(f907(x43391),x43391,f319(f163(x43391),x43392),f319(f18(f913(f907(x43391),f907(x43391)),x43391),f319(f319(f9(f907(x43391),f907(x43391),f907(x43391)),f126(x43391)),x43392))),x43393),f319(f163(x43391),f319(f319(f126(x43391),x43393),x43392)))
% 22.40/22.29 [4367]P1(f319(f319(f225(f913(f913(x43671,a904),a904)),f319(f319(f93(f913(f913(x43671,a904),a904)),f319(f300(x43671),x43672)),f319(f300(x43671),x43673))),f319(f300(x43671),f319(f319(f93(f913(x43671,a904)),x43672),x43673))))
% 22.40/22.29 [4456]E(f319(f254(x44561),f319(f319(f20(x44561,a904,a904),f319(f319(f10(a904,f913(a904,a904),x44561),a317),f319(f319(f9(x44561,f913(x44561,a904),a904),f321(x44561)),x44562))),f319(f319(f10(a904,a904,x44561),a314),f319(f319(f9(x44561,f913(x44561,a904),a904),f321(x44561)),x44563)))),f319(f319(f3(f913(x44561,a904)),x44562),x44563))
% 22.40/22.29 [4482]E(f319(f29(a906),f319(f254(a906),f319(f319(f20(a906,a904,a904),f319(f319(f10(a904,f913(a904,a904),a906),a317),f319(f319(f9(a906,a906,a904),f226(a906)),f319(f182(f907(x44821)),x44822)))),f319(f319(f10(x44821,a904,a906),x44823),f319(f156(x44821),x44822))))),f319(f182(f907(x44821)),f319(f128(x44821,x44823),x44822)))
% 22.40/22.29 [4484]E(f319(f182(f907(x44841)),f168(x44841,x44842,x44843)),f319(f29(a906),f319(f254(a906),f319(f319(f20(a906,a904,a904),f319(f319(f10(a904,f913(a904,a904),a906),a317),f319(f319(f9(a906,a906,a904),f226(a906)),f319(f182(f907(x44841)),x44842)))),f319(f319(f9(a906,f913(a906,a904),a904),f321(a906)),x44843)))))
% 22.40/22.29 [4594]E(f319(f319(f94(f913(f912(f907(x45941),f907(x45941)),a904)),f319(f302(f912(f912(x45941,f907(x45941)),f912(x45941,f907(x45941))),f912(f907(x45941),f907(x45941)),f250(f912(x45941,f907(x45941)),f907(x45941),f912(x45941,f907(x45941)),f907(x45941),f319(f249(x45941,f907(x45941),f907(x45941)),f143(x45941)),f319(f249(x45941,f907(x45941),f907(x45941)),f143(x45941)))),f312(x45941,f907(x45941),x45942,f319(f135(x45941,x45942),x45943)))),f319(f254(f912(f907(x45941),f907(x45941))),f319(f249(f907(x45941),f907(x45941),a904),f319(f319(f9(f907(x45941),f913(f907(x45941),a904),f913(f907(x45941),a904)),f319(f319(f10(f913(a904,a904),f913(f913(f907(x45941),a904),f913(f907(x45941),a904)),f907(x45941)),f10(a904,a904,f907(x45941))),f319(f319(f10(a904,f913(a904,a904),f907(x45941)),a317),f319(f319(f9(f907(x45941),a906,a904),f319(f319(f10(a906,f913(a906,a904),f907(x45941)),a316),f182(f907(x45941)))),f319(a104,x45943))))),f319(f319(f9(f907(x45941),a906,a904),f319(f319(f10(a906,f913(a906,a904),f907(x45941)),a316),f182(f907(x45941)))),f319(a104,x45943)))))),f319(f135(x45941,x45942),f319(a104,x45943)))
% 22.40/22.29 [4083]E(f39(a906,f319(a104,f319(f319(f74(a906),f319(f319(f75(a906),x40831),x40832)),x40833)),x40832),f39(a906,f319(a104,x40833),x40832))
% 22.40/22.29 [4321]E(f319(f254(x43211),f319(f319(f20(x43211,a904,a904),f319(f319(f10(a904,f913(a904,a904),x43211),a317),x43212)),x43213)),f319(f319(f94(f913(x43211,a904)),f319(f254(x43211),x43212)),f319(f254(x43211),x43213)))
% 22.40/22.29 [4322]E(f319(f254(x43221),f319(f319(f20(x43221,a904,a904),f319(f319(f10(a904,f913(a904,a904),x43221),a318),x43222)),x43223)),f319(f319(f93(f913(x43221,a904)),f319(f254(x43221),x43222)),f319(f254(x43221),x43223)))
% 22.40/22.29 [4324]E(f319(f319(f126(x43241),f319(f319(f130(x43241),f39(a906,x43242,f319(f182(f907(x43241)),x43243))),x43243)),f319(f319(f167(x43241),f39(a906,x43242,f319(f182(f907(x43241)),x43243))),x43243)),f319(f319(f319(f175(f907(x43241),f907(x43241)),x43242),f159(x43241)),x43243))
% 22.40/22.29 [4330]E(f319(f254(x43301),f319(f319(f20(x43301,a904,a904),f319(f319(f10(a904,f913(a904,a904),x43301),a322),x43302)),x43303)),f319(f319(f93(f913(x43301,a904)),f319(f73(f913(x43301,a904)),f319(f254(x43301),x43302))),f319(f254(x43301),x43303)))
% 22.40/22.29 [4352]E(f319(f319(f74(a906),f319(f182(f907(x43521)),f319(f128(x43521,x43522),x43523))),f319(f182(f907(x43521)),f319(f128(x43521,f319(f319(f10(a904,a904,x43521),a314),x43522)),x43523))),f319(f182(f907(x43521)),x43523))
% 22.40/22.29 [4375]P1(f319(f319(f225(f913(x43751,a904)),f319(f319(f93(f913(x43751,a904)),f32(f913(x43751,a904),x43752)),f32(f913(x43751,a904),x43753))),f32(f913(x43751,a904),f319(f319(f94(f913(f913(x43751,a904),a904)),x43752),x43753))))
% 22.40/22.29 [4388]E(f319(f164(x43881),f319(f128(x43881,f319(f319(f10(a904,a904,x43881),a314),f319(f319(f9(x43881,x43881,a904),a316),x43882))),x43883)),f319(f319(f3(f913(x43881,a904)),f319(f164(x43881),x43883)),f319(f319(f301(x43881),x43882),f181(f913(x43881,a904)))))
% 22.40/22.29 [4397]P1(f319(f319(f225(f913(f912(x43971,x43971),a904)),f319(f319(f93(f913(f912(x43971,x43971),a904)),f299(x43971,x43972)),f299(x43971,x43973))),f299(x43971,f319(f319(f93(f913(f912(x43971,x43971),a904)),x43972),x43973))))
% 22.40/22.29 [4421]E(f319(f319(f75(a906),f319(a104,f319(a104,f2(a906)))),f319(f319(f8(a906,a906),f319(f319(f10(a906,a906,a906),f319(f74(a906),x44211)),f319(f319(f9(a906,a906,a906),f75(a906)),x44212))),f319(f274(a906),x44213))),f319(f319(f75(a906),x44213),f319(f319(f74(a906),x44211),f319(f319(f74(a906),x44211),f319(f319(f75(a906),f319(f319(f3(a906),x44213),f72(a906))),x44212)))))
% 22.40/22.29 [4433]E(f319(f254(x44331),f319(f319(f20(x44331,a904,a904),f319(f319(f10(a904,f913(a904,a904),x44331),a317),f319(f319(f9(x44331,f913(x44331,a904),a904),f321(x44331)),f319(f164(x44331),x44332)))),x44333)),f319(f164(x44331),f319(f128(x44331,x44333),x44332)))
% 22.40/22.29 [4593]E(f319(f254(x45931),f319(f319(f10(f913(a906,a904),a904,x45931),f80(a906)),f319(f319(f9(x45931,f913(a906,a904),f913(a906,a904)),f319(f319(f10(f913(a906,f913(a904,a904)),f913(f913(a906,a904),f913(a906,a904)),x45931),f20(a906,a904,a904)),f319(f319(f10(f913(a906,a904),f913(a906,f913(a904,a904)),x45931),f319(f10(a904,f913(a904,a904),a906),a317)),f319(f319(f9(x45931,f913(a906,x45931),f913(a906,a904)),f319(f319(f10(f913(x45931,a904),f913(f913(a906,x45931),f913(a906,a904)),x45931),f10(x45931,a904,a906)),a316)),f319(f156(x45931),x45932))))),f319(f319(f20(a906,a904,a904),f319(f319(f10(a904,f913(a904,a904),a906),a317),f319(f319(f9(a906,a906,a904),f226(a906)),f319(f182(f907(x45931)),x45932)))),f319(f319(f9(a906,f913(a906,a904),a904),f321(a906)),x45933))))),f319(f164(x45931),f168(x45931,x45932,x45933)))
% 22.40/22.29 [4470]E(f319(f254(x44701),f319(f319(f20(x44701,a904,a904),f319(f319(f10(a904,f913(a904,a904),x44701),a322),f319(f319(f10(a904,a904,x44701),a314),f319(f319(f9(x44701,x44701,a904),a316),x44702)))),x44703)),f319(f319(f301(x44701),x44702),f319(f254(x44701),x44703)))
% 22.40/22.29 [4508]E(f319(f319(f146(f912(x45081,a906),x45081),f243(x45081,a906)),f319(f128(f912(x45081,a906),f319(f319(f9(f912(x45081,a906),f913(a906,a904),a904),f319(f319(f10(a906,f913(f913(a906,a904),a904),f912(x45081,a906)),f321(a906)),f248(x45081,a906))),x45082)),f319(f319(f173(x45081,a906),x45083),f131(a906,f319(f294(a906,f2(a906)),f319(f182(f907(x45081)),x45083)))))),f168(x45081,x45083,x45082))
% 22.40/22.29 [4576]E(f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(f319(f8(a906,a1),f319(f319(f10(a1,a1,a906),f319(f74(a1),x45761)),f319(f319(f9(a906,a1,a1),f319(f319(f10(a1,f913(a1,a1),a906),f75(a1)),f92(a1))),x45762))),f319(f274(a906),x45763))),f319(f319(f75(a1),f319(f92(a1),x45763)),f319(f319(f74(a1),x45761),f319(f319(f74(a1),x45761),f319(f319(f75(a1),f319(f92(a1),f319(f319(f3(a906),x45763),f72(a906)))),x45762)))))
% 22.40/22.29 [4586]E(f319(f254(f912(x45861,x45862)),f319(f249(x45861,x45862,a904),f319(f319(f9(x45861,f913(f912(x45862,x45861),a904),f913(x45862,a904)),f319(f319(f10(f913(x45862,f913(f913(f912(x45862,x45861),a904),a904)),f913(f913(f912(x45862,x45861),a904),f913(x45862,a904)),x45861),f9(x45862,f913(f912(x45862,x45861),a904),a904)),f319(f319(f10(f913(x45862,f912(x45862,x45861)),f913(x45862,f913(f913(f912(x45862,x45861),a904),a904)),x45861),f319(f10(f912(x45862,x45861),f913(f913(f912(x45862,x45861),a904),a904),x45862),f321(f912(x45862,x45861)))),f319(f9(x45862,x45861,f912(x45862,x45861)),f244(x45862,x45861))))),x45863))),f319(f278(x45862,x45861),x45863))
% 22.40/22.29 [4605]E(f319(f254(f907(x46051)),f319(f319(f10(f913(x46051,a904),a904,f907(x46051)),f80(x46051)),f319(f319(f10(f913(x46051,f913(f907(x46051),a904)),f913(x46051,a904),f907(x46051)),f319(f10(f913(f907(x46051),a904),a904,x46051),f80(f907(x46051)))),f319(f319(f9(f907(x46051),f913(x46051,f913(f907(x46051),a904)),f913(x46051,f913(f907(x46051),a904))),f319(f319(f10(f913(x46051,f913(f913(f907(x46051),a904),f913(f907(x46051),a904))),f913(f913(x46051,f913(f907(x46051),a904)),f913(x46051,f913(f907(x46051),a904))),f907(x46051)),f20(x46051,f913(f907(x46051),a904),f913(f907(x46051),a904))),f319(f319(f10(f913(x46051,f913(f907(x46051),f913(a904,a904))),f913(x46051,f913(f913(f907(x46051),a904),f913(f907(x46051),a904))),f907(x46051)),f319(f10(f913(f907(x46051),f913(a904,a904)),f913(f913(f907(x46051),a904),f913(f907(x46051),a904)),x46051),f20(f907(x46051),a904,a904))),f319(f319(f10(f913(x46051,f913(f907(x46051),a904)),f913(x46051,f913(f907(x46051),f913(a904,a904))),f907(x46051)),f319(f10(f913(f907(x46051),a904),f913(f907(x46051),f913(a904,a904)),x46051),f319(f10(a904,f913(a904,a904),f907(x46051)),a317))),f319(f319(f9(f907(x46051),f913(x46051,f913(f907(x46051),f907(x46051))),f913(x46051,f913(f907(x46051),a904))),f319(f319(f10(f913(f913(f907(x46051),f907(x46051)),f913(f907(x46051),a904)),f913(f913(x46051,f913(f907(x46051),f907(x46051))),f913(x46051,f913(f907(x46051),a904))),f907(x46051)),f10(f913(f907(x46051),f907(x46051)),f913(f907(x46051),a904),x46051)),f319(f319(f10(f913(f907(x46051),a904),f913(f913(f907(x46051),f907(x46051)),f913(f907(x46051),a904)),f907(x46051)),f10(f907(x46051),a904,f907(x46051))),a316))),f143(x46051)))))),f319(f319(f9(x46051,f913(f907(x46051),a904),f913(f907(x46051),a904)),f319(f319(f10(f913(a904,a904),f913(f913(f907(x46051),a904),f913(f907(x46051),a904)),x46051),f10(a904,a904,f907(x46051))),f319(f319(f10(a904,f913(a904,a904),x46051),a317),f319(f319(f9(x46051,f913(x46051,a904),a904),f321(x46051)),x46052)))),f319(f319(f9(f907(x46051),f913(f907(x46051),a904),a904),f321(f907(x46051))),x46053)))))),f166(x46051,x46052,x46053))
% 22.40/22.29 [4606]E(f319(f319(f82(a1,f912(a1,a1)),f319(f319(f3(a1),x46061),x46062)),f319(f319(f9(a1,f912(a1,a1),f912(a1,a1)),f319(f319(f20(a1,f912(a1,a1),f913(f912(a1,a1),f912(a1,a1))),f319(f319(f10(a904,f913(f912(a1,a1),f913(f912(a1,a1),f912(a1,a1))),a1),f86(f912(a1,a1))),f319(f225(a1),f2(a1)))),f319(f244(a1,a1),f319(f319(f74(a1),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x46063)),f72(a1))))),f319(f319(f244(a1,a1),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x46063)),x46061))),f319(f37(x46062),f319(f319(f244(a1,a1),x46063),x46061)))
% 22.40/22.29 [3654]E(f108(x36541,f319(x36542,x36543),f319(x36544,x36543)),f319(f196(x36541,x36542,x36544),x36543))
% 22.40/22.29 [3706]E(f319(f319(f237(x37061,x37062,x37063),x37064),f2(a906)),x37062)
% 22.40/22.29 [3745]E(f177(x37451,x37452,x37453,f319(a104,x37454)),f319(x37453,x37454))
% 22.40/22.29 [3787]E(f162(x37871,x37872,f162(x37871,x37873,x37874)),f162(x37871,x37873,f162(x37871,x37872,x37874)))
% 22.40/22.29 [3788]E(f118(x37881,x37882,f108(x37881,x37883,x37884)),f108(x37881,f118(x37881,x37882,x37883),x37884))
% 22.40/22.29 [3918]E(f319(f148(x39181,x39182,x39183,x39184),f105(x39182)),x39183)
% 22.40/22.29 [3919]E(f319(f134(x39191,x39192,x39193,x39194),f105(x39192)),x39194)
% 22.40/22.29 [3956]E(f319(f182(f911(x39561,x39562)),f213(x39561,x39562,x39563,x39564)),f2(a906))
% 22.40/22.29 [3979]E(f319(f249(x39791,x39792,x39793),f247(x39791,x39792,x39793,x39794)),x39794)
% 22.40/22.29 [4019]E(f319(f319(f126(x40191),f161(x40191,x40192,x40193)),f161(x40191,x40194,x40193)),f319(f319(f126(x40191),f161(x40191,x40194,x40193)),f161(x40191,x40192,x40193)))
% 22.40/22.29 [4103]E(f319(f319(f251(x41031,x41032,x41033,f912(x41032,x41033)),x41034),f244(x41032,x41033)),x41034)
% 22.40/22.29 [4113]E(f119(x41131,x41132,x41133,x41134,f111(x41132)),x41133)
% 22.40/22.29 [4120]E(f68(x41201,x41202,x41203,x41204,f319(x41203,x41204)),x41203)
% 22.40/22.29 [4382]P43(x43821,x43822,x43823,x43824,f181(f913(x43821,a904)),x43824)
% 22.40/22.29 [3461]E(f319(f319(f18(x34611,x34612),x34613),x34614),x34613)
% 22.40/22.29 [3735]E(f162(x37351,x37352,f319(f128(x37351,x37353),x37354)),f319(f128(x37351,x37353),f162(x37351,x37352,x37354)))
% 22.40/22.29 [3770]E(f319(f319(f58(x37701,x37702,x37703),x37704),f181(f913(x37701,a904))),x37704)
% 22.40/22.29 [3795]E(f319(f319(f156(x37951),f319(f319(f143(x37951),x37952),x37953)),f319(a104,x37954)),f319(f319(f156(x37951),x37953),x37954))
% 22.40/22.29 [3861]E(f319(f319(x38611,x38612),f319(f176(x38613,x38614,x38611),x38612)),f319(f176(x38613,x38614,x38611),f319(a104,x38612)))
% 22.40/22.29 [3895]E(f247(x38951,x38952,x38953,f319(f249(x38951,x38952,x38953),x38954)),x38954)
% 22.40/22.29 [3954]E(f319(f319(f151(x39541,f319(f319(f143(x39541),x39542),x39543)),f2(a906)),x39544),f319(f319(f143(x39541),x39544),x39543))
% 22.40/22.29 [3964]E(f319(f319(f33(f913(x39641,a904),f913(x39642,a904)),x39643),f302(x39641,x39642,x39644)),f319(f302(x39641,x39642,x39644),f31(f913(x39641,a904),x39643)))
% 22.40/22.29 [3965]E(f319(f319(f33(f913(x39651,a904),f913(x39652,a904)),x39653),f303(x39652,x39651,x39654)),f319(f303(x39652,x39651,x39654),f31(f913(x39651,a904),x39653)))
% 22.40/22.29 [3988]E(f112(x39881,f122(x39882,f908(x39881),x39883,x39884)),f319(f110(x39882,x39881,x39884),x39883))
% 22.40/22.29 [4057]E(f319(f117(x40571,x40572),f118(x40571,x40573,x40574)),f319(f319(f74(a906),f319(f319(f74(a906),f319(x40572,x40573)),f319(f117(x40571,x40572),x40574))),f319(a104,f2(a906))))
% 22.40/22.29 [4078]E(f319(f134(x40781,x40782,f319(f9(x40782,x40781,x40781),x40783),x40784),f319(f160(x40782),f105(x40782))),x40784)
% 22.40/22.29 [4123]E(f70(x41231,x41232,x41233,x41234,f181(f913(x41231,a904))),x41233)
% 22.40/22.29 [4182]E(f216(x41821,f912(x41822,f908(x41822)),x41823,f319(f249(x41822,f908(x41822),x41821),x41824),f319(f127(x41822),f111(x41822))),x41823)
% 22.40/22.29 [4306]E(f319(f249(x43061,x43062,x43063),f319(f319(f10(f913(x43062,f912(x43061,x43062)),f913(x43062,x43063),x43061),f319(f10(f912(x43061,x43062),x43063,x43062),x43064)),f244(x43061,x43062))),x43064)
% 22.40/22.29 [3645]E(f319(f248(x36451,x36452),f319(f319(f244(x36451,x36452),x36453),x36454)),x36454)
% 22.40/22.29 [3646]E(f319(f243(x36461,x36462),f319(f319(f244(x36461,x36462),x36463),x36464)),x36463)
% 22.40/22.29 [3680]E(f319(f182(f907(x36801)),f319(f319(f151(x36801,x36802),x36803),x36804)),f319(f182(f907(x36801)),x36802))
% 22.40/22.29 [3681]E(f319(f182(f907(x36811)),f319(f319(f146(x36812,x36811),x36813),x36814)),f319(f182(f907(x36812)),x36814))
% 22.40/22.29 [3700]E(f319(f319(f130(x37001),f319(a104,x37002)),f319(f319(f143(x37001),x37003),x37004)),f319(f319(f130(x37001),x37002),x37004))
% 22.40/22.29 [3765]E(f319(f319(f167(x37651),x37652),f161(x37651,x37653,x37654)),f161(x37651,f319(f319(f230(a906),x37652),x37653),x37654))
% 22.40/22.29 [3766]E(f319(f319(f130(x37661),x37662),f161(x37661,x37663,x37664)),f161(x37661,f319(f319(f3(a906),x37663),x37662),x37664))
% 22.40/22.29 [3772]E(f319(f319(f301(x37721),x37722),f319(f319(f301(x37721),x37723),x37724)),f319(f319(f301(x37721),x37723),f319(f319(f301(x37721),x37722),x37724)))
% 22.40/22.29 [3776]E(f319(f319(f146(x37761,x37762),x37763),f106(x37761,x37764)),f106(x37762,f319(f319(f146(x37761,x37762),x37763),x37764)))
% 22.40/22.29 [3793]E(f319(f160(x37931),f319(f319(f146(x37932,x37931),x37933),x37934)),f319(f319(f146(x37932,x37931),x37933),f319(f160(x37932),x37934)))
% 22.40/22.29 [3794]E(f319(f319(f146(x37941,x37942),x37943),f319(f163(x37941),x37944)),f319(f163(x37942),f319(f319(f146(x37941,x37942),x37943),x37944)))
% 22.40/22.29 [3808]E(f319(f319(f167(x38081),f319(a104,x38082)),f319(f319(f143(x38081),x38083),x38084)),f319(f319(f143(x38081),x38083),f319(f319(f167(x38081),x38082),x38084)))
% 22.40/22.29 [3811]E(f319(f164(x38111),f319(f319(f146(x38112,x38111),x38113),x38114)),f319(f302(x38112,x38111,x38113),f319(f164(x38112),x38114)))
% 22.40/22.29 [3824]E(f319(f319(f146(x38241,x38242),f319(f18(x38242,x38241),x38243)),x38244),f161(x38242,f319(f182(f907(x38241)),x38244),x38243))
% 22.40/22.29 [3860]E(f19(x38601,x38602,x38603,f319(a5,f319(a104,f319(a22,x38604)))),f319(x38603,x38604))
% 22.40/22.29 [3864]E(f319(f319(f126(x38641),f319(f128(x38641,x38642),x38643)),f319(f128(x38641,x38642),x38644)),f319(f128(x38641,x38642),f319(f319(f126(x38641),x38643),x38644)))
% 22.40/22.29 [3871]E(f144(x38711,f319(f319(f146(x38712,x38711),x38713),f144(x38712,x38714))),f144(x38711,f319(f319(f146(x38712,x38711),x38713),x38714)))
% 22.40/22.29 [3885]E(f319(f278(x38851,x38851),f319(f319(f280(x38852,x38851),x38853),x38854)),f319(f319(f280(x38852,x38851),f319(f278(x38852,x38852),x38853)),x38854))
% 22.40/22.29 [3896]E(f319(f319(f281(x38961,x38962,x38963),x38964),f181(f913(f912(x38962,x38963),a904))),f181(f913(f912(x38961,x38963),a904)))
% 22.40/22.29 [3897]E(f319(f319(f167(x38971),f319(f319(f3(a906),x38972),x38973)),f319(f319(f130(x38971),x38973),x38974)),f319(f319(f130(x38971),x38973),f319(f319(f167(x38971),x38972),x38974)))
% 22.40/22.29 [3921]E(f319(f319(f126(x39211),f161(x39211,x39212,x39213)),f161(x39211,x39214,x39213)),f161(x39211,f319(f319(f74(a906),x39212),x39214),x39213))
% 22.40/22.29 [3922]E(f319(f319(f319(f270(x39221),x39222),x39223),x39224),f319(f244(f913(a91,f913(a904,f910(f908(x39221)))),f912(a91,a91)),f319(f36(x39221),x39222)))
% 22.40/22.29 [3947]E(f32(f913(x39471,a904),f319(f302(x39472,f913(x39471,a904),x39473),x39474)),f319(f319(f34(x39472,f913(x39471,a904)),x39474),x39473))
% 22.40/22.29 [3948]E(f31(f913(x39481,a904),f319(f302(x39482,f913(x39481,a904),x39483),x39484)),f319(f319(f33(x39482,f913(x39481,a904)),x39484),x39483))
% 22.40/22.29 [3949]E(f319(f182(f907(f912(x39491,x39492))),f319(f319(f173(x39491,x39492),x39493),x39494)),f319(f319(f230(a906),f319(f182(f907(x39491)),x39493)),f319(f182(f907(x39492)),x39494)))
% 22.40/22.29 [3951]E(f319(f303(x39511,x39512,x39513),f319(f73(f913(x39512,a904)),x39514)),f319(f73(f913(x39511,a904)),f319(f303(x39511,x39512,x39513),x39514)))
% 22.40/22.29 [3998]E(f319(f303(x39981,x39982,x39983),f319(f254(x39982),x39984)),f319(f254(x39981),f319(f319(f10(x39982,a904,x39981),x39984),x39983)))
% 22.40/22.29 [4015]E(f319(f319(f156(x40151),f319(f319(f126(x40151),x40152),f319(f319(f143(x40151),x40153),x40154))),f319(f182(f907(x40151)),x40152)),x40153)
% 22.40/22.29 [4034]E(f319(f302(x40341,x40342,x40343),f319(f303(x40341,x40342,x40343),x40344)),f319(f319(f94(f913(x40342,a904)),x40344),f319(f302(x40341,x40342,x40343),f234(f913(x40341,a904)))))
% 22.40/22.29 [4053]P1(f319(f319(f321(x40531),f319(x40532,x40533)),f319(f302(x40534,x40531,x40532),f234(f913(x40534,a904)))))
% 22.40/22.29 [4062]E(f21(x40621,x40622,x40623,f319(a5,f319(a104,f319(a22,x40624)))),f319(f319(x40623,x40624),f21(x40621,x40622,x40623,x40624)))
% 22.40/22.29 [4066]E(f319(f319(f126(x40661),f161(x40661,x40662,x40663)),f319(f319(f143(x40661),x40663),x40664)),f319(f319(f143(x40661),x40663),f319(f319(f126(x40661),f161(x40661,x40662,x40663)),x40664)))
% 22.40/22.29 [4068]E(f319(f319(f246(x40681,x40682),f319(f164(x40681),x40683)),f319(f18(f913(x40682,a904),x40681),f319(f164(x40682),x40684))),f319(f164(f912(x40681,x40682)),f53(x40681,x40682,x40683,x40684)))
% 22.40/22.29 [4080]E(f147(x40801,x40802,f319(f319(f143(x40801),x40803),x40804)),f319(f319(f74(a906),f319(f319(f74(a906),f319(x40802,x40803)),f147(x40801,x40802,x40804))),f319(a104,f2(a906))))
% 22.40/22.29 [4095]E(f177(f907(x40951),f319(f319(f143(x40951),x40952),x40953),f319(f319(f9(a906,f907(x40951),f907(x40951)),f130(x40951)),x40953),x40954),f319(f319(f130(x40951),x40954),f319(f319(f143(x40951),x40952),x40953)))
% 22.40/22.29 [4096]P25(x40961,f912(x40962,x40961),f323(x40963,x40964,x40962,x40961),f319(f319(f33(x40962,f913(x40961,a904)),x40964),x40963))
% 22.40/22.29 [4104]E(f319(f319(f3(f913(x41041,a904)),f319(f319(f3(f913(x41041,a904)),x41042),x41043)),f319(f319(f301(x41041),x41044),f181(f913(x41041,a904)))),f319(f319(f3(f913(x41041,a904)),x41042),f319(f319(f301(x41041),x41044),x41043)))
% 22.40/22.29 [4118]E(f319(f319(f175(f913(x41181,x41182),f913(x41181,x41182)),x41183),f66(x41182,x41182,x41181,x41184)),f66(x41182,x41182,x41181,f319(f319(f175(x41182,x41182),x41183),x41184)))
% 22.40/22.29 [4187]E(f319(f319(f319(f175(f907(x41871),f907(x41871)),x41872),f159(x41871)),f319(f319(f319(f175(f907(x41871),f907(x41871)),x41873),f159(x41871)),x41874)),f319(f319(f319(f175(f907(x41871),f907(x41871)),f319(f319(f74(a906),x41872),x41873)),f159(x41871)),x41874))
% 22.40/22.29 [4268]P1(f319(f319(f225(f913(x42681,a904)),f319(f164(x42681),f319(f319(f151(x42681,x42682),x42683),x42684))),f319(f319(f301(x42681),x42684),f319(f164(x42681),x42682))))
% 22.40/22.29 [4294]E(f319(f319(f33(f913(x42941,a904),f913(f912(x42941,x42942),a904)),x42943),f319(f319(f9(f913(x42941,a904),f913(x42941,f913(x42942,a904)),f913(f912(x42941,x42942),a904)),f246(x42941,x42942)),x42944)),f319(f319(f246(x42941,x42942),f31(f913(x42941,a904),x42943)),x42944))
% 22.40/22.29 [4338]E(f202(x43381,x43382,x43383,f319(f66(x43382,f913(a91,f913(a91,f913(f912(a91,a91),f913(a91,f908(x43382))))),x43381,f201(x43382)),x43384)),f203(x43381,x43382,x43384,x43383))
% 22.40/22.29 [4355]E(f198(x43551,x43552,x43553,f319(f66(x43552,f913(a91,f913(a91,f913(f912(a91,a91),f913(a91,f908(f910(x43552)))))),x43551,f197(x43552)),x43554)),f199(x43551,x43552,x43554,x43553))
% 22.40/22.29 [4362]P1(f319(f60(x43621,x43622,x43623,x43624,f181(f913(x43621,a904))),x43624))
% 22.40/22.29 [4400]E(f319(f319(f33(x44001,f913(x44002,a904)),x44003),f319(f319(f9(x44001,f913(x44002,a904),f913(x44002,a904)),f319(f319(f10(x44002,f913(f913(x44002,a904),f913(x44002,a904)),x44001),f301(x44002)),x44004)),f181(f913(x44002,a904)))),f319(f302(x44001,x44002,x44004),x44003))
% 22.40/22.29 [4407]P1(f319(f319(f225(f913(x44071,a904)),f319(f276(x44072,x44071),f319(f319(f94(f913(f912(x44072,x44071),a904)),x44073),x44074))),f319(f319(f94(f913(x44071,a904)),f319(f276(x44072,x44071),x44073)),f319(f276(x44072,x44071),x44074))))
% 22.40/22.29 [4408]P1(f319(f319(f225(f913(x44081,a904)),f319(f256(x44081,x44082),f319(f319(f94(f913(f912(x44081,x44082),a904)),x44083),x44084))),f319(f319(f94(f913(x44081,a904)),f319(f256(x44081,x44082),x44083)),f319(f256(x44081,x44082),x44084))))
% 22.40/22.29 [4466]P1(f319(f319(f225(f913(f912(x44661,x44662),a904)),f319(f302(x44662,f912(x44661,x44662),f323(x44663,x44664,x44661,x44662)),f319(f319(f33(x44661,f913(x44662,a904)),x44664),x44663))),f319(f319(f246(x44661,x44662),x44664),x44663)))
% 22.40/22.29 [4467]E(f319(f110(x44671,f912(x44671,x44672),x44673),f319(f319(f10(f913(x44672,f908(f912(x44671,x44672))),f908(f912(x44671,x44672)),x44671),f110(x44672,f912(x44671,x44672),x44674)),f319(f319(f10(f913(x44672,f912(x44671,x44672)),f913(x44672,f908(f912(x44671,x44672))),x44671),f319(f10(f912(x44671,x44672),f908(f912(x44671,x44672)),x44672),f121(f912(x44671,x44672)))),f244(x44671,x44672)))),f123(x44671,x44672,x44673,x44674))
% 22.40/22.29 [4468]E(f268(x44681,x44682,x44683,f319(f66(x44682,f913(a91,f913(a91,f913(f912(a91,a91),f912(f913(a91,f913(a904,f910(f908(x44682)))),f912(a91,a91))))),x44681,f270(x44682)),x44684)),f271(x44681,x44682,x44684,x44683))
% 22.40/22.29 [4514]E(f79(f912(x45141,x45142),f319(f249(x45141,x45142,a904),f319(f319(f9(x45141,f913(x45142,a904),f913(x45142,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x45142,a904),f913(x45142,a904)),x45141),f10(a904,a904,x45142)),f319(f319(f10(a904,f913(a904,a904),x45141),a317),f319(a316,x45143)))),f319(a316,x45144)))),f319(f319(f244(x45141,x45142),x45143),x45144))
% 22.40/22.29 [4515]E(f84(f912(x45151,x45152),f319(f249(x45151,x45152,a904),f319(f319(f9(x45151,f913(x45152,a904),f913(x45152,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x45152,a904),f913(x45152,a904)),x45151),f10(a904,a904,x45152)),f319(f319(f10(a904,f913(a904,a904),x45151),a317),f319(a316,x45153)))),f319(a316,x45154)))),f319(f319(f244(x45151,x45152),x45153),x45154))
% 22.40/22.29 [4595]E(f319(f319(f249(f907(x45951),f907(x45951),f912(f907(x45951),f907(x45951))),f319(f319(f20(f907(x45951),f913(f907(x45951),f912(f907(x45951),f907(x45951))),f913(f907(x45951),f912(f907(x45951),f907(x45951)))),f319(f319(f10(f913(f907(x45951),f913(f912(f907(x45951),f907(x45951)),f912(f907(x45951),f907(x45951)))),f913(f913(f907(x45951),f912(f907(x45951),f907(x45951))),f913(f907(x45951),f912(f907(x45951),f907(x45951)))),f907(x45951)),f20(f907(x45951),f912(f907(x45951),f907(x45951)),f912(f907(x45951),f907(x45951)))),f319(f319(f10(f913(f907(x45951),f912(f907(x45951),f907(x45951))),f913(f907(x45951),f913(f912(f907(x45951),f907(x45951)),f912(f907(x45951),f907(x45951)))),f907(x45951)),f319(f10(f912(f907(x45951),f907(x45951)),f913(f912(f907(x45951),f907(x45951)),f912(f907(x45951),f907(x45951))),f907(x45951)),f319(f86(f912(f907(x45951),f907(x45951))),f319(x45952,x45953)))),f319(f319(f10(f907(x45951),f913(f907(x45951),f912(f907(x45951),f907(x45951))),f907(x45951)),f244(f907(x45951),f907(x45951))),f319(f143(x45951),x45953))))),f319(f319(f9(f907(x45951),f913(f907(x45951),f907(x45951)),f913(f907(x45951),f912(f907(x45951),f907(x45951)))),f319(f319(f10(f913(f907(x45951),f912(f907(x45951),f907(x45951))),f913(f913(f907(x45951),f907(x45951)),f913(f907(x45951),f912(f907(x45951),f907(x45951)))),f907(x45951)),f10(f907(x45951),f912(f907(x45951),f907(x45951)),f907(x45951))),f244(f907(x45951),f907(x45951)))),f319(f143(x45951),x45953)))),f158(x45951,x45952,x45954)),f158(x45951,x45952,f319(f319(f143(x45951),x45953),x45954)))
% 22.40/22.29 [3840]E(f319(f319(f167(x38401),x38402),f319(f319(f167(x38401),x38403),x38404)),f319(f319(f167(x38401),f319(f319(f230(a906),x38402),x38403)),x38404))
% 22.40/22.29 [3841]E(f319(f319(f130(x38411),x38412),f319(f319(f130(x38411),x38413),x38414)),f319(f319(f130(x38411),f319(f319(f74(a906),x38412),x38413)),x38414))
% 22.40/22.29 [3852]E(f319(f319(f126(x38521),f319(f319(f143(x38521),x38522),x38523)),x38524),f319(f319(f143(x38521),x38522),f319(f319(f126(x38521),x38523),x38524)))
% 22.40/22.29 [3853]E(f319(f319(f126(x38531),f319(f319(f126(x38531),x38532),x38533)),x38534),f319(f319(f126(x38531),x38532),f319(f319(f126(x38531),x38533),x38534)))
% 22.40/22.29 [3932]E(f319(f319(f156(x39321),f319(f319(f143(x39321),x39322),x39323)),x39324),f177(x39321,x39322,f319(f156(x39321),x39323),x39324))
% 22.40/22.29 [3940]E(f319(f319(f175(x39401,x39401),x39402),f319(f319(f175(x39401,x39401),x39403),x39404)),f319(f319(f175(x39401,x39401),f319(f319(f75(a906),x39403),x39402)),x39404))
% 22.40/22.29 [3967]E(f319(f319(f93(f913(x39671,a904)),x39672),f319(f319(f301(x39671),x39673),x39674)),f319(f319(f301(x39671),x39673),f319(f319(f93(f913(x39671,a904)),x39672),x39674)))
% 22.40/22.29 [3982]E(f319(f319(f319(f175(x39821,x39821),x39822),x39823),f319(x39823,x39824)),f319(x39823,f319(f319(f319(f175(x39821,x39821),x39822),x39823),x39824)))
% 22.40/22.29 [3989]E(f319(f319(f281(x39891,x39892,x39893),f181(f913(f912(x39891,x39892),a904))),x39894),f181(f913(f912(x39891,x39893),a904)))
% 22.40/22.29 [4003]E(f319(f319(f93(f913(x40031,a904)),f319(f319(f301(x40031),x40032),x40033)),x40034),f319(f319(f301(x40031),x40032),f319(f319(f93(f913(x40031,a904)),x40033),x40034)))
% 22.40/22.29 [4021]E(f319(f29(f912(x40211,x40212)),f319(f319(f246(x40211,x40212),x40213),f319(f18(f913(x40212,a904),x40211),x40214))),f319(f319(f75(a906),f319(f29(x40211),x40213)),f319(f29(x40212),x40214)))
% 22.40/22.29 [4027]E(f319(f319(f94(f913(x40271,a904)),f319(f319(f301(x40271),x40272),x40273)),f319(f319(f301(x40271),x40272),x40274)),f319(f319(f301(x40271),x40272),f319(f319(f94(f913(x40271,a904)),x40273),x40274)))
% 22.40/22.29 [4038]E(f319(f319(f93(f913(x40381,a904)),x40382),f319(f319(f93(f913(x40381,a904)),x40383),x40384)),f319(f319(f93(f913(x40381,a904)),x40383),f319(f319(f93(f913(x40381,a904)),x40382),x40384)))
% 22.40/22.29 [4039]E(f319(f319(f94(f913(x40391,a904)),x40392),f319(f319(f94(f913(x40391,a904)),x40393),x40394)),f319(f319(f94(f913(x40391,a904)),x40393),f319(f319(f94(f913(x40391,a904)),x40392),x40394)))
% 22.40/22.29 [4049]E(f58(x40491,x40492,f319(f319(f10(x40492,f913(x40492,x40492),x40491),x40493),x40494)),f319(f59(x40492,x40491,x40493),x40494))
% 22.40/22.29 [4058]E(f171(x40581,f319(f319(f146(f907(x40582),f907(x40581)),f319(f146(x40582,x40581),x40583)),x40584)),f319(f319(f146(f907(x40582),f907(x40581)),f319(f146(x40582,x40581),x40583)),f171(x40582,x40584)))
% 22.40/22.29 [4077]E(f319(f134(f907(x40771),f907(x40771),f126(x40771),f105(x40771)),f319(f319(f146(x40772,f907(x40771)),x40773),x40774)),f155(x40772,x40771,x40773,x40774))
% 22.40/22.29 [4136]E(f319(f66(x41361,x41361,x41361,f319(f319(f175(x41361,x41361),x41362),x41363)),f319(f319(f175(x41361,x41361),x41364),x41363)),f319(f319(f175(x41361,x41361),f319(f319(f74(a906),x41362),x41364)),x41363))
% 22.40/22.29 [4158]E(f319(f319(f94(f913(x41581,a904)),f319(f319(f93(f913(x41581,a904)),x41582),x41583)),f319(f319(f93(f913(x41581,a904)),x41582),x41584)),f319(f319(f93(f913(x41581,a904)),x41582),f319(f319(f94(f913(x41581,a904)),x41583),x41584)))
% 22.40/22.29 [4159]E(f319(f319(f93(f913(x41591,a904)),f319(f319(f94(f913(x41591,a904)),x41592),x41593)),f319(f319(f94(f913(x41591,a904)),x41592),x41594)),f319(f319(f94(f913(x41591,a904)),x41592),f319(f319(f93(f913(x41591,a904)),x41593),x41594)))
% 22.40/22.29 [4160]E(f319(f319(f3(f913(x41601,a904)),f319(f319(f94(f913(x41601,a904)),x41602),x41603)),f319(f319(f94(f913(x41601,a904)),x41602),x41604)),f319(f319(f94(f913(x41601,a904)),x41602),f319(f319(f3(f913(x41601,a904)),x41603),x41604)))
% 22.40/22.29 [4161]E(f319(f319(f94(f913(x41611,a904)),f319(f319(f3(f913(x41611,a904)),x41612),x41613)),f319(f319(f3(f913(x41611,a904)),x41612),x41614)),f319(f319(f3(f913(x41611,a904)),x41612),f319(f319(f93(f913(x41611,a904)),x41613),x41614)))
% 22.40/22.29 [4162]E(f319(f319(f93(f913(x41621,a904)),f319(f319(f3(f913(x41621,a904)),x41622),x41623)),f319(f319(f3(f913(x41621,a904)),x41622),x41624)),f319(f319(f3(f913(x41621,a904)),x41622),f319(f319(f94(f913(x41621,a904)),x41623),x41624)))
% 22.40/22.29 [4167]E(f319(f29(f912(x41671,x41672)),f319(f319(f246(x41671,x41672),f319(f319(f301(x41671),x41673),f181(f913(x41671,a904)))),f319(f18(f913(x41672,a904),x41671),x41674))),f319(f29(x41672),x41674))
% 22.40/22.29 [4201]E(f319(f319(f34(x42011,f913(x42012,a904)),x42013),f319(f319(f10(f913(x42012,a904),f913(x42012,a904),x42011),f73(f913(x42012,a904))),x42014)),f319(f73(f913(x42012,a904)),f319(f319(f33(x42011,f913(x42012,a904)),x42013),x42014)))
% 22.40/22.29 [4202]E(f319(f319(f33(x42021,f913(x42022,a904)),x42023),f319(f319(f10(f913(x42022,a904),f913(x42022,a904),x42021),f73(f913(x42022,a904))),x42024)),f319(f73(f913(x42022,a904)),f319(f319(f34(x42021,f913(x42022,a904)),x42023),x42024)))
% 22.40/22.29 [4216]E(f319(f319(f281(x42161,x42161,x42161),f319(f319(f175(f912(x42161,x42161),a904),x42162),x42163)),f319(f319(f175(f912(x42161,x42161),a904),x42164),x42163)),f319(f319(f175(f912(x42161,x42161),a904),f319(f319(f74(a906),x42162),x42164)),x42163))
% 22.40/22.29 [4246]E(f319(f319(f34(x42461,f913(f913(x42462,a904),a904)),x42463),f319(f319(f10(f913(x42462,a904),f913(f913(x42462,a904),a904),x42461),f300(x42462)),x42464)),f319(f300(x42462),f319(f319(f34(x42461,f913(x42462,a904)),x42463),x42464)))
% 22.40/22.29 [4273]E(f319(f319(f33(f913(x42731,a904),f913(x42732,a904)),x42733),f319(f319(f9(f913(x42731,a904),f913(x42731,f913(x42732,a904)),f913(x42732,a904)),f33(x42731,f913(x42732,a904))),x42734)),f319(f319(f33(x42731,f913(x42732,a904)),f31(f913(x42731,a904),x42733)),x42734))
% 22.40/22.29 [4274]E(f319(f319(f34(f913(x42741,a904),f913(x42742,a904)),x42743),f319(f319(f9(f913(x42741,a904),f913(x42741,f913(x42742,a904)),f913(x42742,a904)),f34(x42741,f913(x42742,a904))),x42744)),f319(f319(f34(x42741,f913(x42742,a904)),f31(f913(x42741,a904),x42743)),x42744))
% 22.40/22.29 [4277]E(f319(f319(f146(x42771,x42772),x42773),f319(f134(f907(x42771),f907(x42771),f126(x42771),f105(x42771)),x42774)),f319(f134(f907(x42772),f907(x42772),f126(x42772),f105(x42772)),f319(f319(f146(f907(x42771),f907(x42772)),f319(f146(x42771,x42772),x42773)),x42774)))
% 22.40/22.29 [4279]E(f177(f907(x42791),f105(x42791),f319(f319(f10(f907(x42791),f907(x42791),a906),f319(f143(x42791),x42792)),f319(f319(f9(a906,f907(x42791),f907(x42791)),f167(x42791)),x42793)),x42794),f319(f319(f167(x42791),x42794),f319(f319(f143(x42791),x42792),x42793)))
% 22.40/22.29 [4315]P1(f319(f319(f225(f913(x43151,a904)),f319(f302(x43152,x43151,x43153),f319(f303(x43152,x43151,x43153),x43154))),x43154))
% 22.40/22.29 [4317]E(f319(f302(f912(x43171,x43172),f912(x43172,x43171),f319(f249(x43171,x43172,f912(x43172,x43171)),f319(f9(x43172,x43171,f912(x43172,x43171)),f244(x43172,x43171)))),f319(f319(f246(x43171,x43172),x43173),f319(f18(f913(x43172,a904),x43171),x43174))),f319(f319(f246(x43172,x43171),x43174),f319(f18(f913(x43171,a904),x43172),x43173)))
% 22.40/22.29 [4326]E(f319(f319(f33(x43261,f913(x43262,a904)),x43263),f319(f319(f10(f913(x43261,a904),f913(x43262,a904),x43261),f277(x43261,x43262,x43264)),f319(f319(f9(x43261,f913(x43261,a904),f913(x43261,a904)),f301(x43261)),f181(f913(x43261,a904))))),f319(f277(x43261,x43262,x43264),x43263))
% 22.40/22.29 [4327]E(f319(f319(f33(x43271,f913(x43272,a904)),x43273),f319(f319(f10(f913(x43271,a904),f913(x43272,a904),x43271),f303(x43272,x43271,x43274)),f319(f319(f9(x43271,f913(x43271,a904),f913(x43271,a904)),f301(x43271)),f181(f913(x43271,a904))))),f319(f303(x43272,x43271,x43274),x43273))
% 22.40/22.29 [4420]E(f319(f319(f94(f913(x44201,a904)),f319(f319(f94(f913(x44201,a904)),f319(f319(f93(f913(x44201,a904)),x44202),x44203)),f319(f319(f93(f913(x44201,a904)),x44203),x44204))),f319(f319(f93(f913(x44201,a904)),x44204),x44202)),f319(f319(f93(f913(x44201,a904)),f319(f319(f93(f913(x44201,a904)),f319(f319(f94(f913(x44201,a904)),x44202),x44203)),f319(f319(f94(f913(x44201,a904)),x44203),x44204))),f319(f319(f94(f913(x44201,a904)),x44204),x44202)))
% 22.40/22.29 [4483]E(f319(f134(f907(x44831),f907(x44831),f126(x44831),f105(x44831)),f319(f319(f146(x44832,f907(x44831)),f319(f319(f9(x44832,f907(x44831),f907(x44831)),f319(f319(f10(x44831,f913(f907(x44831),f907(x44831)),x44832),f143(x44831)),x44833)),f105(x44831))),x44834)),f319(f319(f146(x44832,x44831),x44833),x44834))
% 22.40/22.29 [4498]E(f319(f319(f82(a1,x44981),f319(f96(a1),f319(f319(f74(a1),x44982),a89))),f319(f319(f20(a1,x44981,x44981),f319(f319(f9(a1,x44981,f913(x44981,x44981)),f319(f319(f10(a904,f913(x44981,f913(x44981,x44981)),a1),f86(x44981)),a186)),x44983)),f319(f319(f10(a906,x44981,a1),x44984),a97))),f177(x44981,x44983,x44984,f319(f96(a906),x44982)))
% 22.40/22.29 [4527]E(f319(f254(x45271),f319(f319(f10(f913(x45272,a904),a904,x45271),f80(x45272)),f319(f319(f10(f913(x45272,a904),f913(x45272,a904),x45271),f319(f20(x45272,a904,a904),f319(f319(f10(a904,f913(a904,a904),x45272),a317),f319(f319(f9(x45272,f913(x45272,a904),a904),f321(x45272)),x45273)))),f319(f9(x45272,x45271,a904),x45274)))),f319(f277(x45272,x45271,f319(f254(f912(x45272,x45271)),f319(f249(x45272,x45271,a904),x45274))),x45273))
% 22.40/22.29 [4669]~P1(f319(f319(f181(f913(x46691,f913(x46692,a904))),x46693),x46694))
% 22.40/22.29 [3992]E(f319(f319(f156(x39921),f319(f319(f126(x39921),x39922),x39923)),f319(f319(f74(a906),f319(f182(f907(x39921)),x39922)),x39924)),f319(f319(f156(x39921),x39923),x39924))
% 22.40/22.29 [3997]E(f319(f319(f130(x39971),x39972),f319(f319(f167(x39971),f319(f319(f74(a906),x39973),x39972)),x39974)),f319(f319(f167(x39971),x39973),f319(f319(f130(x39971),x39972),x39974)))
% 22.40/22.29 [4093]E(f319(f319(f93(f913(x40931,a904)),f319(f276(x40932,x40931),x40933)),f319(f276(x40932,x40931),x40934)),f319(f276(x40932,x40931),f319(f319(f93(f913(f912(x40932,x40931),a904)),x40933),x40934)))
% 22.40/22.29 [4094]E(f319(f319(f93(f913(x40941,a904)),f319(f256(x40941,x40942),x40943)),f319(f256(x40941,x40942),x40944)),f319(f256(x40941,x40942),f319(f319(f93(f913(f912(x40941,x40942),a904)),x40943),x40944)))
% 22.40/22.29 [4098]E(f319(f319(f93(f913(x40981,a904)),f319(f319(f93(f913(x40981,a904)),x40982),x40983)),x40984),f319(f319(f93(f913(x40981,a904)),x40982),f319(f319(f93(f913(x40981,a904)),x40983),x40984)))
% 22.40/22.29 [4099]E(f319(f319(f94(f913(x40991,a904)),f319(f319(f94(f913(x40991,a904)),x40992),x40993)),x40994),f319(f319(f94(f913(x40991,a904)),x40992),f319(f319(f94(f913(x40991,a904)),x40993),x40994)))
% 22.40/22.29 [4100]E(f319(f319(f3(f913(x41001,a904)),f319(f319(f94(f913(x41001,a904)),x41002),x41003)),x41004),f319(f319(f94(f913(x41001,a904)),x41002),f319(f319(f3(f913(x41001,a904)),x41003),x41004)))
% 22.40/22.29 [4138]E(f319(f319(f93(f913(f912(x41381,x41382),a904)),f319(f278(x41382,x41381),x41383)),f319(f278(x41382,x41381),x41384)),f319(f278(x41382,x41381),f319(f319(f93(f913(f912(x41382,x41381),a904)),x41383),x41384)))
% 22.40/22.29 [4139]E(f319(f319(f94(f913(f912(x41391,x41392),a904)),f319(f278(x41392,x41391),x41393)),f319(f278(x41392,x41391),x41394)),f319(f278(x41392,x41391),f319(f319(f94(f913(f912(x41392,x41391),a904)),x41393),x41394)))
% 22.40/22.29 [4151]E(f319(f319(f93(f913(x41511,f913(x41512,a904))),f235(x41512,x41511,x41513)),f235(x41512,x41511,x41514)),f235(x41512,x41511,f319(f319(f93(f913(x41512,f913(x41511,a904))),x41513),x41514)))
% 22.40/22.29 [4152]E(f319(f319(f94(f913(x41521,f913(x41522,a904))),f235(x41522,x41521,x41523)),f235(x41522,x41521,x41524)),f235(x41522,x41521,f319(f319(f94(f913(x41522,f913(x41521,a904))),x41523),x41524)))
% 22.40/22.29 [4204]E(f319(f319(f94(f913(x42041,a904)),f319(f319(f93(f913(x42041,a904)),x42042),x42043)),f319(f319(f93(f913(x42041,a904)),x42044),x42043)),f319(f319(f93(f913(x42041,a904)),f319(f319(f94(f913(x42041,a904)),x42042),x42044)),x42043))
% 22.40/22.29 [4205]E(f319(f319(f93(f913(x42051,a904)),f319(f319(f94(f913(x42051,a904)),x42052),x42053)),f319(f319(f94(f913(x42051,a904)),x42054),x42053)),f319(f319(f94(f913(x42051,a904)),f319(f319(f93(f913(x42051,a904)),x42052),x42054)),x42053))
% 22.40/22.29 [4206]E(f319(f319(f3(f913(x42061,a904)),f319(f319(f94(f913(x42061,a904)),x42062),x42063)),f319(f319(f94(f913(x42061,a904)),x42064),x42063)),f319(f319(f94(f913(x42061,a904)),f319(f319(f3(f913(x42061,a904)),x42062),x42064)),x42063))
% 22.40/22.29 [4207]E(f319(f319(f93(f913(x42071,a904)),f319(f319(f3(f913(x42071,a904)),x42072),x42073)),f319(f319(f3(f913(x42071,a904)),x42074),x42073)),f319(f319(f3(f913(x42071,a904)),f319(f319(f93(f913(x42071,a904)),x42072),x42074)),x42073))
% 22.40/22.29 [4208]E(f319(f319(f3(f913(x42081,a904)),f319(f319(f94(f913(x42081,a904)),x42082),x42083)),f319(f319(f94(f913(x42081,a904)),x42084),x42083)),f319(f319(f3(f913(x42081,a904)),f319(f319(f94(f913(x42081,a904)),x42082),x42083)),x42084))
% 22.40/22.29 [4219]E(f319(f319(f3(f913(x42191,a904)),f319(f319(f3(f913(x42191,a904)),x42192),f319(f319(f301(x42191),x42193),f181(f913(x42191,a904))))),x42194),f319(f319(f3(f913(x42191,a904)),x42192),f319(f319(f301(x42191),x42193),x42194)))
% 22.40/22.29 [4270]E(f319(f319(f93(f913(x42701,a904)),f319(f319(f301(x42701),x42702),f319(f319(f301(x42701),x42703),f181(f913(x42701,a904))))),f319(f273(x42701),x42704)),f319(f273(x42701),f319(f319(f301(f912(x42701,x42701)),f319(f319(f244(x42701,x42701),x42702),x42703)),x42704)))
% 22.40/22.29 [4291]E(f319(f319(f33(a906,f913(x42911,a904)),f319(f293(a906),x42912)),f319(f319(f10(a906,f913(x42911,a904),a906),x42913),f319(f319(f9(a906,a906,a906),f74(a906)),x42914))),f319(f319(f33(a906,f913(x42911,a904)),f295(a906,x42914,f319(f319(f74(a906),x42912),x42914))),x42913))
% 22.40/22.29 [4292]E(f166(x42921,f319(f277(x42921,x42921,x42922),f319(f319(f301(x42921),x42923),f181(f913(x42921,a904)))),f319(f277(f907(x42921),f907(x42921),f150(x42921,x42922)),f319(f319(f301(f907(x42921)),x42924),f181(f913(f907(x42921),a904))))),f319(f277(f907(x42921),f907(x42921),f150(x42921,x42922)),f319(f319(f301(f907(x42921)),f319(f319(f143(x42921),x42923),x42924)),f181(f913(f907(x42921),a904)))))
% 22.40/22.29 [4365]E(f319(f254(x43651),f319(f319(f9(x43651,f913(x43652,a904),a904),f319(f319(f10(x43652,f913(f913(x43652,a904),a904),x43651),f321(x43652)),x43653)),x43654)),f319(f303(x43651,x43652,x43653),x43654))
% 22.40/22.29 [4449]E(f319(f254(x44491),f319(f319(f9(x44491,f913(f912(x44492,x44491),a904),a904),f319(f319(f10(f912(x44492,x44491),f913(f913(f912(x44492,x44491),a904),a904),x44491),f321(f912(x44492,x44491))),f319(f244(x44492,x44491),x44493))),x44494)),f319(f277(x44492,x44491,x44494),f319(f319(f301(x44492),x44493),f181(f913(x44492,a904)))))
% 22.40/22.29 [4465]E(f319(f319(f146(f912(x44651,a906),x44651),f243(x44651,a906)),f319(f128(f912(x44651,a906),f319(f319(f10(a906,a904,f912(x44651,a906)),x44652),f319(f319(f10(a906,a906,f912(x44651,a906)),a104),f248(x44651,a906)))),f319(f319(f173(x44651,a906),x44653),x44654))),f319(f319(f146(f912(x44651,a906),x44651),f243(x44651,a906)),f319(f128(f912(x44651,a906),f319(f319(f10(a906,a904,f912(x44651,a906)),x44652),f248(x44651,a906))),f319(f319(f173(x44651,a906),x44653),f319(f319(f146(a906,a906),a104),x44654)))))
% 22.40/22.29 [4474]P1(f319(f319(f225(f913(f913(x44741,a904),a904)),f319(f319(f33(x44742,f913(f913(x44741,a904),a904)),x44743),f319(f319(f10(f913(x44741,a904),f913(f913(x44741,a904),a904),x44742),f300(x44741)),x44744))),f319(f300(x44741),f319(f319(f33(x44742,f913(x44741,a904)),x44743),x44744))))
% 22.40/22.29 [4519]E(f319(f319(f82(a1,x45191),f319(f96(a1),f319(f319(f74(a1),x45192),a89))),f319(f319(f20(a1,x45191,x45191),f319(f319(f9(a1,x45191,f913(x45191,x45191)),f319(f319(f10(a904,f913(x45191,f913(x45191,x45191)),a1),f86(x45191)),a186)),x45193)),f319(f319(f20(a1,x45191,x45191),f319(f319(f10(a906,f913(x45191,x45191),a1),x45194),a97)),f319(f319(f10(a906,x45191,a1),f176(x45191,x45193,x45194)),a97)))),f319(f176(x45191,x45193,x45194),f319(f96(a906),x45192)))
% 22.40/22.29 [4549]E(f319(f254(f912(x45491,x45492)),f319(f249(x45491,x45492,a904),f319(f319(f9(x45491,f913(x45492,a904),f913(x45492,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x45492,a904),f913(x45492,a904)),x45491),f10(a904,a904,x45492)),f319(f319(f10(a904,f913(a904,a904),x45491),a317),f319(f319(f9(x45491,f913(x45491,a904),a904),f321(x45491)),x45493)))),f319(f319(f9(x45492,f913(x45492,a904),a904),f321(x45492)),x45494)))),f222(x45491,x45492,x45493,x45494))
% 22.40/22.29 [4590]E(f319(f319(f33(x45901,f913(f912(x45901,x45902),a904)),x45903),f319(f319(f20(x45901,f913(x45902,f913(f912(x45901,x45902),a904)),f913(f912(x45901,x45902),a904)),f319(f319(f10(f913(x45902,a904),f913(f913(x45902,f913(f912(x45901,x45902),a904)),f913(f912(x45901,x45902),a904)),x45901),f33(x45902,f913(f912(x45901,x45902),a904))),x45904)),f319(f319(f9(x45901,f913(f912(x45901,x45902),a904),f913(x45902,f913(f912(x45901,x45902),a904))),f319(f319(f10(f913(x45902,f913(f913(f912(x45901,x45902),a904),f913(f912(x45901,x45902),a904))),f913(f913(f912(x45901,x45902),a904),f913(x45902,f913(f912(x45901,x45902),a904))),x45901),f9(x45902,f913(f912(x45901,x45902),a904),f913(f912(x45901,x45902),a904))),f319(f319(f10(f913(x45902,f912(x45901,x45902)),f913(x45902,f913(f913(f912(x45901,x45902),a904),f913(f912(x45901,x45902),a904))),x45901),f319(f10(f912(x45901,x45902),f913(f913(f912(x45901,x45902),a904),f913(f912(x45901,x45902),a904)),x45902),f301(f912(x45901,x45902)))),f244(x45901,x45902)))),f181(f913(f912(x45901,x45902),a904))))),f319(f319(f246(x45901,x45902),x45903),x45904))
% 22.40/22.29 [4146]E(f319(f319(f126(x41461),f319(f319(f167(x41461),x41462),x41463)),f319(f319(f167(x41461),f319(f319(f3(a906),x41462),f319(f182(f907(x41461)),x41463))),x41464)),f319(f319(f167(x41461),x41462),f319(f319(f126(x41461),x41463),x41464)))
% 22.40/22.29 [4147]E(f319(f319(f126(x41471),f319(f319(f130(x41471),x41472),x41473)),f319(f319(f130(x41471),f319(f319(f3(a906),x41472),f319(f182(f907(x41471)),x41473))),x41474)),f319(f319(f130(x41471),x41472),f319(f319(f126(x41471),x41473),x41474)))
% 22.40/22.29 [4195]E(f319(f319(f74(a906),f319(f319(f75(a906),x41951),x41952)),f319(f319(f74(a906),f319(f319(f75(a906),x41953),x41952)),x41954)),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f74(a906),x41951),x41953)),x41952)),x41954))
% 22.40/22.29 [4336]E(f84(x43361,f319(f319(f9(x43361,x43362,a904),f319(f319(f10(x43362,f913(x43362,a904),x43361),a316),x43363)),x43364)),f319(f85(x43361,x43362,f234(f913(x43361,a904)),x43363),x43364))
% 22.40/22.29 [4385]P1(f319(f319(f225(f913(x43851,a904)),f319(f319(f3(f913(x43851,a904)),f319(f276(x43852,x43851),x43853)),f319(f276(x43852,x43851),x43854))),f319(f276(x43852,x43851),f319(f319(f3(f913(f912(x43852,x43851),a904)),x43853),x43854))))
% 22.40/22.29 [4386]P1(f319(f319(f225(f913(x43861,a904)),f319(f319(f3(f913(x43861,a904)),f319(f256(x43861,x43862),x43863)),f319(f256(x43861,x43862),x43864))),f319(f256(x43861,x43862),f319(f319(f3(f913(f912(x43861,x43862),a904)),x43863),x43864))))
% 22.40/22.29 [4500]E(f319(f319(f74(a1),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x45001),x45002)),f181(f913(f912(a906,a906),a904)))))),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x45003),x45004)),f181(f913(f912(a906,a906),a904)))))),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),f319(f319(f74(a906),x45001),x45003)),f319(f319(f74(a906),x45002),x45004))),f181(f913(f912(a906,a906),a904))))))
% 22.40/22.29 [4544]E(f319(f319(f75(a1),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x45441),x45442)),f181(f913(f912(a906,a906),a904)))))),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x45443),x45444)),f181(f913(f912(a906,a906),a904)))))),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),f319(f319(f74(a906),f319(f319(f75(a906),x45441),x45443)),f319(f319(f75(a906),x45442),x45444))),f319(f319(f74(a906),f319(f319(f75(a906),x45441),x45444)),f319(f319(f75(a906),x45442),x45443)))),f181(f913(f912(a906,a906),a904))))))
% 22.40/22.29 [4571]E(f319(f254(x45711),f319(f319(f10(f913(x45712,a904),a904,x45711),f81(x45712)),f319(f319(f10(f913(x45712,a904),f913(x45712,a904),x45711),f319(f20(x45712,a904,a904),f319(f319(f10(a904,f913(a904,a904),x45712),a322),f319(f319(f9(x45712,f913(x45712,a904),a904),f321(x45712)),x45713)))),f319(f319(f9(x45711,f913(x45712,f913(x45711,a904)),f913(x45712,a904)),f319(f319(f10(f913(f913(x45711,a904),a904),f913(f913(x45712,f913(x45711,a904)),f913(x45712,a904)),x45711),f10(f913(x45711,a904),a904,x45712)),f321(x45711))),x45714)))),f319(f319(f34(x45712,f913(x45711,a904)),x45713),x45714))
% 22.40/22.29 [4602]E(f319(f319(f281(x46021,x46021,x46021),f319(f319(f301(f912(x46021,x46021)),f319(f319(f244(x46021,x46021),x46022),x46023)),x46024)),f299(x46021,f319(f319(f301(f912(x46021,x46021)),f319(f319(f244(x46021,x46021),x46022),x46023)),x46024))),f319(f319(f93(f913(f912(x46021,x46021),a904)),f319(f319(f281(x46021,x46021,x46021),x46024),f299(x46021,x46024))),f319(f254(f912(x46021,x46021)),f319(f249(x46021,x46021,a904),f319(f319(f9(x46021,f913(x46021,a904),f913(x46021,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x46021,a904),f913(x46021,a904)),x46021),f10(a904,a904,x46021)),f319(f319(f10(a904,f913(a904,a904),x46021),a317),f319(f319(f9(x46021,f913(f912(x46021,x46021),a904),a904),f319(f319(f10(f912(x46021,x46021),f913(f913(f912(x46021,x46021),a904),a904),x46021),f321(f912(x46021,x46021))),f319(f319(f9(x46021,x46021,f912(x46021,x46021)),f244(x46021,x46021)),x46022))),f299(x46021,x46024))))),f319(f319(f9(x46021,f913(f912(x46021,x46021),a904),a904),f319(f319(f10(f912(x46021,x46021),f913(f913(f912(x46021,x46021),a904),a904),x46021),f321(f912(x46021,x46021))),f319(f244(x46021,x46021),x46023))),f299(x46021,x46024)))))))
% 22.40/22.29 [4387]E(f319(f128(x43871,f319(f319(f20(x43871,a904,a904),f319(f319(f10(a904,f913(a904,a904),x43871),a317),x43872)),x43873)),x43874),f319(f128(x43871,x43873),f319(f128(x43871,x43872),x43874)))
% 22.40/22.29 [4494]E(f319(f319(f126(x44941),f319(f319(f319(f86(f907(x44941)),f319(f319(f321(a906),f2(a906)),x44942)),f319(f319(f143(x44941),x44943),f105(x44941))),f105(x44941))),f168(x44941,x44944,f319(f254(a906),f319(f319(f9(a906,f913(a906,a904),a904),f319(f319(f10(a906,f913(f913(a906,a904),a904),a906),f321(a906)),a104)),x44942)))),f168(x44941,f319(f319(f143(x44941),x44943),x44944),x44942))
% 22.40/22.29 [4598]E(f319(f254(f912(x45981,x45982)),f319(f319(f10(f913(a906,a904),a904,f912(x45981,x45982)),f80(a906)),f319(f319(f9(f912(x45981,x45982),f913(a906,a904),f913(a906,a904)),f319(f319(f10(f913(a906,f913(a904,a904)),f913(f913(a906,a904),f913(a906,a904)),f912(x45981,x45982)),f20(a906,a904,a904)),f319(f319(f10(f913(a906,a904),f913(a906,f913(a904,a904)),f912(x45981,x45982)),f319(f10(a904,f913(a904,a904),a906),a317)),f319(f319(f9(f912(x45981,x45982),f913(a906,f912(x45981,x45982)),f913(a906,a904)),f319(f319(f10(f913(f912(x45981,x45982),a904),f913(f913(a906,f912(x45981,x45982)),f913(a906,a904)),f912(x45981,x45982)),f10(f912(x45981,x45982),a904,a906)),a316)),f319(f319(f20(a906,x45982,f912(x45981,x45982)),f319(f319(f10(x45981,f913(x45982,f912(x45981,x45982)),a906),f244(x45981,x45982)),f319(f156(x45981),x45983))),f319(f156(x45982),x45984)))))),f319(f319(f9(a906,a906,a904),f226(a906)),f319(f319(f230(a906),f319(f182(f907(x45981)),x45983)),f319(f182(f907(x45982)),x45984)))))),f319(f164(f912(x45981,x45982)),f319(f319(f173(x45981,x45982),x45983),x45984)))
% 22.40/22.29 [4513]E(f319(f254(f912(x45131,x45132)),f319(f249(x45131,x45132,a904),f319(f319(f9(x45131,f913(x45132,a904),f913(x45132,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x45132,a904),f913(x45132,a904)),x45131),f10(a904,a904,x45132)),f319(f319(f10(a904,f913(a904,a904),x45131),a317),x45133))),x45134))),f319(f319(f246(x45131,x45132),f319(f254(x45131),x45133)),f319(f18(f913(x45132,a904),x45131),f319(f254(x45132),x45134))))
% 22.40/22.29 [4516]E(f319(f254(f912(x45161,x45162)),f319(f249(x45161,x45162,a904),f319(f319(f20(x45161,f913(x45162,a904),f913(x45162,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x45162,a904),f913(x45162,a904)),x45161),f10(a904,a904,x45162)),f319(f319(f10(a904,f913(a904,a904),x45161),a317),x45163))),x45164))),f319(f319(f246(x45161,x45162),f319(f254(x45161),x45163)),f319(f319(f10(f913(x45162,a904),f913(x45162,a904),x45161),f254(x45162)),x45164)))
% 22.40/22.29 [4526]E(f319(f254(x45261),f319(f319(f10(f913(x45262,a904),a904,x45261),f81(x45262)),f319(f319(f10(f913(x45262,a904),f913(x45262,a904),x45261),f319(f20(x45262,a904,a904),f319(f319(f10(a904,f913(a904,a904),x45262),a322),f319(f319(f9(x45262,f913(x45262,a904),a904),f321(x45262)),x45263)))),x45264))),f319(f319(f34(x45262,f913(x45261,a904)),x45263),f319(f319(f10(f913(x45261,a904),f913(x45261,a904),x45262),f254(x45261)),f319(f9(x45261,x45262,a904),x45264))))
% 22.40/22.29 [4582]E(f319(f319(f146(f912(x45821,a906),x45821),f243(x45821,a906)),f319(f128(f912(x45821,a906),f319(f319(f9(f912(x45821,a906),f913(a906,a904),a904),f319(f319(f10(a906,f913(f913(a906,a904),a904),f912(x45821,a906)),f321(a906)),f248(x45821,a906))),x45822)),f319(f319(f173(x45821,a906),x45823),f131(a906,f319(f294(a906,x45824),f319(f319(f74(a906),x45824),f319(f182(f907(x45821)),x45823))))))),f319(f319(f146(f912(x45821,a906),x45821),f243(x45821,a906)),f319(f128(f912(x45821,a906),f319(f319(f9(f912(x45821,a906),f913(a906,a904),a904),f319(f319(f10(a906,f913(f913(a906,a904),a904),f912(x45821,a906)),f321(a906)),f319(f319(f9(f912(x45821,a906),a906,a906),f319(f319(f10(a906,f913(a906,a906),f912(x45821,a906)),f74(a906)),f248(x45821,a906))),x45824))),x45822)),f319(f319(f173(x45821,a906),x45823),f131(a906,f319(f294(a906,f2(a906)),f319(f182(f907(x45821)),x45823)))))))
% 22.40/22.29 [4583]E(f319(a104,f319(f319(f180(a906),f319(f182(f907(x45831)),x45832)),f319(f134(a906,f907(x45833),f319(f9(f907(x45833),a906,a906),f319(f319(f10(a906,f913(a906,a906),f907(x45833)),f180(a906)),f319(f319(f9(f907(x45833),a906,a906),f319(f319(f10(a906,f913(a906,a906),f907(x45833)),f3(a906)),f182(f907(x45833)))),f319(a104,f2(a906))))),f2(a906)),f319(f160(f907(x45833)),f319(f128(f907(x45833),f319(f319(f10(a904,a904,f907(x45833)),a314),f319(f319(f9(f907(x45833),f907(x45833),a904),a316),f105(x45833)))),x45834))))),f319(f319(f180(a906),f319(a104,f319(f182(f907(x45831)),x45832))),f319(f134(a906,f907(x45833),f319(f9(f907(x45833),a906,a906),f319(f319(f10(a906,f913(a906,a906),f907(x45833)),f180(a906)),f182(f907(x45833)))),f2(a906)),f319(f160(f907(x45833)),x45834))))
% 22.40/22.29 [4525]E(f319(f319(f126(x45251),f168(x45251,x45252,x45253)),f168(x45251,x45254,f319(f254(a906),f319(f319(f9(a906,f913(a906,a904),a904),f319(f319(f10(a906,f913(f913(a906,a904),a904),a906),f321(a906)),f319(f319(f9(a906,a906,a906),f74(a906)),f319(f182(f907(x45251)),x45252)))),x45253)))),f168(x45251,f319(f319(f126(x45251),x45252),x45254),x45253))
% 22.40/22.29 [4584]E(f31(f913(x45841,a904),f319(f254(f913(x45841,a904)),f319(f319(f10(f913(x45842,a904),a904,f913(x45841,a904)),f80(x45842)),f319(f319(f10(f913(x45842,a904),f913(x45842,a904),f913(x45841,a904)),f319(f20(x45842,a904,a904),f319(f319(f10(a904,f913(a904,a904),x45842),a317),f319(f319(f9(x45842,f913(x45842,a904),a904),f321(x45842)),x45843)))),f319(f319(f9(f913(x45841,a904),f913(x45842,f913(x45841,a904)),f913(x45842,a904)),f319(f319(f10(f913(f913(x45841,a904),a904),f913(f913(x45842,f913(x45841,a904)),f913(x45842,a904)),f913(x45841,a904)),f10(f913(x45841,a904),a904,x45842)),a316)),x45844))))),f319(f319(f33(x45842,f913(x45841,a904)),x45843),x45844))
% 22.40/22.29 [4585]E(f32(f913(x45851,a904),f319(f254(f913(x45851,a904)),f319(f319(f10(f913(x45852,a904),a904,f913(x45851,a904)),f80(x45852)),f319(f319(f10(f913(x45852,a904),f913(x45852,a904),f913(x45851,a904)),f319(f20(x45852,a904,a904),f319(f319(f10(a904,f913(a904,a904),x45852),a317),f319(f319(f9(x45852,f913(x45852,a904),a904),f321(x45852)),x45853)))),f319(f319(f9(f913(x45851,a904),f913(x45852,f913(x45851,a904)),f913(x45852,a904)),f319(f319(f10(f913(f913(x45851,a904),a904),f913(f913(x45852,f913(x45851,a904)),f913(x45852,a904)),f913(x45851,a904)),f10(f913(x45851,a904),a904,x45852)),a316)),x45854))))),f319(f319(f34(x45852,f913(x45851,a904)),x45853),x45854))
% 22.40/22.29 [4592]E(f319(f319(f143(f907(x45921)),f319(f319(f143(x45921),x45922),f319(f134(f907(x45921),f907(x45921),f126(x45921),f105(x45921)),f319(f319(f146(f907(x45921),f907(x45921)),f148(f907(x45921),x45921,f105(x45921),f319(f319(f10(f907(x45921),f913(f907(x45921),f907(x45921)),x45921),f18(f907(x45921),f907(x45921))),f319(f319(f9(x45921,f907(x45921),f907(x45921)),f143(x45921)),f105(x45921))))),x45923)))),f171(x45921,f319(f319(f143(f907(x45921)),x45924),f319(f134(f907(f907(x45921)),f907(f907(x45921)),f126(f907(x45921)),f105(f907(x45921))),f319(f319(f146(f907(x45921),f907(f907(x45921))),f148(f907(f907(x45921)),x45921,f105(f907(x45921)),f319(f18(f913(f907(x45921),f907(f907(x45921))),x45921),f319(f319(f9(f907(x45921),f907(f907(x45921)),f907(f907(x45921))),f143(f907(x45921))),f105(f907(x45921)))))),x45923))))),f171(x45921,f319(f319(f143(f907(x45921)),f319(f319(f143(x45921),x45922),x45924)),x45923)))
% 22.40/22.29 [4599]E(f319(f254(f912(x45991,x45991)),f319(f249(x45991,x45991,a904),f319(f319(f9(x45991,f913(f912(x45992,x45992),a904),f913(x45991,a904)),f319(f319(f10(f913(x45991,f913(f913(f912(x45992,x45992),a904),a904)),f913(f913(f912(x45992,x45992),a904),f913(x45991,a904)),x45991),f9(x45991,f913(f912(x45992,x45992),a904),a904)),f319(f319(f10(f913(x45991,f912(x45992,x45992)),f913(x45991,f913(f913(f912(x45992,x45992),a904),a904)),x45991),f319(f10(f912(x45992,x45992),f913(f913(f912(x45992,x45992),a904),a904),x45991),f321(f912(x45992,x45992)))),f319(f319(f9(x45991,f913(x45991,x45992),f913(x45991,f912(x45992,x45992))),f319(f319(f10(f913(x45992,f912(x45992,x45992)),f913(f913(x45991,x45992),f913(x45991,f912(x45992,x45992))),x45991),f10(x45992,f912(x45992,x45992),x45991)),f319(f319(f10(x45992,f913(x45992,f912(x45992,x45992)),x45991),f244(x45992,x45992)),x45993))),x45993)))),x45994))),f319(f319(f280(x45992,x45991),x45994),x45993))
% 22.40/22.29 [3736]E(f319(f319(f146(x37361,x37362),x37363),f161(x37361,x37364,x37365)),f161(x37362,x37364,f319(x37363,x37365)))
% 22.40/22.29 [4059]E(f122(x40591,x40592,x40593,f118(x40591,x40594,x40595)),f118(x40592,f319(x40593,x40594),f122(x40591,x40592,x40593,x40595)))
% 22.40/22.29 [4283]E(f319(f68(x42831,x42832,x42833,x42834,x42835),x42834),x42835)
% 22.40/22.29 [4337]E(f245(x43371,x43372,x43373,f235(x43372,x43371,x43374),f235(x43373,x43372,x43375)),f235(x43373,x43371,f245(x43373,x43372,x43371,x43375,x43374)))
% 22.40/22.29 [3926]E(f319(f319(f249(x39261,x39262,x39263),x39264),x39265),f319(f319(x39264,f319(f243(x39261,x39262),x39265)),f319(f248(x39261,x39262),x39265)))
% 22.40/22.29 [3959]E(f319(f319(f319(f59(x39591,x39592,x39593),x39594),x39595),f181(f913(x39592,a904))),x39595)
% 22.40/22.29 [4227]E(f319(f66(f907(x42271),f907(x42272),f907(x42273),f319(f146(x42271,x42272),x42274)),f319(f146(x42273,x42271),x42275)),f319(f146(x42273,x42272),f319(f66(x42271,x42272,x42273,x42274),x42275)))
% 22.40/22.29 [4293]E(f79(x42931,f60(x42932,x42931,x42933,x42934,x42935)),f319(f319(f58(x42932,x42931,x42933),x42934),x42935))
% 22.40/22.29 [4329]E(f319(f319(f74(a906),f319(f319(f74(a906),f319(x43291,f319(f243(x43292,x43293),x43294))),f319(x43295,f319(f248(x43292,x43293),x43294)))),f319(a104,f2(a906))),f253(x43292,x43293,x43291,x43295,x43294))
% 22.40/22.29 [3865]E(f319(f319(f167(x38651),x38652),f319(f319(f146(x38653,x38651),x38654),x38655)),f319(f319(f146(x38653,x38651),x38654),f319(f319(f167(x38653),x38652),x38655)))
% 22.40/22.29 [3866]E(f319(f319(f130(x38661),x38662),f319(f319(f146(x38663,x38661),x38664),x38665)),f319(f319(f146(x38663,x38661),x38664),f319(f319(f130(x38663),x38662),x38665)))
% 22.40/22.29 [3890]E(f319(f319(f146(x38901,x38902),x38903),f319(f319(f143(x38901),x38904),x38905)),f319(f319(f143(x38902),f319(x38903,x38904)),f319(f319(f146(x38901,x38902),x38903),x38905)))
% 22.40/22.29 [3955]E(f319(f302(x39551,x39552,x39553),f319(f319(f301(x39551),x39554),x39555)),f319(f319(f301(x39552),f319(x39553,x39554)),f319(f302(x39551,x39552,x39553),x39555)))
% 22.40/22.29 [3983]E(f165(x39831,f319(f319(f143(x39831),x39832),x39833),f319(f319(f143(x39831),x39834),x39835)),f319(f319(f143(x39831),x39832),f319(f319(f143(x39831),x39834),f165(x39831,x39833,x39835))))
% 22.40/22.29 [4017]E(f319(f319(f173(x40171,x40172),f319(f319(f167(x40171),x40173),x40174)),f319(f319(f167(x40172),x40173),x40175)),f319(f319(f167(f912(x40171,x40172)),x40173),f319(f319(f173(x40171,x40172),x40174),x40175)))
% 22.40/22.29 [4018]E(f319(f319(f173(x40181,x40182),f319(f319(f130(x40181),x40183),x40184)),f319(f319(f130(x40182),x40183),x40185)),f319(f319(f130(f912(x40181,x40182)),x40183),f319(f319(f173(x40181,x40182),x40184),x40185)))
% 22.40/22.29 [4026]E(f319(f319(f151(x40261,f319(f319(f143(x40261),x40262),x40263)),f319(a104,x40264)),x40265),f319(f319(f143(x40261),x40262),f319(f319(f151(x40261,x40263),x40264),x40265)))
% 22.40/22.29 [4028]E(f319(f319(f126(x40281),f319(f319(f146(x40282,x40281),x40283),x40284)),f319(f319(f146(x40282,x40281),x40283),x40285)),f319(f319(f146(x40282,x40281),x40283),f319(f319(f126(x40282),x40284),x40285)))
% 22.40/22.29 [4032]E(f319(f319(x40321,x40322),f319(f319(f237(x40323,x40324,x40321),x40322),x40325)),f319(f319(f237(x40323,x40324,x40321),x40322),f319(a104,x40325)))
% 22.40/22.29 [4063]E(f155(x40631,x40632,x40633,f319(f319(f143(x40631),x40634),x40635)),f319(f319(f126(x40632),f319(x40633,x40634)),f155(x40631,x40632,x40633,x40635)))
% 22.40/22.29 [4075]E(f319(f319(f281(x40751,x40752,x40753),f319(f278(x40752,x40751),x40754)),f319(f278(x40753,x40752),x40755)),f319(f278(x40753,x40751),f319(f319(f281(x40753,x40752,x40751),x40755),x40754)))
% 22.40/22.29 [4108]E(f319(f319(f319(f175(f907(x41081),f907(x41081)),x41082),f159(x41081)),f319(f319(f146(x41083,x41081),x41084),x41085)),f319(f319(f146(x41083,x41081),x41084),f319(f319(f319(f175(f907(x41083),f907(x41083)),x41082),f159(x41083)),x41085)))
% 22.40/22.29 [4109]E(f319(f319(f251(x41091,x41092,x41091,x41093),f319(f244(x41092,x41091),x41094)),x41095),f319(x41095,x41094))
% 22.40/22.29 [4133]E(f147(x41331,x41332,f319(f319(f146(x41333,x41331),x41334),x41335)),f147(x41333,f319(f66(x41331,a906,x41333,x41332),x41334),x41335))
% 22.40/22.29 [4194]E(f169(f912(x41941,x41942),f319(f66(x41942,a904,f912(x41941,x41942),x41943),f248(x41941,x41942)),f319(f319(f173(x41941,x41942),x41944),x41945)),f319(f319(f173(x41941,x41942),x41944),f169(x41942,x41943,x41945)))
% 22.40/22.29 [4199]E(f319(f302(x41991,x41992,f319(f319(f10(x41993,x41992,x41991),x41994),x41995)),f234(f913(x41991,a904))),f319(f302(x41993,x41992,x41994),f319(f302(x41991,x41993,x41995),f234(f913(x41991,a904)))))
% 22.40/22.29 [4210]E(f169(f912(x42101,x42102),f319(f66(x42101,a904,f912(x42101,x42102),x42103),f243(x42101,x42102)),f319(f319(f173(x42101,x42102),x42104),x42105)),f319(f319(f173(x42101,x42102),f169(x42101,x42103,x42104)),x42105))
% 22.40/22.29 [4232]E(f319(f319(f93(f913(x42321,a904)),f319(f303(x42321,x42322,x42323),f319(f319(f301(x42322),x42324),f181(f913(x42322,a904))))),f319(f303(x42321,x42322,x42323),x42325)),f319(f303(x42321,x42322,x42323),f319(f319(f301(x42322),x42324),x42325)))
% 22.40/22.29 [4282]E(f319(f319(f126(f912(x42821,x42822)),f319(f319(f146(x42822,f912(x42821,x42822)),f319(f244(x42821,x42822),x42823)),x42824)),f53(x42821,x42822,x42825,x42824)),f53(x42821,x42822,f319(f319(f143(x42821),x42823),x42825),x42824))
% 22.40/22.29 [4284]E(f319(f319(f146(x42841,x42842),x42843),f169(x42841,f319(f66(x42842,a904,x42841,x42844),x42843),x42845)),f169(x42842,x42844,f319(f319(f146(x42841,x42842),x42843),x42845)))
% 22.40/22.29 [4289]E(f319(f134(x42891,x42892,f319(f9(x42892,x42891,x42891),f319(f9(x42891,x42892,x42891),x42893)),x42894),f319(f160(x42892),f319(f160(x42892),x42895))),f319(f134(x42891,x42892,x42893,x42894),x42895))
% 22.40/22.29 [4395]P1(f319(f319(f225(f913(x43951,a904)),f319(f302(x43952,x43951,x43953),f319(f319(f94(f913(x43952,a904)),x43954),x43955))),f319(f319(f94(f913(x43951,a904)),f319(f302(x43952,x43951,x43953),x43954)),f319(f302(x43952,x43951,x43953),x43955))))
% 22.40/22.29 [4396]P1(f319(f319(f225(f913(x43961,a904)),f319(f277(x43962,x43961,x43963),f319(f319(f94(f913(x43962,a904)),x43964),x43965))),f319(f319(f94(f913(x43961,a904)),f319(f277(x43962,x43961,x43963),x43964)),f319(f277(x43962,x43961,x43963),x43965))))
% 22.40/22.29 [4501]E(f319(f248(x45011,x45012),f319(f250(x45013,x45011,x45012,x45012,x45014,f25(x45012)),x45015)),f319(f248(x45013,x45012),x45015))
% 22.40/22.29 [4502]E(f319(f243(x45021,x45022),f319(f250(x45021,x45021,x45023,x45022,f25(x45021),x45024),x45025)),f319(f243(x45021,x45023),x45025))
% 22.40/22.29 [3707]E(f319(f319(f319(f319(f197(x37071),x37072),x37073),x37074),x37075),f185(x37071,x37072))
% 22.40/22.29 [3708]E(f319(f319(f319(f319(f201(x37081),x37082),x37083),x37084),x37085),f192(x37081,x37082))
% 22.40/22.29 [4064]E(f319(f319(f33(x40641,f913(x40642,a904)),f319(f319(f301(x40641),x40643),x40644)),x40645),f319(f319(f93(f913(x40642,a904)),f319(x40645,x40643)),f319(f319(f33(x40641,f913(x40642,a904)),x40644),x40645)))
% 22.40/22.29 [4065]E(f319(f319(f34(x40651,f913(x40652,a904)),f319(f319(f301(x40651),x40653),x40654)),x40655),f319(f319(f94(f913(x40652,a904)),f319(x40655,x40653)),f319(f319(f34(x40651,f913(x40652,a904)),x40654),x40655)))
% 22.40/22.29 [4117]E(f319(f110(x41171,x41172,f319(x41173,x41174)),f319(f319(f9(x41171,a91,f908(x41172)),x41175),x41174)),f319(f190(x41171,x41172,x41173,x41175),x41174))
% 22.40/22.29 [4127]E(f319(f319(f93(f913(x41271,a904)),f319(f302(x41272,x41271,x41273),x41274)),f319(f302(x41272,x41271,x41273),x41275)),f319(f302(x41272,x41271,x41273),f319(f319(f93(f913(x41272,a904)),x41274),x41275)))
% 22.40/22.29 [4128]E(f319(f319(f93(f913(x41281,a904)),f319(f277(x41282,x41281,x41283),x41284)),f319(f277(x41282,x41281,x41283),x41285)),f319(f277(x41282,x41281,x41283),f319(f319(f93(f913(x41282,a904)),x41284),x41285)))
% 22.40/22.29 [4129]E(f319(f319(f93(f913(x41291,a904)),f319(f303(x41291,x41292,x41293),x41294)),f319(f303(x41291,x41292,x41293),x41295)),f319(f303(x41291,x41292,x41293),f319(f319(f93(f913(x41292,a904)),x41294),x41295)))
% 22.40/22.29 [4130]E(f319(f319(f94(f913(x41301,a904)),f319(f303(x41301,x41302,x41303),x41304)),f319(f303(x41301,x41302,x41303),x41305)),f319(f303(x41301,x41302,x41303),f319(f319(f94(f913(x41302,a904)),x41304),x41305)))
% 22.40/22.29 [4131]E(f319(f319(f3(f913(x41311,a904)),f319(f303(x41311,x41312,x41313),x41314)),f319(f303(x41311,x41312,x41313),x41315)),f319(f303(x41311,x41312,x41313),f319(f319(f3(f913(x41312,a904)),x41314),x41315)))
% 22.40/22.29 [4190]E(f319(f319(f151(x41901,f319(f319(f126(x41901),x41902),f319(f319(f143(x41901),x41903),x41904))),f319(f182(f907(x41901)),x41902)),x41905),f319(f319(f126(x41901),x41902),f319(f319(f143(x41901),x41905),x41904)))
% 22.40/22.29 [4197]E(f319(f319(f34(x41971,f913(x41972,a904)),x41973),f319(f319(f10(f913(x41972,a904),f913(x41972,a904),x41971),f319(f301(x41972),x41974)),x41975)),f319(f319(f301(x41972),x41974),f319(f319(f34(x41971,f913(x41972,a904)),x41973),x41975)))
% 22.40/22.29 [4347]E(f319(f319(f146(x43471,x43472),x43473),f319(f128(x43471,f319(f66(x43472,a904,x43471,x43474),x43473)),x43475)),f319(f128(x43472,x43474),f319(f319(f146(x43471,x43472),x43473),x43475)))
% 22.40/22.29 [4354]E(f319(f182(f907(x43541)),f319(f128(x43541,x43542),f319(f319(f146(x43543,x43541),x43544),x43545))),f319(f182(f907(x43543)),f319(f128(x43543,f319(f66(x43541,a904,x43543,x43542),x43544)),x43545)))
% 22.40/22.29 [4578]E(f319(f148(f907(f912(x45781,x45782)),x45782,f105(f912(x45781,x45782)),f319(f319(f9(x45782,f913(f907(x45782),f907(f912(x45781,x45782))),f913(f907(x45782),f907(f912(x45781,x45782)))),f319(f319(f10(f913(f907(f912(x45781,x45782)),f907(f912(x45781,x45782))),f913(f913(f907(x45782),f907(f912(x45781,x45782))),f913(f907(x45782),f907(f912(x45781,x45782)))),x45782),f10(f907(f912(x45781,x45782)),f907(f912(x45781,x45782)),f907(x45782))),f319(f319(f10(f912(x45781,x45782),f913(f907(f912(x45781,x45782)),f907(f912(x45781,x45782))),x45782),f143(f912(x45781,x45782))),f319(f244(x45781,x45782),x45783)))),f319(f173(x45781,x45782),x45784))),x45785),f319(f319(f173(x45781,x45782),f319(f319(f143(x45781),x45783),x45784)),x45785))
% 22.40/22.29 [4056]E(f319(f319(f151(x40561,f319(f319(f151(x40561,x40562),x40563),x40564)),x40563),x40565),f319(f319(f151(x40561,x40562),x40563),x40565))
% 22.40/22.29 [4110]E(f319(f276(x41101,x41102),f319(f319(f301(f912(x41101,x41102)),f319(f319(f244(x41101,x41102),x41103),x41104)),x41105)),f319(f319(f301(x41102),x41104),f319(f276(x41101,x41102),x41105)))
% 22.40/22.29 [4111]E(f319(f256(x41111,x41112),f319(f319(f301(f912(x41111,x41112)),f319(f319(f244(x41111,x41112),x41113),x41114)),x41115)),f319(f319(f301(x41111),x41113),f319(f256(x41111,x41112),x41115)))
% 22.40/22.29 [4156]E(f114(x41561,x41562,f319(x41563,x41564),f319(f319(f9(x41561,a91,f908(f910(x41562))),x41565),x41564)),f319(f188(x41561,x41562,x41563,x41565),x41564))
% 22.40/22.29 [4183]E(f319(f319(f93(f913(f912(x41831,x41832),a904)),f319(f319(f246(x41831,x41832),x41833),x41834)),f319(f319(f246(x41831,x41832),x41835),x41834)),f319(f319(f246(x41831,x41832),f319(f319(f93(f913(x41831,a904)),x41833),x41835)),x41834))
% 22.40/22.29 [4184]E(f319(f319(f94(f913(f912(x41841,x41842),a904)),f319(f319(f246(x41841,x41842),x41843),x41844)),f319(f319(f246(x41841,x41842),x41845),x41844)),f319(f319(f246(x41841,x41842),f319(f319(f94(f913(x41841,a904)),x41843),x41845)),x41844))
% 22.40/22.29 [4185]E(f319(f319(f3(f913(f912(x41851,x41852),a904)),f319(f319(f246(x41851,x41852),x41853),x41854)),f319(f319(f246(x41851,x41852),x41855),x41854)),f319(f319(f246(x41851,x41852),f319(f319(f3(f913(x41851,a904)),x41853),x41855)),x41854))
% 22.40/22.29 [4242]E(f319(f319(f93(f913(x42421,a904)),f319(f319(f33(x42422,f913(x42421,a904)),x42423),x42424)),f319(f319(f33(x42422,f913(x42421,a904)),x42425),x42424)),f319(f319(f33(x42422,f913(x42421,a904)),f319(f319(f93(f913(x42422,a904)),x42423),x42425)),x42424))
% 22.40/22.29 [4243]E(f319(f319(f94(f913(x42431,a904)),f319(f319(f34(x42432,f913(x42431,a904)),x42433),x42434)),f319(f319(f34(x42432,f913(x42431,a904)),x42435),x42434)),f319(f319(f34(x42432,f913(x42431,a904)),f319(f319(f93(f913(x42432,a904)),x42433),x42435)),x42434))
% 22.40/22.29 [4257]E(f319(f319(f33(x42571,f913(x42572,a904)),x42573),f319(f319(f10(f913(x42572,a904),f913(x42572,a904),x42571),f319(f94(f913(x42572,a904)),x42574)),x42575)),f319(f319(f94(f913(x42572,a904)),x42574),f319(f319(f33(x42571,f913(x42572,a904)),x42573),x42575)))
% 22.40/22.29 [4258]E(f319(f319(f33(x42581,f913(x42582,a904)),x42583),f319(f319(f10(f913(x42582,a904),f913(x42582,a904),x42581),f319(f3(f913(x42582,a904)),x42584)),x42585)),f319(f319(f3(f913(x42582,a904)),x42584),f319(f319(f34(x42581,f913(x42582,a904)),x42583),x42585)))
% 22.40/22.29 [4259]E(f319(f319(f34(x42591,f913(x42592,a904)),x42593),f319(f319(f10(f913(x42592,a904),f913(x42592,a904),x42591),f319(f93(f913(x42592,a904)),x42594)),x42595)),f319(f319(f93(f913(x42592,a904)),x42594),f319(f319(f34(x42591,f913(x42592,a904)),x42593),x42595)))
% 22.40/22.29 [4307]E(f177(f907(x43071),f319(f319(f143(x43071),x43072),x43073),f319(f319(f10(f907(x43071),f907(x43071),a906),f319(f143(x43071),x43074)),f319(f319(f9(a906,x43071,f907(x43071)),f151(x43071,x43073)),x43072)),x43075),f319(f319(f151(x43071,f319(f319(f143(x43071),x43074),x43073)),x43075),x43072))
% 22.40/22.29 [4311]E(f319(f319(f33(x43111,f913(f912(x43112,x43113),a904)),x43114),f319(f319(f10(f913(f912(x43113,x43112),a904),f913(f912(x43112,x43113),a904),x43111),f278(x43113,x43112)),x43115)),f319(f278(x43113,x43112),f319(f319(f33(x43111,f913(f912(x43113,x43112),a904)),x43114),x43115)))
% 22.40/22.29 [4312]E(f319(f319(f34(x43121,f913(f912(x43122,x43123),a904)),x43124),f319(f319(f10(f913(f912(x43123,x43122),a904),f913(f912(x43122,x43123),a904),x43121),f278(x43123,x43122)),x43125)),f319(f278(x43123,x43122),f319(f319(f34(x43121,f913(f912(x43123,x43122),a904)),x43124),x43125)))
% 22.40/22.29 [4419]P1(f319(f319(f225(f913(x44191,a904)),f319(f319(f3(f913(x44191,a904)),f319(f302(x44192,x44191,x44193),x44194)),f319(f302(x44192,x44191,x44193),x44195))),f319(f302(x44192,x44191,x44193),f319(f319(f3(f913(x44192,a904)),x44194),x44195))))
% 22.40/22.29 [4581]E(f319(f148(f907(f912(x45811,x45812)),x45811,f105(f912(x45811,x45812)),f319(f319(f9(x45811,f913(f907(x45811),f907(f912(x45811,x45812))),f913(f907(x45811),f907(f912(x45811,x45812)))),f319(f319(f10(f913(f907(f912(x45811,x45812)),f907(f912(x45811,x45812))),f913(f913(f907(x45811),f907(f912(x45811,x45812))),f913(f907(x45811),f907(f912(x45811,x45812)))),x45811),f10(f907(f912(x45811,x45812)),f907(f912(x45811,x45812)),f907(x45811))),f319(f319(f10(f912(x45811,x45812),f913(f907(f912(x45811,x45812)),f907(f912(x45811,x45812))),x45811),f143(f912(x45811,x45812))),f319(f319(f9(x45811,x45812,f912(x45811,x45812)),f244(x45811,x45812)),x45813)))),f319(f319(f9(f907(x45811),f907(x45812),f907(f912(x45811,x45812))),f173(x45811,x45812)),x45814))),x45815),f319(f319(f173(x45811,x45812),x45815),f319(f319(f143(x45812),x45813),x45814)))
% 22.40/22.29 [4278]E(f319(f319(f93(f913(x42781,a904)),f319(f277(x42782,x42781,x42783),x42784)),f319(f277(x42782,x42781,x42785),x42784)),f319(f277(x42782,x42781,f319(f319(f93(f913(f912(x42782,x42781),a904)),x42783),x42785)),x42784))
% 22.40/22.29 [4313]E(f319(f319(f126(f912(x43131,x43132)),f319(f319(f173(x43131,x43132),x43133),f319(f319(f167(x43132),f319(f182(f907(x43131)),x43133)),x43134))),f319(f319(f173(x43131,x43132),x43135),f319(f319(f130(x43132),f319(f182(f907(x43131)),x43133)),x43134))),f319(f319(f173(x43131,x43132),f319(f319(f126(x43131),x43133),x43135)),x43134))
% 22.40/22.29 [4424]E(f319(f319(f246(x44241,x44242),x44243),f319(f319(f20(x44241,f913(x44242,a904),f913(x44242,a904)),f319(f319(f10(f913(x44242,a904),f913(f913(x44242,a904),f913(x44242,a904)),x44241),f93(f913(x44242,a904))),x44244)),x44245)),f319(f319(f93(f913(f912(x44241,x44242),a904)),f319(f319(f246(x44241,x44242),x44243),x44244)),f319(f319(f246(x44241,x44242),x44243),x44245)))
% 22.40/22.29 [4425]E(f319(f319(f246(x44251,x44252),x44253),f319(f319(f20(x44251,f913(x44252,a904),f913(x44252,a904)),f319(f319(f10(f913(x44252,a904),f913(f913(x44252,a904),f913(x44252,a904)),x44251),f94(f913(x44252,a904))),x44254)),x44255)),f319(f319(f94(f913(f912(x44251,x44252),a904)),f319(f319(f246(x44251,x44252),x44253),x44254)),f319(f319(f246(x44251,x44252),x44253),x44255)))
% 22.40/22.29 [4426]E(f319(f319(f246(x44261,x44262),x44263),f319(f319(f20(x44261,f913(x44262,a904),f913(x44262,a904)),f319(f319(f10(f913(x44262,a904),f913(f913(x44262,a904),f913(x44262,a904)),x44261),f3(f913(x44262,a904))),x44264)),x44265)),f319(f319(f3(f913(f912(x44261,x44262),a904)),f319(f319(f246(x44261,x44262),x44263),x44264)),f319(f319(f246(x44261,x44262),x44263),x44265)))
% 22.40/22.29 [4430]E(f319(f319(f33(x44301,f913(x44302,a904)),x44303),f319(f319(f9(x44301,f913(x44302,a904),f913(x44302,a904)),f319(f319(f10(f913(x44302,a904),f913(f913(x44302,a904),f913(x44302,a904)),x44301),f94(f913(x44302,a904))),x44304)),x44305)),f319(f319(f94(f913(x44302,a904)),f319(f319(f33(x44301,f913(x44302,a904)),x44303),x44304)),x44305))
% 22.40/22.29 [4431]E(f319(f319(f33(x44311,f913(x44312,a904)),x44313),f319(f319(f9(x44311,f913(x44312,a904),f913(x44312,a904)),f319(f319(f10(f913(x44312,a904),f913(f913(x44312,a904),f913(x44312,a904)),x44311),f3(f913(x44312,a904))),x44314)),x44315)),f319(f319(f3(f913(x44312,a904)),f319(f319(f33(x44311,f913(x44312,a904)),x44313),x44314)),x44315))
% 22.40/22.29 [4432]E(f319(f319(f34(x44321,f913(x44322,a904)),x44323),f319(f319(f9(x44321,f913(x44322,a904),f913(x44322,a904)),f319(f319(f10(f913(x44322,a904),f913(f913(x44322,a904),f913(x44322,a904)),x44321),f93(f913(x44322,a904))),x44324)),x44325)),f319(f319(f93(f913(x44322,a904)),f319(f319(f34(x44321,f913(x44322,a904)),x44323),x44324)),x44325))
% 22.40/22.29 [4436]E(f319(f319(f33(x44361,f913(x44362,a904)),x44363),f319(f319(f20(x44361,f913(x44362,a904),f913(x44362,a904)),f319(f319(f10(f913(x44362,a904),f913(f913(x44362,a904),f913(x44362,a904)),x44361),f93(f913(x44362,a904))),x44364)),x44365)),f319(f319(f93(f913(x44362,a904)),f319(f319(f33(x44361,f913(x44362,a904)),x44363),x44364)),f319(f319(f33(x44361,f913(x44362,a904)),x44363),x44365)))
% 22.40/22.29 [4437]E(f319(f319(f34(x44371,f913(x44372,a904)),x44373),f319(f319(f20(x44371,f913(x44372,a904),f913(x44372,a904)),f319(f319(f10(f913(x44372,a904),f913(f913(x44372,a904),f913(x44372,a904)),x44371),f94(f913(x44372,a904))),x44374)),x44375)),f319(f319(f94(f913(x44372,a904)),f319(f319(f34(x44371,f913(x44372,a904)),x44373),x44374)),f319(f319(f34(x44371,f913(x44372,a904)),x44373),x44375)))
% 22.40/22.29 [4446]E(f319(f319(f33(x44461,f913(x44462,a904)),x44463),f319(f319(f20(x44461,f913(x44462,a904),f913(x44462,a904)),f319(f319(f10(f913(x44462,a904),f913(f913(x44462,a904),f913(x44462,a904)),x44461),f93(f913(x44462,a904))),x44464)),x44465)),f319(f319(f93(f913(x44462,a904)),f31(f913(x44462,a904),f319(f302(x44461,f913(x44462,a904),x44464),x44463))),f31(f913(x44462,a904),f319(f302(x44461,f913(x44462,a904),x44465),x44463))))
% 22.40/22.29 [4447]E(f319(f319(f34(x44471,f913(x44472,a904)),x44473),f319(f319(f20(x44471,f913(x44472,a904),f913(x44472,a904)),f319(f319(f10(f913(x44472,a904),f913(f913(x44472,a904),f913(x44472,a904)),x44471),f94(f913(x44472,a904))),x44474)),x44475)),f319(f319(f94(f913(x44472,a904)),f32(f913(x44472,a904),f319(f302(x44471,f913(x44472,a904),x44474),x44473))),f32(f913(x44472,a904),f319(f302(x44471,f913(x44472,a904),x44475),x44473))))
% 22.40/22.29 [4485]E(f319(f319(f130(x44851),f319(f182(f907(x44851)),f169(x44851,x44852,f319(f319(f146(x44853,x44851),x44854),x44855)))),f319(f319(f146(x44853,x44851),x44854),x44855)),f319(f319(f146(x44853,x44851),x44854),f319(f319(f130(x44853),f319(f182(f907(x44853)),f169(x44853,f319(f66(x44851,a904,x44853,x44852),x44854),x44855))),x44855)))
% 22.40/22.29 [4364]E(f319(f319(f126(f912(x43641,x43642)),f319(f319(f173(x43641,x43642),f319(f319(f167(x43641),f319(f182(f907(x43642)),x43643)),x43644)),x43643)),f319(f319(f173(x43641,x43642),f319(f319(f130(x43641),f319(f182(f907(x43642)),x43643)),x43644)),x43645)),f319(f319(f173(x43641,x43642),x43644),f319(f319(f126(x43642),x43643),x43645)))
% 22.40/22.29 [4475]E(f79(x44751,f319(f319(f20(x44751,a904,a904),f319(f319(f10(a904,f913(a904,a904),x44751),a317),f319(f319(f9(x44751,f913(x44751,a904),a904),f321(x44751)),x44752))),f319(f319(f9(x44751,x44753,a904),f319(f319(f10(x44753,f913(x44753,a904),x44751),a316),x44754)),x44755))),f319(f71(x44751,x44753,x44752,x44754),x44755))
% 22.40/22.29 [4476]E(f84(x44761,f319(f319(f20(x44761,a904,a904),f319(f319(f10(a904,f913(a904,a904),x44761),a317),f319(f319(f9(x44761,f913(x44761,a904),a904),f321(x44761)),x44762))),f319(f319(f9(x44761,x44763,a904),f319(f319(f10(x44763,f913(x44763,a904),x44761),a316),x44764)),x44765))),f319(f85(x44761,x44763,x44762,x44764),x44765))
% 22.40/22.29 [4528]E(f319(f319(f82(a1,x45281),f319(f96(a1),f319(f319(f74(a1),x45282),a89))),f319(f319(f20(a1,x45281,x45281),f319(f319(f9(a1,x45281,f913(x45281,x45281)),f319(f319(f10(a904,f913(x45281,f913(x45281,x45281)),a1),f86(x45281)),a186)),f177(x45281,x45283,x45284,x45285))),f319(f319(f10(a906,x45281,a1),x45284),f319(f319(f9(a1,a906,a906),f319(f319(f10(a906,f913(a906,a906),a1),f74(a906)),a97)),x45285)))),f177(x45281,x45283,x45284,f319(f319(f74(a906),f319(f96(a906),x45282)),x45285)))
% 22.40/22.29 [4575]E(f319(f319(f82(a1,x45751),f319(f96(a1),f319(f319(f74(a1),x45752),a89))),f319(f319(f20(a1,x45751,x45751),f319(f319(f9(a1,x45751,f913(x45751,x45751)),f319(f319(f10(a904,f913(x45751,f913(x45751,x45751)),a1),f86(x45751)),a186)),f319(f176(x45751,x45753,x45754),x45755))),f319(f319(f20(a1,x45751,x45751),f319(f319(f10(a906,f913(x45751,x45751),a1),x45754),f319(f319(f9(a1,a906,a906),f319(f319(f10(a906,f913(a906,a906),a1),f74(a906)),a97)),x45755))),f319(f319(f10(a906,x45751,a1),f176(x45751,x45753,x45754)),f319(f319(f9(a1,a906,a906),f319(f319(f10(a906,f913(a906,a906),a1),f74(a906)),a97)),x45755))))),f319(f176(x45751,x45753,x45754),f319(f319(f74(a906),f319(f96(a906),x45752)),x45755)))
% 22.40/22.29 [4607]E(f319(f254(f912(x46071,x46072)),f319(f249(x46071,x46072,a904),f319(f319(f10(f913(x46072,f913(x46073,a904)),f913(x46072,a904),x46071),f319(f10(f913(x46073,a904),a904,x46072),f80(x46073))),f319(f319(f9(x46071,f913(x46072,f913(x46073,a904)),f913(x46072,f913(x46073,a904))),f319(f319(f10(f913(f913(x46073,a904),f913(x46073,a904)),f913(f913(x46072,f913(x46073,a904)),f913(x46072,f913(x46073,a904))),x46071),f10(f913(x46073,a904),f913(x46073,a904),x46072)),f319(f319(f10(f913(x46073,f913(a904,a904)),f913(f913(x46073,a904),f913(x46073,a904)),x46071),f20(x46073,a904,a904)),f319(f319(f10(f913(x46073,a904),f913(x46073,f913(a904,a904)),x46071),f319(f10(a904,f913(a904,a904),x46073),a317)),f319(f319(f9(x46071,f913(f912(x46071,x46073),a904),f913(x46073,a904)),f319(f319(f10(f913(x46073,f913(f913(f912(x46071,x46073),a904),a904)),f913(f913(f912(x46071,x46073),a904),f913(x46073,a904)),x46071),f9(x46073,f913(f912(x46071,x46073),a904),a904)),f319(f319(f10(f913(x46073,f912(x46071,x46073)),f913(x46073,f913(f913(f912(x46071,x46073),a904),a904)),x46071),f319(f10(f912(x46071,x46073),f913(f913(f912(x46071,x46073),a904),a904),x46073),f321(f912(x46071,x46073)))),f244(x46071,x46073)))),x46074))))),f319(f319(f9(x46072,f913(f912(x46073,x46072),a904),f913(x46073,a904)),f319(f319(f10(f913(x46073,f913(f913(f912(x46073,x46072),a904),a904)),f913(f913(f912(x46073,x46072),a904),f913(x46073,a904)),x46072),f9(x46073,f913(f912(x46073,x46072),a904),a904)),f319(f319(f10(f913(x46073,f912(x46073,x46072)),f913(x46073,f913(f913(f912(x46073,x46072),a904),a904)),x46072),f319(f10(f912(x46073,x46072),f913(f913(f912(x46073,x46072),a904),a904),x46073),f321(f912(x46073,x46072)))),f319(f9(x46073,x46072,f912(x46073,x46072)),f244(x46073,x46072))))),x46075))))),f319(f319(f281(x46071,x46073,x46072),x46074),x46075))
% 22.40/22.29 [4211]E(f217(x42111,x42112,x42113,x42114,f213(x42111,x42112,x42115,x42116)),f319(f319(x42114,x42115),x42116))
% 22.40/22.29 [4212]E(f218(x42121,x42122,x42123,x42124,f213(x42121,x42122,x42125,x42126)),f319(f319(x42124,x42125),x42126))
% 22.40/22.29 [4332]E(f119(x43321,x43322,x43323,x43324,f118(x43322,x43325,x43326)),f319(f319(f319(x43324,x43325),x43326),f119(x43321,x43322,x43323,x43324,x43326)))
% 22.40/22.29 [4356]E(f68(x43561,x43562,f68(x43561,x43562,x43563,x43564,x43565),x43564,x43566),f68(x43561,x43562,x43563,x43564,x43566))
% 22.40/22.29 [4463]E(f319(f66(f912(x44631,x44632),x44632,f912(x44633,x44634),f248(x44631,x44632)),f250(x44633,x44631,x44634,x44632,x44635,x44636)),f319(f66(x44634,x44632,f912(x44633,x44634),x44636),f248(x44633,x44634)))
% 22.40/22.29 [4464]E(f319(f66(f912(x44641,x44642),x44641,f912(x44643,x44644),f243(x44641,x44642)),f250(x44643,x44641,x44644,x44642,x44645,x44646)),f319(f66(x44643,x44641,f912(x44643,x44644),x44645),f243(x44643,x44644)))
% 22.40/22.29 [4086]E(f319(f319(f66(x40861,x40862,x40863,x40864),x40865),x40866),f319(x40864,f319(x40865,x40866)))
% 22.40/22.29 [4221]E(f216(x42211,f912(x42212,f908(x42212)),x42213,f319(f249(x42212,f908(x42212),x42211),x42214),f319(f127(x42212),f118(x42212,x42215,x42216))),f319(f319(x42214,x42215),x42216))
% 22.40/22.29 [4269]E(f219(x42691,x42692,x42693,x42694,f213(x42691,x42692,x42695,x42696)),f319(f319(f74(a906),f319(f319(f74(a906),f319(x42693,x42695)),f319(x42694,x42696))),f319(a104,f2(a906))))
% 22.40/22.29 [3889]E(f319(f319(f249(x38891,x38892,x38893),x38894),f319(f319(f244(x38891,x38892),x38895),x38896)),f319(f319(x38894,x38895),x38896))
% 22.40/22.29 [3952]E(f319(f319(f319(f10(x39521,x39522,x39523),x39524),x39525),x39526),f319(x39524,f319(x39525,x39526)))
% 22.40/22.29 [3953]E(f319(f319(f319(f9(x39531,x39532,x39533),x39534),x39535),x39536),f319(f319(x39534,x39536),x39535))
% 22.40/22.29 [3969]E(f319(f319(f319(f20(x39691,x39692,x39693),x39694),x39695),x39696),f319(f319(x39694,x39696),f319(x39695,x39696)))
% 22.40/22.29 [3990]E(f319(f148(x39901,x39902,x39903,x39904),f319(f319(f143(x39902),x39905),x39906)),f319(f319(x39904,x39905),x39906))
% 22.40/22.29 [4025]E(f161(f912(x40251,x40252),f319(f319(f230(a906),x40253),x40254),f319(f319(f244(x40251,x40252),x40255),x40256)),f319(f319(f173(x40251,x40252),f161(x40251,x40253,x40255)),f161(x40252,x40254,x40256)))
% 22.40/22.29 [4091]E(f319(f319(f143(f912(x40911,x40912)),f319(f319(f244(x40911,x40912),x40913),x40914)),f319(f319(f173(x40911,x40912),x40915),x40916)),f319(f319(f173(x40911,x40912),f319(f319(f143(x40911),x40913),x40915)),f319(f319(f143(x40912),x40914),x40916)))
% 22.40/22.29 [4092]E(f319(f319(f146(x40921,x40922),x40923),f319(f319(f151(x40921,x40924),x40925),x40926)),f319(f319(f151(x40922,f319(f319(f146(x40921,x40922),x40923),x40924)),x40925),f319(x40923,x40926)))
% 22.40/22.29 [4116]E(f319(f319(f247(x41161,x41162,x41163,x41164),x41165),x41166),f319(x41164,f319(f319(f244(x41161,x41162),x41165),x41166)))
% 22.40/22.29 [4132]E(f319(f134(x41321,x41322,x41323,x41324),f319(f319(f143(x41322),x41325),x41326)),f319(f134(x41321,x41322,x41323,f319(f319(x41323,x41324),x41325)),x41326))
% 22.40/22.29 [4157]E(f252(x41571,x41572,x41573,x41574,f319(f319(f244(x41571,x41572),x41575),x41576)),f319(f319(x41574,x41575),x41576))
% 22.40/22.29 [4236]E(f319(f319(f33(x42361,f913(x42362,a904)),x42363),f319(f66(x42364,f913(x42362,a904),x42361,x42365),x42366)),f319(f319(f33(x42364,f913(x42362,a904)),f319(f302(x42361,x42364,x42366),x42363)),x42365))
% 22.40/22.29 [4281]E(f319(f319(f146(x42811,x42812),x42813),f319(f319(f146(x42814,x42811),x42815),x42816)),f319(f319(f146(x42814,x42812),f319(f66(x42811,x42812,x42814,x42813),x42815)),x42816))
% 22.40/22.29 [4287]E(f319(f302(x42871,x42872,f319(f66(x42873,x42872,x42871,x42874),x42875)),x42876),f319(f302(x42873,x42872,x42874),f319(f302(x42871,x42873,x42875),x42876)))
% 22.40/22.29 [4288]E(f319(f303(x42881,x42882,f319(f66(x42883,x42882,x42881,x42884),x42885)),x42886),f319(f303(x42881,x42883,x42885),f319(f303(x42883,x42882,x42884),x42886)))
% 22.40/22.29 [4314]E(f319(f134(x43141,x43142,x43143,f319(f134(x43141,x43142,x43143,x43144),x43145)),x43146),f319(f134(x43141,x43142,x43143,x43144),f319(f319(f126(x43142),x43145),x43146)))
% 22.40/22.29 [4451]E(f319(f250(x44511,x44511,x44512,x44513,f25(x44511),x44514),f319(f319(f244(x44511,x44512),x44515),x44516)),f319(f319(f244(x44511,x44513),x44515),f319(x44514,x44516)))
% 22.40/22.29 [4452]E(f319(f250(x44521,x44522,x44523,x44523,x44524,f25(x44523)),f319(f319(f244(x44521,x44523),x44525),x44526)),f319(f319(f244(x44522,x44523),f319(x44524,x44525)),x44526))
% 22.40/22.29 [4554]E(f319(f319(f146(f912(x45541,x45542),f912(x45541,x45543)),f319(f249(x45541,x45542,f912(x45541,x45543)),f319(f319(f9(x45541,f913(x45542,x45543),f913(x45542,f912(x45541,x45543))),f319(f319(f10(f913(x45543,f912(x45541,x45543)),f913(f913(x45542,x45543),f913(x45542,f912(x45541,x45543))),x45541),f10(x45543,f912(x45541,x45543),x45542)),f244(x45541,x45543))),x45544))),f319(f319(f173(x45541,x45542),x45545),x45546)),f319(f319(f173(x45541,x45543),x45545),f319(f319(f146(x45542,x45543),x45544),x45546)))
% 22.40/22.29 [4142]E(f319(f319(f66(x41421,x41422,x41423,f319(f18(x41422,x41421),x41424)),x41425),x41426),x41424)
% 22.40/22.29 [4173]E(f319(f302(x41731,x41732,x41733),f319(f302(x41734,x41731,x41735),x41736)),f319(f302(x41734,x41732,f319(f319(f10(x41731,x41732,x41734),x41733),x41735)),x41736))
% 22.40/22.29 [4178]E(f319(f319(f33(x41781,f913(x41782,a904)),f319(f302(x41783,x41781,x41784),x41785)),x41786),f319(f319(f33(x41783,f913(x41782,a904)),x41785),f319(f319(f10(x41781,f913(x41782,a904),x41783),x41786),x41784)))
% 22.40/22.29 [4179]E(f319(f319(f34(x41791,f913(x41792,a904)),f319(f302(x41793,x41791,x41794),x41795)),x41796),f319(f319(f34(x41793,f913(x41792,a904)),x41795),f319(f319(f10(x41791,f913(x41792,a904),x41793),x41796),x41794)))
% 22.40/22.29 [4180]E(f319(f319(f33(x41801,f913(x41802,a904)),x41803),f319(f319(f10(x41804,f913(x41802,a904),x41801),x41805),x41806)),f319(f319(f33(x41804,f913(x41802,a904)),f319(f302(x41801,x41804,x41806),x41803)),x41805))
% 22.40/22.29 [4181]E(f319(f319(f34(x41811,f913(x41812,a904)),x41813),f319(f319(f10(x41814,f913(x41812,a904),x41811),x41815),x41816)),f319(f319(f34(x41814,f913(x41812,a904)),f319(f302(x41811,x41814,x41816),x41813)),x41815))
% 22.40/22.29 [4238]E(f319(f319(f33(x42381,f913(x42382,a904)),x42383),f319(f319(f10(f913(x42384,a904),f913(x42382,a904),x42381),f302(x42384,x42382,x42385)),x42386)),f319(f302(x42384,x42382,x42385),f319(f319(f33(x42381,f913(x42384,a904)),x42383),x42386)))
% 22.40/22.29 [4239]E(f319(f319(f33(x42391,f913(x42392,a904)),x42393),f319(f319(f10(f913(x42394,a904),f913(x42392,a904),x42391),f277(x42394,x42392,x42395)),x42396)),f319(f277(x42394,x42392,x42395),f319(f319(f33(x42391,f913(x42394,a904)),x42393),x42396)))
% 22.40/22.29 [4240]E(f319(f319(f33(x42401,f913(x42402,a904)),x42403),f319(f319(f10(f913(x42404,a904),f913(x42402,a904),x42401),f303(x42402,x42404,x42405)),x42406)),f319(f303(x42402,x42404,x42405),f319(f319(f33(x42401,f913(x42404,a904)),x42403),x42406)))
% 22.40/22.29 [4241]E(f319(f319(f34(x42411,f913(x42412,a904)),x42413),f319(f319(f10(f913(x42414,a904),f913(x42412,a904),x42411),f303(x42412,x42414,x42415)),x42416)),f319(f303(x42412,x42414,x42415),f319(f319(f34(x42411,f913(x42414,a904)),x42413),x42416)))
% 22.40/22.29 [4319]E(f319(f134(x43191,x43192,f319(f9(x43192,x43191,x43191),x43193),x43194),f319(f160(x43192),f319(f319(f143(x43192),x43195),x43196))),f319(f319(x43193,x43195),f319(f134(x43191,x43192,f319(f9(x43192,x43191,x43191),x43193),x43194),f319(f160(x43192),x43196))))
% 22.40/22.29 [4383]E(f319(f319(f20(f912(x43831,x43832),x43832,x43833),f319(f319(f10(x43834,f913(x43832,x43833),f912(x43831,x43832)),x43835),f319(f319(f10(x43831,x43834,f912(x43831,x43832)),x43836),f243(x43831,x43832)))),f248(x43831,x43832)),f319(f249(x43831,x43832,x43833),f319(f319(f10(x43834,f913(x43832,x43833),x43831),x43835),x43836)))
% 22.40/22.29 [4389]E(f319(f134(x43891,x43892,f319(f9(x43892,x43891,x43891),x43893),f319(f134(x43891,x43892,f319(f9(x43892,x43891,x43891),x43893),x43894),f319(f160(x43892),x43895))),f319(f160(x43892),x43896)),f319(f134(x43891,x43892,f319(f9(x43892,x43891,x43891),x43893),x43894),f319(f160(x43892),f319(f319(f126(x43892),x43896),x43895))))
% 22.40/22.29 [4391]E(f319(f319(f146(f912(x43911,x43912),f912(x43913,x43912)),f319(f249(x43911,x43912,f912(x43913,x43912)),f319(f319(f10(x43913,f913(x43912,f912(x43913,x43912)),x43911),f244(x43913,x43912)),x43914))),f319(f319(f173(x43911,x43912),x43915),x43916)),f319(f319(f173(x43913,x43912),f319(f319(f146(x43911,x43913),x43914),x43915)),x43916))
% 22.40/22.29 [4439]P1(f319(f319(f225(f913(x44391,a904)),f319(f277(x44392,x44391,x44393),f319(f319(f34(x44394,f913(x44392,a904)),x44395),x44396))),f319(f319(f34(x44394,f913(x44391,a904)),x44395),f319(f319(f10(f913(x44392,a904),f913(x44391,a904),x44394),f277(x44392,x44391,x44393)),x44396))))
% 22.40/22.29 [4250]E(f319(f319(f173(x42501,x42502),f319(f319(f151(x42501,x42503),x42504),f319(f243(x42501,x42502),x42505))),f319(f319(f151(x42502,x42506),x42504),f319(f248(x42501,x42502),x42505))),f319(f319(f151(f912(x42501,x42502),f319(f319(f173(x42501,x42502),x42503),x42506)),x42504),x42505))
% 22.40/22.29 [4302]E(f319(f319(f93(f913(f912(x43021,x43022),a904)),f319(f319(f281(x43021,x43023,x43022),x43024),x43025)),f319(f319(f281(x43021,x43023,x43022),x43024),x43026)),f319(f319(f281(x43021,x43023,x43022),x43024),f319(f319(f93(f913(f912(x43023,x43022),a904)),x43025),x43026)))
% 22.40/22.29 [4403]E(f319(f319(f301(f912(x44031,x44032)),f319(f319(f244(x44031,x44032),x44033),x44034)),f319(f319(f93(f913(f912(x44031,x44032),a904)),f319(f319(f246(x44031,x44032),x44035),f319(f18(f913(x44032,a904),x44031),f319(f319(f301(x44032),x44034),x44036)))),f319(f319(f246(x44031,x44032),f319(f319(f301(x44031),x44033),x44035)),f319(f18(f913(x44032,a904),x44031),x44036)))),f319(f319(f246(x44031,x44032),f319(f319(f301(x44031),x44033),x44035)),f319(f18(f913(x44032,a904),x44031),f319(f319(f301(x44032),x44034),x44036))))
% 22.40/22.29 [4481]E(f319(f319(f94(f913(x44811,a904)),f319(f303(x44811,x44812,f319(f66(f912(x44812,x44813),x44812,x44811,f243(x44812,x44813)),x44814)),x44815)),f319(f303(x44811,x44813,f319(f66(f912(x44812,x44813),x44813,x44811,f248(x44812,x44813)),x44814)),x44816)),f319(f303(x44811,f912(x44812,x44813),x44814),f319(f319(f246(x44812,x44813),x44815),f319(f18(f913(x44813,a904),x44812),x44816))))
% 22.40/22.29 [4325]E(f319(f319(f93(f913(f912(x43251,x43252),a904)),f319(f319(f281(x43251,x43253,x43252),x43254),x43255)),f319(f319(f281(x43251,x43253,x43252),x43256),x43255)),f319(f319(f281(x43251,x43253,x43252),f319(f319(f93(f913(f912(x43251,x43253),a904)),x43254),x43256)),x43255))
% 22.40/22.29 [4461]E(f319(f319(f33(x44611,f913(x44612,a904)),x44613),f319(f319(f9(x44611,f913(x44614,f913(x44612,a904)),f913(x44612,a904)),f319(f319(f10(f913(x44614,a904),f913(f913(x44614,f913(x44612,a904)),f913(x44612,a904)),x44611),f33(x44614,f913(x44612,a904))),x44615)),x44616)),f319(f319(f33(x44614,f913(x44612,a904)),f319(f319(f33(x44611,f913(x44614,a904)),x44613),x44615)),x44616))
% 22.40/22.29 [4462]E(f319(f319(f34(x44621,f913(x44622,a904)),x44623),f319(f319(f9(x44621,f913(x44624,f913(x44622,a904)),f913(x44622,a904)),f319(f319(f10(f913(x44624,a904),f913(f913(x44624,f913(x44622,a904)),f913(x44622,a904)),x44621),f34(x44624,f913(x44622,a904))),x44625)),x44626)),f319(f319(f34(x44624,f913(x44622,a904)),f319(f319(f33(x44621,f913(x44624,a904)),x44623),x44625)),x44626))
% 22.40/22.29 [4518]E(f319(f249(x45181,x45182,f912(x45183,x45184)),f319(f319(f9(x45181,f913(x45182,x45184),f913(x45182,f912(x45183,x45184))),f319(f319(f10(f913(x45184,f912(x45183,x45184)),f913(f913(x45182,x45184),f913(x45182,f912(x45183,x45184))),x45181),f10(x45184,f912(x45183,x45184),x45182)),f319(f319(f10(x45183,f913(x45184,f912(x45183,x45184)),x45181),f244(x45183,x45184)),x45185))),x45186)),f250(x45181,x45183,x45182,x45184,x45185,x45186))
% 22.40/22.29 [4547]E(f319(f302(x45471,x45472,f319(f319(f20(x45471,x45472,x45472),f319(f319(f20(x45471,x45472,f913(x45472,x45472)),f319(f319(f10(a904,f913(x45472,f913(x45472,x45472)),x45471),f86(x45472)),x45473)),x45474)),x45475)),x45476),f319(f319(f93(f913(x45472,a904)),f319(f302(x45471,x45472,x45474),f319(f319(f94(f913(x45471,a904)),x45476),f319(f254(x45471),x45473)))),f319(f302(x45471,x45472,x45475),f319(f319(f94(f913(x45471,a904)),x45476),f319(f254(x45471),f319(f319(f10(a904,a904,x45471),a314),x45473))))))
% 22.40/22.29 [4561]E(f319(f302(x45611,f912(x45612,x45613),f319(f319(f20(x45611,x45613,f912(x45612,x45613)),f319(f319(f10(x45612,f913(x45613,f912(x45612,x45613)),x45611),f244(x45612,x45613)),x45614)),x45615)),x45616),f319(f319(f246(x45612,x45613),f319(f302(x45611,x45612,x45614),x45616)),f319(f319(f10(f913(x45611,a904),f913(x45613,a904),x45612),f302(x45611,x45613,x45615)),f319(f319(f9(x45612,f913(x45611,a904),f913(x45611,a904)),f319(f319(f10(f913(x45611,a904),f913(f913(x45611,a904),f913(x45611,a904)),x45612),f94(f913(x45611,a904))),f319(f319(f10(f913(x45612,a904),f913(x45611,a904),x45612),f303(x45611,x45612,x45614)),f319(f319(f9(x45612,f913(x45612,a904),f913(x45612,a904)),f301(x45612)),f181(f913(x45612,a904)))))),x45616))))
% 22.40/22.29 [4589]E(f238(x45891,x45892,x45893,x45894,x45895,x45896),f319(x45894,f319(f254(x45891),f319(f319(f10(f913(f913(x45893,x45891),a904),a904,x45891),f80(f913(x45893,x45891))),f319(f319(f10(f913(f913(x45893,x45891),a904),f913(f913(x45893,x45891),a904),x45891),f319(f20(f913(x45893,x45891),a904,a904),f319(f319(f10(a904,f913(a904,a904),f913(x45893,x45891)),a317),f319(f319(f9(f913(x45893,x45891),f913(f913(x45893,x45891),a904),a904),f321(f913(x45893,x45891))),x45895)))),f319(f319(f9(x45891,f913(f913(x45893,x45891),x45891),f913(f913(x45893,x45891),a904)),f319(f319(f10(f913(x45891,a904),f913(f913(f913(x45893,x45891),x45891),f913(f913(x45893,x45891),a904)),x45891),f10(x45891,a904,f913(x45893,x45891))),a316)),f319(f319(f9(f913(x45893,x45891),x45893,x45891),f7(f913(x45893,x45891))),x45896)))))))
% 22.40/22.29 [4366]E(f319(f66(x43661,x43662,x43663,x43664),f68(x43663,x43661,x43665,x43666,x43667)),f68(x43663,x43662,f319(f66(x43661,x43662,x43663,x43664),x43665),x43666,f319(x43664,x43667)))
% 22.40/22.29 [4503]E(f319(f248(x45031,x45032),f319(f250(x45033,x45031,x45034,x45032,x45035,x45036),x45037)),f319(x45036,f319(f248(x45033,x45034),x45037)))
% 22.40/22.29 [4504]E(f319(f243(x45041,x45042),f319(f250(x45043,x45041,x45044,x45042,x45045,x45046),x45047)),f319(x45045,f319(f243(x45043,x45044),x45047)))
% 22.40/22.29 [4213]E(f319(f319(f173(x42131,x42132),f319(f319(f151(x42131,x42133),x42134),x42135)),f319(f319(f151(x42132,x42136),x42134),x42137)),f319(f319(f151(f912(x42131,x42132),f319(f319(f173(x42131,x42132),x42133),x42136)),x42134),f319(f319(f244(x42131,x42132),x42135),x42137)))
% 22.40/22.29 [4276]E(f319(f319(f319(f251(x42761,x42762,x42763,x42764),x42765),x42766),x42767),f319(f319(f249(x42762,x42763,x42764),x42766),f319(x42765,x42767)))
% 22.40/22.29 [4286]E(f319(f319(f319(f251(x42861,x42862,x42863,x42864),x42865),x42866),x42867),f319(f319(x42866,f319(f243(x42862,x42863),f319(x42865,x42867))),f319(f248(x42862,x42863),f319(x42865,x42867))))
% 22.40/22.29 [4340]E(f319(f66(x43401,x43402,x43403,x43404),f319(f66(x43405,x43401,x43403,x43406),x43407)),f319(f66(x43405,x43402,x43403,f319(f66(x43401,x43402,x43405,x43404),x43406)),x43407))
% 22.40/22.29 [4522]E(f319(f250(x45221,x45222,x45223,x45223,x45224,f25(x45223)),f319(f250(x45221,x45221,x45225,x45223,f25(x45221),x45226),x45227)),f319(f319(f244(x45222,x45223),f319(x45224,f319(f243(x45221,x45225),x45227))),f319(x45226,f319(f248(x45221,x45225),x45227))))
% 22.40/22.29 [4523]E(f319(f250(x45231,x45231,x45232,x45233,f25(x45231),x45234),f319(f250(x45235,x45231,x45232,x45232,x45236,f25(x45232)),x45237)),f319(f319(f244(x45231,x45233),f319(x45236,f319(f243(x45235,x45232),x45237))),f319(x45234,f319(f248(x45235,x45232),x45237))))
% 22.40/22.29 [4545]E(f319(f250(x45451,x45452,x45453,x45453,x45454,f25(x45453)),f319(f250(x45455,x45451,x45453,x45453,x45456,f25(x45453)),x45457)),f319(f250(x45455,x45452,x45453,x45453,f319(f66(x45451,x45452,x45455,x45454),x45456),f25(x45453)),x45457))
% 22.40/22.29 [4546]E(f319(f250(x45461,x45461,x45462,x45463,f25(x45461),x45464),f319(f250(x45461,x45461,x45465,x45462,f25(x45461),x45466),x45467)),f319(f250(x45461,x45461,x45465,x45463,f25(x45461),f319(f66(x45462,x45463,x45465,x45464),x45466)),x45467))
% 22.40/22.29 [4558]E(f319(f250(x45581,x45582,x45583,x45583,x45584,f25(x45583)),f319(f250(x45581,x45581,x45585,x45583,f25(x45581),x45586),x45587)),f319(f250(x45582,x45582,x45585,x45583,f25(x45582),x45586),f319(f250(x45581,x45582,x45585,x45585,x45584,f25(x45585)),x45587)))
% 22.40/22.29 [4247]E(f319(f319(f281(x42471,x42472,x42473),f319(f319(f281(x42471,x42474,x42472),x42475),x42476)),x42477),f319(f319(f281(x42471,x42474,x42473),x42475),f319(f319(f281(x42474,x42472,x42473),x42476),x42477)))
% 22.40/22.29 [4308]E(f319(f319(f249(x43081,x43082,x43083),f319(f66(x43084,f913(x43082,x43083),x43081,x43085),x43086)),x43087),f319(f319(x43085,f319(x43086,f319(f243(x43081,x43082),x43087))),f319(f248(x43081,x43082),x43087)))
% 22.40/22.29 [4394]E(f319(f134(x43941,x43942,f319(f9(x43942,x43941,x43941),x43943),x43944),f319(f160(x43942),f319(f319(f146(x43945,x43942),x43946),x43947))),f319(f134(x43941,x43945,f319(f9(x43945,x43941,x43941),f319(f66(x43942,f913(x43941,x43941),x43945,x43943),x43946)),x43944),f319(f160(x43945),x43947)))
% 22.40/22.29 [4341]E(f319(f319(f33(x43411,f913(f912(x43412,x43413),a904)),x43414),f319(f319(f10(f913(f912(x43415,x43413),a904),f913(f912(x43412,x43413),a904),x43411),f319(f281(x43412,x43415,x43413),x43416)),x43417)),f319(f319(f281(x43412,x43415,x43413),x43416),f319(f319(f33(x43411,f913(f912(x43415,x43413),a904)),x43414),x43417)))
% 22.40/22.29 [4486]E(f319(f319(f33(x44861,f913(f912(x44862,x44863),a904)),x44864),f319(f319(f9(x44861,f913(f912(x44865,x44863),a904),f913(f912(x44862,x44863),a904)),f319(f319(f10(f913(f912(x44862,x44865),a904),f913(f913(f912(x44865,x44863),a904),f913(f912(x44862,x44863),a904)),x44861),f281(x44862,x44865,x44863)),x44866)),x44867)),f319(f319(f281(x44862,x44865,x44863),f319(f319(f33(x44861,f913(f912(x44862,x44865),a904)),x44864),x44866)),x44867))
% 22.40/22.29 [4487]E(f319(f134(x44871,x44872,f319(f319(f9(x44871,f913(x44872,x44873),f913(x44872,x44871)),f319(f319(f10(f913(x44873,x44871),f913(f913(x44872,x44873),f913(x44872,x44871)),x44871),f10(x44873,x44871,x44872)),x44874)),x44875),x44876),x44877),f319(f134(x44871,x44873,x44874,x44876),f319(f319(f146(x44872,x44873),x44875),x44877)))
% 22.40/22.29 [4559]E(f319(f319(f34(x45591,f913(x45592,a904)),x45593),f319(f319(f10(f913(x45594,f913(x45592,a904)),f913(x45592,a904),x45591),f319(f34(x45594,f913(x45592,a904)),x45595)),f319(f319(f9(x45591,f913(x45594,f913(x45592,a904)),f913(x45594,f913(x45592,a904))),f319(f319(f10(f913(f913(x45592,a904),f913(x45592,a904)),f913(f913(x45594,f913(x45592,a904)),f913(x45594,f913(x45592,a904))),x45591),f10(f913(x45592,a904),f913(x45592,a904),x45594)),f319(f319(f10(f913(x45592,a904),f913(f913(x45592,a904),f913(x45592,a904)),x45591),f93(f913(x45592,a904))),x45596))),x45597))),f319(f319(f93(f913(x45592,a904)),f319(f319(f34(x45591,f913(x45592,a904)),x45593),x45596)),f319(f319(f34(x45594,f913(x45592,a904)),x45595),x45597)))
% 22.40/22.29 [4560]E(f319(f319(f33(x45601,f913(x45602,a904)),x45603),f319(f319(f10(f913(x45604,f913(x45602,a904)),f913(x45602,a904),x45601),f319(f33(x45604,f913(x45602,a904)),x45605)),f319(f319(f9(x45601,f913(x45604,f913(x45602,a904)),f913(x45604,f913(x45602,a904))),f319(f319(f10(f913(f913(x45602,a904),f913(x45602,a904)),f913(f913(x45604,f913(x45602,a904)),f913(x45604,f913(x45602,a904))),x45601),f10(f913(x45602,a904),f913(x45602,a904),x45604)),f319(f319(f10(f913(x45602,a904),f913(f913(x45602,a904),f913(x45602,a904)),x45601),f94(f913(x45602,a904))),x45606))),x45607))),f319(f319(f94(f913(x45602,a904)),f319(f319(f33(x45601,f913(x45602,a904)),x45603),x45606)),f319(f319(f33(x45604,f913(x45602,a904)),x45605),x45607)))
% 22.40/22.29 [4550]E(f190(x45501,x45502,f319(f319(f319(x45503,x45504),x45505),x45506),f319(f319(f9(x45501,f912(a91,a91),f913(a91,f908(x45502))),f319(f319(f9(x45501,a91,f913(f912(a91,a91),f913(a91,f908(x45502)))),f319(f319(f9(x45501,a91,f913(a91,f913(f912(a91,a91),f913(a91,f908(x45502))))),x45507),x45504)),x45505)),x45506)),f319(f319(f319(f202(x45501,x45502,x45503,x45507),x45504),x45505),x45506))
% 22.40/22.29 [4562]E(f191(x45621,x45622,f319(f319(f319(x45623,x45624),x45625),x45626),f319(f319(f9(x45621,f912(a91,a91),f913(a91,f908(x45622))),f319(f319(f9(x45621,a91,f913(f912(a91,a91),f913(a91,f908(x45622)))),f319(f319(f9(x45621,a91,f913(a91,f913(f912(a91,a91),f913(a91,f908(x45622))))),x45627),x45624)),x45625)),x45626)),f204(x45621,x45622,x45623,x45627,x45624,x45625,x45626))
% 22.40/22.29 [4557]E(f188(x45571,x45572,f319(f319(f319(x45573,x45574),x45575),x45576),f319(f319(f9(x45571,f912(a91,a91),f913(a91,f908(f910(x45572)))),f319(f319(f9(x45571,a91,f913(f912(a91,a91),f913(a91,f908(f910(x45572))))),f319(f319(f9(x45571,a91,f913(a91,f913(f912(a91,a91),f913(a91,f908(f910(x45572)))))),x45577),x45574)),x45575)),x45576)),f319(f319(f319(f198(x45571,x45572,x45573,x45577),x45574),x45575),x45576))
% 22.40/22.29 [4572]E(f189(x45721,x45722,f319(f319(f319(x45723,x45724),x45725),x45726),f319(f319(f9(x45721,f912(a91,a91),f913(a91,f908(f910(x45722)))),f319(f319(f9(x45721,a91,f913(f912(a91,a91),f913(a91,f908(f910(x45722))))),f319(f319(f9(x45721,a91,f913(a91,f913(f912(a91,a91),f913(a91,f908(f910(x45722)))))),x45727),x45724)),x45725)),x45726)),f200(x45721,x45722,x45723,x45727,x45724,x45725,x45726))
% 22.40/22.29 [4453]E(f319(f250(x44531,x44532,x44533,x44534,x44535,x44536),f319(f319(f244(x44531,x44533),x44537),x44538)),f319(f319(f244(x44532,x44534),f319(x44535,x44537)),f319(x44536,x44538)))
% 22.40/22.29 [4574]E(f319(f319(f146(f912(x45741,x45742),f912(x45743,x45744)),f319(f249(x45741,x45742,f912(x45743,x45744)),f319(f319(f9(x45741,f913(x45742,x45744),f913(x45742,f912(x45743,x45744))),f319(f319(f10(f913(x45744,f912(x45743,x45744)),f913(f913(x45742,x45744),f913(x45742,f912(x45743,x45744))),x45741),f10(x45744,f912(x45743,x45744),x45742)),f319(f319(f10(x45743,f913(x45744,f912(x45743,x45744)),x45741),f244(x45743,x45744)),x45745))),x45746))),f319(f319(f173(x45741,x45742),x45747),x45748)),f319(f319(f173(x45743,x45744),f319(f319(f146(x45741,x45743),x45745),x45747)),f319(f319(f146(x45742,x45744),x45746),x45748)))
% 22.40/22.29 [4579]E(f319(f319(f146(f912(x45791,x45792),x45793),f319(f249(x45791,x45792,x45793),f319(f319(f10(f913(x45792,f912(x45791,x45794)),f913(x45792,x45793),x45791),f319(f10(f912(x45791,x45794),x45793,x45792),x45795)),f319(f319(f9(x45791,f913(x45792,x45794),f913(x45792,f912(x45791,x45794))),f319(f319(f10(f913(x45794,f912(x45791,x45794)),f913(f913(x45792,x45794),f913(x45792,f912(x45791,x45794))),x45791),f10(x45794,f912(x45791,x45794),x45792)),f244(x45791,x45794))),x45796)))),f319(f319(f173(x45791,x45792),x45797),x45798)),f319(f319(f146(f912(x45791,x45794),x45793),x45795),f319(f319(f173(x45791,x45794),x45797),f319(f319(f146(x45792,x45794),x45796),x45798))))
% 22.40/22.29 [4495]E(f319(f319(f146(f912(x44951,x44952),x44953),f319(f249(x44951,x44952,x44953),f319(f319(f10(f913(x44952,f912(x44954,x44952)),f913(x44952,x44953),x44951),f319(f10(f912(x44954,x44952),x44953,x44952),x44955)),f319(f319(f10(x44954,f913(x44952,f912(x44954,x44952)),x44951),f244(x44954,x44952)),x44956)))),f319(f319(f173(x44951,x44952),x44957),x44958)),f319(f319(f146(f912(x44954,x44952),x44953),x44955),f319(f319(f173(x44954,x44952),f319(f319(f146(x44951,x44954),x44956),x44957)),x44958)))
% 22.40/22.29 [4444]E(f319(f319(f249(x44441,x44442,x44443),f319(f319(f10(f913(x44442,f912(x44444,x44445)),f913(x44442,x44443),x44441),f319(f10(f912(x44444,x44445),x44443,x44442),f319(f249(x44444,x44445,x44443),x44446))),x44447)),x44448),f319(f319(f249(x44444,x44445,x44443),x44446),f319(f319(f249(x44441,x44442,f912(x44444,x44445)),x44447),x44448)))
% 22.40/22.29 [4580]E(f319(f319(f33(f912(x45801,x45802),f913(f912(x45803,x45804),a904)),f319(f319(f246(x45801,x45802),x45805),f319(f18(f913(x45802,a904),x45801),x45806))),f319(f249(x45801,x45802,f913(f912(x45803,x45804),a904)),f319(f319(f9(x45801,f913(x45802,f913(x45803,f913(x45804,a904))),f913(x45802,f913(f912(x45803,x45804),a904))),f319(f319(f10(f913(f913(x45803,f913(x45804,a904)),f913(f912(x45803,x45804),a904)),f913(f913(x45802,f913(x45803,f913(x45804,a904))),f913(x45802,f913(f912(x45803,x45804),a904))),x45801),f10(f913(x45803,f913(x45804,a904)),f913(f912(x45803,x45804),a904),x45802)),f319(f319(f10(f913(x45803,a904),f913(f913(x45803,f913(x45804,a904)),f913(f912(x45803,x45804),a904)),x45801),f246(x45803,x45804)),x45807))),f319(f319(f10(f913(x45804,a904),f913(x45803,f913(x45804,a904)),x45802),f18(f913(x45804,a904),x45803)),x45808)))),f319(f319(f246(x45803,x45804),f319(f319(f33(x45801,f913(x45803,a904)),x45805),x45807)),f319(f18(f913(x45804,a904),x45803),f319(f319(f33(x45802,f913(x45804,a904)),x45806),x45808))))
% 22.40/22.29 [4509]E(f319(f319(f251(x45091,x45092,x45093,x45094),f319(f319(f251(x45091,x45095,x45096,f912(x45092,x45093)),x45097),x45098)),x45099),f319(f319(f251(x45091,x45095,x45096,x45094),x45097),f319(f319(f9(x45095,f913(x45092,f913(x45093,x45094)),f913(x45096,x45094)),f319(f319(f10(f913(x45096,f912(x45092,x45093)),f913(f913(x45092,f913(x45093,x45094)),f913(x45096,x45094)),x45095),f251(x45096,x45092,x45093,x45094)),x45098)),x45099)))
% 22.40/22.29 [4542]E(f319(f66(f912(x45421,x45422),f912(x45423,x45424),f912(x45425,x45426),f250(x45421,x45423,x45422,x45424,x45427,x45428)),f250(x45425,x45421,x45426,x45422,x45429,x454210)),f250(x45425,x45423,x45426,x45424,f319(f66(x45421,x45423,x45425,x45427),x45429),f319(f66(x45422,x45424,x45426,x45428),x454210)))
% 22.40/22.29 [4548]E(f319(f250(x45481,x45482,x45483,x45484,x45485,x45486),f319(f250(x45487,x45481,x45488,x45483,x45489,x454810),x454811)),f319(f250(x45487,x45482,x45488,x45484,f319(f66(x45481,x45482,x45487,x45485),x45489),f319(f66(x45483,x45484,x45488,x45486),x454810)),x454811))
% 22.40/22.29 [4680]~P68(x46801)+P68(f910(x46801))
% 22.40/22.29 [4681]~P71(x46811)+P71(f910(x46811))
% 22.40/22.29 [4682]~P109(x46821)+P109(f907(x46821))
% 22.40/22.29 [4685]~P144(x46851)+~E(f72(x46851),f2(x46851))
% 22.40/22.29 [4687]~E(x46871,f2(a91))+E(f319(a24,x46871),f2(a1))
% 22.40/22.29 [4688]~E(x46881,f2(a1))+E(f76(a1,x46881),f2(a1))
% 22.40/22.29 [4694]~P146(x46941)+P28(x46941,f2(x46941))
% 22.40/22.29 [4696]~P4(x46961)+P13(x46961,f105(x46961))
% 22.40/22.29 [4705]P1(x47051)+P1(f319(a314,x47051))
% 22.40/22.29 [4759]~P146(x47591)+~P28(x47591,f72(x47591))
% 22.40/22.29 [4794]~P1(x47941)+~P1(f319(a314,x47941))
% 22.40/22.29 [4815]E(f319(a97,x48151),f2(a906))+~P1(f319(a186,x48151))
% 22.40/22.29 [4881]~P77(x48811)+P17(x48811,x48811,f75(x48811))
% 22.40/22.29 [4882]~P106(x48821)+P15(x48821,x48821,f93(x48821))
% 22.40/22.29 [4883]~P107(x48831)+P15(x48831,x48831,f94(x48831))
% 22.40/22.29 [4884]~P4(x48841)+P15(x48841,x48841,f180(x48841))
% 22.40/22.29 [4885]~P4(x48851)+P15(x48851,x48851,f230(x48851))
% 22.40/22.29 [4886]~P100(x48861)+P15(x48861,x48861,f75(x48861))
% 22.40/22.29 [4691]~E(x46911,f2(a906))+E(f319(f92(a1),x46911),f2(a1))
% 22.40/22.29 [4698]~P98(x46981)+E(f319(f96(x46981),a77),f2(x46981))
% 22.40/22.29 [4701]~E(f573(x47011),f2(a906))+E(f319(f157(a906),x47011),f2(a906))
% 22.40/22.29 [4702]~P3(x47021)+E(f227(x47021,f225(x47021)),f180(x47021))
% 22.40/22.29 [4703]~P3(x47031)+E(f228(x47031,f225(x47031)),f230(x47031))
% 22.40/22.29 [4704]~P94(x47041)+E(f76(x47041,f2(x47041)),f2(x47041))
% 22.40/22.29 [4713]~P146(x47131)+E(f319(f92(x47131),f72(a906)),f72(x47131))
% 22.40/22.29 [4714]~P146(x47141)+E(f319(f92(x47141),f2(a906)),f2(x47141))
% 22.40/22.29 [4715]~P141(x47151)+E(f319(f95(x47151),f72(a1)),f72(x47151))
% 22.40/22.29 [4716]~P141(x47161)+E(f319(f95(x47161),f2(a1)),f2(x47161))
% 22.40/22.29 [4717]E(x47171,f2(a906))+~E(f319(f92(a1),x47171),f2(a1))
% 22.40/22.29 [4753]~P63(x47531)+E(f319(f73(x47531),f234(x47531)),f181(x47531))
% 22.40/22.29 [4754]~P63(x47541)+E(f319(f73(x47541),f181(x47541)),f234(x47541))
% 22.40/22.29 [4755]~P66(x47551)+E(f319(f73(x47551),f2(x47551)),f2(x47551))
% 22.40/22.29 [4756]~P113(x47561)+E(f319(f69(x47561),f72(x47561)),f72(x47561))
% 22.40/22.29 [4757]~P92(x47571)+E(f319(f69(x47571),f2(x47571)),f2(x47571))
% 22.40/22.29 [4758]~P88(x47581)+E(f319(f157(x47581),f105(x47581)),f2(x47581))
% 22.40/22.29 [4776]~P36(x47761)+P41(f319(f164(a1),x47761))
% 22.40/22.29 [4799]~P98(x47991)+E(f319(f73(x47991),f72(x47991)),f319(f96(x47991),a89))
% 22.40/22.29 [4814]~P98(x48141)+P28(x48141,f319(f96(x48141),a77))
% 22.40/22.29 [4840]P36(x48401)+~P41(f319(f164(a1),x48401))
% 22.40/22.29 [4887]E(f319(f92(a1),f319(a97,x48871)),x48871)+P1(f319(a186,x48871))
% 22.40/22.29 [4955]~P116(x49551)+E(f237(x49551,f72(x49551),f75(x49551)),f236(x49551))
% 22.40/22.29 [4988]~P98(x49881)+~P28(x49881,f319(f96(x49881),a89))
% 22.40/22.29 [5137]E(f319(f69(a1),x51371),x51371)+P1(f319(f319(f226(a1),x51371),f2(a1)))
% 22.40/22.29 [5155]~E(f319(a97,x51551),f2(a906))+P1(f319(f319(f225(a1),x51551),f2(a1)))
% 22.40/22.29 [5224]~P1(f319(a186,x52241))+P1(f319(f319(f226(a1),x52241),f2(a1)))
% 22.40/22.29 [5266]~P126(x52661)+P1(f319(f319(f225(x52661),f2(x52661)),f72(x52661)))
% 22.40/22.29 [5267]~P141(x52671)+P1(f319(f319(f321(x52671),f72(x52671)),f102(x52671)))
% 22.40/22.29 [5268]~P146(x52681)+P1(f319(f319(f321(x52681),f72(x52681)),f178(x52681)))
% 22.40/22.29 [5269]~P141(x52691)+P1(f319(f319(f321(x52691),f2(x52691)),f102(x52691)))
% 22.40/22.29 [5270]~P146(x52701)+P1(f319(f319(f321(x52701),f2(x52701)),f178(x52701)))
% 22.40/22.29 [5271]~P126(x52711)+P1(f319(f319(f226(x52711),f2(x52711)),f72(x52711)))
% 22.40/22.29 [5324]E(x53241,f2(a906))+~P1(f319(f319(f225(a906),x53241),f2(a906)))
% 22.40/22.29 [5366]E(f319(a97,x53661),f2(a906))+~P1(f319(f319(f225(a1),x53661),f2(a1)))
% 22.40/22.29 [5422]P1(f319(a186,x54221))+~P1(f319(f319(f226(a1),x54221),f2(a1)))
% 22.40/22.29 [5429]~P4(x54291)+P17(x54291,f907(x54291),f140(x54291,x54291,f7(x54291)))
% 22.40/22.29 [5447]P41(x54471)+~P1(f319(f319(f225(a1),f2(a1)),f325(x54471)))
% 22.40/22.29 [5452]E(f319(f69(a1),x54521),f319(f73(a1),x54521))+~P1(f319(f319(f226(a1),x54521),f2(a1)))
% 22.40/22.29 [5622]~P126(x56221)+~P1(f319(f319(f225(x56221),f72(x56221)),f2(x56221)))
% 22.40/22.29 [5623]~P126(x56231)+~P1(f319(f319(f226(x56231),f72(x56231)),f2(x56231)))
% 22.40/22.29 [5639]~E(x56391,f2(a906))+P1(f319(f319(f225(a1),f319(f92(a1),x56391)),f2(a1)))
% 22.40/22.29 [5640]~E(x56401,f2(a1))+P1(f319(f319(f226(a1),f319(f69(a1),x56401)),f72(a1)))
% 22.40/22.29 [5765]~P88(x57651)+E(f134(x57651,x57651,f74(x57651),f2(x57651)),f157(x57651))
% 22.40/22.29 [5944]~P108(x59441)+P25(a906,x59441,f92(x59441),f234(f913(a906,a904)))
% 22.40/22.29 [6142]E(x61421,f2(a906))+~P1(f319(f319(f225(a1),f319(f92(a1),x61421)),f2(a1)))
% 22.40/22.29 [6143]E(x61431,f2(a1))+~P1(f319(f319(f226(a1),f319(f69(a1),x61431)),f72(a1)))
% 22.40/22.29 [8026]E(x80261,f319(a5,f2(a906)))+P1(f319(f319(f226(a906),f319(f319(f3(a906),f319(a22,x80261)),f319(a104,f2(a906)))),f319(a22,x80261)))
% 22.40/22.29 [8876]~P1(f319(f319(f226(a1),x88761),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x88761)),x88761)),f2(a1)))
% 22.40/22.29 [9263]P1(f319(f319(f226(a1),x92631),f2(a1)))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92631)),x92631)),f2(a1)))
% 22.40/22.29 [9730]~P1(f319(f319(f226(a1),x97301),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97301)),x97301)),a89)),f2(a1)))
% 22.40/22.29 [9901]P1(f319(f319(f226(a1),x99011),f2(a1)))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99011)),x99011)),a89)),f2(a1)))
% 22.40/22.29 [4800]E(x48001,f2(a1))+E(f319(f319(f30(a1),x48001),x48001),f72(a1))
% 22.40/22.29 [4945]~P5(x49451)+E(f32(x49451,f234(f913(x49451,a904))),f181(x49451))
% 22.40/22.29 [4946]~P5(x49461)+E(f32(x49461,f181(f913(x49461,a904))),f234(x49461))
% 22.40/22.29 [4947]~P5(x49471)+E(f31(x49471,f234(f913(x49471,a904))),f234(x49471))
% 22.40/22.29 [4948]~P5(x49481)+E(f31(x49481,f181(f913(x49481,a904))),f181(x49481))
% 22.40/22.29 [4949]~P4(x49491)+E(f131(x49491,f181(f913(x49491,a904))),f105(x49491))
% 22.40/22.29 [5092]E(x50921,f2(a906))+P1(f319(f319(f226(a906),f2(a906)),x50921))
% 22.40/22.29 [5112]~P6(x51121)+P1(f319(f319(f225(a1),f2(a1)),x51121))
% 22.40/22.29 [5146]~E(f319(f96(a906),x51461),f2(a906))+P1(f319(f319(f225(a1),x51461),a77))
% 22.40/22.29 [5151]P41(x51511)+P1(f319(f319(f321(a1),f325(x51511)),x51511))
% 22.40/22.29 [5152]E(x51521,f319(a5,f2(a906)))+P1(f319(f319(f225(a91),f72(a91)),x51521))
% 22.40/22.29 [5195]P1(f319(a186,x51951))+P1(f319(f319(f225(a1),f2(a1)),x51951))
% 22.40/22.29 [5248]E(f319(f92(a1),f319(a97,x52481)),f2(a1))+P1(f319(f319(f225(a1),f2(a1)),x52481))
% 22.40/22.29 [5306]E(f319(f92(a1),f319(f96(a906),x53061)),f319(f96(a1),x53061))+P1(f319(a186,f319(f96(a1),x53061)))
% 22.40/22.29 [5330]E(f319(f96(a906),x53301),f2(a906))+~P1(f319(a186,f319(f96(a1),x53301)))
% 22.40/22.29 [5331]E(f319(f96(a906),x53311),f2(a906))+~P1(f319(f319(f225(a1),x53311),a77))
% 22.40/22.29 [5363]P6(x53631)+~P1(f319(f319(f225(a1),f2(a1)),x53631))
% 22.40/22.29 [5398]~E(x53981,f319(a104,f2(a906)))+P1(f319(f319(f279(a906),x53981),f319(a104,f2(a906))))
% 22.40/22.29 [5432]E(f319(a104,f328(x54321)),x54321)+~P1(f319(f319(f226(a906),f2(a906)),x54321))
% 22.40/22.29 [5441]E(f319(a104,f319(f96(a906),x54411)),f72(a906))+~P1(f319(a186,f319(f96(a1),x54411)))
% 22.40/22.29 [5448]E(f319(f92(a1),f443(x54481)),x54481)+~P1(f319(f319(f226(a1),f2(a1)),x54481))
% 22.40/22.29 [5455]~E(x54551,f319(a5,f2(a906)))+~P1(f319(f319(f225(a91),f72(a91)),x54551))
% 22.40/22.29 [5462]E(f319(f92(a1),f319(f96(a906),x54621)),f2(a1))+~P1(f319(a186,f319(f96(a1),x54621)))
% 22.40/22.29 [5487]E(f319(f157(a906),x54871),f2(a906))+P1(f319(f319(f321(a906),f573(x54871)),f319(f164(a906),x54871)))
% 22.40/22.29 [5508]E(f319(f92(a1),f319(a97,x55081)),x55081)+~P1(f319(f319(f225(a1),f2(a1)),x55081))
% 22.40/22.29 [5516]~P1(f319(a186,x55161))+~P1(f319(f319(f225(a1),f2(a1)),x55161))
% 22.40/22.29 [5615]E(f319(f319(f74(a906),f72(a906)),f319(f96(a906),x56151)),f72(a906))+~P1(f319(f319(f226(a1),x56151),a77))
% 22.40/22.29 [5681]E(x56811,f2(a906))+~P1(f319(f319(f226(a906),x56811),f319(a104,f2(a906))))
% 22.40/22.29 [5705]E(x57051,f319(a104,f2(a906)))+~P1(f319(f319(f279(a906),x57051),f319(a104,f2(a906))))
% 22.40/22.29 [5723]E(f319(f319(f3(a906),f319(f96(a906),x57231)),f72(a906)),f2(a906))+~P1(f319(f319(f225(a1),x57231),a77))
% 22.40/22.29 [5724]E(f319(f319(f74(a906),f319(f96(a906),x57241)),f72(a906)),f72(a906))+~P1(f319(f319(f226(a1),x57241),a77))
% 22.40/22.29 [5736]~P41(x57361)+E(f319(f29(a906),f319(f302(a1,a906,a97),x57361)),f319(f29(a1),x57361))
% 22.40/22.29 [5766]~P4(x57661)+E(f227(x57661,f319(f9(x57661,x57661,a904),f225(x57661))),f230(x57661))
% 22.40/22.29 [5767]~P4(x57671)+E(f228(x57671,f319(f9(x57671,x57671,a904),f225(x57671))),f180(x57671))
% 22.40/22.29 [5777]E(f39(a906,f319(a104,f2(a906)),f319(f96(a906),x57771)),f319(a104,f2(a906)))+~P1(f319(a186,f319(f96(a1),x57771)))
% 22.40/22.29 [5786]~P1(f319(f319(f226(a1),f2(a1)),x57861))+P1(f319(f319(f225(a1),f72(a1)),x57861))
% 22.40/22.29 [5787]P1(f319(f319(f226(a1),f2(a1)),x57871))+~P1(f319(f319(f225(a1),f72(a1)),x57871))
% 22.40/22.29 [5798]E(f319(a104,f319(f319(f3(a906),x57981),f72(a906))),x57981)+~P1(f319(f319(f226(a906),f2(a906)),x57981))
% 22.40/22.29 [5854]P1(f319(f319(f226(a906),f2(a906)),f443(x58541)))+~P1(f319(f319(f226(a1),f2(a1)),x58541))
% 22.40/22.29 [5915]E(f39(a1,f319(f96(a1),a89),x59151),f319(f319(f3(a1),x59151),f72(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x59151))
% 22.40/22.29 [5957]~P1(f319(f319(f226(a1),a77),x59571))+P1(f319(f319(f226(a906),f2(a906)),f319(f96(a906),x59571)))
% 22.40/22.29 [5962]E(f319(a22,f798(x59621)),x59621)+~P1(f319(f319(f321(a906),x59621),f234(f913(a906,a904))))
% 22.40/22.29 [6011]P1(f319(f319(f226(a906),f2(a906)),f319(a97,x60111)))+~P1(f319(f319(f226(a1),f2(a1)),x60111))
% 22.40/22.29 [6059]~P1(f319(f319(f226(a906),f2(a906)),x60591))+P1(f319(f319(f226(a1),f2(a1)),f319(f92(a1),x60591)))
% 22.40/22.29 [6094]~P1(f319(f319(f226(a906),f2(a906)),f319(a97,x60941)))+P1(f319(f319(f226(a1),f2(a1)),x60941))
% 22.40/22.29 [6111]~P41(x61111)+E(f319(f302(a906,a1,f92(a1)),f319(f302(a1,a906,a97),x61111)),x61111)
% 22.40/22.29 [6122]P1(f319(f319(f226(a1),a77),x61221))+~P1(f319(f319(f226(a906),f2(a906)),f319(f96(a906),x61221)))
% 22.40/22.29 [6178]P1(f319(f319(f226(a906),f2(a906)),x61781))+~P1(f319(f319(f226(a1),f2(a1)),f319(f92(a1),x61781)))
% 22.40/22.29 [6293]E(f319(f302(a906,a1,f92(a1)),f319(f274(a906),f319(a97,x62931))),f319(f294(a1,f2(a1)),x62931))+~P1(f319(f319(f225(a1),f2(a1)),x62931))
% 22.40/22.29 [6311]~P126(x63111)+P1(f319(f319(f226(x63111),f2(x63111)),f319(f319(f74(x63111),f72(x63111)),f72(x63111))))
% 22.40/22.29 [6360]P1(f319(f319(f226(a906),f319(a104,f2(a906))),f319(a97,x63601)))+~P1(f319(f319(f226(a1),f72(a1)),x63601))
% 22.40/22.29 [6457]E(x64571,f2(a1))+P1(f319(f43(f2(a1),x64571),f319(f319(f244(a1,a1),f2(a1)),f2(a1))))
% 22.40/22.29 [6629]~P1(f319(f319(f226(a906),f319(a104,f2(a906))),f319(a97,x66291)))+P1(f319(f319(f226(a1),f72(a1)),x66291))
% 22.40/22.29 [7054]~P117(x70541)+P37(x70541,f319(f254(f912(x70541,x70541)),f319(f249(x70541,x70541,a904),f226(x70541))))
% 22.40/22.29 [5668]E(f319(f96(a906),f319(f319(f3(a1),x56681),a89)),f319(a104,f319(f96(a906),x56681)))+P1(f319(a186,f319(f96(a1),x56681)))
% 22.40/22.29 [5684]~P36(x56841)+E(f319(f319(f146(a906,a1),f92(a1)),f319(f319(f146(a1,a906),a97),x56841)),x56841)
% 22.40/22.29 [5804]E(f319(f73(a1),f319(f92(a1),f319(a104,f444(x58041)))),x58041)+~P1(f319(f319(f226(a1),x58041),f2(a1)))
% 22.40/22.29 [5814]E(f319(f319(f74(a906),f72(a906)),f319(f96(a906),x58141)),f319(f96(a906),f319(f319(f3(a1),x58141),a89)))+P1(f319(f319(f226(a1),x58141),a77))
% 22.40/22.29 [5856]E(f319(f319(f30(a1),f319(f96(a1),a89)),x58561),f319(f96(a1),a89))+~P1(f319(f319(f226(a1),f2(a1)),x58561))
% 22.40/22.29 [5953]E(f319(f319(f3(a906),f319(f96(a906),x59531)),f72(a906)),f319(f96(a906),f319(f319(f74(a1),x59531),a89)))+P1(f319(f319(f225(a1),x59531),a77))
% 22.40/22.29 [5954]E(f319(f319(f74(a906),f319(f96(a906),x59541)),f72(a906)),f319(f96(a906),f319(f319(f3(a1),x59541),a89)))+P1(f319(f319(f226(a1),x59541),a77))
% 22.40/22.29 [5998]E(f319(a97,f319(f319(f74(a1),f72(a1)),x59981)),f319(a104,f319(a97,x59981)))+~P1(f319(f319(f225(a1),f2(a1)),x59981))
% 22.40/22.29 [6032]E(f319(a104,f319(f319(f3(a906),x60321),f319(a104,f2(a906)))),x60321)+~P1(f319(f319(f226(a906),f2(a906)),x60321))
% 22.40/22.29 [6245]E(f39(a906,f319(a104,f2(a906)),f319(f96(a906),x62451)),f319(a97,f39(a1,f72(a1),f319(f96(a1),x62451))))+P1(f319(a186,f319(f96(a1),x62451)))
% 22.40/22.29 [6471]~P1(f319(f55(x64711),f234(f913(x64711,a904))))+P1(f319(f55(f910(x64711)),f234(f913(f910(x64711),a904))))
% 22.40/22.29 [6560]~P1(f319(f319(f225(a1),f2(a1)),x65601))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f74(a1),f72(a1)),x65601)))
% 22.40/22.29 [6567]E(f319(f243(a1,a1),f41(f72(a1),f319(f96(a1),x65671))),f319(f319(f30(a1),f72(a1)),f319(f96(a1),x65671)))+~P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x65671)))
% 22.40/22.29 [6588]E(f319(f248(a1,a1),f41(f72(a1),f319(f96(a1),x65881))),f39(a1,f72(a1),f319(f96(a1),x65881)))+~P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x65881)))
% 22.40/22.29 [6600]P1(f319(f55(x66001),f234(f913(x66001,a904))))+~P1(f319(f55(f910(x66001)),f234(f913(f910(x66001),a904))))
% 22.40/22.29 [6948]~P1(f319(f55(x69481),f234(f913(x69481,a904))))+P1(f319(f319(f226(a906),f2(a906)),f319(f29(x69481),f234(f913(x69481,a904)))))
% 22.40/22.29 [7525]P1(f319(f55(a906),x75251))+~P1(f319(f55(a1),f319(f302(a906,a1,f92(a1)),x75251)))
% 22.40/22.29 [5698]~E(a89,x56981)+E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x56981)),x56981),a89)
% 22.40/22.29 [5699]~E(x56991,a89)+E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x56991)),x56991),a89)
% 22.40/22.29 [6256]E(x62561,a89)+~E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x62561)),x62561),a89)
% 22.40/22.29 [6257]E(a89,x62571)+~E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x62571)),x62571),a89)
% 22.40/22.29 [6529]~E(f319(f96(a906),x65291),f2(a906))+P1(f319(a186,f319(f96(a1),f319(f319(f74(a1),x65291),a89))))
% 22.40/22.29 [7200]E(f319(f96(a906),x72001),f2(a906))+~P1(f319(a186,f319(f96(a1),f319(f319(f74(a1),x72001),a89))))
% 22.40/22.29 [7798]E(f319(a99,f515(x77981)),x77981)+~P1(f319(f319(f321(f913(f912(a906,a906),a904)),x77981),a90))
% 22.40/22.29 [6643]~P98(x66431)+E(f319(f96(x66431),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),f72(x66431))
% 22.40/22.29 [7072]~P1(f319(a186,f319(f96(a1),x70721)))+E(f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x70721)),x70721)),f2(a906))
% 22.40/22.29 [7976]~P1(f319(f319(f226(a1),f319(f96(a1),x79761)),f2(a1)))+E(f319(f243(a1,a1),f319(a45,f44(f319(f73(a1),f72(a1)),f319(f73(a1),f319(f96(a1),x79761))))),f319(f319(f30(a1),f72(a1)),f319(f96(a1),x79761)))
% 22.40/22.29 [7985]~P1(f319(f319(f226(a1),f319(f96(a1),x79851)),f2(a1)))+E(f319(f248(a1,a1),f319(a45,f44(f319(f73(a1),f72(a1)),f319(f73(a1),f319(f96(a1),x79851))))),f39(a1,f72(a1),f319(f96(a1),x79851)))
% 22.40/22.29 [8162]~P1(f319(f319(f225(a1),a77),x81621))+P1(f319(f319(f225(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x81621)),x81621)))
% 22.40/22.29 [8163]~P1(f319(f319(f225(a1),a89),x81631))+P1(f319(f319(f225(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x81631)),x81631)))
% 22.40/22.29 [8164]~P1(f319(f319(f225(a1),a77),x81641))+P1(f319(f319(f226(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x81641)),x81641)))
% 22.40/22.29 [8165]~P1(f319(f319(f226(a1),a89),x81651))+P1(f319(f319(f226(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x81651)),x81651)))
% 22.40/22.29 [8496]~P98(x84961)+~P28(x84961,f319(f96(x84961),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))
% 22.40/22.29 [8616]P1(f319(f319(f225(a1),a77),x86161))+~P1(f319(f319(f225(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x86161)),x86161)))
% 22.40/22.29 [8617]P1(f319(f319(f225(a1),a77),x86171))+~P1(f319(f319(f226(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x86171)),x86171)))
% 22.40/22.29 [8618]P1(f319(f319(f225(a1),a89),x86181))+~P1(f319(f319(f225(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x86181)),x86181)))
% 22.40/22.29 [8619]P1(f319(f319(f226(a1),a89),x86191))+~P1(f319(f319(f226(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x86191)),x86191)))
% 22.40/22.29 [8847]E(f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x88471)),x88471)),f319(f319(f82(a906,a906),f319(f96(a906),x88471)),f319(f319(f10(a906,a906,a906),a104),f319(f319(f20(a906,a906,a906),f74(a906)),f7(a906)))))+P1(f319(a186,f319(f96(a1),x88471)))
% 22.40/22.29 [9703]E(x97031,f181(f913(f912(a906,a906),a904)))+P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),x97031),f181(f913(f912(a906,a906),a904)))),a27))
% 22.40/22.29 [7886]~E(a77,x78861)+E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x78861)),x78861)),a89),a77)
% 22.40/22.29 [7887]~E(x78871,a77)+E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x78871)),x78871)),a89),a77)
% 22.40/22.29 [8511]E(x85111,a77)+~E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x85111)),x85111)),a89),a77)
% 22.40/22.29 [8512]E(a77,x85121)+~E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x85121)),x85121)),a89),a77)
% 22.40/22.29 [8862]~P1(f319(a186,f319(f96(a1),x88621)))+P1(f319(a186,f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x88621)),x88621))))
% 22.40/22.29 [8863]~P1(f319(f319(f226(a1),x88631),a77))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x88631)),x88631)),a77))
% 22.40/22.29 [8864]~P1(f319(f319(f225(a1),x88641),a89))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x88641)),x88641)),a89))
% 22.40/22.29 [8865]~P1(f319(f319(f226(a1),x88651),a77))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x88651)),x88651)),a77))
% 22.40/22.29 [8866]~P1(f319(f319(f226(a1),x88661),a89))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x88661)),x88661)),a89))
% 22.40/22.29 [8948]~P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x89481)))+P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x89481)),x89481))))
% 22.40/22.29 [9255]P1(f319(a186,f319(f96(a1),x92551)))+~P1(f319(a186,f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92551)),x92551))))
% 22.40/22.29 [9256]P1(f319(f319(f225(a1),x92561),a89))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92561)),x92561)),a89))
% 22.40/22.29 [9257]P1(f319(f319(f226(a1),x92571),a77))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92571)),x92571)),a77))
% 22.40/22.29 [9258]P1(f319(f319(f226(a1),x92581),a77))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92581)),x92581)),a77))
% 22.40/22.29 [9259]P1(f319(f319(f226(a1),x92591),a89))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92591)),x92591)),a89))
% 22.40/22.29 [9753]~P1(f319(f55(f912(a906,a906)),x97531))+P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),f181(f913(f912(a906,a906),a904))),x97531)),a63))
% 22.40/22.29 [9420]~P1(f319(f319(f225(a1),a77),x94201))+P1(f319(f319(f225(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94201)),x94201)),a89)))
% 22.40/22.29 [9421]~P1(f319(f319(f226(a1),a89),x94211))+P1(f319(f319(f225(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94211)),x94211)),a89)))
% 22.40/22.29 [9422]~P1(f319(f319(f226(a1),a77),x94221))+P1(f319(f319(f226(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94221)),x94221)),a89)))
% 22.40/22.29 [9423]~P1(f319(f319(f226(a1),a89),x94231))+P1(f319(f319(f226(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94231)),x94231)),a89)))
% 22.40/22.29 [9643]P1(f319(f319(f225(a1),a77),x96431))+~P1(f319(f319(f225(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96431)),x96431)),a89)))
% 22.40/22.29 [9644]P1(f319(f319(f226(a1),a77),x96441))+~P1(f319(f319(f226(a1),a77),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96441)),x96441)),a89)))
% 22.40/22.29 [9645]P1(f319(f319(f226(a1),a89),x96451))+~P1(f319(f319(f225(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96451)),x96451)),a89)))
% 22.40/22.29 [9646]P1(f319(f319(f226(a1),a89),x96461))+~P1(f319(f319(f226(a1),a89),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96461)),x96461)),a89)))
% 22.40/22.29 [9725]~P1(f319(a186,f319(f96(a1),x97251)))+P1(f319(a186,f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97251)),x97251)),a89))))
% 22.40/22.29 [9726]~P1(f319(f319(f225(a1),x97261),a77))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97261)),x97261)),a89)),a77))
% 22.40/22.29 [9727]~P1(f319(f319(f225(a1),x97271),a89))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97271)),x97271)),a89)),a89))
% 22.40/22.29 [9728]~P1(f319(f319(f226(a1),x97281),a77))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97281)),x97281)),a89)),a77))
% 22.40/22.29 [9729]~P1(f319(f319(f225(a1),x97291),a89))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97291)),x97291)),a89)),a89))
% 22.40/22.29 [9732]~P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x97321)))+P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97321)),x97321)),a89))))
% 22.40/22.29 [9896]P1(f319(a186,f319(f96(a1),x98961)))+~P1(f319(a186,f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x98961)),x98961)),a89))))
% 22.40/22.29 [9897]P1(f319(f319(f225(a1),x98971),a77))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x98971)),x98971)),a89)),a77))
% 22.40/22.29 [9898]P1(f319(f319(f225(a1),x98981),a89))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x98981)),x98981)),a89)),a89))
% 22.40/22.29 [9899]P1(f319(f319(f225(a1),x98991),a89))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x98991)),x98991)),a89)),a89))
% 22.40/22.29 [9900]P1(f319(f319(f226(a1),x99001),a77))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99001)),x99001)),a89)),a77))
% 22.40/22.29 [10000]~P98(x100001)+E(f319(f319(f74(x100001),f72(x100001)),f72(x100001)),f319(f96(x100001),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))
% 22.40/22.29 [10069]~P146(x100691)+E(f319(f319(f236(x100691),f72(x100691)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f72(x100691))
% 22.40/22.29 [10070]~P146(x100701)+E(f319(f319(f236(x100701),f2(x100701)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f2(x100701))
% 22.40/22.29 [10210]~P1(f319(f319(f226(a906),f72(a906)),x102101))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f30(a906),x102101),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.29 [10214]~P1(f319(f319(f226(a906),f2(a906)),x102141))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f30(a906),f319(f319(f74(a906),x102141),f72(a906))),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.29 [10242]~E(f39(a906,x102421,f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f72(a906))+P1(f319(f319(f226(a906),f2(a906)),f39(a906,x102421,f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.29 [10271]E(f39(a906,x102711,f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f72(a906))+~P1(f319(f319(f226(a906),f2(a906)),f39(a906,x102711,f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.29 [4722]~P7(x47221,x47222)+P49(x47221,x47222)
% 22.40/22.29 [4723]~P37(x47231,x47232)+P59(x47231,x47232)
% 22.40/22.29 [4724]~P44(x47241,x47242)+P59(x47241,x47242)
% 22.40/22.29 [4726]~P7(x47261,x47262)+P51(x47261,x47262)
% 22.40/22.29 [4728]~P16(x47281,x47282)+P51(x47281,x47282)
% 22.40/22.29 [4730]~P7(x47301,x47302)+P52(x47301,x47302)
% 22.40/22.29 [4732]~P16(x47321,x47322)+P52(x47321,x47322)
% 22.40/22.29 [4733]~P7(x47331,x47332)+P16(x47331,x47332)
% 22.40/22.29 [4683]~E(x46831,x46832)+E(f261(x46831,x46832),f72(a91))
% 22.40/22.29 [4686]E(f209(x46861,x46862),x46861)+~E(x46862,f2(a906))
% 22.40/22.29 [4693]~E(x46932,f105(x46931))+E(f144(x46931,x46932),f105(x46931))
% 22.40/22.29 [4712]~E(f144(x47122,x47121),f105(x47122))+E(x47121,f105(x47122))
% 22.40/22.29 [4737]~P2(x47372)+P2(f913(x47371,x47372))
% 22.40/22.29 [4738]~P3(x47382)+P3(f913(x47381,x47382))
% 22.40/22.29 [4739]~P111(x47392)+P111(f913(x47391,x47392))
% 22.40/22.29 [4740]~P5(x47402)+P5(f913(x47401,x47402))
% 22.40/22.29 [4741]~P112(x47412)+P112(f913(x47411,x47412))
% 22.40/22.29 [4742]~P62(x47422)+P62(f913(x47421,x47422))
% 22.40/22.29 [4743]~P63(x47432)+P63(f913(x47431,x47432))
% 22.40/22.29 [4744]~P64(x47442)+P64(f913(x47441,x47442))
% 22.40/22.29 [4745]~P101(x47452)+P101(f913(x47451,x47452))
% 22.40/22.29 [4746]~P102(x47462)+P102(f913(x47461,x47462))
% 22.40/22.29 [4747]~P101(x47472)+P106(f913(x47471,x47472))
% 22.40/22.29 [4748]~P101(x47482)+P107(f913(x47481,x47482))
% 22.40/22.29 [4749]~P104(x47492)+P103(f913(x47491,x47492))
% 22.40/22.29 [4750]~P104(x47502)+P105(f913(x47501,x47502))
% 22.40/22.29 [4751]~P84(x47512)+P84(f913(x47511,x47512))
% 22.40/22.29 [4752]~P104(x47522)+P104(f913(x47521,x47522))
% 22.40/22.29 [4765]E(x47651,x47652)+~E(f319(a104,x47651),f319(a104,x47652))
% 22.40/22.29 [4766]E(x47661,x47662)+~E(f319(a99,x47661),f319(a99,x47662))
% 22.40/22.29 [4767]E(x47671,x47672)+~E(f319(a5,x47671),f319(a5,x47672))
% 22.40/22.29 [4769]E(x47691,x47692)+~E(f319(a22,x47691),f319(a22,x47692))
% 22.40/22.29 [4816]P39(x48161,x48162)+~E(f696(x48162,x48161),f697(x48162,x48161))
% 22.40/22.29 [4846]~P59(x48461,x48462)+P39(x48461,f299(x48461,x48462))
% 22.40/22.29 [4847]~P53(x48471,x48472)+P53(x48471,f299(x48471,x48472))
% 22.40/22.29 [4860]~P69(x48601)+E(f39(x48601,x48602,x48602),f2(x48601))
% 22.40/22.29 [4894]~P37(x48941,x48942)+P37(f907(x48941),f138(x48941,x48942))
% 22.40/22.29 [4895]~P37(x48951,x48952)+P37(f907(x48951),f137(x48951,x48952))
% 22.40/22.29 [4896]~P38(x48961,x48962)+P38(f907(x48961),f139(x48961,x48962))
% 22.40/22.29 [4897]~P38(x48971,x48972)+P38(f907(x48971),f150(x48971,x48972))
% 22.40/22.29 [4898]~P53(x48981,x48982)+P53(f907(x48981),f150(x48981,x48982))
% 22.40/22.29 [4993]~P37(x49931,x49932)+P37(f913(x49931,a904),f310(x49931,x49932))
% 22.40/22.29 [4994]~P37(x49941,x49942)+P37(f913(x49941,a904),f311(x49941,x49942))
% 22.40/22.29 [5121]~P6(x51211)+P41(f295(a1,x51211,x51212))
% 22.40/22.29 [5227]~P37(x52271,x52272)+P61(x52271,f61(x52271,x52271,x52272))
% 22.40/22.29 [5730]~P65(x57301)+P25(x57301,x57301,f73(x57301),x57302)
% 22.40/22.29 [4707]~E(x47072,f105(x47071))+E(f319(f159(x47071),x47072),f105(x47071))
% 22.40/22.29 [4708]~E(x47082,f105(x47081))+E(f319(f160(x47081),x47082),f105(x47081))
% 22.40/22.29 [4771]E(x47711,f319(a97,x47712))+~E(f319(f92(a1),x47711),x47712)
% 22.40/22.29 [4774]E(x47741,f105(x47742))+~E(f319(f159(x47742),x47741),f105(x47742))
% 22.40/22.29 [4775]E(x47751,f105(x47752))+~E(f319(f160(x47752),x47751),f105(x47752))
% 22.40/22.29 [4787]~P98(x47871)+E(f319(f96(x47871),x47872),f319(f95(x47871),x47872))
% 22.40/22.29 [4793]~P68(x47931)+P1(f319(f55(x47931),x47932))
% 22.40/22.29 [4801]~E(f657(x48012,x48011),f105(x48011))+E(f171(x48011,x48012),f105(f907(x48011)))
% 22.40/22.29 [4810]~E(x48102,f105(x48101))+E(f319(f164(x48101),x48102),f181(f913(x48101,a904)))
% 22.40/22.29 [4811]~E(x48112,f105(x48111))+E(f181(f913(x48111,a904)),f319(f164(x48111),x48112))
% 22.40/22.29 [4813]E(x48131,x48132)+~E(f319(f92(a1),x48131),f319(f92(a1),x48132))
% 22.40/22.29 [4817]E(f207(x48171,x48172),f2(a906))+P1(f319(f55(x48171),x48172))
% 22.40/22.29 [4835]~P113(x48351)+E(f76(x48351,f76(x48351,x48352)),f76(x48351,x48352))
% 22.40/22.29 [4849]~P119(x48491)+E(f319(f319(f236(x48491),x48492),f72(a906)),x48492)
% 22.40/22.29 [4850]~P87(x48501)+E(f319(f319(f236(x48501),x48502),f72(a906)),x48502)
% 22.40/22.29 [4851]~P53(x48511,x48512)+E(f319(f278(x48511,x48511),x48512),x48512)
% 22.40/22.29 [4855]E(x48551,x48552)+E(f261(x48551,x48552),f319(f319(f74(a91),x48552),f72(a91)))
% 22.40/22.29 [4858]E(f319(f29(x48581),x48582),f2(a906))+P1(f319(f55(x48581),x48582))
% 22.40/22.29 [4861]~E(f144(x48611,x48612),x48612)+P1(f319(f129(x48611),x48612))
% 22.40/22.29 [4864]~P103(x48641)+E(f319(f319(f93(x48641),x48642),f181(x48641)),x48642)
% 22.40/22.29 [4865]~P105(x48651)+E(f319(f319(f94(x48651),x48652),f234(x48651)),x48652)
% 22.40/22.29 [4866]~P66(x48661)+E(f319(f319(f3(x48661),x48662),f2(x48661)),x48662)
% 22.40/22.29 [4867]~P76(x48671)+E(f319(f319(f74(x48671),x48672),f2(x48671)),x48672)
% 22.40/22.29 [4868]~P119(x48681)+E(f319(f319(f74(x48681),x48682),f2(x48681)),x48682)
% 22.40/22.29 [4869]~P88(x48691)+E(f319(f319(f74(x48691),x48692),f2(x48691)),x48692)
% 22.40/22.29 [4870]~P119(x48701)+E(f319(f319(f75(x48701),x48702),f72(x48701)),x48702)
% 22.40/22.29 [4871]~P82(x48711)+E(f319(f319(f75(x48711),x48712),f72(x48711)),x48712)
% 22.40/22.29 [4872]~P87(x48721)+E(f319(f319(f75(x48721),x48722),f72(x48721)),x48722)
% 22.40/22.29 [4873]~P120(x48731)+E(f319(f319(f282(x48731),x48732),f72(x48731)),x48732)
% 22.40/22.29 [4874]~P69(x48741)+E(f319(f319(f30(x48741),x48742),f72(x48741)),x48742)
% 22.40/22.29 [4875]~P119(x48751)+E(f319(f319(f236(x48751),x48752),f2(a906)),f72(x48751))
% 22.40/22.29 [4876]~P116(x48761)+E(f319(f319(f236(x48761),x48762),f2(a906)),f72(x48761))
% 22.40/22.29 [4877]~E(x48772,f181(f913(x48771,a904)))+E(f319(f29(x48771),x48772),f2(a906))
% 22.40/22.29 [4888]~P69(x48881)+E(f39(x48881,x48882,f2(x48881)),x48882)
% 22.40/22.29 [4899]~P105(x48991)+E(f319(f319(f93(x48991),x48992),f234(x48991)),f234(x48991))
% 22.40/22.29 [4900]~P103(x49001)+E(f319(f319(f94(x49001),x49002),f181(x49001)),f181(x49001))
% 22.40/22.29 [4901]~P119(x49011)+E(f319(f319(f75(x49011),x49012),f2(x49011)),f2(x49011))
% 22.40/22.29 [4902]~P130(x49021)+E(f319(f319(f75(x49021),x49022),f2(x49021)),f2(x49021))
% 22.40/22.29 [4903]~P121(x49031)+E(f319(f319(f282(x49031),x49032),f2(x49031)),f2(x49031))
% 22.40/22.29 [4904]~P69(x49041)+E(f319(f319(f30(x49041),x49042),f2(x49041)),f2(x49041))
% 22.40/22.29 [4906]~P69(x49061)+E(f39(x49061,x49062,f72(x49061)),f2(x49061))
% 22.40/22.29 [4907]~P69(x49071)+E(f39(x49071,f2(x49071),x49072),f2(x49071))
% 22.40/22.29 [4934]E(x49341,f2(a906))+E(f49(x49342,x49341,f105(x49342)),f105(f907(x49342)))
% 22.40/22.29 [4957]P53(x49571,x49572)+~E(f319(f278(x49571,x49571),x49572),x49572)
% 22.40/22.29 [4958]P37(x49581,x49582)+~E(f574(x49582,x49581),f181(f913(x49581,a904)))
% 22.40/22.29 [4959]E(x49591,f105(x49592))+~E(f319(f164(x49592),x49591),f181(f913(x49592,a904)))
% 22.40/22.29 [4960]E(x49601,f105(x49602))+~E(f181(f913(x49602,a904)),f319(f164(x49602),x49601))
% 22.40/22.29 [4963]~E(x49631,x49632)+P1(f319(f319(a316,x49631),x49632))
% 22.40/22.29 [4973]P1(x49731)+P1(f319(f319(a322,x49731),x49732))
% 22.40/22.29 [4974]E(x49741,f105(x49742))+E(f319(f319(f156(x49742),x49741),f2(a906)),f319(f133(x49742),x49741))
% 22.40/22.29 [4977]E(f144(x49771,x49772),x49772)+~P1(f319(f129(x49771),x49772))
% 22.40/22.29 [4984]~P1(x49842)+P1(f319(f319(a322,x49841),x49842))
% 22.40/22.29 [4985]~P1(x49852)+P1(f319(f319(a318,x49851),x49852))
% 22.40/22.29 [4986]~P1(x49861)+P1(f319(f319(a318,x49861),x49862))
% 22.40/22.29 [4996]~E(f658(x49962,x49961),f662(x49962,x49961))+P1(f319(f129(x49961),x49962))
% 22.40/22.29 [5003]E(f319(f254(x50031),x50032),f181(f913(x50031,a904)))+P1(f319(x50032,f530(x50032)))
% 22.40/22.29 [5004]E(f181(f913(x50041,a904)),f319(f254(x50041),x50042))+P1(f319(x50042,f531(x50042)))
% 22.40/22.29 [5074]~P113(x50741)+E(f319(f319(f75(x50741),x50742),f76(x50741,x50742)),f319(f69(x50741),x50742))
% 22.40/22.29 [5085]~E(x50851,f2(a1))+E(f40(x50851,x50852),f319(f319(f244(a1,a1),f2(a1)),f2(a1)))
% 22.40/22.29 [5117]~P59(x51171,x51172)+P59(x51171,f319(f278(x51171,x51171),x51172))
% 22.40/22.29 [5118]~P38(x51181,x51182)+P38(x51181,f319(f278(x51181,x51181),x51182))
% 22.40/22.29 [5119]~P39(x51191,x51192)+P39(x51191,f319(f278(x51191,x51191),x51192))
% 22.40/22.29 [5120]~P53(x51201,x51202)+P53(x51201,f319(f278(x51201,x51201),x51202))
% 22.40/22.29 [5142]E(x51421,x51422)+~P1(f319(f319(a316,x51421),x51422))
% 22.40/22.29 [5153]P1(x51531)+~P1(f319(f319(a317,x51532),x51531))
% 22.40/22.29 [5154]P1(x51541)+~P1(f319(f319(a317,x51541),x51542))
% 22.40/22.29 [5159]~P112(x51591)+P1(f319(f319(f225(x51591),x51592),f234(x51591)))
% 22.40/22.29 [5160]~P119(x51601)+P1(f319(f319(f279(x51601),x51602),f2(x51601)))
% 22.40/22.29 [5164]E(x51641,x51642)+~E(f319(x51641,f326(x51642,x51641)),f319(x51642,f326(x51642,x51641)))
% 22.40/22.29 [5197]E(x51971,f2(a906))+E(f209(x51971,f39(a906,x51972,x51971)),f209(x51972,x51971))
% 22.40/22.29 [5202]~P4(x52021)+P13(x52021,f319(f319(f143(x52021),x52022),f105(x52021)))
% 22.40/22.29 [5206]E(x52061,f2(a1))+P1(f319(f43(x52062,x52061),f40(x52062,x52061)))
% 22.40/22.29 [5222]~P16(x52222,x52221)+P1(f319(f319(x52221,f791(x52221)),f791(x52221)))
% 22.40/22.29 [5225]~E(x52251,x52252)+P1(f319(f319(f226(a906),x52251),f319(a104,x52252)))
% 22.40/22.29 [5235]~E(x52351,f2(a906))+P1(f319(f319(f226(a906),x52351),f319(a104,x52352)))
% 22.40/22.29 [5247]P1(f319(x52471,x52472))+P1(f319(f319(f225(a1),f2(a1)),f422(x52471)))
% 22.40/22.29 [5311]P59(x53111,x53112)+~P59(x53111,f319(f278(x53111,x53111),x53112))
% 22.40/22.29 [5312]P38(x53121,x53122)+~P38(x53121,f319(f278(x53121,x53121),x53122))
% 22.40/22.29 [5313]P39(x53131,x53132)+~P39(x53131,f319(f278(x53131,x53131),x53132))
% 22.40/22.29 [5314]P53(x53141,x53142)+~P53(x53141,f319(f278(x53141,x53141),x53142))
% 22.40/22.29 [5317]~E(f39(a906,x53172,x53171),f2(a906))+E(f319(f319(f75(a906),x53171),f438(x53171,x53172)),x53172)
% 22.40/22.29 [5318]~E(f39(a1,x53182,x53181),f2(a1))+E(f319(f319(f75(a1),x53181),f437(x53181,x53182)),x53182)
% 22.40/22.29 [5344]~P1(f319(x53441,x53442))+P1(f319(f319(f225(a1),f2(a1)),f352(x53441)))
% 22.40/22.29 [5355]E(f319(f319(f3(a906),f319(a97,x53551)),f319(a97,x53552)),f319(a97,x53551))+~P1(f319(a186,x53552))
% 22.40/22.29 [5378]E(f264(x53781,x53782),f72(a91))+~P1(f319(f319(f225(a91),x53781),f72(a91)))
% 22.40/22.29 [5473]E(f319(f319(f156(x54731),x54732),f658(x54732,x54731)),f319(f319(f156(x54731),x54732),f662(x54732,x54731)))+P1(f319(f129(x54731),x54732))
% 22.40/22.29 [5517]~P1(f319(x55171,f84(x55172,x55171)))+P1(f319(x55171,f575(x55172,x55171)))
% 22.40/22.29 [5582]P61(x55821,x55822)+~P1(f319(f307(x55821,x55822),f543(x55822,x55821)))
% 22.40/22.29 [5727]~P16(x57272,x57271)+P1(f319(f319(x57271,f792(x57271,x57272)),f792(x57271,x57272)))
% 22.40/22.29 [5728]~P16(x57282,x57281)+P1(f319(f319(x57281,f795(x57281,x57282)),f795(x57281,x57282)))
% 22.40/22.29 [5737]~E(f319(a104,f39(a906,x57371,x57372)),x57372)+E(f39(a906,f319(a104,x57371),x57372),f2(a906))
% 22.40/22.29 [5793]P37(x57931,x57932)+P1(f319(f319(f321(x57931),f592(x57932,x57931)),f593(x57932,x57931)))
% 22.40/22.29 [5800]~P98(x58001)+P1(f319(f319(f321(x58001),f319(f96(x58001),x58002)),f102(x58001)))
% 22.40/22.29 [5801]~P141(x58011)+P1(f319(f319(f321(x58011),f319(f92(x58011),x58012)),f102(x58011)))
% 22.40/22.29 [5802]~P146(x58021)+P1(f319(f319(f321(x58021),f319(f92(x58021),x58022)),f178(x58021)))
% 22.40/22.29 [5803]~P141(x58031)+P1(f319(f319(f321(x58031),f319(f95(x58031),x58032)),f102(x58031)))
% 22.40/22.29 [5941]~P38(x59411,x59412)+E(f319(f319(f281(x59411,x59411,x59411),x59412),f299(x59411,x59412)),x59412)
% 22.40/22.29 [5956]E(f319(a104,f39(a906,x59561,x59562)),x59562)+E(f39(a906,f319(a104,x59561),x59562),f319(a104,f39(a906,x59561,x59562)))
% 22.40/22.29 [6373]P37(x63731,x63732)+~P1(f319(f319(f321(x63731),f544(x63732,x63731)),f308(x63731,x63732)))
% 22.40/22.29 [6409]~P126(x64091)+~P1(f319(f319(f226(x64091),f319(f92(x64091),x64092)),f2(x64091)))
% 22.40/22.29 [6410]~P92(x64101)+~P1(f319(f319(f226(x64101),f319(f69(x64101),x64102)),f2(x64101)))
% 22.40/22.29 [6500]P1(f319(f319(f226(a1),x65001),f39(a1,x65002,x65001)))+~P1(f319(f319(f226(a1),x65001),f2(a1)))
% 22.40/22.29 [6602]E(f319(f319(f301(a906),f319(a104,x66021)),f295(a906,x66022,x66021)),f295(a906,x66022,f319(a104,x66021)))+~P1(f319(f319(f225(a906),x66022),f319(a104,x66021)))
% 22.40/22.29 [6689]~P4(x66891)+P13(x66891,f142(x66891,x66891,f7(x66891),x66892))
% 22.40/22.29 [6827]E(f319(f159(x68271),x68272),x68272)+~P1(f319(f319(f225(a906),f319(f182(f907(x68271)),x68272)),f72(a906)))
% 22.40/22.29 [6847]~P92(x68471)+P1(f319(f319(f225(x68471),f319(f73(x68471),f319(f69(x68471),x68472))),f2(x68471)))
% 22.40/22.29 [6880]~P37(x68801,x68802)+P37(x68801,f319(f319(f281(x68801,x68801,x68801),x68802),f299(x68801,x68802)))
% 22.40/22.29 [6881]~P53(x68811,x68812)+P53(x68811,f319(f319(f281(x68811,x68811,x68811),x68812),f299(x68811,x68812)))
% 22.40/22.29 [7096]~P1(f319(f319(f226(a1),x70962),f2(a1)))+P1(f319(f319(f225(a1),f39(a1,x70961,x70962)),f2(a1)))
% 22.40/22.29 [7483]~P146(x74831)+E(f183(x74831,f319(f319(f9(x74831,x74831,x74831),f74(x74831)),f72(x74831)),x74832,f2(x74831)),f319(f92(x74831),x74832))
% 22.40/22.29 [7511]~P128(x75111)+~P1(f319(f319(f226(x75111),f319(f319(f75(x75111),x75112),x75112)),f2(x75111)))
% 22.40/22.29 [10307]~P113(x103071)+~P1(f319(f319(f226(x103071),f319(f319(f236(x103071),x103072),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f2(x103071)))
% 22.40/22.29 [4772]~E(x47722,f105(x47721))+E(f319(f182(f907(x47721)),x47722),f2(a906))
% 22.40/22.29 [4802]~E(x48021,f2(a906))+E(f319(f319(f74(a906),x48021),x48022),x48022)
% 22.40/22.29 [4803]~E(x48032,f2(a906))+E(f319(f319(f75(a906),x48031),x48032),f2(a906))
% 22.40/22.29 [4805]~E(x48051,f2(a906))+E(f319(f319(f75(a906),x48051),x48052),f2(a906))
% 22.40/22.29 [4806]~E(x48062,f2(a906))+E(f319(f319(f236(a906),x48061),x48062),f72(a906))
% 22.40/22.29 [4807]~E(x48072,f2(a1))+E(f319(f319(f30(a1),x48071),x48072),f2(a1))
% 22.40/22.29 [4818]E(x48181,f105(x48182))+~E(f319(f182(f907(x48182)),x48181),f2(a906))
% 22.40/22.29 [4819]~P101(x48191)+E(f319(f319(f93(x48191),x48192),x48192),x48192)
% 22.40/22.29 [4821]~P106(x48211)+E(f319(f319(f93(x48211),x48212),x48212),x48212)
% 22.40/22.29 [4822]~P101(x48221)+E(f319(f319(f94(x48221),x48222),x48222),x48222)
% 22.40/22.29 [4824]~P107(x48241)+E(f319(f319(f94(x48241),x48242),x48242),x48242)
% 22.40/22.29 [4826]~P4(x48261)+E(f319(f319(f180(x48261),x48262),x48262),x48262)
% 22.40/22.29 [4828]~P4(x48281)+E(f319(f319(f230(x48281),x48282),x48282),x48282)
% 22.40/22.29 [4830]~P100(x48301)+E(f319(f319(f75(x48301),x48302),x48302),x48302)
% 22.40/22.29 [4848]~P66(x48481)+E(f319(f319(f3(x48481),x48482),x48482),f2(x48481))
% 22.40/22.29 [4862]~P63(x48621)+E(f319(f73(x48621),f319(f73(x48621),x48622)),x48622)
% 22.40/22.29 [4863]~P66(x48631)+E(f319(f73(x48631),f319(f73(x48631),x48632)),x48632)
% 22.40/22.29 [4880]~E(x48802,f2(a906))+E(f319(f319(f236(a906),x48801),x48802),f319(a104,f2(a906)))
% 22.40/22.29 [4915]~P103(x49151)+E(f319(f319(f93(x49151),f181(x49151)),x49152),x49152)
% 22.40/22.29 [4916]~P105(x49161)+E(f319(f319(f94(x49161),f234(x49161)),x49162),x49162)
% 22.40/22.29 [4917]~P76(x49171)+E(f319(f319(f74(x49171),f2(x49171)),x49172),x49172)
% 22.40/22.29 [4918]~P119(x49181)+E(f319(f319(f74(x49181),f2(x49181)),x49182),x49182)
% 22.40/22.29 [4919]~P88(x49191)+E(f319(f319(f74(x49191),f2(x49191)),x49192),x49192)
% 22.40/22.29 [4920]~P119(x49201)+E(f319(f319(f75(x49201),f72(x49201)),x49202),x49202)
% 22.40/22.29 [4921]~P82(x49211)+E(f319(f319(f75(x49211),f72(x49211)),x49212),x49212)
% 22.40/22.29 [4922]~P87(x49221)+E(f319(f319(f75(x49221),f72(x49221)),x49222),x49222)
% 22.40/22.29 [4938]~P105(x49381)+E(f319(f319(f93(x49381),f234(x49381)),x49382),f234(x49381))
% 22.40/22.29 [4939]~P103(x49391)+E(f319(f319(f94(x49391),f181(x49391)),x49392),f181(x49391))
% 22.40/22.29 [4940]~P119(x49401)+E(f319(f319(f75(x49401),f2(x49401)),x49402),f2(x49401))
% 22.40/22.29 [4941]~P130(x49411)+E(f319(f319(f75(x49411),f2(x49411)),x49412),f2(x49411))
% 22.40/22.29 [4942]~P120(x49421)+E(f319(f319(f282(x49421),f2(x49421)),x49422),f2(x49421))
% 22.40/22.29 [4943]~P87(x49431)+E(f319(f319(f236(x49431),f72(x49431)),x49432),f72(x49431))
% 22.40/22.29 [4944]~P69(x49441)+E(f319(f319(f30(x49441),f2(x49441)),x49442),f2(x49441))
% 22.40/22.29 [4952]E(x49521,f105(x49522))+E(f136(x49522,f319(f160(x49522),x49521)),f319(f133(x49522),x49521))
% 22.40/22.29 [4953]E(x49531,f105(x49532))+E(f319(f133(x49532),f319(f160(x49532),x49531)),f136(x49532,x49531))
% 22.40/22.29 [4954]E(x49541,f2(a906))+~E(f319(f319(f74(a906),x49542),x49541),x49542)
% 22.40/22.29 [4961]~P98(x49611)+E(f319(f95(x49611),f319(f96(a1),x49612)),f319(f96(x49611),x49612))
% 22.40/22.29 [4962]~P141(x49621)+E(f319(f95(x49621),f319(f92(a1),x49622)),f319(f92(x49621),x49622))
% 22.40/22.29 [4969]E(x49691,f72(a906))+~E(f319(f319(f75(a906),x49692),x49691),f72(a906))
% 22.40/22.29 [4970]E(x49701,f72(a906))+~E(f319(f319(f75(a906),x49701),x49702),f72(a906))
% 22.40/22.29 [4971]E(x49711,f2(a906))+~E(f319(f319(f74(a906),x49712),x49711),f2(a906))
% 22.40/22.29 [4972]E(x49721,f2(a906))+~E(f319(f319(f74(a906),x49721),x49722),f2(a906))
% 22.40/22.29 [4989]~P92(x49891)+E(f319(f69(x49891),f319(f73(x49891),x49892)),f319(f69(x49891),x49892))
% 22.40/22.29 [4990]~P113(x49901)+E(f319(f69(x49901),f319(f92(x49901),x49902)),f319(f92(x49901),x49902))
% 22.40/22.29 [4991]~P92(x49911)+E(f319(f69(x49911),f319(f69(x49911),x49912)),f319(f69(x49911),x49912))
% 22.40/22.29 [4992]~P76(x49921)+E(f319(f157(x49921),f319(f160(x49921),x49922)),f319(f157(x49921),x49922))
% 22.40/22.29 [4997]~E(x49971,f319(a104,f2(a906)))+E(f319(f319(f236(a906),x49971),x49972),f319(a104,f2(a906)))
% 22.40/22.29 [5006]~P66(x50061)+E(f319(f319(f3(x50061),f2(x50061)),x50062),f319(f73(x50061),x50062))
% 22.40/22.29 [5007]~E(x50072,f2(a906))+E(f131(a906,f319(f294(a906,x50071),x50072)),f105(a906))
% 22.40/22.29 [5016]~P98(x50161)+E(f319(f319(f74(x50161),x50162),f319(f96(x50161),a77)),x50162)
% 22.40/22.29 [5017]E(x50171,f2(a1))+E(f41(f319(f69(a1),x50172),f319(f69(a1),x50171)),f47(x50172,x50171))
% 22.40/22.29 [5033]~E(x50331,x50332)+P1(f319(f319(f225(a906),x50331),x50332))
% 22.40/22.29 [5040]~E(x50401,f2(a91))+E(f319(f319(f74(a906),f319(a22,x50401)),x50402),x50402)
% 22.40/22.29 [5042]~P5(x50421)+E(f87(x50421,f319(f18(x50421,x50421),x50422)),x50422)
% 22.40/22.29 [5055]~P6(x50551)+P6(f319(f319(f236(a1),x50551),x50552))
% 22.40/22.29 [5056]~P63(x50561)+E(f319(f319(f93(x50561),x50562),f319(f73(x50561),x50562)),f234(x50561))
% 22.40/22.29 [5057]~P63(x50571)+E(f319(f319(f94(x50571),x50572),f319(f73(x50571),x50572)),f181(x50571))
% 22.40/22.29 [5058]~P66(x50581)+E(f319(f319(f74(x50581),x50582),f319(f73(x50581),x50582)),f2(x50581))
% 22.40/22.29 [5082]E(x50821,f2(a906))+~E(f319(f73(a1),f319(f92(a1),x50822)),f319(f92(a1),x50821))
% 22.40/22.29 [5083]E(x50831,f2(a906))+~E(f319(f73(a1),f319(f92(a1),x50831)),f319(f92(a1),x50832))
% 22.40/22.29 [5093]E(f187(x50931,x50932),f2(a1))+P1(f319(f319(f225(a1),x50932),x50931))
% 22.40/22.29 [5094]E(f170(x50941,x50942),f105(a1))+P1(f319(f319(f225(a1),x50941),x50942))
% 22.40/22.29 [5095]E(f233(x50951,x50952),f2(a91))+P1(f319(f319(f226(a91),x50951),x50952))
% 22.40/22.29 [5108]E(x51081,f319(a104,f2(a906)))+~E(f319(f319(f75(a906),x51082),x51081),f319(a104,f2(a906)))
% 22.40/22.29 [5109]E(x51091,f319(a104,f2(a906)))+~E(f319(f319(f75(a906),x51091),x51092),f319(a104,f2(a906)))
% 22.40/22.29 [5110]~P2(x51101)+P1(f319(f319(f225(x51101),x51102),x51102))
% 22.40/22.29 [5111]~P119(x51111)+P1(f319(f319(f279(x51111),x51112),x51112))
% 22.40/22.29 [5114]~P98(x51141)+E(f319(f319(f75(x51141),x51142),f319(f96(x51141),a89)),f319(f73(x51141),x51142))
% 22.40/22.29 [5134]~P98(x51341)+E(f319(f73(x51341),f319(f96(x51341),x51342)),f319(f96(x51341),f319(f73(a1),x51342)))
% 22.40/22.29 [5135]~P141(x51351)+E(f319(f73(x51351),f319(f95(x51351),x51352)),f319(f95(x51351),f319(f73(a1),x51352)))
% 22.40/22.29 [5165]~E(x51651,f319(a104,x51652))+P1(f319(f319(f226(a906),f2(a906)),x51651))
% 22.40/22.29 [5183]~P4(x51831)+E(f319(f73(f913(x51831,a904)),f319(f296(x51831),x51832)),f319(f293(x51831),x51832))
% 22.40/22.29 [5184]~P4(x51841)+E(f319(f73(f913(x51841,a904)),f319(f274(x51841),x51842)),f319(f275(x51841),x51842))
% 22.40/22.29 [5185]~P4(x51851)+E(f319(f73(f913(x51851,a904)),f319(f275(x51851),x51852)),f319(f274(x51851),x51852))
% 22.40/22.29 [5186]~P4(x51861)+E(f319(f73(f913(x51861,a904)),f319(f293(x51861),x51862)),f319(f296(x51861),x51862))
% 22.40/22.29 [5196]~E(f319(f92(a1),x51962),x51961)+P1(f319(f319(f225(a1),f2(a1)),x51961))
% 22.40/22.29 [5205]~E(x52052,f2(a1))+E(f47(x52051,x52052),f319(f319(f244(a1,a1),f2(a1)),f319(f69(a1),x52051)))
% 22.40/22.29 [5207]~P62(x52071)+P1(f319(f319(f225(x52071),f181(x52071)),x52072))
% 22.40/22.29 [5246]~P1(f319(x52461,x52462))+P1(f319(x52461,f319(a97,f352(x52461))))
% 22.40/22.29 [5272]~P113(x52721)+E(f319(f319(f75(x52721),f76(x52721,x52722)),f319(f69(x52721),x52722)),x52722)
% 22.40/22.29 [5279]~E(x52792,f2(a906))+E(f79(f912(a906,a906),f42(x52791,x52792)),f319(f319(f244(a906,a906),f2(a906)),x52791))
% 22.40/22.29 [5284]~E(x52841,x52842)+~P1(f319(f319(f226(a906),x52841),x52842))
% 22.40/22.29 [5285]~E(x52851,x52852)+~P1(f319(f319(f226(a1),x52851),x52852))
% 22.40/22.29 [5288]~P146(x52881)+E(f319(f319(f74(x52881),f72(x52881)),f319(f92(x52881),x52882)),f319(f92(x52881),f319(a104,x52882)))
% 22.40/22.29 [5292]~E(x52921,f2(a906))+~P1(f319(f319(f226(a906),x52922),x52921))
% 22.40/22.29 [5307]E(f144(x53071,x53072),x53072)+~E(f319(f182(f907(x53071)),f144(x53071,x53072)),f319(f182(f907(x53071)),x53072))
% 22.40/22.29 [5308]E(f319(f29(x53081),f319(f164(x53081),x53082)),f319(f182(f907(x53081)),x53082))+~P1(f319(f129(x53081),x53082))
% 22.40/22.29 [5322]~P1(f319(x53221,f425(x53221)))+P1(f319(x53221,f319(f92(a1),x53222)))
% 22.40/22.29 [5332]E(f233(x53321,x53322),x53322)+~P1(f319(f319(f226(a91),x53321),x53322))
% 22.40/22.29 [5334]E(f264(x53341,x53342),f72(a91))+~P1(f319(f319(f226(a91),x53342),x53341))
% 22.40/22.29 [5335]E(f170(x53351,x53352),f105(a1))+~P1(f319(f319(f226(a1),x53352),x53351))
% 22.40/22.29 [5336]E(f120(x53361,x53362),f107(a1))+~P1(f319(f319(f226(a1),x53361),x53362))
% 22.40/22.29 [5338]~P111(x53381)+E(f295(x53381,x53382,x53382),f319(f319(f301(x53381),x53382),f181(f913(x53381,a904))))
% 22.40/22.29 [5358]~E(f319(f319(f3(a906),x53581),x53582),f2(a906))+P1(f319(f319(f225(a906),x53581),x53582))
% 22.40/22.29 [5375]~E(x53752,f2(a906))+E(f49(x53751,x53752,f105(x53751)),f319(f319(f143(f907(x53751)),f105(x53751)),f105(f907(x53751))))
% 22.40/22.29 [5379]~P2(x53791)+~P1(f319(f319(f226(x53791),x53792),x53792))
% 22.40/22.29 [5381]~E(f39(a1,x53811,x53812),f2(a1))+E(f39(a1,x53811,f319(f73(a1),x53812)),f2(a1))
% 22.40/22.29 [5383]~E(f39(a1,x53831,x53832),f2(a1))+E(f39(a1,f319(f73(a1),x53831),x53832),f2(a1))
% 22.40/22.29 [5390]E(f319(f294(a906,x53901),f319(a104,x53902)),f181(f913(a906,a904)))+P1(f319(f319(f225(a906),x53901),x53902))
% 22.40/22.29 [5414]E(f131(a906,f319(f294(a906,x54141),x54142)),f105(a906))+P1(f319(f319(f226(a906),x54141),x54142))
% 22.40/22.29 [5419]~E(f319(f29(x54191),f319(f164(x54191),x54192)),f319(f182(f907(x54191)),x54192))+P1(f319(f129(x54191),x54192))
% 22.40/22.29 [5423]~P1(f319(f129(x54231),x54232))+P1(f319(f129(x54231),f319(f159(x54231),x54232)))
% 22.40/22.29 [5424]~P1(f319(f129(x54241),x54242))+P1(f319(f129(x54241),f319(f163(x54241),x54242)))
% 22.40/22.29 [5425]~P1(f319(f129(x54251),x54252))+P1(f319(f129(x54251),f319(f160(x54251),x54252)))
% 22.40/22.29 [5433]P1(f319(x54331,x54332))+~P1(f319(x54331,f319(a97,f422(x54331))))
% 22.40/22.29 [5434]P1(f319(f319(f225(a906),x54342),x54341))+P1(f319(f319(f225(a906),x54341),x54342))
% 22.40/22.29 [5435]P1(f319(f319(f225(a1),x54352),x54351))+P1(f319(f319(f225(a1),x54351),x54352))
% 22.40/22.29 [5439]~P92(x54391)+P1(f319(f319(f225(x54391),x54392),f319(f69(x54391),x54392)))
% 22.40/22.29 [5442]P1(f319(x54421,f431(x54421)))+~P1(f319(x54421,f319(f92(a1),x54422)))
% 22.40/22.29 [5466]E(f319(f319(f3(a906),x54661),x54662),f2(a906))+~P1(f319(f319(f225(a906),x54661),x54662))
% 22.40/22.29 [5467]E(f319(f319(f30(a906),x54671),x54672),f2(a906))+~P1(f319(f319(f226(a906),x54671),x54672))
% 22.40/22.29 [5485]E(f39(a906,x54851,x54852),x54851)+~P1(f319(f319(f226(a906),x54851),x54852))
% 22.40/22.29 [5493]E(f39(a1,x54931,f319(f73(a1),x54932)),f283(x54931,x54932))+P1(f319(f319(f225(a1),f2(a1)),x54932))
% 22.40/22.29 [5506]E(f319(f319(f3(a1),x55061),x55062),f187(x55061,x55062))+~P1(f319(f319(f225(a1),x55062),x55061))
% 22.40/22.29 [5526]P1(f319(f319(f225(a1),f2(a1)),f425(x55261)))+P1(f319(x55261,f319(f92(a1),x55262)))
% 22.40/22.29 [5539]~P126(x55391)+P1(f319(f319(f225(x55391),f2(x55391)),f319(f92(x55391),x55392)))
% 22.40/22.29 [5540]~P92(x55401)+P1(f319(f319(f225(x55401),f2(x55401)),f319(f69(x55401),x55402)))
% 22.40/22.29 [5568]E(f319(f319(f74(a906),x55681),f847(x55682,x55681)),x55682)+~P1(f319(f319(f225(a906),x55681),x55682))
% 22.40/22.29 [5583]E(f295(a1,x55831,x55832),f181(f913(a1,a904)))+~P1(f319(f319(f226(a1),x55832),x55831))
% 22.40/22.29 [5586]~P113(x55861)+E(f319(f319(f75(x55861),f319(f69(x55861),x55862)),f319(f69(x55861),x55862)),f319(f319(f75(x55861),x55862),x55862))
% 22.40/22.29 [5591]E(f131(a906,f319(f294(a906,x55911),f319(a104,x55912))),f105(a906))+P1(f319(f319(f225(a906),x55911),x55912))
% 22.40/22.29 [5593]E(f319(f319(f30(a1),x55931),x55932),f284(x55931,x55932))+~P1(f319(f319(f225(a1),f2(a1)),x55932))
% 22.40/22.29 [5613]P1(f319(f129(x56131),x56132))+~P1(f319(f129(x56131),f319(f159(x56131),x56132)))
% 22.40/22.29 [5614]P1(f319(f129(x56141),x56142))+~P1(f319(f129(x56141),f319(f160(x56141),x56142)))
% 22.40/22.29 [5641]P1(f319(f55(a906),x56411))+P1(f319(f319(f321(a906),f848(x56411,x56412)),x56411))
% 22.40/22.29 [5642]P1(f319(f55(a906),x56421))+P1(f319(f319(f321(a906),f885(x56421,x56422)),x56421))
% 22.40/22.29 [5645]P1(f319(f319(f226(a906),x56452),f319(a104,x56451)))+P1(f319(f319(f226(a906),x56451),x56452))
% 22.40/22.29 [5646]E(f39(a1,x56461,x56462),f283(x56461,x56462))+~P1(f319(f319(f225(a1),f2(a1)),x56462))
% 22.40/22.29 [5649]E(f131(a906,f319(f294(a906,x56491),x56492)),f105(a906))+~P1(f319(f319(f225(a906),x56492),x56491))
% 22.40/22.29 [5650]~P65(x56501)+E(f319(f302(x56501,x56501,f73(x56501)),f319(f296(x56501),x56502)),f319(f274(x56501),f319(f73(x56501),x56502)))
% 22.40/22.29 [5651]~P65(x56511)+E(f319(f302(x56511,x56511,f73(x56511)),f319(f274(x56511),x56512)),f319(f296(x56511),f319(f73(x56511),x56512)))
% 22.40/22.29 [5652]~P65(x56521)+E(f319(f302(x56521,x56521,f73(x56521)),f319(f275(x56521),x56522)),f319(f293(x56521),f319(f73(x56521),x56522)))
% 22.40/22.29 [5653]~P65(x56531)+E(f319(f302(x56531,x56531,f73(x56531)),f319(f293(x56531),x56532)),f319(f275(x56531),f319(f73(x56531),x56532)))
% 22.40/22.29 [5664]E(x56641,f181(f913(x56642,a904)))+P1(f319(f319(f321(x56642),f576(x56641,x56642)),x56641))
% 22.40/22.29 [5665]E(x56651,f181(f913(x56652,a904)))+P1(f319(f319(f321(x56652),f588(x56651,x56652)),x56651))
% 22.40/22.29 [5676]~P1(f319(f319(f226(a906),x56761),x56762))+P1(f319(f319(f225(a906),x56761),x56762))
% 22.40/22.29 [5677]~P1(f319(f319(f226(a1),x56771),x56772))+P1(f319(f319(f225(a1),x56771),x56772))
% 22.40/22.29 [5693]E(f41(x56931,x56932),f319(f319(f244(a1,a1),f2(a1)),x56931))+~P1(f319(f319(f226(a1),x56931),x56932))
% 22.40/22.29 [5695]E(f208(f319(f73(a1),x56951),f319(f73(a1),x56952)),f208(x56951,x56952))+~P1(f319(f319(f226(a1),x56952),f2(a1)))
% 22.40/22.29 [5709]E(x57091,x57092)+~E(f319(a5,f319(a104,f319(a22,x57091))),f319(a5,f319(a104,f319(a22,x57092))))
% 22.40/22.29 [5714]E(f41(x57141,x57142),f319(f319(f244(a1,a1),f2(a1)),x57141))+~P1(f319(f319(f225(a1),x57142),f2(a1)))
% 22.40/22.29 [5743]E(f39(a906,f319(f96(a906),x57431),f319(f96(a906),x57432)),f2(a906))+~P1(f319(a186,f319(f96(a1),x57431)))
% 22.40/22.29 [5758]P1(f319(f319(f225(a1),f2(a1)),f431(x57581)))+~P1(f319(x57581,f319(f92(a1),x57582)))
% 22.40/22.29 [5791]P41(f295(a1,x57911,x57912))+~P1(f319(f319(f225(a1),f2(a1)),x57911))
% 22.40/22.29 [5796]~P1(f319(f55(x57961),x57962))+P1(f319(f55(f913(x57961,a904)),f319(f300(x57961),x57962)))
% 22.40/22.29 [5809]E(f319(f319(f74(a1),x58091),f319(f92(a1),f434(x58092,x58091))),x58092)+~P1(f319(f319(f225(a1),x58091),x58092))
% 22.40/22.29 [5817]P1(f319(f319(f225(a906),x58171),x58172))+P1(f319(f319(f225(a906),f319(a104,x58172)),x58171))
% 22.40/22.29 [5861]E(f319(f319(f30(a906),f319(f96(a906),x58611)),f319(f96(a906),x58612)),f2(a906))+~P1(f319(a186,f319(f96(a1),x58611)))
% 22.40/22.29 [5862]E(f319(f319(f75(a906),f319(f96(a906),x58621)),f319(f96(a906),x58622)),f2(a906))+~P1(f319(f319(f226(a1),x58621),a77))
% 22.40/22.29 [5864]P1(f319(f319(f225(a906),x58641),f319(a104,x58642)))+~P1(f319(f319(f225(a906),x58641),x58642))
% 22.40/22.29 [5866]P1(f319(f319(f226(a906),x58661),f319(a104,x58662)))+~P1(f319(f319(f225(a906),x58661),x58662))
% 22.40/22.29 [5868]P1(f319(f319(f226(a906),x58681),f319(a104,x58682)))+~P1(f319(f319(f226(a906),x58681),x58682))
% 22.40/22.29 [5871]~E(x58711,x58712)+P1(f319(f319(f226(a1),x58711),f319(f319(f74(a1),x58712),f72(a1))))
% 22.40/22.29 [5874]E(f39(a1,x58741,x58742),f2(a1))+E(f319(f319(f3(a1),x58742),f39(a1,x58741,x58742)),f39(a1,f319(f73(a1),x58741),x58742))
% 22.40/22.29 [5883]E(x58831,f105(x58832))+P1(f319(f319(f321(x58832),f136(x58832,x58831)),f319(f164(x58832),x58831)))
% 22.40/22.29 [5895]E(f79(f912(a906,a906),f42(x58951,x58952)),f319(f319(f244(a906,a906),f2(a906)),x58951))+~P1(f319(f319(f226(a906),x58951),x58952))
% 22.40/22.29 [5934]E(f319(f319(f3(a906),f319(f96(a906),x59341)),f319(f96(a906),x59342)),f319(f96(a906),x59341))+~P1(f319(f319(f226(a1),x59342),a77))
% 22.40/22.29 [5935]E(f319(f319(f74(a906),f319(f96(a906),x59351)),f319(f96(a906),x59352)),f319(f96(a906),x59352))+~P1(f319(f319(f226(a1),x59351),a77))
% 22.40/22.29 [5942]E(f319(a104,f319(f319(f74(a906),x59421),f889(x59422,x59421))),x59422)+~P1(f319(f319(f226(a906),x59421),x59422))
% 22.40/22.29 [5967]P1(f319(x59671,x59672))+~P1(f319(x59671,f319(a83,f565(x59672,x59671))))
% 22.40/22.29 [5968]P1(f319(x59681,x59682))+~P1(f319(x59681,f319(a5,f807(x59682,x59681))))
% 22.40/22.29 [5977]~P1(f319(f319(f226(a906),x59771),f319(a104,x59772)))+P1(f319(f319(f225(a906),x59771),x59772))
% 22.40/22.29 [6023]E(f319(f319(f301(a906),x60231),f319(f294(a906,x60232),x60231)),f319(f294(a906,x60232),f319(a104,x60231)))+~P1(f319(f319(f225(a906),x60232),x60231))
% 22.40/22.29 [6025]E(x60251,f105(x60252))+E(f319(f319(f126(x60252),f106(x60252,x60251)),f319(f319(f143(x60252),f136(x60252,x60251)),f105(x60252))),x60251)
% 22.40/22.29 [6041]P1(f319(f55(x60411),x60412))+~P1(f319(f319(f226(a906),f2(a906)),f319(f29(x60411),x60412)))
% 22.40/22.29 [6044]~E(x60441,f181(f913(x60442,a904)))+~P1(f319(f319(f226(a906),f2(a906)),f319(f29(x60442),x60441)))
% 22.40/22.29 [6056]~P1(f319(f319(f226(a906),x60561),x60562))+P1(f319(f319(f225(a906),f319(a104,x60561)),x60562))
% 22.40/22.29 [6060]~P4(x60601)+E(f142(x60601,x60601,f7(x60601),f144(x60601,x60602)),f131(x60601,f319(f164(x60601),x60602)))
% 22.40/22.29 [6063]E(x60631,f105(x60632))+P1(f319(f319(f321(x60632),f319(f133(x60632),x60631)),f319(f164(x60632),x60631)))
% 22.40/22.29 [6069]~P126(x60691)+P1(f319(f319(f226(x60691),x60692),f319(f319(f74(x60691),x60692),f72(x60691))))
% 22.40/22.29 [6071]~P92(x60711)+P1(f319(f319(f225(x60711),f319(f73(x60711),x60712)),f319(f69(x60711),x60712)))
% 22.40/22.29 [6103]P1(f319(f55(a906),x61031))+~P1(f319(f319(f225(a906),f848(x61031,x61032)),x61032))
% 22.40/22.29 [6104]P1(f319(f55(a906),x61041))+~P1(f319(f319(f226(a906),f885(x61041,x61042)),x61042))
% 22.40/22.29 [6108]~P1(f319(f55(f912(x61081,x61081)),x61082))+P1(f319(f55(x61081),f319(f273(x61081),x61082)))
% 22.40/22.29 [6162]~P1(f319(f319(f226(a906),x61622),f319(a104,x61621)))+~P1(f319(f319(f226(a906),x61621),x61622))
% 22.40/22.29 [6163]~P111(x61631)+E(f319(f319(f94(f913(x61631,a904)),f319(f293(x61631),x61632)),f319(f275(x61631),x61632)),f319(f319(f301(x61631),x61632),f181(f913(x61631,a904))))
% 22.40/22.29 [6175]P1(f319(f55(x61751),x61752))+~P1(f319(f55(f913(x61751,a904)),f319(f300(x61751),x61752)))
% 22.40/22.29 [6197]P1(f319(f319(f225(a906),f319(a104,x61971)),f319(a104,x61972)))+~P1(f319(f319(f225(a906),x61971),x61972))
% 22.40/22.29 [6198]P1(f319(f319(f225(a906),f319(a22,x61981)),f319(a22,x61982)))+~P1(f319(f319(f225(a91),x61981),x61982))
% 22.40/22.29 [6199]P1(f319(f319(f225(a91),f319(a5,x61991)),f319(a5,x61992)))+~P1(f319(f319(f225(a906),x61991),x61992))
% 22.40/22.29 [6201]P1(f319(f319(f226(a906),f319(a104,x62011)),f319(a104,x62012)))+~P1(f319(f319(f226(a906),x62011),x62012))
% 22.40/22.29 [6202]P1(f319(f319(f226(a906),f319(a22,x62021)),f319(a22,x62022)))+~P1(f319(f319(f226(a91),x62021),x62022))
% 22.40/22.29 [6203]P1(f319(f319(f226(a91),f319(a5,x62031)),f319(a5,x62032)))+~P1(f319(f319(f226(a906),x62031),x62032))
% 22.40/22.29 [6208]E(x62081,x62082)+~E(f319(f302(a906,a1,f92(a1)),x62081),f319(f302(a906,a1,f92(a1)),x62082))
% 22.40/22.29 [6224]P1(f319(f319(f225(a906),x62241),x62242))+~P1(f319(f319(f225(a906),f319(a104,x62241)),x62242))
% 22.40/22.29 [6227]P1(f319(f319(f226(a906),x62271),x62272))+~P1(f319(f319(f225(a906),f319(a104,x62271)),x62272))
% 22.40/22.29 [6228]P1(f319(f319(f226(a906),x62281),x62282))+~P1(f319(f319(f226(a906),f319(a104,x62281)),x62282))
% 22.40/22.29 [6248]E(f39(a1,x62481,x62482),f2(a1))+E(f319(f319(f3(a1),f39(a1,x62481,x62482)),x62482),f39(a1,x62481,f319(f73(a1),x62482)))
% 22.40/22.29 [6314]E(f319(f29(f913(x63141,a904)),f319(f300(x63141),x63142)),f319(f319(f236(a906),f319(a104,f319(a104,f2(a906)))),f319(f29(x63141),x63142)))+~P1(f319(f55(x63141),x63142))
% 22.40/22.29 [6317]E(x63171,f105(x63172))+E(f319(f319(f156(x63172),x63171),f319(f319(f3(a906),f319(f182(f907(x63172)),x63171)),f72(a906))),f136(x63172,x63171))
% 22.40/22.29 [6339]E(x63391,f105(x63392))+E(f319(f319(f126(x63392),f319(f163(x63392),x63391)),f319(f319(f143(x63392),f319(f133(x63392),x63391)),f105(x63392))),f319(f159(x63392),x63391))
% 22.40/22.29 [6370]~P1(f319(f55(x63701),f31(f913(x63701,a904),x63702)))+P1(f319(f55(f913(x63701,a904)),x63702))
% 22.40/22.29 [6392]P1(f319(f319(f225(a906),f319(f96(a906),x63921)),f319(f96(a906),x63922)))+~P1(f319(f319(f225(a1),x63921),a77))
% 22.40/22.29 [6412]~P1(f319(f319(f226(a1),x64121),x64122))+P1(f319(f319(f225(a1),x64121),f319(f319(f3(a1),x64122),f72(a1))))
% 22.40/22.29 [6413]~P1(f319(f319(f225(a1),x64131),x64132))+P1(f319(f319(f226(a1),x64131),f319(f319(f74(a1),x64132),f72(a1))))
% 22.40/22.29 [6414]~P1(f319(f319(f226(a1),x64141),x64142))+P1(f319(f319(f226(a1),x64141),f319(f319(f74(a1),x64142),f72(a1))))
% 22.40/22.29 [6416]~P1(f319(f319(f225(a1),x64161),x64162))+P1(f319(f319(f225(a906),f319(f96(a906),x64161)),f319(f96(a906),x64162)))
% 22.40/22.29 [6417]~P1(f319(f319(f225(a1),x64171),x64172))+P1(f319(f319(f225(a1),f319(f96(a1),x64171)),f319(f96(a1),x64172)))
% 22.40/22.29 [6419]~P1(f319(f319(f225(a906),x64191),x64192))+P1(f319(f319(f225(a1),f319(f92(a1),x64191)),f319(f92(a1),x64192)))
% 22.40/22.29 [6420]~P1(f319(f319(f226(a1),x64201),x64202))+P1(f319(f319(f226(a1),f319(f96(a1),x64201)),f319(f96(a1),x64202)))
% 22.40/22.29 [6422]~P1(f319(f319(f226(a906),x64221),x64222))+P1(f319(f319(f226(a1),f319(f92(a1),x64221)),f319(f92(a1),x64222)))
% 22.40/22.29 [6442]~P1(f319(f319(f225(a906),x64421),x64422))+~P1(f319(f319(f225(a906),f319(a104,x64422)),x64421))
% 22.40/22.29 [6484]~P1(f319(f319(f225(a906),f319(a104,x64841)),f319(a104,x64842)))+P1(f319(f319(f225(a906),x64841),x64842))
% 22.40/22.29 [6485]~P1(f319(f319(f225(a91),f319(a5,x64851)),f319(a5,x64852)))+P1(f319(f319(f225(a906),x64851),x64852))
% 22.40/22.29 [6486]~P1(f319(f319(f225(a906),f319(a22,x64861)),f319(a22,x64862)))+P1(f319(f319(f225(a91),x64861),x64862))
% 22.40/22.29 [6488]~P1(f319(f319(f226(a906),f319(a104,x64881)),f319(a104,x64882)))+P1(f319(f319(f226(a906),x64881),x64882))
% 22.40/22.29 [6489]~P1(f319(f319(f226(a91),f319(a5,x64891)),f319(a5,x64892)))+P1(f319(f319(f226(a906),x64891),x64892))
% 22.40/22.29 [6490]~P1(f319(f319(f226(a906),f319(a97,x64901)),f319(a97,x64902)))+P1(f319(f319(f226(a1),x64901),x64902))
% 22.40/22.29 [6491]~P1(f319(f319(f226(a906),f319(a22,x64911)),f319(a22,x64912)))+P1(f319(f319(f226(a91),x64911),x64912))
% 22.40/22.29 [6535]~P1(f319(f319(f226(a906),f319(a97,x65352)),f319(a97,x65351)))+P1(f319(f319(f226(a1),f2(a1)),x65351))
% 22.40/22.29 [6566]P1(f319(f319(f225(a1),f2(a1)),f39(a1,x65661,x65662)))+~P1(f319(f319(f226(a1),f2(a1)),x65662))
% 22.40/22.29 [6727]P37(x67271,x67272)+~E(f319(f319(f281(x67271,x67271,x67271),x67272),x67272),f181(f913(f912(x67271,x67271),a904)))
% 22.40/22.29 [6741]~P37(x67411,x67412)+P37(x67411,f319(f319(f281(x67411,x67411,x67411),x67412),x67412))
% 22.40/22.29 [6752]P1(f319(f319(f225(a1),x67521),x67522))+~P1(f319(f319(f226(a1),x67521),f319(f319(f74(a1),x67522),f72(a1))))
% 22.40/22.29 [6753]P1(f319(f319(f226(a1),x67531),x67532))+~P1(f319(f319(f225(a1),x67531),f319(f319(f3(a1),x67532),f72(a1))))
% 22.40/22.29 [6756]P1(f319(f319(f225(a906),x67561),x67562))+~P1(f319(f319(f225(a1),f319(f92(a1),x67561)),f319(f92(a1),x67562)))
% 22.40/22.29 [6757]P1(f319(f319(f225(a1),x67571),x67572))+~P1(f319(f319(f225(a1),f319(f96(a1),x67571)),f319(f96(a1),x67572)))
% 22.40/22.29 [6759]P1(f319(f319(f226(a906),x67591),x67592))+~P1(f319(f319(f226(a1),f319(f92(a1),x67591)),f319(f92(a1),x67592)))
% 22.40/22.29 [6760]P1(f319(f319(f226(a1),x67601),x67602))+~P1(f319(f319(f226(a906),f319(f96(a906),x67601)),f319(f96(a906),x67602)))
% 22.40/22.29 [6761]P1(f319(f319(f226(a1),x67611),x67612))+~P1(f319(f319(f226(a1),f319(f96(a1),x67611)),f319(f96(a1),x67612)))
% 22.40/22.29 [6862]~E(f687(x68622,x68621),f105(x68621))+E(f319(f134(f907(x68621),f907(x68621),f126(x68621),f105(x68621)),x68622),f105(x68621))
% 22.40/22.29 [6863]~E(f693(x68632,x68631),f105(x68631))+E(f319(f134(f907(x68631),f907(x68631),f126(x68631),f105(x68631)),x68632),f105(x68631))
% 22.40/22.29 [6867]~P5(x68671)+E(f319(f134(x68671,x68671,f94(x68671),f234(x68671)),x68672),f32(x68671,f319(f164(x68671),x68672)))
% 22.40/22.29 [6868]~P5(x68681)+E(f319(f134(x68681,x68681,f93(x68681),f181(x68681)),x68682),f31(x68681,f319(f164(x68681),x68682)))
% 22.40/22.29 [6882]E(x68821,f2(a91))+E(f319(f319(f74(a906),f319(a22,f319(f319(f3(a91),x68821),f72(a91)))),f319(a104,x68822)),f319(f319(f74(a906),f319(a22,x68821)),x68822))
% 22.40/22.29 [6926]P1(f319(f319(f226(a1),f319(f319(f3(a1),x69261),x69262)),f2(a1)))+~P1(f319(f319(f226(a1),x69261),x69262))
% 22.40/22.29 [6950]~P4(x69501)+E(f319(f319(f93(f913(x69501,a904)),f319(f319(f301(x69501),x69502),f181(f913(x69501,a904)))),f319(f296(x69501),x69502)),f319(f275(x69501),x69502))
% 22.40/22.29 [7023]~P61(x70231,x70232)+P37(x70231,f319(f254(f912(x70231,x70231)),f319(f249(x70231,x70231,a904),x70232)))
% 22.40/22.29 [7024]~P61(x70241,x70242)+P59(x70241,f319(f254(f912(x70241,x70241)),f319(f249(x70241,x70241,a904),x70242)))
% 22.40/22.29 [7025]~P51(x70251,x70252)+P38(x70251,f319(f254(f912(x70251,x70251)),f319(f249(x70251,x70251,a904),x70252)))
% 22.40/22.29 [7026]~P52(x70261,x70262)+P53(x70261,f319(f254(f912(x70261,x70261)),f319(f249(x70261,x70261,a904),x70262)))
% 22.40/22.29 [7027]E(x70271,f181(f913(x70272,a904)))+~P1(f319(f319(f225(f913(x70272,a904)),x70271),f181(f913(x70272,a904))))
% 22.40/22.29 [7112]~P1(f319(f319(f226(a906),f2(a906)),x71122))+P1(f319(f319(f225(a906),f39(a906,x71121,x71122)),x71122))
% 22.40/22.29 [7113]~P1(f319(f319(f225(a1),f2(a1)),x71131))+P1(f319(f319(f225(a1),f39(a1,x71131,x71132)),x71131))
% 22.40/22.29 [7114]~P1(f319(f319(f226(a906),f2(a906)),x71142))+P1(f319(f319(f226(a906),f39(a906,x71141,x71142)),x71142))
% 22.40/22.29 [7116]~P1(f319(f319(f226(a1),f2(a1)),x71162))+P1(f319(f319(f226(a1),f39(a1,x71161,x71162)),x71162))
% 22.40/22.29 [7191]~P111(x71911)+E(f319(f319(f3(f913(x71911,a904)),f319(f319(f301(x71911),x71912),f181(f913(x71911,a904)))),f319(f274(x71911),x71912)),f319(f319(f301(x71911),x71912),f181(f913(x71911,a904))))
% 22.40/22.29 [7263]~P49(x72631,x72632)+P54(x72631,f234(f913(x72631,a904)),f319(f254(f912(x72631,x72631)),f319(f249(x72631,x72631,a904),x72632)))
% 22.40/22.29 [7264]P1(f319(x72641,x72642))+P1(f319(f319(f321(f913(f912(a906,a906),a904)),f565(x72642,x72641)),a90))
% 22.40/22.29 [7308]E(f319(f319(f126(a906),f131(a906,f319(f294(a906,x73081),x73082))),f319(f319(f143(a906),x73082),f105(a906))),f131(a906,f319(f294(a906,x73081),f319(a104,x73082))))+~P1(f319(f319(f225(a906),x73081),x73082))
% 22.40/22.29 [7450]E(x74501,f2(a906))+~E(f319(f134(a906,a906,f74(a906),x74501),x74502),f2(a906))
% 22.40/22.29 [7475]~P1(f319(f319(f226(a1),f319(f319(f3(a1),x74751),x74752)),f2(a1)))+P1(f319(f319(f226(a1),x74751),x74752))
% 22.40/22.29 [7503]P37(x75031,x75032)+~P37(x75031,f319(f319(f281(x75031,x75031,x75031),x75032),x75032))
% 22.40/22.29 [7528]~P1(f319(f319(f225(a906),f319(a104,x75281)),x75282))+P1(f177(a904,a231,f319(f225(a906),x75281),x75282))
% 22.40/22.29 [7679]P25(a906,a906,f319(f319(f9(a906,a906,a906),f3(a906)),x76791),x76792)+P1(f319(f319(f321(a906),f577(x76791,x76792)),x76792))
% 22.40/22.29 [7733]E(f319(f319(f319(f59(a906,x77331,f74(a906)),f319(f18(a906,x77331),f72(a906))),f2(a906)),x77332),f319(f29(x77331),x77332))+~P1(f319(f55(x77331),x77332))
% 22.40/22.29 [7775]P25(a906,a906,f319(f319(f9(a906,a906,a906),f3(a906)),x77751),x77752)+~P1(f319(f319(f225(a906),x77751),f577(x77751,x77752)))
% 22.40/22.29 [7829]P37(x78291,x78292)+P1(f319(f319(f225(f913(x78291,a904)),f574(x78292,x78291)),f319(f277(x78291,x78291,x78292),f574(x78292,x78291))))
% 22.40/22.29 [7834]P61(x78341,x78342)+~P37(x78341,f319(f254(f912(x78341,x78341)),f319(f249(x78341,x78341,a904),x78342)))
% 22.40/22.29 [7835]P51(x78351,x78352)+~P38(x78351,f319(f254(f912(x78351,x78351)),f319(f249(x78351,x78351,a904),x78352)))
% 22.40/22.29 [7836]P52(x78361,x78362)+~P53(x78361,f319(f254(f912(x78361,x78361)),f319(f249(x78361,x78361,a904),x78362)))
% 22.40/22.29 [7906]P1(f319(f319(f225(a906),f319(a104,x79061)),x79062))+~P1(f177(a904,a231,f319(f225(a906),x79061),x79062))
% 22.40/22.29 [7964]P1(f319(f319(f321(f912(a906,a906)),f319(f319(f244(a906,a906),x79641),x79642)),f299(a906,a309)))+~P1(f319(f319(f225(a906),x79641),x79642))
% 22.40/22.29 [8052]P49(x80521,x80522)+~P54(x80521,f234(f913(x80521,a904)),f319(f254(f912(x80521,x80521)),f319(f249(x80521,x80521,a904),x80522)))
% 22.40/22.29 [8105]~P1(f319(f129(x81051),x81052))+P1(f319(f129(f913(x81051,a904)),f319(f319(f146(f907(x81051),f913(x81051,a904)),f164(x81051)),f48(x81051,x81052))))
% 22.40/22.29 [8308]~P37(x83081,f319(f278(x83081,x83081),x83082))+P37(x83081,f319(f278(x83081,x83081),f319(f319(f281(x83081,x83081,x83081),x83082),f299(x83081,x83082))))
% 22.40/22.29 [8403]P26(x84031,a906,f811(x84032,x84031),x84032,f319(f294(a906,f2(a906)),f319(f29(x84031),x84032)))+~P1(f319(f55(x84031),x84032))
% 22.40/22.29 [8404]P26(a906,x84041,f812(x84042,x84041),f319(f294(a906,f2(a906)),f319(f29(x84041),x84042)),x84042)+~P1(f319(f55(x84041),x84042))
% 22.40/22.29 [8422]P26(a906,x84221,f813(x84222,x84221),f295(a906,f72(a906),f319(f29(x84221),x84222)),x84222)+~P1(f319(f55(x84221),x84222))
% 22.40/22.29 [8432]P1(f319(f55(f912(x84321,x84321)),f319(f319(f281(x84321,x84321,x84321),x84322),f299(x84321,x84322))))+~P1(f319(f55(f912(x84321,x84321)),x84322))
% 22.40/22.29 [8456]E(x84561,f2(a1))+P1(f319(f43(x84562,x84561),f319(f319(f244(a1,a1),f319(f319(f30(a1),x84562),x84561)),f39(a1,x84562,x84561))))
% 22.40/22.29 [8469]~P1(f319(f319(f321(f912(a906,a906)),f319(f319(f244(a906,a906),x84691),x84692)),f299(a906,a309)))+P1(f319(f319(f225(a906),x84691),x84692))
% 22.40/22.29 [8485]~P88(x84851)+E(f319(f134(x84851,x84851,f319(f9(x84851,x84851,x84851),f74(x84851)),f2(x84851)),f319(f160(x84851),x84852)),f319(f134(x84851,x84851,f74(x84851),f2(x84851)),x84852))
% 22.40/22.29 [8660]~P4(x86601)+E(f319(f134(f907(x86601),x86601,f319(f9(x86601,f907(x86601),f907(x86601)),f140(x86601,x86601,f7(x86601))),f105(x86601)),x86602),f142(x86601,x86601,f7(x86601),x86602))
% 22.40/22.29 [8765]~P59(x87651,f319(f254(f912(x87651,x87651)),f319(f249(x87651,x87651,a904),x87652)))+P59(x87651,f319(f254(f912(x87651,x87651)),f319(f249(x87651,x87651,a904),f235(x87651,x87651,x87652))))
% 22.40/22.29 [8779]P1(f319(f319(f321(f912(a906,a906)),f319(f319(f244(a906,a906),x87791),x87792)),f319(f319(f281(a906,a906,a906),a309),f299(a906,a309))))+~P1(f319(f319(f226(a906),x87791),x87792))
% 22.40/22.29 [8823]~P1(f319(f55(f912(x88231,x88231)),f319(f319(f281(x88231,x88231,x88231),x88232),f299(x88231,x88232))))+P1(f319(f55(f912(x88231,x88231)),x88232))
% 22.40/22.29 [8881]~P59(x88811,f319(f254(f912(x88811,x88811)),f319(f249(x88811,x88811,a904),f235(x88811,x88811,x88812))))+P59(x88811,f319(f254(f912(x88811,x88811)),f319(f249(x88811,x88811,a904),x88812)))
% 22.40/22.30 [9089]P59(x90891,x90892)+P1(f319(f319(f321(f912(x90891,x90891)),f319(f319(f244(x90891,x90891),f605(x90892,x90891)),f605(x90892,x90891))),f319(f319(f281(x90891,x90891,x90891),x90892),f299(x90891,x90892))))
% 22.40/22.30 [9090]P59(x90901,x90902)+P1(f319(f319(f321(f912(x90901,x90901)),f319(f319(f244(x90901,x90901),f614(x90902,x90901)),f614(x90902,x90901))),f319(f319(f281(x90901,x90901,x90901),x90902),f299(x90901,x90902))))
% 22.40/22.30 [9195]~P1(f319(f319(f321(f912(a906,a906)),f319(f319(f244(a906,a906),x91951),x91952)),f319(f319(f281(a906,a906,a906),a309),f299(a906,a309))))+P1(f319(f319(f226(a906),x91951),x91952))
% 22.40/22.30 [5179]~P98(x51791)+E(f319(f319(f74(x51791),f319(f96(x51791),a77)),x51792),x51792)
% 22.40/22.30 [5212]~P63(x52121)+E(f319(f319(f93(x52121),f319(f73(x52121),x52122)),x52122),f234(x52121))
% 22.40/22.30 [5213]~P63(x52131)+E(f319(f319(f94(x52131),f319(f73(x52131),x52132)),x52132),f181(x52131))
% 22.40/22.30 [5214]~P66(x52141)+E(f319(f319(f74(x52141),f319(f73(x52141),x52142)),x52142),f2(x52141))
% 22.40/22.30 [5215]~P67(x52151)+E(f319(f319(f74(x52151),f319(f73(x52151),x52152)),x52152),f2(x52151))
% 22.40/22.30 [5250]~P98(x52501)+E(f319(f319(f75(x52501),f319(f96(x52501),a89)),x52502),f319(f73(x52501),x52502))
% 22.40/22.30 [5406]~P115(x54061)+E(f319(f319(f75(x54061),f319(f73(x54061),f72(x54061))),x54062),f319(f73(x54061),x54062))
% 22.40/22.30 [5451]E(f319(f69(a1),x54511),f72(a1))+~E(f319(f69(a1),f319(f319(f75(a1),x54511),x54512)),f72(a1))
% 22.40/22.30 [5542]~P98(x55421)+E(f319(f319(f74(x55421),f72(x55421)),f319(f96(x55421),x55422)),f319(f96(x55421),f319(f319(f3(a1),x55422),a89)))
% 22.40/22.30 [5594]~P5(x55941)+E(f32(x55941,f319(f319(f301(x55941),x55942),f181(f913(x55941,a904)))),x55942)
% 22.40/22.30 [5595]~P5(x55951)+E(f31(x55951,f319(f319(f301(x55951),x55952),f181(f913(x55951,a904)))),x55952)
% 22.40/22.30 [5596]~P101(x55961)+E(f12(x55961,f319(f319(f301(x55961),x55962),f181(f913(x55961,a904)))),x55962)
% 22.40/22.30 [5597]~P101(x55971)+E(f15(x55971,f319(f319(f301(x55971),x55972),f181(f913(x55971,a904)))),x55972)
% 22.40/22.30 [5598]~P4(x55981)+E(f16(x55981,f319(f319(f301(x55981),x55982),f181(f913(x55981,a904)))),x55982)
% 22.40/22.30 [5599]~P4(x55991)+E(f17(x55991,f319(f319(f301(x55991),x55992),f181(f913(x55991,a904)))),x55992)
% 22.40/22.30 [5621]E(f319(f319(f74(a906),x56211),f319(f319(f3(a906),x56212),x56211)),x56212)+P1(f319(f319(f226(a906),x56212),x56211))
% 22.40/22.30 [5659]E(x56591,f105(x56592))+P1(f319(f319(f226(a906),f2(a906)),f319(f182(f907(x56592)),x56591)))
% 22.40/22.30 [5788]~P4(x57881)+E(f13(x57881,f180(x57881),f319(f319(f301(x57881),x57882),f181(f913(x57881,a904)))),x57882)
% 22.40/22.30 [5789]~P4(x57891)+E(f14(x57891,f230(x57891),f319(f319(f301(x57891),x57892),f181(f913(x57891,a904)))),x57892)
% 22.40/22.30 [5850]E(f319(f319(f3(a906),x58501),f319(f319(f3(a906),x58501),x58502)),x58502)+~P1(f319(f319(f225(a906),x58502),x58501))
% 22.40/22.30 [5851]E(f319(f319(f74(a906),x58511),f319(f319(f3(a906),x58512),x58511)),x58512)+~P1(f319(f319(f225(a906),x58511),x58512))
% 22.40/22.30 [5873]E(f39(a906,f319(f319(f3(a906),x58731),x58732),x58732),f39(a906,x58731,x58732))+P1(f319(f319(f226(a906),x58731),x58732))
% 22.40/22.30 [5884]E(f319(f73(a1),f319(f319(f30(a1),x58841),f319(f73(a1),x58842))),f284(x58841,x58842))+P1(f319(f319(f225(a1),f2(a1)),x58842))
% 22.40/22.30 [5886]~E(x58862,f2(a906))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f236(a906),x58861),x58862)))
% 22.40/22.30 [5945]~P98(x59451)+E(f319(f319(f74(x59451),f319(f73(x59451),f72(x59451))),f319(f96(x59451),x59452)),f319(f96(x59451),f319(f319(f74(a1),x59452),a89)))
% 22.40/22.30 [5947]E(f319(f319(f236(a906),f319(f96(a906),x59471)),x59472),f319(f319(f236(a906),f2(a906)),x59472))+~P1(f319(a186,f319(f96(a1),x59471)))
% 22.40/22.30 [6048]E(f319(f133(a906),f131(a906,f319(f294(a906,x60481),x60482))),x60481)+~P1(f319(f319(f226(a906),x60481),x60482))
% 22.40/22.30 [6064]E(f319(f319(f75(a906),f319(f96(a906),x60641)),f319(f96(a906),x60642)),f319(f96(a906),f319(f319(f75(a1),x60641),x60642)))+P1(f319(f319(f226(a1),x60641),a77))
% 22.40/22.30 [6070]~P128(x60701)+P1(f319(f319(f225(x60701),f2(x60701)),f319(f319(f75(x60701),x60702),x60702)))
% 22.40/22.30 [6082]E(f319(f319(f3(a906),f319(a104,x60821)),x60822),f319(a104,f319(f319(f3(a906),x60821),x60822)))+~P1(f319(f319(f225(a906),x60822),x60821))
% 22.40/22.30 [6085]E(f39(a906,f319(f319(f3(a906),x60851),x60852),x60852),f39(a906,x60851,x60852))+~P1(f319(f319(f225(a906),x60852),x60851))
% 22.40/22.30 [6138]E(f319(f319(f236(a906),f319(a97,x61381)),x61382),f319(a97,f319(f319(f236(a1),x61381),x61382)))+~P1(f319(f319(f225(a1),f2(a1)),x61381))
% 22.40/22.30 [6156]P1(f319(f129(x61561),x61562))+P1(f319(f319(f226(a906),f658(x61562,x61561)),f319(f182(f907(x61561)),x61562)))
% 22.40/22.30 [6157]P1(f319(f129(x61571),x61572))+P1(f319(f319(f226(a906),f662(x61572,x61571)),f319(f182(f907(x61571)),x61572)))
% 22.40/22.30 [6169]~E(x61691,f105(x61692))+~P1(f319(f319(f226(a906),f2(a906)),f319(f182(f907(x61692)),x61691)))
% 22.40/22.30 [6180]E(f136(a906,f131(a906,f319(f294(a906,x61801),x61802))),f319(f319(f3(a906),x61802),f72(a906)))+~P1(f319(f319(f226(a906),x61801),x61802))
% 22.40/22.30 [6183]E(f319(f319(f74(a1),x61831),f319(f92(a1),f319(a104,f435(x61832,x61831)))),x61832)+~P1(f319(f319(f226(a1),x61831),x61832))
% 22.40/22.30 [6190]E(x61901,f2(a906))+E(f319(f319(f75(a906),x61902),f319(f319(f236(a906),x61902),f319(f319(f3(a906),x61901),f72(a906)))),f319(f319(f236(a906),x61902),x61901))
% 22.40/22.30 [6218]E(f319(f319(f75(a906),f319(a97,x62181)),f319(a97,x62182)),f319(a97,f319(f319(f75(a1),x62181),x62182)))+~P1(f319(f319(f225(a1),f2(a1)),x62181))
% 22.40/22.30 [6219]E(f319(f319(f30(a906),f319(a97,x62191)),f319(a97,x62192)),f319(a97,f319(f319(f30(a1),x62191),x62192)))+~P1(f319(f319(f225(a1),f2(a1)),x62191))
% 22.40/22.30 [6234]~P119(x62341)+E(f319(f319(f74(x62341),x62342),x62342),f319(f319(f75(x62341),f319(f319(f74(x62341),f72(x62341)),f72(x62341))),x62342))
% 22.40/22.30 [6259]E(f319(f319(f3(a1),f319(f92(a1),x62591)),f319(f92(a1),x62592)),f319(f92(a1),f319(f319(f3(a906),x62591),x62592)))+~P1(f319(f319(f225(a906),x62592),x62591))
% 22.40/22.30 [6261]E(f319(f319(f244(a1,a1),f319(f96(a1),a89)),f319(f319(f74(a1),x62611),x62612)),f44(x62611,x62612))+~P1(f319(f319(f225(a1),x62612),f2(a1)))
% 22.40/22.30 [6290]E(f171(x62901,x62902),f105(f907(x62901)))+P1(f319(f319(f321(f907(x62901)),f657(x62902,x62901)),f319(f164(f907(x62901)),x62902)))
% 22.40/22.30 [6300]E(f108(a1,f319(f121(a1),x63001),f120(x63002,f319(f319(f74(a1),x63001),f72(a1)))),f120(x63002,x63001))+P1(f319(f319(f226(a1),x63002),x63001))
% 22.40/22.30 [6376]E(f319(f319(f143(a1),x63761),f170(f319(f319(f74(a1),x63761),f72(a1)),x63762)),f170(x63761,x63762))+~P1(f319(f319(f225(a1),x63761),x63762))
% 22.40/22.30 [6415]~P1(f319(f319(f226(a906),x64152),x64151))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f3(a906),x64151),x64152)))
% 22.40/22.30 [6445]~P1(f319(f319(f226(a906),x64451),f319(a97,x64452)))+P1(f319(f319(f226(a1),f319(f92(a1),x64451)),x64452))
% 22.40/22.30 [6475]~P4(x64751)+E(f319(f319(f93(f913(x64751,a904)),f319(f274(x64751),x64752)),f319(f319(f301(x64751),x64752),f181(f913(x64751,a904)))),f319(f293(x64751),x64752))
% 22.40/22.30 [6476]~P1(f319(f319(f225(a1),f2(a1)),x64761))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f236(a1),x64761),x64762)))
% 22.40/22.30 [6479]~P1(f319(f319(f226(a906),f2(a906)),x64791))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f236(a906),x64791),x64792)))
% 22.40/22.30 [6508]~E(f319(x65081,f2(a906)),f2(a906))+E(f319(f319(f8(a906,a906),x65081),f295(a906,f319(a104,f2(a906)),x65082)),f319(f319(f8(a906,a906),x65081),f295(a906,f2(a906),x65082)))
% 22.40/22.30 [6590]E(f319(f319(f301(a1),x65901),f295(a1,f319(f319(f74(a1),x65901),f72(a1)),x65902)),f295(a1,x65901,x65902))+P1(f319(f319(f226(a1),x65902),x65901))
% 22.40/22.30 [6591]P1(f319(f319(f226(a906),x65911),f319(a97,x65912)))+~P1(f319(f319(f226(a1),f319(f92(a1),x65911)),x65912))
% 22.40/22.30 [6692]E(f319(a97,f319(f319(f30(a1),f319(f96(a1),x66921)),f319(f96(a1),x66922))),f319(f319(f30(a906),f319(f96(a906),x66921)),f319(f96(a906),x66922)))+P1(f319(a186,f319(f96(a1),x66921)))
% 22.40/22.30 [6754]P1(f319(f319(f226(a906),x67541),x67542))+~P1(f319(f319(f226(a906),f2(a906)),f319(f319(f3(a906),x67542),x67541)))
% 22.40/22.30 [6799]P1(f319(f319(f226(a906),f2(a906)),x67991))+~P1(f319(f319(f226(a906),f2(a906)),f319(f319(f75(a906),x67992),x67991)))
% 22.40/22.30 [6800]P1(f319(f319(f226(a906),f2(a906)),x68001))+~P1(f319(f319(f226(a906),f2(a906)),f319(f319(f75(a906),x68001),x68002)))
% 22.40/22.30 [6821]~P1(f319(f319(f225(a1),x68211),f2(a1)))+E(f319(f319(f75(a906),f319(a97,f319(f73(a1),x68211))),f319(a97,f319(f73(a1),x68212))),f319(a97,f319(f319(f75(a1),x68211),x68212)))
% 22.40/22.30 [6879]~E(x68792,f181(f913(x68791,a904)))+P1(f319(f319(f225(f913(x68791,a904)),x68792),f319(f73(f913(x68791,a904)),x68792)))
% 22.40/22.30 [6989]~P1(f319(f319(f226(a1),x69891),x69892))+P1(f319(f319(f225(a1),f319(f319(f74(a1),x69891),f72(a1))),x69892))
% 22.40/22.30 [7055]E(x70551,f2(a906))+~P1(f319(f319(f225(a1),f319(f92(a1),x70552)),f319(f73(a1),f319(f92(a1),x70551))))
% 22.40/22.30 [7056]E(x70561,f2(a906))+~P1(f319(f319(f225(a1),f319(f92(a1),x70561)),f319(f73(a1),f319(f92(a1),x70562))))
% 22.40/22.30 [7159]E(f319(f319(f244(a1,a1),f319(f96(a1),a89)),f319(f319(f74(a1),x71591),x71592)),f44(x71591,x71592))+~P1(f319(f319(f225(a1),f2(a1)),f319(f319(f74(a1),x71591),x71592)))
% 22.40/22.30 [7202]~P27(x72021,x72022)+P37(x72021,f319(f243(f913(f912(x72021,x72021),a904),f913(f912(x72021,x72021),a904)),x72022))
% 22.40/22.30 [7221]~P1(f319(f319(f225(a906),f319(a104,f2(a906))),x72211))+P1(f319(f319(f225(a906),f319(a104,f2(a906))),f319(f319(f236(a906),x72211),x72212)))
% 22.40/22.30 [7451]~P1(f319(f319(f226(a906),f2(a906)),x74511))+P1(f319(f319(f226(a906),f319(f319(f3(a906),x74511),f319(a104,x74512))),x74511))
% 22.40/22.30 [7486]P1(f319(f319(f225(a906),f319(a104,f2(a906))),x74861))+~P1(f319(f319(f225(a906),f319(a104,f2(a906))),f319(f319(f75(a906),x74862),x74861)))
% 22.40/22.30 [7487]P1(f319(f319(f225(a906),f319(a104,f2(a906))),x74871))+~P1(f319(f319(f225(a906),f319(a104,f2(a906))),f319(f319(f75(a906),x74871),x74872)))
% 22.40/22.30 [7490]P1(f319(f319(f225(a906),f319(f319(f156(a906),x74901),x74902)),f319(f157(a906),x74901)))+~P1(f319(f319(f226(a906),x74902),f319(f182(f907(a906)),x74901)))
% 22.40/22.30 [7527]P1(f319(f319(f226(a1),x75271),x75272))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),x75271),f72(a1))),x75272))
% 22.40/22.30 [7569]P1(f319(f55(x75691),f234(f913(x75691,a904))))+~P1(f319(f55(f913(x75692,x75691)),f234(f913(f913(x75692,x75691),a904))))
% 22.40/22.30 [7570]P1(f319(f55(x75701),f234(f913(x75701,a904))))+~P1(f319(f55(f914(x75702,x75701)),f234(f913(f914(x75702,x75701),a904))))
% 22.40/22.30 [7571]P1(f319(f55(x75711),f234(f913(x75711,a904))))+~P1(f319(f55(f914(x75711,x75712)),f234(f913(f914(x75711,x75712),a904))))
% 22.40/22.30 [7609]E(x76091,f181(f913(x76092,a904)))+~P1(f319(f319(f225(f913(x76092,a904)),x76091),f319(f73(f913(x76092,a904)),x76091)))
% 22.40/22.30 [7743]E(f319(f134(f907(x77431),f907(x77431),f126(x77431),f105(x77431)),x77432),f105(x77431))+P1(f319(f319(f321(f907(x77431)),f687(x77432,x77431)),f319(f164(f907(x77431)),x77432)))
% 22.40/22.30 [7744]E(f319(f134(f907(x77441),f907(x77441),f126(x77441),f105(x77441)),x77442),f105(x77441))+P1(f319(f319(f321(f907(x77441)),f693(x77442,x77441)),f319(f164(f907(x77441)),x77442)))
% 22.40/22.30 [8071]~P119(x80711)+E(f319(f319(f75(x80711),f319(f319(f74(x80711),f72(x80711)),f72(x80711))),f319(f319(f8(a906,x80711),f92(x80711)),f295(a906,f72(a906),x80712))),f319(f319(f75(x80711),f319(f92(x80711),x80712)),f319(f319(f74(x80711),f319(f92(x80711),x80712)),f72(x80711))))
% 22.40/22.30 [8119]P1(f319(f319(f321(a906),x81191),x81192))+~P1(f319(f319(f321(a1),f319(f92(a1),x81191)),f319(f302(a906,a1,f92(a1)),x81192)))
% 22.40/22.30 [8279]~P1(f319(f55(x82791),x82792))+E(f319(f302(a906,x82791,f546(x82792,x82791)),f319(f254(a906),f319(f319(f9(a906,a906,a904),f226(a906)),f547(x82792,x82791)))),x82792)
% 22.40/22.30 [8554]P55(x85541,x85542)+P1(f319(f319(f321(f912(x85541,x85541)),f319(f319(f244(x85541,x85541),f491(x85542,x85541)),f491(x85542,x85541))),x85542))
% 22.40/22.30 [8555]P38(x85551,x85552)+P1(f319(f319(f321(f912(x85551,x85551)),f319(f319(f244(x85551,x85551),f778(x85552,x85551)),f781(x85552,x85551))),x85552))
% 22.40/22.30 [8556]P38(x85561,x85562)+P1(f319(f319(f321(f912(x85561,x85561)),f319(f319(f244(x85561,x85561),f781(x85562,x85561)),f783(x85562,x85561))),x85562))
% 22.40/22.30 [8557]P39(x85571,x85572)+P1(f319(f319(f321(f912(x85571,x85571)),f319(f319(f244(x85571,x85571),f697(x85572,x85571)),f696(x85572,x85571))),x85572))
% 22.40/22.30 [8558]P39(x85581,x85582)+P1(f319(f319(f321(f912(x85581,x85581)),f319(f319(f244(x85581,x85581),f696(x85582,x85581)),f697(x85582,x85581))),x85582))
% 22.40/22.30 [8559]P53(x85591,x85592)+P1(f319(f319(f321(f912(x85591,x85591)),f319(f319(f244(x85591,x85591),f793(x85592,x85591)),f794(x85592,x85591))),x85592))
% 22.40/22.30 [8820]~P1(f319(f319(f226(f913(a906,a904)),x88201),x88202))+P1(f319(f319(f226(f913(a1,a904)),f319(f302(a906,a1,f92(a1)),x88201)),f319(f302(a906,a1,f92(a1)),x88202)))
% 22.40/22.30 [8855]~P98(x88551)+E(f319(f319(f3(x88551),f72(x88551)),f319(f96(x88551),x88552)),f319(f96(x88551),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),f319(f73(a1),x88552))))
% 22.40/22.30 [8931]~P1(f319(f319(f321(a906),x89311),f319(f164(a906),x89312)))+P1(f319(f319(f225(a906),x89311),f319(f134(a906,a906,f74(a906),f2(a906)),x89312)))
% 22.40/22.30 [9029]P46(x90291,x90292)+~P1(f319(f319(f321(f912(x90291,x90291)),f319(f319(f244(x90291,x90291),f465(x90292,x90291)),f465(x90292,x90291))),x90292))
% 22.40/22.30 [9030]P38(x90301,x90302)+~P1(f319(f319(f321(f912(x90301,x90301)),f319(f319(f244(x90301,x90301),f778(x90302,x90301)),f783(x90302,x90301))),x90302))
% 22.40/22.30 [9031]P53(x90311,x90312)+~P1(f319(f319(f321(f912(x90311,x90311)),f319(f319(f244(x90311,x90311),f794(x90312,x90311)),f793(x90312,x90311))),x90312))
% 22.40/22.30 [9166]~P1(f319(f319(f225(f913(a1,a904)),f319(f302(a906,a1,f92(a1)),x91661)),f319(f302(a906,a1,f92(a1)),x91662)))+P1(f319(f319(f225(f913(a906,a904)),x91661),x91662))
% 22.40/22.30 [9167]~P1(f319(f319(f226(f913(a1,a904)),f319(f302(a906,a1,f92(a1)),x91671)),f319(f302(a906,a1,f92(a1)),x91672)))+P1(f319(f319(f226(f913(a906,a904)),x91671),x91672))
% 22.40/22.30 [10144]~P109(x101441)+E(f108(f907(x101441),f319(f121(f907(x101441)),f105(x101441)),f319(f319(f319(f86(f908(f907(x101441))),f319(f319(f226(a1),f2(a1)),x101442)),f319(f110(f912(x101441,f907(x101441)),f907(x101441),f123(x101441,f907(x101441),f124(x101441,f319(f319(f3(a1),x101442),f72(a1))),f124(f907(x101441),f319(f319(f3(a1),x101442),f72(a1))))),f319(f249(x101441,f907(x101441),f908(f907(x101441))),f319(f319(f10(f913(f907(x101441),f907(x101441)),f913(f907(x101441),f908(f907(x101441))),x101441),f319(f10(f907(x101441),f908(f907(x101441)),f907(x101441)),f121(f907(x101441)))),f143(x101441))))),f107(f907(x101441)))),f124(f907(x101441),x101442))
% 22.40/22.30 [10165]~P1(f319(f55(x101651),x101652))+E(f319(f182(f907(x101651)),f84(f907(x101651),f319(f319(f20(f907(x101651),a904,a904),f319(f319(f10(a904,f913(a904,a904),f907(x101651)),a317),f319(f319(f9(f907(x101651),f913(x101651,a904),a904),f319(f319(f10(f913(x101651,a904),f913(f913(x101651,a904),a904),f907(x101651)),a316),f164(x101651))),x101652))),f129(x101651)))),f207(x101651,x101652))
% 22.40/22.30 [6179]E(f319(f319(f74(a906),f319(f319(f3(a906),x61791),x61792)),x61792),x61791)+~P1(f319(f319(f225(a906),x61792),x61791))
% 22.40/22.30 [6253]E(f319(f319(f30(a906),f319(f319(f75(a906),x62531),x62532)),x62532),x62531)+~P1(f319(f319(f226(a906),f2(a906)),x62532))
% 22.40/22.30 [6254]E(f319(f319(f30(a906),f319(f319(f75(a906),x62541),x62542)),x62541),x62542)+~P1(f319(f319(f226(a906),f2(a906)),x62541))
% 22.40/22.30 [6260]~P76(x62601)+E(f319(f319(f8(a906,x62601),f319(f156(x62601),x62602)),f319(f294(a906,f2(a906)),f319(f182(f907(x62601)),x62602))),f319(f157(x62601),x62602))
% 22.40/22.30 [6368]E(f39(a906,f319(a104,f319(f319(f75(a906),x63681),x63682)),x63681),f72(a906))+~P1(f319(f319(f226(a906),f72(a906)),x63681))
% 22.40/22.30 [6374]E(f319(a104,f319(f319(f74(a906),f319(f96(a906),x63741)),x63742)),f319(f319(f74(a906),f72(a906)),x63742))+~P1(f319(a186,f319(f96(a1),x63741)))
% 22.40/22.30 [6403]E(f319(a97,f319(f319(f236(a1),f319(f96(a1),x64031)),x64032)),f319(f319(f236(a906),f319(f96(a906),x64031)),x64032))+P1(f319(a186,f319(f96(a1),x64031)))
% 22.40/22.30 [6641]E(f319(f319(f3(a906),x66411),f319(f96(a906),f319(f319(f74(a1),x66412),a89))),f319(f319(f3(a906),f319(a104,x66411)),f319(f96(a906),x66412)))+~P1(f319(f319(f226(a1),a77),x66412))
% 22.40/22.30 [6726]E(x67261,f2(a906))+E(f319(a104,f319(f319(f74(a906),f319(f319(f3(a906),x67261),f72(a906))),x67262)),f319(f319(f74(a906),x67261),x67262))
% 22.40/22.30 [6767]E(x67671,f2(a1))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x67671)),x67672)))
% 22.40/22.30 [6783]~E(x67832,f2(a906))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x67831)),x67832)))
% 22.40/22.30 [6824]E(x68241,f2(a906))+E(f319(f319(f74(a906),x68242),f319(f319(f75(a906),f319(f319(f3(a906),x68241),f72(a906))),x68242)),f319(f319(f75(a906),x68241),x68242))
% 22.40/22.30 [6872]~P1(f319(f319(f225(a1),x68721),x68722))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x68721),a89)),x68722))
% 22.40/22.30 [6992]E(f319(f319(f143(a906),x69921),f131(a906,f319(f294(a906,f319(a104,x69921)),x69922))),f131(a906,f319(f294(a906,x69921),x69922)))+~P1(f319(f319(f226(a906),x69921),x69922))
% 22.40/22.30 [7196]E(x71961,f105(x71962))+E(f258(x71962,f319(f319(f146(x71962,f912(a91,x71962)),f319(f244(a91,x71962),f72(a91))),x71961)),f267(x71962,x71961))
% 22.40/22.30 [7426]P1(f319(f319(f225(a1),x74261),x74262))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),x74261),a89)),x74262))
% 22.40/22.30 [7427]E(x74271,x74272)+~E(f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x74271)),x74271),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x74272)),x74272))
% 22.40/22.30 [7883]~P1(f319(f319(f226(a906),x78831),x78832))+P1(f319(f319(f321(f912(a906,a906)),f319(f319(f244(a906,a906),x78831),x78832)),a232))
% 22.40/22.30 [8096]~P1(f319(f319(f226(a91),f2(a91)),x80961))+P1(f319(f319(f226(a91),f319(f243(a91,f912(a91,a91)),f319(f259(x80961),x80962))),x80961))
% 22.40/22.30 [8358]~P38(x83581,x83582)+P38(x83581,f319(f319(f93(f913(f912(x83581,x83581),a904)),x83582),f299(x83581,f181(f913(f912(x83581,x83581),a904)))))
% 22.40/22.30 [8359]~P39(x83591,x83592)+P39(x83591,f319(f319(f93(f913(f912(x83591,x83591),a904)),x83592),f299(x83591,f181(f913(f912(x83591,x83591),a904)))))
% 22.40/22.30 [8408]~P92(x84081)+P1(f319(f319(f225(x84081),f319(f69(x84081),f319(f157(x84081),x84082))),f319(f157(x84081),f319(f319(f146(x84081,x84081),f69(x84081)),x84082))))
% 22.40/22.30 [8434]P1(f319(f319(f226(a906),x84341),x84342))+~P1(f319(f319(f321(f912(a906,a906)),f319(f319(f244(a906,a906),x84341),x84342)),a232))
% 22.40/22.30 [8580]E(f319(f319(f244(x85801,x85801),f612(x85802,x85801)),f612(x85802,x85801)),x85802)+~P1(f319(f319(f321(f912(x85801,x85801)),x85802),f299(x85801,f181(f913(f912(x85801,x85801),a904)))))
% 22.40/22.30 [8624]E(f319(f294(a906,x86241),f319(f319(f74(a906),x86241),f319(f29(a906),x86242))),x86242)+~P1(f319(f319(f225(f913(a906,a904)),x86242),f319(f294(a906,x86241),f319(f319(f74(a906),x86241),f319(f29(a906),x86242)))))
% 22.40/22.30 [8849]P39(x88491,x88492)+~P39(x88491,f319(f319(f93(f913(f912(x88491,x88491),a904)),x88492),f299(x88491,f181(f913(f912(x88491,x88491),a904)))))
% 22.40/22.30 [9074]~P38(x90741,x90742)+P1(f319(f319(f225(f913(f912(x90741,x90741),a904)),f319(f319(f281(x90741,x90741,x90741),x90742),x90742)),x90742))
% 22.40/22.30 [9100]E(f169(f907(x91001),f319(f319(f10(a904,a904,f907(x91001)),a314),f319(f319(f9(f907(x91001),f907(x91001),a904),a316),f105(x91001))),x91002),f171(x91001,f171(x91001,x91002)))+~P13(a906,f319(f160(a906),f319(f319(f146(f907(x91001),a906),f182(f907(x91001))),x91002)))
% 22.40/22.30 [9980]P1(f319(a186,x99802))+E(f319(f319(f82(a1,a906),f319(f319(f3(a1),x99801),x99802)),f319(f319(f20(a1,a906,a906),f319(f319(f9(a1,a906,f913(a906,a906)),f319(f319(f10(a904,f913(a906,f913(a906,a906)),a1),f86(a906)),a186)),f2(a906))),a97)),f319(f319(f3(a906),f319(a97,x99801)),f319(a97,x99802)))
% 22.40/22.30 [9992]E(f319(f319(f82(a1,a906),f319(f96(a1),f319(f319(f74(a1),x99921),f319(f73(a1),x99922)))),f319(f319(f20(a1,a906,a906),f319(f319(f9(a1,a906,f913(a906,a906)),f319(f319(f10(a904,f913(a906,f913(a906,a906)),a1),f86(a906)),a186)),f2(a906))),a97)),f319(f319(f3(a906),f319(f96(a906),x99921)),f319(f96(a906),x99922)))+P1(f319(f319(f226(a1),x99922),a77))
% 22.40/22.30 [9993]~P27(x99931,x99932)+P1(f319(f319(f225(f913(f912(x99931,x99931),a904)),f319(f319(f281(x99931,x99931,x99931),f319(f243(f913(f912(x99931,x99931),a904),f913(f912(x99931,x99931),a904)),x99932)),f319(f248(f913(f912(x99931,x99931),a904),f913(f912(x99931,x99931),a904)),x99932))),f319(f243(f913(f912(x99931,x99931),a904),f913(f912(x99931,x99931),a904)),x99932)))
% 22.40/22.30 [10037]~E(f319(f29(a906),f319(f254(a906),f319(f319(f20(a906,a904,a904),f319(f319(f10(a904,f913(a904,a904),a906),a317),f319(f319(f9(a906,f913(a906,a904),a904),f321(a906)),x100371))),f319(f319(f9(a906,a906,a904),f226(a906)),f319(a104,x100372))))),f2(a906))+~P1(f319(f319(f321(a906),f2(a906)),x100371))
% 22.40/22.30 [10134]~P5(x101341)+E(f31(x101341,f319(f254(x101341),f319(f319(f10(f913(x101341,a904),a904,x101341),f81(x101341)),f319(f319(f10(f913(x101341,a904),f913(x101341,a904),x101341),f319(f20(x101341,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101341),a322),f319(f319(f9(x101341,f913(x101341,a904),a904),f321(x101341)),x101342)))),f225(x101341))))),f32(x101341,x101342))
% 22.40/22.30 [10160]~P37(x101601,x101602)+P61(x101601,f319(f319(f9(x101601,f913(f912(x101601,x101601),a904),f913(x101601,a904)),f319(f319(f10(f913(x101601,f913(f913(f912(x101601,x101601),a904),a904)),f913(f913(f912(x101601,x101601),a904),f913(x101601,a904)),x101601),f9(x101601,f913(f912(x101601,x101601),a904),a904)),f319(f319(f10(f913(x101601,f912(x101601,x101601)),f913(x101601,f913(f913(f912(x101601,x101601),a904),a904)),x101601),f319(f10(f912(x101601,x101601),f913(f913(f912(x101601,x101601),a904),a904),x101601),f321(f912(x101601,x101601)))),f244(x101601,x101601)))),x101602))
% 22.40/22.30 [10161]~P8(x101611,f234(f913(x101611,a904)),x101612)+P7(x101611,f319(f319(f9(x101611,f913(f912(x101611,x101611),a904),f913(x101611,a904)),f319(f319(f10(f913(x101611,f913(f913(f912(x101611,x101611),a904),a904)),f913(f913(f912(x101611,x101611),a904),f913(x101611,a904)),x101611),f9(x101611,f913(f912(x101611,x101611),a904),a904)),f319(f319(f10(f913(x101611,f912(x101611,x101611)),f913(x101611,f913(f913(f912(x101611,x101611),a904),a904)),x101611),f319(f10(f912(x101611,x101611),f913(f913(f912(x101611,x101611),a904),a904),x101611),f321(f912(x101611,x101611)))),f244(x101611,x101611)))),x101612))
% 22.40/22.30 [10199]P37(x101991,x101992)+~P61(x101991,f319(f319(f9(x101991,f913(f912(x101991,x101991),a904),f913(x101991,a904)),f319(f319(f10(f913(x101991,f913(f913(f912(x101991,x101991),a904),a904)),f913(f913(f912(x101991,x101991),a904),f913(x101991,a904)),x101991),f9(x101991,f913(f912(x101991,x101991),a904),a904)),f319(f319(f10(f913(x101991,f912(x101991,x101991)),f913(x101991,f913(f913(f912(x101991,x101991),a904),a904)),x101991),f319(f10(f912(x101991,x101991),f913(f913(f912(x101991,x101991),a904),a904),x101991),f321(f912(x101991,x101991)))),f244(x101991,x101991)))),x101992))
% 22.40/22.30 [10200]P8(x102001,f234(f913(x102001,a904)),x102002)+~P7(x102001,f319(f319(f9(x102001,f913(f912(x102001,x102001),a904),f913(x102001,a904)),f319(f319(f10(f913(x102001,f913(f913(f912(x102001,x102001),a904),a904)),f913(f913(f912(x102001,x102001),a904),f913(x102001,a904)),x102001),f9(x102001,f913(f912(x102001,x102001),a904),a904)),f319(f319(f10(f913(x102001,f912(x102001,x102001)),f913(x102001,f913(f913(f912(x102001,x102001),a904),a904)),x102001),f319(f10(f912(x102001,x102001),f913(f913(f912(x102001,x102001),a904),a904),x102001),f321(f912(x102001,x102001)))),f244(x102001,x102001)))),x102002))
% 22.40/22.30 [7378]E(f319(f319(f74(a906),f319(f96(a906),f319(f319(f3(a1),x73781),a89))),x73782),f319(a104,f319(f319(f74(a906),f319(f96(a906),x73781)),x73782)))+P1(f319(a186,f319(f96(a1),x73781)))
% 22.40/22.30 [7864]~P98(x78641)+E(f319(f319(f74(x78641),f319(f319(f74(x78641),f72(x78641)),f319(f96(x78641),x78642))),f319(f96(x78641),x78642)),f319(f96(x78641),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x78642)),x78642)))
% 22.40/22.30 [9223]~P1(f319(f319(f225(a1),x92231),x92232))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92231)),x92231)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92232)),x92232)))
% 22.40/22.30 [9225]~P1(f319(f319(f226(a1),x92251),x92252))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92251)),x92251)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92252)),x92252)))
% 22.40/22.30 [9466]~P1(f319(f55(x94661),x94662))+P1(f319(f55(f913(x94661,a904)),f319(f254(f913(x94661,a904)),f319(f319(f9(f913(x94661,a904),f913(x94661,a904),a904),f225(f913(x94661,a904))),x94662))))
% 22.40/22.30 [9491]P1(f319(f319(f225(a1),x94911),x94912))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94911)),x94911)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94912)),x94912)))
% 22.40/22.30 [9493]P1(f319(f319(f226(a1),x94931),x94932))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94931)),x94931)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94932)),x94932)))
% 22.40/22.30 [9520]~E(f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),x95201),f181(f913(f912(a906,a906),a904)))),f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),x95202),f181(f913(f912(a906,a906),a904)))))+P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),x95201),x95202)),a101))
% 22.40/22.30 [9600]E(f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),x96001),f181(f913(f912(a906,a906),a904)))),f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),x96002),f181(f913(f912(a906,a906),a904)))))+~P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),x96001),x96002)),a101))
% 22.40/22.30 [9648]P1(f319(f319(f225(a1),f2(a1)),f633(x96481,x96482)))+E(f319(f254(a1),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),x96481)),f319(f254(a1),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),x96482)))
% 22.40/22.30 [9764]~P1(f319(f319(f225(a1),x97641),x97642))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97641)),x97641)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97642)),x97642)))
% 22.40/22.30 [9766]~P1(f319(f319(f225(a1),x97661),x97662))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97661)),x97661)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97662)),x97662)))
% 22.40/22.30 [9923]P1(f319(f319(f225(a1),x99231),x99232))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99231)),x99231)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99232)),x99232)))
% 22.40/22.30 [9925]P1(f319(f319(f225(a1),x99251),x99252))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99251)),x99251)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99252)),x99252)))
% 22.40/22.30 [10143]~P5(x101431)+E(f32(x101431,f319(f254(x101431),f319(f319(f10(f913(x101431,a904),a904,x101431),f81(x101431)),f319(f319(f10(f913(x101431,a904),f913(x101431,a904),x101431),f319(f20(x101431,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101431),a322),f319(f319(f9(x101431,f913(x101431,a904),a904),f321(x101431)),x101432)))),f319(f9(x101431,x101431,a904),f225(x101431)))))),f31(x101431,x101432))
% 22.40/22.30 [10164]P1(f319(f319(f321(a906),f2(a906)),x101641))+E(f319(f29(a906),f319(f254(a906),f319(f319(f20(a906,a904,a904),f319(f319(f10(a904,f913(a904,a904),a906),a317),f319(f319(f9(a906,f913(a906,a904),a904),f319(f319(f10(a906,f913(f913(a906,a904),a904),a906),f321(a906)),a104)),x101641))),f319(f319(f9(a906,a906,a904),f226(a906)),x101642)))),f319(f29(a906),f319(f254(a906),f319(f319(f20(a906,a904,a904),f319(f319(f10(a904,f913(a904,a904),a906),a317),f319(f319(f9(a906,f913(a906,a904),a904),f321(a906)),x101641))),f319(f319(f9(a906,a906,a904),f226(a906)),f319(a104,x101642))))))
% 22.40/22.30 [10227]P1(f319(f319(f279(a906),x102271),x102272))+~P1(f319(f319(f321(a906),x102272),f286(a906,f319(f319(f20(a906,f913(a906,a904),f913(a906,a904)),f319(f319(f10(f913(a906,f913(a904,a904)),f913(f913(a906,a904),f913(a906,a904)),a906),f20(a906,a904,a904)),f319(f319(f10(f913(a906,a904),f913(a906,f913(a904,a904)),a906),f319(f10(a904,f913(a904,a904),a906),a317)),f279(a906)))),f319(f319(f10(f913(a906,a904),f913(a906,a904),a906),f319(f10(a904,a904,a906),a314)),f319(f9(a906,a906,a904),f279(a906)))),x102271)))
% 22.40/22.30 [10228]P1(f319(f319(f279(a906),x102281),x102282))+~P1(f319(f319(f321(a906),x102281),f290(a906,f319(f319(f20(a906,f913(a906,a904),f913(a906,a904)),f319(f319(f10(f913(a906,f913(a904,a904)),f913(f913(a906,a904),f913(a906,a904)),a906),f20(a906,a904,a904)),f319(f319(f10(f913(a906,a904),f913(a906,f913(a904,a904)),a906),f319(f10(a904,f913(a904,a904),a906),a317)),f279(a906)))),f319(f319(f10(f913(a906,a904),f913(a906,a904),a906),f319(f10(a904,a904,a906),a314)),f319(f9(a906,a906,a904),f279(a906)))),x102282)))
% 22.40/22.30 [10229]~P1(f319(f319(f279(a906),x102291),x102292))+~P1(f319(f319(f321(a906),x102292),f290(a906,f319(f319(f20(a906,f913(a906,a904),f913(a906,a904)),f319(f319(f10(f913(a906,f913(a904,a904)),f913(f913(a906,a904),f913(a906,a904)),a906),f20(a906,a904,a904)),f319(f319(f10(f913(a906,a904),f913(a906,f913(a904,a904)),a906),f319(f10(a904,f913(a904,a904),a906),a317)),f279(a906)))),f319(f319(f10(f913(a906,a904),f913(a906,a904),a906),f319(f10(a904,a904,a906),a314)),f319(f9(a906,a906,a904),f279(a906)))),x102291)))
% 22.40/22.30 [10230]~P1(f319(f319(f279(a906),x102301),x102302))+~P1(f319(f319(f321(a906),x102301),f286(a906,f319(f319(f20(a906,f913(a906,a904),f913(a906,a904)),f319(f319(f10(f913(a906,f913(a904,a904)),f913(f913(a906,a904),f913(a906,a904)),a906),f20(a906,a904,a904)),f319(f319(f10(f913(a906,a904),f913(a906,f913(a904,a904)),a906),f319(f10(a904,f913(a904,a904),a906),a317)),f279(a906)))),f319(f319(f10(f913(a906,a904),f913(a906,a904),a906),f319(f10(a904,a904,a906),a314)),f319(f9(a906,a906,a904),f279(a906)))),x102302)))
% 22.40/22.30 [7928]~P98(x79281)+E(f319(f319(f75(x79281),x79282),f319(f96(x79281),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),x79282)
% 22.40/22.30 [8154]~P98(x81541)+E(f319(f319(f74(x81541),f319(f96(x81541),x81542)),f72(x81541)),f319(f96(x81541),f319(f319(f74(a1),x81542),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))))
% 22.40/22.30 [8197]P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x81972)))+E(f319(f319(f236(a1),x81971),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x81972)),x81972))),f72(a1))
% 22.40/22.30 [9231]E(x92311,x92312)+~E(f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92311)),x92311)),a89),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x92312)),x92312)),a89))
% 22.40/22.30 [9503]~P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x95032)))+E(f319(f319(f236(a1),x95031),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x95032)),x95032))),f319(f319(f82(a1,a1),f319(f319(f236(a1),x95031),f319(f96(a906),x95032))),f319(f319(f20(a1,a1,a1),f319(f319(f10(a1,f913(a1,a1),a1),f75(a1)),f319(f75(a1),x95031))),f7(a1))))
% 22.40/22.30 [9890]~P1(f319(f319(f225(a906),f638(x98902,x98901)),f319(x98901,f638(x98902,x98901))))+P1(f319(f55(a906),f319(f254(a906),f319(f319(f9(a906,a906,a904),f319(f319(f10(a906,f913(a906,a904),a906),f225(a906)),x98901)),x98902))))
% 22.40/22.30 [10028]~P1(f319(f319(f225(a906),f319(f96(a906),x100281)),f319(a104,x100282)))+P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x100281),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f9(a1,a906,a904),f319(f319(f10(a906,f913(a906,a904),a1),f225(a906)),a97)),x100282))))
% 22.40/22.30 [10029]~P1(f319(f319(f226(a906),f319(f96(a906),x100291)),f319(a104,x100292)))+P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x100291),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f9(a1,a906,a904),f319(f319(f10(a906,f913(a906,a904),a1),f226(a906)),a97)),x100292))))
% 22.40/22.30 [10062]P1(f319(f319(f225(a906),f319(f96(a906),x100621)),f319(a104,x100622)))+~P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x100621),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f9(a1,a906,a904),f319(f319(f10(a906,f913(a906,a904),a1),f225(a906)),a97)),x100622))))
% 22.40/22.30 [10063]P1(f319(f319(f226(a906),f319(f96(a906),x100631)),f319(a104,x100632)))+~P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x100631),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f9(a1,a906,a904),f319(f319(f10(a906,f913(a906,a904),a1),f226(a906)),a97)),x100632))))
% 22.40/22.30 [10092]~P1(f319(f319(f225(a906),f319(a104,x100922)),f319(f96(a906),x100921)))+P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x100921),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f10(a906,a904,a1),f319(f225(a906),x100922)),a97)))))
% 22.40/22.30 [10093]~P1(f319(f319(f226(a906),f319(a104,x100932)),f319(f96(a906),x100931)))+P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x100931),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f10(a906,a904,a1),f319(f226(a906),x100932)),a97)))))
% 22.40/22.30 [10132]P1(f319(f319(f225(a906),f319(a104,x101321)),f319(f96(a906),x101322)))+~P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x101322),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f10(a906,a904,a1),f319(f225(a906),x101321)),a97)))))
% 22.40/22.30 [10133]P1(f319(f319(f226(a906),f319(a104,x101331)),f319(f96(a906),x101332)))+~P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x101332),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f10(a906,a904,a1),f319(f226(a906),x101331)),a97)))))
% 22.40/22.30 [10218]~P1(f319(f319(f321(a906),f2(a906)),x102181))+E(f319(a104,f319(f29(a906),f319(f254(a906),f319(f319(f20(a906,a904,a904),f319(f319(f10(a904,f913(a904,a904),a906),a317),f319(f319(f9(a906,f913(a906,a904),a904),f319(f319(f10(a906,f913(f913(a906,a904),a904),a906),f321(a906)),a104)),x102181))),f319(f319(f9(a906,a906,a904),f226(a906)),x102182))))),f319(f29(a906),f319(f254(a906),f319(f319(f20(a906,a904,a904),f319(f319(f10(a904,f913(a904,a904),a906),a317),f319(f319(f9(a906,f913(a906,a904),a904),f321(a906)),x102181))),f319(f319(f9(a906,a906,a904),f226(a906)),f319(a104,x102182))))))
% 22.40/22.30 [8785]~P98(x87851)+E(f319(f319(f75(x87851),f319(f96(x87851),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),x87852),x87852)
% 22.40/22.30 [8829]~P98(x88291)+E(f319(f319(f74(x88291),f72(x88291)),f319(f96(x88291),x88292)),f319(f96(x88291),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),x88292)))
% 22.40/22.30 [8870]~P98(x88701)+E(f319(f319(f3(x88701),f319(f96(x88701),x88702)),f72(x88701)),f319(f96(x88701),f319(f319(f74(a1),x88702),f319(f73(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))))
% 22.40/22.30 [8963]~P98(x89631)+E(f319(f319(f75(x89631),f319(f319(f74(x89631),f72(x89631)),f72(x89631))),f319(f96(x89631),x89632)),f319(f96(x89631),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x89632)),x89632)),a89)))
% 22.40/22.30 [8995]~P1(f319(f319(f226(a906),f319(f96(a906),a77)),x89952))+E(f319(f319(f3(a906),x89951),f319(f319(f3(a906),x89952),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))),f319(f319(f3(a906),f319(a104,x89951)),x89952))
% 22.40/22.30 [9018]~P98(x90181)+E(f319(f96(x90181),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x90182)),x90182)),a89)),f319(f319(f74(x90181),f319(f319(f74(x90181),f2(x90181)),f319(f96(x90181),x90182))),f319(f96(x90181),x90182)))
% 22.40/22.30 [9615]~P1(f319(f319(f226(a1),x96151),x96152))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96151)),x96151)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96152)),x96152)),a89)))
% 22.40/22.30 [9617]~P1(f319(f319(f226(a1),x96171),x96172))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96171)),x96171)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96172)),x96172)),a89)))
% 22.40/22.30 [9778]P1(f319(f319(f226(a1),x97781),x97782))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97781)),x97781)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97782)),x97782)),a89)))
% 22.40/22.30 [9780]P1(f319(f319(f226(a1),x97801),x97802))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97801)),x97801)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x97802)),x97802)),a89)))
% 22.40/22.30 [9835]~P87(x98351)+E(f319(f319(f236(x98351),x98352),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))),f319(f319(f75(x98351),f319(f319(f75(x98351),x98352),x98352)),x98352))
% 22.40/22.30 [9885]~P1(f319(f319(f225(a1),x98851),x98852))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x98851)),x98851)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x98852)),x98852)),a89)))
% 22.40/22.30 [9887]~P1(f319(f319(f226(a1),x98871),x98872))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x98871)),x98871)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x98872)),x98872)),a89)))
% 22.40/22.30 [9989]P1(f319(f319(f225(a1),x99891),x99892))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99891)),x99891)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99892)),x99892)),a89)))
% 22.40/22.30 [9991]P1(f319(f319(f226(a1),x99911),x99912))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99911)),x99911)),a89)),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x99912)),x99912)),a89)))
% 22.40/22.30 [9632]~P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x96322)))+E(f319(f319(f30(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96321)),x96321))),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96322)),x96322)),a89))),f319(f319(f30(a1),f319(f96(a1),x96321)),f319(f96(a1),x96322)))
% 22.40/22.30 [9655]P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x96552)))+E(f319(f319(f30(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96551)),x96551))),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96552)),x96552)),a89))),f319(f319(f30(a1),f319(f319(f74(a1),f319(f96(a1),x96551)),f72(a1))),f319(f96(a1),x96552)))
% 22.40/22.30 [10122]~E(f319(a104,x101222),f319(f96(a906),x101221))+P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x101221),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f9(a1,a906,a904),f319(f319(f10(a906,f913(a906,a904),a1),a316),a97)),x101222)))))
% 22.40/22.30 [10123]~E(f319(f96(a906),x101231),f319(a104,x101232))+P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x101231),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f9(a1,a906,a904),f319(f319(f10(a906,f913(a906,a904),a1),a316),a97)),x101232)))))
% 22.40/22.30 [10167]E(f319(a104,x101671),f319(f96(a906),x101672))+~P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x101672),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f9(a1,a906,a904),f319(f319(f10(a906,f913(a906,a904),a1),a316),a97)),x101671)))))
% 22.40/22.30 [10168]E(f319(f96(a906),x101681),f319(a104,x101682))+~P1(f319(f319(f82(a1,a904),f319(f96(a1),f319(f319(f74(a1),x101681),a89))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a322),f319(f319(f10(a904,a904,a1),a314),a186))),f319(f319(f9(a1,a906,a904),f319(f319(f10(a906,f913(a906,a904),a1),a316),a97)),x101682)))))
% 22.40/22.30 [10219]~P16(x102191,x102192)+P1(f319(f319(f321(f913(x102191,a904)),f802(x102192,x102191)),f319(f319(f10(f913(x102191,a904),a904,f913(x102191,a904)),f80(x102191)),f319(f319(f10(f913(x102191,a904),f913(x102191,a904),f913(x102191,a904)),f319(f20(x102191,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102191),a317),f319(f319(f20(x102191,x102191,a904),x102192),f7(x102191))))),f319(f319(f9(f913(x102191,a904),f913(x102191,f913(x102191,a904)),f913(x102191,a904)),f319(f319(f10(f913(f913(x102191,a904),a904),f913(f913(x102191,f913(x102191,a904)),f913(x102191,a904)),f913(x102191,a904)),f10(f913(x102191,a904),a904,x102191)),a316)),x102192)))))
% 22.40/22.30 [10293]~P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x102932)))+E(f39(a1,f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x102931)),x102931)),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x102932)),x102932)),a89))),f319(f319(f74(a1),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f39(a1,f319(f96(a1),x102931),f319(f96(a1),x102932)))),f72(a1)))
% 22.40/22.30 [10295]P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x102952)))+E(f39(a1,f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x102951)),x102951)),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x102952)),x102952)),a89))),f319(f319(f3(a1),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f39(a1,f319(f319(f74(a1),f319(f96(a1),x102951)),f72(a1)),f319(f96(a1),x102952)))),f72(a1)))
% 22.40/22.30 [10072]~P119(x100721)+E(f319(f319(f75(x100721),x100722),x100722),f319(f319(f236(x100721),x100722),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.30 [10073]~P87(x100731)+E(f319(f319(f236(x100731),x100732),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(f319(f75(x100731),x100732),x100732))
% 22.40/22.30 [10074]~P98(x100741)+E(f319(f319(f75(x100741),x100742),f319(f96(x100741),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(f319(f74(x100741),x100742),x100742))
% 22.40/22.30 [10148]~P141(x101481)+E(f319(f319(f236(x101481),f319(f73(x101481),x101482)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(f319(f236(x101481),x101482),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.30 [10149]~P113(x101491)+E(f319(f319(f236(x101491),f319(f69(x101491),x101492)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(f319(f236(x101491),x101492),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.30 [10147]~P98(x101471)+E(f319(f319(f75(x101471),f319(f96(x101471),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x101472),f319(f319(f74(x101471),x101472),x101472))
% 22.40/22.30 [10187]~P113(x101871)+E(f319(f69(x101871),f319(f319(f236(x101871),x101872),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x101871),x101872),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.30 [10208]~P113(x102081)+P1(f319(f319(f225(x102081),f2(x102081)),f319(f319(f236(x102081),x102082),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.30 [10206]~P98(x102061)+E(f319(f319(f236(x102061),f319(f96(x102061),a89)),f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102062)),f72(x102061))
% 22.40/22.30 [10207]~P141(x102071)+E(f319(f319(f236(x102071),f319(f73(x102071),f72(x102071))),f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102072)),f72(x102071))
% 22.40/22.30 [10317]~P1(f319(f319(f225(a1),f2(a1)),x103172))+E(f39(a1,f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103171)),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103172)),f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f39(a1,x103171,x103172))))
% 22.40/22.30 [10330]~P1(f319(f319(f225(a1),f2(a1)),x103302))+E(f319(f319(f30(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103301))),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103302)),f319(f319(f30(a1),x103301),x103302))
% 22.40/22.30 [10331]~P1(f319(f319(f225(a1),x103312),f2(a1)))+E(f319(f319(f30(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103311))),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103312)),f319(f319(f30(a1),f319(f319(f74(a1),x103311),f72(a1))),x103312))
% 22.40/22.30 [10332]~P1(f319(f319(f225(a1),x103322),f2(a1)))+E(f39(a1,f319(f319(f74(a1),f72(a1)),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103321)),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103322)),f319(f319(f3(a1),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f39(a1,f319(f319(f74(a1),x103321),f72(a1)),x103322))),f72(a1)))
% 22.40/22.30 [10276]~P98(x102761)+E(f319(f319(f236(x102761),f319(f96(x102761),a89)),f319(a104,f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102762))),f319(f96(x102761),a89))
% 22.40/22.30 [10278]~P141(x102781)+E(f319(f319(f236(x102781),f319(f73(x102781),f72(x102781))),f319(a104,f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102782))),f319(f73(x102781),f72(x102781)))
% 22.40/22.30 [5044]P38(x50441,x50442)+~P8(x50441,x50443,x50442)
% 22.40/22.30 [5046]P53(x50461,x50462)+~P8(x50461,x50463,x50462)
% 22.40/22.30 [5221]~P8(x52211,x52212,x52213)+P54(x52211,x52212,x52213)
% 22.40/22.30 [8134]~E(x81342,x81343)+P34(x81341,x81341,a316,x81342,x81343)
% 22.40/22.30 [8681]E(x86811,x86812)+~P34(x86813,x86813,a316,x86811,x86812)
% 22.40/22.30 [4853]E(f161(x48531,x48532,x48533),f105(x48531))+~E(x48532,f2(a906))
% 22.40/22.30 [5019]~E(f161(x50192,x50191,x50193),f105(x50192))+E(x50191,f2(a906))
% 22.40/22.30 [5226]~P37(x52261,x52263)+P37(x52261,f313(x52261,x52262,x52263))
% 22.40/22.30 [5337]~P29(x53371,x53372,x53373)+P31(a1,x53371,f170(x53372,x53373))
% 22.40/22.30 [5404]P29(x54041,x54042,x54043)+~P31(a1,x54041,f170(x54042,x54043))
% 22.40/22.30 [5474]~P8(x54741,x54742,x54743)+P8(f907(x54741),f153(x54741,x54742),f150(x54741,x54743))
% 22.40/22.30 [5475]~P54(x54751,x54752,x54753)+P54(f907(x54751),f153(x54751,x54752),f150(x54751,x54753))
% 22.40/22.30 [5588]P56(x55881,x55882,x55883)+~E(f586(x55883,x55882,x55881),f587(x55883,x55882,x55881))
% 22.40/22.30 [5589]P57(x55891,x55892,x55893)+~E(f608(x55893,x55892,x55891),f609(x55893,x55892,x55891))
% 22.40/22.30 [8140]~E(x81402,x81403)+P26(x81401,x81401,f25(x81401),x81402,x81403)
% 22.40/22.30 [8689]E(x86891,x86892)+~P26(x86893,x86893,f25(x86893),x86891,x86892)
% 22.40/22.30 [4808]~E(f319(f160(x48082),x48081),x48083)+E(x48081,f319(f160(x48082),x48083))
% 22.40/22.30 [4809]~E(x48092,f319(f160(x48091),x48093))+E(f319(f160(x48091),x48092),x48093)
% 22.40/22.30 [4859]E(x48591,x48592)+~E(f319(f160(x48593),x48591),f319(f160(x48593),x48592))
% 22.40/22.30 [5070]~P7(x50703,x50701)+P1(f319(f319(x50701,x50702),x50702))
% 22.40/22.30 [5071]~P49(x50713,x50711)+P1(f319(f319(x50711,x50712),x50712))
% 22.40/22.30 [5073]~P61(x50731,x50732)+P1(f319(f307(x50731,x50732),x50733))
% 22.40/22.30 [5138]~P37(x51381,x51382)+P37(f907(x51381),f319(f135(x51381,x51382),x51383))
% 22.40/22.30 [5143]~P1(f319(x51432,x51433))+~E(f319(f254(x51431),x51432),f181(f913(x51431,a904)))
% 22.40/22.30 [5144]~P1(f319(x51442,x51443))+~E(f181(f913(x51441,a904)),f319(f254(x51441),x51442))
% 22.40/22.30 [5156]E(x51561,f2(a906))+E(f136(x51562,f161(x51562,x51561,x51563)),x51563)
% 22.40/22.30 [5175]~P1(f319(x51751,x51753))+P1(f319(x51751,f84(x51752,x51751)))
% 22.40/22.30 [5176]~P1(f319(x51761,x51763))+P1(f319(x51761,f728(x51761,x51762)))
% 22.40/22.30 [5188]E(x51881,f2(a906))+E(f319(f133(x51882),f161(x51882,x51881,x51883)),x51883)
% 22.40/22.30 [5300]~E(x53002,x53003)+P1(f319(f319(f321(x53001),x53002),f319(a316,x53003)))
% 22.40/22.30 [5315]~E(x53152,f2(a906))+E(f319(f164(x53151),f161(x53151,x53152,x53153)),f181(f913(x53151,a904)))
% 22.40/22.30 [5359]E(f319(f160(x53591),x53592),f319(f319(f143(x53591),x53593),f105(x53591)))+~E(x53592,f319(f319(f143(x53591),x53593),f105(x53591)))
% 22.40/22.30 [5360]~E(x53603,f319(f319(f143(x53601),x53602),f105(x53601)))+E(f319(f319(f143(x53601),x53602),f105(x53601)),f319(f160(x53601),x53603))
% 22.40/22.30 [5400]~P33(x54001,x54002,x54003)+P33(x54001,x54002,f319(f160(x54001),x54003))
% 22.40/22.30 [5401]~P31(x54011,x54012,x54013)+P31(x54011,x54012,f319(f160(x54011),x54013))
% 22.40/22.30 [5405]E(f319(f29(x54051),f327(x54052,x54053,x54051)),x54052)+~E(f319(f29(x54051),x54053),f319(a104,x54052))
% 22.40/22.30 [5412]~P37(x54121,x54123)+P1(f319(f319(f321(x54121),x54122),f308(x54121,x54123)))
% 22.40/22.30 [5416]~E(f319(f160(x54162),x54161),f319(f319(f143(x54162),x54163),f105(x54162)))+E(x54161,f319(f319(f143(x54162),x54163),f105(x54162)))
% 22.40/22.30 [5417]~E(f319(f319(f143(x54172),x54173),f105(x54172)),f319(f160(x54172),x54171))+E(x54171,f319(f319(f143(x54172),x54173),f105(x54172)))
% 22.40/22.30 [5440]E(f79(f912(a906,a906),f42(x54401,x54402)),x54403)+~P1(f319(f42(x54401,x54402),x54403))
% 22.40/22.30 [5478]P33(x54781,x54782,x54783)+~P33(x54781,x54782,f319(f160(x54781),x54783))
% 22.40/22.30 [5479]P31(x54791,x54792,x54793)+~P31(x54791,x54792,f319(f160(x54791),x54793))
% 22.40/22.30 [5518]P1(f319(f319(x55181,x55182),x55182))+~P1(f319(f262(x55183,x55181),x55182))
% 22.40/22.30 [5519]~P1(f319(f319(x55192,x55193),x55193))+P1(f319(f262(x55191,x55192),x55193))
% 22.40/22.30 [5541]~E(x55412,f105(x55411))+P1(f319(f319(f321(f907(x55411)),x55412),f153(x55411,x55413)))
% 22.40/22.30 [5551]~P54(x55511,x55512,x55513)+P54(x55511,x55512,f319(f278(x55511,x55511),x55513))
% 22.40/22.30 [5552]~P57(x55521,x55522,x55523)+P57(x55521,x55522,f319(f278(x55521,x55521),x55523))
% 22.40/22.30 [5569]~P69(x55691)+E(f39(x55691,f39(x55691,x55692,x55693),x55693),f39(x55691,x55692,x55693))
% 22.40/22.30 [5670]E(x56701,x56702)+~P1(f319(f319(f321(x56703),x56701),f319(a316,x56702)))
% 22.40/22.30 [5719]~P146(x57191)+E(f183(x57191,x57192,f2(a906),x57193),x57193)
% 22.40/22.30 [5741]P54(x57411,x57412,x57413)+~P54(x57411,x57412,f319(f278(x57411,x57411),x57413))
% 22.40/22.30 [5742]P57(x57421,x57422,x57423)+~P57(x57421,x57422,f319(f278(x57421,x57421),x57423))
% 22.40/22.30 [5746]~P4(x57462)+E(f142(x57461,x57462,x57463,f105(x57461)),f105(x57461))
% 22.40/22.30 [5759]E(f162(x57591,x57592,f144(x57591,x57593)),f144(x57591,f162(x57591,x57592,x57593)))+~P1(f319(f129(x57591),x57593))
% 22.40/22.30 [5858]~P1(f319(f319(x58583,x58582),x58582))+P1(f319(f319(f321(x58581),x58582),f262(x58581,x58583)))
% 22.40/22.30 [5860]E(f319(f128(x58601,x58602),x58603),f105(x58601))+P1(f319(x58602,f663(x58603,x58602,x58601)))
% 22.40/22.30 [5923]E(f62(x59231,x59232,x59233),x59232)+P1(f319(x59233,f729(x59232,x59231,x59233)))
% 22.40/22.30 [6016]~P1(f319(f129(x60161),x60162))+P1(f319(f129(x60161),f168(x60161,x60162,x60163)))
% 22.40/22.30 [6017]~P1(f319(f129(x60171),x60173))+P1(f319(f129(x60171),f162(x60171,x60172,x60173)))
% 22.40/22.30 [6018]~P1(f319(f129(x60181),x60183))+P1(f319(f129(x60181),f169(x60181,x60182,x60183)))
% 22.40/22.30 [6019]~P1(f319(f129(x60191),x60193))+P1(f319(f129(x60191),f132(x60191,x60192,x60193)))
% 22.40/22.30 [6020]~P147(x60201,x60203,x60202)+P1(f319(x60201,f39(a1,x60202,x60203)))
% 22.40/22.30 [6035]~P33(x60353,x60351,x60352)+P1(f319(x60351,f741(x60352,x60351,x60353)))
% 22.40/22.30 [6036]~P35(x60363,x60361,x60362)+P1(f319(x60361,f747(x60362,x60361,x60363)))
% 22.40/22.30 [6037]~P35(x60373,x60371,x60372)+P1(f319(x60371,f757(x60372,x60371,x60373)))
% 22.40/22.30 [6038]~P33(x60383,x60381,x60382)+P1(f319(x60381,f785(x60381,x60382,x60383)))
% 22.40/22.30 [6039]~P33(x60393,x60391,x60392)+P1(f319(x60391,f786(x60392,x60391,x60393)))
% 22.40/22.30 [6043]P1(f319(f319(x60431,x60432),x60432))+~P1(f319(f319(f321(x60433),x60432),f262(x60433,x60431)))
% 22.40/22.30 [6058]E(f319(f128(x60581,x60582),x60583),f169(x60581,x60582,x60583))+P1(f319(x60582,f712(x60583,x60582,x60581)))
% 22.40/22.30 [6099]~P1(f319(f129(x60991),x60993))+P1(f319(f129(f907(x60991)),f49(x60991,x60992,x60993)))
% 22.40/22.30 [6132]~P111(x61321)+E(f319(f319(f94(f913(x61321,a904)),f319(f274(x61321),x61322)),f295(x61321,x61322,x61323)),f181(f913(x61321,a904)))
% 22.40/22.30 [6133]~P111(x61331)+E(f319(f319(f94(f913(x61331,a904)),f319(f293(x61331),x61332)),f298(x61331,x61332,x61333)),f181(f913(x61331,a904)))
% 22.40/22.30 [6134]~P111(x61341)+E(f319(f319(f94(f913(x61341,a904)),f319(f293(x61341),x61342)),f297(x61341,x61342,x61343)),f181(f913(x61341,a904)))
% 22.40/22.30 [6363]E(f319(f128(x63631,x63632),x63633),x63633)+~P1(f319(x63632,f664(x63633,x63632,x63631)))
% 22.40/22.30 [6365]E(f319(f319(f301(x63651),f345(x63652,x63653,x63651)),f327(x63652,x63653,x63651)),x63653)+~E(f319(f29(x63651),x63653),f319(a104,x63652))
% 22.40/22.30 [6381]P147(x63811,x63812,x63813)+~P1(f319(x63811,f39(a1,x63813,x63812)))
% 22.40/22.30 [6430]P31(x64301,x64302,x64303)+~P1(f319(x64302,f748(x64303,x64302,x64301)))
% 22.40/22.30 [6431]P31(x64311,x64312,x64313)+~P1(f319(x64312,f755(x64312,x64313,x64311)))
% 22.40/22.30 [6432]P31(x64321,x64322,x64323)+~P1(f319(x64322,f756(x64323,x64322,x64321)))
% 22.40/22.30 [6433]P29(x64331,x64332,x64333)+~P1(f319(x64331,f774(x64333,x64332,x64331)))
% 22.40/22.30 [6434]P30(x64341,x64342,x64343)+~P1(f319(x64341,f819(x64343,x64342,x64341)))
% 22.40/22.30 [6436]E(f169(x64361,x64362,x64363),x64363)+~P1(f319(x64362,f708(x64363,x64362,x64361)))
% 22.40/22.30 [6518]~P1(f319(x65182,f566(x65183,x65182,x65181)))+P1(f319(f240(x65181,x65182),x65183))
% 22.40/22.30 [6519]~P1(f319(x65192,f665(x65193,x65192,x65191)))+P1(f319(f152(x65191,x65192),x65193))
% 22.40/22.30 [6768]~P1(f319(f307(x67681,x67682),f459(x67683,x67682,x67681)))+P1(f319(f307(x67681,x67682),x67683))
% 22.40/22.30 [6769]~P1(f319(f307(x67691,x67692),f486(x67693,x67692,x67691)))+P1(f319(f307(x67691,x67692),x67693))
% 22.40/22.30 [7379]~P69(x73791)+E(f319(f319(f74(x73791),f319(f319(f75(x73791),x73792),f319(f319(f30(x73791),x73793),x73792))),f39(x73791,x73793,x73792)),x73793)
% 22.40/22.30 [7404]P29(x74041,x74042,x74043)+P1(f319(f319(f321(a1),f774(x74043,x74042,x74041)),f295(a1,x74042,x74043)))
% 22.40/22.30 [7821]E(f319(f319(f244(x78211,x78211),f516(x78212,x78213,x78211)),f516(x78212,x78213,x78211)),x78213)+~P1(f319(f319(f321(f912(x78211,x78211)),x78213),f255(x78211,x78212)))
% 22.40/22.30 [7942]~P1(f319(f319(f321(x79421),f522(x79423,x79422,x79421)),f308(x79421,x79423)))+P1(f319(f319(f321(x79421),x79422),f308(x79421,x79423)))
% 22.40/22.30 [7943]~P1(f319(f319(f321(x79431),f589(x79433,x79432,x79431)),f308(x79431,x79433)))+P1(f319(f319(f321(x79431),x79432),f308(x79431,x79433)))
% 22.40/22.30 [7944]~P1(f319(f319(f321(x79441),f591(x79443,x79442,x79441)),f308(x79441,x79443)))+P1(f319(f319(f321(x79441),x79442),f308(x79441,x79443)))
% 22.40/22.30 [8033]P33(a1,x80331,f170(x80332,x80333))+P29(f319(f66(a904,a904,a1,a314),x80331),x80332,x80333)
% 22.40/22.30 [8115]~P69(x81151)+E(f319(f319(f74(x81151),f319(f319(f75(x81151),f319(f319(f30(x81151),x81152),x81153)),x81153)),f39(x81151,x81152,x81153)),x81152)
% 22.40/22.30 [8166]~E(f319(f29(x81661),x81662),f319(a104,x81663))+~P1(f319(f319(f321(x81661),f345(x81663,x81662,x81661)),f327(x81663,x81662,x81661)))
% 22.40/22.30 [8596]~P33(a1,x85961,f170(x85962,x85963))+~P29(f319(f66(a904,a904,a1,a314),x85961),x85962,x85963)
% 22.40/22.30 [8780]P1(f319(f319(f225(f913(f912(x87801,x87801),a904)),f299(x87801,x87802)),f299(x87801,x87803)))+~P1(f319(f319(f225(f913(f912(x87801,x87801),a904)),x87802),f299(x87801,x87803)))
% 22.40/22.30 [9070]E(x90701,f105(x90702))+~P1(f319(f319(f321(f912(f907(x90702),f907(x90702))),f319(f319(f244(f907(x90702),f907(x90702)),x90701),f105(x90702))),f150(x90702,x90703)))
% 22.40/22.30 [9094]E(x90941,f105(x90942))+~P1(f319(f319(f321(f912(f907(x90942),f907(x90942))),f319(f319(f244(f907(x90942),f907(x90942)),f105(x90942)),x90941)),f150(x90942,x90943)))
% 22.40/22.30 [9207]E(f319(f319(f143(x92071),f681(x92072,x92073,x92071)),f683(x92072,x92073,x92071)),x92073)+~P1(f319(f319(f321(f912(f907(x92071),f907(x92071))),f319(f319(f244(f907(x92071),f907(x92071)),f105(x92071)),x92073)),f139(x92071,x92072)))
% 22.40/22.30 [9459]~P128(x94591)+~P1(f319(f319(f226(x94591),f319(f319(f74(x94591),f319(f319(f75(x94591),x94592),x94592)),f319(f319(f75(x94591),x94593),x94593))),f2(x94591)))
% 22.40/22.30 [9513]P1(f319(f55(x95131),x95132))+~P1(f319(f319(f321(f912(f913(x95131,a904),f913(x95131,a904))),f319(f319(f244(f913(x95131,a904),f913(x95131,a904)),x95133),x95132)),f306(x95131)))
% 22.40/22.30 [9827]~P47(x98271,x98272,x98273)+P1(f319(f319(f225(a1),f319(f319(f66(f912(a1,a1),a1,x98271,f243(a1,a1)),f205(x98271)),f223(x98271,x98272,f220(x98271,x98273)))),f2(a1)))
% 22.40/22.30 [9828]~P48(x98281,x98282,x98283)+P1(f319(f319(f226(a1),f319(f319(f66(f912(a1,a1),a1,x98281,f243(a1,a1)),f205(x98281)),f223(x98281,x98282,f220(x98281,x98283)))),f2(a1)))
% 22.40/22.30 [9962]P48(x99621,x99622,x99623)+~P1(f319(f319(f226(a1),f319(f319(f66(f912(a1,a1),a1,x99621,f243(a1,a1)),f205(x99621)),f223(x99621,x99622,f220(x99621,x99623)))),f2(a1)))
% 22.40/22.30 [9963]P47(x99631,x99632,x99633)+~P1(f319(f319(f225(a1),f319(f319(f66(f912(a1,a1),a1,x99631,f243(a1,a1)),f205(x99631)),f223(x99631,x99632,f220(x99631,x99633)))),f2(a1)))
% 22.40/22.30 [10377]~P113(x103771)+~P1(f319(f319(f226(x103771),f319(f319(f74(x103771),f319(f319(f236(x103771),x103772),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103771),x103773),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))),f2(x103771)))
% 22.40/22.30 [4838]~E(x48383,f105(x48381))+E(f319(f319(f126(x48381),x48382),x48383),x48382)
% 22.40/22.30 [4839]~E(x48392,f105(x48391))+E(f319(f319(f126(x48391),x48392),x48393),x48393)
% 22.40/22.30 [4845]~E(x48452,f2(a906))+E(f319(f319(f167(x48451),x48452),x48453),f105(x48451))
% 22.40/22.30 [4854]~E(x48543,f105(x48541))+E(f319(f319(f167(x48541),x48542),x48543),f105(x48541))
% 22.40/22.30 [4893]~E(x48931,x48933)+E(x48931,f319(f319(f126(x48932),f105(x48932)),x48933))
% 22.40/22.30 [4981]~P112(x49812)+E(f319(f234(f913(x49811,x49812)),x49813),f234(x49812))
% 22.40/22.30 [4983]~P62(x49832)+E(f319(f181(f913(x49831,x49832)),x49833),f181(x49832))
% 22.40/22.30 [5001]E(x50011,f105(x50012))+~E(f319(f319(f126(x50012),x50013),x50011),x50013)
% 22.40/22.30 [5002]E(x50021,f105(x50022))+~E(f319(f319(f126(x50022),x50021),x50023),x50023)
% 22.40/22.30 [5010]E(x50101,f105(x50102))+~E(f319(f319(f126(x50102),x50103),x50101),f105(x50102))
% 22.40/22.30 [5011]E(x50111,f105(x50112))+~E(f319(f319(f126(x50112),x50111),x50113),f105(x50112))
% 22.40/22.30 [5036]~E(x50362,f2(a906))+E(f319(f319(f75(a906),x50361),x50362),f319(f319(f75(a906),x50363),x50362))
% 22.40/22.30 [5038]~E(x50381,f2(a906))+E(f319(f319(f75(a906),x50381),x50382),f319(f319(f75(a906),x50381),x50383))
% 22.40/22.30 [5096]~P101(x50961)+E(f319(f319(f93(x50961),x50962),x50963),f319(f319(f93(x50961),x50963),x50962))
% 22.40/22.30 [5098]~P106(x50981)+E(f319(f319(f93(x50981),x50982),x50983),f319(f319(f93(x50981),x50983),x50982))
% 22.40/22.30 [5099]~P101(x50991)+E(f319(f319(f94(x50991),x50992),x50993),f319(f319(f94(x50991),x50993),x50992))
% 22.40/22.30 [5101]~P107(x51011)+E(f319(f319(f94(x51011),x51012),x51013),f319(f319(f94(x51011),x51013),x51012))
% 22.40/22.30 [5103]~P4(x51031)+E(f319(f319(f180(x51031),x51032),x51033),f319(f319(f180(x51031),x51033),x51032))
% 22.40/22.30 [5105]~P4(x51051)+E(f319(f319(f230(x51051),x51052),x51053),f319(f319(f230(x51051),x51053),x51052))
% 22.40/22.30 [5106]~P119(x51061)+E(f319(f319(f74(x51061),x51062),x51063),f319(f319(f74(x51061),x51063),x51062))
% 22.40/22.30 [5107]~P119(x51071)+E(f319(f319(f75(x51071),x51072),x51073),f319(f319(f75(x51071),x51073),x51072))
% 22.40/22.30 [5170]E(f39(a906,x51701,x51702),f2(a906))+~E(x51701,f319(f319(f75(a906),x51702),x51703))
% 22.40/22.30 [5171]E(f39(a1,x51711,x51712),f2(a1))+~E(x51711,f319(f319(f75(a1),x51712),x51713))
% 22.40/22.30 [5238]E(x52381,x52382)+~E(f319(f319(f74(a906),x52383),x52381),f319(f319(f74(a906),x52383),x52382))
% 22.40/22.30 [5239]E(x52391,x52392)+~E(f319(f319(f74(a906),x52391),x52393),f319(f319(f74(a906),x52392),x52393))
% 22.40/22.30 [5251]~P63(x52511)+E(f319(f319(f94(x52511),x52512),f319(f73(x52511),x52513)),f319(f319(f3(x52511),x52512),x52513))
% 22.40/22.30 [5252]~P66(x52521)+E(f319(f319(f74(x52521),x52522),f319(f73(x52521),x52523)),f319(f319(f3(x52521),x52522),x52523))
% 22.40/22.30 [5253]~P67(x52531)+E(f319(f319(f74(x52531),x52532),f319(f73(x52531),x52533)),f319(f319(f3(x52531),x52532),x52533))
% 22.40/22.30 [5254]~P115(x52541)+E(f319(f319(f74(x52541),x52542),f319(f73(x52541),x52543)),f319(f319(f3(x52541),x52542),x52543))
% 22.40/22.30 [5255]~P66(x52551)+E(f319(f319(f3(x52551),x52552),f319(f73(x52551),x52553)),f319(f319(f74(x52551),x52552),x52553))
% 22.40/22.30 [5293]~P1(f319(x52933,x52932))+P1(f319(f319(f321(x52931),x52932),x52933))
% 22.40/22.30 [5295]~P76(x52952)+E(f319(f319(f8(x52951,x52952),x52953),f181(f913(x52951,a904))),f2(x52952))
% 22.40/22.30 [5297]~P82(x52972)+E(f319(f319(f11(x52971,x52972),x52973),f181(f913(x52971,a904))),f72(x52972))
% 22.40/22.30 [5349]~E(x53492,f319(f319(f74(a906),x53491),x53493))+P1(f319(f319(f225(a906),x53491),x53492))
% 22.40/22.30 [5352]~E(x53522,f181(f913(x53521,a904)))+E(f319(f319(f54(x53521),x53522),x53523),f181(f913(f913(x53521,a904),a904)))
% 22.40/22.30 [5353]~E(x53532,f181(f913(x53531,a904)))+E(f181(f913(f913(x53531,a904),a904)),f319(f319(f54(x53531),x53532),x53533))
% 22.40/22.30 [5420]~E(f319(f276(x54202,x54203),x54201),f181(f913(x54203,a904)))+E(x54201,f181(f913(f912(x54202,x54203),a904)))
% 22.40/22.30 [5421]~E(f319(f256(x54212,x54213),x54211),f181(f913(x54212,a904)))+E(x54211,f181(f913(f912(x54212,x54213),a904)))
% 22.40/22.30 [5453]E(f319(f276(x54531,x54532),x54533),f181(f913(x54532,a904)))+~E(x54533,f181(f913(f912(x54531,x54532),a904)))
% 22.40/22.30 [5454]E(f319(f256(x54541,x54542),x54543),f181(f913(x54541,a904)))+~E(x54543,f181(f913(f912(x54541,x54542),a904)))
% 22.40/22.30 [5457]E(f266(x54571,x54572,x54573),f319(f319(f3(a91),x54572),x54573))+P1(f319(f319(f226(a91),x54572),x54573))
% 22.40/22.30 [5472]P1(f319(x54721,x54722))+~P1(f319(f319(f321(x54723),x54722),x54721))
% 22.40/22.30 [5511]E(x55111,x55112)+~E(f319(f73(f913(x55113,a904)),x55111),f319(f73(f913(x55113,a904)),x55112))
% 22.40/22.30 [5522]~E(x55221,f181(f913(x55222,a904)))+~P1(f319(f319(f321(x55222),x55223),x55221))
% 22.40/22.30 [5553]~E(x55532,f319(f319(f74(a1),x55531),f319(f92(a1),x55533)))+P1(f319(f319(f225(a1),x55531),x55532))
% 22.40/22.30 [5567]E(f319(f319(f301(x55671),x55672),x55673),x55673)+~P1(f319(f319(f321(x55671),x55672),x55673))
% 22.40/22.30 [5578]E(x55781,f181(f913(x55782,a904)))+~E(f319(f319(f54(x55782),x55781),x55783),f181(f913(f913(x55782,a904),a904)))
% 22.40/22.30 [5579]E(x55791,f181(f913(x55792,a904)))+~E(f181(f913(f913(x55792,a904),a904)),f319(f319(f54(x55792),x55791),x55793))
% 22.40/22.30 [5585]~P124(x55851)+E(f319(f319(f75(x55851),f319(f73(x55851),x55852)),f319(f73(x55851),x55853)),f319(f319(f75(x55851),x55852),x55853))
% 22.40/22.30 [5587]~P72(x55871)+E(f319(f319(f282(x55871),f319(f73(x55871),x55872)),f319(f73(x55871),x55873)),f319(f319(f282(x55871),x55872),x55873))
% 22.40/22.30 [5617]~P1(f319(x56173,x56172))+P1(f319(f319(f321(x56171),x56172),f319(f254(x56171),x56173)))
% 22.40/22.30 [5644]E(x56441,f2(a906))+E(f319(f164(x56442),f161(x56442,x56441,x56443)),f319(f319(f301(x56442),x56443),f181(f913(x56442,a904))))
% 22.40/22.30 [5663]E(f162(x56631,x56632,x56633),x56633)+P1(f319(f319(f321(x56631),x56632),f319(f164(x56631),x56633)))
% 22.40/22.30 [5750]~P1(f319(f129(x57501),x57503))+P1(f319(f129(x57501),f319(f128(x57501,x57502),x57503)))
% 22.40/22.30 [5794]~P69(x57941)+E(f319(f319(f30(x57941),f39(x57941,x57942,x57943)),x57943),f2(x57941))
% 22.40/22.30 [5813]E(f168(x58131,f319(f319(f143(x58131),x58132),f105(x58131)),x58133),f105(x58131))+P1(f319(f319(f321(a906),f2(a906)),x58133))
% 22.40/22.30 [5819]E(x58191,f2(a906))+E(f319(f163(x58192),f161(x58192,x58191,x58193)),f161(x58192,f319(f319(f3(a906),x58191),f72(a906)),x58193))
% 22.40/22.30 [5870]E(f319(f319(f143(x58701),x58702),x58703),f132(x58701,x58702,x58703))+P1(f319(f319(f321(x58701),x58702),f319(f164(x58701),x58703)))
% 22.40/22.30 [5879]E(x58791,x58792)+~E(f319(f319(f75(a906),f319(a104,x58793)),x58791),f319(f319(f75(a906),f319(a104,x58793)),x58792))
% 22.40/22.30 [5880]~E(x58802,f319(f319(f74(a1),x58801),f319(f92(a1),f319(a104,x58803))))+P1(f319(f319(f226(a1),x58801),x58802))
% 22.40/22.30 [5946]~P30(x59461,x59462,x59463)+P31(a906,x59461,f131(a906,f319(f294(a906,x59462),x59463)))
% 22.40/22.30 [5997]~E(x59973,f105(x59971))+E(f319(f319(f319(f175(f907(x59971),f907(x59971)),x59972),f159(x59971)),x59973),f105(x59971))
% 22.40/22.30 [6001]P1(f319(x60011,x60012))+~P1(f319(f319(f321(x60013),x60012),f319(f254(x60013),x60011)))
% 22.40/22.30 [6031]E(x60311,x60312)+~E(f319(f319(f301(x60313),x60311),f181(f913(x60313,a904))),f319(f319(f301(x60313),x60312),f181(f913(x60313,a904))))
% 22.40/22.30 [6045]~P111(x60451)+E(f319(f319(f94(f913(x60451,a904)),f319(f274(x60451),x60452)),f319(f294(x60451,x60452),x60453)),f181(f913(x60451,a904)))
% 22.40/22.30 [6084]E(f132(x60841,x60842,x60843),x60843)+~P1(f319(f319(f321(x60841),x60842),f319(f164(x60841),x60843)))
% 22.40/22.30 [6107]~P65(x61071)+E(f319(f302(x61071,x61071,f73(x61071)),f319(f294(x61071,x61072),x61073)),f297(x61071,f319(f73(x61071),x61073),f319(f73(x61071),x61072)))
% 22.40/22.30 [6118]E(f319(f182(f907(x61181)),f162(x61181,x61182,x61183)),f319(f182(f907(x61181)),x61183))+P1(f319(f319(f321(x61181),x61182),f319(f164(x61181),x61183)))
% 22.40/22.30 [6168]~P111(x61681)+E(f319(f319(f94(f913(x61681,a904)),f319(f294(x61681,x61682),x61683)),f319(f275(x61681),x61683)),f181(f913(x61681,a904)))
% 22.40/22.30 [6188]~P65(x61881)+E(f319(f302(x61881,x61881,f73(x61881)),f298(x61881,x61882,x61883)),f298(x61881,f319(f73(x61881),x61883),f319(f73(x61881),x61882)))
% 22.40/22.30 [6189]~P65(x61891)+E(f319(f302(x61891,x61891,f73(x61891)),f295(x61891,x61892,x61893)),f295(x61891,f319(f73(x61891),x61893),f319(f73(x61891),x61892)))
% 22.40/22.30 [6255]E(f168(x62551,f319(f319(f143(x62551),x62552),f105(x62551)),x62553),f319(f319(f143(x62551),x62552),f105(x62551)))+~P1(f319(f319(f321(a906),f2(a906)),x62553))
% 22.40/22.30 [6262]P30(x62621,x62622,x62623)+~P31(a906,x62621,f131(a906,f319(f294(a906,x62622),x62623)))
% 22.40/22.30 [6265]~P65(x62651)+E(f319(f302(x62651,x62651,f73(x62651)),f297(x62651,x62652,x62653)),f319(f294(x62651,f319(f73(x62651),x62653)),f319(f73(x62651),x62652)))
% 22.40/22.30 [6286]~P70(x62861)+E(f39(x62861,f319(f73(x62861),f39(x62861,x62862,x62863)),x62863),f39(x62861,f319(f73(x62861),x62862),x62863))
% 22.40/22.30 [6379]~P1(f319(f55(f912(x63792,x63791)),x63793))+P1(f319(f55(x63791),f319(f276(x63792,x63791),x63793)))
% 22.40/22.30 [6380]~P1(f319(f55(f912(x63801,x63802)),x63803))+P1(f319(f55(x63801),f319(f256(x63801,x63802),x63803)))
% 22.40/22.30 [6385]~P111(x63851)+E(f319(f319(f94(f913(x63851,a904)),f298(x63851,x63852,x63853)),f319(f275(x63851),x63853)),f181(f913(x63851,a904)))
% 22.40/22.30 [6386]~P111(x63861)+E(f319(f319(f94(f913(x63861,a904)),f297(x63861,x63862,x63863)),f319(f296(x63861),x63863)),f181(f913(x63861,a904)))
% 22.40/22.30 [6387]~P111(x63871)+E(f319(f319(f94(f913(x63871,a904)),f295(x63871,x63872,x63873)),f319(f296(x63871),x63873)),f181(f913(x63871,a904)))
% 22.40/22.30 [6455]E(f319(f319(f156(x64551),x64552),f610(x64552,x64553,x64551)),x64553)+~P1(f319(f319(f321(x64551),x64553),f319(f164(x64551),x64552)))
% 22.40/22.30 [6601]E(x66011,f105(x66012))+~E(f319(f319(f319(f175(f907(x66012),f907(x66012)),x66013),f159(x66012)),x66011),f105(x66012))
% 22.40/22.30 [6706]~P1(f319(f55(f912(x67062,x67061)),x67063))+P1(f319(f55(f912(x67061,x67062)),f319(f278(x67062,x67061),x67063)))
% 22.40/22.30 [6864]P57(x68641,x68642,x68643)+P1(f319(f319(f321(x68641),f609(x68643,x68642,x68641)),x68642))
% 22.40/22.30 [6865]P57(x68651,x68652,x68653)+P1(f319(f319(f321(x68651),f608(x68653,x68652,x68651)),x68652))
% 22.40/22.30 [6875]P1(f319(f307(x68751,x68752),x68753))+P1(f319(f319(x68752,f459(x68753,x68752,x68751)),x68753))
% 22.40/22.30 [6876]P1(f319(f307(x68761,x68762),x68763))+P1(f319(f319(x68762,f486(x68763,x68762,x68761)),x68763))
% 22.40/22.30 [6902]E(f319(f182(f907(x69021)),f162(x69021,x69022,x69023)),f319(f319(f3(a906),f319(f182(f907(x69021)),x69023)),f72(a906)))+~P1(f319(f319(f321(x69021),x69022),f319(f164(x69021),x69023)))
% 22.40/22.30 [6939]P1(f319(f240(x69391,x69392),x69393))+P1(f319(f319(f321(x69391),f566(x69393,x69392,x69391)),x69393))
% 22.40/22.30 [6949]~P1(f319(f55(f912(x69492,x69491)),f319(f278(x69491,x69492),x69493)))+P1(f319(f55(f912(x69491,x69492)),x69493))
% 22.40/22.30 [7004]~P1(f319(f319(f321(x70041),x70042),f319(f164(x70041),f106(x70041,x70043))))+P1(f319(f319(f321(x70041),x70042),f319(f164(x70041),x70043)))
% 22.40/22.30 [7038]E(f319(f128(x70381,x70382),x70383),x70383)+P1(f319(f319(f321(x70381),f664(x70383,x70382,x70381)),f319(f164(x70381),x70383)))
% 22.40/22.30 [7053]E(f319(f128(x70531,x70532),x70533),f105(x70531))+P1(f319(f319(f321(x70531),f663(x70533,x70532,x70531)),f319(f164(x70531),x70533)))
% 22.40/22.30 [7080]P31(x70801,x70802,x70803)+P1(f319(f319(f321(x70801),f748(x70803,x70802,x70801)),f319(f164(x70801),x70803)))
% 22.40/22.30 [7081]P31(x70811,x70812,x70813)+P1(f319(f319(f321(x70811),f756(x70813,x70812,x70811)),f319(f164(x70811),x70813)))
% 22.40/22.30 [7082]P31(x70821,x70822,x70823)+P1(f319(f319(f321(x70821),f755(x70822,x70823,x70821)),f319(f164(x70821),x70823)))
% 22.40/22.30 [7085]E(f169(x70851,x70852,x70853),x70853)+P1(f319(f319(f321(x70851),f708(x70853,x70852,x70851)),f319(f164(x70851),x70853)))
% 22.40/22.30 [7160]P1(f319(f152(x71601,x71602),x71603))+P1(f319(f319(f321(x71601),f665(x71603,x71602,x71601)),f319(f164(x71601),x71603)))
% 22.40/22.30 [7169]~P33(x71691,x71693,x71692)+P1(f319(f319(f321(x71691),f741(x71692,x71693,x71691)),f319(f164(x71691),x71692)))
% 22.40/22.30 [7170]~P35(x71701,x71703,x71702)+P1(f319(f319(f321(x71701),f747(x71702,x71703,x71701)),f319(f164(x71701),x71702)))
% 22.40/22.30 [7171]~P35(x71711,x71713,x71712)+P1(f319(f319(f321(x71711),f757(x71712,x71713,x71711)),f319(f164(x71711),x71712)))
% 22.40/22.30 [7172]~P33(x71721,x71722,x71723)+P1(f319(f319(f321(x71721),f785(x71722,x71723,x71721)),f319(f164(x71721),x71723)))
% 22.40/22.30 [7173]~P33(x71731,x71733,x71732)+P1(f319(f319(f321(x71731),f786(x71732,x71733,x71731)),f319(f164(x71731),x71732)))
% 22.40/22.30 [7206]P1(f319(f319(f321(x72061),x72062),f377(x72063,x72062,x72061)))+~P1(f319(f319(f321(x72061),x72062),f31(f913(x72061,a904),x72063)))
% 22.40/22.30 [7207]~P76(x72071)+E(f319(f319(f74(x72071),f319(f319(f8(a906,x72071),x72072),f319(f274(a906),x72073))),f319(x72072,x72073)),f319(f319(f8(a906,x72071),x72072),f319(f274(a906),f319(a104,x72073))))
% 22.40/22.30 [7219]P30(x72191,x72192,x72193)+P1(f319(f319(f321(a906),f819(x72193,x72192,x72191)),f319(f294(a906,x72192),x72193)))
% 22.40/22.30 [7297]~P33(x72972,x72971,x72973)+P1(f319(x72971,f319(f319(f156(x72972),x72973),f744(x72973,x72971,x72972))))
% 22.40/22.30 [7309]~P1(f319(f319(f321(x73091),x73092),f866(x73092,x73093,x73091)))+P1(f319(f319(f321(x73091),x73092),f32(f913(x73091,a904),x73093)))
% 22.40/22.30 [7342]~P76(x73421)+E(f319(f319(f74(x73421),f319(f319(f8(a906,x73421),x73422),f319(f293(a906),x73423))),f319(x73422,f319(a104,x73423))),f319(f319(f8(a906,x73421),x73422),f319(f293(a906),f319(a104,x73423))))
% 22.40/22.30 [7473]P1(f319(f319(f321(f907(x74731)),x74732),f153(x74731,x74733)))+P1(f319(f319(f321(x74731),f649(x74733,x74732,x74731)),f319(f164(x74731),x74732)))
% 22.40/22.30 [7488]~P1(f319(f319(f321(f907(x74881)),x74882),f153(x74881,f308(x74881,x74883))))+P1(f319(f319(f321(f907(x74881)),x74882),f308(f907(x74881),f149(x74881,x74883))))
% 22.40/22.30 [7512]~P1(f319(f319(f321(f907(x75121)),x75122),f308(f907(x75121),f149(x75121,x75123))))+P1(f319(f319(f321(f907(x75121)),x75122),f153(x75121,f308(x75121,x75123))))
% 22.40/22.30 [7545]E(f319(f319(f319(f175(f907(x75451),f907(x75451)),x75452),f159(x75451)),x75453),x75453)+~P1(f319(f319(f225(a906),f319(f182(f907(x75451)),x75453)),f72(a906)))
% 22.40/22.30 [7578]E(f319(f319(f126(x75781),f750(x75782,x75783,x75781)),f319(f319(f143(x75781),x75783),f752(x75782,x75783,x75781))),x75782)+~P1(f319(f319(f321(x75781),x75783),f319(f164(x75781),x75782)))
% 22.40/22.30 [7579]E(f319(f319(f126(x75791),f745(x75792,x75793,x75791)),f319(f319(f143(x75791),x75793),f746(x75792,x75793,x75791))),x75792)+~P1(f319(f319(f321(x75791),x75793),f319(f164(x75791),x75792)))
% 22.40/22.30 [7580]E(f319(f319(f126(x75801),f753(x75802,x75803,x75801)),f319(f319(f143(x75801),x75803),f754(x75802,x75803,x75801))),x75802)+~P1(f319(f319(f321(x75801),x75803),f319(f164(x75801),x75802)))
% 22.40/22.30 [7601]~P25(x76011,x76012,x76013,f234(f913(x76011,a904)))+P25(f907(x76011),f907(x76012),f319(f146(x76011,x76012),x76013),f234(f913(f907(x76011),a904)))
% 22.40/22.30 [7745]E(x77451,f319(f319(f74(a906),f319(f319(f75(a906),f319(f243(a906,a906),x77452)),x77453)),f319(f248(a906,a906),x77452)))+~P1(f319(f42(x77451,x77453),x77452))
% 22.40/22.30 [7753]P25(x77531,x77532,x77533,f234(f913(x77531,a904)))+~P25(f907(x77531),f907(x77532),f319(f146(x77531,x77532),x77533),f234(f913(f907(x77531),a904)))
% 22.40/22.30 [7797]P1(f319(f319(f321(f913(x77971,a904)),f866(x77972,x77973,x77971)),x77973))+P1(f319(f319(f321(x77971),x77972),f32(f913(x77971,a904),x77973)))
% 22.40/22.30 [7889]P1(f319(f319(f321(f907(x78891)),x78892),f153(x78891,x78893)))+~P1(f319(f319(f321(x78891),f649(x78893,x78892,x78891)),x78893))
% 22.40/22.30 [7987]P31(x79871,x79872,x79873)+~P1(f319(x79872,f319(f319(f156(x79871),x79873),f749(x79873,x79872,x79871))))
% 22.40/22.30 [8011]E(x80111,x80112)+~E(f319(f319(f9(x80113,f913(x80113,a904),a904),f321(x80113)),x80111),f319(f319(f9(x80113,f913(x80113,a904),a904),f321(x80113)),x80112))
% 22.40/22.30 [8019]~P1(f319(f319(f321(f912(x80191,x80191)),x80193),f255(x80191,x80192)))+P1(f319(f319(f321(x80191),f516(x80192,x80193,x80191)),x80192))
% 22.40/22.30 [8021]~P1(f319(f319(f321(x80211),x80213),f31(f913(x80211,a904),x80212)))+P1(f319(f319(f321(f913(x80211,a904)),f377(x80212,x80213,x80211)),x80212))
% 22.40/22.30 [8135]P25(x81351,x81352,f85(x81352,x81351,f234(f913(x81352,a904)),x81353),f234(f913(x81351,a904)))+~E(f319(f302(x81352,x81351,x81353),f234(f913(x81352,a904))),f234(f913(x81351,a904)))
% 22.40/22.30 [8192]~P1(f319(f319(f321(x81921),x81922),f319(f164(x81921),f745(x81923,x81922,x81921))))+~P1(f319(f319(f321(x81921),x81922),f319(f164(x81921),x81923)))
% 22.40/22.30 [8193]~P1(f319(f319(f321(x81931),x81932),f319(f164(x81931),f754(x81933,x81932,x81931))))+~P1(f319(f319(f321(x81931),x81932),f319(f164(x81931),x81933)))
% 22.40/22.30 [8218]P30(f319(f66(a904,a904,a906,a314),x82181),x82182,x82183)+P33(a906,x82181,f131(a906,f319(f294(a906,x82182),x82183)))
% 22.40/22.30 [8378]E(x83781,f105(x83782))+P1(f319(f319(f321(x83782),f319(f243(x83782,f912(a91,a91)),f319(f267(x83782,x83781),x83783))),f319(f164(x83782),x83781)))
% 22.40/22.30 [8474]~P78(x84741)+E(f319(f134(x84741,x84741,f319(f9(x84741,x84741,x84741),f74(x84741)),x84742),f319(f160(x84741),x84743)),f319(f134(x84741,x84741,f74(x84741),x84742),x84743))
% 22.40/22.30 [8669]~P25(x86692,x86691,x86693,f234(f913(x86692,a904)))+E(f319(f302(x86691,x86692,f85(x86692,x86691,f234(f913(x86692,a904)),x86693)),f234(f913(x86691,a904))),f234(f913(x86692,a904)))
% 22.40/22.30 [8739]~P30(f319(f66(a904,a904,a906,a314),x87391),x87392,x87393)+~P33(a906,x87391,f131(a906,f319(f294(a906,x87392),x87393)))
% 22.40/22.30 [8984]~P4(x89841)+E(f319(f164(x89841),f141(x89841,x89841,f7(x89841),x89842,x89843)),f319(f319(f301(x89841),x89842),f319(f164(x89841),x89843)))
% 22.40/22.30 [8996]~E(f319(x89963,f319(f85(x89961,x89962,f234(f913(x89961,a904)),x89963),f800(x89963,x89962,x89961))),f800(x89963,x89962,x89961))+E(f319(f302(x89961,x89962,x89963),f234(f913(x89961,a904))),f234(f913(x89962,a904)))
% 22.40/22.30 [8998]P1(f319(f319(f226(a906),f2(a906)),f616(x89981,x89982,x89983)))+~P1(f319(f319(f321(f912(x89983,x89983)),x89982),f319(f319(f281(x89983,x89983,x89983),x89981),f299(x89983,x89981))))
% 22.40/22.30 [9275]~P59(x92751,x92752)+~P1(f319(f319(f321(f912(x92751,x92751)),f319(f319(f244(x92751,x92751),x92753),x92753)),f319(f319(f281(x92751,x92751,x92751),x92752),f299(x92751,x92752))))
% 22.40/22.30 [9414]~E(f319(f319(f94(f913(f912(x94141,x94141),a904)),f319(f278(x94141,x94141),x94142)),f299(x94141,x94142)),f181(f913(f912(x94141,x94141),a904)))+~P1(f319(f319(f321(f912(x94141,x94141)),f319(f319(f244(x94141,x94141),x94143),x94143)),f319(f319(f281(x94141,x94141,x94141),x94142),f299(x94141,x94142))))
% 22.40/22.30 [9593]~P1(f319(f55(x95931),x95932))+P1(f319(f319(f225(a906),f319(f29(x95931),f319(f319(f3(f913(x95931,a904)),x95932),f319(f319(f301(x95931),x95933),f181(f913(x95931,a904)))))),f319(f29(x95931),x95932)))
% 22.40/22.30 [5158]~E(x51583,f105(x51581))+E(f136(x51581,f319(f319(f143(x51581),x51582),x51583)),x51582)
% 22.40/22.30 [5167]~E(x51673,f105(x51671))+E(f106(x51671,f319(f319(f143(x51671),x51672),x51673)),f105(x51671))
% 22.40/22.30 [5199]E(x51991,f105(x51992))+E(f136(x51992,f319(f319(f143(x51992),x51993),x51991)),f136(x51992,x51991))
% 22.40/22.30 [5201]E(x52011,f105(x52012))+E(f136(x52012,f319(f319(f126(x52012),x52013),x52011)),f136(x52012,x52011))
% 22.40/22.30 [5208]~E(x52083,f105(x52081))+E(f106(x52081,f319(f319(f126(x52081),x52082),x52083)),f106(x52081,x52082))
% 22.40/22.30 [5210]~E(x52103,f105(x52101))+E(f136(x52101,f319(f319(f126(x52101),x52102),x52103)),f136(x52101,x52102))
% 22.40/22.30 [5245]E(x52451,f105(x52452))+E(f319(f133(x52452),f319(f319(f126(x52452),x52451),x52453)),f319(f133(x52452),x52451))
% 22.40/22.30 [5273]~E(x52732,f105(x52731))+E(f319(f133(x52731),f319(f319(f126(x52731),x52732),x52733)),f319(f133(x52731),x52733))
% 22.40/22.30 [5325]~P101(x53251)+E(f319(f319(f93(x53251),x53252),f319(f319(f94(x53251),x53252),x53253)),x53252)
% 22.40/22.30 [5326]~P101(x53261)+E(f319(f319(f94(x53261),x53262),f319(f319(f93(x53261),x53262),x53263)),x53262)
% 22.40/22.30 [5327]~P4(x53271)+E(f319(f319(f180(x53271),x53272),f319(f319(f230(x53271),x53272),x53273)),x53272)
% 22.40/22.30 [5328]~P4(x53281)+E(f319(f319(f230(x53281),x53282),f319(f319(f180(x53281),x53282),x53283)),x53282)
% 22.40/22.30 [5347]~P69(x53471)+E(f39(x53471,f319(f319(f75(x53471),x53472),x53473),x53473),f2(x53471))
% 22.40/22.30 [5348]~P69(x53481)+E(f39(x53481,f319(f319(f75(x53481),x53482),x53483),x53482),f2(x53481))
% 22.40/22.30 [5415]~P67(x54151)+E(f319(f73(x54151),f319(f319(f3(x54151),x54152),x54153)),f319(f319(f3(x54151),x54153),x54152))
% 22.40/22.30 [5476]E(x54761,f105(x54762))+E(f106(x54762,f319(f319(f143(x54762),x54763),x54761)),f319(f319(f143(x54762),x54763),f106(x54762,x54761)))
% 22.40/22.30 [5477]E(x54771,f105(x54772))+E(f106(x54772,f319(f319(f126(x54772),x54773),x54771)),f319(f319(f126(x54772),x54773),f106(x54772,x54771)))
% 22.40/22.30 [5480]~P5(x54801)+E(f32(x54801,f319(f319(f301(x54801),x54802),x54803)),f319(f319(f94(x54801),x54802),f32(x54801,x54803)))
% 22.40/22.30 [5481]~P5(x54811)+E(f31(x54811,f319(f319(f301(x54811),x54812),x54813)),f319(f319(f93(x54811),x54812),f31(x54811,x54813)))
% 22.40/22.30 [5527]~P101(x55271)+E(f319(f319(f93(x55271),x55272),f319(f319(f93(x55271),x55272),x55273)),f319(f319(f93(x55271),x55272),x55273))
% 22.40/22.30 [5529]~P106(x55291)+E(f319(f319(f93(x55291),x55292),f319(f319(f93(x55291),x55292),x55293)),f319(f319(f93(x55291),x55292),x55293))
% 22.40/22.30 [5530]~P101(x55301)+E(f319(f319(f94(x55301),x55302),f319(f319(f94(x55301),x55302),x55303)),f319(f319(f94(x55301),x55302),x55303))
% 22.40/22.30 [5532]~P107(x55321)+E(f319(f319(f94(x55321),x55322),f319(f319(f94(x55321),x55322),x55323)),f319(f319(f94(x55321),x55322),x55323))
% 22.40/22.30 [5534]~P4(x55341)+E(f319(f319(f180(x55341),x55342),f319(f319(f180(x55341),x55342),x55343)),f319(f319(f180(x55341),x55342),x55343))
% 22.40/22.30 [5536]~P4(x55361)+E(f319(f319(f230(x55361),x55362),f319(f319(f230(x55361),x55362),x55363)),f319(f319(f230(x55361),x55362),x55363))
% 22.40/22.30 [5537]~P100(x55371)+E(f319(f319(f75(x55371),x55372),f319(f319(f75(x55371),x55372),x55373)),f319(f319(f75(x55371),x55372),x55373))
% 22.40/22.30 [5544]~P69(x55441)+E(f39(x55441,f319(f319(f74(x55441),x55442),x55443),x55443),f39(x55441,x55442,x55443))
% 22.40/22.30 [5545]~P69(x55451)+E(f39(x55451,f319(f319(f74(x55451),x55452),x55453),x55452),f39(x55451,x55453,x55452))
% 22.40/22.30 [5554]~P124(x55541)+E(f319(f319(f75(x55541),x55542),f319(f73(x55541),x55543)),f319(f73(x55541),f319(f319(f75(x55541),x55542),x55543)))
% 22.40/22.30 [5555]~P72(x55551)+E(f319(f319(f282(x55551),x55552),f319(f73(x55551),x55553)),f319(f73(x55551),f319(f319(f282(x55551),x55552),x55553)))
% 22.40/22.30 [5556]~P88(x55561)+E(f319(f319(f74(x55561),x55562),f319(f157(x55561),x55563)),f319(f157(x55561),f319(f319(f143(x55561),x55562),x55563)))
% 22.40/22.30 [5584]~P124(x55841)+E(f319(f319(f75(x55841),f319(f73(x55841),x55842)),x55843),f319(f319(f75(x55841),x55842),f319(f73(x55841),x55843)))
% 22.40/22.30 [5590]~P8(x55901,x55902,x55903)+E(f31(f913(x55901,a904),f319(f319(f54(x55901),x55902),x55903)),x55902)
% 22.40/22.30 [5655]~P116(x56551)+E(f319(f319(f75(x56551),x56552),f319(f319(f236(x56551),x56552),x56553)),f319(f319(f236(x56551),x56552),f319(a104,x56553)))
% 22.40/22.30 [5656]~P119(x56561)+E(f319(f319(f75(x56561),x56562),f319(f319(f236(x56561),x56562),x56563)),f319(f319(f236(x56561),x56562),f319(a104,x56563)))
% 22.40/22.30 [5666]~P66(x56661)+E(f319(f319(f74(x56661),f319(f73(x56661),x56662)),f319(f319(f74(x56661),x56662),x56663)),x56663)
% 22.40/22.30 [5689]~P146(x56891)+E(f319(f319(f236(x56891),f319(f92(x56891),x56892)),x56893),f319(f92(x56891),f319(f319(f236(a906),x56892),x56893)))
% 22.40/22.30 [5690]~P141(x56901)+E(f319(f319(f236(x56901),f319(f95(x56901),x56902)),x56903),f319(f95(x56901),f319(f319(f236(a1),x56902),x56903)))
% 22.40/22.30 [5696]~P92(x56961)+E(f319(f69(x56961),f319(f319(f3(x56961),x56962),x56963)),f319(f69(x56961),f319(f319(f3(x56961),x56963),x56962)))
% 22.40/22.30 [5700]~P113(x57001)+E(f319(f319(f75(x57001),f76(x57001,x57002)),f76(x57001,x57003)),f76(x57001,f319(f319(f75(x57001),x57002),x57003)))
% 22.40/22.30 [5704]E(x57041,f105(x57042))+E(f319(f319(f126(x57042),f319(f163(x57042),x57041)),x57043),f319(f163(x57042),f319(f319(f126(x57042),x57041),x57043)))
% 22.40/22.30 [5710]~E(x57102,f319(a104,f319(f319(f74(a906),x57101),x57103)))+P1(f319(f319(f226(a906),x57101),x57102))
% 22.40/22.30 [5711]~P124(x57111)+E(f319(f319(f75(x57111),f319(f73(x57111),x57112)),x57113),f319(f73(x57111),f319(f319(f75(x57111),x57112),x57113)))
% 22.40/22.30 [5712]~P120(x57121)+E(f319(f319(f282(x57121),f319(f73(x57121),x57122)),x57123),f319(f73(x57121),f319(f319(f282(x57121),x57122),x57123)))
% 22.40/22.30 [5713]~P113(x57131)+E(f319(f319(f236(x57131),f319(f69(x57131),x57132)),x57133),f319(f69(x57131),f319(f319(f236(x57131),x57132),x57133)))
% 22.40/22.30 [5812]E(f353(x58121,x58122,x58123),f361(x58121,x58122,x58123))+E(f319(f319(f94(f913(x58123,a904)),x58122),x58121),f181(f913(x58123,a904)))
% 22.40/22.30 [5827]~P76(x58272)+E(f319(f319(f8(x58271,x58272),f319(f18(x58272,x58271),f2(x58272))),x58273),f2(x58272))
% 22.40/22.30 [5828]~P82(x58282)+E(f319(f319(f11(x58281,x58282),f319(f18(x58282,x58281),f72(x58282))),x58283),f72(x58282))
% 22.40/22.30 [5830]~P98(x58301)+E(f319(f319(f3(x58301),f319(f96(x58301),x58302)),f319(f96(x58301),x58303)),f319(f96(x58301),f319(f319(f3(a1),x58302),x58303)))
% 22.40/22.30 [5833]~P146(x58331)+E(f319(f319(f74(x58331),f319(f92(x58331),x58332)),f319(f92(x58331),x58333)),f319(f92(x58331),f319(f319(f74(a906),x58332),x58333)))
% 22.40/22.30 [5834]~P146(x58341)+E(f319(f319(f75(x58341),f319(f92(x58341),x58342)),f319(f92(x58341),x58343)),f319(f92(x58341),f319(f319(f75(a906),x58342),x58343)))
% 22.40/22.30 [5835]~P141(x58351)+E(f319(f319(f3(x58351),f319(f95(x58351),x58352)),f319(f95(x58351),x58353)),f319(f95(x58351),f319(f319(f3(a1),x58352),x58353)))
% 22.40/22.30 [5836]~P141(x58361)+E(f319(f319(f74(x58361),f319(f95(x58361),x58362)),f319(f95(x58361),x58363)),f319(f95(x58361),f319(f319(f74(a1),x58362),x58363)))
% 22.40/22.30 [5837]~P141(x58371)+E(f319(f319(f75(x58371),f319(f95(x58371),x58372)),f319(f95(x58371),x58373)),f319(f95(x58371),f319(f319(f75(a1),x58372),x58373)))
% 22.40/22.30 [5838]~P98(x58381)+E(f319(f319(f74(x58381),f319(f96(x58381),x58382)),f319(f96(x58381),x58383)),f319(f96(x58381),f319(f319(f74(a1),x58382),x58383)))
% 22.40/22.30 [5839]~P98(x58391)+E(f319(f319(f75(x58391),f319(f96(x58391),x58392)),f319(f96(x58391),x58393)),f319(f96(x58391),f319(f319(f75(a1),x58392),x58393)))
% 22.40/22.30 [5887]~E(x58873,x58872)+P1(f319(f319(f225(f913(x58871,a904)),x58872),x58873))
% 22.40/22.30 [5893]~E(x58932,x58933)+P1(f319(f319(f225(f913(x58931,a904)),x58932),x58933))
% 22.40/22.30 [5898]~P63(x58981)+E(f319(f319(f94(x58981),f319(f73(x58981),x58982)),f319(f73(x58981),x58983)),f319(f73(x58981),f319(f319(f93(x58981),x58982),x58983)))
% 22.40/22.30 [5899]~P63(x58991)+E(f319(f319(f93(x58991),f319(f73(x58991),x58992)),f319(f73(x58991),x58993)),f319(f73(x58991),f319(f319(f94(x58991),x58992),x58993)))
% 22.40/22.30 [5900]~P83(x59001)+E(f319(f319(f230(x59001),f319(f73(x59001),x59002)),f319(f73(x59001),x59003)),f319(f73(x59001),f319(f319(f180(x59001),x59002),x59003)))
% 22.40/22.30 [5901]~P83(x59011)+E(f319(f319(f180(x59011),f319(f73(x59011),x59012)),f319(f73(x59011),x59013)),f319(f73(x59011),f319(f319(f230(x59011),x59012),x59013)))
% 22.40/22.30 [5902]~P66(x59021)+E(f319(f319(f74(x59021),f319(f73(x59021),x59022)),f319(f73(x59021),x59023)),f319(f73(x59021),f319(f319(f74(x59021),x59023),x59022)))
% 22.40/22.30 [5903]~P67(x59031)+E(f319(f319(f74(x59031),f319(f73(x59031),x59032)),f319(f73(x59031),x59033)),f319(f73(x59031),f319(f319(f74(x59031),x59032),x59033)))
% 22.40/22.30 [5904]~P113(x59041)+E(f319(f319(f75(x59041),f319(f69(x59041),x59042)),f319(f69(x59041),x59043)),f319(f69(x59041),f319(f319(f75(x59041),x59042),x59043)))
% 22.40/22.30 [5905]~P74(x59051)+E(f319(f319(f282(x59051),f319(f69(x59051),x59052)),f319(f69(x59051),x59053)),f319(f69(x59051),f319(f319(f282(x59051),x59052),x59053)))
% 22.40/22.30 [5906]~P88(x59061)+E(f319(f319(f74(x59061),f319(f157(x59061),x59062)),f319(f157(x59061),x59063)),f319(f157(x59061),f319(f319(f126(x59061),x59062),x59063)))
% 22.40/22.30 [5907]E(x59071,f181(f913(x59072,a904)))+~E(f319(f319(f93(f913(x59072,a904)),x59073),x59071),f181(f913(x59072,a904)))
% 22.40/22.30 [5908]E(x59081,f181(f913(x59082,a904)))+~E(f319(f319(f93(f913(x59082,a904)),x59081),x59083),f181(f913(x59082,a904)))
% 22.40/22.30 [5909]~P148(x59091,x59093,x59092)+P1(f319(x59091,f319(f319(f30(a1),x59092),x59093)))
% 22.40/22.30 [5970]~P1(f319(f55(x59701),x59703))+P1(f319(f55(x59701),f319(f319(f301(x59701),x59702),x59703)))
% 22.40/22.30 [5971]~P1(f319(f129(x59711),x59713))+P1(f319(f129(x59711),f319(f319(f167(x59711),x59712),x59713)))
% 22.40/22.30 [5972]~P1(f319(f129(x59721),x59723))+P1(f319(f129(x59721),f319(f319(f130(x59721),x59722),x59723)))
% 22.40/22.30 [6002]~P101(x60021)+P1(f319(f319(f225(x60021),x60022),f319(f319(f93(x60021),x60023),x60022)))
% 22.40/22.30 [6003]~P106(x60031)+P1(f319(f319(f225(x60031),x60032),f319(f319(f93(x60031),x60033),x60032)))
% 22.40/22.30 [6004]~P101(x60041)+P1(f319(f319(f225(x60041),x60042),f319(f319(f93(x60041),x60042),x60043)))
% 22.40/22.30 [6005]~P106(x60051)+P1(f319(f319(f225(x60051),x60052),f319(f319(f93(x60051),x60052),x60053)))
% 22.40/22.30 [6006]~P4(x60061)+P1(f319(f319(f225(x60061),x60062),f319(f319(f180(x60061),x60063),x60062)))
% 22.40/22.30 [6007]~P4(x60071)+P1(f319(f319(f225(x60071),x60072),f319(f319(f180(x60071),x60072),x60073)))
% 22.40/22.30 [6021]~E(x60211,f2(a906))+E(f319(f319(f30(a906),f319(f319(f75(a906),x60211),x60212)),f319(f319(f75(a906),x60211),x60213)),f2(a906))
% 22.40/22.30 [6101]~P98(x61011)+E(f319(f319(f3(x61011),f319(f96(x61011),x61012)),f319(f96(x61011),x61013)),f319(f96(x61011),f319(f319(f74(a1),x61012),f319(f73(a1),x61013))))
% 22.40/22.30 [6158]E(x61581,f2(a906))+E(f319(f319(f30(a906),f319(f319(f75(a906),x61581),x61582)),f319(f319(f75(a906),x61581),x61583)),f319(f319(f30(a906),x61582),x61583))
% 22.40/22.30 [6186]E(f144(x61861,f319(f319(f143(x61861),x61862),x61863)),f319(f319(f143(x61861),x61862),f144(x61861,x61863)))+P1(f319(f319(f321(x61861),x61862),f319(f164(x61861),x61863)))
% 22.40/22.30 [6222]P148(x62221,x62222,x62223)+~P1(f319(x62221,f319(f319(f30(a1),x62223),x62222)))
% 22.40/22.30 [6295]E(x62951,f105(x62952))+E(f319(f319(f143(x62952),f319(f133(x62952),x62951)),f319(f319(f167(x62952),x62953),f319(f163(x62952),x62951))),f319(f319(f167(x62952),f319(a104,x62953)),x62951))
% 22.40/22.30 [6303]E(f319(f319(f3(f913(x63031,a904)),x63032),x63033),x63032)+~E(f319(f319(f94(f913(x63031,a904)),x63032),x63033),f181(f913(x63031,a904)))
% 22.40/22.30 [6318]E(f144(x63181,f319(f319(f143(x63181),x63182),x63183)),f144(x63181,x63183))+~P1(f319(f319(f321(x63181),x63182),f319(f164(x63181),x63183)))
% 22.40/22.30 [6348]~P1(f319(f319(f225(a906),x63481),x63483))+P1(f319(f319(f225(a906),x63481),f319(f319(f74(a906),x63482),x63483)))
% 22.40/22.30 [6350]~P1(f319(f319(f225(a906),x63501),x63502))+P1(f319(f319(f225(a906),x63501),f319(f319(f74(a906),x63502),x63503)))
% 22.40/22.30 [6352]~P1(f319(f319(f226(a906),x63521),x63523))+P1(f319(f319(f226(a906),x63521),f319(f319(f74(a906),x63522),x63523)))
% 22.40/22.30 [6354]~P1(f319(f319(f226(a906),x63541),x63542))+P1(f319(f319(f226(a906),x63541),f319(f319(f74(a906),x63542),x63543)))
% 22.40/22.30 [6393]P1(f319(f55(x63931),x63932))+~P1(f319(f55(x63931),f319(f319(f301(x63931),x63933),x63932)))
% 22.40/22.30 [6394]P1(f319(f129(x63941),x63942))+~P1(f319(f129(x63941),f319(f319(f143(x63941),x63943),x63942)))
% 22.40/22.30 [6395]P1(f319(f129(x63951),x63952))+~P1(f319(f129(x63951),f319(f319(f126(x63951),x63953),x63952)))
% 22.40/22.30 [6396]P1(f319(f129(x63961),x63962))+~P1(f319(f129(x63961),f319(f319(f126(x63961),x63962),x63963)))
% 22.40/22.30 [6444]~P119(x64441)+E(f319(f319(f74(x64441),x64442),f319(f319(f75(x64441),x64443),x64442)),f319(f319(f75(x64441),f319(f319(f74(x64441),x64443),f72(x64441))),x64442))
% 22.40/22.30 [6492]~E(x64921,x64922)+~P1(f319(f319(f226(f913(x64923,a904)),x64921),x64922))
% 22.40/22.30 [6540]P1(f319(f319(f321(x65401),x65402),x65403))+P1(f319(f319(f321(x65401),x65402),f319(f73(f913(x65401,a904)),x65403)))
% 22.40/22.30 [6546]E(f136(x65461,f319(f319(f130(x65461),x65462),x65463)),f136(x65461,x65463))+~P1(f319(f319(f226(a906),x65462),f319(f182(f907(x65461)),x65463)))
% 22.40/22.30 [6547]E(f319(f319(f167(x65471),x65472),f106(x65471,x65473)),f319(f319(f167(x65471),x65472),x65473))+~P1(f319(f319(f226(a906),x65472),f319(f182(f907(x65471)),x65473)))
% 22.40/22.30 [6603]E(f319(f319(f319(f175(f907(x66031),f907(x66031)),x66032),f159(x66031)),x66033),x66033)+~E(f39(a906,x66032,f319(f182(f907(x66031)),x66033)),f2(a906))
% 22.40/22.30 [6610]~P8(x66101,x66103,x66102)+E(f319(f319(f281(x66101,x66101,x66101),f319(f278(x66101,x66101),x66102)),x66102),x66102)
% 22.40/22.30 [6650]~E(f319(f319(f93(f913(x66501,a904)),x66502),x66503),x66503)+P1(f319(f319(f225(f913(x66501,a904)),x66502),x66503))
% 22.40/22.30 [6655]~P56(x66551,x66551,x66553)+P56(x66551,x66551,f319(f319(f175(f912(x66551,x66551),a904),x66552),x66553))
% 22.40/22.30 [6658]~P1(f319(f319(f321(x66581),x66583),f319(f164(x66581),x66582)))+P1(f319(f319(f226(a906),f2(a906)),f319(f182(f907(x66581)),x66582)))
% 22.40/22.30 [6685]~P92(x66851)+E(f319(f69(x66851),f319(f319(f74(x66851),f319(f69(x66851),x66852)),f319(f69(x66851),x66853))),f319(f319(f74(x66851),f319(f69(x66851),x66852)),f319(f69(x66851),x66853)))
% 22.40/22.30 [6695]E(f319(f319(f30(a906),f319(f319(f75(a906),x66951),x66952)),f319(f319(f75(a906),x66951),x66953)),f319(f319(f30(a906),x66952),x66953))+~P1(f319(f319(f226(a906),f2(a906)),x66951))
% 22.40/22.30 [6842]~P1(f319(f55(x68421),x68423))+E(f319(f319(f58(x68421,f913(x68421,a904),f301(x68421)),x68422),x68423),f319(f319(f93(f913(x68421,a904)),x68423),x68422))
% 22.40/22.30 [6895]E(f319(f319(f93(f913(x68951,a904)),x68952),x68953),x68952)+~P1(f319(f319(f225(f913(x68951,a904)),x68953),x68952))
% 22.40/22.30 [6897]E(f319(f319(f93(f913(x68971,a904)),x68972),x68973),x68973)+~P1(f319(f319(f225(f913(x68971,a904)),x68972),x68973))
% 22.40/22.30 [6898]E(f319(f319(f94(f913(x68981,a904)),x68982),x68983),x68983)+~P1(f319(f319(f225(f913(x68981,a904)),x68983),x68982))
% 22.40/22.30 [6899]E(f319(f319(f94(f913(x68991,a904)),x68992),x68993),x68992)+~P1(f319(f319(f225(f913(x68991,a904)),x68992),x68993))
% 22.40/22.30 [6947]~P1(f319(f129(x69471),x69472))+E(f319(f319(f3(f913(x69471,a904)),f319(f164(x69471),x69472)),f319(f319(f301(x69471),x69473),f181(f913(x69471,a904)))),f319(f164(x69471),f162(x69471,x69473,x69472)))
% 22.40/22.30 [6999]P37(x69991,x69992)+~P37(x69991,f319(f319(f175(f912(x69991,x69991),a904),x69993),x69992))
% 22.40/22.30 [7065]P1(f319(f43(x70651,x70652),f319(a45,x70653)))+~P1(f319(f43(f319(f73(a1),x70651),f319(f73(a1),x70652)),x70653))
% 22.40/22.30 [7070]E(f319(f319(f3(f913(x70701,a904)),f319(f319(f301(x70701),x70702),x70703)),f319(f319(f301(x70701),x70702),f181(f913(x70701,a904)))),x70703)+P1(f319(f319(f321(x70701),x70702),x70703))
% 22.40/22.30 [7094]E(f319(f319(f94(f913(x70941,a904)),f319(f164(x70941),x70942)),f319(f164(x70941),x70943)),f181(f913(x70941,a904)))+~P1(f319(f129(x70941),f319(f319(f126(x70941),x70942),x70943)))
% 22.40/22.30 [7109]~P1(f319(f319(f321(x71091),x71092),f319(f164(x71091),x71093)))+~P1(f319(f129(x71091),f319(f319(f143(x71091),x71092),x71093)))
% 22.40/22.30 [7179]P31(x71791,x71792,x71793)+P1(f319(f319(f226(a906),f749(x71793,x71792,x71791)),f319(f182(f907(x71791)),x71793)))
% 22.40/22.30 [7189]E(f319(f319(f94(f913(x71891,a904)),x71892),x71893),f181(f913(x71891,a904)))+P1(f319(f319(f321(x71891),f353(x71893,x71892,x71891)),x71892))
% 22.40/22.30 [7190]E(f319(f319(f94(f913(x71901,a904)),x71902),x71903),f181(f913(x71901,a904)))+P1(f319(f319(f321(x71901),f361(x71903,x71902,x71901)),x71903))
% 22.40/22.30 [7193]E(f106(x71931,f319(f319(f167(x71931),x71932),x71933)),f319(f319(f167(x71931),f319(f319(f3(a906),x71932),f72(a906))),x71933))+~P1(f319(f319(f225(a906),x71932),f319(f182(f907(x71931)),x71933)))
% 22.40/22.30 [7252]~P33(x72523,x72522,x72521)+P1(f319(f319(f226(a906),f744(x72521,x72522,x72523)),f319(f182(f907(x72523)),x72521)))
% 22.40/22.30 [7270]P1(f319(f319(f226(a906),f2(a906)),x72701))+P1(f319(f319(f225(a906),f319(f319(f75(a906),x72702),x72701)),f319(f319(f75(a906),x72703),x72701)))
% 22.40/22.30 [7271]P1(f319(f319(f226(a906),f2(a906)),x72711))+P1(f319(f319(f225(a906),f319(f319(f75(a906),x72711),x72712)),f319(f319(f75(a906),x72711),x72713)))
% 22.40/22.30 [7274]~P1(f319(f319(f321(x72741),x72742),x72743))+~P1(f319(f319(f321(x72741),x72742),f319(f73(f913(x72741,a904)),x72743)))
% 22.40/22.30 [7280]~P1(f319(f319(f226(f913(x72801,a904)),x72802),x72803))+P1(f319(f319(f225(f913(x72801,a904)),x72802),x72803))
% 22.40/22.30 [7387]~P1(f319(f319(f225(a906),x73873),x73872))+P1(f319(f319(f225(a906),f319(f319(f3(a906),x73871),x73872)),f319(f319(f3(a906),x73871),x73873)))
% 22.40/22.30 [7388]~P1(f319(f319(f225(a906),x73881),x73883))+P1(f319(f319(f225(a906),f319(f319(f3(a906),x73881),x73882)),f319(f319(f3(a906),x73883),x73882)))
% 22.40/22.30 [7389]~P1(f319(f319(f225(a906),x73892),x73893))+P1(f319(f319(f225(a906),f319(f319(f74(a906),x73891),x73892)),f319(f319(f74(a906),x73891),x73893)))
% 22.40/22.30 [7390]~P1(f319(f319(f225(a906),x73901),x73903))+P1(f319(f319(f225(a906),f319(f319(f74(a906),x73901),x73902)),f319(f319(f74(a906),x73903),x73902)))
% 22.40/22.30 [7392]~P1(f319(f319(f225(a906),x73922),x73923))+P1(f319(f319(f225(a906),f319(f319(f75(a906),x73921),x73922)),f319(f319(f75(a906),x73921),x73923)))
% 22.40/22.30 [7394]~P1(f319(f319(f225(a906),x73941),x73943))+P1(f319(f319(f225(a906),f319(f319(f75(a906),x73941),x73942)),f319(f319(f75(a906),x73943),x73942)))
% 22.40/22.30 [7395]~P1(f319(f319(f225(a906),x73951),x73953))+P1(f319(f319(f225(a906),f319(f319(f30(a906),x73951),x73952)),f319(f319(f30(a906),x73953),x73952)))
% 22.40/22.30 [7396]~P1(f319(f319(f225(a1),x73962),x73963))+P1(f319(f319(f225(a1),f319(f319(f74(a1),x73961),x73962)),f319(f319(f74(a1),x73961),x73963)))
% 22.40/22.30 [7397]~P1(f319(f319(f226(a906),x73972),x73973))+P1(f319(f319(f226(a906),f319(f319(f74(a906),x73971),x73972)),f319(f319(f74(a906),x73971),x73973)))
% 22.40/22.30 [7398]~P1(f319(f319(f226(a906),x73981),x73983))+P1(f319(f319(f226(a906),f319(f319(f74(a906),x73981),x73982)),f319(f319(f74(a906),x73983),x73982)))
% 22.40/22.30 [7399]~P1(f319(f319(f226(a1),x73991),x73993))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x73991),x73992)),f319(f319(f74(a1),x73993),x73992)))
% 22.40/22.30 [7472]E(x74721,x74722)+~P1(f319(f319(f321(x74723),x74721),f319(f319(f301(x74723),x74722),f181(f913(x74723,a904)))))
% 22.40/22.30 [7474]~E(f319(f319(f94(f913(x74741,a904)),x74742),x74743),f181(f913(x74741,a904)))+P1(f319(f319(f225(f913(x74741,a904)),x74742),f319(f73(f913(x74741,a904)),x74743)))
% 22.40/22.30 [7479]P1(f319(f319(f321(f913(x74791,a904)),x74792),f319(f300(x74791),x74793)))+~P1(f319(f319(f225(f913(x74791,a904)),x74792),x74793))
% 22.40/22.30 [7529]E(f319(f319(f143(x75291),f319(f319(f156(x75291),x75292),x75293)),f319(f319(f130(x75291),f319(a104,x75293)),x75292)),f319(f319(f130(x75291),x75293),x75292))+~P1(f319(f319(f226(a906),x75293),f319(f182(f907(x75291)),x75292)))
% 22.40/22.30 [7555]P1(f319(f319(f321(f912(x75551,x75551)),x75552),f299(x75551,x75553)))+~P1(f319(f319(f321(f912(x75551,x75551)),x75552),x75553))
% 22.40/22.30 [7564]~P1(f319(f319(f321(f913(x75641,a904)),x75642),f319(f300(x75641),x75643)))+P1(f319(f319(f225(f913(x75641,a904)),x75642),x75643))
% 22.40/22.30 [7607]P1(f319(f319(f225(f913(x76071,a904)),x76072),f31(f913(x76071,a904),x76073)))+~P1(f319(f319(f321(f913(x76071,a904)),x76072),x76073))
% 22.40/22.30 [7630]~P141(x76301)+E(f319(f319(f75(x76301),f319(f319(f236(x76301),f319(f73(x76301),f72(x76301))),x76302)),f319(f319(f236(x76301),x76303),x76302)),f319(f319(f236(x76301),f319(f73(x76301),x76303)),x76302))
% 22.40/22.30 [7652]E(f319(f319(f156(x76521),x76522),f319(f319(f3(a906),f319(f182(f907(x76521)),x76522)),f319(a104,x76523))),f319(f319(f156(x76521),f319(f160(x76521),x76522)),x76523))+~P1(f319(f319(f226(a906),x76523),f319(f182(f907(x76521)),x76522)))
% 22.40/22.30 [7669]~E(f319(f319(f94(f913(x76691,a904)),f383(x76693,x76692,x76691)),x76693),f181(f913(x76691,a904)))+E(f319(f319(f94(f913(x76691,a904)),f31(f913(x76691,a904),x76692)),x76693),f181(f913(x76691,a904)))
% 22.40/22.30 [7728]~P1(f319(f319(f321(x77283),x77282),f319(f164(x77283),x77281)))+P1(f319(f319(f226(a906),f610(x77281,x77282,x77283)),f319(f182(f907(x77283)),x77281)))
% 22.40/22.30 [7736]P1(f319(f319(f321(x77361),f319(f319(f156(x77361),x77362),x77363)),f319(f164(x77361),x77362)))+~P1(f319(f319(f226(a906),x77363),f319(f182(f907(x77361)),x77362)))
% 22.40/22.30 [7832]~P1(f319(x78322,f709(x78323,x78322,x78321)))+E(f319(f319(f130(x78321),f319(f182(f907(x78321)),f169(x78321,x78322,x78323))),x78323),f105(x78321))
% 22.40/22.30 [7845]P1(f319(f319(f225(f913(f907(x78451),a904)),f153(x78451,x78452)),f153(x78451,x78453)))+~P1(f319(f319(f225(f913(x78451,a904)),x78452),x78453))
% 22.40/22.30 [7846]P1(f319(f319(f225(f913(f907(x78461),a904)),f152(x78461,x78462)),f152(x78461,x78463)))+~P1(f319(f319(f225(f913(x78461,a904)),x78462),x78463))
% 22.40/22.30 [7873]E(f319(f319(f94(f913(x78731,a904)),f31(f913(x78731,a904),x78732)),x78733),f181(f913(x78731,a904)))+P1(f319(f319(f321(f913(x78731,a904)),f383(x78733,x78732,x78731)),x78732))
% 22.40/22.30 [7875]~P1(f319(f319(f321(f913(x78751,a904)),x78753),x78752))+P1(f319(f319(f225(f913(x78751,a904)),f32(f913(x78751,a904),x78752)),x78753))
% 22.40/22.30 [7877]E(f319(f319(f94(f913(x78771,a904)),x78772),x78773),f181(f913(x78771,a904)))+~P1(f319(f319(f225(f913(x78771,a904)),x78772),f319(f73(f913(x78771,a904)),x78773)))
% 22.40/22.30 [7927]E(f319(f319(f3(a906),f319(f319(f74(a906),f319(f157(a906),x79271)),x79272)),f319(f319(f156(a906),x79271),x79273)),f319(f157(a906),f319(f319(f151(a906,x79271),x79273),x79272)))+~P1(f319(f319(f226(a906),x79273),f319(f182(f907(a906)),x79271)))
% 22.40/22.30 [7980]P1(f319(f319(f225(a906),x79801),x79802))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),x79803),x79801)),f319(f319(f74(a906),x79803),x79802)))
% 22.40/22.30 [7981]P1(f319(f319(f226(a906),x79811),x79812))+~P1(f319(f319(f226(a906),f319(f319(f74(a906),x79813),x79811)),f319(f319(f74(a906),x79813),x79812)))
% 22.40/22.30 [7982]P1(f319(f319(f226(a906),x79821),x79822))+~P1(f319(f319(f226(a906),f319(f319(f75(a906),x79823),x79821)),f319(f319(f75(a906),x79823),x79822)))
% 22.40/22.30 [7983]P1(f319(f319(f226(a906),x79831),x79832))+~P1(f319(f319(f226(a906),f319(f319(f75(a906),x79831),x79833)),f319(f319(f75(a906),x79832),x79833)))
% 22.40/22.30 [8009]P1(f319(f319(f226(a906),f2(a906)),x80091))+~P1(f319(f319(f226(a906),f319(f319(f75(a906),x80092),x80091)),f319(f319(f75(a906),x80093),x80091)))
% 22.40/22.30 [8010]P1(f319(f319(f226(a906),f2(a906)),x80101))+~P1(f319(f319(f226(a906),f319(f319(f75(a906),x80101),x80102)),f319(f319(f75(a906),x80101),x80103)))
% 22.40/22.30 [8079]E(f239(x80791,x80792,x80793),x80792)+~P1(f319(f319(f225(f913(x80791,a904)),x80793),f319(f319(f301(x80791),x80792),f181(f913(x80791,a904)))))
% 22.40/22.30 [8128]~P1(f319(f129(x81281),x81283))+E(f319(f128(x81281,f319(f319(f10(a904,a904,x81281),a314),f319(a316,x81282))),x81283),f162(x81281,x81282,x81283))
% 22.40/22.30 [8153]E(f319(f319(f130(x81531),f319(f182(f907(x81531)),f169(x81531,x81532,x81533))),x81533),f105(x81531))+P1(f319(f319(f321(x81531),f709(x81533,x81532,x81531)),f319(f164(x81531),x81533)))
% 22.40/22.30 [8158]E(f319(f319(f126(x81581),f319(f319(f167(x81581),x81582),x81583)),f319(f319(f143(x81581),f319(f319(f156(x81581),x81583),x81582)),f105(x81581))),f319(f319(f167(x81581),f319(a104,x81582)),x81583))+~P1(f319(f319(f226(a906),x81582),f319(f182(f907(x81581)),x81583)))
% 22.40/22.30 [8224]E(f319(f128(x82241,f319(f319(f10(a904,a904,x82241),a314),f319(a316,x82242))),x82243),x82243)+P1(f319(f319(f321(x82241),x82242),f319(f164(x82241),x82243)))
% 22.40/22.30 [8230]P1(f319(f319(f225(f913(f913(x82301,a904),a904)),f240(x82301,x82302)),f240(x82301,x82303)))+~P1(f319(f319(f225(f913(x82301,a904)),x82302),x82303))
% 22.40/22.30 [8270]~P1(f319(f129(x82701),x82703))+P1(f319(f129(x82701),f319(f319(f319(f175(f907(x82701),f907(x82701)),x82702),f159(x82701)),x82703)))
% 22.40/22.30 [8276]~P1(f319(f319(f226(a906),x82762),x82763))+P1(f319(f319(f226(a906),f319(f319(f75(a906),f319(a104,x82761)),x82762)),f319(f319(f75(a906),f319(a104,x82761)),x82763)))
% 22.40/22.30 [8296]P1(f319(f319(f225(f913(f913(x82961,a904),a904)),f319(f300(x82961),x82962)),f319(f300(x82961),x82963)))+~P1(f319(f319(f225(f913(x82961,a904)),x82962),x82963))
% 22.40/22.30 [8363]~E(f319(f302(x83631,x83632,x83633),f234(f913(x83631,a904))),f234(f913(x83632,a904)))+E(f319(f66(x83631,x83632,x83632,x83633),f85(x83631,x83632,f234(f913(x83631,a904)),x83633)),f25(x83632))
% 22.40/22.30 [8455]~P1(f319(f319(f225(f913(x84551,a904)),x84553),x84552))+P1(f319(f319(f225(f913(x84551,a904)),f319(f73(f913(x84551,a904)),x84552)),f319(f73(f913(x84551,a904)),x84553)))
% 22.40/22.30 [8488]E(f319(f302(a906,a906,f319(f319(f9(a906,a906,a906),f3(a906)),x84881)),f319(f294(a906,x84882),x84883)),f319(f294(a906,f319(f319(f3(a906),x84882),x84881)),f319(f319(f3(a906),x84883),x84881)))+~P1(f319(f319(f226(a906),x84881),x84883))
% 22.40/22.30 [8510]~P88(x85101)+E(f319(f319(f74(x85101),x85102),f319(f134(x85101,x85101,f74(x85101),f2(x85101)),x85103)),f319(f134(x85101,x85101,f74(x85101),x85102),x85103))
% 22.40/22.30 [8590]~P92(x85901)+P1(f319(f319(f225(x85901),f319(f69(x85901),f319(f319(f3(x85901),x85902),x85903))),f319(f319(f74(x85901),f319(f69(x85901),x85902)),f319(f69(x85901),x85903))))
% 22.40/22.30 [8591]~P92(x85911)+P1(f319(f319(f225(x85911),f319(f69(x85911),f319(f319(f74(x85911),x85912),x85913))),f319(f319(f74(x85911),f319(f69(x85911),x85912)),f319(f69(x85911),x85913))))
% 22.40/22.30 [8602]E(f319(f319(f74(a1),f319(f319(f75(a1),x86021),f39(a1,f319(f319(f30(a1),x86022),x86021),x86023))),f39(a1,x86022,x86021)),f39(a1,x86022,f319(f319(f75(a1),x86021),x86023)))+~P1(f319(f319(f226(a1),f2(a1)),x86023))
% 22.40/22.30 [8607]E(f319(f319(f126(x86071),f319(f319(f167(x86071),x86072),x86073)),f319(f319(f143(x86071),f319(f133(x86071),f319(f319(f130(x86071),x86072),x86073))),f105(x86071))),f319(f319(f167(x86071),f319(a104,x86072)),x86073))+~P1(f319(f319(f226(a906),x86072),f319(f182(f907(x86071)),x86073)))
% 22.40/22.30 [8631]E(f319(f260(x86311,f319(f319(f146(x86311,f912(a91,x86311)),f319(f244(a91,x86311),f72(a91))),x86312)),f319(a5,x86313)),f319(f319(f156(x86311),x86312),x86313))+~P1(f319(f319(f226(a906),x86313),f319(f182(f907(x86311)),x86312)))
% 22.40/22.30 [8699]P1(f319(f319(f321(f912(x86991,x86991)),x86992),f319(f319(f281(x86991,x86991,x86991),x86993),f299(x86991,x86993))))+~P1(f319(f319(f321(f912(x86991,x86991)),x86992),x86993))
% 22.40/22.30 [8709]E(f319(f302(x87091,x87092,x87093),f234(f913(x87091,a904))),f234(f913(x87092,a904)))+~E(f319(f66(x87091,x87092,x87092,x87093),f85(x87091,x87092,f234(f913(x87091,a904)),x87093)),f25(x87092))
% 22.40/22.30 [8720]P1(f319(f319(f225(a906),x87201),x87202))+~P1(f319(f319(f225(a906),f319(f319(f75(a906),f319(a104,x87203)),x87201)),f319(f319(f75(a906),f319(a104,x87203)),x87202)))
% 22.40/22.30 [8735]P1(f319(f319(f225(f913(x87351,a904)),x87352),x87353))+~P1(f319(f319(f225(f913(x87351,a904)),f319(f73(f913(x87351,a904)),x87353)),f319(f73(f913(x87351,a904)),x87352)))
% 22.40/22.30 [8758]P1(f319(f129(x87581),x87582))+~P1(f319(f129(x87581),f319(f319(f319(f175(f907(x87581),f907(x87581)),x87583),f159(x87581)),x87582)))
% 22.40/22.30 [8824]E(f319(f277(x88241,x88241,f299(x88241,x88242)),x88243),x88243)+~P1(f319(f319(f225(f913(x88241,a904)),f319(f277(x88241,x88241,x88242),x88243)),x88243))
% 22.40/22.30 [8872]~P4(x88721)+P13(x88721,f319(f128(x88721,f319(f319(f9(x88721,x88721,a904),a316),f319(x88722,x88723))),x88723))
% 22.40/22.30 [8879]~P1(f319(f319(f225(a906),x88791),x88792))+P1(f319(f319(f225(a906),x88791),f319(f134(a906,a906,f74(a906),x88792),x88793)))
% 22.40/22.30 [8971]~P1(f319(f319(f321(f912(x89711,x89711)),x89712),f299(x89711,x89713)))+P1(f319(f319(f321(f912(x89711,x89711)),x89712),f319(f319(f175(f912(x89711,x89711),a904),f615(x89713,x89712,x89711)),x89713)))
% 22.40/22.30 [9056]~P88(x90561)+E(f319(f319(f74(x90561),x90562),f319(f134(x90561,x90561,f319(f9(x90561,x90561,x90561),f74(x90561)),f2(x90561)),f319(f160(x90561),x90563))),f319(f134(x90561,x90561,f74(x90561),x90562),x90563))
% 22.40/22.30 [9168]~P26(x91682,x91681,x91683,f234(f913(x91682,a904)),f234(f913(x91681,a904)))+E(f85(x91681,x91682,f234(f913(x91681,a904)),f85(x91682,x91681,f234(f913(x91682,a904)),x91683)),x91683)
% 22.40/22.30 [9326]P56(x93261,x93262,x93263)+P1(f319(f319(f321(f912(x93261,x93262)),f319(f319(f244(x93261,x93262),f606(x93263,x93262,x93261)),f587(x93263,x93262,x93261))),x93263))
% 22.40/22.30 [9327]P56(x93271,x93272,x93273)+P1(f319(f319(f321(f912(x93271,x93272)),f319(f319(f244(x93271,x93272),f606(x93273,x93272,x93271)),f586(x93273,x93272,x93271))),x93273))
% 22.40/22.30 [9396]~P1(f319(f319(f321(f912(x93961,x93961)),x93962),f319(f319(f281(x93961,x93961,x93961),x93963),f299(x93961,x93963))))+P1(f319(f319(f321(f912(x93961,x93961)),x93962),f319(f319(f175(f912(x93961,x93961),a904),f616(x93963,x93962,x93961)),x93963)))
% 22.40/22.30 [9397]~P1(f319(x93971,f319(f319(f156(x93972),x93973),f319(f182(f907(x93972)),f169(x93972,x93971,x93973)))))+~P1(f319(f319(f226(a906),f319(f182(f907(x93972)),f169(x93972,x93971,x93973))),f319(f182(f907(x93972)),x93973)))
% 22.40/22.30 [9489]~P1(f319(f319(f225(f913(x94891,a904)),x94892),x94893))+P1(f319(f319(f225(f913(x94891,a904)),f319(f319(f9(x94891,f913(x94891,a904),a904),f321(x94891)),x94892)),f319(f319(f9(x94891,f913(x94891,a904),a904),f321(x94891)),x94893)))
% 22.40/22.30 [9547]~P1(f319(f319(f321(f912(f913(x95471,a904),f913(x95471,a904))),f319(f319(f244(f913(x95471,a904),f913(x95471,a904)),x95472),x95473)),f306(x95471)))+P1(f319(f319(f226(f913(x95471,a904)),x95472),x95473))
% 22.40/22.30 [9571]P57(x95711,x95712,x95713)+~P1(f319(f319(f321(f912(x95711,x95711)),f319(f319(f244(x95711,x95711),f609(x95713,x95712,x95711)),f608(x95713,x95712,x95711))),x95713))
% 22.40/22.30 [9572]P57(x95721,x95722,x95723)+~P1(f319(f319(f321(f912(x95721,x95721)),f319(f319(f244(x95721,x95721),f608(x95723,x95722,x95721)),f609(x95723,x95722,x95721))),x95723))
% 22.40/22.30 [9607]~P1(f319(f319(f321(f912(f907(x96071),f907(x96071))),f319(f319(f244(f907(x96071),f907(x96071)),x96072),x96072)),f139(x96071,x96073)))+P1(f319(f319(f321(f912(x96071,x96071)),f319(f319(f244(x96071,x96071),f637(x96072,x96073,x96071)),f637(x96072,x96073,x96071))),x96073))
% 22.40/22.30 [9670]P1(f319(f319(f225(f913(x96701,a904)),x96702),x96703))+~P1(f319(f319(f225(f913(x96701,a904)),f319(f319(f9(x96701,f913(x96701,a904),a904),f321(x96701)),x96702)),f319(f319(f9(x96701,f913(x96701,a904),a904),f321(x96701)),x96703)))
% 22.40/22.30 [9757]E(f319(f319(f3(a906),f319(f319(f8(a906,a906),x97571),f319(f274(a906),x97572))),f319(f319(f8(a906,a906),x97573),f319(f274(a906),x97572))),f319(f319(f8(a906,a906),f319(f319(f20(a906,a906,a906),f319(f319(f10(a906,f913(a906,a906),a906),f3(a906)),x97571)),x97573)),f319(f274(a906),x97572)))+~P1(f319(f319(f225(a906),f319(x97573,f504(x97572,x97571,x97573))),f319(x97571,f504(x97572,x97571,x97573))))
% 22.40/22.30 [5747]~P66(x57471)+E(f319(f319(f3(x57471),f319(f319(f74(x57471),x57472),x57473)),x57473),x57472)
% 22.40/22.30 [5748]~P66(x57481)+E(f319(f319(f74(x57481),f319(f319(f3(x57481),x57482),x57483)),x57483),x57482)
% 22.40/22.30 [5979]~P66(x59791)+E(f319(f319(f74(x59791),x59792),f319(f319(f74(x59791),f319(f73(x59791),x59792)),x59793)),x59793)
% 22.40/22.30 [6061]~P87(x60611)+E(f319(f319(f75(x60611),f319(f319(f236(x60611),x60612),x60613)),x60612),f319(f319(f236(x60611),x60612),f319(a104,x60613)))
% 22.40/22.30 [6062]~P119(x60621)+E(f319(f319(f75(x60621),f319(f319(f236(x60621),x60622),x60623)),x60622),f319(f319(f236(x60621),x60622),f319(a104,x60623)))
% 22.40/22.30 [6283]~P113(x62831)+E(f319(f69(x62831),f319(f319(f236(x62831),f319(f73(x62831),x62832)),x62833)),f319(f69(x62831),f319(f319(f236(x62831),x62832),x62833)))
% 22.40/22.30 [6336]~P87(x63361)+E(f319(f319(f75(x63361),f319(f319(f236(x63361),x63362),x63363)),x63362),f319(f319(f75(x63361),x63362),f319(f319(f236(x63361),x63362),x63363)))
% 22.40/22.30 [6384]E(f319(f319(f3(a91),f319(f319(f74(a91),x63841),x63842)),x63843),f266(x63841,x63842,x63843))+~P1(f319(f319(f226(a91),x63842),x63843))
% 22.40/22.30 [6406]~E(f319(f319(f130(x64061),x64063),x64062),f105(x64061))+P1(f319(f319(f225(a906),f319(f182(f907(x64061)),x64062)),x64063))
% 22.40/22.30 [6545]E(f319(f319(f75(a906),f319(f96(a906),x65451)),f319(f319(f75(a906),f319(f96(a906),x65452)),x65453)),f2(a906))+~P1(f319(f319(f226(a1),x65451),a77))
% 22.40/22.30 [6561]~P72(x65611)+E(f319(f319(f236(x65611),f319(f319(f282(x65611),f72(x65611)),x65612)),x65613),f319(f319(f282(x65611),f72(x65611)),f319(f319(f236(x65611),x65612),x65613)))
% 22.40/22.30 [6635]E(f319(f319(f3(a906),f319(f319(f74(a906),x66351),x66352)),x66353),f319(f319(f3(a906),x66351),f319(f319(f3(a906),x66353),x66352)))+~P1(f319(f319(f225(a906),x66352),x66353))
% 22.40/22.30 [6637]E(f319(f319(f3(a906),f319(f319(f74(a906),x66371),x66372)),x66373),f319(f319(f74(a906),x66371),f319(f319(f3(a906),x66372),x66373)))+~P1(f319(f319(f225(a906),x66373),x66372))
% 22.40/22.30 [6676]~P101(x66761)+P1(f319(f319(f225(x66761),f319(f319(f94(x66761),x66762),x66763)),x66763))
% 22.40/22.30 [6677]~P107(x66771)+P1(f319(f319(f225(x66771),f319(f319(f94(x66771),x66772),x66773)),x66773))
% 22.40/22.30 [6678]~P101(x66781)+P1(f319(f319(f225(x66781),f319(f319(f94(x66781),x66782),x66783)),x66782))
% 22.40/22.30 [6679]~P107(x66791)+P1(f319(f319(f225(x66791),f319(f319(f94(x66791),x66792),x66793)),x66792))
% 22.40/22.30 [6680]~P4(x66801)+P1(f319(f319(f225(x66801),f319(f319(f230(x66801),x66802),x66803)),x66803))
% 22.40/22.30 [6681]~P4(x66811)+P1(f319(f319(f225(x66811),f319(f319(f230(x66811),x66812),x66813)),x66812))
% 22.40/22.30 [6694]E(f319(f319(f30(a1),f319(f319(f30(a1),x66941),x66942)),x66943),f319(f319(f30(a1),x66941),f319(f319(f75(a1),x66942),x66943)))+~P1(f319(f319(f226(a1),f2(a1)),x66943))
% 22.40/22.30 [6750]~P119(x67501)+E(f319(f319(f74(x67501),f319(f319(f75(x67501),x67502),x67503)),x67503),f319(f319(f75(x67501),f319(f319(f74(x67501),x67502),f72(x67501))),x67503))
% 22.40/22.30 [6751]~P98(x67511)+E(f319(f319(f75(x67511),f319(f73(x67511),f319(f96(x67511),x67512))),x67513),f319(f319(f75(x67511),f319(f96(x67511),f319(f73(a1),x67512))),x67513))
% 22.40/22.30 [6828]~P88(x68281)+E(f319(f157(x68281),f319(f319(f146(x68282,x68281),f319(f18(x68281,x68282),f2(x68281))),x68283)),f2(x68281))
% 22.40/22.30 [6844]E(f319(f319(f74(a906),f319(f96(a906),x68441)),f319(f319(f74(a906),f319(f96(a906),x68442)),x68443)),f319(f319(f74(a906),f319(f96(a906),x68442)),x68443))+~P1(f319(a186,f319(f96(a1),x68441)))
% 22.40/22.30 [6858]~P5(x68581)+E(f32(x68581,f319(f319(f301(x68581),x68582),f319(f319(f301(x68581),x68583),f181(f913(x68581,a904))))),f319(f319(f94(x68581),x68582),x68583))
% 22.40/22.30 [6859]~P5(x68591)+E(f31(x68591,f319(f319(f301(x68591),x68592),f319(f319(f301(x68591),x68593),f181(f913(x68591,a904))))),f319(f319(f93(x68591),x68592),x68593))
% 22.40/22.30 [6883]E(f319(f319(f167(x68831),x68832),x68833),x68833)+~P1(f319(f319(f225(a906),f319(f182(f907(x68831)),x68833)),x68832))
% 22.40/22.30 [6890]E(f319(f319(f130(x68901),x68902),x68903),f105(x68901))+~P1(f319(f319(f225(a906),f319(f182(f907(x68901)),x68903)),x68902))
% 22.40/22.30 [6901]E(f319(f319(f74(a906),f319(f319(f3(a906),x69011),x69012)),x69013),f319(f319(f3(a906),f319(f319(f74(a906),x69011),x69013)),x69012))+~P1(f319(f319(f225(a906),x69012),x69011))
% 22.40/22.30 [6915]~P1(f319(f319(f226(a906),x69151),x69153))+P1(f319(f319(f226(a906),f319(f319(f3(a906),x69151),x69152)),x69153))
% 22.40/22.30 [6940]~P4(x69401)+E(f162(x69401,x69402,f319(f319(f140(x69401,x69401,f7(x69401)),x69402),x69403)),x69403)
% 22.40/22.30 [7028]E(f319(f319(f3(a906),f319(f319(f74(a906),x70281),x70282)),f319(a104,x70283)),f319(f319(f3(a906),x70281),f319(a104,f319(f319(f3(a906),x70283),x70282))))+~P1(f319(f319(f225(a906),x70282),x70283))
% 22.40/22.30 [7029]~P113(x70291)+P1(f319(f319(f225(x70291),f2(x70291)),f319(f319(f236(x70291),f319(f69(x70291),x70292)),x70293)))
% 22.40/22.30 [7078]P14(x70781,x70782,x70783)+~P1(f319(f319(f225(f913(f905(x70781),a904)),x70783),x70782))
% 22.40/22.30 [7121]~P1(f319(f55(x71211),x71213))+P1(f319(f55(x71211),f319(f319(f94(f913(x71211,a904)),x71212),x71213)))
% 22.40/22.30 [7122]~P1(f319(f55(x71221),x71222))+P1(f319(f55(x71221),f319(f319(f94(f913(x71221,a904)),x71222),x71223)))
% 22.40/22.30 [7123]~P1(f319(f55(x71231),x71232))+P1(f319(f55(x71231),f319(f319(f3(f913(x71231,a904)),x71232),x71233)))
% 22.40/22.30 [7260]~P37(x72601,x72603)+P37(x72601,f319(f319(f94(f913(f912(x72601,x72601),a904)),x72602),x72603))
% 22.40/22.30 [7261]~P37(x72611,x72612)+P37(x72611,f319(f319(f94(f913(f912(x72611,x72611),a904)),x72612),x72613))
% 22.40/22.30 [7383]~P101(x73831)+E(f12(x73831,f319(f164(x73831),f319(f319(f143(x73831),x73832),x73833))),f319(f134(x73831,x73831,f94(x73831),x73832),x73833))
% 22.40/22.30 [7384]~P101(x73841)+E(f15(x73841,f319(f164(x73841),f319(f319(f143(x73841),x73842),x73843))),f319(f134(x73841,x73841,f93(x73841),x73842),x73843))
% 22.40/22.30 [7385]~P4(x73851)+E(f16(x73851,f319(f164(x73851),f319(f319(f143(x73851),x73852),x73853))),f319(f134(x73851,x73851,f180(x73851),x73852),x73853))
% 22.40/22.30 [7386]~P4(x73861)+E(f17(x73861,f319(f164(x73861),f319(f319(f143(x73861),x73862),x73863))),f319(f134(x73861,x73861,f230(x73861),x73862),x73863))
% 22.40/22.30 [7446]~P1(f319(f55(x74461),x74462))+P1(f319(f319(f225(a906),f319(f29(x74461),x74462)),f319(f29(x74461),f319(f319(f301(x74461),x74463),x74462))))
% 22.40/22.30 [7447]E(f319(f319(f93(f913(a906,a904)),f319(f294(a906,x74471),x74472)),f319(f294(a906,x74472),f319(f319(f74(a906),x74472),x74473))),f319(f294(a906,x74471),f319(f319(f74(a906),x74472),x74473)))+~P1(f319(f319(f225(a906),x74471),x74472))
% 22.40/22.30 [7456]P1(f319(f319(f225(a906),x74561),x74562))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),x74563),x74561)),x74562))
% 22.40/22.30 [7457]P1(f319(f319(f225(a906),x74571),x74572))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),x74571),x74573)),x74572))
% 22.40/22.30 [7458]P1(f319(f319(f226(a906),x74581),x74582))+~P1(f319(f319(f226(a906),f319(f319(f74(a906),x74581),x74583)),x74582))
% 22.40/22.30 [7497]~P4(x74971)+E(f13(x74971,f180(x74971),f319(f164(x74971),f319(f319(f143(x74971),x74972),x74973))),f319(f134(x74971,x74971,f180(x74971),x74972),x74973))
% 22.40/22.30 [7498]~P4(x74981)+E(f14(x74981,f230(x74981),f319(f164(x74981),f319(f319(f143(x74981),x74982),x74983))),f319(f134(x74981,x74981,f230(x74981),x74982),x74983))
% 22.40/22.30 [7502]~E(x75022,f181(f913(f912(x75021,x75021),a904)))+P1(f319(f319(f225(f913(f912(x75021,x75021),a904)),x75022),x75023))
% 22.40/22.30 [7602]E(f319(f319(f93(f913(x76021,a904)),x76022),f319(f319(f3(f913(x76021,a904)),x76023),x76022)),x76023)+~P1(f319(f319(f225(f913(x76021,a904)),x76022),x76023))
% 22.40/22.30 [7603]~P1(f319(f319(f225(a906),x76031),f319(f319(f74(a906),x76033),x76032)))+P1(f319(f319(f225(a906),f319(f319(f3(a906),x76031),x76032)),x76033))
% 22.40/22.30 [7604]~P1(f319(f319(f226(a906),x76041),f319(f319(f3(a906),x76043),x76042)))+P1(f319(f319(f226(a906),f319(f319(f74(a906),x76041),x76042)),x76043))
% 22.40/22.30 [7659]E(x76591,f105(x76592))+E(f319(f133(x76592),f319(f319(f319(f175(f907(x76592),f907(x76592)),x76593),f159(x76592)),x76591)),f319(f319(f156(x76592),x76591),f39(a906,x76593,f319(f182(f907(x76592)),x76591))))
% 22.40/22.30 [7668]E(f319(f319(f301(x76681),x76682),f319(f319(f3(f913(x76681,a904)),x76683),f319(f319(f301(x76681),x76682),f181(f913(x76681,a904))))),x76683)+~P1(f319(f319(f321(x76681),x76682),x76683))
% 22.40/22.30 [7823]P1(f319(f319(f225(a906),x78231),f319(f319(f74(a906),x78232),x78233)))+~P1(f319(f319(f225(a906),f319(f319(f3(a906),x78231),x78233)),x78232))
% 22.40/22.30 [7824]P1(f319(f319(f226(a906),x78241),f319(f319(f3(a906),x78242),x78243)))+~P1(f319(f319(f226(a906),f319(f319(f74(a906),x78241),x78243)),x78242))
% 22.40/22.30 [7849]P1(f319(f55(x78491),x78492))+~P1(f319(f55(x78491),f319(f319(f93(f913(x78491,a904)),x78493),x78492)))
% 22.40/22.30 [7850]P1(f319(f55(x78501),x78502))+~P1(f319(f55(x78501),f319(f319(f93(f913(x78501,a904)),x78502),x78503)))
% 22.40/22.30 [7925]~P46(x79251,x79253)+P1(f319(f319(f321(f912(x79251,x79251)),f319(f319(f244(x79251,x79251),x79252),x79252)),x79253))
% 22.40/22.30 [8053]E(f319(f319(f156(a906),f131(a906,f319(f294(a906,x80531),x80532))),x80533),f319(f319(f74(a906),x80531),x80533))+~P1(f319(f319(f226(a906),f319(f319(f74(a906),x80531),x80533)),x80532))
% 22.40/22.30 [8117]E(f319(f319(f167(a906),x81171),f131(a906,f319(f294(a906,x81172),x81173))),f131(a906,f319(f294(a906,x81172),f319(f319(f74(a906),x81172),x81171))))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),x81172),x81171)),x81173))
% 22.40/22.30 [8435]E(f319(f319(f126(x84351),f319(f319(f167(x84351),x84352),x84353)),f319(f319(f143(x84351),f319(f319(f156(x84351),x84353),x84352)),f319(f319(f130(x84351),f319(a104,x84352)),x84353))),x84353)+~P1(f319(f319(f226(a906),x84352),f319(f182(f907(x84351)),x84353)))
% 22.40/22.30 [8443]P1(f319(f319(f225(f913(x84431,a904)),f307(x84431,x84432)),f307(x84431,x84433)))+~P1(f319(f319(f225(f913(x84431,f913(x84431,a904))),x84433),x84432))
% 22.40/22.30 [8444]~P57(x84441,x84442,x84443)+P57(x84441,x84442,f319(f319(f3(f913(f912(x84441,x84441),a904)),x84443),f299(x84441,f181(f913(f912(x84441,x84441),a904)))))
% 22.40/22.30 [8463]P1(f319(f319(f225(f913(x84631,a904)),f308(x84631,x84632)),f308(x84631,x84633)))+~P1(f319(f319(f225(f913(f912(x84631,x84631),a904)),x84633),x84632))
% 22.40/22.30 [8470]~P128(x84701)+P1(f319(f319(f225(x84701),f2(x84701)),f319(f319(f74(x84701),f319(f319(f75(x84701),x84702),x84702)),f319(f319(f75(x84701),x84703),x84703))))
% 22.40/22.30 [8503]P1(f319(f319(f225(f913(x85031,a904)),f319(f273(x85031),x85032)),f319(f273(x85031),x85033)))+~P1(f319(f319(f225(f913(f912(x85031,x85031),a904)),x85032),x85033))
% 22.40/22.30 [8532]~P55(x85321,x85322)+~P1(f319(f319(f321(f912(x85321,x85321)),f319(f319(f244(x85321,x85321),x85323),x85323)),x85322))
% 22.40/22.30 [8534]~P37(x85341,x85342)+~P1(f319(f319(f321(f912(x85341,x85341)),f319(f319(f244(x85341,x85341),x85343),x85343)),x85342))
% 22.40/22.30 [8592]P1(f319(f319(f225(f913(x85921,a904)),f32(f913(x85921,a904),x85922)),f32(f913(x85921,a904),x85923)))+~P1(f319(f319(f225(f913(f913(x85921,a904),a904)),x85923),x85922))
% 22.40/22.30 [8593]P1(f319(f319(f225(f913(x85931,a904)),f31(f913(x85931,a904),x85932)),f31(f913(x85931,a904),x85933)))+~P1(f319(f319(f225(f913(f913(x85931,a904),a904)),x85932),x85933))
% 22.40/22.30 [8650]~P8(x86501,x86503,x86502)+P1(f319(f319(f225(f913(f912(x86501,x86501),a904)),x86502),f319(f319(f246(x86501,x86501),x86503),f319(f18(f913(x86501,a904),x86501),x86503))))
% 22.40/22.30 [8651]~P54(x86511,x86513,x86512)+P1(f319(f319(f225(f913(f912(x86511,x86511),a904)),x86512),f319(f319(f246(x86511,x86511),x86513),f319(f18(f913(x86511,a904),x86511),x86513))))
% 22.40/22.30 [8700]~P92(x87001)+P1(f319(f319(f225(x87001),f319(f319(f3(x87001),f319(f69(x87001),x87002)),f319(f69(x87001),x87003))),f319(f69(x87001),f319(f319(f3(x87001),x87003),x87002))))
% 22.40/22.30 [8701]~P92(x87011)+P1(f319(f319(f225(x87011),f319(f319(f3(x87011),f319(f69(x87011),x87012)),f319(f69(x87011),x87013))),f319(f69(x87011),f319(f319(f3(x87011),x87012),x87013))))
% 22.40/22.30 [8733]P1(f319(f319(f225(f913(f912(x87331,x87331),a904)),f299(x87331,x87332)),f299(x87331,x87333)))+~P1(f319(f319(f225(f913(f912(x87331,x87331),a904)),x87332),x87333))
% 22.40/22.30 [8837]~P25(x88372,x88371,x88373,f234(f913(x88372,a904)))+E(f319(f66(x88371,x88372,x88372,f85(x88372,x88371,f234(f913(x88372,a904)),x88373)),x88373),f25(x88372))
% 22.40/22.30 [8897]P57(x88971,x88972,x88973)+~P57(x88971,x88972,f319(f319(f3(f913(f912(x88971,x88971),a904)),x88973),f299(x88971,f181(f913(f912(x88971,x88971),a904)))))
% 22.40/22.30 [8917]P1(f319(f319(f225(f913(f912(f907(x89171),f907(x89171)),a904)),f149(x89171,x89172)),f149(x89171,x89173)))+~P1(f319(f319(f225(f913(f912(x89171,x89171),a904)),x89172),x89173))
% 22.40/22.30 [8918]P1(f319(f319(f225(f913(f912(f907(x89181),f907(x89181)),a904)),f150(x89181,x89182)),f150(x89181,x89183)))+~P1(f319(f319(f225(f913(f912(x89181,x89181),a904)),x89182),x89183))
% 22.40/22.30 [8941]~P54(x89411,x89413,x89412)+P1(f319(f319(f225(f913(f912(x89411,x89411),a904)),x89412),f319(f319(f281(x89411,x89411,x89411),f319(f278(x89411,x89411),x89412)),x89412)))
% 22.40/22.30 [8999]~P1(f319(f129(x89991),x89992))+E(f319(f128(x89991,f319(f319(f9(x89991,f913(x89991,a904),a904),f321(x89991)),f319(f164(x89991),f168(x89991,x89992,x89993)))),x89992),f168(x89991,x89992,x89993))
% 22.40/22.30 [9054]E(x90541,x90542)+~P1(f319(f319(f321(f912(x90543,x90543)),f319(f319(f244(x90543,x90543),x90541),x90542)),f299(x90543,f181(f913(f912(x90543,x90543),a904)))))
% 22.40/22.30 [9137]P1(f319(f319(f321(x91371),x91372),f308(x91371,x91373)))+P1(f319(f319(f321(f912(x91371,x91371)),f319(f319(f244(x91371,x91371),f522(x91373,x91372,x91371)),x91372)),x91373))
% 22.40/22.30 [9138]P1(f319(f319(f321(x91381),x91382),f308(x91381,x91383)))+P1(f319(f319(f321(f912(x91381,x91381)),f319(f319(f244(x91381,x91381),f589(x91383,x91382,x91381)),x91382)),x91383))
% 22.40/22.30 [9139]P1(f319(f319(f321(x91391),x91392),f308(x91391,x91393)))+P1(f319(f319(f321(f912(x91391,x91391)),f319(f319(f244(x91391,x91391),f591(x91393,x91392,x91391)),x91392)),x91393))
% 22.40/22.30 [9169]P25(x91691,x91692,x91693,f234(f913(x91691,a904)))+~E(f319(f66(x91692,x91691,x91691,f85(x91691,x91692,f234(f913(x91691,a904)),x91693)),x91693),f25(x91691))
% 22.40/22.30 [9216]~P1(f319(f319(f321(f907(x92161)),x92163),f153(x92161,x92162)))+P1(f319(f152(x92161,f319(f319(f9(x92161,f913(x92161,a904),a904),f321(x92161)),x92162)),x92163))
% 22.40/22.30 [9246]P1(f319(x92463,x92462))+E(f319(f254(x92461),f319(f319(f20(x92461,a904,a904),f319(f319(f10(a904,f913(a904,a904),x92461),a317),f319(a316,x92462))),x92463)),f181(f913(x92461,a904)))
% 22.40/22.30 [9265]~P92(x92651)+P1(f319(f319(f225(x92651),f319(f69(x92651),f319(f319(f3(x92651),f319(f69(x92651),x92652)),f319(f69(x92651),x92653)))),f319(f69(x92651),f319(f319(f3(x92651),x92652),x92653))))
% 22.40/22.30 [9282]~P1(f319(x92823,x92822))+E(f319(f254(x92821),f319(f319(f20(x92821,a904,a904),f319(f319(f10(a904,f913(a904,a904),x92821),a317),f319(a316,x92822))),x92823)),f319(f319(f301(x92821),x92822),f181(f913(x92821,a904))))
% 22.40/22.30 [9289]~P1(f319(f319(f321(f913(x92891,a904)),x92893),f319(f300(x92891),x92892)))+P1(f319(f240(x92891,f319(f319(f9(x92891,f913(x92891,a904),a904),f321(x92891)),x92892)),x92893))
% 22.40/22.30 [9325]P37(x93251,x93252)+P1(f319(f319(f321(f912(x93251,x93251)),f319(f319(f244(x93251,x93251),f319(f559(x93252,x93251),f319(a104,x93253))),f319(f559(x93252,x93251),x93253))),x93252))
% 22.40/22.30 [9468]P1(f319(f319(f321(f907(x94681)),x94682),f153(x94681,x94683)))+~P1(f319(f152(x94681,f319(f319(f9(x94681,f913(x94681,a904),a904),f321(x94681)),x94683)),x94682))
% 22.40/22.30 [9481]P1(f319(f319(f321(f913(x94811,a904)),x94812),f319(f300(x94811),x94813)))+~P1(f319(f240(x94811,f319(f319(f9(x94811,f913(x94811,a904),a904),f321(x94811)),x94813)),x94812))
% 22.40/22.30 [9542]P1(f319(f319(f321(x95421),f319(f260(x95421,x95422),x95423)),f319(f164(x95421),f319(f319(f146(f912(a91,x95421),x95421),f248(a91,x95421)),x95422))))+~P1(f319(f319(f226(a91),x95423),f319(f157(a91),f319(f319(f146(f912(a91,x95421),a91),f243(a91,x95421)),x95422))))
% 22.40/22.30 [9586]P1(f319(f319(f225(f913(f912(f907(x95861),f907(x95861)),a904)),f150(x95861,x95862)),f319(f319(f246(f907(x95861),f907(x95861)),f153(x95861,x95863)),f319(f18(f913(f907(x95861),a904),f907(x95861)),f153(x95861,x95863)))))+~P1(f319(f319(f225(f913(f912(x95861,x95861),a904)),x95862),f319(f319(f246(x95861,x95861),x95863),f319(f18(f913(x95861,a904),x95861),x95863))))
% 22.40/22.30 [9610]P1(f319(f319(f321(x96101),f319(f243(x96101,f912(a91,a91)),f319(f258(x96101,x96102),x96103))),f319(f164(x96101),f319(f319(f146(f912(a91,x96101),x96101),f248(a91,x96101)),x96102))))+~P1(f319(f319(f226(a91),f2(a91)),f319(f157(a91),f319(f319(f146(f912(a91,x96101),a91),f243(a91,x96101)),x96102))))
% 22.40/22.30 [9633]~P1(f319(f319(f225(f913(f912(x96331,x96331),a904)),x96332),f319(f319(f246(x96331,x96331),x96333),f319(f18(f913(x96331,a904),x96331),x96333))))+P1(f319(f319(f225(f913(f912(x96331,x96331),a904)),f319(f319(f281(x96331,x96331,x96331),x96332),f299(x96331,x96332))),f319(f319(f246(x96331,x96331),x96333),f319(f18(f913(x96331,a904),x96331),x96333))))
% 22.40/22.30 [9965]~P37(x99651,x99652)+~P1(f319(f319(f321(f912(x99651,x99651)),f319(f319(f244(x99651,x99651),f319(x99653,f319(a104,f560(x99652,x99651,x99653)))),f319(x99653,f560(x99652,x99651,x99653)))),x99652))
% 22.40/22.30 [9966]~P37(x99661,x99662)+~P1(f319(f319(f321(f912(x99661,x99661)),f319(f319(f244(x99661,x99661),f319(x99663,f319(a104,f600(x99663,x99662,x99661)))),f319(x99663,f600(x99663,x99662,x99661)))),x99662))
% 22.40/22.30 [10179]P1(f319(f319(f225(f913(f912(f913(x101791,a904),f913(x101791,a904)),a904)),f319(f319(f281(f913(x101791,a904),f913(x101791,a904),f913(x101791,a904)),f310(x101791,x101792)),f319(f319(f93(f913(f912(f913(x101791,a904),f913(x101791,a904)),a904)),f310(x101791,x101793)),f319(f319(f301(f912(f913(x101791,a904),f913(x101791,a904))),f319(f319(f244(f913(x101791,a904),f913(x101791,a904)),f181(f913(x101791,a904))),f181(f913(x101791,a904)))),f181(f913(f912(f913(x101791,a904),f913(x101791,a904)),a904)))))),f310(x101791,x101792)))+~P1(f319(f319(f225(f913(f912(x101791,x101791),a904)),f319(f319(f281(x101791,x101791,x101791),x101792),x101793)),x101792))
% 22.40/22.30 [10180]P1(f319(f319(f225(f913(f912(f913(x101801,a904),f913(x101801,a904)),a904)),f319(f319(f281(f913(x101801,a904),f913(x101801,a904),f913(x101801,a904)),f311(x101801,x101802)),f319(f319(f93(f913(f912(f913(x101801,a904),f913(x101801,a904)),a904)),f311(x101801,x101803)),f319(f319(f301(f912(f913(x101801,a904),f913(x101801,a904))),f319(f319(f244(f913(x101801,a904),f913(x101801,a904)),f181(f913(x101801,a904))),f181(f913(x101801,a904)))),f181(f913(f912(f913(x101801,a904),f913(x101801,a904)),a904)))))),f311(x101801,x101802)))+~P1(f319(f319(f225(f913(f912(x101801,x101801),a904)),f319(f319(f281(x101801,x101801,x101801),x101802),x101803)),x101802))
% 22.40/22.30 [7382]~P1(f319(f319(f225(a906),x73822),x73821))+E(f319(f319(f3(a906),f319(a104,f319(f319(f3(a906),x73821),x73822))),x73823),f319(f319(f3(a906),f319(a104,x73821)),f319(f319(f74(a906),x73822),x73823)))
% 22.40/22.30 [7417]~P69(x74171)+E(f319(f319(f74(x74171),f39(x74171,x74172,x74173)),f319(f319(f75(x74171),f319(f319(f30(x74171),x74172),x74173)),x74173)),x74172)
% 22.40/22.30 [7608]E(f319(f319(f75(a906),f319(f96(a906),x76081)),f319(f319(f75(a906),f319(f96(a906),x76082)),x76083)),f319(f319(f75(a906),f319(f96(a906),f319(f319(f75(a1),x76081),x76082))),x76083))+P1(f319(f319(f226(a1),x76081),a77))
% 22.40/22.30 [8062]~P1(f319(f319(f225(a906),x80623),x80622))+P1(f319(f319(f225(a906),x80621),f319(f319(f3(a906),f319(f319(f74(a906),x80622),x80621)),x80623)))
% 22.40/22.30 [8261]~P1(f319(f319(f225(a906),x82611),x82612))+E(f319(f319(f126(a906),f131(a906,f319(f294(a906,x82611),x82612))),f131(a906,f319(f294(a906,x82612),f319(f319(f74(a906),x82612),x82613)))),f131(a906,f319(f294(a906,x82611),f319(f319(f74(a906),x82612),x82613))))
% 22.40/22.30 [8507]~P1(f319(f55(x85071),x85072))+E(f319(a104,f319(f29(x85071),f319(f319(f3(f913(x85071,a904)),x85072),f319(f319(f301(x85071),x85073),f181(f913(x85071,a904)))))),f319(f29(x85071),f319(f319(f301(x85071),x85073),x85072)))
% 22.40/22.30 [8551]~P1(f319(f55(x85511),x85512))+E(f319(f319(f74(a906),f72(a906)),f319(f29(x85511),f319(f319(f3(f913(x85511,a904)),x85512),f319(f319(f301(x85511),x85513),f181(f913(x85511,a904)))))),f319(f29(x85511),f319(f319(f301(x85511),x85513),x85512)))
% 22.40/22.30 [8742]E(f319(f319(f3(a906),f319(f29(x87421),x87422)),f319(f29(x87421),f319(f319(f94(f913(x87421,a904)),x87422),x87423))),f319(f29(x87421),f319(f319(f3(f913(x87421,a904)),x87422),x87423)))+~P1(f319(f55(x87421),f319(f319(f94(f913(x87421,a904)),x87422),x87423)))
% 22.40/22.30 [8993]~P6(f319(x89932,f489(x89932,x89933,x89931)))+E(f319(f92(a1),f319(f319(f8(x89931,a906),f319(f319(f10(a1,a906,x89931),a97),x89932)),x89933)),f319(f319(f8(x89931,a1),x89932),x89933))
% 22.40/22.30 [8994]~P6(f319(x89942,f490(x89942,x89943,x89941)))+E(f319(f92(a1),f319(f319(f11(x89941,a906),f319(f319(f10(a1,a906,x89941),a97),x89942)),x89943)),f319(f319(f11(x89941,a1),x89942),x89943))
% 22.40/22.30 [9037]~P1(f319(f55(x90371),x90373))+P1(f319(f319(f225(a906),f319(f319(f3(a906),f319(f29(x90371),x90372)),f319(f29(x90371),x90373))),f319(f29(x90371),f319(f319(f3(f913(x90371,a904)),x90372),x90373))))
% 22.40/22.30 [9065]P1(f319(f319(f321(x90651),f489(x90652,x90653,x90651)),x90653))+E(f319(f92(a1),f319(f319(f8(x90651,a906),f319(f319(f10(a1,a906,x90651),a97),x90652)),x90653)),f319(f319(f8(x90651,a1),x90652),x90653))
% 22.40/22.30 [9066]P1(f319(f319(f321(x90661),f490(x90662,x90663,x90661)),x90663))+E(f319(f92(a1),f319(f319(f11(x90661,a906),f319(f319(f10(a1,a906,x90661),a97),x90662)),x90663)),f319(f319(f11(x90661,a1),x90662),x90663))
% 22.40/22.30 [9129]E(f79(x91291,f319(f319(f9(x91291,f913(x91291,a904),a904),f321(x91291)),f319(f319(f3(f913(x91291,a904)),x91292),f319(f319(f301(x91291),x91293),f181(f913(x91291,a904)))))),f239(x91291,x91293,x91292))+P1(f319(f319(f225(f913(x91291,a904)),x91292),f319(f319(f301(x91291),x91293),f181(f913(x91291,a904)))))
% 22.40/22.30 [9482]E(f319(f319(f146(f907(x94821),x94821),f319(f319(f9(f907(x94821),a906,x94821),f156(x94821)),x94822)),f319(f128(f907(x94821),f319(f319(f10(a906,a904,f907(x94821)),f319(f226(a906),x94822)),f182(f907(x94821)))),x94823)),f319(f319(f156(f907(x94821)),f171(x94821,x94823)),x94822))+~P1(f319(f319(f226(a906),x94822),f319(f182(f907(f907(x94821))),f171(x94821,x94823))))
% 22.40/22.30 [9560]E(f319(f128(x95601,x95602),x95603),f169(x95601,x95602,x95603))+P1(f319(f319(f321(x95601),f712(x95603,x95602,x95601)),f319(f164(x95601),f319(f319(f130(x95601),f319(f182(f907(x95601)),f169(x95601,x95602,x95603))),x95603))))
% 22.40/22.30 [9710]E(f319(f319(f130(x97101),f319(f182(f907(x97101)),f169(x97101,x97102,x97103))),x97103),f105(x97101))+~P1(f319(x97102,f319(f133(x97101),f319(f319(f130(x97101),f319(f182(f907(x97101)),f169(x97101,x97102,x97103))),x97103))))
% 22.40/22.30 [9816]~P1(f319(f319(f321(f912(x98161,x98161)),x98162),f299(x98161,x98163)))+P1(f319(f319(f321(f912(x98161,x98161)),x98162),f319(f319(f33(a906,f913(f912(x98161,x98161),a904)),f234(f913(a906,a904))),f319(f319(f9(a906,f913(f912(x98161,x98161),a904),f913(f912(x98161,x98161),a904)),f175(f912(x98161,x98161),a904)),x98163))))
% 22.40/22.30 [9878]~P1(f319(f319(f225(f913(x98781,a904)),f319(f319(f33(a906,f913(x98781,a904)),f319(f294(a906,f2(a906)),f498(x98783,x98782,x98781))),x98782)),x98783))+P1(f319(f319(f225(f913(x98781,a904)),f319(f319(f33(a906,f913(x98781,a904)),f234(f913(a906,a904))),x98782)),x98783))
% 22.40/22.30 [9940]~P1(f319(f319(f226(a1),f2(a1)),x99403))+P1(f319(f319(f226(a1),x99401),f319(f319(f74(a1),x99402),f319(f319(f75(a1),f319(f319(f74(a1),f319(f69(a1),f319(f319(f3(a1),x99402),x99401))),f72(a1))),x99403))))
% 22.40/22.30 [9952]~P37(x99521,f319(f319(f93(f913(f912(x99521,x99521),a904)),x99522),x99523))+P37(x99521,f319(f319(f93(f913(f912(x99521,x99521),a904)),f319(f319(f93(f913(f912(x99521,x99521),a904)),f319(f319(f281(x99521,x99521,x99521),x99522),x99522)),f319(f319(f281(x99521,x99521,x99521),x99523),x99522))),x99523))
% 22.40/22.30 [10022]P37(x100221,f319(f319(f93(f913(f912(x100221,x100221),a904)),x100222),x100223))+~P37(x100221,f319(f319(f93(f913(f912(x100221,x100221),a904)),f319(f319(f93(f913(f912(x100221,x100221),a904)),f319(f319(f281(x100221,x100221,x100221),x100222),x100222)),f319(f319(f281(x100221,x100221,x100221),x100223),x100222))),x100223))
% 22.40/22.30 [9565]~P141(x95651)+E(f319(f95(x95651),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x95652),x95653)),f181(f913(f912(a906,a906),a904)))))),f319(f319(f3(x95651),f319(f92(x95651),x95652)),f319(f92(x95651),x95653)))
% 22.40/22.30 [9658]P1(f319(x96583,x96582))+E(f319(f254(x96581),f319(f319(f20(x96581,a904,a904),f319(f319(f10(a904,f913(a904,a904),x96581),a317),f319(f319(f9(x96581,x96581,a904),a316),x96582))),x96583)),f181(f913(x96581,a904)))
% 22.40/22.30 [9660]~P1(f319(x96603,x96602))+E(f319(f254(x96601),f319(f319(f20(x96601,a904,a904),f319(f319(f10(a904,f913(a904,a904),x96601),a317),f319(f319(f9(x96601,x96601,a904),a316),x96602))),x96603)),f319(f319(f301(x96601),x96602),f181(f913(x96601,a904))))
% 22.40/22.30 [9917]E(x99171,x99172)+P1(f319(f319(f235(x99173,x99173,f319(f319(f10(f913(x99173,a904),f913(x99173,a904),x99173),f319(f10(a904,a904,x99173),a314)),a316)),x99171),x99172))
% 22.40/22.30 [10002]~E(x100021,x100022)+~P1(f319(f319(f235(x100023,x100023,f319(f319(f10(f913(x100023,a904),f913(x100023,a904),x100023),f319(f10(a904,a904,x100023),a314)),a316)),x100021),x100022))
% 22.40/22.30 [10014]~P1(f319(f55(x100141),x100143))+E(f319(f319(f58(x100141,f913(x100141,a904),f319(f319(f10(f913(x100141,a904),f913(f913(x100141,a904),f913(x100141,a904)),x100141),f319(f9(f913(x100141,a904),f913(x100141,a904),f913(x100141,a904)),f3(f913(x100141,a904)))),f319(f319(f9(x100141,f913(x100141,a904),f913(x100141,a904)),f301(x100141)),f181(f913(x100141,a904))))),x100142),x100143),f319(f319(f3(f913(x100141,a904)),x100142),x100143))
% 22.40/22.30 [10041]~P1(f319(f319(f226(a1),f2(a1)),x100413))+P1(f319(f319(f226(a1),f319(f319(f3(a1),x100411),f319(f319(f75(a1),f319(f319(f74(a1),f319(f69(a1),f319(f319(f3(a1),x100411),x100412))),f72(a1))),x100413))),x100412))
% 22.40/22.30 [10298]~P1(f319(f319(f321(x102981),x102983),f308(x102981,x102982)))+P1(f319(f307(x102981,f319(f319(f9(x102981,f913(f912(x102981,x102981),a904),f913(x102981,a904)),f319(f319(f10(f913(x102981,f913(f913(f912(x102981,x102981),a904),a904)),f913(f913(f912(x102981,x102981),a904),f913(x102981,a904)),x102981),f9(x102981,f913(f912(x102981,x102981),a904),a904)),f319(f319(f10(f913(x102981,f912(x102981,x102981)),f913(x102981,f913(f913(f912(x102981,x102981),a904),a904)),x102981),f319(f10(f912(x102981,x102981),f913(f913(f912(x102981,x102981),a904),a904),x102981),f321(f912(x102981,x102981)))),f244(x102981,x102981)))),x102982)),x102983))
% 22.40/22.30 [10312]P1(f319(f319(f321(x103121),x103122),f308(x103121,x103123)))+~P1(f319(f307(x103121,f319(f319(f9(x103121,f913(f912(x103121,x103121),a904),f913(x103121,a904)),f319(f319(f10(f913(x103121,f913(f913(f912(x103121,x103121),a904),a904)),f913(f913(f912(x103121,x103121),a904),f913(x103121,a904)),x103121),f9(x103121,f913(f912(x103121,x103121),a904),a904)),f319(f319(f10(f913(x103121,f912(x103121,x103121)),f913(x103121,f913(f913(f912(x103121,x103121),a904),a904)),x103121),f319(f10(f912(x103121,x103121),f913(f913(f912(x103121,x103121),a904),a904),x103121),f321(f912(x103121,x103121)))),f244(x103121,x103121)))),x103123)),x103122))
% 22.40/22.30 [9876]~P1(f319(f55(x98761),f319(f254(x98761),x98763)))+P1(f319(f55(x98761),f319(f254(x98761),f319(f319(f20(x98761,a904,a904),f319(f319(f10(a904,f913(a904,a904),x98761),a317),x98762)),x98763))))
% 22.40/22.30 [9877]~P1(f319(f55(x98771),f319(f254(x98771),x98772)))+P1(f319(f55(x98771),f319(f254(x98771),f319(f319(f20(x98771,a904,a904),f319(f319(f10(a904,f913(a904,a904),x98771),a317),x98772)),x98773))))
% 22.40/22.30 [9986]P1(f319(f55(x99861),f319(f254(x99861),x99862)))+~P1(f319(f55(x99861),f319(f254(x99861),f319(f319(f20(x99861,a904,a904),f319(f319(f10(a904,f913(a904,a904),x99861),a318),x99863)),x99862))))
% 22.40/22.30 [9987]P1(f319(f55(x99871),f319(f254(x99871),x99872)))+~P1(f319(f55(x99871),f319(f254(x99871),f319(f319(f20(x99871,a904,a904),f319(f319(f10(a904,f913(a904,a904),x99871),a318),x99872)),x99873))))
% 22.40/22.30 [10254]~P1(f319(f55(x102541),x102542))+P1(f319(f55(f907(x102541)),f319(f254(f907(x102541)),f319(f319(f20(f907(x102541),a904,a904),f319(f319(f10(a904,f913(a904,a904),f907(x102541)),a317),f319(f319(f9(f907(x102541),f913(x102541,a904),a904),f319(f319(f10(f913(x102541,a904),f913(f913(x102541,a904),a904),f907(x102541)),f225(f913(x102541,a904))),f164(x102541))),x102542))),f319(f319(f9(f907(x102541),a906,a904),f319(f319(f10(a906,f913(a906,a904),f907(x102541)),a316),f182(f907(x102541)))),x102543)))))
% 22.40/22.30 [10255]~P1(f319(f55(x102551),x102552))+P1(f319(f55(f907(x102551)),f319(f254(f907(x102551)),f319(f319(f20(f907(x102551),a904,a904),f319(f319(f10(a904,f913(a904,a904),f907(x102551)),a317),f319(f319(f9(f907(x102551),f913(x102551,a904),a904),f319(f319(f10(f913(x102551,a904),f913(f913(x102551,a904),a904),f907(x102551)),f225(f913(x102551,a904))),f164(x102551))),x102552))),f319(f319(f9(f907(x102551),a906,a904),f319(f319(f10(a906,f913(a906,a904),f907(x102551)),f225(a906)),f182(f907(x102551)))),x102553)))))
% 22.40/22.30 [9524]~P98(x95241)+E(f319(f319(f236(x95241),x95242),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x95243)),x95243)),a89))),f319(f319(f82(x95241,x95241),f319(f319(f236(x95241),x95242),f319(f96(a906),x95243))),f319(f319(f20(x95241,x95241,x95241),f75(x95241)),f7(x95241))))
% 22.40/22.30 [10211]~P119(x102111)+E(f319(f319(f236(x102111),x102112),f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102113)),f319(f319(f75(x102111),f319(f319(f236(x102111),x102112),x102113)),f319(f319(f236(x102111),x102112),x102113)))
% 22.40/22.30 [10231]~P87(x102311)+E(f319(f319(f236(x102311),f319(f319(f236(x102311),x102312),x102313)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(f319(f236(x102311),x102312),f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102313)))
% 22.40/22.30 [10277]~P141(x102771)+E(f319(f319(f236(x102771),f319(f73(x102771),x102772)),f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102773)),f319(f319(f236(x102771),x102772),f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102773)))
% 22.40/22.30 [10336]~P113(x103361)+P1(f319(f319(f225(x103361),f2(x103361)),f319(f319(f74(x103361),f319(f319(f236(x103361),x103362),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103361),x103363),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))))
% 22.40/22.30 [10285]~P119(x102851)+E(f319(f319(f236(x102851),x102852),f319(a104,f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102853))),f319(f319(f75(x102851),x102852),f319(f319(f75(x102851),f319(f319(f236(x102851),x102852),x102853)),f319(f319(f236(x102851),x102852),x102853))))
% 22.40/22.30 [10304]~P87(x103041)+E(f319(f319(f75(x103041),x103042),f319(f319(f236(x103041),f319(f319(f236(x103041),x103042),x103043)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103041),x103042),f319(a104,f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103043))))
% 22.40/22.30 [10316]~P113(x103161)+P1(f319(f319(f225(x103161),f2(x103161)),f319(f319(f236(x103161),x103162),f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103163))))
% 22.40/22.30 [10357]~P98(x103571)+E(f319(f319(f3(x103571),f319(f319(f74(x103571),f319(f319(f236(x103571),x103572),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103571),x103573),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))),f319(f319(f75(x103571),f319(f319(f75(x103571),f319(f96(x103571),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103572)),x103573)),f319(f319(f236(x103571),f319(f319(f3(x103571),x103572),x103573)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.30 [10358]~P98(x103581)+E(f319(f319(f74(x103581),f319(f319(f74(x103581),f319(f319(f236(x103581),x103582),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103581),x103583),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))),f319(f319(f75(x103581),f319(f319(f75(x103581),f319(f96(x103581),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103582)),x103583)),f319(f319(f236(x103581),f319(f319(f74(x103581),x103582),x103583)),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.30 [7867]P25(x78671,x78672,x78673,x78674)+~E(f447(x78674,x78673,x78672,x78671),f456(x78674,x78673,x78672,x78671))
% 22.40/22.30 [8151]P34(x81511,x81512,x81513,x81514,f105(x81512))+~E(x81514,f105(x81511))
% 22.40/22.30 [8152]P34(x81521,x81522,x81523,f105(x81521),x81524)+~E(x81524,f105(x81522))
% 22.40/22.30 [8690]~P34(x86902,x86903,x86904,x86901,f105(x86903))+E(x86901,f105(x86902))
% 22.40/22.30 [8691]~P34(x86913,x86912,x86914,f105(x86913),x86911)+E(x86911,f105(x86912))
% 22.40/22.30 [5163]~P18(x51633,x51631,x51634)+E(f319(f319(x51631,x51632),x51632),x51632)
% 22.40/22.30 [5413]P1(f319(x54132,x54134))+E(f319(f128(x54131,x54132),f161(x54131,x54133,x54134)),f105(x54131))
% 22.40/22.30 [5450]~E(x54504,f181(f913(x54501,a904)))+E(f319(f302(x54501,x54502,x54503),x54504),f181(f913(x54502,a904)))
% 22.40/22.30 [5694]~P1(f319(x56942,x56944))+E(f319(f128(x56941,x56942),f161(x56941,x56943,x56944)),f161(x56941,x56943,x56944))
% 22.40/22.30 [5726]~E(f319(f302(x57262,x57263,x57264),x57261),f181(f913(x57263,a904)))+E(x57261,f181(f913(x57262,a904)))
% 22.40/22.30 [5914]~P7(x59141,x59143)+E(f263(x59141,x59142,f262(x59141,x59143),x59144),x59144)
% 22.40/22.30 [6022]~P4(x60222)+E(f319(f319(f140(x60221,x60222,x60223),x60224),f105(x60221)),f319(f319(f143(x60221),x60224),f105(x60221)))
% 22.40/22.30 [6378]~E(x63781,f181(f913(x63782,a904)))+~P1(f319(f56(x63782,x63783,x63781),x63784))
% 22.40/22.30 [6400]~P60(x64001,x64003,x64004,x64002)+P1(f319(f55(x64001),x64002))
% 22.40/22.30 [6402]~P60(x64021,x64023,x64022,x64024)+P1(f319(f55(x64021),x64022))
% 22.40/22.30 [6408]~P60(x64082,x64083,x64084,x64081)+~E(x64081,f181(f913(x64082,a904)))
% 22.40/22.30 [6441]~P111(x64411)+E(f319(f319(f94(f913(x64411,a904)),f319(f294(x64411,x64412),x64413)),f295(x64411,x64413,x64414)),f181(f913(x64411,a904)))
% 22.40/22.30 [6467]~P1(f319(f319(x64673,x64674),x64672))+P1(f319(f319(f321(x64671),x64672),f285(x64671,x64673,x64674)))
% 22.40/22.30 [6468]~P1(f319(f319(x64683,x64684),x64682))+P1(f319(f319(f321(x64681),x64682),f286(x64681,x64683,x64684)))
% 22.40/22.30 [6469]~P1(f319(f319(x64693,x64692),x64694))+P1(f319(f319(f321(x64691),x64692),f287(x64691,x64693,x64694)))
% 22.40/22.30 [6470]~P1(f319(f319(x64703,x64702),x64704))+P1(f319(f319(f321(x64701),x64702),f290(x64701,x64703,x64704)))
% 22.40/22.30 [6614]~P111(x66141)+E(f319(f319(f94(f913(x66141,a904)),f298(x66141,x66142,x66143)),f295(x66141,x66143,x66144)),f181(f913(x66141,a904)))
% 22.40/22.30 [6615]~P111(x66151)+E(f319(f319(f94(f913(x66151,a904)),f297(x66151,x66152,x66153)),f298(x66151,x66153,x66154)),f181(f913(x66151,a904)))
% 22.40/22.30 [6616]~P111(x66161)+E(f319(f319(f94(f913(x66161,a904)),f297(x66161,x66162,x66163)),f297(x66161,x66163,x66164)),f181(f913(x66161,a904)))
% 22.40/22.30 [6617]~P111(x66171)+E(f319(f319(f94(f913(x66171,a904)),f295(x66171,x66172,x66173)),f298(x66171,x66173,x66174)),f181(f913(x66171,a904)))
% 22.40/22.30 [6618]~P111(x66181)+E(f319(f319(f94(f913(x66181,a904)),f295(x66181,x66182,x66183)),f297(x66181,x66183,x66184)),f181(f913(x66181,a904)))
% 22.40/22.30 [6653]P1(f319(f319(x66531,x66532),f558(x66532,x66531)))+~P1(f319(f241(x66533,x66534,x66531),x66532))
% 22.40/22.30 [6735]~P4(x67352)+E(f319(f164(x67351),f142(x67351,x67352,x67353,x67354)),f319(f164(x67351),x67354))
% 22.40/22.30 [6788]~P146(x67881)+E(f183(x67881,x67882,f319(a104,x67883),x67884),f183(x67881,x67882,x67883,f319(x67882,x67884)))
% 22.40/22.30 [6853]~P1(f319(f319(f321(x68534),x68533),f285(x68534,x68531,x68532)))+P1(f319(f319(x68531,x68532),x68533))
% 22.40/22.30 [6854]~P1(f319(f319(f321(x68544),x68543),f286(x68544,x68541,x68542)))+P1(f319(f319(x68541,x68542),x68543))
% 22.40/22.30 [6855]~P1(f319(f319(f321(x68554),x68552),f287(x68554,x68551,x68553)))+P1(f319(f319(x68551,x68552),x68553))
% 22.40/22.30 [6856]~P1(f319(f319(f321(x68564),x68562),f290(x68564,x68561,x68563)))+P1(f319(f319(x68561,x68562),x68563))
% 22.40/22.30 [6927]E(f319(f29(f914(x69271,x69272)),f305(x69271,x69272,x69273,x69274)),f2(a906))+P1(f319(f55(x69272),x69274))
% 22.40/22.30 [6928]E(f319(f29(f914(x69281,x69282)),f305(x69281,x69282,x69283,x69284)),f2(a906))+P1(f319(f55(x69281),x69283))
% 22.40/22.30 [7129]~P15(x71294,x71291,x71292)+E(f319(f66(x71291,x71291,x71291,f319(x71292,x71293)),f319(x71292,x71293)),f319(x71292,x71293))
% 22.40/22.30 [7367]E(f269(x73671,x73672,x73673,x73674),f319(f244(f913(a91,f913(a904,f910(f908(x73671)))),f912(a91,a91)),f35(x73671)))+~P1(f319(f319(f225(a91),x73673),f2(a91)))
% 22.40/22.30 [7988]~E(x79882,x79883)+P1(f319(f319(f321(f912(x79881,x79881)),f319(f319(f244(x79881,x79881),x79882),x79883)),f299(x79881,x79884)))
% 22.40/22.30 [8017]~P25(x80171,x80172,x80173,f234(f913(x80171,a904)))+E(f319(f71(x80171,x80172,f234(f913(x80171,a904)),x80173),f319(x80173,x80174)),x80174)
% 22.40/22.30 [8018]~P25(x80181,x80182,x80183,f234(f913(x80181,a904)))+E(f319(f85(x80181,x80182,f234(f913(x80181,a904)),x80183),f319(x80183,x80184)),x80184)
% 22.40/22.30 [8100]~P1(f319(f319(f321(f907(x81001)),f319(f319(f143(x81001),x81004),x81002)),f153(x81001,x81003)))+P1(f319(f319(f321(f907(x81001)),x81002),f153(x81001,x81003)))
% 22.40/22.30 [8101]~P1(f319(f319(f321(f907(x81011)),f319(f319(f126(x81011),x81014),x81012)),f153(x81011,x81013)))+P1(f319(f319(f321(f907(x81011)),x81012),f153(x81011,x81013)))
% 22.40/22.30 [8102]~P1(f319(f319(f321(f907(x81021)),f319(f319(f126(x81021),x81022),x81024)),f153(x81021,x81023)))+P1(f319(f319(f321(f907(x81021)),x81022),f153(x81021,x81023)))
% 22.40/22.30 [8113]~P4(x81131)+P13(x81131,f319(f319(f146(x81132,x81131),x81133),f142(x81132,x81131,x81133,x81134)))
% 22.40/22.30 [8217]P25(x82174,x82173,x82171,x82172)+E(f319(x82171,f447(x82172,x82171,x82173,x82174)),f319(x82171,f456(x82172,x82171,x82173,x82174)))
% 22.40/22.30 [8324]~P25(x83242,x83241,x83244,x83243)+P25(x83241,x83242,f71(x83242,x83241,x83243,x83244),f319(f302(x83242,x83241,x83244),x83243))
% 22.40/22.30 [8461]P37(f912(x84612,x84614),f272(x84612,x84614,x84611,x84613))+P1(f319(x84611,f563(x84612,x84613,x84614,x84611)))
% 22.40/22.30 [8578]E(x85781,x85782)+~P1(f319(f319(f321(f912(x85783,x85783)),f319(f319(f244(x85783,x85783),x85781),x85782)),f255(x85783,x85784)))
% 22.40/22.30 [8642]~P1(f319(f55(f914(x86423,x86421)),f305(x86423,x86421,x86424,x86422)))+P1(f319(f55(x86421),x86422))
% 22.40/22.30 [8643]~P1(f319(f55(f914(x86431,x86433)),f305(x86431,x86433,x86432,x86434)))+P1(f319(f55(x86431),x86432))
% 22.40/22.30 [8652]~P25(x86521,x86522,x86523,x86524)+P26(x86521,x86522,x86523,x86524,f319(f302(x86521,x86522,x86523),x86524))
% 22.40/22.30 [8654]P11(x86541,x86542,x86543,x86544)+~E(f319(x86544,f820(x86542,x86544,x86543,x86541)),f319(x86544,f821(x86542,x86544,x86543,x86541)))
% 22.40/22.30 [8743]~P26(x87432,x87433,x87434,x87431,f181(f913(x87433,a904)))+E(x87431,f181(f913(x87432,a904)))
% 22.40/22.30 [8744]~P26(x87443,x87442,x87444,f181(f913(x87443,a904)),x87441)+E(x87441,f181(f913(x87442,a904)))
% 22.40/22.30 [8828]P37(f912(x88281,x88282),f272(x88281,x88282,x88283,x88284))+~P37(x88282,f319(x88284,f563(x88281,x88284,x88282,x88283)))
% 22.40/22.30 [9401]E(f319(f319(f151(x94011,x94012),f660(x94013,x94014,x94012,x94011)),f661(x94013,x94014,x94012,x94011)),x94014)+~P1(f319(f319(f321(f912(f907(x94011),f907(x94011))),f319(f319(f244(f907(x94011),f907(x94011)),x94012),x94014)),f149(x94011,x94013)))
% 22.40/22.30 [9409]~P1(f319(f319(f321(f912(f907(x94091),f907(x94091))),f319(f319(f244(f907(x94091),f907(x94091)),x94092),x94093)),f137(x94091,x94094)))+P1(f319(f319(f321(f912(f907(x94091),f907(x94091))),f319(f319(f244(f907(x94091),f907(x94091)),x94092),x94093)),f139(x94091,x94094)))
% 22.40/22.30 [9521]P1(f319(f55(x95211),x95212))+~P1(f319(f319(f321(f912(f913(x95211,a904),f913(x95211,a904))),f319(f319(f244(f913(x95211,a904),f913(x95211,a904)),x95213),x95212)),f311(x95211,x95214)))
% 22.40/22.30 [9522]P1(f319(f55(x95221),x95222))+~P1(f319(f319(f321(f912(f913(x95221,a904),f913(x95221,a904))),f319(f319(f244(f913(x95221,a904),f913(x95221,a904)),x95222),x95223)),f311(x95221,x95224)))
% 22.40/22.30 [9523]~E(x95231,f181(f913(x95232,a904)))+~P1(f319(f319(f321(f912(f913(x95232,a904),f913(x95232,a904))),f319(f319(f244(f913(x95232,a904),f913(x95232,a904)),x95233),x95231)),f311(x95232,x95234)))
% 22.40/22.30 [10159]P11(x101591,x101592,x101593,x101594)+~P1(f319(f319(f249(x101591,x101591,a904),f319(f319(f9(x101591,f913(x101591,x101592),f913(x101591,a904)),f319(f319(f10(f913(x101592,a904),f913(f913(x101591,x101592),f913(x101591,a904)),x101591),f10(x101592,a904,x101591)),f319(f319(f10(x101592,f913(x101592,a904),x101591),a316),x101594))),x101594)),f571(x101594,x101593,x101592,x101591)))
% 22.40/22.30 [5062]~E(x50622,f105(x50621))+E(f319(f319(f151(x50621,x50622),x50623),x50624),f105(x50621))
% 22.40/22.30 [5063]~E(x50634,f105(x50631))+E(f319(f319(f146(x50631,x50632),x50633),x50634),f105(x50632))
% 22.40/22.30 [5302]E(x53021,f105(x53022))+~E(f319(f319(f146(x53022,x53023),x53024),x53021),f105(x53023))
% 22.40/22.30 [5303]E(x53031,f105(x53032))+~E(f319(f319(f151(x53032,x53031),x53033),x53034),f105(x53032))
% 22.40/22.30 [5339]E(x53391,x53392)+~E(f319(f319(f126(x53393),x53394),x53391),f319(f319(f126(x53393),x53394),x53392))
% 22.40/22.30 [5340]E(x53401,x53402)+~E(f319(f319(f126(x53403),x53401),x53404),f319(f319(f126(x53403),x53402),x53404))
% 22.40/22.30 [5486]P1(f319(x54863,x54862))+E(f162(x54861,x54862,f319(f128(x54861,x54863),x54864)),f319(f128(x54861,x54863),x54864))
% 22.40/22.30 [5488]~P1(f319(x54882,x54883))+P33(x54881,x54882,f319(f319(f143(x54881),x54883),x54884))
% 22.40/22.30 [5498]E(x54981,x54982)+~E(f131(a906,f319(f294(a906,x54981),x54983)),f319(f319(f143(a906),x54982),x54984))
% 22.40/22.30 [5547]~P27(x55472,x55473)+P27(x55471,f319(f319(f67(x55472,x55471),x55473),x55474))
% 22.40/22.30 [5548]~P37(x55482,x55483)+P37(x55481,f319(f319(f280(x55482,x55481),x55483),x55484))
% 22.40/22.30 [5549]~P38(x55492,x55493)+P38(x55491,f319(f319(f280(x55492,x55491),x55493),x55494))
% 22.40/22.30 [5550]~P53(x55502,x55503)+P53(x55501,f319(f319(f280(x55502,x55501),x55503),x55504))
% 22.40/22.30 [5678]~P33(x56781,x56782,x56784)+P33(x56781,x56782,f319(f319(f143(x56781),x56783),x56784))
% 22.40/22.30 [5679]~P33(x56791,x56792,x56794)+P33(x56791,x56792,f319(f319(f126(x56791),x56793),x56794))
% 22.40/22.30 [5680]~P33(x56801,x56802,x56803)+P33(x56801,x56802,f319(f319(f126(x56801),x56803),x56804))
% 22.40/22.30 [5770]~E(x57701,f105(x57702))+~E(f319(f319(f126(x57702),x57703),f319(f319(f143(x57702),x57704),f105(x57702))),x57701)
% 22.40/22.30 [5795]~P31(x57953,x57951,f319(f319(f143(x57953),x57952),x57954))+P1(f319(x57951,x57952))
% 22.40/22.30 [5805]E(f106(x58051,x58052),x58053)+~E(f319(f319(f126(x58051),x58053),f319(f319(f143(x58051),x58054),f105(x58051))),x58052)
% 22.40/22.30 [5806]E(f136(x58061,x58062),x58063)+~E(f319(f319(f126(x58061),x58064),f319(f319(f143(x58061),x58063),f105(x58061))),x58062)
% 22.40/22.30 [5916]~E(f131(a906,f319(f294(a906,x59161),x59162)),f319(f319(f143(a906),x59163),x59164))+P1(f319(f319(f226(a906),x59161),x59162))
% 22.40/22.30 [5929]P31(x59291,x59292,x59293)+~P31(x59291,x59292,f319(f319(f143(x59291),x59294),x59293))
% 22.40/22.30 [5930]P31(x59301,x59302,x59303)+~P31(x59301,x59302,f319(f319(f126(x59301),x59304),x59303))
% 22.40/22.30 [5931]P31(x59311,x59312,x59313)+~P31(x59311,x59312,f319(f319(f126(x59311),x59313),x59314))
% 22.40/22.30 [6123]E(x61231,f319(f319(f126(x61232),f319(f160(x61232),x61233)),f319(f319(f143(x61232),x61234),f105(x61232))))+~E(f319(f160(x61232),x61231),f319(f319(f143(x61232),x61234),x61233))
% 22.40/22.30 [6298]~P111(x62981)+E(f319(f319(f94(f913(x62981,a904)),f319(f294(x62981,x62982),x62983)),f319(f294(x62981,x62983),x62984)),f181(f913(x62981,a904)))
% 22.40/22.30 [6310]E(f319(f319(f156(x63101),f161(x63101,x63102,x63103)),x63104),x63103)+~P1(f319(f319(f226(a906),x63104),x63102))
% 22.40/22.30 [6337]~P76(x63371)+E(f319(f157(x63371),f319(f319(f146(a1,x63371),x63372),f170(x63373,x63374))),f319(f319(f8(a1,x63371),x63372),f319(f164(a1),f170(x63373,x63374))))
% 22.40/22.30 [6338]~P76(x63381)+E(f319(f319(f8(a1,x63381),x63382),f319(f164(a1),f170(x63383,x63384))),f319(f157(x63381),f319(f319(f146(a1,x63381),x63382),f170(x63383,x63384))))
% 22.40/22.30 [6480]~E(x64802,f319(f319(f126(x64801),f319(f160(x64801),x64804)),f319(f319(f143(x64801),x64803),f105(x64801))))+E(f319(f160(x64801),x64802),f319(f319(f143(x64801),x64803),x64804))
% 22.40/22.30 [6498]~P20(x64982,x64983,x64984,x64981)+E(f319(x64981,f181(f913(x64982,a904))),f25(x64983))
% 22.40/22.30 [6526]~P111(x65261)+E(f319(f319(f94(f913(x65261,a904)),f298(x65261,x65262,x65263)),f319(f294(x65261,x65263),x65264)),f181(f913(x65261,a904)))
% 22.40/22.30 [6738]E(x67381,f181(f913(x67382,a904)))+~E(f305(x67383,x67382,x67384,x67381),f181(f913(f914(x67383,x67382),a904)))
% 22.40/22.30 [6739]E(x67391,f181(f913(x67392,a904)))+~E(f305(x67392,x67393,x67391,x67394),f181(f913(f914(x67392,x67393),a904)))
% 22.40/22.30 [6812]~P4(x68122)+E(f319(f182(f907(x68121)),f142(x68121,x68122,x68123,x68124)),f319(f182(f907(x68121)),x68124))
% 22.40/22.30 [6823]~P1(f319(f242(x68233,x68234,x68231),x68232))+P1(f319(f319(x68231,f545(x68232,x68231)),x68232))
% 22.40/22.30 [6866]~P1(f319(f55(x68662),x68664))+P1(f319(f55(x68661),f319(f302(x68662,x68661,x68663),x68664)))
% 22.40/22.30 [7090]~P25(x70902,x70901,x70903,x70904)+E(f319(f29(x70901),f319(f302(x70902,x70901,x70903),x70904)),f319(f29(x70902),x70904))
% 22.40/22.30 [7108]E(f319(f302(x71081,x71082,x71083),f319(f303(x71081,x71082,x71083),x71084)),x71084)+~E(f319(f302(x71081,x71082,x71083),f234(f913(x71081,a904))),f234(f913(x71082,a904)))
% 22.40/22.30 [7510]~P25(x75101,x75102,x75103,f234(f913(x75101,a904)))+E(f319(f303(x75101,x75102,x75103),f319(f302(x75101,x75102,x75103),x75104)),x75104)
% 22.40/22.30 [7785]E(x77851,x77852)+~P1(f319(f319(f321(x77853),x77851),f319(f164(x77853),f161(x77853,x77854,x77852))))
% 22.40/22.30 [7794]~E(x77941,f2(a906))+~P1(f319(f319(f321(x77942),x77943),f319(f164(x77942),f161(x77942,x77941,x77944))))
% 22.40/22.30 [7826]P1(f319(x78261,x78262))+~P1(f319(f319(f321(x78263),x78262),f319(f164(x78263),f169(x78263,x78261,x78264))))
% 22.40/22.30 [7939]~P1(f319(f319(f321(f907(x79391)),f319(f319(f143(x79391),x79392),x79394)),f153(x79391,x79393)))+P1(f319(f319(f321(x79391),x79392),x79393))
% 22.40/22.30 [8059]~P1(f319(f319(f321(x80591),x80592),f319(f164(x80591),f168(x80591,x80593,x80594))))+P1(f319(f319(f321(x80591),x80592),f319(f164(x80591),x80593)))
% 22.40/22.30 [8060]~P1(f319(f319(f321(x80601),x80602),f319(f164(x80601),f162(x80601,x80604,x80603))))+P1(f319(f319(f321(x80601),x80602),f319(f164(x80601),x80603)))
% 22.40/22.30 [8061]~P1(f319(f319(f321(x80611),x80612),f319(f164(x80611),f169(x80611,x80614,x80613))))+P1(f319(f319(f321(x80611),x80612),f319(f164(x80611),x80613)))
% 22.40/22.30 [8070]E(f319(f182(f907(x80701)),x80702),x80703)+~P1(f319(f319(f321(f907(x80701)),x80702),f319(f164(f907(x80701)),f49(x80701,x80703,x80704))))
% 22.40/22.30 [8169]P1(f319(x81693,x81692))+E(f319(f128(x81691,f319(f319(f10(a904,a904,x81691),a314),f319(a316,x81692))),f319(f128(x81691,x81693),x81694)),f319(f128(x81691,x81693),x81694))
% 22.40/22.30 [8277]E(f319(f319(f156(x82771),f169(x82771,x82772,x82773)),x82774),f319(f319(f156(x82771),x82773),x82774))+~P1(f319(f319(f226(a906),x82774),f319(f182(f907(x82771)),f169(x82771,x82772,x82773))))
% 22.40/22.30 [8361]~P76(x83611)+E(f319(f319(f8(a906,x83611),f319(f319(f10(a906,x83611,a906),x83612),a104)),f319(f294(a906,x83613),x83614)),f319(f319(f8(a906,x83611),x83612),f319(f294(a906,f319(a104,x83613)),f319(a104,x83614))))
% 22.40/22.30 [8370]~P76(x83701)+E(f319(f319(f8(a906,x83701),f319(f319(f10(a906,x83701,a906),x83702),a104)),f295(a906,x83703,x83704)),f319(f319(f8(a906,x83701),x83702),f295(a906,f319(a104,x83703),f319(a104,x83704))))
% 22.40/22.30 [8497]~P25(x84971,x84973,x84974,f234(f913(x84971,a904)))+P25(x84971,f913(x84972,x84973),f319(f319(f10(x84973,f913(x84972,x84973),x84971),f18(x84973,x84972)),x84974),f234(f913(x84971,a904)))
% 22.40/22.30 [8581]~P25(x85812,x85811,x85814,x85813)+E(f319(f302(x85811,x85812,f71(x85812,x85811,x85813,x85814)),f319(f302(x85812,x85811,x85814),x85813)),x85813)
% 22.40/22.30 [8644]~P1(f319(f319(f321(f912(x86441,x86441)),f319(f319(f244(x86441,x86441),x86442),x86444)),f255(x86441,x86443)))+P1(f319(f319(f321(x86441),x86442),x86443))
% 22.40/22.30 [8762]~P25(x87622,x87621,x87623,f234(f913(x87622,a904)))+E(f319(f302(x87621,x87622,f85(x87622,x87621,f234(f913(x87622,a904)),x87623)),f319(f302(x87622,x87621,x87623),x87624)),x87624)
% 22.40/22.30 [8835]~P26(x88351,x88352,x88353,x88354,f234(f913(x88352,a904)))+E(f319(f302(x88351,x88352,x88353),f234(f913(x88351,a904))),f234(f913(x88352,a904)))
% 22.40/22.30 [8867]~E(f319(f319(f8(x88671,a906),x88674),x88673),f319(a104,x88672))+P1(f319(f319(f321(x88671),f370(x88672,x88673,x88674,x88671)),x88673))
% 22.40/22.30 [8889]~E(f319(f319(f8(x88894,a906),x88891),x88893),f319(a104,x88892))+P1(f319(f319(f226(a906),f2(a906)),f319(x88891,f370(x88892,x88893,x88891,x88894))))
% 22.40/22.30 [8900]~P1(f319(f55(x89002),x89004))+P1(f319(f319(f225(a906),f319(f29(x89001),f319(f302(x89002,x89001,x89003),x89004))),f319(f29(x89002),x89004)))
% 22.40/22.30 [8901]E(f319(f319(f244(x89011,x89012),f631(x89013,x89014,x89012,x89011)),f632(x89013,x89014,x89012,x89011)),x89014)+~P1(f319(f319(f321(f912(x89011,x89012)),x89014),f319(f278(x89012,x89011),x89013)))
% 22.40/22.30 [8909]P25(x89091,x89092,x89093,x89094)+P1(f319(f319(f321(x89091),f447(x89094,x89093,x89092,x89091)),x89094))
% 22.40/22.30 [8910]P25(x89101,x89102,x89103,x89104)+P1(f319(f319(f321(x89101),f456(x89104,x89103,x89102,x89101)),x89104))
% 22.40/22.30 [8983]P11(x89831,x89832,x89833,x89834)+P1(f319(f319(f321(f912(x89831,x89831)),f571(x89834,x89833,x89832,x89831)),x89833))
% 22.40/22.30 [9042]P1(f319(x90421,x90422))+~P1(f319(x90421,f319(f319(f244(x90423,x90424),f480(x90424,x90423,x90421)),f481(x90424,x90423,x90421))))
% 22.40/22.30 [9059]E(f319(f182(f907(x90591)),x90592),f319(f182(f907(x90591)),x90593))+~P1(f319(f319(f321(f912(f907(x90591),f907(x90591))),f319(f319(f244(f907(x90591),f907(x90591)),x90592),x90593)),f137(x90591,x90594)))
% 22.40/22.30 [9060]E(f319(f182(f907(x90601)),x90602),f319(f182(f907(x90601)),x90603))+~P1(f319(f319(f321(f912(f907(x90601),f907(x90601))),f319(f319(f244(f907(x90601),f907(x90601)),x90602),x90603)),f149(x90601,x90604)))
% 22.40/22.30 [9063]E(f319(f182(f907(x90631)),x90632),f319(f182(f907(x90631)),x90633))+~P1(f319(f319(f321(f912(f907(x90631),f907(x90631))),f319(f319(f244(f907(x90631),f907(x90631)),x90632),x90633)),f150(x90631,x90634)))
% 22.40/22.30 [9133]P1(f319(f319(f225(a906),f147(x91331,x91332,x91333)),f147(x91331,x91334,x91333)))+P1(f319(f319(f321(x91331),f659(x91334,x91332,x91333,x91331)),f319(f164(x91331),x91333)))
% 22.40/22.30 [9136]E(f319(f182(f907(x91361)),x91362),f319(f182(f907(x91361)),x91363))+~P1(f319(f319(f321(f912(f907(x91361),f907(x91361))),f319(f319(f244(f907(x91361),f907(x91361)),x91362),x91363)),f299(f907(x91361),f149(x91361,x91364))))
% 22.40/22.30 [9249]P1(f319(f319(f279(a906),x92491),x92492))+P1(f319(f319(f225(f913(a906,a904)),f288(a906,f279(a906),x92491,x92492)),f288(a906,f279(a906),x92493,x92494)))
% 22.40/22.30 [9371]~P25(x93711,x93712,x93713,x93714)+~P1(f319(f319(f226(a906),f319(f29(x93712),f319(f302(x93711,x93712,x93713),x93714))),f319(f29(x93711),x93714)))
% 22.40/22.30 [9426]~P1(f319(f319(f321(f912(f907(x94261),f907(x94261))),f319(f319(f244(f907(x94261),f907(x94261)),x94262),x94263)),f149(x94261,x94264)))+P1(f319(f319(f321(f912(f907(x94261),f907(x94261))),f319(f319(f244(f907(x94261),f907(x94261)),x94262),x94263)),f150(x94261,f299(x94261,x94264))))
% 22.40/22.30 [9430]~P1(f319(f319(f321(f912(f907(x94301),f907(x94301))),f319(f319(f244(f907(x94301),f907(x94301)),x94302),x94303)),f150(x94301,x94304)))+P1(f319(f319(f321(f912(f907(x94301),f907(x94301))),f319(f319(f244(f907(x94301),f907(x94301)),x94302),x94303)),f299(f907(x94301),f149(x94301,x94304))))
% 22.40/22.30 [9442]P1(f319(f319(f321(f912(x94421,x94421)),f319(f319(f244(x94421,x94421),x94422),x94423)),f299(x94421,x94424)))+~P1(f319(f319(f321(f912(x94421,x94421)),f319(f319(f244(x94421,x94421),x94422),x94423)),f319(f319(f281(x94421,x94421,x94421),x94424),f299(x94421,x94424))))
% 22.40/22.30 [9634]E(f319(f319(f126(x96341),f675(x96342,x96343,x96344,x96341)),f319(f319(f143(x96341),f676(x96342,x96343,x96344,x96341)),f678(x96342,x96343,x96344,x96341))),x96344)+~P1(f319(f319(f321(f912(f907(x96341),f907(x96341))),f319(f319(f244(f907(x96341),f907(x96341)),x96344),x96343)),f149(x96341,x96342)))
% 22.40/22.30 [9635]E(f319(f319(f126(x96351),f675(x96352,x96353,x96354,x96351)),f319(f319(f143(x96351),f677(x96352,x96353,x96354,x96351)),f678(x96352,x96353,x96354,x96351))),x96353)+~P1(f319(f319(f321(f912(f907(x96351),f907(x96351))),f319(f319(f244(f907(x96351),f907(x96351)),x96354),x96353)),f149(x96351,x96352)))
% 22.40/22.30 [9717]P1(f319(f319(f321(f912(x97171,x97171)),f319(f319(f244(x97171,x97171),x97172),f627(x97173,x97174,x97172,x97171))),f299(x97171,x97173)))+~P1(f319(f319(f321(f912(x97171,x97171)),f319(f319(f244(x97171,x97171),x97172),x97174)),f319(f319(f281(x97171,x97171,x97171),x97173),f299(x97171,x97173))))
% 22.40/22.30 [9800]P1(f319(f319(f225(a906),f147(x98001,x98002,x98003)),f147(x98001,x98004,x98003)))+~P1(f319(f319(f226(a906),f319(x98002,f659(x98004,x98002,x98003,x98001))),f319(x98004,f659(x98004,x98002,x98003,x98001))))
% 22.40/22.30 [9872]P1(f319(f319(f321(f912(x98721,x98721)),f319(f319(f244(x98721,x98721),f626(x98722,x98723,x98724,x98721)),x98723)),f299(x98721,x98722)))+~P1(f319(f319(f321(f912(x98721,x98721)),f319(f319(f244(x98721,x98721),x98724),x98723)),f319(f319(f281(x98721,x98721,x98721),x98722),f299(x98721,x98722))))
% 22.40/22.30 [5321]~E(x53212,x53213)+E(f162(x53211,x53212,f319(f319(f143(x53211),x53213),x53214)),x53214)
% 22.40/22.30 [5443]P1(f319(x54432,x54433))+E(f169(x54431,x54432,f319(f319(f143(x54431),x54433),x54434)),f105(x54431))
% 22.40/22.30 [5510]~P64(x55102)+E(f319(f319(f73(f913(x55101,x55102)),x55103),x55104),f319(f73(x55102),f319(x55103,x55104)))
% 22.40/22.30 [5523]~E(x55232,f2(a906))+E(f319(f319(f130(x55231),x55232),f319(f319(f143(x55231),x55233),x55234)),f319(f319(f143(x55231),x55233),x55234))
% 22.40/22.30 [5524]P1(f319(x55242,x55243))+E(f319(f128(x55241,x55242),f319(f319(f143(x55241),x55243),x55244)),f319(f128(x55241,x55242),x55244))
% 22.40/22.30 [5661]~E(x56612,x56614)+P1(f319(f319(f319(f301(x56611),x56612),x56613),x56614))
% 22.40/22.30 [5669]E(x56691,f105(x56692))+E(f136(x56693,f319(f319(f146(x56692,x56693),x56694),x56691)),f319(x56694,f136(x56692,x56691)))
% 22.40/22.30 [5683]~E(x56831,f57(x56832,x56834))+E(f319(x56831,f319(f319(f301(x56832),x56833),f181(f913(x56832,a904)))),x56833)
% 22.40/22.30 [5721]E(x57211,f105(x57212))+E(f319(f133(x57213),f319(f319(f146(x57212,x57213),x57214),x57211)),f319(x57214,f319(f133(x57212),x57211)))
% 22.40/22.30 [5825]~P1(f319(x58253,x58254))+P1(f319(f319(f319(f301(x58251),x58252),x58253),x58254))
% 22.40/22.30 [5949]~P19(x59492,x59494,x59491)+E(f319(x59491,f319(f319(f301(x59492),x59493),f181(f913(x59492,a904)))),x59493)
% 22.40/22.30 [5975]~E(x59752,x59753)+P1(f319(f319(f321(x59751),x59752),f319(f319(f301(x59751),x59753),x59754)))
% 22.40/22.30 [5980]~P101(x59801)+E(f319(f319(f93(x59801),x59802),f319(f319(f93(x59801),x59803),x59804)),f319(f319(f93(x59801),x59803),f319(f319(f93(x59801),x59802),x59804)))
% 22.40/22.30 [5982]~P106(x59821)+E(f319(f319(f93(x59821),x59822),f319(f319(f93(x59821),x59823),x59824)),f319(f319(f93(x59821),x59823),f319(f319(f93(x59821),x59822),x59824)))
% 22.40/22.30 [5983]~P101(x59831)+E(f319(f319(f94(x59831),x59832),f319(f319(f94(x59831),x59833),x59834)),f319(f319(f94(x59831),x59833),f319(f319(f94(x59831),x59832),x59834)))
% 22.40/22.30 [5985]~P107(x59851)+E(f319(f319(f94(x59851),x59852),f319(f319(f94(x59851),x59853),x59854)),f319(f319(f94(x59851),x59853),f319(f319(f94(x59851),x59852),x59854)))
% 22.40/22.30 [5987]~P4(x59871)+E(f319(f319(f180(x59871),x59872),f319(f319(f180(x59871),x59873),x59874)),f319(f319(f180(x59871),x59873),f319(f319(f180(x59871),x59872),x59874)))
% 22.40/22.30 [5989]~P4(x59891)+E(f319(f319(f230(x59891),x59892),f319(f319(f230(x59891),x59893),x59894)),f319(f319(f230(x59891),x59893),f319(f319(f230(x59891),x59892),x59894)))
% 22.40/22.30 [5990]~P119(x59901)+E(f319(f319(f74(x59901),x59902),f319(f319(f74(x59901),x59903),x59904)),f319(f319(f74(x59901),x59903),f319(f319(f74(x59901),x59902),x59904)))
% 22.40/22.30 [5991]~P119(x59911)+E(f319(f319(f75(x59911),x59912),f319(f319(f75(x59911),x59913),x59914)),f319(f319(f75(x59911),x59913),f319(f319(f75(x59911),x59912),x59914)))
% 22.40/22.30 [5996]E(x59961,x59962)+E(f162(x59963,x59961,f319(f319(f143(x59963),x59962),x59964)),f319(f319(f143(x59963),x59962),f162(x59963,x59961,x59964)))
% 22.40/22.30 [6009]~P1(f319(x60092,x60093))+E(f319(f128(x60091,x60092),f319(f319(f143(x60091),x60093),x60094)),f319(f319(f143(x60091),x60093),f319(f128(x60091,x60092),x60094)))
% 22.40/22.30 [6144]~P1(f319(x61442,x61443))+E(f169(x61441,x61442,f319(f319(f143(x61441),x61443),x61444)),f319(f319(f143(x61441),x61443),f169(x61441,x61442,x61444)))
% 22.40/22.30 [6206]E(x62061,f181(f913(x62062,a904)))+E(f319(f319(f33(x62062,f913(x62063,a904)),x62061),f319(f18(f913(x62063,a904),x62062),x62064)),x62064)
% 22.40/22.30 [6207]E(x62071,f181(f913(x62072,a904)))+E(f319(f319(f34(x62072,f913(x62073,a904)),x62071),f319(f18(f913(x62073,a904),x62072),x62074)),x62074)
% 22.40/22.30 [6216]~E(x62164,f181(f913(x62162,a904)))+E(f319(f319(f246(x62161,x62162),x62163),f319(f18(f913(x62162,a904),x62161),x62164)),f181(f913(f912(x62161,x62162),a904)))
% 22.40/22.30 [6217]~E(x62173,f181(f913(x62171,a904)))+E(f319(f319(f246(x62171,x62172),x62173),f319(f18(f913(x62172,a904),x62171),x62174)),f181(f913(f912(x62171,x62172),a904)))
% 22.40/22.30 [6274]E(x62741,f2(a906))+E(f319(f319(f130(x62742),x62741),f319(f319(f143(x62742),x62743),x62744)),f319(f319(f130(x62742),f319(f319(f3(a906),x62741),f72(a906))),x62744))
% 22.40/22.30 [6291]E(x62911,f181(f913(x62912,a904)))+E(f319(f302(x62912,x62913,f319(f18(x62913,x62912),x62914)),x62911),f319(f319(f301(x62913),x62914),f181(f913(x62913,a904))))
% 22.40/22.30 [6294]E(f319(f303(x62941,x62942,f319(f18(x62942,x62941),x62943)),x62944),f181(f913(x62941,a904)))+P1(f319(f319(f321(x62942),x62943),x62944))
% 22.40/22.30 [6361]~E(x63613,f181(f913(x63611,a904)))+E(f319(f319(f33(x63611,f913(x63612,a904)),x63613),f319(f18(f913(x63612,a904),x63611),x63614)),f181(f913(x63612,a904)))
% 22.40/22.30 [6362]~E(x63623,f181(f913(x63621,a904)))+E(f319(f319(f34(x63621,f913(x63622,a904)),x63623),f319(f18(f913(x63622,a904),x63621),x63624)),f234(f913(x63622,a904)))
% 22.40/22.30 [6364]~P69(x63641)+E(f39(x63641,f319(f319(f75(x63641),x63642),x63643),f319(f319(f75(x63641),x63642),x63644)),f319(f319(f75(x63641),x63642),f39(x63641,x63643,x63644)))
% 22.40/22.30 [6536]E(f319(f303(x65361,x65362,f319(f18(x65362,x65361),x65363)),x65364),f234(f913(x65361,a904)))+~P1(f319(f319(f321(x65362),x65363),x65364))
% 22.40/22.30 [6559]~P1(f319(f319(f321(x65591),x65592),x65594))+P1(f319(f319(f321(x65591),x65592),f319(f319(f301(x65591),x65593),x65594)))
% 22.40/22.30 [6564]P1(f319(x65641,x65642))+~P1(f319(f152(x65643,x65641),f319(f319(f143(x65643),x65642),x65644)))
% 22.40/22.30 [6573]~E(x65733,f319(f319(f3(a906),f319(f182(f907(x65731)),x65732)),f72(a906)))+E(f106(x65731,f319(f319(f151(x65731,x65732),x65733),x65734)),f106(x65731,x65732))
% 22.40/22.30 [6592]~P4(x65921)+E(f319(f319(f94(f913(x65921,a904)),f319(f293(x65921),x65922)),f295(x65921,x65923,x65924)),f295(x65921,x65923,f319(f319(f230(x65921),x65922),x65924)))
% 22.40/22.30 [6593]~P4(x65931)+E(f319(f319(f94(f913(x65931,a904)),f319(f275(x65931),x65932)),f295(x65931,x65933,x65934)),f295(x65931,f319(f319(f180(x65931),x65932),x65933),x65934))
% 22.40/22.30 [6609]E(f319(f319(f94(f913(x66091,a904)),x66092),f319(f319(f301(x66091),x66093),x66094)),f319(f319(f94(f913(x66091,a904)),x66092),x66094))+P1(f319(f319(f321(x66091),x66093),x66092))
% 22.40/22.30 [6621]E(f162(x66211,x66212,f319(f319(f126(x66211),x66213),x66214)),f319(f319(f126(x66211),x66213),f162(x66211,x66212,x66214)))+P1(f319(f319(f321(x66211),x66212),f319(f164(x66211),x66213)))
% 22.40/22.30 [6626]~P87(x66261)+E(f319(f319(f75(x66261),f319(f319(f236(x66261),x66262),x66263)),f319(f319(f236(x66261),x66262),x66264)),f319(f319(f236(x66261),x66262),f319(f319(f74(a906),x66263),x66264)))
% 22.40/22.30 [6627]~P119(x66271)+E(f319(f319(f75(x66271),f319(f319(f236(x66271),x66272),x66273)),f319(f319(f236(x66271),x66272),x66274)),f319(f319(f236(x66271),x66272),f319(f319(f74(a906),x66273),x66274)))
% 22.40/22.30 [6661]~P102(x66611)+E(f319(f319(f94(x66611),f319(f319(f93(x66611),x66612),x66613)),f319(f319(f93(x66611),x66612),x66614)),f319(f319(f93(x66611),x66612),f319(f319(f94(x66611),x66613),x66614)))
% 22.40/22.30 [6662]~P102(x66621)+E(f319(f319(f93(x66621),f319(f319(f94(x66621),x66622),x66623)),f319(f319(f94(x66621),x66622),x66624)),f319(f319(f94(x66621),x66622),f319(f319(f93(x66621),x66623),x66624)))
% 22.40/22.30 [6663]~P4(x66631)+E(f319(f319(f230(x66631),f319(f319(f180(x66631),x66632),x66633)),f319(f319(f180(x66631),x66632),x66634)),f319(f319(f180(x66631),x66632),f319(f319(f230(x66631),x66633),x66634)))
% 22.40/22.30 [6664]~P4(x66641)+E(f319(f319(f180(x66641),f319(f319(f230(x66641),x66642),x66643)),f319(f319(f230(x66641),x66642),x66644)),f319(f319(f230(x66641),x66642),f319(f319(f180(x66641),x66643),x66644)))
% 22.40/22.30 [6665]~P119(x66651)+E(f319(f319(f74(x66651),f319(f319(f75(x66651),x66652),x66653)),f319(f319(f75(x66651),x66652),x66654)),f319(f319(f75(x66651),x66652),f319(f319(f74(x66651),x66653),x66654)))
% 22.40/22.30 [6701]~P69(x67011)+E(f39(x67011,f319(f319(f75(x67011),x67012),x67013),f319(f319(f75(x67011),x67014),x67013)),f319(f319(f75(x67011),f39(x67011,x67012,x67014)),x67013))
% 22.40/22.30 [6704]~E(f319(f182(f907(x67041)),x67043),f319(f182(f907(x67042)),x67044))+E(f319(f319(f146(f912(x67041,x67042),x67042),f248(x67041,x67042)),f319(f319(f173(x67041,x67042),x67043),x67044)),x67044)
% 22.40/22.30 [6705]~E(f319(f182(f907(x67051)),x67053),f319(f182(f907(x67052)),x67054))+E(f319(f319(f146(f912(x67051,x67052),x67051),f243(x67051,x67052)),f319(f319(f173(x67051,x67052),x67053),x67054)),x67053)
% 22.40/22.30 [6710]P1(f319(f152(x67101,x67102),x67103))+~P1(f319(f152(x67101,x67102),f319(f319(f143(x67101),x67104),x67103)))
% 22.40/22.30 [6711]P1(f319(f152(x67111,x67112),x67113))+~P1(f319(f152(x67111,x67112),f319(f319(f126(x67111),x67114),x67113)))
% 22.40/22.30 [6712]P1(f319(f152(x67121,x67122),x67123))+~P1(f319(f152(x67121,x67122),f319(f319(f126(x67121),x67123),x67124)))
% 22.40/22.30 [6717]~P70(x67171)+E(f39(x67171,f319(f319(f3(x67171),x67172),f39(x67171,x67173,x67174)),x67174),f39(x67171,f319(f319(f3(x67171),x67172),x67173),x67174))
% 22.40/22.30 [6719]~P69(x67191)+E(f39(x67191,f319(f319(f75(x67191),x67192),f39(x67191,x67193,x67194)),x67194),f39(x67191,f319(f319(f75(x67191),x67192),x67193),x67194))
% 22.40/22.30 [6720]~P69(x67201)+E(f39(x67201,f319(f319(f74(x67201),x67202),f39(x67201,x67203,x67204)),x67204),f39(x67201,f319(f319(f74(x67201),x67202),x67203),x67204))
% 22.40/22.30 [6802]~P4(x68021)+E(f319(f319(f94(f913(x68021,a904)),f295(x68021,x68022,x68023)),f319(f293(x68021),x68024)),f295(x68021,x68022,f319(f319(f230(x68021),x68023),x68024)))
% 22.40/22.30 [6803]~P4(x68031)+E(f319(f319(f94(f913(x68031,a904)),f295(x68031,x68032,x68033)),f319(f275(x68031),x68034)),f295(x68031,f319(f319(f180(x68031),x68032),x68034),x68033))
% 22.40/22.30 [6806]~E(f319(f182(f907(x68061)),x68063),f319(f182(f907(x68062)),x68064))+E(f319(f319(f173(x68061,x68062),f319(f160(x68061),x68063)),f319(f160(x68062),x68064)),f319(f160(f912(x68061,x68062)),f319(f319(f173(x68061,x68062),x68063),x68064)))
% 22.40/22.30 [6820]E(x68201,f319(f319(f3(a906),f319(f182(f907(x68202)),x68203)),f72(a906)))+E(f106(x68202,f319(f319(f151(x68202,x68203),x68201),x68204)),f319(f319(f151(x68202,f106(x68202,x68203)),x68201),x68204))
% 22.40/22.30 [6835]~P1(f319(f129(x68352),x68354))+P1(f319(f129(f912(x68351,x68352)),f319(f319(f173(x68351,x68352),x68353),x68354)))
% 22.40/22.30 [6836]~P1(f319(f129(x68361),x68363))+P1(f319(f129(f912(x68361,x68362)),f319(f319(f173(x68361,x68362),x68363),x68364)))
% 22.40/22.30 [7093]E(f319(f319(f30(a906),x70931),x70932),x70933)+~P1(f319(f42(x70931,x70932),f319(f319(f244(a906,a906),x70933),x70934)))
% 22.40/22.30 [7117]E(f39(a906,x71171,x71172),x71173)+~P1(f319(f42(x71171,x71172),f319(f319(f244(a906,a906),x71174),x71173)))
% 22.40/22.30 [7120]P1(f319(f129(x71201),x71202))+~P1(f319(f129(x71203),f319(f319(f146(x71201,x71203),x71204),x71202)))
% 22.40/22.30 [7201]E(f162(x72011,x72012,f319(f319(f126(x72011),x72013),x72014)),f319(f319(f126(x72011),f162(x72011,x72012,x72013)),x72014))+~P1(f319(f319(f321(x72011),x72012),f319(f164(x72011),x72013)))
% 22.40/22.30 [7292]~P70(x72921)+E(f39(x72921,f319(f319(f3(x72921),f39(x72921,x72922,x72923)),x72924),x72923),f39(x72921,f319(f319(f3(x72921),x72922),x72924),x72923))
% 22.40/22.30 [7295]~P69(x72951)+E(f39(x72951,f319(f319(f74(x72951),f39(x72951,x72952,x72953)),x72954),x72953),f39(x72951,f319(f319(f74(x72951),x72952),x72954),x72953))
% 22.40/22.30 [7296]~P69(x72961)+E(f39(x72961,f319(f319(f75(x72961),f39(x72961,x72962,x72963)),x72964),x72963),f39(x72961,f319(f319(f75(x72961),x72962),x72964),x72963))
% 22.40/22.30 [7481]~E(x74811,f319(f319(f143(x74812),x74813),x74814))+~P1(f319(f319(f225(a906),f319(f182(f907(x74812)),x74811)),f319(f182(f907(x74812)),x74814)))
% 22.40/22.30 [7680]P25(x76801,x76802,x76803,f319(f164(x76801),x76804))+~P1(f319(f129(x76802),f319(f319(f146(x76801,x76802),x76803),x76804)))
% 22.40/22.30 [7751]~P1(f319(f319(f225(f913(x77511,a904)),x77512),x77514))+P1(f319(f319(f225(f913(x77511,a904)),x77512),f319(f319(f301(x77511),x77513),x77514)))
% 22.40/22.30 [7786]~P70(x77861)+E(f39(x77861,f319(f319(f3(x77861),f39(x77861,x77862,x77863)),f39(x77861,x77864,x77863)),x77863),f39(x77861,f319(f319(f3(x77861),x77862),x77864),x77863))
% 22.40/22.30 [7787]~P69(x77871)+E(f39(x77871,f319(f319(f74(x77871),f39(x77871,x77872,x77873)),f39(x77871,x77874,x77873)),x77873),f39(x77871,f319(f319(f74(x77871),x77872),x77874),x77873))
% 22.40/22.30 [7788]~P69(x77881)+E(f39(x77881,f319(f319(f75(x77881),f39(x77881,x77882,x77883)),f39(x77881,x77884,x77883)),x77883),f39(x77881,f319(f319(f75(x77881),x77882),x77884),x77883))
% 22.40/22.30 [7893]~E(f319(x78934,f461(x78934,x78933,x78931,x78932)),f234(f913(x78932,a904)))+E(f319(f319(f34(x78931,f913(x78932,a904)),x78933),x78934),f234(f913(x78932,a904)))
% 22.40/22.30 [7894]~E(f319(x78944,f463(x78944,x78943,x78941,x78942)),f181(f913(x78942,a904)))+E(f319(f319(f33(x78941,f913(x78942,a904)),x78943),x78944),f181(f913(x78942,a904)))
% 22.40/22.30 [7895]~E(f319(x78954,f464(x78954,x78953,x78952,x78951)),f181(f913(x78952,a904)))+E(f319(f319(f33(x78951,f913(x78952,a904)),x78953),x78954),f181(f913(x78952,a904)))
% 22.40/22.30 [7896]~E(f319(x78964,f462(x78964,x78963,x78962,x78961)),f234(f913(x78962,a904)))+E(f319(f319(f34(x78961,f913(x78962,a904)),x78963),x78964),f234(f913(x78962,a904)))
% 22.40/22.30 [8278]P1(f319(x82781,x82782))+~P1(f319(f319(f321(x82783),x82782),f319(f319(f94(f913(x82783,a904)),x82784),f319(f254(x82783),x82781))))
% 22.40/22.30 [8314]~P1(f319(f319(f225(f913(x83141,a904)),x83143),x83144))+P1(f319(f319(f225(f913(x83141,a904)),f319(f319(f301(x83141),x83142),x83143)),f319(f319(f301(x83141),x83142),x83144)))
% 22.40/22.30 [8489]P1(f319(x84892,x84893))+E(f319(f319(f130(x84891),f319(f182(f907(x84891)),f169(x84891,x84892,f319(f319(f143(x84891),x84893),x84894)))),f319(f319(f143(x84891),x84893),x84894)),f319(f319(f143(x84891),x84893),x84894))
% 22.40/22.30 [8595]~P1(f319(f319(f226(a906),f319(x85954,x85952)),f319(x85954,x85953)))+P1(f319(f319(f321(f912(x85951,x85951)),f319(f319(f244(x85951,x85951),x85952),x85953)),f319(f319(f280(a906,x85951),a232),x85954)))
% 22.40/22.30 [8694]~P1(f319(x86942,f731(x86944,x86942,x86943,x86941)))+E(f169(x86941,x86942,f319(f319(f126(x86941),x86943),x86944)),f319(f319(f126(x86941),x86943),f169(x86941,x86942,x86944)))
% 22.40/22.30 [8766]P25(f907(x87661),f907(x87662),f319(f146(x87661,x87662),x87663),x87664)+~P25(x87661,x87662,x87663,f31(f913(x87661,a904),f319(f302(f907(x87661),f913(x87661,a904),f164(x87661)),x87664)))
% 22.40/22.30 [8839]~P1(f319(x88392,x88393))+E(f319(f319(f130(x88391),f319(f182(f907(x88391)),f169(x88391,x88392,f319(f319(f143(x88391),x88393),x88394)))),f319(f319(f143(x88391),x88393),x88394)),f319(f319(f130(x88391),f319(f182(f907(x88391)),f169(x88391,x88392,x88394))),x88394))
% 22.40/22.30 [8880]~E(x88802,x88803)+E(f319(f128(x88801,f319(f319(f10(a904,a904,x88801),a314),f319(a316,x88802))),f319(f319(f143(x88801),x88803),x88804)),f319(f128(x88801,f319(f319(f10(a904,a904,x88801),a314),f319(a316,x88802))),x88804))
% 22.40/22.30 [8890]E(f319(f319(f34(x88901,f913(x88902,a904)),x88903),x88904),f234(f913(x88902,a904)))+P1(f319(f319(f321(x88901),f461(x88904,x88903,x88901,x88902)),x88903))
% 22.40/22.30 [8891]E(f319(f319(f33(x88911,f913(x88912,a904)),x88913),x88914),f181(f913(x88912,a904)))+P1(f319(f319(f321(x88911),f463(x88914,x88913,x88911,x88912)),x88913))
% 22.40/22.30 [8892]E(f319(f319(f33(x88921,f913(x88922,a904)),x88923),x88924),f181(f913(x88922,a904)))+P1(f319(f319(f321(x88921),f464(x88924,x88923,x88922,x88921)),x88923))
% 22.40/22.30 [8893]E(f319(f319(f34(x88931,f913(x88932,a904)),x88933),x88934),f234(f913(x88932,a904)))+P1(f319(f319(f321(x88931),f462(x88934,x88933,x88932,x88931)),x88933))
% 22.40/22.30 [8933]P1(f319(f319(f226(a906),f319(x89331,x89332)),f319(x89331,x89333)))+~P1(f319(f319(f321(f912(x89334,x89334)),f319(f319(f244(x89334,x89334),x89332),x89333)),f319(f319(f280(a906,x89334),a232),x89331)))
% 22.40/22.30 [8961]E(f169(x89611,x89612,f319(f319(f126(x89611),x89613),x89614)),f319(f319(f126(x89611),x89613),f169(x89611,x89612,x89614)))+P1(f319(f319(f321(x89611),f731(x89614,x89612,x89613,x89611)),f319(f164(x89611),x89613)))
% 22.40/22.30 [9019]~P26(x90191,x90192,x90193,f234(f913(x90191,a904)),f234(f913(x90192,a904)))+E(f319(f302(x90191,x90192,x90193),f319(f73(f913(x90191,a904)),x90194)),f319(f73(f913(x90192,a904)),f319(f302(x90191,x90192,x90193),x90194)))
% 22.40/22.30 [9122]P1(f319(f319(f321(x91221),f511(x91222,x91223,x91224,x91221)),x91223))+~P1(f319(f319(f321(f913(x91221,a904)),x91224),f319(f319(f54(x91221),x91223),x91222)))
% 22.40/22.30 [9125]E(x91251,x91252)+~P1(f319(f319(f321(f912(x91253,x91253)),f319(f319(f244(x91253,x91253),x91251),x91252)),f319(f319(f175(f912(x91253,x91253),a904),f2(a906)),x91254)))
% 22.40/22.30 [9194]E(f319(f277(x91941,x91941,x91942),f319(f319(f301(x91941),f511(x91942,x91943,x91944,x91941)),f181(f913(x91941,a904)))),x91944)+~P1(f319(f319(f321(f913(x91941,a904)),x91944),f319(f319(f54(x91941),x91943),x91942)))
% 22.40/22.30 [9199]~P1(f319(f319(f321(f912(x91991,x91991)),f319(f319(f244(x91991,x91991),x91993),x91992)),f299(x91991,x91994)))+P1(f319(f319(f321(f912(x91991,x91991)),f319(f319(f244(x91991,x91991),x91992),x91993)),f299(x91991,f319(f278(x91991,x91991),x91994))))
% 22.40/22.30 [9212]~P69(x92121)+E(f319(f319(f74(x92121),f319(f319(f74(x92121),f319(f319(f75(x92121),x92122),f319(f319(f30(x92121),x92123),x92122))),f39(x92121,x92123,x92122))),x92124),f319(f319(f74(x92121),x92123),x92124))
% 22.40/22.30 [9229]~P1(f319(f319(f321(x92291),x92293),x92294))+P1(f319(f319(f321(f913(x92291,a904)),f319(f277(x92291,x92291,x92292),f319(f319(f301(x92291),x92293),f181(f913(x92291,a904))))),f319(f319(f54(x92291),x92294),x92292)))
% 22.40/22.30 [9242]P1(f319(f319(f321(f912(x92421,x92421)),f319(f319(f244(x92421,x92421),x92422),x92423)),f299(x92421,x92424)))+~P1(f319(f319(f321(f912(x92421,x92421)),f319(f319(f244(x92421,x92421),x92423),x92422)),f299(x92421,f319(f278(x92421,x92421),x92424))))
% 22.40/22.30 [9330]E(f319(f319(f151(x93301,f319(f160(x93301),x93302)),f319(f319(f3(a906),f319(f319(f3(a906),f319(f182(f907(x93301)),x93302)),x93303)),f72(a906))),x93304),f319(f160(x93301),f319(f319(f151(x93301,x93302),x93303),x93304)))+~P1(f319(f319(f226(a906),x93303),f319(f182(f907(x93301)),x93302)))
% 22.40/22.30 [9334]~P1(f319(x93342,f726(x93344,x93342,x93343,x93341)))+E(f319(f319(f130(x93341),f319(f182(f907(x93341)),f169(x93341,x93342,f319(f319(f126(x93341),x93343),x93344)))),f319(f319(f126(x93341),x93343),x93344)),f319(f319(f130(x93341),f319(f182(f907(x93341)),f169(x93341,x93342,x93344))),x93344))
% 22.40/22.30 [9379]~P25(x93792,x93791,x93793,f234(f913(x93792,a904)))+P1(f319(f319(f225(f913(x93791,a904)),f319(f302(x93792,x93791,x93793),f319(f73(f913(x93792,a904)),x93794))),f319(f73(f913(x93791,a904)),f319(f302(x93792,x93791,x93793),x93794))))
% 22.40/22.30 [9392]~P5(x93921)+E(f319(f134(x93921,x93922,f319(f9(x93922,x93921,x93921),f319(f319(f10(x93921,f913(x93921,x93921),x93922),f93(x93921)),x93923)),f181(x93921)),x93924),f319(f319(f33(x93922,x93921),f319(f164(x93922),x93924)),x93923))
% 22.40/22.30 [9393]~P5(x93931)+E(f319(f134(x93931,x93932,f319(f9(x93932,x93931,x93931),f319(f319(f10(x93931,f913(x93931,x93931),x93932),f94(x93931)),x93933)),f234(x93931)),x93934),f319(f319(f34(x93932,x93931),f319(f164(x93932),x93934)),x93933))
% 22.40/22.30 [9405]E(f319(f319(f130(x94051),f319(f182(f907(x94051)),f169(x94051,x94052,f319(f319(f126(x94051),x94053),x94054)))),f319(f319(f126(x94051),x94053),x94054)),f319(f319(f130(x94051),f319(f182(f907(x94051)),f169(x94051,x94052,x94054))),x94054))+P1(f319(f319(f321(x94051),f726(x94054,x94052,x94053,x94051)),f319(f164(x94051),x94053)))
% 22.40/22.30 [9476]~P1(f319(f319(f321(f912(f907(x94764),f907(x94764))),f319(f319(f244(f907(x94764),f907(x94764)),x94763),x94762)),f149(x94764,x94761)))+P1(f319(f319(f226(a906),f660(x94761,x94762,x94763,x94764)),f319(f182(f907(x94764)),x94763)))
% 22.40/22.30 [9477]~P69(x94771)+E(f319(f319(f74(x94771),f319(f319(f74(x94771),f319(f319(f75(x94771),f319(f319(f30(x94771),x94772),x94773)),x94773)),f39(x94771,x94772,x94773))),x94774),f319(f319(f74(x94771),x94772),x94774))
% 22.40/22.30 [9509]~P1(f319(f319(f321(f912(f907(x95091),f907(x95091))),f319(f319(f244(f907(x95091),f907(x95091)),x95092),x95093)),f319(f278(f907(x95091),f907(x95091)),f149(x95091,x95094))))+P1(f319(f319(f321(f912(f907(x95091),f907(x95091))),f319(f319(f244(f907(x95091),f907(x95091)),x95092),x95093)),f149(x95091,f319(f278(x95091,x95091),x95094))))
% 22.40/22.30 [9510]P1(f319(f319(f321(f912(f907(x95101),f907(x95101))),f319(f319(f244(f907(x95101),f907(x95101)),x95102),x95103)),f319(f278(f907(x95101),f907(x95101)),f149(x95101,x95104))))+~P1(f319(f319(f321(f912(f907(x95101),f907(x95101))),f319(f319(f244(f907(x95101),f907(x95101)),x95102),x95103)),f149(x95101,f319(f278(x95101,x95101),x95104))))
% 22.40/22.30 [9545]~P1(f319(f319(f321(x95451),x95453),f319(f256(x95451,x95452),x95454)))+P1(f319(f319(f321(f912(x95451,x95452)),f319(f319(f244(x95451,x95452),x95453),f561(x95454,x95452,x95453,x95451))),x95454))
% 22.40/22.30 [9546]~P1(f319(f319(f321(x95461),x95463),f319(f256(x95461,x95462),x95464)))+P1(f319(f319(f321(f912(x95461,x95462)),f319(f319(f244(x95461,x95462),x95463),f562(x95464,x95462,x95463,x95461))),x95464))
% 22.40/22.30 [9712]~P1(f319(f319(f321(f912(x97121,x97121)),f319(f319(f244(x97121,x97121),x97122),x97124)),f319(f319(f281(x97121,x97121,x97121),x97123),f299(x97121,x97123))))+P1(f319(f319(f321(f912(x97121,x97121)),f319(f319(f244(x97121,x97121),x97122),f626(x97123,x97124,x97122,x97121))),x97123))
% 22.40/22.30 [9891]P11(x98911,x98912,x98913,x98914)+P1(f319(f319(f321(f912(x98911,x98911)),f319(f319(f244(x98911,x98911),f821(x98912,x98914,x98913,x98911)),f820(x98912,x98914,x98913,x98911))),x98913))
% 22.40/22.30 [9905]~P1(f319(f319(f321(f912(x99052,x99051)),x99054),f319(f278(x99051,x99052),x99053)))+P1(f319(f319(f321(f912(x99051,x99052)),f319(f319(f244(x99051,x99052),f632(x99053,x99054,x99051,x99052)),f631(x99053,x99054,x99051,x99052))),x99053))
% 22.40/22.30 [9934]~P1(f319(f319(f321(f912(f907(x99341),f907(x99341))),f319(f319(f244(f907(x99341),f907(x99341)),x99344),x99343)),f149(x99341,x99342)))+P1(f319(f319(f321(f912(x99341,x99341)),f319(f319(f244(x99341,x99341),f676(x99342,x99343,x99344,x99341)),f677(x99342,x99343,x99344,x99341))),x99342))
% 22.40/22.30 [10016]~P1(f319(f319(f321(f912(f907(x100161),f907(x100161))),f319(f319(f244(f907(x100161),f907(x100161)),x100162),x100164)),f149(x100161,x100163)))+P1(f319(f319(f321(f912(x100161,x100161)),f319(f319(f244(x100161,x100161),f319(f319(f156(x100161),x100162),f660(x100163,x100164,x100162,x100161))),f661(x100163,x100164,x100162,x100161))),x100163))
% 22.40/22.30 [10035]~P1(f319(f55(x100352),x100354))+E(f319(f319(f319(f59(f913(x100351,a904),x100352,f93(f913(x100351,a904))),f319(f319(f9(x100352,f913(x100351,a904),f913(x100351,a904)),f319(f319(f10(x100351,f913(f913(x100351,a904),f913(x100351,a904)),x100352),f301(x100351)),x100353)),f181(f913(x100351,a904)))),f181(f913(x100351,a904))),x100354),f319(f302(x100352,x100351,x100353),x100354))
% 22.40/22.30 [10111]~P25(x101111,x101112,x101113,f234(f913(x101111,a904)))+P1(f319(f319(f225(f913(x101111,a904)),f319(f303(x101111,x101112,x101113),f319(f319(f301(x101112),x101114),f181(f913(x101112,a904))))),f319(f319(f301(x101111),f79(x101111,f319(f319(f9(x101111,x101112,a904),f319(f319(f10(x101112,f913(x101112,a904),x101111),a316),x101113)),x101114))),f181(f913(x101111,a904)))))
% 22.40/22.30 [5732]~E(f319(f319(f126(x57321),x57322),x57324),x57323)+E(f319(f319(f167(x57321),f319(f182(f907(x57321)),x57322)),x57323),x57322)
% 22.40/22.30 [5733]~E(f319(f319(f126(x57332),x57333),x57331),x57334)+E(x57331,f319(f319(f130(x57332),f319(f182(f907(x57332)),x57333)),x57334))
% 22.40/22.30 [5744]~E(x57444,f2(a906))+E(f319(f319(f156(x57441),f319(f319(f143(x57441),x57442),x57443)),x57444),x57442)
% 22.40/22.30 [6287]~P119(x62871)+E(f319(f319(f236(x62871),f319(f319(f236(x62871),x62872),x62873)),x62874),f319(f319(f236(x62871),x62872),f319(f319(f75(a906),x62873),x62874)))
% 22.40/22.30 [6288]~P87(x62881)+E(f319(f319(f236(x62881),f319(f319(f236(x62881),x62882),x62883)),x62884),f319(f319(f236(x62881),x62882),f319(f319(f75(a906),x62883),x62884)))
% 22.40/22.30 [6292]E(x62921,f2(a906))+E(f319(f319(f156(x62922),f319(f319(f143(x62922),x62923),x62924)),x62921),f319(f319(f156(x62922),x62924),f319(f319(f3(a906),x62921),f72(a906))))
% 22.40/22.30 [6321]~P120(x63211)+E(f319(f319(f282(x63211),f319(f319(f75(x63211),x63212),x63213)),x63214),f319(f319(f75(x63211),x63212),f319(f319(f282(x63211),x63213),x63214)))
% 22.40/22.30 [6322]~P101(x63221)+E(f319(f319(f93(x63221),f319(f319(f93(x63221),x63222),x63223)),x63224),f319(f319(f93(x63221),x63222),f319(f319(f93(x63221),x63223),x63224)))
% 22.40/22.30 [6324]~P106(x63241)+E(f319(f319(f93(x63241),f319(f319(f93(x63241),x63242),x63243)),x63244),f319(f319(f93(x63241),x63242),f319(f319(f93(x63241),x63243),x63244)))
% 22.40/22.30 [6325]~P101(x63251)+E(f319(f319(f94(x63251),f319(f319(f94(x63251),x63252),x63253)),x63254),f319(f319(f94(x63251),x63252),f319(f319(f94(x63251),x63253),x63254)))
% 22.40/22.30 [6327]~P107(x63271)+E(f319(f319(f94(x63271),f319(f319(f94(x63271),x63272),x63273)),x63274),f319(f319(f94(x63271),x63272),f319(f319(f94(x63271),x63273),x63274)))
% 22.40/22.30 [6329]~P4(x63291)+E(f319(f319(f180(x63291),f319(f319(f180(x63291),x63292),x63293)),x63294),f319(f319(f180(x63291),x63292),f319(f319(f180(x63291),x63293),x63294)))
% 22.40/22.30 [6331]~P4(x63311)+E(f319(f319(f230(x63311),f319(f319(f230(x63311),x63312),x63313)),x63314),f319(f319(f230(x63311),x63312),f319(f319(f230(x63311),x63313),x63314)))
% 22.40/22.30 [6332]~P78(x63321)+E(f319(f319(f74(x63321),f319(f319(f74(x63321),x63322),x63323)),x63324),f319(f319(f74(x63321),x63322),f319(f319(f74(x63321),x63323),x63324)))
% 22.40/22.30 [6333]~P119(x63331)+E(f319(f319(f74(x63331),f319(f319(f74(x63331),x63332),x63333)),x63334),f319(f319(f74(x63331),x63332),f319(f319(f74(x63331),x63333),x63334)))
% 22.40/22.30 [6334]~P77(x63341)+E(f319(f319(f75(x63341),f319(f319(f75(x63341),x63342),x63343)),x63344),f319(f319(f75(x63341),x63342),f319(f319(f75(x63341),x63343),x63344)))
% 22.40/22.30 [6335]~P119(x63351)+E(f319(f319(f75(x63351),f319(f319(f75(x63351),x63352),x63353)),x63354),f319(f319(f75(x63351),x63352),f319(f319(f75(x63351),x63353),x63354)))
% 22.40/22.30 [6345]~P69(x63451)+E(f39(x63451,f319(f319(f74(x63451),x63452),f319(f319(f75(x63451),x63453),x63454)),x63454),f39(x63451,x63452,x63454))
% 22.40/22.30 [6346]~P69(x63461)+E(f39(x63461,f319(f319(f74(x63461),x63462),f319(f319(f75(x63461),x63463),x63464)),x63463),f39(x63461,x63462,x63463))
% 22.40/22.30 [6481]E(f319(f319(f156(x64811),f319(f319(f167(x64811),x64812),x64813)),x64814),f319(f319(f156(x64811),x64813),x64814))+~P1(f319(f319(f226(a906),x64814),x64812))
% 22.40/22.30 [6657]~E(x66572,x66574)+P1(f319(f319(f164(x66571),f319(f319(f143(x66571),x66572),x66573)),x66574))
% 22.40/22.30 [6659]~P119(x66591)+E(f319(f319(f74(x66591),f319(f319(f74(x66591),x66592),x66593)),x66594),f319(f319(f74(x66591),f319(f319(f74(x66591),x66592),x66594)),x66593))
% 22.40/22.30 [6660]~P119(x66601)+E(f319(f319(f75(x66601),f319(f319(f75(x66601),x66602),x66603)),x66604),f319(f319(f75(x66601),f319(f319(f75(x66601),x66602),x66604)),x66603))
% 22.40/22.30 [6723]~P146(x67232)+E(f319(f319(f8(x67231,x67232),f319(f18(x67232,x67231),x67233)),x67234),f319(f319(f75(x67232),f319(f92(x67232),f319(f29(x67231),x67234))),x67233))
% 22.40/22.30 [6893]E(f319(f319(f94(f913(x68931,a904)),f319(f319(f301(x68931),x68932),x68933)),x68934),f319(f319(f94(f913(x68931,a904)),x68933),x68934))+P1(f319(f319(f321(x68931),x68932),x68934))
% 22.40/22.30 [6959]~P102(x69591)+E(f319(f319(f94(x69591),f319(f319(f93(x69591),x69592),x69593)),f319(f319(f93(x69591),x69594),x69593)),f319(f319(f93(x69591),f319(f319(f94(x69591),x69592),x69594)),x69593))
% 22.40/22.30 [6960]~P102(x69601)+E(f319(f319(f93(x69601),f319(f319(f94(x69601),x69602),x69603)),f319(f319(f94(x69601),x69604),x69603)),f319(f319(f94(x69601),f319(f319(f93(x69601),x69602),x69604)),x69603))
% 22.40/22.30 [6961]~P4(x69611)+E(f319(f319(f230(x69611),f319(f319(f180(x69611),x69612),x69613)),f319(f319(f180(x69611),x69614),x69613)),f319(f319(f180(x69611),f319(f319(f230(x69611),x69612),x69614)),x69613))
% 22.40/22.30 [6962]~P4(x69621)+E(f319(f319(f180(x69621),f319(f319(f230(x69621),x69622),x69623)),f319(f319(f230(x69621),x69624),x69623)),f319(f319(f230(x69621),f319(f319(f180(x69621),x69622),x69624)),x69623))
% 22.40/22.30 [6963]~P65(x69631)+E(f319(f319(f180(x69631),f319(f319(f3(x69631),x69632),x69633)),f319(f319(f3(x69631),x69634),x69633)),f319(f319(f3(x69631),f319(f319(f180(x69631),x69632),x69634)),x69633))
% 22.40/22.30 [6964]~P65(x69641)+E(f319(f319(f230(x69641),f319(f319(f3(x69641),x69642),x69643)),f319(f319(f3(x69641),x69644),x69643)),f319(f319(f3(x69641),f319(f319(f230(x69641),x69642),x69644)),x69643))
% 22.40/22.30 [6965]~P90(x69651)+E(f319(f319(f180(x69651),f319(f319(f74(x69651),x69652),x69653)),f319(f319(f74(x69651),x69654),x69653)),f319(f319(f74(x69651),f319(f319(f180(x69651),x69652),x69654)),x69653))
% 22.40/22.30 [6966]~P90(x69661)+E(f319(f319(f230(x69661),f319(f319(f74(x69661),x69662),x69663)),f319(f319(f74(x69661),x69664),x69663)),f319(f319(f74(x69661),f319(f319(f230(x69661),x69662),x69664)),x69663))
% 22.40/22.30 [6967]~P114(x69671)+E(f319(f319(f74(x69671),f319(f319(f75(x69671),x69672),x69673)),f319(f319(f75(x69671),x69674),x69673)),f319(f319(f75(x69671),f319(f319(f74(x69671),x69672),x69674)),x69673))
% 22.40/22.30 [6969]~P120(x69691)+E(f319(f319(f3(x69691),f319(f319(f282(x69691),x69692),x69693)),f319(f319(f282(x69691),x69694),x69693)),f319(f319(f282(x69691),f319(f319(f3(x69691),x69692),x69694)),x69693))
% 22.40/22.30 [6970]~P120(x69701)+E(f319(f319(f74(x69701),f319(f319(f282(x69701),x69702),x69703)),f319(f319(f282(x69701),x69704),x69703)),f319(f319(f282(x69701),f319(f319(f74(x69701),x69702),x69704)),x69703))
% 22.40/22.30 [6971]~P119(x69711)+E(f319(f319(f75(x69711),f319(f319(f236(x69711),x69712),x69713)),f319(f319(f236(x69711),x69714),x69713)),f319(f319(f236(x69711),f319(f319(f75(x69711),x69712),x69714)),x69713))
% 22.40/22.30 [6972]~P82(x69721)+E(f319(f319(f75(x69721),f319(f319(f236(x69721),x69722),x69723)),f319(f319(f236(x69721),x69724),x69723)),f319(f319(f236(x69721),f319(f319(f75(x69721),x69722),x69724)),x69723))
% 22.40/22.30 [6973]~P72(x69731)+E(f319(f319(f282(x69731),f319(f319(f236(x69731),x69732),x69733)),f319(f319(f236(x69731),x69734),x69733)),f319(f319(f236(x69731),f319(f319(f282(x69731),x69732),x69734)),x69733))
% 22.40/22.30 [6974]~P119(x69741)+E(f319(f319(f74(x69741),f319(f319(f75(x69741),x69742),x69743)),f319(f319(f75(x69741),x69744),x69743)),f319(f319(f75(x69741),f319(f319(f74(x69741),x69742),x69744)),x69743))
% 22.40/22.30 [7005]E(f319(f319(f151(x70051,x70052),x70053),x70054),x70052)+~P1(f319(f319(f225(a906),f319(f182(f907(x70051)),x70052)),x70053))
% 22.40/22.30 [7031]~P1(f319(x70313,x70314))+P1(f319(f319(f319(f93(f913(x70311,a904)),x70312),x70313),x70314))
% 22.40/22.30 [7033]~P1(f319(x70332,x70334))+P1(f319(f319(f319(f93(f913(x70331,a904)),x70332),x70333),x70334))
% 22.40/22.30 [7052]E(f319(f319(f156(x70521),f319(f319(f126(x70521),x70522),x70523)),x70524),f319(f319(f156(x70521),x70522),x70524))+~P1(f319(f319(f226(a906),x70524),f319(f182(f907(x70521)),x70522)))
% 22.40/22.30 [7063]E(f319(f319(f3(f913(x70631,a904)),f319(f319(f301(x70631),x70632),x70633)),x70634),f319(f319(f3(f913(x70631,a904)),x70633),x70634))+~P1(f319(f319(f321(x70631),x70632),x70634))
% 22.40/22.30 [7106]~E(f131(a906,f319(f294(a906,x71061),x71062)),f319(f319(f143(a906),x71064),x71063))+E(f131(a906,f319(f294(a906,f319(f319(f74(a906),x71061),f72(a906))),x71062)),x71063)
% 22.40/22.30 [7128]~P1(f319(f319(f164(x71281),x71283),x71284))+P1(f319(f319(f164(x71281),f319(f319(f143(x71281),x71282),x71283)),x71284))
% 22.40/22.30 [7177]E(x71771,f2(a906))+E(f319(f319(f143(x71772),x71773),f319(f319(f167(x71772),f319(f319(f3(a906),x71771),f72(a906))),x71774)),f319(f319(f167(x71772),x71771),f319(f319(f143(x71772),x71773),x71774)))
% 22.40/22.30 [7276]E(f319(f319(f156(x72761),x72762),f319(f319(f3(a906),x72763),f319(f182(f907(x72761)),x72764))),f319(f319(f156(x72761),f319(f319(f126(x72761),x72764),x72762)),x72763))+P1(f319(f319(f226(a906),x72763),f319(f182(f907(x72761)),x72764)))
% 22.40/22.30 [7305]E(f319(f319(f94(f913(x73051,a904)),x73052),f319(f319(f301(x73051),x73053),x73054)),f319(f319(f301(x73051),x73053),f319(f319(f94(f913(x73051,a904)),x73052),x73054)))+~P1(f319(f319(f321(x73051),x73053),x73052))
% 22.40/22.30 [7343]E(f319(f319(f156(x73431),f319(f319(f151(x73431,x73432),x73433),x73434)),x73433),x73434)+~P1(f319(f319(f226(a906),x73433),f319(f182(f907(x73431)),x73432)))
% 22.40/22.30 [7365]E(x73651,f181(f913(x73652,a904)))+E(f319(f302(f912(x73653,x73652),x73653,f243(x73653,x73652)),f319(f319(f246(x73653,x73652),x73654),f319(f18(f913(x73652,a904),x73653),x73651))),x73654)
% 22.40/22.30 [7366]E(x73661,f181(f913(x73662,a904)))+E(f319(f302(f912(x73662,x73663),x73663,f248(x73662,x73663)),f319(f319(f246(x73662,x73663),x73661),f319(f18(f913(x73663,a904),x73662),x73664))),x73664)
% 22.40/22.30 [7437]E(f319(f319(f3(f913(x74371,a904)),f319(f319(f301(x74371),x74372),x74373)),x74374),f319(f319(f301(x74371),x74372),f319(f319(f3(f913(x74371,a904)),x74373),x74374)))+P1(f319(f319(f321(x74371),x74372),x74374))
% 22.40/22.30 [7466]~E(x74664,f181(f913(x74662,a904)))+E(f319(f302(f912(x74661,x74662),x74661,f243(x74661,x74662)),f319(f319(f246(x74661,x74662),x74663),f319(f18(f913(x74662,a904),x74661),x74664))),f181(f913(x74661,a904)))
% 22.40/22.30 [7467]~E(x74673,f181(f913(x74671,a904)))+E(f319(f302(f912(x74671,x74672),x74672,f248(x74671,x74672)),f319(f319(f246(x74671,x74672),x74673),f319(f18(f913(x74672,a904),x74671),x74674))),f181(f913(x74672,a904)))
% 22.40/22.30 [7519]~P1(f319(f319(f321(x75191),x75192),x75194))+P1(f319(f319(f321(x75191),x75192),f319(f319(f93(f913(x75191,a904)),x75193),x75194)))
% 22.40/22.30 [7522]~P1(f319(f319(f321(x75221),x75222),x75223))+P1(f319(f319(f321(x75221),x75222),f319(f319(f93(f913(x75221,a904)),x75223),x75224)))
% 22.40/22.30 [7540]E(f319(f319(f94(f913(x75401,a904)),f319(f319(f301(x75401),x75402),x75403)),x75404),f319(f319(f301(x75401),x75402),f319(f319(f94(f913(x75401,a904)),x75403),x75404)))+~P1(f319(f319(f321(x75401),x75402),x75404))
% 22.40/22.30 [7807]P1(f319(x78071,x78072))+~P1(f319(f319(f319(f94(f913(x78073,a904)),x78074),x78071),x78072))
% 22.40/22.30 [7808]P1(f319(x78081,x78082))+~P1(f319(f319(f319(f94(f913(x78083,a904)),x78081),x78084),x78082))
% 22.40/22.30 [7809]E(f319(f319(f8(x78091,a906),x78092),f319(f319(f3(f913(x78091,a904)),x78093),f319(f319(f301(x78091),x78094),f181(f913(x78091,a904))))),f319(f319(f8(x78091,a906),x78092),x78093))+P1(f319(f319(f321(x78091),x78094),x78093))
% 22.40/22.30 [7814]~P76(x78141)+E(f319(f157(x78141),f319(f319(f146(a906,x78141),x78142),f131(a906,f319(f294(a906,x78143),x78144)))),f319(f319(f8(a906,x78141),x78142),f319(f164(a906),f131(a906,f319(f294(a906,x78143),x78144)))))
% 22.40/22.30 [7815]~P76(x78151)+E(f319(f319(f8(a906,x78151),x78152),f319(f164(a906),f131(a906,f319(f294(a906,x78153),x78154)))),f319(f157(x78151),f319(f319(f146(a906,x78151),x78152),f131(a906,f319(f294(a906,x78153),x78154)))))
% 22.40/22.30 [7931]~E(x79313,x79314)+P1(f319(f56(x79311,x79312,f319(f319(f301(x79311),x79313),f181(f913(x79311,a904)))),x79314))
% 22.40/22.30 [8024]P1(f319(f319(f321(x80241),x80242),f319(f164(x80241),x80243)))+~P1(f319(f319(f321(x80241),x80242),f319(f164(x80241),f319(f319(f167(x80241),x80244),x80243))))
% 22.40/22.30 [8025]P1(f319(f319(f321(x80251),x80252),f319(f164(x80251),x80253)))+~P1(f319(f319(f321(x80251),x80252),f319(f164(x80251),f319(f319(f130(x80251),x80254),x80253))))
% 22.40/22.30 [8089]P1(f319(f319(f321(x80891),x80892),x80893))+~P1(f319(f319(f321(x80891),x80892),f319(f319(f94(f913(x80891,a904)),x80894),x80893)))
% 22.40/22.30 [8092]P1(f319(f319(f321(x80921),x80922),x80923))+~P1(f319(f319(f321(x80921),x80922),f319(f319(f94(f913(x80921,a904)),x80923),x80924)))
% 22.40/22.30 [8095]P1(f319(f319(f321(x80951),x80952),x80953))+~P1(f319(f319(f321(x80951),x80952),f319(f319(f3(f913(x80951,a904)),x80953),x80954)))
% 22.40/22.30 [8110]E(f319(f319(f126(x81101),f319(f319(f167(x81101),x81102),x81103)),f319(f319(f143(x81101),x81104),f319(f319(f130(x81101),f319(a104,x81102)),x81103))),f319(f319(f151(x81101,x81103),x81102),x81104))+~P1(f319(f319(f226(a906),x81102),f319(f182(f907(x81101)),x81103)))
% 22.40/22.30 [8133]P1(f319(f319(f321(x81331),x81332),x81333))+~P1(f319(f319(f225(f913(x81331,a904)),f319(f319(f301(x81331),x81332),x81334)),x81333))
% 22.40/22.30 [8175]~P1(f319(f319(f321(x81751),x81752),x81753))+~P1(f319(f319(f321(x81751),x81752),f319(f319(f3(f913(x81751,a904)),x81754),x81753)))
% 22.40/22.30 [8204]~P1(f319(f319(f226(a906),x82044),f319(f182(f907(x82041)),x82043)))+P1(f319(f319(f321(x82041),x82042),f319(f164(x82041),f319(f319(f151(x82041,x82043),x82044),x82042))))
% 22.40/22.30 [8257]E(f319(f319(f156(x82571),f319(f319(f130(x82571),x82572),x82573)),x82574),f319(f319(f156(x82571),x82573),f319(f319(f74(a906),x82572),x82574)))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),x82572),x82574)),f319(f182(f907(x82571)),x82573)))
% 22.40/22.30 [8266]~P146(x82662)+E(f319(f319(f8(x82661,x82662),f319(f319(f10(a906,x82662,x82661),f92(x82662)),x82663)),x82664),f319(f92(x82662),f319(f319(f8(x82661,a906),x82663),x82664)))
% 22.40/22.30 [8267]~P141(x82672)+E(f319(f319(f8(x82671,x82672),f319(f319(f10(a1,x82672,x82671),f95(x82672)),x82673)),x82674),f319(f95(x82672),f319(f319(f8(x82671,a1),x82673),x82674)))
% 22.40/22.30 [8316]~P75(x83162)+E(f319(f319(f11(x83161,x83162),f319(f319(f10(x83162,x83162,x83161),f69(x83162)),x83163)),x83164),f319(f69(x83162),f319(f319(f11(x83161,x83162),x83163),x83164)))
% 22.40/22.30 [8317]~P67(x83172)+E(f319(f319(f8(x83171,x83172),f319(f319(f10(x83172,x83172,x83171),f73(x83172)),x83173)),x83174),f319(f73(x83172),f319(f319(f8(x83171,x83172),x83173),x83174)))
% 22.40/22.30 [8319]E(f319(f319(f8(x83191,a906),x83192),f319(f319(f3(f913(x83191,a904)),x83193),f319(f319(f301(x83191),x83194),f181(f913(x83191,a904))))),f319(f319(f3(a906),f319(f319(f8(x83191,a906),x83192),x83193)),f319(x83192,x83194)))+~P1(f319(f319(f321(x83191),x83194),x83193))
% 22.40/22.30 [8337]P1(f319(f319(f225(f913(x83371,a904)),x83372),x83373))+~P1(f319(f319(f225(f913(x83371,a904)),f319(f319(f301(x83371),x83374),x83372)),x83373))
% 22.40/22.30 [8459]~E(f319(f302(x84592,x84593,x84591),f234(f913(x84592,a904))),f234(f913(x84593,a904)))+E(f319(x84591,f319(f85(x84592,x84593,f234(f913(x84592,a904)),x84591),x84594)),x84594)
% 22.40/22.30 [8542]P37(x85421,x85422)+~P37(x85421,f319(f319(f301(f912(x85421,x85421)),f319(f319(f244(x85421,x85421),x85423),x85424)),x85422))
% 22.40/22.30 [8543]P59(x85431,x85432)+~P59(x85431,f319(f319(f301(f912(x85431,x85431)),f319(f319(f244(x85431,x85431),x85433),x85434)),x85432))
% 22.40/22.30 [8548]~P4(x85481)+E(f319(f319(f140(x85481,x85481,f7(x85481)),x85482),f319(f319(f140(x85481,x85481,f7(x85481)),x85483),x85484)),f319(f319(f140(x85481,x85481,f7(x85481)),x85483),f319(f319(f140(x85481,x85481,f7(x85481)),x85482),x85484)))
% 22.40/22.30 [8563]E(x85631,x85632)+~P1(f319(f56(x85633,x85634,f319(f319(f301(x85633),x85631),f181(f913(x85633,a904)))),x85632))
% 22.40/22.30 [8574]E(f319(f319(f126(x85741),f319(f319(f167(x85741),x85742),x85743)),f319(f319(f167(x85741),x85744),f319(f319(f130(x85741),x85742),x85743))),f319(f319(f167(x85741),f319(f319(f74(a906),x85742),x85744)),x85743))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),x85742),x85744)),f319(f182(f907(x85741)),x85743)))
% 22.40/22.30 [8610]P1(f319(f55(x86101),x86102))+~E(x86102,f319(f302(a906,x86101,x86103),f319(f254(a906),f319(f319(f9(a906,a906,a904),f226(a906)),x86104))))
% 22.40/22.30 [8634]~P95(x86341)+E(f319(f134(x86341,x86341,f74(x86341),f319(f319(f74(x86341),x86342),x86343)),x86344),f319(f319(f74(x86341),x86342),f319(f134(x86341,x86341,f74(x86341),x86343),x86344)))
% 22.40/22.30 [8670]P1(f319(f319(f225(f913(x86701,a904)),f319(f256(x86701,x86702),x86703)),f319(f256(x86701,x86702),x86704)))+~P1(f319(f319(f225(f913(f912(x86701,x86702),a904)),x86703),x86704))
% 22.40/22.30 [8682]~P1(f319(f319(f225(a906),x86822),x86824))+P1(f319(f319(f225(f913(x86821,a904)),f319(f164(x86821),f319(f319(f167(x86821),x86822),x86823))),f319(f164(x86821),f319(f319(f167(x86821),x86824),x86823))))
% 22.40/22.30 [8683]~P1(f319(f319(f225(a906),x86834),x86832))+P1(f319(f319(f225(f913(x86831,a904)),f319(f164(x86831),f319(f319(f130(x86831),x86832),x86833))),f319(f164(x86831),f319(f319(f130(x86831),x86834),x86833))))
% 22.40/22.30 [8740]~P1(f319(f55(x87401),f319(f319(f3(f913(x87401,a904)),x87402),x87404)))+P1(f319(f55(x87401),f319(f319(f3(f913(x87401,a904)),x87402),f319(f319(f301(x87401),x87403),x87404))))
% 22.40/22.30 [8777]P1(f319(f319(f321(f912(x87771,x87771)),x87772),f299(x87771,x87773)))+~P1(f319(f319(f321(f912(x87771,x87771)),x87772),f319(f319(f175(f912(x87771,x87771),a904),x87774),x87773)))
% 22.40/22.30 [8856]~P1(f319(f55(x88561),f319(f319(f3(f913(x88561,a904)),x88562),f319(f319(f301(x88561),x88564),x88563))))+P1(f319(f55(x88561),f319(f319(f3(f913(x88561,a904)),x88562),x88563)))
% 22.40/22.30 [9083]~P101(x90831)+P1(f319(f319(f225(x90831),f319(f319(f93(x90831),x90832),f319(f319(f94(x90831),x90833),x90834))),f319(f319(f94(x90831),f319(f319(f93(x90831),x90832),x90833)),f319(f319(f93(x90831),x90832),x90834))))
% 22.40/22.30 [9084]~P4(x90841)+P1(f319(f319(f225(x90841),f319(f319(f180(x90841),x90842),f319(f319(f230(x90841),x90843),x90844))),f319(f319(f230(x90841),f319(f319(f180(x90841),x90842),x90843)),f319(f319(f180(x90841),x90842),x90844))))
% 22.40/22.30 [9220]E(x92201,x92202)+~P1(f319(f319(f321(f912(x92203,x92203)),f319(f319(f244(x92203,x92203),x92201),x92202)),f319(f164(f912(x92203,x92203)),f319(f319(f173(x92203,x92203),x92204),x92204))))
% 22.40/22.30 [9253]~P1(f319(f319(f321(f912(x92531,x92531)),f319(f319(f244(x92531,x92531),x92533),x92532)),f299(x92531,x92534)))+~P37(x92531,f319(f319(f301(f912(x92531,x92531)),f319(f319(f244(x92531,x92531),x92532),x92533)),x92534))
% 22.40/22.30 [9254]~P1(f319(f319(f321(f912(x92541,x92541)),f319(f319(f244(x92541,x92541),x92543),x92542)),f299(x92541,x92544)))+~P59(x92541,f319(f319(f301(f912(x92541,x92541)),f319(f319(f244(x92541,x92541),x92542),x92543)),x92544))
% 22.40/22.30 [9264]E(x92641,x92642)+E(f319(f128(x92643,f319(f319(f10(a904,a904,x92643),a314),f319(a316,x92641))),f319(f319(f143(x92643),x92642),x92644)),f319(f319(f143(x92643),x92642),f319(f128(x92643,f319(f319(f10(a904,a904,x92643),a314),f319(a316,x92641))),x92644)))
% 22.40/22.30 [9295]~P26(x92952,x92951,x92953,f234(f913(x92952,a904)),f234(f913(x92951,a904)))+E(f319(f302(x92951,x92952,f85(x92952,x92951,f234(f913(x92952,a904)),x92953)),x92954),f319(f303(x92952,x92951,x92953),x92954))
% 22.40/22.30 [9311]~P101(x93111)+P1(f319(f319(f225(x93111),f319(f319(f93(x93111),f319(f319(f94(x93111),x93112),x93113)),f319(f319(f94(x93111),x93112),x93114))),f319(f319(f94(x93111),x93112),f319(f319(f93(x93111),x93113),x93114))))
% 22.40/22.30 [9312]~P4(x93121)+P1(f319(f319(f225(x93121),f319(f319(f180(x93121),f319(f319(f230(x93121),x93122),x93123)),f319(f319(f230(x93121),x93122),x93124))),f319(f319(f230(x93121),x93122),f319(f319(f180(x93121),x93123),x93124))))
% 22.40/22.30 [9373]~P26(x93732,x93731,x93734,f234(f913(x93732,a904)),f234(f913(x93731,a904)))+E(f319(f254(x93731),f319(f319(f10(x93732,a904,x93731),x93733),f85(x93732,x93731,f234(f913(x93732,a904)),x93734))),f319(f302(x93732,x93731,x93734),f319(f254(x93732),x93733)))
% 22.40/22.30 [9387]~E(f319(f302(x93872,x93871,x93873),f234(f913(x93872,a904))),f234(f913(x93871,a904)))+P1(f319(f319(f225(f913(x93871,a904)),f319(f73(f913(x93871,a904)),f319(f302(x93872,x93871,x93873),x93874))),f319(f302(x93872,x93871,x93873),f319(f73(f913(x93872,a904)),x93874))))
% 22.40/22.30 [9731]P1(f319(f319(f321(f912(x97311,x97311)),f319(f319(f244(x97311,x97311),x97312),x97313)),f319(f278(x97311,x97311),f319(f319(f281(x97311,x97311,x97311),x97314),f299(x97311,x97314)))))+~P1(f319(f319(f321(f912(x97311,x97311)),f319(f319(f244(x97311,x97311),x97312),x97313)),f319(f319(f281(x97311,x97311,x97311),f319(f278(x97311,x97311),x97314)),f299(x97311,f319(f278(x97311,x97311),x97314)))))
% 22.40/22.30 [9733]~P1(f319(f319(f321(f912(x97331,x97331)),f319(f319(f244(x97331,x97331),x97332),x97333)),f319(f278(x97331,x97331),f319(f319(f281(x97331,x97331,x97331),x97334),f299(x97331,x97334)))))+P1(f319(f319(f321(f912(x97331,x97331)),f319(f319(f244(x97331,x97331),x97332),x97333)),f319(f319(f281(x97331,x97331,x97331),f319(f278(x97331,x97331),x97334)),f299(x97331,f319(f278(x97331,x97331),x97334)))))
% 22.40/22.30 [9754]~P1(f319(f319(f321(x97542),x97544),f319(f276(x97541,x97542),x97543)))+P1(f319(f319(f321(f912(x97541,x97542)),f319(f319(f244(x97541,x97542),f554(x97543,x97541,x97544,x97542)),x97544)),x97543))
% 22.40/22.30 [9755]~P1(f319(f319(f321(x97552),x97554),f319(f276(x97551,x97552),x97553)))+P1(f319(f319(f321(f912(x97551,x97552)),f319(f319(f244(x97551,x97552),f555(x97553,x97551,x97554,x97552)),x97554)),x97553))
% 22.40/22.30 [9789]~P1(f319(f319(f321(x97891),x97894),f319(f319(f93(f913(x97891,a904)),x97892),x97893)))+P1(f319(f319(f319(f93(f913(x97891,a904)),f319(f319(f9(x97891,f913(x97891,a904),a904),f321(x97891)),x97892)),f319(f319(f9(x97891,f913(x97891,a904),a904),f321(x97891)),x97893)),x97894))
% 22.40/22.30 [9790]~P1(f319(f319(f321(x97901),x97904),f319(f319(f94(f913(x97901,a904)),x97902),x97903)))+P1(f319(f319(f319(f94(f913(x97901,a904)),f319(f319(f9(x97901,f913(x97901,a904),a904),f321(x97901)),x97902)),f319(f319(f9(x97901,f913(x97901,a904),a904),f321(x97901)),x97903)),x97904))
% 22.40/22.30 [9870]~P1(f319(f319(f321(f912(x98701,x98701)),f319(f319(f244(x98701,x98701),x98704),x98703)),f319(f319(f281(x98701,x98701,x98701),x98702),f299(x98701,x98702))))+P1(f319(f319(f321(f912(x98701,x98701)),f319(f319(f244(x98701,x98701),f627(x98702,x98703,x98704,x98701)),x98703)),x98702))
% 22.40/22.30 [9918]P1(f319(f319(f321(x99181),x99182),f319(f319(f93(f913(x99181,a904)),x99183),x99184)))+~P1(f319(f319(f319(f93(f913(x99181,a904)),f319(f319(f9(x99181,f913(x99181,a904),a904),f321(x99181)),x99183)),f319(f319(f9(x99181,f913(x99181,a904),a904),f321(x99181)),x99184)),x99182))
% 22.40/22.30 [9919]P1(f319(f319(f321(x99191),x99192),f319(f319(f94(f913(x99191,a904)),x99193),x99194)))+~P1(f319(f319(f319(f94(f913(x99191,a904)),f319(f319(f9(x99191,f913(x99191,a904),a904),f321(x99191)),x99193)),f319(f319(f9(x99191,f913(x99191,a904),a904),f321(x99191)),x99194)),x99192))
% 22.40/22.30 [10162]P32(x101621,f319(f319(f9(x101621,f913(f912(x101621,x101621),a904),f913(x101621,a904)),f319(f319(f10(f913(x101621,f913(f913(f912(x101621,x101621),a904),a904)),f913(f913(f912(x101621,x101621),a904),f913(x101621,a904)),x101621),f9(x101621,f913(f912(x101621,x101621),a904),a904)),f319(f319(f10(f913(x101621,f912(x101621,x101621)),f913(x101621,f913(f913(f912(x101621,x101621),a904),a904)),x101621),f319(f10(f912(x101621,x101621),f913(f913(f912(x101621,x101621),a904),a904),x101621),f321(f912(x101621,x101621)))),f244(x101621,x101621)))),x101622),x101623,x101624)+~P1(f319(f319(f321(f912(f907(x101621),f907(x101621))),f319(f319(f244(f907(x101621),f907(x101621)),x101623),x101624)),f150(x101621,x101622)))
% 22.40/22.30 [10166]P60(x101661,f319(f319(f9(x101661,f913(f912(x101661,x101661),a904),f913(x101661,a904)),f319(f319(f10(f913(x101661,f913(f913(f912(x101661,x101661),a904),a904)),f913(f913(f912(x101661,x101661),a904),f913(x101661,a904)),x101661),f9(x101661,f913(f912(x101661,x101661),a904),a904)),f319(f319(f10(f913(x101661,f912(x101661,x101661)),f913(x101661,f913(f913(f912(x101661,x101661),a904),a904)),x101661),f319(f10(f912(x101661,x101661),f913(f913(f912(x101661,x101661),a904),a904),x101661),f321(f912(x101661,x101661)))),f244(x101661,x101661)))),x101662),x101663,x101664)+~P1(f319(f319(f321(f912(f913(x101661,a904),f913(x101661,a904))),f319(f319(f244(f913(x101661,a904),f913(x101661,a904)),x101663),x101664)),f311(x101661,x101662)))
% 22.40/22.30 [10198]E(x101981,x101982)+~E(f319(f319(f9(x101983,f913(f912(x101983,x101984),a904),f913(x101984,a904)),f319(f319(f10(f913(x101984,f913(f913(f912(x101983,x101984),a904),a904)),f913(f913(f912(x101983,x101984),a904),f913(x101984,a904)),x101983),f9(x101984,f913(f912(x101983,x101984),a904),a904)),f319(f319(f10(f913(x101984,f912(x101983,x101984)),f913(x101984,f913(f913(f912(x101983,x101984),a904),a904)),x101983),f319(f10(f912(x101983,x101984),f913(f913(f912(x101983,x101984),a904),a904),x101984),f321(f912(x101983,x101984)))),f244(x101983,x101984)))),x101981),f319(f319(f9(x101983,f913(f912(x101983,x101984),a904),f913(x101984,a904)),f319(f319(f10(f913(x101984,f913(f913(f912(x101983,x101984),a904),a904)),f913(f913(f912(x101983,x101984),a904),f913(x101984,a904)),x101983),f9(x101984,f913(f912(x101983,x101984),a904),a904)),f319(f319(f10(f913(x101984,f912(x101983,x101984)),f913(x101984,f913(f913(f912(x101983,x101984),a904),a904)),x101983),f319(f10(f912(x101983,x101984),f913(f913(f912(x101983,x101984),a904),a904),x101984),f321(f912(x101983,x101984)))),f244(x101983,x101984)))),x101982))
% 22.40/22.30 [10201]~P32(x102011,f319(f319(f9(x102011,f913(f912(x102011,x102011),a904),f913(x102011,a904)),f319(f319(f10(f913(x102011,f913(f913(f912(x102011,x102011),a904),a904)),f913(f913(f912(x102011,x102011),a904),f913(x102011,a904)),x102011),f9(x102011,f913(f912(x102011,x102011),a904),a904)),f319(f319(f10(f913(x102011,f912(x102011,x102011)),f913(x102011,f913(f913(f912(x102011,x102011),a904),a904)),x102011),f319(f10(f912(x102011,x102011),f913(f913(f912(x102011,x102011),a904),a904),x102011),f321(f912(x102011,x102011)))),f244(x102011,x102011)))),x102014),x102012,x102013)+P1(f319(f319(f321(f912(f907(x102011),f907(x102011))),f319(f319(f244(f907(x102011),f907(x102011)),x102012),x102013)),f150(x102011,x102014)))
% 22.40/22.30 [10202]~P60(x102021,f319(f319(f9(x102021,f913(f912(x102021,x102021),a904),f913(x102021,a904)),f319(f319(f10(f913(x102021,f913(f913(f912(x102021,x102021),a904),a904)),f913(f913(f912(x102021,x102021),a904),f913(x102021,a904)),x102021),f9(x102021,f913(f912(x102021,x102021),a904),a904)),f319(f319(f10(f913(x102021,f912(x102021,x102021)),f913(x102021,f913(f913(f912(x102021,x102021),a904),a904)),x102021),f319(f10(f912(x102021,x102021),f913(f913(f912(x102021,x102021),a904),a904),x102021),f321(f912(x102021,x102021)))),f244(x102021,x102021)))),x102024),x102022,x102023)+P1(f319(f319(f321(f912(f913(x102021,a904),f913(x102021,a904))),f319(f319(f244(f913(x102021,a904),f913(x102021,a904)),x102022),x102023)),f311(x102021,x102024)))
% 22.40/22.30 [7590]~P98(x75901)+E(f319(f319(f74(x75901),f319(f96(x75901),x75902)),f319(f319(f3(x75901),f319(f96(x75901),x75903)),x75904)),f319(f319(f3(x75901),f319(f96(x75901),f319(f319(f74(a1),x75902),x75903))),x75904))
% 22.40/22.30 [7591]~P98(x75911)+E(f319(f319(f74(x75911),f319(f96(x75911),x75912)),f319(f319(f74(x75911),f319(f96(x75911),x75913)),x75914)),f319(f319(f74(x75911),f319(f96(x75911),f319(f319(f74(a1),x75912),x75913))),x75914))
% 22.40/22.30 [7592]~P98(x75921)+E(f319(f319(f75(x75921),f319(f96(x75921),x75922)),f319(f319(f75(x75921),f319(f96(x75921),x75923)),x75924)),f319(f319(f75(x75921),f319(f96(x75921),f319(f319(f75(a1),x75922),x75923))),x75924))
% 22.40/22.30 [7631]~P146(x76311)+E(f319(f157(x76311),f319(f319(f146(x76312,x76311),f319(f18(x76311,x76312),x76313)),x76314)),f319(f319(f75(x76311),f319(f92(x76311),f319(f182(f907(x76312)),x76314))),x76313))
% 22.40/22.30 [7863]E(f319(f260(x78631,f319(f319(f143(f912(a91,x78631)),x78632),x78633)),x78634),f319(f248(a91,x78631),x78632))+~P1(f319(f319(f226(a91),x78634),f319(f243(a91,x78631),x78632)))
% 22.40/22.30 [7907]~P98(x79071)+E(f319(f319(f74(x79071),f319(f96(x79071),x79072)),f319(f319(f3(x79071),x79073),f319(f96(x79071),x79074))),f319(f319(f74(x79071),f319(f96(x79071),f319(f319(f74(a1),x79072),f319(f73(a1),x79074)))),x79073))
% 22.40/22.30 [8034]E(f319(f260(x80341,x80342),f319(f319(f3(a91),x80343),f319(f243(a91,x80341),x80344))),f319(f260(x80341,f319(f319(f143(f912(a91,x80341)),x80344),x80342)),x80343))+P1(f319(f319(f226(a91),x80343),f319(f243(a91,x80341),x80344)))
% 22.40/22.30 [8465]~P1(f319(f319(f321(x84651),x84652),f319(f164(x84651),f106(x84651,x84654))))+P1(f319(f319(f321(x84651),x84652),f319(f164(x84651),f106(x84651,f319(f319(f126(x84651),x84653),x84654)))))
% 22.40/22.30 [8466]~P1(f319(f319(f321(x84661),x84662),f319(f164(x84661),f106(x84661,x84663))))+P1(f319(f319(f321(x84661),x84662),f319(f164(x84661),f106(x84661,f319(f319(f126(x84661),x84663),x84664)))))
% 22.40/22.30 [8484]E(f319(f319(f93(f913(x84841,a904)),f319(f319(f94(f913(x84841,a904)),x84842),x84843)),x84844),f319(f319(f94(f913(x84841,a904)),x84842),f319(f319(f93(f913(x84841,a904)),x84843),x84844)))+~P1(f319(f319(f225(f913(x84841,a904)),x84844),x84842))
% 22.40/22.30 [8789]~E(f319(f319(f93(f913(x87891,a904)),f319(f319(f94(f913(x87891,a904)),x87893),x87894)),x87892),f319(f319(f94(f913(x87891,a904)),x87893),f319(f319(f93(f913(x87891,a904)),x87894),x87892)))+P1(f319(f319(f225(f913(x87891,a904)),x87892),x87893))
% 22.40/22.30 [9088]~P1(f319(f319(f225(f913(x90881,a904)),x90882),f319(f319(f93(f913(x90881,a904)),x90883),x90884)))+P1(f319(f319(f225(f913(x90881,a904)),f319(f319(f3(f913(x90881,a904)),x90882),x90883)),x90884))
% 22.40/22.30 [9192]~E(f319(f302(x91921,x91922,x91923),f234(f913(x91921,a904))),f234(f913(x91922,a904)))+E(f319(f302(x91921,x91922,x91923),f319(f302(x91922,x91921,f85(x91921,x91922,f234(f913(x91921,a904)),x91923)),x91924)),x91924)
% 22.40/22.30 [9196]P1(f319(f319(f225(f913(x91961,a904)),x91962),f319(f319(f93(f913(x91961,a904)),x91963),x91964)))+~P1(f319(f319(f225(f913(x91961,a904)),f319(f319(f3(f913(x91961,a904)),x91962),x91963)),x91964))
% 22.40/22.30 [9291]~P92(x92911)+E(f319(f69(x92911),f319(f319(f8(x92912,x92911),f319(f319(f10(x92911,x92911,x92912),f69(x92911)),x92913)),x92914)),f319(f319(f8(x92912,x92911),f319(f319(f10(x92911,x92911,x92912),f69(x92911)),x92913)),x92914))
% 22.40/22.30 [9467]~P92(x94671)+P1(f319(f319(f225(x94671),f2(x94671)),f319(f319(f8(x94672,x94671),f319(f319(f10(x94671,x94671,x94672),f69(x94671)),x94673)),x94674)))
% 22.40/22.30 [9471]~P67(x94711)+E(f319(f157(x94711),f319(f319(f146(x94712,x94711),f319(f66(x94711,x94711,x94712,f73(x94711)),x94713)),x94714)),f319(f73(x94711),f319(f157(x94711),f319(f319(f146(x94712,x94711),x94713),x94714))))
% 22.40/22.30 [9609]~P92(x96091)+P1(f319(f319(f225(x96091),f319(f69(x96091),f319(f319(f8(x96092,x96091),x96093),x96094))),f319(f319(f8(x96092,x96091),f319(f319(f10(x96091,x96091,x96092),f69(x96091)),x96093)),x96094)))
% 22.40/22.30 [9650]~E(f319(f319(f74(a906),x96501),x96504),f319(f319(f74(a906),x96503),x96502))+P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),f319(f319(f244(a906,a906),x96501),x96502)),f319(f319(f244(a906,a906),x96503),x96504))),a101))
% 22.40/22.30 [9651]~P1(f319(f319(f226(a906),x96511),x96513))+P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),f319(f319(f244(a906,a906),x96511),x96512)),f319(f319(f244(a906,a906),x96513),x96514))),a26))
% 22.40/22.30 [9652]~P1(f319(f319(f226(a906),x96521),x96523))+P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),f319(f319(f244(a906,a906),x96521),x96522)),f319(f319(f244(a906,a906),x96523),x96524))),a64))
% 22.40/22.30 [9812]E(f319(f319(f74(a906),x98121),x98122),f319(f319(f74(a906),x98123),x98124))+~P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),f319(f319(f244(a906,a906),x98121),x98124)),f319(f319(f244(a906,a906),x98123),x98122))),a101))
% 22.40/22.30 [9844]E(f319(f319(f156(x98441),f319(f319(f130(x98441),f319(f182(f907(x98441)),f169(x98441,x98442,x98443))),x98443)),x98444),f319(f319(f156(x98441),x98443),f319(f319(f74(a906),x98444),f319(f182(f907(x98441)),f169(x98441,x98442,x98443)))))+~P1(f319(f319(f226(a906),x98444),f319(f182(f907(x98441)),f319(f319(f130(x98441),f319(f182(f907(x98441)),f169(x98441,x98442,x98443))),x98443))))
% 22.40/22.30 [9861]~P1(f319(f319(f321(x98612),x98614),f319(f319(f33(x98611,f913(x98612,a904)),f234(f913(x98611,a904))),x98613)))+P1(f319(f319(f319(f33(x98611,f913(x98612,a904)),f234(f913(x98611,a904))),f319(f319(f10(f913(x98612,a904),f913(x98612,a904),x98611),f319(f9(x98612,f913(x98612,a904),a904),f321(x98612))),x98613)),x98614))
% 22.40/22.30 [9862]~P1(f319(f319(f321(x98622),x98624),f319(f319(f34(x98621,f913(x98622,a904)),f234(f913(x98621,a904))),x98623)))+P1(f319(f319(f319(f34(x98621,f913(x98622,a904)),f234(f913(x98621,a904))),f319(f319(f10(f913(x98622,a904),f913(x98622,a904),x98621),f319(f9(x98622,f913(x98622,a904),a904),f321(x98622))),x98623)),x98624))
% 22.40/22.30 [9946]~P1(f319(f43(x99461,x99462),f319(f319(f244(a1,a1),x99464),x99463)))+P1(f319(f43(f319(f73(a1),x99461),x99462),f319(f319(f244(a1,a1),f319(f319(f319(f86(a1),f319(f319(a316,x99463),f2(a1))),f319(f73(a1),x99464)),f319(f319(f3(a1),f319(f73(a1),x99464)),f72(a1)))),f319(f319(f319(f86(a1),f319(f319(a316,x99463),f2(a1))),f2(a1)),f319(f319(f3(a1),x99462),x99463)))))
% 22.40/22.30 [9957]P1(f319(f319(f321(x99571),x99572),f319(f319(f33(x99573,f913(x99571,a904)),f234(f913(x99573,a904))),x99574)))+~P1(f319(f319(f319(f33(x99573,f913(x99571,a904)),f234(f913(x99573,a904))),f319(f319(f10(f913(x99571,a904),f913(x99571,a904),x99573),f319(f9(x99571,f913(x99571,a904),a904),f321(x99571))),x99574)),x99572))
% 22.40/22.30 [9958]P1(f319(f319(f321(x99581),x99582),f319(f319(f34(x99583,f913(x99581,a904)),f234(f913(x99583,a904))),x99584)))+~P1(f319(f319(f319(f34(x99583,f913(x99581,a904)),f234(f913(x99583,a904))),f319(f319(f10(f913(x99581,a904),f913(x99581,a904),x99583),f319(f9(x99581,f913(x99581,a904),a904),f321(x99581))),x99584)),x99582))
% 22.40/22.30 [9970]E(f319(f319(f33(a906,f913(x99701,a904)),f234(f913(a906,a904))),x99702),f319(f319(f33(a906,f913(x99701,a904)),f234(f913(a906,a904))),x99703))+~E(f319(f319(f33(a906,f913(x99701,a904)),f319(f294(a906,f2(a906)),f499(x99702,x99704,x99703,x99701))),x99703),f319(f319(f33(a906,f913(x99701,a904)),f319(f294(a906,f2(a906)),f319(f319(f74(a906),f499(x99702,x99704,x99703,x99701)),x99704))),x99702))
% 22.40/22.30 [10310]~P1(f319(f319(f225(f913(f912(x103101,x103102),a904)),x103103),x103104))+P1(f319(f319(f225(f913(x103101,f913(x103102,a904))),f319(f319(f9(x103101,f913(f912(x103101,x103102),a904),f913(x103102,a904)),f319(f319(f10(f913(x103102,f913(f913(f912(x103101,x103102),a904),a904)),f913(f913(f912(x103101,x103102),a904),f913(x103102,a904)),x103101),f9(x103102,f913(f912(x103101,x103102),a904),a904)),f319(f319(f10(f913(x103102,f912(x103101,x103102)),f913(x103102,f913(f913(f912(x103101,x103102),a904),a904)),x103101),f319(f10(f912(x103101,x103102),f913(f913(f912(x103101,x103102),a904),a904),x103102),f321(f912(x103101,x103102)))),f244(x103101,x103102)))),x103103)),f319(f319(f9(x103101,f913(f912(x103101,x103102),a904),f913(x103102,a904)),f319(f319(f10(f913(x103102,f913(f913(f912(x103101,x103102),a904),a904)),f913(f913(f912(x103101,x103102),a904),f913(x103102,a904)),x103101),f9(x103102,f913(f912(x103101,x103102),a904),a904)),f319(f319(f10(f913(x103102,f912(x103101,x103102)),f913(x103102,f913(f913(f912(x103101,x103102),a904),a904)),x103101),f319(f10(f912(x103101,x103102),f913(f913(f912(x103101,x103102),a904),a904),x103102),f321(f912(x103101,x103102)))),f244(x103101,x103102)))),x103104)))
% 22.40/22.30 [10333]P1(f319(f319(f225(f913(f912(x103331,x103332),a904)),x103333),x103334))+~P1(f319(f319(f225(f913(x103331,f913(x103332,a904))),f319(f319(f9(x103331,f913(f912(x103331,x103332),a904),f913(x103332,a904)),f319(f319(f10(f913(x103332,f913(f913(f912(x103331,x103332),a904),a904)),f913(f913(f912(x103331,x103332),a904),f913(x103332,a904)),x103331),f9(x103332,f913(f912(x103331,x103332),a904),a904)),f319(f319(f10(f913(x103332,f912(x103331,x103332)),f913(x103332,f913(f913(f912(x103331,x103332),a904),a904)),x103331),f319(f10(f912(x103331,x103332),f913(f913(f912(x103331,x103332),a904),a904),x103332),f321(f912(x103331,x103332)))),f244(x103331,x103332)))),x103333)),f319(f319(f9(x103331,f913(f912(x103331,x103332),a904),f913(x103332,a904)),f319(f319(f10(f913(x103332,f913(f913(f912(x103331,x103332),a904),a904)),f913(f913(f912(x103331,x103332),a904),f913(x103332,a904)),x103331),f9(x103332,f913(f912(x103331,x103332),a904),a904)),f319(f319(f10(f913(x103332,f912(x103331,x103332)),f913(x103332,f913(f913(f912(x103331,x103332),a904),a904)),x103331),f319(f10(f912(x103331,x103332),f913(f913(f912(x103331,x103332),a904),a904),x103332),f321(f912(x103331,x103332)))),f244(x103331,x103332)))),x103334)))
% 22.40/22.30 [9337]~P1(f319(f319(f321(f912(x93371,x93371)),x93372),f299(x93371,x93374)))+P1(f319(f319(f321(f912(x93371,x93371)),x93372),f299(x93371,f319(f319(f93(f913(f912(x93371,x93371),a904)),x93373),x93374))))
% 22.40/22.30 [9338]~P1(f319(f319(f321(f912(x93381,x93381)),x93382),f299(x93381,x93383)))+P1(f319(f319(f321(f912(x93381,x93381)),x93382),f299(x93381,f319(f319(f93(f913(f912(x93381,x93381),a904)),x93383),x93384))))
% 22.40/22.30 [10045]~P1(f319(f319(f225(a906),f319(f319(f74(a906),x100451),x100454)),f319(f319(f74(a906),x100453),x100452)))+P1(f319(f319(f225(a1),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x100451),x100452)),f181(f913(f912(a906,a906),a904)))))),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x100453),x100454)),f181(f913(f912(a906,a906),a904)))))))
% 22.40/22.30 [10046]~P1(f319(f319(f226(a906),f319(f319(f74(a906),x100461),x100464)),f319(f319(f74(a906),x100463),x100462)))+P1(f319(f319(f226(a1),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x100461),x100462)),f181(f913(f912(a906,a906),a904)))))),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x100463),x100464)),f181(f913(f912(a906,a906),a904)))))))
% 22.40/22.30 [10109]P1(f319(f319(f225(a906),f319(f319(f74(a906),x101091),x101092)),f319(f319(f74(a906),x101093),x101094)))+~P1(f319(f319(f225(a1),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x101091),x101094)),f181(f913(f912(a906,a906),a904)))))),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x101093),x101092)),f181(f913(f912(a906,a906),a904)))))))
% 22.40/22.30 [10110]P1(f319(f319(f226(a906),f319(f319(f74(a906),x101101),x101102)),f319(f319(f74(a906),x101103),x101104)))+~P1(f319(f319(f226(a1),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x101101),x101104)),f181(f913(f912(a906,a906),a904)))))),f319(a83,f319(f277(f912(a906,a906),f912(a906,a906),a101),f319(f319(f301(f912(a906,a906)),f319(f319(f244(a906,a906),x101103),x101102)),f181(f913(f912(a906,a906),a904)))))))
% 22.40/22.30 [10150]P1(f319(f319(f225(f913(x101501,a904)),f319(f319(f33(a906,f913(x101501,a904)),f234(f913(a906,a904))),x101502)),f319(f319(f33(a906,f913(x101501,a904)),f234(f913(a906,a904))),x101503)))+~P1(f319(f319(f225(f913(x101501,a904)),f319(f319(f33(a906,f913(x101501,a904)),f319(f294(a906,f2(a906)),f494(x101503,x101504,x101502,x101501))),x101502)),f319(f319(f33(a906,f913(x101501,a904)),f319(f294(a906,f2(a906)),f319(f319(f74(a906),f494(x101503,x101504,x101502,x101501)),x101504))),x101503)))
% 22.40/22.30 [10205]P1(f319(f319(f225(a91),x102054),f2(a91)))+E(f319(f319(f251(f912(a91,a91),f912(x102051,f913(a909,a315)),f912(a91,a91),f912(f913(a91,f913(a904,f910(f908(x102051)))),f912(a91,a91))),f319(x102052,x102053)),f319(f319(f10(f913(f913(a91,f913(a904,f910(f908(x102051)))),f913(f912(a91,a91),f912(f913(a91,f913(a904,f910(f908(x102051)))),f912(a91,a91)))),f913(f912(a91,a91),f912(f913(a91,f913(a904,f910(f908(x102051)))),f912(a91,a91))),f912(x102051,f913(a909,a315))),f319(f251(f912(a91,a91),f913(a91,f913(a904,f910(f908(x102051)))),f912(a91,a91),f912(f913(a91,f913(a904,f910(f908(x102051)))),f912(a91,a91))),f269(x102051,x102052,f319(f319(f3(a91),x102054),f72(a91)),x102053))),f319(f319(f10(f913(f913(a91,f913(a904,f910(f908(x102051)))),f913(a91,f913(a904,f910(f908(x102051))))),f913(f913(a91,f913(a904,f910(f908(x102051)))),f913(f912(a91,a91),f912(f913(a91,f913(a904,f910(f908(x102051)))),f912(a91,a91)))),f912(x102051,f913(a909,a315))),f319(f10(f913(a91,f913(a904,f910(f908(x102051)))),f913(f912(a91,a91),f912(f913(a91,f913(a904,f910(f908(x102051)))),f912(a91,a91))),f913(a91,f913(a904,f910(f908(x102051))))),f244(f913(a91,f913(a904,f910(f908(x102051)))),f912(a91,a91)))),f319(f319(f10(f913(a91,f913(a904,f910(f908(x102051)))),f913(f913(a91,f913(a904,f910(f908(x102051)))),f913(a91,f913(a904,f910(f908(x102051))))),f912(x102051,f913(a909,a315))),f38(x102051)),f319(f319(f10(x102051,f913(a91,f913(a904,f910(f908(x102051)))),f912(x102051,f913(a909,a315))),f36(x102051)),f243(x102051,f913(a909,a315))))))),f269(x102051,x102052,x102054,x102053))
% 22.40/22.30 [10299]~P1(f319(f319(f321(x102992),x102994),f319(f276(x102991,x102992),x102993)))+P1(f319(f242(x102991,x102992,f319(f319(f9(x102991,f913(f912(x102991,x102992),a904),f913(x102992,a904)),f319(f319(f10(f913(x102992,f913(f913(f912(x102991,x102992),a904),a904)),f913(f913(f912(x102991,x102992),a904),f913(x102992,a904)),x102991),f9(x102992,f913(f912(x102991,x102992),a904),a904)),f319(f319(f10(f913(x102992,f912(x102991,x102992)),f913(x102992,f913(f913(f912(x102991,x102992),a904),a904)),x102991),f319(f10(f912(x102991,x102992),f913(f913(f912(x102991,x102992),a904),a904),x102992),f321(f912(x102991,x102992)))),f244(x102991,x102992)))),x102993)),x102994))
% 22.40/22.30 [10300]~P1(f319(f319(f321(x103001),x103004),f319(f256(x103001,x103002),x103003)))+P1(f319(f241(x103001,x103002,f319(f319(f9(x103001,f913(f912(x103001,x103002),a904),f913(x103002,a904)),f319(f319(f10(f913(x103002,f913(f913(f912(x103001,x103002),a904),a904)),f913(f913(f912(x103001,x103002),a904),f913(x103002,a904)),x103001),f9(x103002,f913(f912(x103001,x103002),a904),a904)),f319(f319(f10(f913(x103002,f912(x103001,x103002)),f913(x103002,f913(f913(f912(x103001,x103002),a904),a904)),x103001),f319(f10(f912(x103001,x103002),f913(f913(f912(x103001,x103002),a904),a904),x103002),f321(f912(x103001,x103002)))),f244(x103001,x103002)))),x103003)),x103004))
% 22.40/22.30 [10313]P1(f319(f319(f321(x103131),x103132),f319(f276(x103133,x103131),x103134)))+~P1(f319(f242(x103133,x103131,f319(f319(f9(x103133,f913(f912(x103133,x103131),a904),f913(x103131,a904)),f319(f319(f10(f913(x103131,f913(f913(f912(x103133,x103131),a904),a904)),f913(f913(f912(x103133,x103131),a904),f913(x103131,a904)),x103133),f9(x103131,f913(f912(x103133,x103131),a904),a904)),f319(f319(f10(f913(x103131,f912(x103133,x103131)),f913(x103131,f913(f913(f912(x103133,x103131),a904),a904)),x103133),f319(f10(f912(x103133,x103131),f913(f913(f912(x103133,x103131),a904),a904),x103131),f321(f912(x103133,x103131)))),f244(x103133,x103131)))),x103134)),x103132))
% 22.40/22.30 [10314]P1(f319(f319(f321(x103141),x103142),f319(f256(x103141,x103143),x103144)))+~P1(f319(f241(x103141,x103143,f319(f319(f9(x103141,f913(f912(x103141,x103143),a904),f913(x103143,a904)),f319(f319(f10(f913(x103143,f913(f913(f912(x103141,x103143),a904),a904)),f913(f913(f912(x103141,x103143),a904),f913(x103143,a904)),x103141),f9(x103143,f913(f912(x103141,x103143),a904),a904)),f319(f319(f10(f913(x103143,f912(x103141,x103143)),f913(x103143,f913(f913(f912(x103141,x103143),a904),a904)),x103141),f319(f10(f912(x103141,x103143),f913(f913(f912(x103141,x103143),a904),a904),x103143),f321(f912(x103141,x103143)))),f244(x103141,x103143)))),x103144)),x103142))
% 22.40/22.30 [9981]P1(f319(f152(x99811,x99812),x99813))+~P1(f319(f152(x99811,f319(f319(f20(x99811,a904,a904),f319(f319(f10(a904,f913(a904,a904),x99811),a317),x99814)),x99812)),x99813))
% 22.40/22.30 [9982]P1(f319(f152(x99821,x99822),x99823))+~P1(f319(f152(x99821,f319(f319(f20(x99821,a904,a904),f319(f319(f10(a904,f913(a904,a904),x99821),a317),x99822)),x99824)),x99823))
% 22.40/22.30 [10047]~P119(x100471)+E(f319(f319(f75(x100471),f319(f319(f74(x100471),f72(x100471)),f72(x100471))),f319(f319(f8(a906,x100471),f319(f319(f10(x100471,x100471,a906),f319(f74(x100471),x100472)),f319(f319(f9(a906,x100471,x100471),f319(f319(f10(x100471,f913(x100471,x100471),a906),f75(x100471)),f92(x100471))),x100473))),f319(f274(a906),x100474))),f319(f319(f75(x100471),f319(f92(x100471),x100474)),f319(f319(f74(x100471),x100472),f319(f319(f74(x100471),x100472),f319(f319(f75(x100471),f319(f92(x100471),f319(f319(f3(a906),x100474),f72(a906)))),x100473)))))
% 22.40/22.30 [10169]P1(f319(x101691,f564(x101692,x101693,x101694,x101691)))+P37(x101692,f319(f254(f912(x101692,x101692)),f319(f249(x101692,x101692,a904),f319(f319(f10(f913(x101692,a904),f913(x101692,a904),x101692),f319(f20(x101692,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101692),a317),x101691))),f319(f319(f9(x101692,f913(x101692,x101692),f913(x101692,a904)),f319(f319(f10(f913(x101692,a904),f913(f913(x101692,x101692),f913(x101692,a904)),x101692),f10(x101692,a904,x101692)),a316)),x101693)))))
% 22.40/22.30 [10181]~P1(f319(f319(f226(a906),f319(x101814,f319(x101813,f564(x101811,x101813,x101814,x101812)))),f319(x101814,f564(x101811,x101813,x101814,x101812))))+P37(x101811,f319(f254(f912(x101811,x101811)),f319(f249(x101811,x101811,a904),f319(f319(f10(f913(x101811,a904),f913(x101811,a904),x101811),f319(f20(x101811,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101811),a317),x101812))),f319(f319(f9(x101811,f913(x101811,x101811),f913(x101811,a904)),f319(f319(f10(f913(x101811,a904),f913(f913(x101811,x101811),f913(x101811,a904)),x101811),f10(x101811,a904,x101811)),a316)),x101813)))))
% 22.40/22.30 [10265]~P5(x102651)+E(f32(x102651,f319(f254(x102651),f319(f319(f10(f913(f913(x102652,x102651),a904),a904,x102651),f80(f913(x102652,x102651))),f319(f319(f10(f913(f913(x102652,x102651),a904),f913(f913(x102652,x102651),a904),x102651),f319(f20(f913(x102652,x102651),a904,a904),f319(f319(f10(a904,f913(a904,a904),f913(x102652,x102651)),a317),f319(f319(f9(f913(x102652,x102651),f913(f913(x102652,x102651),a904),a904),f321(f913(x102652,x102651))),x102653)))),f319(f319(f9(x102651,f913(f913(x102652,x102651),x102651),f913(f913(x102652,x102651),a904)),f319(f319(f10(f913(x102651,a904),f913(f913(f913(x102652,x102651),x102651),f913(f913(x102652,x102651),a904)),x102651),f10(x102651,a904,f913(x102652,x102651))),a316)),f319(f319(f9(f913(x102652,x102651),x102652,x102651),f7(f913(x102652,x102651))),x102654)))))),f319(f32(f913(x102652,x102651),x102653),x102654))
% 22.40/22.30 [10266]~P5(x102661)+E(f32(x102661,f319(f254(x102661),f319(f319(f10(f913(f913(x102662,x102661),a904),a904,x102661),f80(f913(x102662,x102661))),f319(f319(f10(f913(f913(x102662,x102661),a904),f913(f913(x102662,x102661),a904),x102661),f319(f20(f913(x102662,x102661),a904,a904),f319(f319(f10(a904,f913(a904,a904),f913(x102662,x102661)),a317),f319(f319(f9(f913(x102662,x102661),f913(f913(x102662,x102661),a904),a904),f321(f913(x102662,x102661))),x102663)))),f319(f319(f9(x102661,f913(f913(x102662,x102661),x102661),f913(f913(x102662,x102661),a904)),f319(f319(f10(f913(x102661,a904),f913(f913(f913(x102662,x102661),x102661),f913(f913(x102662,x102661),a904)),x102661),f10(x102661,a904,f913(x102662,x102661))),a316)),f319(f319(f9(f913(x102662,x102661),x102662,x102661),f7(f913(x102662,x102661))),x102664)))))),f319(f32(f913(x102662,x102661),x102663),x102664))
% 22.40/22.30 [10267]~P5(x102671)+E(f31(x102671,f319(f254(x102671),f319(f319(f10(f913(f913(x102672,x102671),a904),a904,x102671),f80(f913(x102672,x102671))),f319(f319(f10(f913(f913(x102672,x102671),a904),f913(f913(x102672,x102671),a904),x102671),f319(f20(f913(x102672,x102671),a904,a904),f319(f319(f10(a904,f913(a904,a904),f913(x102672,x102671)),a317),f319(f319(f9(f913(x102672,x102671),f913(f913(x102672,x102671),a904),a904),f321(f913(x102672,x102671))),x102673)))),f319(f319(f9(x102671,f913(f913(x102672,x102671),x102671),f913(f913(x102672,x102671),a904)),f319(f319(f10(f913(x102671,a904),f913(f913(f913(x102672,x102671),x102671),f913(f913(x102672,x102671),a904)),x102671),f10(x102671,a904,f913(x102672,x102671))),a316)),f319(f319(f9(f913(x102672,x102671),x102672,x102671),f7(f913(x102672,x102671))),x102674)))))),f319(f31(f913(x102672,x102671),x102673),x102674))
% 22.40/22.30 [10268]~P5(x102681)+E(f31(x102681,f319(f254(x102681),f319(f319(f10(f913(f913(x102682,x102681),a904),a904,x102681),f80(f913(x102682,x102681))),f319(f319(f10(f913(f913(x102682,x102681),a904),f913(f913(x102682,x102681),a904),x102681),f319(f20(f913(x102682,x102681),a904,a904),f319(f319(f10(a904,f913(a904,a904),f913(x102682,x102681)),a317),f319(f319(f9(f913(x102682,x102681),f913(f913(x102682,x102681),a904),a904),f321(f913(x102682,x102681))),x102683)))),f319(f319(f9(x102681,f913(f913(x102682,x102681),x102681),f913(f913(x102682,x102681),a904)),f319(f319(f10(f913(x102681,a904),f913(f913(f913(x102682,x102681),x102681),f913(f913(x102682,x102681),a904)),x102681),f10(x102681,a904,f913(x102682,x102681))),a316)),f319(f319(f9(f913(x102682,x102681),x102682,x102681),f7(f913(x102682,x102681))),x102684)))))),f319(f31(f913(x102682,x102681),x102683),x102684))
% 22.40/22.30 [10352]~P1(f319(f319(f321(f912(x103521,x103521)),f319(f319(f244(x103521,x103521),x103523),x103524)),f319(f319(f93(f913(f912(x103521,x103521),a904)),x103522),f299(x103521,f181(f913(f912(x103521,x103521),a904))))))+P1(f319(f319(f319(f319(f93(f913(x103521,f913(x103521,a904))),f319(f319(f9(x103521,f913(f912(x103521,x103521),a904),f913(x103521,a904)),f319(f319(f10(f913(x103521,f913(f913(f912(x103521,x103521),a904),a904)),f913(f913(f912(x103521,x103521),a904),f913(x103521,a904)),x103521),f9(x103521,f913(f912(x103521,x103521),a904),a904)),f319(f319(f10(f913(x103521,f912(x103521,x103521)),f913(x103521,f913(f913(f912(x103521,x103521),a904),a904)),x103521),f319(f10(f912(x103521,x103521),f913(f913(f912(x103521,x103521),a904),a904),x103521),f321(f912(x103521,x103521)))),f244(x103521,x103521)))),x103522)),a316),x103523),x103524))
% 22.40/22.30 [10368]P1(f319(f319(f321(f912(x103681,x103681)),f319(f319(f244(x103681,x103681),x103682),x103683)),f319(f319(f93(f913(f912(x103681,x103681),a904)),x103684),f299(x103681,f181(f913(f912(x103681,x103681),a904))))))+~P1(f319(f319(f319(f319(f93(f913(x103681,f913(x103681,a904))),f319(f319(f9(x103681,f913(f912(x103681,x103681),a904),f913(x103681,a904)),f319(f319(f10(f913(x103681,f913(f913(f912(x103681,x103681),a904),a904)),f913(f913(f912(x103681,x103681),a904),f913(x103681,a904)),x103681),f9(x103681,f913(f912(x103681,x103681),a904),a904)),f319(f319(f10(f913(x103681,f912(x103681,x103681)),f913(x103681,f913(f913(f912(x103681,x103681),a904),a904)),x103681),f319(f10(f912(x103681,x103681),f913(f913(f912(x103681,x103681),a904),a904),x103681),f321(f912(x103681,x103681)))),f244(x103681,x103681)))),x103684)),a316),x103682),x103683))
% 22.40/22.30 [10296]E(f319(f319(f143(f907(x102961)),f319(f319(f143(x102961),x102962),f319(f134(f907(x102961),f907(x102961),f126(x102961),f105(x102961)),f319(f319(f146(f907(x102961),f907(x102961)),f148(f907(x102961),x102961,f105(x102961),f319(f319(f10(f907(x102961),f913(f907(x102961),f907(x102961)),x102961),f18(f907(x102961),f907(x102961))),f319(f319(f9(x102961,f907(x102961),f907(x102961)),f143(x102961)),f105(x102961))))),x102963)))),f171(x102961,f319(f319(f143(f907(x102961)),x102964),f319(f134(f907(f907(x102961)),f907(f907(x102961)),f126(f907(x102961)),f105(f907(x102961))),f319(f319(f146(f907(x102961),f907(f907(x102961))),f148(f907(f907(x102961)),x102961,f105(f907(x102961)),f319(f18(f913(f907(x102961),f907(f907(x102961))),x102961),f319(f319(f9(f907(x102961),f907(f907(x102961)),f907(f907(x102961))),f143(f907(x102961))),f105(f907(x102961)))))),x102963))))),f171(x102961,f319(f319(f143(f907(x102961)),f319(f319(f143(x102961),x102962),x102964)),x102963)))+~P1(f319(f307(f907(f907(x102961)),f172(x102961)),f319(f319(f143(f907(x102961)),f319(f319(f143(x102961),x102962),x102964)),x102963)))
% 22.40/22.30 [10351]~P1(f319(f55(x103512),f319(f254(x103512),x103514)))+P1(f319(f55(x103511),f319(f254(x103511),f319(f319(f10(f913(x103512,a904),a904,x103511),f80(x103512)),f319(f319(f9(x103511,f913(x103512,a904),f913(x103512,a904)),f319(f319(f10(f913(x103512,f913(a904,a904)),f913(f913(x103512,a904),f913(x103512,a904)),x103511),f20(x103512,a904,a904)),f319(f319(f10(f913(x103512,a904),f913(x103512,f913(a904,a904)),x103511),f319(f10(a904,f913(a904,a904),x103512),a317)),f319(f319(f9(x103511,f913(x103512,x103511),f913(x103512,a904)),f319(f319(f10(f913(x103511,a904),f913(f913(x103512,x103511),f913(x103512,a904)),x103511),f10(x103511,a904,x103512)),a316)),x103513)))),x103514)))))
% 22.40/22.30 [8826]P25(x88261,x88262,x88263,x88264)+~P26(x88261,x88262,x88263,x88264,x88265)
% 22.40/22.30 [5367]E(x53671,x53672)+~E(f161(x53673,x53671,x53674),f161(x53673,x53672,x53675))
% 22.40/22.30 [5368]E(x53681,x53682)+~E(f118(x53683,x53684,x53681),f118(x53683,x53685,x53682))
% 22.40/22.30 [5369]E(x53691,x53692)+~E(f118(x53693,x53691,x53694),f118(x53693,x53692,x53695))
% 22.40/22.30 [8168]~E(f319(x81683,x81684),x81685)+E(f68(x81681,x81682,x81683,x81684,x81685),x81683)
% 22.40/22.30 [8692]~E(f68(x86924,x86925,x86921,x86922,x86923),x86921)+E(f319(x86921,x86922),x86923)
% 22.40/22.30 [9309]~P26(x93092,x93091,x93094,x93093,x93095)+P26(x93091,x93092,f71(x93092,x93091,x93093,x93094),x93095,x93093)
% 22.40/22.30 [9310]~P26(x93102,x93101,x93104,x93103,x93105)+P26(x93101,x93102,f85(x93102,x93101,x93103,x93104),x93105,x93103)
% 22.40/22.30 [6172]P1(f319(f242(x61721,x61722,x61723),x61724))+~P1(f319(f319(x61723,x61725),x61724))
% 22.40/22.30 [6174]P1(f319(f241(x61741,x61742,x61743),x61744))+~P1(f319(f319(x61743,x61744),x61745))
% 22.40/22.30 [6648]~E(x66485,f2(a91))+E(f319(f191(x66481,x66482,x66483,x66484),x66485),f107(x66482))
% 22.40/22.30 [6649]~E(x66495,f2(a91))+E(f319(f189(x66491,x66492,x66493,x66494),x66495),f116(x66492))
% 22.40/22.30 [6790]~E(x67903,f2(a91))+E(f319(f265(x67901,x67902,x67903,x67904),x67905),f319(f244(x67901,x67902),x67905))
% 22.40/22.30 [7819]~P21(x78194,x78191,x78192,x78195)+E(f319(f66(x78191,x78191,x78191,f319(x78192,x78193)),f319(x78192,x78193)),f319(x78192,x78193))
% 22.40/22.30 [8205]~P17(x82055,x82051,x82052)+E(f319(f66(x82051,x82051,x82051,f319(x82052,x82053)),f319(x82052,x82054)),f319(f66(x82051,x82051,x82051,f319(x82052,x82054)),f319(x82052,x82053)))
% 22.40/22.30 [8524]P1(f319(f319(f321(f912(x85241,x85241)),f319(f319(f244(x85241,x85241),x85242),x85243)),f313(x85241,x85244,x85245)))+~P1(f319(f319(f226(a906),f319(x85244,x85242)),f319(x85244,x85243)))
% 22.40/22.30 [8620]~P1(f319(f319(f321(x86204),x86203),f288(x86204,x86201,x86202,x86205)))+P1(f319(f319(x86201,x86202),x86203))
% 22.40/22.30 [8621]~P1(f319(f319(f321(x86214),x86213),f291(x86214,x86211,x86212,x86215)))+P1(f319(f319(x86211,x86212),x86213))
% 22.40/22.30 [8622]~P1(f319(f319(f321(x86224),x86222),f288(x86224,x86221,x86225,x86223)))+P1(f319(f319(x86221,x86222),x86223))
% 22.40/22.30 [8623]~P1(f319(f319(f321(x86234),x86232),f291(x86234,x86231,x86235,x86233)))+P1(f319(f319(x86231,x86232),x86233))
% 22.40/22.30 [8703]~P26(x87031,x87033,x87035,x87032,x87034)+E(f319(f29(x87031),x87032),f319(f29(x87033),x87034))
% 22.40/22.30 [8752]~P26(x87521,x87522,x87523,x87524,x87525)+E(f319(f302(x87521,x87522,x87523),x87524),x87525)
% 22.40/22.30 [8767]~P58(x87672,x87671,x87675,x87673,x87674)+E(f319(f302(x87671,x87672,x87673),x87674),f234(f913(x87672,a904)))
% 22.40/22.30 [9208]~P34(x92081,x92082,x92083,x92084,x92085)+P34(x92081,x92082,x92083,f319(f160(x92081),x92084),f319(f160(x92082),x92085))
% 22.40/22.30 [9210]~P34(x92101,x92102,x92103,f319(f160(x92101),x92104),x92105)+P34(x92101,x92102,x92103,x92104,f319(f160(x92102),x92105))
% 22.40/22.30 [9211]~P34(x92111,x92112,x92113,x92114,f319(f160(x92112),x92115))+P34(x92111,x92112,x92113,f319(f160(x92111),x92114),x92115)
% 22.40/22.30 [9217]P34(x92171,x92172,x92173,x92174,x92175)+~P34(x92171,x92172,x92173,f319(f160(x92171),x92174),f319(f160(x92172),x92175))
% 22.40/22.30 [9636]P1(f319(f319(f321(f912(f907(x96361),f907(x96361))),f319(f319(f244(f907(x96361),f907(x96361)),f319(f319(f143(x96361),x96362),x96363)),f319(f319(f143(x96361),x96362),x96364))),f149(x96361,x96365)))+~P1(f319(f319(f321(f912(f907(x96361),f907(x96361))),f319(f319(f244(f907(x96361),f907(x96361)),x96363),x96364)),f149(x96361,x96365)))
% 22.40/22.30 [9637]P1(f319(f319(f321(f912(f907(x96371),f907(x96371))),f319(f319(f244(f907(x96371),f907(x96371)),f319(f319(f126(x96371),x96372),x96373)),f319(f319(f126(x96371),x96372),x96374))),f139(x96371,x96375)))+~P1(f319(f319(f321(f912(f907(x96371),f907(x96371))),f319(f319(f244(f907(x96371),f907(x96371)),x96373),x96374)),f139(x96371,x96375)))
% 22.40/22.30 [9851]E(f319(f319(f143(x98511),f642(x98512,x98513,x98514,x98515,x98511)),f643(x98512,x98513,x98514,x98515,x98511)),x98515)+~P1(f319(f319(f321(f912(f907(x98511),f907(x98511))),f319(f319(f244(f907(x98511),f907(x98511)),x98515),f319(f319(f143(x98511),x98514),x98513))),f150(x98511,x98512)))
% 22.40/22.30 [9873]E(f319(f319(f143(x98731),f644(x98732,x98733,x98734,x98735,x98731)),f645(x98732,x98733,x98734,x98735,x98731)),x98733)+~P1(f319(f319(f321(f912(f907(x98731),f907(x98731))),f319(f319(f244(f907(x98731),f907(x98731)),f319(f319(f143(x98731),x98735),x98734)),x98733)),f150(x98731,x98732)))
% 22.40/22.30 [10025]~P1(f319(f319(f321(f912(f907(x100251),f907(x100251))),f319(f319(f244(f907(x100251),f907(x100251)),f319(f319(f143(x100251),x100255),x100252)),x100254)),f150(x100251,x100253)))+P1(f319(f319(f321(f912(f907(x100251),f907(x100251))),f319(f319(f244(f907(x100251),f907(x100251)),x100252),f645(x100253,x100254,x100252,x100255,x100251))),f150(x100251,x100253)))
% 22.40/22.30 [10081]~P1(f319(f319(f321(f912(f907(x100811),f907(x100811))),f319(f319(f244(f907(x100811),f907(x100811)),x100815),f319(f319(f143(x100811),x100814),x100813))),f150(x100811,x100812)))+P1(f319(f319(f321(f912(f907(x100811),f907(x100811))),f319(f319(f244(f907(x100811),f907(x100811)),f643(x100812,x100813,x100814,x100815,x100811)),x100813)),f150(x100811,x100812)))
% 22.40/22.30 [10270]P1(f319(f319(f321(f912(x102701,x102701)),f319(f319(f244(x102701,x102701),f319(x102702,f319(f319(f74(a906),x102703),x102704))),f319(x102702,x102703))),f299(x102701,x102705)))+~P1(f319(f319(f321(f912(x102701,x102701)),f319(f319(f244(x102701,x102701),f319(x102702,f319(a104,f607(x102704,x102703,x102705,x102702,x102701)))),f319(x102702,f607(x102704,x102703,x102705,x102702,x102701)))),f299(x102701,x102705)))
% 22.40/22.30 [5341]E(x53411,x53412)+~E(f319(f319(f143(x53413),x53414),x53411),f319(f319(f143(x53413),x53415),x53412))
% 22.40/22.30 [5342]E(x53421,x53422)+~E(f319(f319(f143(x53423),x53421),x53424),f319(f319(f143(x53423),x53422),x53425))
% 22.40/22.30 [5384]P1(f319(x53841,x53842))+~E(f319(f128(x53843,x53841),x53844),f319(f319(f143(x53843),x53842),x53845))
% 22.40/22.30 [5385]P1(f319(x53851,x53852))+~E(f319(f319(f143(x53853),x53852),x53854),f319(f128(x53853,x53851),x53855))
% 22.40/22.30 [5543]~E(f319(f319(f130(x55431),x55433),x55432),f319(f319(f143(x55431),x55434),x55435))+E(f319(f319(f156(x55431),x55432),x55433),x55434)
% 22.40/22.30 [5682]~P15(x56824,x56825,x56821)+E(f319(f319(x56821,x56822),f319(f319(x56821,x56822),x56823)),f319(f319(x56821,x56822),x56823))
% 22.40/22.30 [6231]~E(x62314,f2(a91))+E(f319(f319(f109(x62311,x62312,x62313),x62314),x62315),f319(f319(f244(f907(x62312),x62311),f105(x62312)),x62315))
% 22.40/22.30 [6302]~P4(x63022)+~E(f319(f319(f140(x63021,x63022,x63023),x63024),x63025),f105(x63021))
% 22.40/22.30 [6687]E(x66871,x66872)+~E(f319(f319(f126(x66873),x66874),f319(f319(f143(x66873),x66871),f105(x66873))),f319(f319(f126(x66873),x66875),f319(f319(f143(x66873),x66872),f105(x66873))))
% 22.40/22.30 [6688]E(x66881,x66882)+~E(f319(f319(f126(x66883),x66881),f319(f319(f143(x66883),x66884),f105(x66883))),f319(f319(f126(x66883),x66882),f319(f319(f143(x66883),x66885),f105(x66883))))
% 22.40/22.30 [7003]E(f319(f319(f301(x70031),f319(x70032,x70033)),f319(f302(x70034,x70031,x70032),x70035)),f319(f302(x70034,x70031,x70032),x70035))+~P1(f319(f319(f321(x70034),x70033),x70035))
% 22.40/22.30 [7010]~P1(f319(x70104,f319(x70103,x70105)))+P1(f319(f319(f303(x70101,x70102,x70103),x70104),x70105))
% 22.40/22.30 [7013]~P1(f319(f319(x70133,x70135),x70134))+P1(f319(f319(f235(x70131,x70132,x70133),x70134),x70135))
% 22.40/22.30 [7110]~E(f319(f302(x71101,x71102,x71103),x71104),x71105)+E(f319(f302(f913(x71101,a904),f913(x71102,a904),f302(x71101,x71102,x71103)),f319(f300(x71101),x71104)),f319(f300(x71102),x71105))
% 22.40/22.30 [7137]E(f319(f263(x71371,x71372,x71373,x71374),x71375),f319(x71374,x71375))+~P1(f319(f319(f321(x71371),x71375),x71373))
% 22.40/22.30 [7445]P25(x74451,x74452,x74453,x74454)+~P25(x74451,x74452,x74453,f319(f319(f301(x74451),x74455),x74454))
% 22.40/22.30 [7544]~P1(f319(f319(f321(x75444),x75443),x75445))+P1(f319(f319(f321(x75441),f319(x75442,x75443)),f319(f302(x75444,x75441,x75442),x75445)))
% 22.40/22.30 [7565]~P4(x75652)+E(f142(x75651,x75652,x75653,f319(f128(x75651,x75654),x75655)),f319(f128(x75651,x75654),f142(x75651,x75652,x75653,x75655)))
% 22.40/22.30 [7596]P1(f319(x75961,f319(x75962,x75963)))+~P1(f319(f319(f303(x75964,x75965,x75962),x75961),x75963))
% 22.40/22.30 [7599]P1(f319(f319(x75991,x75992),x75993))+~P1(f319(f319(f235(x75994,x75995,x75991),x75993),x75992))
% 22.40/22.30 [7661]~P1(f319(f319(f321(x76613),f319(x76614,x76612)),x76615))+P1(f319(f319(f321(x76611),x76612),f319(f303(x76611,x76613,x76614),x76615)))
% 22.40/22.30 [8047]~P1(f319(f319(f321(x80475),x80473),f319(f303(x80475,x80471,x80472),x80474)))+P1(f319(f319(f321(x80471),f319(x80472,x80473)),x80474))
% 22.40/22.30 [8342]~P17(x83422,x83421,x83423)+E(f319(f134(x83421,x83422,f319(f9(x83422,x83421,x83421),x83423),x83424),f144(x83422,x83425)),f319(f319(f58(x83422,x83421,x83423),x83424),f319(f164(x83422),x83425)))
% 22.40/22.30 [8364]E(f319(x83641,f603(x83642,x83641,x83643,x83644)),x83644)+~P1(f319(f319(f321(x83645),x83644),f319(f302(x83643,x83645,x83641),x83642)))
% 22.40/22.30 [8668]~E(x86682,f319(f319(f143(x86681),x86684),x86685))+P1(f319(f319(f321(f912(f907(x86681),f907(x86681))),f319(f319(f244(f907(x86681),f907(x86681)),f105(x86681)),x86682)),f139(x86681,x86683)))
% 22.40/22.30 [8712]E(f319(x87121,f319(f85(x87122,x87123,x87124,x87121),x87125)),x87125)+~P1(f319(f319(f321(x87123),x87125),f319(f302(x87122,x87123,x87121),x87124)))
% 22.40/22.30 [8715]P25(x87151,x87152,f85(x87152,x87151,x87153,x87154),x87155)+~P1(f319(f319(f225(f913(x87151,a904)),x87155),f319(f302(x87152,x87151,x87154),x87153)))
% 22.40/22.30 [8724]~P34(x87241,x87243,x87245,x87242,x87244)+E(f319(f182(f907(x87241)),x87242),f319(f182(f907(x87243)),x87244))
% 22.40/22.30 [8734]P1(f319(f319(f225(f913(x87341,a904)),f319(f319(f34(x87342,f913(x87341,a904)),x87343),x87344)),f319(x87344,x87345)))+~P1(f319(f319(f321(x87342),x87345),x87343))
% 22.40/22.30 [8782]~P58(x87821,x87822,x87823,x87825,x87824)+E(f319(f302(x87821,x87822,x87823),f234(f913(x87821,a904))),x87824)
% 22.40/22.30 [9014]E(f319(f128(x90141,x90142),f732(x90143,x90144,x90145,x90142,x90141)),x90143)+~E(f319(f128(x90141,x90142),x90145),f319(f319(f143(x90141),x90144),x90143))
% 22.40/22.30 [9015]E(f319(f128(x90151,x90152),f735(x90153,x90152,x90154,x90155,x90151)),x90154)+~E(f319(f319(f143(x90151),x90155),x90154),f319(f128(x90151,x90152),x90153))
% 22.40/22.30 [9109]E(f319(f182(f907(x91091)),x91092),x91093)+~P1(f319(f319(f321(f912(f907(x91091),f907(x91091))),f319(f319(f244(f907(x91091),f907(x91091)),x91094),x91092)),f319(f135(x91091,x91095),x91093)))
% 22.40/22.30 [9110]E(f319(f182(f907(x91101)),x91102),x91103)+~P1(f319(f319(f321(f912(f907(x91101),f907(x91101))),f319(f319(f244(f907(x91101),f907(x91101)),x91102),x91104)),f319(f135(x91101,x91105),x91103)))
% 22.40/22.30 [9173]P1(f319(f319(f321(x91731),f603(x91732,x91733,x91731,x91734)),x91732))+~P1(f319(f319(f321(x91735),x91734),f319(f302(x91731,x91735,x91733),x91732)))
% 22.40/22.30 [9333]~P40(f913(x93333,a904),f913(x93331,a904),x93332)+P1(f319(f319(f225(f913(x93331,a904)),f319(x93332,f319(f319(f94(f913(x93333,a904)),x93334),x93335))),f319(f319(f94(f913(x93331,a904)),f319(x93332,x93334)),f319(x93332,x93335))))
% 22.40/22.30 [9335]E(f319(f302(x93351,x93352,x93353),f418(x93354,x93353,x93351,x93355,x93352)),x93355)+~P1(f319(f319(f225(f913(x93352,a904)),x93355),f319(f302(x93351,x93352,x93353),x93354)))
% 22.40/22.30 [9659]P1(f319(f319(f321(f912(f907(x96591),f907(x96591))),f319(f319(f244(f907(x96591),f907(x96591)),f319(f319(f143(x96591),x96592),x96593)),f319(f319(f143(x96591),x96592),x96594))),f299(f907(x96591),f149(x96591,x96595))))+~P1(f319(f319(f321(f912(f907(x96591),f907(x96591))),f319(f319(f244(f907(x96591),f907(x96591)),x96593),x96594)),f299(f907(x96591),f149(x96591,x96595))))
% 22.40/22.30 [9690]~E(f319(x96903,f685(x96905,x96904,x96903,x96902,x96901)),f319(x96905,f685(x96905,x96904,x96903,x96902,x96901)))+E(f319(f319(f146(x96901,x96902),x96903),x96904),f319(f319(f146(x96901,x96902),x96905),x96904))
% 22.40/22.30 [9775]~E(f319(f128(x97751,x97755),x97754),f319(f319(f143(x97751),x97753),x97752))+E(f319(f319(f126(x97751),f733(x97752,x97753,x97754,x97755,x97751)),f319(f319(f143(x97751),x97753),f732(x97752,x97753,x97754,x97755,x97751))),x97754)
% 22.40/22.30 [9776]~E(f319(f319(f143(x97761),x97765),x97764),f319(f128(x97761,x97763),x97762))+E(f319(f319(f126(x97761),f737(x97762,x97763,x97764,x97765,x97761)),f319(f319(f143(x97761),x97765),f735(x97762,x97763,x97764,x97765,x97761))),x97762)
% 22.40/22.30 [9784]E(f319(f319(f146(x97841,x97842),x97843),x97844),f319(f319(f146(x97841,x97842),x97845),x97844))+P1(f319(f319(f321(x97841),f685(x97843,x97844,x97845,x97842,x97841)),f319(f164(x97841),x97844)))
% 22.40/22.30 [9813]~P1(f319(f319(f321(x98135),x98134),f319(f277(x98131,x98135,x98133),x98132)))+P1(f319(f319(f321(x98131),f508(x98132,x98133,x98131,x98134,x98135)),x98132))
% 22.40/22.30 [9814]~P1(f319(f319(f321(x98145),x98144),f319(f277(x98141,x98145,x98143),x98142)))+P1(f319(f319(f321(x98141),f513(x98142,x98143,x98141,x98144,x98145)),x98142))
% 22.40/22.30 [9845]~P1(f319(f319(f225(f913(x98455,a904)),x98454),f319(f302(x98451,x98455,x98453),x98452)))+P1(f319(f319(f225(f913(x98451,a904)),f418(x98452,x98453,x98451,x98454,x98455)),x98452))
% 22.40/22.30 [10272]E(x102721,f2(a91))+E(f216(f912(f907(x102722),x102723),f912(x102722,x102723),f319(f319(f244(f907(x102722),x102723),f105(x102722)),x102724),f319(f249(x102722,x102723,f912(f907(x102722),x102723)),f319(f319(f9(x102722,f913(x102723,f912(f907(x102722),x102723)),f913(x102723,f912(f907(x102722),x102723))),f319(f319(f10(f913(f912(f907(x102722),x102723),f912(f907(x102722),x102723)),f913(f913(x102723,f912(f907(x102722),x102723)),f913(x102723,f912(f907(x102722),x102723))),x102722),f10(f912(f907(x102722),x102723),f912(f907(x102722),x102723),x102723)),f319(f319(f10(f913(f907(x102722),f913(x102723,f912(f907(x102722),x102723))),f913(f912(f907(x102722),x102723),f912(f907(x102722),x102723)),x102722),f249(f907(x102722),x102723,f912(f907(x102722),x102723))),f319(f319(f10(f913(f907(x102722),f907(x102722)),f913(f907(x102722),f913(x102723,f912(f907(x102722),x102723))),x102722),f319(f10(f907(x102722),f913(x102723,f912(f907(x102722),x102723)),f907(x102722)),f244(f907(x102722),x102723))),f143(x102722))))),f319(f109(x102723,x102722,x102725),f319(f319(f3(a91),x102721),f72(a91))))),f319(x102725,x102724)),f319(f319(f109(x102723,x102722,x102725),x102721),x102724))
% 22.40/22.30 [6114]E(x61141,x61142)+~E(f319(f248(x61143,x61144),f319(f319(f244(x61143,x61144),x61145),x61141)),x61142)
% 22.40/22.30 [6115]E(x61151,x61152)+~E(f319(f243(x61153,x61154),f319(f319(f244(x61153,x61154),x61151),x61155)),x61152)
% 22.40/22.30 [6377]~E(x63773,f319(f319(f126(x63771),x63774),f319(f319(f143(x63771),x63772),x63775)))+P1(f319(f319(f321(x63771),x63772),f319(f164(x63771),x63773)))
% 22.40/22.30 [6776]E(f319(f302(x67761,x67762,f319(f18(x67762,x67761),x67763)),x67764),f319(f319(f301(x67762),x67763),f181(f913(x67762,a904))))+~P1(f319(f319(f321(x67761),x67765),x67764))
% 22.40/22.30 [6852]E(f319(f319(f93(f913(x68521,a904)),f319(f164(x68521),x68522)),f319(f164(x68521),x68523)),f319(f164(x68521),x68524))+~E(f158(x68521,x68525,x68524),f319(f319(f244(f907(x68521),f907(x68521)),x68522),x68523))
% 22.40/22.30 [6944]~P4(x69442)+E(f319(f182(f907(x69441)),f319(f319(f140(x69441,x69442,x69443),x69444),x69445)),f319(a104,f319(f182(f907(x69441)),x69445)))
% 22.40/22.30 [6958]~P4(x69582)+E(f319(f164(x69581),f319(f319(f140(x69581,x69582,x69583),x69584),x69585)),f319(f319(f301(x69581),x69584),f319(f164(x69581),x69585)))
% 22.40/22.30 [7230]~P119(x72301)+E(f319(f319(f74(x72301),f319(f319(f74(x72301),x72302),x72303)),f319(f319(f74(x72301),x72304),x72305)),f319(f319(f74(x72301),f319(f319(f74(x72301),x72302),x72304)),f319(f319(f74(x72301),x72303),x72305)))
% 22.40/22.30 [7231]~P119(x72311)+E(f319(f319(f75(x72311),f319(f319(f75(x72311),x72312),x72313)),f319(f319(f75(x72311),x72314),x72315)),f319(f319(f75(x72311),f319(f319(f75(x72311),x72312),x72314)),f319(f319(f75(x72311),x72313),x72315)))
% 22.40/22.30 [7232]~P72(x72321)+E(f319(f319(f282(x72321),f319(f319(f75(x72321),x72322),x72323)),f319(f319(f75(x72321),x72324),x72325)),f319(f319(f75(x72321),f319(f319(f282(x72321),x72322),x72324)),f319(f319(f282(x72321),x72323),x72325)))
% 22.40/22.30 [7246]~P4(x72461)+E(f298(x72461,f319(f319(f180(x72461),x72462),x72463),f319(f319(f230(x72461),x72464),x72465)),f319(f319(f94(f913(x72461,a904)),f298(x72461,x72462,x72464)),f298(x72461,x72463,x72465)))
% 22.40/22.30 [7247]~P4(x72471)+E(f297(x72471,f319(f319(f180(x72471),x72472),x72473),f319(f319(f230(x72471),x72474),x72475)),f319(f319(f94(f913(x72471,a904)),f297(x72471,x72472,x72474)),f297(x72471,x72473,x72475)))
% 22.40/22.30 [7248]~P4(x72481)+E(f295(x72481,f319(f319(f180(x72481),x72482),x72483),f319(f319(f230(x72481),x72484),x72485)),f319(f319(f94(f913(x72481,a904)),f295(x72481,x72482,x72484)),f295(x72481,x72483,x72485)))
% 22.40/22.30 [7249]~P4(x72491)+E(f319(f319(f94(f913(x72491,a904)),f319(f294(x72491,x72492),x72493)),f319(f294(x72491,x72494),x72495)),f319(f294(x72491,f319(f319(f180(x72491),x72492),x72494)),f319(f319(f230(x72491),x72493),x72495)))
% 22.40/22.30 [7368]~P1(f319(x73681,f460(x73683,x73682,x73681)))+P1(f319(x73681,f319(f319(f244(x73682,x73683),x73684),x73685)))
% 22.40/22.30 [7470]~E(x74702,f319(x74704,x74705))+P1(f319(f319(f321(x74701),x74702),f319(f302(x74703,x74701,x74704),f234(f913(x74703,a904)))))
% 22.40/22.30 [7541]~P17(x75413,x75412,x75414)+P17(x75411,x75412,f319(f319(f10(x75413,f913(x75412,x75412),x75411),x75414),x75415))
% 22.40/22.30 [7542]~P15(x75423,x75422,x75424)+P15(x75421,x75422,f319(f319(f10(x75423,f913(x75422,x75422),x75421),x75424),x75425))
% 22.40/22.30 [7677]~P25(x76771,x76772,x76773,x76774)+P25(x76771,x76772,x76773,f319(f319(f3(f913(x76771,a904)),x76774),x76775))
% 22.40/22.30 [7828]~P1(f319(f319(x78283,x78284),x78285))+P1(f319(f319(f249(x78281,x78282,a904),x78283),f319(f319(f244(x78281,x78282),x78284),x78285)))
% 22.40/22.30 [7945]~P1(f319(x79452,x79454))+~E(f319(f319(f130(x79451),f319(f182(f907(x79451)),f169(x79451,x79452,x79453))),x79453),f319(f319(f143(x79451),x79454),x79455))
% 22.40/22.30 [7965]P25(x79651,x79652,x79653,x79654)+~P25(x79651,x79652,x79653,f319(f319(f93(f913(x79651,a904)),x79655),x79654))
% 22.40/22.30 [7966]P25(x79661,x79662,x79663,x79664)+~P25(x79661,x79662,x79663,f319(f319(f93(f913(x79661,a904)),x79664),x79665))
% 22.40/22.30 [8008]~P4(x80082)+E(f319(f319(f140(x80081,x80082,x80083),x80084),f142(x80081,x80082,x80083,x80085)),f142(x80081,x80082,x80083,f319(f319(f143(x80081),x80084),x80085)))
% 22.40/22.30 [8320]~P15(x83202,x83201,x83203)+E(f319(f134(x83201,x83202,f319(f9(x83202,x83201,x83201),x83203),x83204),x83205),f319(f319(f58(x83202,x83201,x83203),x83204),f319(f164(x83202),x83205)))
% 22.40/22.30 [8347]~E(f319(f319(f130(x83471),f319(f182(f907(x83471)),f169(x83471,x83472,x83473))),x83473),f319(f319(f143(x83471),x83474),x83475))+E(f319(f319(f126(x83471),f169(x83471,x83472,x83473)),f319(f319(f143(x83471),x83474),x83475)),x83473)
% 22.40/22.30 [8374]P1(f319(f319(x83741,x83742),x83743))+~P1(f319(f319(f249(x83744,x83745,a904),x83741),f319(f319(f244(x83744,x83745),x83742),x83743)))
% 22.40/22.30 [8845]P1(f319(f319(f225(f913(x88451,a904)),f319(f302(x88452,x88451,x88453),x88454)),f319(f302(x88452,x88451,x88453),x88455)))+~P1(f319(f319(f225(f913(x88452,a904)),x88454),x88455))
% 22.40/22.30 [8846]P1(f319(f319(f225(f913(x88461,a904)),f319(f303(x88461,x88462,x88463),x88464)),f319(f303(x88461,x88462,x88463),x88465)))+~P1(f319(f319(f225(f913(x88462,a904)),x88464),x88465))
% 22.40/22.30 [8926]E(x89261,f2(a91))+E(f319(f319(f251(x89262,x89263,x89262,f912(x89263,x89262)),f319(x89264,x89265)),f265(x89263,x89262,f319(f319(f3(a91),x89261),f72(a91)),x89264)),f319(f265(x89263,x89262,x89261,x89264),x89265))
% 22.40/22.30 [9041]P1(f319(f319(f247(x90411,x90412,a904,x90413),x90414),x90415))+~P1(f319(x90413,f319(f319(f244(x90411,x90412),x90414),x90415)))
% 22.40/22.30 [9315]~P1(f319(f319(f247(x93152,x93153,a904,x93151),x93154),x93155))+P1(f319(x93151,f319(f319(f244(x93152,x93153),x93154),x93155)))
% 22.40/22.30 [9504]~P1(f319(f319(f321(x95042),x95045),f319(f302(x95041,x95042,x95044),x95043)))+P1(f319(f319(f321(x95041),f319(f85(x95041,x95042,x95043,x95044),x95045)),x95043))
% 22.40/22.30 [9588]~P1(f319(f55(x95883),f319(f302(x95882,x95883,x95885),f234(f913(x95882,a904)))))+P1(f319(f55(x95881),f319(f302(x95882,x95881,f319(f319(f10(x95883,x95881,x95882),x95884),x95885)),f234(f913(x95882,a904)))))
% 22.40/22.30 [9613]P1(f319(f319(f225(f913(f913(x96131,a904),a904)),f319(f302(f913(x96132,a904),f913(x96131,a904),f302(x96132,x96131,x96133)),f319(f300(x96132),x96134))),f319(f300(x96131),x96135)))+~P1(f319(f319(f225(f913(x96131,a904)),f319(f302(x96132,x96131,x96133),x96134)),x96135))
% 22.40/22.30 [9698]E(x96981,x96982)+~P1(f319(f60(x96983,x96984,x96985,x96981,f181(f913(x96983,a904))),x96982))
% 22.40/22.30 [9713]E(f319(f319(f244(x97131,x97132),f539(x97133,x97134,x97135,x97132,x97131)),f540(x97133,x97134,x97135,x97132,x97131)),x97135)+~P1(f319(f319(f321(f912(x97131,x97132)),x97135),f319(f319(f246(x97131,x97132),x97134),x97133)))
% 22.40/22.30 [9819]P1(f319(f319(f321(x98191),f539(x98192,x98193,x98194,x98195,x98191)),x98193))+~P1(f319(f319(f321(f912(x98191,x98195)),x98194),f319(f319(f246(x98191,x98195),x98193),x98192)))
% 22.40/22.30 [9994]P1(f319(f319(f321(x99941),f540(x99942,x99943,x99944,x99941,x99945)),f319(x99942,f539(x99942,x99943,x99944,x99941,x99945))))+~P1(f319(f319(f321(f912(x99945,x99941)),x99944),f319(f319(f246(x99945,x99941),x99943),x99942)))
% 22.40/22.30 [10005]P1(f319(f319(f321(f912(x100051,x100051)),f319(f319(f244(x100051,x100051),x100052),f628(x100053,x100054,x100055,x100052,x100051))),x100053))+~P1(f319(f319(f321(f912(x100051,x100051)),f319(f319(f244(x100051,x100051),x100052),x100055)),f319(f319(f175(f912(x100051,x100051),a904),f319(a104,x100054)),x100053)))
% 22.40/22.30 [10006]P1(f319(f319(f321(f912(x100061,x100061)),f319(f319(f244(x100061,x100061),x100062),f630(x100063,x100064,x100065,x100062,x100061))),x100063))+~P1(f319(f319(f321(f912(x100061,x100061)),f319(f319(f244(x100061,x100061),x100062),x100065)),f319(f319(f175(f912(x100061,x100061),a904),f319(a104,x100064)),x100063)))
% 22.40/22.30 [10023]~P1(f319(f319(f321(f912(f907(x100231),f907(x100231))),f319(f319(f244(f907(x100231),f907(x100231)),f319(f319(f143(x100231),x100232),x100235)),x100234)),f150(x100231,x100233)))+P1(f319(f319(f321(f912(x100231,x100231)),f319(f319(f244(x100231,x100231),x100232),f644(x100233,x100234,x100235,x100232,x100231))),x100233))
% 22.40/22.30 [6452]P1(f319(x64522,x64524))+E(f169(x64521,x64522,f319(f319(f126(x64521),x64523),f319(f319(f143(x64521),x64524),x64525))),f169(x64521,x64522,x64523))
% 22.40/22.30 [6503]~P101(x65032)+E(f319(f319(f319(f93(f913(x65031,x65032)),x65033),x65034),x65035),f319(f319(f93(x65032),f319(x65033,x65035)),f319(x65034,x65035)))
% 22.40/22.30 [6505]~P101(x65052)+E(f319(f319(f319(f94(f913(x65051,x65052)),x65053),x65054),x65055),f319(f319(f94(x65052),f319(x65053,x65055)),f319(x65054,x65055)))
% 22.40/22.30 [6507]~P84(x65072)+E(f319(f319(f319(f3(f913(x65071,x65072)),x65073),x65074),x65075),f319(f319(f3(x65072),f319(x65073,x65075)),f319(x65074,x65075)))
% 22.40/22.30 [6527]E(x65271,x65272)+E(f319(f319(f156(x65273),f319(f319(f151(x65273,x65274),x65271),x65275)),x65272),f319(f319(f156(x65273),x65274),x65272))
% 22.40/22.30 [6796]~E(x67964,f181(f913(x67963,a904)))+E(f319(f319(f93(f913(x67961,a904)),x67962),f319(f319(f33(x67963,f913(x67961,a904)),x67964),x67965)),x67962)
% 22.40/22.30 [6797]~E(x67974,f181(f913(x67973,a904)))+E(f319(f319(f94(f913(x67971,a904)),x67972),f319(f319(f34(x67973,f913(x67971,a904)),x67974),x67975)),x67972)
% 22.40/22.30 [6798]~E(x67984,f181(f913(x67983,a904)))+E(f319(f319(f3(f913(x67981,a904)),x67982),f319(f319(f33(x67983,f913(x67981,a904)),x67984),x67985)),x67982)
% 22.40/22.30 [6816]~E(x68164,f181(f913(x68163,a904)))+E(f319(f319(f301(x68161),x68162),f319(f319(f33(x68163,f913(x68161,a904)),x68164),x68165)),f319(f319(f301(x68161),x68162),f181(f913(x68161,a904))))
% 22.40/22.30 [7588]E(f319(f319(f156(x75881),f319(f319(f146(x75882,x75881),x75883),x75884)),x75885),f319(x75883,f319(f319(f156(x75882),x75884),x75885)))+~P1(f319(f319(f226(a906),x75885),f319(f182(f907(x75882)),x75884)))
% 22.40/22.30 [7649]E(f319(f319(f93(f913(x76491,a904)),f319(x76492,x76493)),f319(f319(f33(x76494,f913(x76491,a904)),x76495),x76492)),f319(f319(f33(x76494,f913(x76491,a904)),x76495),x76492))+~P1(f319(f319(f321(x76494),x76493),x76495))
% 22.40/22.30 [7650]E(f319(f319(f94(f913(x76501,a904)),f319(x76502,x76503)),f319(f319(f34(x76504,f913(x76501,a904)),x76505),x76502)),f319(f319(f34(x76504,f913(x76501,a904)),x76505),x76502))+~P1(f319(f319(f321(x76504),x76503),x76505))
% 22.40/22.30 [8244]~E(x82443,f181(f913(x82441,a904)))+E(f319(f319(f33(x82441,f913(x82442,a904)),x82443),f319(f319(f10(f913(x82442,a904),f913(x82442,a904),x82441),f319(f301(x82442),x82444)),x82445)),f181(f913(x82442,a904)))
% 22.40/22.30 [8249]~P1(f319(f319(f321(x82494),x82493),x82495))+P1(f319(f319(f225(f913(x82491,a904)),f319(x82492,x82493)),f319(f319(f33(x82494,f913(x82491,a904)),x82495),x82492)))
% 22.40/22.30 [8373]~E(f319(x83734,x83732),x83735)+P1(f319(f319(f321(x83731),x83732),f319(f303(x83731,x83733,x83734),f319(f319(f301(x83733),x83735),f181(f913(x83733,a904))))))
% 22.40/22.30 [8421]~P56(x84211,x84212,f319(f278(x84212,x84211),x84213))+E(f319(f319(f94(f913(x84211,a904)),f319(f277(x84212,x84211,x84213),x84214)),f319(f277(x84212,x84211,x84213),x84215)),f319(f277(x84212,x84211,x84213),f319(f319(f94(f913(x84212,a904)),x84214),x84215)))
% 22.40/22.30 [8493]E(x84931,f2(a91))+E(f319(f110(x84932,x84933,f319(x84934,f319(f319(f3(a91),x84931),f72(a91)))),f319(f319(f9(x84932,a91,f908(x84933)),x84935),x84931)),f319(f191(x84932,x84933,x84934,x84935),x84931))
% 22.40/22.30 [8531]E(x85311,f181(f913(x85312,a904)))+E(f319(f319(f33(x85312,f913(x85313,a904)),x85311),f319(f319(f10(f913(x85313,a904),f913(x85313,a904),x85312),f319(f301(x85313),x85314)),x85315)),f319(f319(f301(x85313),x85314),f319(f319(f33(x85312,f913(x85313,a904)),x85311),x85315)))
% 22.40/22.30 [8582]~P25(x85822,x85821,x85823,f234(f913(x85822,a904)))+E(f319(f319(f94(f913(x85821,a904)),f319(f302(x85822,x85821,x85823),x85824)),f319(f302(x85822,x85821,x85823),x85825)),f319(f302(x85822,x85821,x85823),f319(f319(f94(f913(x85822,a904)),x85824),x85825)))
% 22.40/22.30 [8583]~P25(x85832,x85831,x85833,f234(f913(x85832,a904)))+E(f319(f319(f3(f913(x85831,a904)),f319(f302(x85832,x85831,x85833),x85834)),f319(f302(x85832,x85831,x85833),x85835)),f319(f302(x85832,x85831,x85833),f319(f319(f3(f913(x85832,a904)),x85834),x85835)))
% 22.40/22.30 [8655]~P1(f319(f319(f61(x86551,x86552,x86555),x86553),x86554))+P1(f319(f319(f321(f912(x86551,x86552)),f319(f319(f244(x86551,x86552),x86553),x86554)),x86555))
% 22.40/22.30 [8686]P1(f319(f319(f321(x86861),x86862),f319(f276(x86863,x86861),x86864)))+~P1(f319(f319(f321(f912(x86863,x86861)),f319(f319(f244(x86863,x86861),x86865),x86862)),x86864))
% 22.40/22.30 [8688]P1(f319(f319(f321(x86881),x86882),f319(f256(x86881,x86883),x86884)))+~P1(f319(f319(f321(f912(x86881,x86883)),f319(f319(f244(x86881,x86883),x86882),x86885)),x86884))
% 22.40/22.30 [8827]P1(f319(f319(f61(x88271,x88272,x88273),x88274),x88275))+~P1(f319(f319(f321(f912(x88271,x88272)),f319(f319(f244(x88271,x88272),x88274),x88275)),x88273))
% 22.40/22.30 [8861]E(f319(x88611,x88612),x88613)+~P1(f319(f319(f321(x88614),x88612),f319(f303(x88614,x88615,x88611),f319(f319(f301(x88615),x88613),f181(f913(x88615,a904))))))
% 22.40/22.30 [9106]P1(f319(f319(f321(f912(x91061,x91062)),f319(f319(f244(x91061,x91062),x91063),x91064)),f319(f278(x91062,x91061),x91065)))+~P1(f319(f319(f321(f912(x91062,x91061)),f319(f319(f244(x91062,x91061),x91064),x91063)),x91065))
% 22.40/22.30 [9124]~P1(f319(f319(x91241,x91245),x91244))+P1(f319(f319(x91241,f319(f248(x91242,x91243),f319(f319(f244(x91242,x91243),x91244),x91245))),f319(f243(x91242,x91243),f319(f319(f244(x91242,x91243),x91244),x91245))))
% 22.40/22.30 [9154]~P1(f319(f319(f321(f912(x91542,x91541)),f319(f319(f244(x91542,x91541),x91544),x91543)),f319(f278(x91541,x91542),x91545)))+P1(f319(f319(f321(f912(x91541,x91542)),f319(f319(f244(x91541,x91542),x91543),x91544)),x91545))
% 22.40/22.30 [9180]~P1(f319(f319(f321(f912(x91803,x91801)),f319(f319(f244(x91803,x91801),x91805),x91802)),x91804))+P1(f319(f319(f321(x91801),x91802),f319(f277(x91803,x91801,x91804),f319(f319(f301(x91803),x91805),f181(f913(x91803,a904))))))
% 22.40/22.30 [9227]P1(f319(f319(f321(f912(x92271,x92272)),f319(f319(f244(x92271,x92272),x92273),x92274)),x92275))+~P1(f319(f319(f321(x92272),x92274),f319(f277(x92271,x92272,x92275),f319(f319(f301(x92271),x92273),f181(f913(x92271,a904))))))
% 22.40/22.30 [9322]~P76(x93221)+E(f319(f319(f8(a906,x93221),x93222),f295(a906,f319(f319(f74(a906),x93223),x93224),f319(f319(f74(a906),x93225),x93224))),f319(f319(f8(a906,x93221),f319(f319(f10(a906,x93221,a906),x93222),f319(f319(f9(a906,a906,a906),f74(a906)),x93224))),f295(a906,x93223,x93225)))
% 22.40/22.30 [9340]~P76(x93401)+E(f319(f319(f8(a906,x93401),x93402),f319(f294(a906,f319(f319(f74(a906),x93403),x93404)),f319(f319(f74(a906),x93405),x93404))),f319(f319(f8(a906,x93401),f319(f319(f10(a906,x93401,a906),x93402),f319(f319(f9(a906,a906,a906),f74(a906)),x93404))),f319(f294(a906,x93403),x93405)))
% 22.40/22.30 [9398]~P25(x93981,x93982,x93983,f234(f913(x93981,a904)))+E(f319(f319(f146(x93981,x93982),x93983),f319(f128(x93981,f319(f319(f10(a904,a904,x93981),a314),f319(a316,x93984))),x93985)),f319(f128(x93982,f319(f319(f10(a904,a904,x93982),a314),f319(a316,f319(x93983,x93984)))),f319(f319(f146(x93981,x93982),x93983),x93985)))
% 22.40/22.30 [9419]~P25(x94191,x94192,x94193,f319(f319(f301(x94191),x94194),f319(f164(x94191),x94195)))+E(f319(f319(f146(x94191,x94192),x94193),f319(f128(x94191,f319(f319(f10(a904,a904,x94191),a314),f319(a316,x94194))),x94195)),f319(f128(x94192,f319(f319(f10(a904,a904,x94192),a314),f319(a316,f319(x94193,x94194)))),f319(f319(f146(x94191,x94192),x94193),x94195)))
% 22.40/22.30 [9576]P1(f319(f319(f321(f912(f907(x95761),f907(x95761))),f319(f319(f244(f907(x95761),f907(x95761)),f319(f319(f143(x95761),x95762),x95763)),f319(f319(f143(x95761),x95764),x95763))),f149(x95761,x95765)))+~P1(f319(f319(f321(f912(x95761,x95761)),f319(f319(f244(x95761,x95761),x95762),x95764)),x95765))
% 22.40/22.30 [9708]E(f319(f319(f301(x97081),f365(x97082,x97083,x97084,x97085,x97081)),f366(x97082,x97083,x97084,x97085,x97081)),f319(f319(f301(x97081),x97084),x97083))+~P1(f319(f56(x97081,x97085,f319(f319(f301(x97081),x97084),x97083)),x97082))
% 22.40/22.30 [9709]E(f319(f319(f301(x97091),f367(x97092,x97093,x97094,x97095,x97091)),f368(x97092,x97093,x97094,x97095,x97091)),f319(f319(f301(x97091),x97094),x97093))+~P1(f319(f56(x97091,x97095,f319(f319(f301(x97091),x97094),x97093)),x97092))
% 22.40/22.30 [9803]P1(f319(f319(f321(x98031),f476(x98032,x98033,x98034,x98035,x98031)),x98034))+P1(f319(f319(f319(f34(x98031,f913(x98035,a904)),x98034),x98033),x98032))
% 22.40/22.30 [9808]P1(f319(f319(f321(x98081),f467(x98082,x98083,x98081,x98084,x98085)),x98083))+P1(f319(f319(f321(x98085),x98084),f319(f319(f34(x98081,f913(x98085,a904)),x98083),x98082)))
% 22.40/22.30 [9817]P1(f319(f319(f321(x98171),f470(x98172,x98173,x98171,x98174,x98175)),x98173))+P1(f319(f319(f225(f913(x98175,a904)),x98174),f319(f319(f34(x98171,f913(x98175,a904)),x98173),x98172)))
% 22.40/22.30 [9818]P1(f319(f319(f321(x98181),f828(x98182,x98183,x98184,x98185,x98181)),x98185))+P1(f319(f319(f225(f913(x98184,a904)),x98183),f319(f319(f34(x98181,f913(x98184,a904)),x98185),x98182)))
% 22.40/22.30 [9820]P1(f319(f319(x98201,f468(x98202,x98201,x98203,x98204,x98205)),x98202))+~P1(f319(f319(f319(f33(x98205,f913(x98204,a904)),x98203),x98201),x98202))
% 22.40/22.30 [9824]P1(f319(f319(f321(x98241),f468(x98242,x98243,x98244,x98245,x98241)),x98244))+~P1(f319(f319(f319(f33(x98241,f913(x98245,a904)),x98244),x98243),x98242))
% 22.40/22.30 [9825]P54(x98254,f319(f319(f34(x98251,f913(x98254,a904)),x98255),x98253),f319(f319(f34(x98251,f913(f912(x98254,x98254),a904)),x98255),x98252))+P1(f319(f319(f321(x98251),f764(x98252,x98253,x98254,x98255,x98251)),x98255))
% 22.40/22.30 [9826]P54(x98264,f319(f319(f33(x98261,f913(x98264,a904)),x98265),x98263),f319(f319(f33(x98261,f913(f912(x98264,x98264),a904)),x98265),x98262))+P1(f319(f319(f321(x98261),f818(x98262,x98263,x98264,x98265,x98261)),x98265))
% 22.40/22.30 [9837]P1(f319(f319(f321(x98371),f469(x98372,x98373,x98371,x98374,x98375)),x98373))+~P1(f319(f319(f321(x98375),x98374),f319(f319(f33(x98371,f913(x98375,a904)),x98373),x98372)))
% 22.40/22.30 [9843]P1(f319(f319(f321(x98431),x98432),f319(x98433,f469(x98433,x98434,x98435,x98432,x98431))))+~P1(f319(f319(f321(x98431),x98432),f319(f319(f33(x98435,f913(x98431,a904)),x98434),x98433)))
% 22.40/22.30 [9941]~P1(f319(f319(x99414,f476(x99415,x99414,x99413,x99412,x99411)),x99415))+P1(f319(f319(f319(f34(x99411,f913(x99412,a904)),x99413),x99414),x99415))
% 22.40/22.30 [9944]~P1(f319(f319(f321(x99441),x99442),f319(x99445,f467(x99445,x99444,x99443,x99442,x99441))))+P1(f319(f319(f321(x99441),x99442),f319(f319(f34(x99443,f913(x99441,a904)),x99444),x99445)))
% 22.40/22.30 [9947]~P54(x99471,f319(x99474,f818(x99475,x99474,x99471,x99473,x99472)),f319(x99475,f818(x99475,x99474,x99471,x99473,x99472)))+P54(x99471,f319(f319(f33(x99472,f913(x99471,a904)),x99473),x99474),f319(f319(f33(x99472,f913(f912(x99471,x99471),a904)),x99473),x99475))
% 22.40/22.30 [9948]~P54(x99481,f319(x99484,f764(x99485,x99484,x99481,x99483,x99482)),f319(x99485,f764(x99485,x99484,x99481,x99483,x99482)))+P54(x99481,f319(f319(f34(x99482,f913(x99481,a904)),x99483),x99484),f319(f319(f34(x99482,f913(f912(x99481,x99481),a904)),x99483),x99485))
% 22.40/22.30 [9949]~P1(f319(f319(f225(f913(x99491,a904)),x99492),f319(x99495,f470(x99495,x99494,x99493,x99492,x99491))))+P1(f319(f319(f225(f913(x99491,a904)),x99492),f319(f319(f34(x99493,f913(x99491,a904)),x99494),x99495)))
% 22.40/22.30 [9950]~P1(f319(f319(f225(f913(x99501,a904)),x99502),f319(x99505,f828(x99505,x99502,x99501,x99504,x99503))))+P1(f319(f319(f225(f913(x99501,a904)),x99502),f319(f319(f34(x99503,f913(x99501,a904)),x99504),x99505)))
% 22.40/22.30 [10009]~P1(f319(f319(f321(x100091),f365(x100095,x100094,x100093,x100092,x100091)),f366(x100095,x100094,x100093,x100092,x100091)))+~P1(f319(f56(x100091,x100092,f319(f319(f301(x100091),x100093),x100094)),x100095))
% 22.40/22.30 [10010]~P1(f319(f319(f321(x100101),f367(x100105,x100104,x100103,x100102,x100101)),f368(x100105,x100104,x100103,x100102,x100101)))+~P1(f319(f56(x100101,x100102,f319(f319(f301(x100101),x100103),x100104)),x100105))
% 22.40/22.30 [10011]~P1(f319(f319(f321(f912(x100111,x100111)),f319(f319(f244(x100111,x100111),x100112),x100115)),f319(f319(f175(f912(x100111,x100111),a904),f319(a104,x100114)),x100113)))+P1(f319(f319(f321(f912(x100111,x100111)),f319(f319(f244(x100111,x100111),x100112),f629(x100113,x100114,x100115,x100112,x100111))),f319(f319(f175(f912(x100111,x100111),a904),x100114),x100113)))
% 22.40/22.30 [10017]P1(f319(f60(x100171,x100171,x100172,f365(x100173,x100174,x100175,x100172,x100171),f366(x100173,x100174,x100175,x100172,x100171)),x100173))+~P1(f319(f56(x100171,x100172,f319(f319(f301(x100171),x100175),x100174)),x100173))
% 22.40/22.30 [10018]P1(f319(f60(x100181,x100181,x100182,f367(x100183,x100184,x100185,x100182,x100181),f368(x100183,x100184,x100185,x100182,x100181)),x100183))+~P1(f319(f56(x100181,x100182,f319(f319(f301(x100181),x100185),x100184)),x100183))
% 22.40/22.30 [10027]~P4(x100271)+P13(x100271,f319(f319(f146(x100272,x100271),x100273),f319(f128(x100272,f319(f319(f9(x100272,x100271,a904),f319(f319(f10(x100271,f913(x100271,a904),x100272),a316),x100273)),f319(x100274,x100275))),x100275)))
% 22.40/22.30 [10060]~P1(f319(f319(f321(x100602),x100605),f319(f277(x100601,x100602,x100604),x100603)))+P1(f319(f319(f321(f912(x100601,x100602)),f319(f319(f244(x100601,x100602),f508(x100603,x100604,x100601,x100605,x100602)),x100605)),x100604))
% 22.40/22.30 [10061]~P1(f319(f319(f321(x100612),x100615),f319(f277(x100611,x100612,x100614),x100613)))+P1(f319(f319(f321(f912(x100611,x100612)),f319(f319(f244(x100611,x100612),f513(x100613,x100614,x100611,x100615,x100612)),x100615)),x100614))
% 22.40/22.30 [10066]~P1(f319(f319(f321(f912(x100661,x100661)),f319(f319(f244(x100661,x100661),x100665),x100664)),f319(f319(f175(f912(x100661,x100661),a904),f319(a104,x100663)),x100662)))+P1(f319(f319(f321(f912(x100661,x100661)),f319(f319(f244(x100661,x100661),f629(x100662,x100663,x100664,x100665,x100661)),x100664)),x100662))
% 22.40/22.30 [10078]~P1(f319(f319(f321(f912(x100781,x100781)),f319(f319(f244(x100781,x100781),x100785),x100784)),f319(f319(f175(f912(x100781,x100781),a904),f319(a104,x100783)),x100782)))+P1(f319(f319(f321(f912(x100781,x100781)),f319(f319(f244(x100781,x100781),f628(x100782,x100783,x100784,x100785,x100781)),x100784)),f319(f319(f175(f912(x100781,x100781),a904),x100783),x100782)))
% 22.40/22.30 [10079]~P1(f319(f319(f321(f912(x100791,x100791)),f319(f319(f244(x100791,x100791),x100795),x100794)),f319(f319(f175(f912(x100791,x100791),a904),f319(a104,x100793)),x100792)))+P1(f319(f319(f321(f912(x100791,x100791)),f319(f319(f244(x100791,x100791),f630(x100792,x100793,x100794,x100795,x100791)),x100794)),f319(f319(f175(f912(x100791,x100791),a904),x100793),x100792)))
% 22.40/22.30 [10080]~P1(f319(f319(f321(f912(f907(x100801),f907(x100801))),f319(f319(f244(f907(x100801),f907(x100801)),x100805),f319(f319(f143(x100801),x100804),x100803))),f150(x100801,x100802)))+P1(f319(f319(f321(f912(x100801,x100801)),f319(f319(f244(x100801,x100801),f642(x100802,x100803,x100804,x100805,x100801)),x100804)),x100802))
% 22.40/22.30 [7670]~E(x76703,f181(f913(x76702,a904)))+E(f319(f319(f93(f913(x76701,a904)),f319(f319(f33(x76702,f913(x76701,a904)),x76703),x76704)),x76705),x76705)
% 22.40/22.30 [7671]~E(x76713,f181(f913(x76712,a904)))+E(f319(f319(f94(f913(x76711,a904)),f319(f319(f34(x76712,f913(x76711,a904)),x76713),x76714)),x76715),x76715)
% 22.40/22.30 [8084]~E(x80843,f181(f913(x80842,a904)))+E(f319(f319(f3(f913(x80841,a904)),f319(f319(f34(x80842,f913(x80841,a904)),x80843),x80844)),x80845),f319(f319(f3(f913(x80841,a904)),f234(f913(x80841,a904))),x80845))
% 22.40/22.30 [8216]E(f319(f319(f151(x82161,f319(f319(f126(x82161),x82162),x82163)),x82164),x82165),f319(f319(f126(x82161),f319(f319(f151(x82161,x82162),x82164),x82165)),x82163))+~P1(f319(f319(f226(a906),x82164),f319(f182(f907(x82161)),x82162)))
% 22.40/22.30 [8483]E(f319(f319(f156(x84831),f319(f319(f146(a906,x84831),x84832),f131(a906,f319(f294(a906,x84833),x84834)))),x84835),f319(x84832,f319(f319(f74(a906),x84833),x84835)))+~P1(f319(f319(f226(a906),x84835),f319(f319(f3(a906),x84834),x84833)))
% 22.40/22.30 [8498]E(x84981,f2(a91))+E(f114(x84982,x84983,f319(x84984,f319(f319(f3(a91),x84981),f72(a91))),f319(f319(f9(x84982,a91,f908(f910(x84983))),x84985),x84981)),f319(f189(x84982,x84983,x84984,x84985),x84981))
% 22.40/22.30 [8521]~E(x85213,f181(f913(x85211,a904)))+E(f319(f319(f33(x85211,f913(x85212,a904)),x85213),f319(f319(f10(f913(x85212,a904),f913(x85212,a904),x85211),f319(f93(f913(x85212,a904)),x85214)),x85215)),f181(f913(x85212,a904)))
% 22.40/22.30 [8522]~E(x85223,f181(f913(x85221,a904)))+E(f319(f319(f34(x85221,f913(x85222,a904)),x85223),f319(f319(f10(f913(x85222,a904),f913(x85222,a904),x85221),f319(f94(f913(x85222,a904)),x85224)),x85225)),f234(f913(x85222,a904)))
% 22.40/22.30 [8523]~E(x85233,f181(f913(x85231,a904)))+E(f319(f319(f34(x85231,f913(x85232,a904)),x85233),f319(f319(f10(f913(x85232,a904),f913(x85232,a904),x85231),f319(f3(f913(x85232,a904)),x85234)),x85235)),f234(f913(x85232,a904)))
% 22.40/22.30 [8525]~P145(x85252)+E(f319(f319(f8(x85251,x85252),f319(f319(f10(x85252,x85252,x85251),f319(f75(x85252),x85253)),x85254)),x85255),f319(f319(f75(x85252),x85253),f319(f319(f8(x85251,x85252),x85254),x85255)))
% 22.40/22.30 [8812]E(x88121,f181(f913(x88122,a904)))+E(f319(f319(f33(x88122,f913(x88123,a904)),x88121),f319(f319(f10(f913(x88123,a904),f913(x88123,a904),x88122),f319(f93(f913(x88123,a904)),x88124)),x88125)),f319(f319(f93(f913(x88123,a904)),x88124),f319(f319(f33(x88122,f913(x88123,a904)),x88121),x88125)))
% 22.40/22.30 [8813]E(x88131,f181(f913(x88132,a904)))+E(f319(f319(f34(x88132,f913(x88133,a904)),x88131),f319(f319(f10(f913(x88133,a904),f913(x88133,a904),x88132),f319(f94(f913(x88133,a904)),x88134)),x88135)),f319(f319(f94(f913(x88133,a904)),x88134),f319(f319(f34(x88132,f913(x88133,a904)),x88131),x88135)))
% 22.40/22.30 [8814]E(x88141,f181(f913(x88142,a904)))+E(f319(f319(f34(x88142,f913(x88143,a904)),x88141),f319(f319(f10(f913(x88143,a904),f913(x88143,a904),x88142),f319(f3(f913(x88143,a904)),x88144)),x88145)),f319(f319(f3(f913(x88143,a904)),x88144),f319(f319(f33(x88142,f913(x88143,a904)),x88141),x88145)))
% 22.40/22.30 [9024]~P1(f319(f319(f226(a906),f319(x90244,x90242)),f319(x90244,x90243)))+P1(f319(f319(f321(f912(x90241,x90241)),f319(f319(f244(x90241,x90241),x90242),x90243)),f145(x90241,f319(f319(f143(f913(x90241,a906)),x90244),x90245))))
% 22.40/22.30 [9268]~P40(f913(x92685,a904),f913(x92681,a904),x92682)+P1(f319(f319(f225(f913(x92681,a904)),f319(f319(f93(f913(x92681,a904)),f319(x92682,x92683)),f319(x92682,x92684))),f319(x92682,f319(f319(f93(f913(x92685,a904)),x92683),x92684))))
% 22.40/22.30 [9287]~P25(x92872,x92871,x92873,f319(f319(f93(f913(x92872,a904)),x92874),x92875))+E(f319(f319(f94(f913(x92871,a904)),f319(f302(x92872,x92871,x92873),f319(f319(f3(f913(x92872,a904)),x92874),x92875))),f319(f302(x92872,x92871,x92873),f319(f319(f3(f913(x92872,a904)),x92875),x92874))),f181(f913(x92871,a904)))
% 22.40/22.30 [9544]~P25(x95443,x95441,x95445,f234(f913(x95443,a904)))+E(f319(f66(x95441,x95442,x95443,f319(f66(x95443,x95442,x95441,x95444),f85(x95443,x95441,f234(f913(x95443,a904)),x95445))),x95445),x95444)
% 22.40/22.30 [9574]~P1(f319(f319(f225(f913(x95743,a904)),f319(f277(x95741,x95743,x95744),x95742)),x95745))+P1(f319(f319(f225(f913(x95741,a904)),x95742),f319(f73(f913(x95741,a904)),f319(f277(x95743,x95741,f319(f278(x95741,x95743),x95744)),f319(f73(f913(x95743,a904)),x95745)))))
% 22.40/22.30 [9597]~P25(x95971,x95972,x95973,f319(f319(f301(x95971),x95974),x95975))+~P1(f319(f319(f321(x95972),f319(x95973,x95974)),f319(f302(x95971,x95972,x95973),f319(f319(f3(f913(x95971,a904)),x95975),f319(f319(f301(x95971),x95974),f181(f913(x95971,a904)))))))
% 22.40/22.30 [9663]P1(f319(f319(f225(f913(x96631,a904)),f319(f277(x96632,x96631,x96633),x96634)),x96635))+~P1(f319(f319(f225(f913(x96632,a904)),x96634),f319(f73(f913(x96632,a904)),f319(f277(x96631,x96632,f319(f278(x96632,x96631),x96633)),f319(f73(f913(x96631,a904)),x96635)))))
% 22.40/22.30 [9742]~P92(x97421)+P1(f319(f319(f225(x97421),f319(f69(x97421),f319(f319(f3(x97421),f319(f319(f74(x97421),x97422),x97423)),f319(f319(f74(x97421),x97424),x97425)))),f319(f319(f74(x97421),f319(f69(x97421),f319(f319(f3(x97421),x97422),x97424))),f319(f69(x97421),f319(f319(f3(x97421),x97423),x97425)))))
% 22.40/22.30 [9858]P1(f319(f319(f321(x98581),f471(x98582,x98583,x98584,x98581,x98585)),x98584))+P1(f319(f319(f225(f913(x98585,a904)),f319(f319(f33(x98581,f913(x98585,a904)),x98584),x98583)),x98582))
% 22.40/22.30 [10043]~P1(f319(f319(f225(f913(x100431,a904)),f319(x100434,f471(x100435,x100434,x100433,x100432,x100431))),x100435))+P1(f319(f319(f225(f913(x100431,a904)),f319(f319(f33(x100432,f913(x100431,a904)),x100433),x100434)),x100435))
% 22.40/22.30 [8633]E(f319(f319(f126(x86331),x86332),f319(f319(f151(x86331,x86333),f319(f319(f3(a906),x86334),f319(f182(f907(x86331)),x86332))),x86335)),f319(f319(f151(x86331,f319(f319(f126(x86331),x86332),x86333)),x86334),x86335))+P1(f319(f319(f226(a906),x86334),f319(f182(f907(x86331)),x86332)))
% 22.40/22.30 [8662]~P139(x86621)+E(f319(f319(f74(x86621),f319(f319(f75(x86621),x86622),x86623)),f319(f319(f74(x86621),f319(f319(f75(x86621),x86624),x86623)),x86625)),f319(f319(f74(x86621),f319(f319(f75(x86621),f319(f319(f74(x86621),x86622),x86624)),x86623)),x86625))
% 22.40/22.30 [9237]~P145(x92371)+E(f319(f157(x92371),f319(f319(f146(x92372,x92371),f319(f319(f10(x92371,x92371,x92372),f319(f75(x92371),x92373)),x92374)),x92375)),f319(f319(f75(x92371),x92373),f319(f157(x92371),f319(f319(f146(x92372,x92371),x92374),x92375))))
% 22.40/22.30 [9418]E(f319(f182(f907(x94181)),f319(f319(f167(x94181),f319(f319(f230(a906),f319(f182(f907(x94181)),x94182)),f319(f182(f907(x94183)),x94184))),x94182)),f319(f182(f907(x94183)),f319(f319(f167(x94183),f319(f319(f230(a906),f319(f182(f907(x94181)),x94182)),f319(f182(f907(x94183)),x94184))),x94184)))+P1(f319(x94185,f319(f319(f173(x94181,x94183),x94182),x94184)))
% 22.40/22.30 [9673]~P145(x96732)+E(f319(f319(f8(x96731,x96732),f319(f319(f9(x96731,x96732,x96732),f319(f319(f10(x96732,f913(x96732,x96732),x96731),f75(x96732)),x96733)),x96734)),x96735),f319(f319(f75(x96732),f319(f319(f8(x96731,x96732),x96733),x96735)),x96734))
% 22.40/22.30 [9674]~P73(x96742)+E(f319(f319(f8(x96741,x96742),f319(f319(f9(x96741,x96742,x96742),f319(f319(f10(x96742,f913(x96742,x96742),x96741),f282(x96742)),x96743)),x96744)),x96745),f319(f319(f282(x96742),f319(f319(f8(x96741,x96742),x96743),x96745)),x96744))
% 22.40/22.30 [9681]~P67(x96812)+E(f319(f319(f8(x96811,x96812),f319(f319(f20(x96811,x96812,x96812),f319(f319(f10(x96812,f913(x96812,x96812),x96811),f3(x96812)),x96813)),x96814)),x96815),f319(f319(f3(x96812),f319(f319(f8(x96811,x96812),x96813),x96815)),f319(f319(f8(x96811,x96812),x96814),x96815)))
% 22.40/22.30 [9682]~P76(x96822)+E(f319(f319(f8(x96821,x96822),f319(f319(f20(x96821,x96822,x96822),f319(f319(f10(x96822,f913(x96822,x96822),x96821),f74(x96822)),x96823)),x96824)),x96825),f319(f319(f74(x96822),f319(f319(f8(x96821,x96822),x96823),x96825)),f319(f319(f8(x96821,x96822),x96824),x96825)))
% 22.40/22.30 [9683]~P82(x96832)+E(f319(f319(f11(x96831,x96832),f319(f319(f20(x96831,x96832,x96832),f319(f319(f10(x96832,f913(x96832,x96832),x96831),f75(x96832)),x96833)),x96834)),x96835),f319(f319(f75(x96832),f319(f319(f11(x96831,x96832),x96833),x96835)),f319(f319(f11(x96831,x96832),x96834),x96835)))
% 22.40/22.30 [9720]~E(x97203,f181(f913(x97201,a904)))+E(f319(f319(f33(x97201,f913(x97202,a904)),x97203),f319(f319(f9(x97201,f913(x97202,a904),f913(x97202,a904)),f319(f319(f10(f913(x97202,a904),f913(f913(x97202,a904),f913(x97202,a904)),x97201),f93(f913(x97202,a904))),x97204)),x97205)),f181(f913(x97202,a904)))
% 22.40/22.30 [9721]~E(x97213,f181(f913(x97211,a904)))+E(f319(f319(f34(x97211,f913(x97212,a904)),x97213),f319(f319(f9(x97211,f913(x97212,a904),f913(x97212,a904)),f319(f319(f10(f913(x97212,a904),f913(f913(x97212,a904),f913(x97212,a904)),x97211),f94(f913(x97212,a904))),x97214)),x97215)),f234(f913(x97212,a904)))
% 22.40/22.30 [9722]~E(x97223,f181(f913(x97221,a904)))+E(f319(f319(f34(x97221,f913(x97222,a904)),x97223),f319(f319(f9(x97221,f913(x97222,a904),f913(x97222,a904)),f319(f319(f10(f913(x97222,a904),f913(f913(x97222,a904),f913(x97222,a904)),x97221),f3(f913(x97222,a904))),x97224)),x97225)),f234(f913(x97222,a904)))
% 22.40/22.30 [9750]E(x97501,f181(f913(x97502,a904)))+E(f319(f319(f33(x97502,f913(x97503,a904)),x97501),f319(f319(f9(x97502,f913(x97503,a904),f913(x97503,a904)),f319(f319(f10(f913(x97503,a904),f913(f913(x97503,a904),f913(x97503,a904)),x97502),f93(f913(x97503,a904))),x97504)),x97505)),f319(f319(f93(f913(x97503,a904)),f319(f319(f33(x97502,f913(x97503,a904)),x97501),x97504)),x97505))
% 22.40/22.30 [9751]E(x97511,f181(f913(x97512,a904)))+E(f319(f319(f34(x97512,f913(x97513,a904)),x97511),f319(f319(f9(x97512,f913(x97513,a904),f913(x97513,a904)),f319(f319(f10(f913(x97513,a904),f913(f913(x97513,a904),f913(x97513,a904)),x97512),f94(f913(x97513,a904))),x97514)),x97515)),f319(f319(f94(f913(x97513,a904)),f319(f319(f34(x97512,f913(x97513,a904)),x97511),x97514)),x97515))
% 22.40/22.30 [9752]E(x97521,f181(f913(x97522,a904)))+E(f319(f319(f34(x97522,f913(x97523,a904)),x97521),f319(f319(f9(x97522,f913(x97523,a904),f913(x97523,a904)),f319(f319(f10(f913(x97523,a904),f913(f913(x97523,a904),f913(x97523,a904)),x97522),f3(f913(x97523,a904))),x97524)),x97525)),f319(f319(f3(f913(x97523,a904)),f319(f319(f34(x97522,f913(x97523,a904)),x97521),x97524)),x97525))
% 22.40/22.30 [9292]~P1(f319(f319(f225(a906),x92921),x92924))+E(f319(f319(f3(a906),f319(f319(f74(a906),f319(f319(f75(a906),x92921),x92922)),x92923)),f319(f319(f74(a906),f319(f319(f75(a906),x92924),x92922)),x92925)),f319(f319(f3(a906),x92923),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x92924),x92921)),x92922)),x92925)))
% 22.40/22.30 [9921]~P145(x99211)+E(f319(f157(x99211),f319(f319(f146(x99212,x99211),f319(f319(f9(x99212,x99211,x99211),f319(f319(f10(x99211,f913(x99211,x99211),x99212),f75(x99211)),x99213)),x99214)),x99215)),f319(f319(f75(x99211),f319(f157(x99211),f319(f319(f146(x99212,x99211),x99213),x99215))),x99214))
% 22.40/22.30 [9931]~P67(x99311)+E(f319(f157(x99311),f319(f319(f146(x99312,x99311),f319(f319(f20(x99312,x99311,x99311),f319(f319(f10(x99311,f913(x99311,x99311),x99312),f3(x99311)),x99313)),x99314)),x99315)),f319(f319(f3(x99311),f319(f157(x99311),f319(f319(f146(x99312,x99311),x99313),x99315))),f319(f157(x99311),f319(f319(f146(x99312,x99311),x99314),x99315))))
% 22.40/22.30 [9932]~P76(x99321)+E(f319(f157(x99321),f319(f319(f146(x99322,x99321),f319(f319(f20(x99322,x99321,x99321),f319(f319(f10(x99321,f913(x99321,x99321),x99322),f74(x99321)),x99323)),x99324)),x99325)),f319(f319(f74(x99321),f319(f157(x99321),f319(f319(f146(x99322,x99321),x99323),x99325))),f319(f157(x99321),f319(f319(f146(x99322,x99321),x99324),x99325))))
% 22.40/22.30 [10053]P1(f319(x100531,f319(f319(f173(x100532,x100533),x100534),x100535)))+~P1(f319(x100531,f319(f319(f173(x100532,x100533),f319(f319(f167(x100532),f319(f319(f230(a906),f319(f182(f907(x100532)),x100534)),f319(f182(f907(x100533)),x100535))),x100534)),f319(f319(f167(x100533),f319(f319(f230(a906),f319(f182(f907(x100532)),x100534)),f319(f182(f907(x100533)),x100535))),x100535))))
% 22.40/22.30 [10327]~P1(f319(f319(f321(f912(x103272,x103271)),f319(f319(f244(x103272,x103271),x103274),x103275)),f319(f278(x103271,x103272),x103273)))+P1(f319(f319(f235(x103271,x103272,f319(f319(f9(x103271,f913(f912(x103271,x103272),a904),f913(x103272,a904)),f319(f319(f10(f913(x103272,f913(f913(f912(x103271,x103272),a904),a904)),f913(f913(f912(x103271,x103272),a904),f913(x103272,a904)),x103271),f9(x103272,f913(f912(x103271,x103272),a904),a904)),f319(f319(f10(f913(x103272,f912(x103271,x103272)),f913(x103272,f913(f913(f912(x103271,x103272),a904),a904)),x103271),f319(f10(f912(x103271,x103272),f913(f913(f912(x103271,x103272),a904),a904),x103272),f321(f912(x103271,x103272)))),f244(x103271,x103272)))),x103273)),x103274),x103275))
% 22.40/22.30 [10348]P1(f319(f319(f321(f912(x103481,x103482)),f319(f319(f244(x103481,x103482),x103483),x103484)),f319(f278(x103482,x103481),x103485)))+~P1(f319(f319(f235(x103482,x103481,f319(f319(f9(x103482,f913(f912(x103482,x103481),a904),f913(x103481,a904)),f319(f319(f10(f913(x103481,f913(f913(f912(x103482,x103481),a904),a904)),f913(f913(f912(x103482,x103481),a904),f913(x103481,a904)),x103482),f9(x103481,f913(f912(x103482,x103481),a904),a904)),f319(f319(f10(f913(x103481,f912(x103482,x103481)),f913(x103481,f913(f913(f912(x103482,x103481),a904),a904)),x103482),f319(f10(f912(x103482,x103481),f913(f913(f912(x103482,x103481),a904),a904),x103481),f321(f912(x103482,x103481)))),f244(x103482,x103481)))),x103485)),x103483),x103484))
% 22.40/22.30 [9543]~P1(f319(f319(f225(a906),x95434),x95431))+E(f319(f319(f3(a906),f319(f319(f74(a906),f319(f319(f75(a906),x95431),x95432)),x95433)),f319(f319(f74(a906),f319(f319(f75(a906),x95434),x95432)),x95435)),f319(f319(f3(a906),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x95431),x95434)),x95432)),x95433)),x95435))
% 22.40/22.30 [7376]E(x73761,x73762)+~E(f213(x73763,x73764,x73765,x73761),f213(x73763,x73764,x73766,x73762))
% 22.40/22.30 [7377]E(x73771,x73772)+~E(f213(x73773,x73774,x73771,x73775),f213(x73773,x73774,x73772,x73776))
% 22.40/22.30 [8468]~P20(x84685,x84681,x84682,x84686)+E(f319(f66(x84681,x84681,x84681,f319(x84682,x84683)),f319(x84682,x84684)),f319(f66(x84681,x84681,x84681,f319(x84682,x84684)),f319(x84682,x84683)))
% 22.40/22.30 [8704]~P58(x87044,x87045,x87042,x87041,x87046)+E(f319(x87041,f319(x87042,x87043)),x87043)
% 22.40/22.30 [8860]P25(x88601,x88602,x88603,x88604)+~P25(x88601,x88605,f319(f66(x88602,x88605,x88601,x88606),x88603),x88604)
% 22.40/22.30 [8940]~E(x89406,x89404)+E(f319(f68(x89401,x89402,x89403,x89404,x89405),x89406),x89405)
% 22.40/22.30 [8947]E(x89471,x89472)+E(f319(f68(x89473,x89474,x89475,x89472,x89476),x89471),f319(x89475,x89471))
% 22.40/22.30 [8960]~P25(x89604,x89602,f319(f66(x89601,x89602,x89604,x89603),x89605),x89606)+P25(x89601,x89602,x89603,f319(f302(x89604,x89601,x89605),x89606))
% 22.40/22.30 [9684]P1(f319(f55(x96841),x96842))+~P1(f319(f60(x96841,x96843,x96844,x96845,x96842),x96846))
% 22.40/22.30 [9693]~P1(f319(f319(f321(x96934),x96933),f289(x96934,x96931,x96935,x96932,x96936)))+P1(f319(f319(x96931,x96932),x96933))
% 22.40/22.30 [9694]~P1(f319(f319(f321(x96944),x96943),f292(x96944,x96945,x96941,x96942,x96946)))+P1(f319(f319(x96941,x96942),x96943))
% 22.40/22.30 [9695]~P1(f319(f319(f321(x96954),x96952),f289(x96954,x96955,x96951,x96956,x96953)))+P1(f319(f319(x96951,x96952),x96953))
% 22.40/22.30 [9696]~P1(f319(f319(f321(x96964),x96962),f292(x96964,x96961,x96965,x96966,x96963)))+P1(f319(f319(x96961,x96962),x96963))
% 22.40/22.30 [10182]P12(x101821,x101822,x101823,x101824,x101825,x101826)+~E(f319(f319(x101826,f841(x101823,x101826,x101825,x101822,x101824,x101821)),f843(x101823,x101826,x101825,x101822,x101824,x101821)),f319(f319(x101826,f842(x101823,x101826,x101825,x101822,x101824,x101821)),f844(x101823,x101826,x101825,x101822,x101824,x101821)))
% 22.40/22.30 [5876]E(x58761,x58762)+~E(f319(f319(f244(x58763,x58764),x58765),x58761),f319(f319(f244(x58763,x58764),x58766),x58762))
% 22.40/22.30 [5878]E(x58781,x58782)+~E(f319(f319(f244(x58783,x58784),x58781),x58785),f319(f319(f244(x58783,x58784),x58782),x58786))
% 22.40/22.30 [6015]~P17(x60155,x60156,x60151)+E(f319(f319(x60151,x60152),f319(f319(x60151,x60153),x60154)),f319(f319(x60151,x60153),f319(f319(x60151,x60152),x60154)))
% 22.40/22.30 [7439]~P32(x74394,x74391,f319(f319(f143(x74394),x74392),x74395),f319(f319(f143(x74394),x74393),x74396))+P1(f319(f319(x74391,x74392),x74393))
% 22.40/22.30 [7782]P32(x77821,x77822,x77823,x77824)+~P32(x77821,x77822,f319(f319(f143(x77821),x77825),x77823),f319(f319(f143(x77821),x77826),x77824))
% 22.40/22.30 [8802]~P58(x88025,x88021,x88022,x88026,x88024)+P1(f319(f319(f321(x88021),f319(x88022,x88023)),x88024))
% 22.40/22.30 [8989]E(f319(f70(x89891,x89892,x89893,x89894,x89895),x89896),f319(x89893,x89896))+P1(f319(f319(f321(x89891),x89896),x89895))
% 22.40/22.30 [9012]~E(x90123,f319(f319(f143(x90121),x90125),x90126))+P1(f319(f319(f321(f912(f907(x90121),f907(x90121))),f319(f319(f244(f907(x90121),f907(x90121)),x90122),f319(f319(f126(x90121),x90122),x90123))),f139(x90121,x90124)))
% 22.40/22.30 [9017]E(f319(f70(x90171,x90172,x90173,x90174,x90175),x90176),f319(x90174,x90176))+~P1(f319(f319(f321(x90171),x90176),x90175))
% 22.40/22.30 [9243]~P34(x92431,x92432,x92433,x92435,x92436)+P34(x92431,x92432,x92433,f319(f319(f167(x92431),x92434),x92435),f319(f319(f167(x92432),x92434),x92436))
% 22.40/22.30 [9244]~P34(x92441,x92442,x92443,x92445,x92446)+P34(x92441,x92442,x92443,f319(f319(f130(x92441),x92444),x92445),f319(f319(f130(x92442),x92444),x92446))
% 22.40/22.30 [9514]E(f319(f302(x95141,x95142,f68(x95141,x95142,x95143,x95144,x95145)),x95146),f319(f302(x95141,x95142,x95143),x95146))+P1(f319(f319(f321(x95141),x95144),x95146))
% 22.40/22.30 [9517]E(f319(f319(f146(x95171,x95172),f68(x95171,x95172,x95173,x95174,x95175)),x95176),f319(f319(f146(x95171,x95172),x95173),x95176))+P1(f319(f319(f321(x95171),x95174),f319(f164(x95171),x95176)))
% 22.40/22.30 [9762]~P24(x97624,x97622,x97625,x97623,x97626,x97621)+E(f319(x97621,f181(f913(x97622,a904))),x97623)
% 22.40/22.30 [10012]~E(f319(x100124,f319(f243(x100121,x100123),x100125)),f319(x100126,f319(f243(x100121,x100123),x100125)))+E(f319(f250(x100121,x100122,x100123,x100123,x100124,f25(x100123)),x100125),f319(f250(x100121,x100122,x100123,x100123,x100126,f25(x100123)),x100125))
% 22.40/22.30 [10013]~E(f319(x100134,f319(f248(x100131,x100132),x100135)),f319(x100136,f319(f248(x100131,x100132),x100135)))+E(f319(f250(x100131,x100131,x100132,x100133,f25(x100131),x100134),x100135),f319(f250(x100131,x100131,x100132,x100133,f25(x100131),x100136),x100135))
% 22.40/22.30 [10050]~E(f319(f250(x100502,x100506,x100503,x100503,x100501,f25(x100503)),x100504),f319(f250(x100502,x100506,x100503,x100503,x100505,f25(x100503)),x100504))+E(f319(x100501,f319(f243(x100502,x100503),x100504)),f319(x100505,f319(f243(x100502,x100503),x100504)))
% 22.40/22.30 [10051]~E(f319(f250(x100512,x100512,x100513,x100516,f25(x100512),x100511),x100514),f319(f250(x100512,x100512,x100513,x100516,f25(x100512),x100515),x100514))+E(f319(x100511,f319(f248(x100512,x100513),x100514)),f319(x100515,f319(f248(x100512,x100513),x100514)))
% 22.40/22.30 [8905]P1(f319(f319(f321(x89051),x89052),x89053))+~P1(f319(f319(f321(f912(x89051,x89054)),f319(f319(f244(x89051,x89054),x89052),x89055)),f319(f319(f246(x89051,x89054),x89053),x89056)))
% 22.40/22.30 [8921]P1(f319(f319(f321(x89211),x89212),f319(x89213,x89214)))+~P1(f319(f319(f321(f912(x89215,x89211)),f319(f319(f244(x89215,x89211),x89214),x89212)),f319(f319(f246(x89215,x89211),x89216),x89213)))
% 22.40/22.30 [9364]P1(f319(f319(f321(f912(x93641,x93641)),f319(f319(f244(x93641,x93641),f319(x93642,x93643)),f319(x93642,x93644))),x93645))+~P1(f319(f319(f321(f912(x93646,x93646)),f319(f319(f244(x93646,x93646),x93643),x93644)),f319(f319(f280(x93641,x93646),x93645),x93642)))
% 22.40/22.30 [9384]~P1(f319(f319(f321(f912(x93844,x93844)),f319(f319(f244(x93844,x93844),f319(x93846,x93842)),f319(x93846,x93843))),x93845))+P1(f319(f319(f321(f912(x93841,x93841)),f319(f319(f244(x93841,x93841),x93842),x93843)),f319(f319(f280(x93844,x93841),x93845),x93846)))
% 22.40/22.30 [10052]E(f319(f319(f244(x100521,x100522),f639(x100523,x100524,x100525,x100526,x100522,x100521)),f640(x100523,x100524,x100525,x100526,x100522,x100521)),x100526)+~P1(f319(f319(f321(f912(x100521,x100522)),x100526),f319(f319(f281(x100521,x100525,x100522),x100524),x100523)))
% 22.40/22.30 [10261]~P1(f319(f319(f321(f912(x102611,x102616)),x102615),f319(f319(f281(x102611,x102612,x102616),x102614),x102613)))+P1(f319(f319(f321(f912(x102611,x102612)),f319(f319(f244(x102611,x102612),f639(x102613,x102614,x102612,x102615,x102616,x102611)),f641(x102613,x102614,x102612,x102615,x102616,x102611))),x102614))
% 22.40/22.30 [10262]~P1(f319(f319(f321(f912(x102626,x102622)),x102625),f319(f319(f281(x102626,x102621,x102622),x102624),x102623)))+P1(f319(f319(f321(f912(x102621,x102622)),f319(f319(f244(x102621,x102622),f641(x102623,x102624,x102621,x102625,x102622,x102626)),f640(x102623,x102624,x102621,x102625,x102622,x102626))),x102623))
% 22.40/22.30 [10263]P12(x102631,x102632,x102633,x102634,x102635,x102636)+P1(f319(f319(f321(f912(x102632,x102632)),f319(f319(f244(x102632,x102632),f844(x102633,x102636,x102635,x102632,x102634,x102631)),f843(x102633,x102636,x102635,x102632,x102634,x102631))),x102635))
% 22.40/22.30 [10264]P12(x102641,x102642,x102643,x102644,x102645,x102646)+P1(f319(f319(f321(f912(x102641,x102641)),f319(f319(f244(x102641,x102641),f842(x102643,x102646,x102645,x102642,x102644,x102641)),f841(x102643,x102646,x102645,x102642,x102644,x102641))),x102644))
% 22.40/22.30 [7851]~P5(x78512)+E(f319(f319(f33(x78511,x78512),x78513),f319(f319(f9(x78511,x78514,x78512),x78515),x78516)),f319(f319(f319(f33(x78511,f913(x78514,x78512)),x78513),x78515),x78516))
% 22.40/22.30 [7852]~P5(x78522)+E(f319(f319(f34(x78521,x78522),x78523),f319(f319(f9(x78521,x78524,x78522),x78525),x78526)),f319(f319(f319(f34(x78521,f913(x78524,x78522)),x78523),x78525),x78526))
% 22.40/22.30 [8611]E(f319(f319(f33(x86111,f913(x86112,a904)),x86113),f319(f319(f10(f913(x86112,a904),f913(x86112,a904),x86111),f319(f301(x86112),x86114)),x86115)),f319(f319(f301(x86112),x86114),f319(f319(f33(x86111,f913(x86112,a904)),x86113),x86115)))+~P1(f319(f319(f321(x86111),x86116),x86113))
% 22.40/22.30 [9068]~P5(x90682)+E(f319(f319(f33(x90681,x90682),x90683),f319(f319(f10(f913(x90684,x90682),x90682,x90681),f319(f33(x90684,x90682),x90685)),f319(f9(x90684,x90681,x90682),x90686))),f319(f319(f33(x90684,x90682),x90685),f319(f319(f10(f913(x90681,x90682),x90682,x90684),f319(f33(x90681,x90682),x90683)),x90686)))
% 22.40/22.30 [9069]~P5(x90692)+E(f319(f319(f34(x90691,x90692),x90693),f319(f319(f10(f913(x90694,x90692),x90692,x90691),f319(f34(x90694,x90692),x90695)),f319(f9(x90694,x90691,x90692),x90696))),f319(f319(f34(x90694,x90692),x90695),f319(f319(f10(f913(x90691,x90692),x90692,x90694),f319(f34(x90691,x90692),x90693)),x90696)))
% 22.40/22.30 [9272]P1(f319(f319(f321(x92721),x92722),f319(f164(x92721),x92723)))+~P1(f319(f319(f321(f912(x92724,x92721)),f319(f319(f244(x92724,x92721),x92725),x92722)),f319(f164(f912(x92724,x92721)),f319(f319(f173(x92724,x92721),x92726),x92723))))
% 22.40/22.30 [9273]P1(f319(f319(f321(x92731),x92732),f319(f164(x92731),x92733)))+~P1(f319(f319(f321(f912(x92731,x92734)),f319(f319(f244(x92731,x92734),x92732),x92735)),f319(f164(f912(x92731,x92734)),f319(f319(f173(x92731,x92734),x92733),x92736))))
% 22.40/22.30 [9380]P1(f319(f319(f225(f913(x93801,a904)),f319(f277(x93802,x93801,x93803),x93804)),x93805))+~P1(f319(f319(f225(f913(f912(x93802,x93801),a904)),x93803),f319(f319(f246(x93802,x93801),x93806),f319(f18(f913(x93801,a904),x93802),x93805))))
% 22.40/22.30 [9385]~P26(x93854,x93852,x93855,f234(f913(x93854,a904)),f234(f913(x93852,a904)))+E(f319(f319(f34(x93851,f913(x93852,a904)),x93853),f319(f319(f10(f913(x93854,a904),f913(x93852,a904),x93851),f302(x93854,x93852,x93855)),x93856)),f319(f302(x93854,x93852,x93855),f319(f319(f34(x93851,f913(x93854,a904)),x93853),x93856)))
% 22.40/22.30 [9575]P1(f319(f319(f321(f912(f907(x95751),f907(x95751))),f319(f319(f244(f907(x95751),f907(x95751)),f319(f319(f143(x95751),x95752),x95753)),f319(f319(f143(x95751),x95754),x95755))),f139(x95751,x95756)))+~P1(f319(f319(f321(f912(x95751,x95751)),f319(f319(f244(x95751,x95751),x95752),x95754)),x95756))
% 22.40/22.30 [10049]E(f319(f319(f244(x100491,x100492),f582(x100493,x100494,x100495,x100492,x100491,x100496)),f583(x100493,x100494,x100495,x100492,x100491,x100496)),x100496)+P1(f319(f319(f321(x100495),x100494),f319(f319(f249(x100491,x100492,f913(x100495,a904)),x100493),x100496)))
% 22.40/22.30 [10054]E(f319(f319(f244(x100541,x100542),f584(x100543,x100544,x100542,x100541,x100545,x100546)),f585(x100543,x100544,x100542,x100541,x100545,x100546)),x100543)+~P1(f319(f319(f321(x100546),x100545),f319(f319(f249(x100541,x100542,f913(x100546,a904)),x100544),x100543)))
% 22.40/22.30 [10196]P1(f319(f319(f321(x101961),x101962),f319(f319(x101963,f584(x101964,x101963,x101965,x101966,x101962,x101961)),f585(x101964,x101963,x101965,x101966,x101962,x101961))))+~P1(f319(f319(f321(x101961),x101962),f319(f319(f249(x101966,x101965,f913(x101961,a904)),x101963),x101964)))
% 22.40/22.30 [10232]~P1(f319(f319(f321(x102321),x102322),f319(f319(x102325,f582(x102325,x102322,x102321,x102324,x102323,x102326)),f583(x102325,x102322,x102321,x102324,x102323,x102326))))+P1(f319(f319(f321(x102321),x102322),f319(f319(f249(x102323,x102324,f913(x102321,a904)),x102325),x102326)))
% 22.40/22.30 [8509]E(x85091,x85092)+E(f319(f319(f151(x85093,f319(f319(f151(x85093,x85094),x85091),x85095)),x85092),x85096),f319(f319(f151(x85093,f319(f319(f151(x85093,x85094),x85092),x85096)),x85091),x85095))
% 22.40/22.30 [9647]~P1(f319(f319(f321(x96473),x96476),x96475))+E(f319(f319(f301(x96471),x96472),f319(f302(x96473,x96471,x96474),f319(f319(f3(f913(x96473,a904)),x96475),f319(f319(f301(x96473),x96476),f181(f913(x96473,a904)))))),f319(f302(x96473,x96471,f68(x96473,x96471,x96474,x96476,x96472)),x96475))
% 22.40/22.30 [9147]~P1(f319(f319(x91474,x91475),x91476))+P1(f319(f319(f319(f319(f93(f913(x91471,f913(x91472,a904))),x91473),x91474),x91475),x91476))
% 22.40/22.30 [9149]~P1(f319(f319(x91493,x91495),x91496))+P1(f319(f319(f319(f319(f93(f913(x91491,f913(x91492,a904))),x91493),x91494),x91495),x91496))
% 22.40/22.30 [9439]P1(f319(f319(x94391,x94392),x94393))+~P1(f319(f319(f319(f319(f94(f913(x94394,f913(x94395,a904))),x94396),x94391),x94392),x94393))
% 22.40/22.30 [9440]P1(f319(f319(x94401,x94402),x94403))+~P1(f319(f319(f319(f319(f94(f913(x94404,f913(x94405,a904))),x94401),x94406),x94402),x94403))
% 22.40/22.30 [9909]~P76(x99092)+E(f319(f319(f8(x99091,x99092),f319(f319(f9(x99091,f913(x99093,a904),x99092),f319(f319(f10(f913(x99093,x99092),f913(f913(x99093,a904),x99092),x99091),f8(x99093,x99092)),x99094)),x99095)),x99096),f319(f319(f8(f912(x99091,x99093),x99092),f319(f249(x99091,x99093,x99092),x99094)),f319(f319(f246(x99091,x99093),x99096),f319(f18(f913(x99093,a904),x99091),x99095))))
% 22.40/22.30 [9910]~P82(x99102)+E(f319(f319(f11(x99101,x99102),f319(f319(f9(x99101,f913(x99103,a904),x99102),f319(f319(f10(f913(x99103,x99102),f913(f913(x99103,a904),x99102),x99101),f11(x99103,x99102)),x99104)),x99105)),x99106),f319(f319(f11(f912(x99101,x99103),x99102),f319(f249(x99101,x99103,x99102),x99104)),f319(f319(f246(x99101,x99103),x99106),f319(f18(f913(x99103,a904),x99101),x99105))))
% 22.40/22.30 [10036]~P76(x100362)+E(f319(f319(f8(x100361,x100362),f319(f319(f9(x100361,f913(x100363,a904),x100362),f319(f319(f10(f913(x100363,x100362),f913(f913(x100363,a904),x100362),x100361),f8(x100363,x100362)),f319(f9(x100363,x100361,x100362),x100364))),x100365)),x100366),f319(f319(f8(x100363,x100362),f319(f319(f9(x100363,f913(x100361,a904),x100362),f319(f319(f10(f913(x100361,x100362),f913(f913(x100361,a904),x100362),x100363),f8(x100361,x100362)),x100364)),x100366)),x100365))
% 22.40/22.30 [10365]~P1(f319(f319(f321(f912(x103651,x103652)),f319(f319(f244(x103651,x103652),x103655),x103656)),f319(f319(f93(f913(f912(x103651,x103652),a904)),x103653),x103654)))+P1(f319(f319(f319(f319(f93(f913(x103651,f913(x103652,a904))),f319(f319(f9(x103651,f913(f912(x103651,x103652),a904),f913(x103652,a904)),f319(f319(f10(f913(x103652,f913(f913(f912(x103651,x103652),a904),a904)),f913(f913(f912(x103651,x103652),a904),f913(x103652,a904)),x103651),f9(x103652,f913(f912(x103651,x103652),a904),a904)),f319(f319(f10(f913(x103652,f912(x103651,x103652)),f913(x103652,f913(f913(f912(x103651,x103652),a904),a904)),x103651),f319(f10(f912(x103651,x103652),f913(f913(f912(x103651,x103652),a904),a904),x103652),f321(f912(x103651,x103652)))),f244(x103651,x103652)))),x103653)),f319(f319(f9(x103651,f913(f912(x103651,x103652),a904),f913(x103652,a904)),f319(f319(f10(f913(x103652,f913(f913(f912(x103651,x103652),a904),a904)),f913(f913(f912(x103651,x103652),a904),f913(x103652,a904)),x103651),f9(x103652,f913(f912(x103651,x103652),a904),a904)),f319(f319(f10(f913(x103652,f912(x103651,x103652)),f913(x103652,f913(f913(f912(x103651,x103652),a904),a904)),x103651),f319(f10(f912(x103651,x103652),f913(f913(f912(x103651,x103652),a904),a904),x103652),f321(f912(x103651,x103652)))),f244(x103651,x103652)))),x103654)),x103655),x103656))
% 22.40/22.30 [10366]~P1(f319(f319(f321(f912(x103661,x103662)),f319(f319(f244(x103661,x103662),x103665),x103666)),f319(f319(f94(f913(f912(x103661,x103662),a904)),x103663),x103664)))+P1(f319(f319(f319(f319(f94(f913(x103661,f913(x103662,a904))),f319(f319(f9(x103661,f913(f912(x103661,x103662),a904),f913(x103662,a904)),f319(f319(f10(f913(x103662,f913(f913(f912(x103661,x103662),a904),a904)),f913(f913(f912(x103661,x103662),a904),f913(x103662,a904)),x103661),f9(x103662,f913(f912(x103661,x103662),a904),a904)),f319(f319(f10(f913(x103662,f912(x103661,x103662)),f913(x103662,f913(f913(f912(x103661,x103662),a904),a904)),x103661),f319(f10(f912(x103661,x103662),f913(f913(f912(x103661,x103662),a904),a904),x103662),f321(f912(x103661,x103662)))),f244(x103661,x103662)))),x103663)),f319(f319(f9(x103661,f913(f912(x103661,x103662),a904),f913(x103662,a904)),f319(f319(f10(f913(x103662,f913(f913(f912(x103661,x103662),a904),a904)),f913(f913(f912(x103661,x103662),a904),f913(x103662,a904)),x103661),f9(x103662,f913(f912(x103661,x103662),a904),a904)),f319(f319(f10(f913(x103662,f912(x103661,x103662)),f913(x103662,f913(f913(f912(x103661,x103662),a904),a904)),x103661),f319(f10(f912(x103661,x103662),f913(f913(f912(x103661,x103662),a904),a904),x103662),f321(f912(x103661,x103662)))),f244(x103661,x103662)))),x103664)),x103665),x103666))
% 22.40/22.30 [10380]P1(f319(f319(f321(f912(x103801,x103802)),f319(f319(f244(x103801,x103802),x103803),x103804)),f319(f319(f93(f913(f912(x103801,x103802),a904)),x103805),x103806)))+~P1(f319(f319(f319(f319(f93(f913(x103801,f913(x103802,a904))),f319(f319(f9(x103801,f913(f912(x103801,x103802),a904),f913(x103802,a904)),f319(f319(f10(f913(x103802,f913(f913(f912(x103801,x103802),a904),a904)),f913(f913(f912(x103801,x103802),a904),f913(x103802,a904)),x103801),f9(x103802,f913(f912(x103801,x103802),a904),a904)),f319(f319(f10(f913(x103802,f912(x103801,x103802)),f913(x103802,f913(f913(f912(x103801,x103802),a904),a904)),x103801),f319(f10(f912(x103801,x103802),f913(f913(f912(x103801,x103802),a904),a904),x103802),f321(f912(x103801,x103802)))),f244(x103801,x103802)))),x103805)),f319(f319(f9(x103801,f913(f912(x103801,x103802),a904),f913(x103802,a904)),f319(f319(f10(f913(x103802,f913(f913(f912(x103801,x103802),a904),a904)),f913(f913(f912(x103801,x103802),a904),f913(x103802,a904)),x103801),f9(x103802,f913(f912(x103801,x103802),a904),a904)),f319(f319(f10(f913(x103802,f912(x103801,x103802)),f913(x103802,f913(f913(f912(x103801,x103802),a904),a904)),x103801),f319(f10(f912(x103801,x103802),f913(f913(f912(x103801,x103802),a904),a904),x103802),f321(f912(x103801,x103802)))),f244(x103801,x103802)))),x103806)),x103803),x103804))
% 22.40/22.30 [10381]P1(f319(f319(f321(f912(x103811,x103812)),f319(f319(f244(x103811,x103812),x103813),x103814)),f319(f319(f94(f913(f912(x103811,x103812),a904)),x103815),x103816)))+~P1(f319(f319(f319(f319(f94(f913(x103811,f913(x103812,a904))),f319(f319(f9(x103811,f913(f912(x103811,x103812),a904),f913(x103812,a904)),f319(f319(f10(f913(x103812,f913(f913(f912(x103811,x103812),a904),a904)),f913(f913(f912(x103811,x103812),a904),f913(x103812,a904)),x103811),f9(x103812,f913(f912(x103811,x103812),a904),a904)),f319(f319(f10(f913(x103812,f912(x103811,x103812)),f913(x103812,f913(f913(f912(x103811,x103812),a904),a904)),x103811),f319(f10(f912(x103811,x103812),f913(f913(f912(x103811,x103812),a904),a904),x103812),f321(f912(x103811,x103812)))),f244(x103811,x103812)))),x103815)),f319(f319(f9(x103811,f913(f912(x103811,x103812),a904),f913(x103812,a904)),f319(f319(f10(f913(x103812,f913(f913(f912(x103811,x103812),a904),a904)),f913(f913(f912(x103811,x103812),a904),f913(x103812,a904)),x103811),f9(x103812,f913(f912(x103811,x103812),a904),a904)),f319(f319(f10(f913(x103812,f912(x103811,x103812)),f913(x103812,f913(f913(f912(x103811,x103812),a904),a904)),x103811),f319(f10(f912(x103811,x103812),f913(f913(f912(x103811,x103812),a904),a904),x103812),f321(f912(x103811,x103812)))),f244(x103811,x103812)))),x103816)),x103813),x103814))
% 22.40/22.30 [10354]~P1(f319(f319(f321(f912(x103542,x103543)),f319(f319(f244(x103542,x103543),x103545),x103546)),f319(f319(f33(x103541,f913(f912(x103542,x103543),a904)),f234(f913(x103541,a904))),x103544)))+P1(f319(f319(f319(f319(f33(x103541,f913(x103542,f913(x103543,a904))),f234(f913(x103541,a904))),f319(f319(f10(f913(f912(x103542,x103543),a904),f913(x103542,f913(x103543,a904)),x103541),f319(f9(x103542,f913(f912(x103542,x103543),a904),f913(x103543,a904)),f319(f319(f10(f913(x103543,f913(f913(f912(x103542,x103543),a904),a904)),f913(f913(f912(x103542,x103543),a904),f913(x103543,a904)),x103542),f9(x103543,f913(f912(x103542,x103543),a904),a904)),f319(f319(f10(f913(x103543,f912(x103542,x103543)),f913(x103543,f913(f913(f912(x103542,x103543),a904),a904)),x103542),f319(f10(f912(x103542,x103543),f913(f913(f912(x103542,x103543),a904),a904),x103543),f321(f912(x103542,x103543)))),f244(x103542,x103543))))),x103544)),x103545),x103546))
% 22.40/22.30 [10355]~P1(f319(f319(f321(f912(x103552,x103553)),f319(f319(f244(x103552,x103553),x103555),x103556)),f319(f319(f34(x103551,f913(f912(x103552,x103553),a904)),f234(f913(x103551,a904))),x103554)))+P1(f319(f319(f319(f319(f34(x103551,f913(x103552,f913(x103553,a904))),f234(f913(x103551,a904))),f319(f319(f10(f913(f912(x103552,x103553),a904),f913(x103552,f913(x103553,a904)),x103551),f319(f9(x103552,f913(f912(x103552,x103553),a904),f913(x103553,a904)),f319(f319(f10(f913(x103553,f913(f913(f912(x103552,x103553),a904),a904)),f913(f913(f912(x103552,x103553),a904),f913(x103553,a904)),x103552),f9(x103553,f913(f912(x103552,x103553),a904),a904)),f319(f319(f10(f913(x103553,f912(x103552,x103553)),f913(x103553,f913(f913(f912(x103552,x103553),a904),a904)),x103552),f319(f10(f912(x103552,x103553),f913(f913(f912(x103552,x103553),a904),a904),x103553),f321(f912(x103552,x103553)))),f244(x103552,x103553))))),x103554)),x103555),x103556))
% 22.40/22.30 [10370]P1(f319(f319(f321(f912(x103701,x103702)),f319(f319(f244(x103701,x103702),x103703),x103704)),f319(f319(f33(x103705,f913(f912(x103701,x103702),a904)),f234(f913(x103705,a904))),x103706)))+~P1(f319(f319(f319(f319(f33(x103705,f913(x103701,f913(x103702,a904))),f234(f913(x103705,a904))),f319(f319(f10(f913(f912(x103701,x103702),a904),f913(x103701,f913(x103702,a904)),x103705),f319(f9(x103701,f913(f912(x103701,x103702),a904),f913(x103702,a904)),f319(f319(f10(f913(x103702,f913(f913(f912(x103701,x103702),a904),a904)),f913(f913(f912(x103701,x103702),a904),f913(x103702,a904)),x103701),f9(x103702,f913(f912(x103701,x103702),a904),a904)),f319(f319(f10(f913(x103702,f912(x103701,x103702)),f913(x103702,f913(f913(f912(x103701,x103702),a904),a904)),x103701),f319(f10(f912(x103701,x103702),f913(f913(f912(x103701,x103702),a904),a904),x103702),f321(f912(x103701,x103702)))),f244(x103701,x103702))))),x103706)),x103703),x103704))
% 22.40/22.30 [10371]P1(f319(f319(f321(f912(x103711,x103712)),f319(f319(f244(x103711,x103712),x103713),x103714)),f319(f319(f34(x103715,f913(f912(x103711,x103712),a904)),f234(f913(x103715,a904))),x103716)))+~P1(f319(f319(f319(f319(f34(x103715,f913(x103711,f913(x103712,a904))),f234(f913(x103715,a904))),f319(f319(f10(f913(f912(x103711,x103712),a904),f913(x103711,f913(x103712,a904)),x103715),f319(f9(x103711,f913(f912(x103711,x103712),a904),f913(x103712,a904)),f319(f319(f10(f913(x103712,f913(f913(f912(x103711,x103712),a904),a904)),f913(f913(f912(x103711,x103712),a904),f913(x103712,a904)),x103711),f9(x103712,f913(f912(x103711,x103712),a904),a904)),f319(f319(f10(f913(x103712,f912(x103711,x103712)),f913(x103712,f913(f913(f912(x103711,x103712),a904),a904)),x103711),f319(f10(f912(x103711,x103712),f913(f913(f912(x103711,x103712),a904),a904),x103712),f321(f912(x103711,x103712)))),f244(x103711,x103712))))),x103716)),x103713),x103714))
% 22.40/22.30 [7537]E(f319(x75371,f319(x75372,x75373)),f319(x75374,x75373))+~E(f319(f66(x75375,x75376,x75377,x75371),x75372),x75374)
% 22.40/22.30 [9664]E(x96641,x96642)+E(f68(x96643,x96644,f68(x96643,x96644,x96645,x96641,x96646),x96642,x96647),f68(x96643,x96644,f68(x96643,x96644,x96645,x96642,x96647),x96641,x96646))
% 22.40/22.30 [9761]~P23(x97613,x97614,x97611,x97615,x97616,x97617)+E(f319(f319(x97611,x97612),x97612),x97612)
% 22.40/22.30 [6116]~E(f319(f319(f146(x61161,x61165),x61166),x61162),f319(f319(f146(x61163,x61165),x61167),x61164))+E(f319(f182(f907(x61161)),x61162),f319(f182(f907(x61163)),x61164))
% 22.40/22.30 [8545]E(f319(x85451,f319(x85452,x85453)),f319(x85454,x85453))+~E(f319(f66(x85455,x85456,x85457,x85451),x85452),f319(f66(x85456,x85456,x85457,f25(x85456)),x85454))
% 22.40/22.30 [8894]~P34(x88944,x88945,x88941,f319(f319(f143(x88944),x88942),x88946),f319(f319(f143(x88945),x88943),x88947))+P1(f319(f319(x88941,x88942),x88943))
% 22.40/22.30 [9281]P34(x92811,x92812,x92813,x92814,x92815)+~P34(x92811,x92812,x92813,f319(f319(f143(x92811),x92816),x92814),f319(f319(f143(x92812),x92817),x92815))
% 22.40/22.30 [9945]P1(f319(f319(x99451,x99452),f556(x99453,x99452,x99454,x99451)))+~P1(f319(f319(f245(x99455,x99456,x99457,x99451,x99454),x99452),x99453))
% 22.40/22.30 [9967]P1(f319(f319(x99671,f556(x99672,x99673,x99671,x99674)),x99672))+~P1(f319(f319(f245(x99675,x99676,x99677,x99674,x99671),x99673),x99672))
% 22.40/22.30 [9022]~P21(x90226,x90221,x90223,x90227)+E(f319(f66(x90221,x90221,x90222,f319(x90223,x90224)),f319(f66(x90221,x90221,x90222,f319(x90223,x90224)),x90225)),f319(f66(x90221,x90221,x90222,f319(x90223,x90224)),x90225))
% 22.40/22.30 [9388]~P34(x93883,x93882,x93884,f319(f319(f146(x93881,x93883),x93885),x93886),x93887)+P34(x93881,x93882,f319(f319(f10(x93883,f913(x93882,a904),x93881),x93884),x93885),x93886,x93887)
% 22.40/22.30 [9415]P34(x94151,x94152,x94153,f319(f319(f146(x94154,x94151),x94155),x94156),x94157)+~P34(x94154,x94152,f319(f319(f10(x94151,f913(x94152,a904),x94154),x94153),x94155),x94156,x94157)
% 22.40/22.30 [9021]~P1(f319(f319(f321(x90211),x90212),f319(f319(x90215,x90216),x90217)))+P1(f319(f319(f321(x90211),x90212),f319(f319(f249(x90213,x90214,f913(x90211,a904)),x90215),f319(f319(f244(x90213,x90214),x90216),x90217))))
% 22.40/22.30 [9304]P1(f319(f319(f319(x93041,x93042),x93043),x93044))+~P1(f319(f319(f319(f249(x93045,x93046,f913(x93047,a904)),x93041),f319(f319(f244(x93045,x93046),x93042),x93043)),x93044))
% 22.40/22.30 [9454]P1(f319(f319(f321(x94541),f319(f319(x94542,x94543),x94544)),f319(f302(f912(x94545,x94546),x94541,f319(f249(x94545,x94546,x94541),x94542)),x94547)))+~P1(f319(f319(f321(f912(x94545,x94546)),f319(f319(f244(x94545,x94546),x94543),x94544)),x94547))
% 22.40/22.30 [9815]P1(f319(f319(f321(f912(f907(x98151),f907(x98151))),f319(f319(f244(f907(x98151),f907(x98151)),f319(f319(f126(x98151),x98152),f319(f319(f143(x98151),x98153),x98154))),f319(f319(f126(x98151),x98152),f319(f319(f143(x98151),x98155),x98156)))),f139(x98151,x98157)))+~P1(f319(f319(f321(f912(x98151,x98151)),f319(f319(f244(x98151,x98151),x98153),x98155)),x98157))
% 22.40/22.30 [9882]~P34(x98821,x98823,x98824,x98826,f319(f319(f146(x98822,x98823),x98825),x98827))+P34(x98821,x98822,f319(f319(f9(x98821,f913(x98822,x98823),f913(x98822,a904)),f319(f319(f10(f913(x98823,a904),f913(f913(x98822,x98823),f913(x98822,a904)),x98821),f10(x98823,a904,x98822)),x98824)),x98825),x98826,x98827)
% 22.40/22.30 [9971]P34(x99711,x99712,x99713,x99714,f319(f319(f146(x99715,x99712),x99716),x99717))+~P34(x99711,x99715,f319(f319(f9(x99711,f913(x99715,x99712),f913(x99715,a904)),f319(f319(f10(f913(x99712,a904),f913(f913(x99715,x99712),f913(x99715,a904)),x99711),f10(x99712,a904,x99715)),x99713)),x99716),x99714,x99717)
% 22.40/22.30 [10247]P1(f319(f319(f321(x102471),f478(x102472,x102473,x102474,x102475,x102476,x102477,x102471)),x102475))+P1(f319(f319(f319(f319(f34(x102471,f913(x102477,f913(x102476,a904))),x102475),x102474),x102473),x102472))
% 22.40/22.30 [10248]P1(f319(f319(f321(x102481),f776(x102482,x102483,x102484,x102485,x102486,x102487,x102481)),x102487))+P1(f319(f319(f319(f319(f34(x102481,f913(x102483,f913(x102482,a904))),x102487),x102486),x102485),x102484))
% 22.40/22.30 [10249]P1(f319(f319(f321(x102491),f477(x102492,x102493,x102494,x102495,x102496,x102497,x102491)),x102495))+~P1(f319(f319(f319(f319(f33(x102491,f913(x102497,f913(x102496,a904))),x102495),x102494),x102493),x102492))
% 22.40/22.30 [10250]P1(f319(f319(f321(x102501),f777(x102502,x102503,x102504,x102505,x102506,x102507,x102501)),x102505))+~P1(f319(f319(f319(f319(f33(x102501,f913(x102507,f913(x102506,a904))),x102505),x102504),x102503),x102502))
% 22.40/22.30 [10305]P1(f319(f319(f319(x103051,f477(x103052,x103053,x103051,x103054,x103055,x103056,x103057)),x103053),x103052))+~P1(f319(f319(f319(f319(f33(x103057,f913(x103056,f913(x103055,a904))),x103054),x103051),x103053),x103052))
% 22.40/22.30 [10306]P1(f319(f319(f319(x103061,f777(x103062,x103063,x103061,x103064,x103065,x103066,x103067)),x103063),x103062))+~P1(f319(f319(f319(f319(f33(x103067,f913(x103066,f913(x103065,a904))),x103064),x103061),x103063),x103062))
% 22.40/22.30 [10324]~P1(f319(f319(f319(x103245,f478(x103247,x103246,x103245,x103244,x103243,x103242,x103241)),x103246),x103247))+P1(f319(f319(f319(f319(f34(x103241,f913(x103242,f913(x103243,a904))),x103244),x103245),x103246),x103247))
% 22.40/22.30 [10325]~P1(f319(f319(f319(x103255,f776(x103253,x103252,x103257,x103256,x103255,x103254,x103251)),x103256),x103257))+P1(f319(f319(f319(f319(f34(x103251,f913(x103252,f913(x103253,a904))),x103254),x103255),x103256),x103257))
% 22.40/22.30 [10353]~P1(f319(f319(f321(f912(x103531,x103533)),f319(f319(f244(x103531,x103533),x103536),x103537)),f319(f319(f281(x103531,x103532,x103533),x103534),x103535)))+P1(f319(f319(f245(x103531,x103532,x103533,f319(f319(f9(x103531,f913(f912(x103531,x103532),a904),f913(x103532,a904)),f319(f319(f10(f913(x103532,f913(f913(f912(x103531,x103532),a904),a904)),f913(f913(f912(x103531,x103532),a904),f913(x103532,a904)),x103531),f9(x103532,f913(f912(x103531,x103532),a904),a904)),f319(f319(f10(f913(x103532,f912(x103531,x103532)),f913(x103532,f913(f913(f912(x103531,x103532),a904),a904)),x103531),f319(f10(f912(x103531,x103532),f913(f913(f912(x103531,x103532),a904),a904),x103532),f321(f912(x103531,x103532)))),f244(x103531,x103532)))),x103534),f319(f319(f9(x103532,f913(f912(x103532,x103533),a904),f913(x103533,a904)),f319(f319(f10(f913(x103533,f913(f913(f912(x103532,x103533),a904),a904)),f913(f913(f912(x103532,x103533),a904),f913(x103533,a904)),x103532),f9(x103533,f913(f912(x103532,x103533),a904),a904)),f319(f319(f10(f913(x103533,f912(x103532,x103533)),f913(x103533,f913(f913(f912(x103532,x103533),a904),a904)),x103532),f319(f10(f912(x103532,x103533),f913(f913(f912(x103532,x103533),a904),a904),x103533),f321(f912(x103532,x103533)))),f244(x103532,x103533)))),x103535)),x103536),x103537))
% 22.40/22.30 [10369]P1(f319(f319(f321(f912(x103691,x103692)),f319(f319(f244(x103691,x103692),x103693),x103694)),f319(f319(f281(x103691,x103695,x103692),x103696),x103697)))+~P1(f319(f319(f245(x103691,x103695,x103692,f319(f319(f9(x103691,f913(f912(x103691,x103695),a904),f913(x103695,a904)),f319(f319(f10(f913(x103695,f913(f913(f912(x103691,x103695),a904),a904)),f913(f913(f912(x103691,x103695),a904),f913(x103695,a904)),x103691),f9(x103695,f913(f912(x103691,x103695),a904),a904)),f319(f319(f10(f913(x103695,f912(x103691,x103695)),f913(x103695,f913(f913(f912(x103691,x103695),a904),a904)),x103691),f319(f10(f912(x103691,x103695),f913(f913(f912(x103691,x103695),a904),a904),x103695),f321(f912(x103691,x103695)))),f244(x103691,x103695)))),x103696),f319(f319(f9(x103695,f913(f912(x103695,x103692),a904),f913(x103692,a904)),f319(f319(f10(f913(x103692,f913(f913(f912(x103695,x103692),a904),a904)),f913(f913(f912(x103695,x103692),a904),f913(x103692,a904)),x103695),f9(x103692,f913(f912(x103695,x103692),a904),a904)),f319(f319(f10(f913(x103692,f912(x103695,x103692)),f913(x103692,f913(f913(f912(x103695,x103692),a904),a904)),x103695),f319(f10(f912(x103695,x103692),f913(f913(f912(x103695,x103692),a904),a904),x103692),f321(f912(x103695,x103692)))),f244(x103695,x103692)))),x103697)),x103693),x103694))
% 22.40/22.30 [10258]~P145(x102582)+E(f319(f319(f8(x102581,x102582),f319(f319(f9(x102581,f913(x102583,a904),x102582),f319(f319(f10(f913(x102583,x102582),f913(f913(x102583,a904),x102582),x102581),f8(x102583,x102582)),f319(f319(f9(x102581,f913(x102583,x102582),f913(x102583,x102582)),f319(f319(f10(f913(x102582,x102582),f913(f913(x102583,x102582),f913(x102583,x102582)),x102581),f10(x102582,x102582,x102583)),f319(f319(f10(x102582,f913(x102582,x102582),x102581),f75(x102582)),x102584))),x102585))),x102586)),x102587),f319(f319(f75(x102582),f319(f319(f8(x102581,x102582),x102584),x102587)),f319(f319(f8(x102583,x102582),x102585),x102586)))
% 22.40/22.30 [9336]~P20(x93367,x93361,x93363,x93368)+E(f319(f66(x93361,x93361,x93362,f319(x93363,x93364)),f319(f66(x93361,x93361,x93362,f319(x93363,x93365)),x93366)),f319(f66(x93361,x93361,x93362,f319(x93363,x93365)),f319(f66(x93361,x93361,x93362,f319(x93363,x93364)),x93366)))
% 22.40/22.30 [10361]E(f319(f319(f244(x103611,x103612),f319(x103613,f541(x103614,x103615,x103613,x103616,x103617,x103618,x103612,x103611))),f319(x103615,f542(x103614,x103615,x103613,x103616,x103617,x103618,x103612,x103611))),x103618)+~P1(f319(f319(f321(f912(x103611,x103612)),x103618),f319(f302(f912(x103617,x103616),f912(x103611,x103612),f250(x103617,x103611,x103616,x103612,x103613,x103615)),x103614)))
% 22.40/22.30 [10386]~P1(f319(f319(f321(f912(x103868,x103867)),x103866),f319(f302(f912(x103861,x103862),f912(x103868,x103867),f250(x103861,x103868,x103862,x103867,x103865,x103864)),x103863)))+P1(f319(f319(f321(f912(x103861,x103862)),f319(f319(f244(x103861,x103862),f541(x103863,x103864,x103865,x103862,x103861,x103866,x103867,x103868)),f542(x103863,x103864,x103865,x103862,x103861,x103866,x103867,x103868))),x103863))
% 22.40/22.30 [9804]P1(f319(f319(f321(f912(f912(x98041,x98042),f912(x98041,x98042))),f319(f319(f244(f912(x98041,x98042),f912(x98041,x98042)),f319(f319(f244(x98041,x98042),x98043),x98044)),f319(f319(f244(x98041,x98042),x98045),x98046))),f312(x98041,x98042,x98047,x98048)))+~P1(f319(f319(f321(f912(x98041,x98041)),f319(f319(f244(x98041,x98041),x98043),x98045)),x98047))
% 22.40/22.30 [10347]E(f319(f134(x103471,x103472,f319(f9(x103472,x103471,x103471),x103473),f319(x103474,x103475)),x103476),f319(x103474,f319(f134(x103477,x103472,f319(f9(x103472,x103477,x103477),x103478),x103475),x103476)))+P1(f319(f319(f321(x103472),f723(x103475,x103478,x103474,x103473,x103477,x103471,x103476,x103472)),f319(f164(x103472),x103476)))
% 22.40/22.30 [10373]~E(f319(f66(x103731,x103731,x103737,f319(x103733,f723(x103735,x103738,x103734,x103733,x103737,x103731,x103736,x103732))),x103734),f319(f66(x103737,x103731,x103737,x103734),f319(x103738,f723(x103735,x103738,x103734,x103733,x103737,x103731,x103736,x103732))))+E(f319(f134(x103731,x103732,f319(f9(x103732,x103731,x103731),x103733),f319(x103734,x103735)),x103736),f319(x103734,f319(f134(x103737,x103732,f319(f9(x103732,x103737,x103737),x103738),x103735),x103736)))
% 22.40/22.30 [8550]E(f319(x85501,f319(x85502,x85503)),f319(x85504,f319(x85505,x85503)))+~E(f319(f66(x85506,x85507,x85508,x85501),x85502),f319(f66(x85509,x85507,x85508,x85504),x85505))
% 22.40/22.30 [10163]P1(f319(f319(f321(f912(x101631,x101632)),f319(f319(f244(x101631,x101632),f319(x101633,x101634)),f319(x101635,x101636))),f319(f302(f912(x101637,x101638),f912(x101631,x101632),f250(x101637,x101631,x101638,x101632,x101633,x101635)),x101639)))+~P1(f319(f319(f321(f912(x101637,x101638)),f319(f319(f244(x101637,x101638),x101634),x101636)),x101639))
% 22.40/22.30 [8840]~E(f319(x88404,f319(x88405,x88406)),f319(x88409,f319(x884010,x884011)))+E(f319(f319(f66(x88401,x88402,x88403,x88404),x88405),x88406),f319(f319(f66(x88407,x88402,x88408,x88409),x884010),x884011))
% 22.40/22.30 [4689]~P4(x46891)+~P106(x46891)+E(f93(x46891),f180(x46891))
% 22.40/22.30 [4690]~P4(x46901)+~P107(x46901)+E(f94(x46901),f230(x46901))
% 22.40/22.30 [4933]~P113(x49331)+~P98(x49331)+E(f319(f69(x49331),f319(f96(x49331),a89)),f72(x49331))
% 22.40/22.30 [5223]E(x52231,f2(a1))+E(f76(a1,x52231),f319(f73(a1),f72(a1)))+P1(f319(f319(f226(a1),f2(a1)),x52231))
% 22.40/22.30 [5428]E(x54281,f2(a1))+E(f76(a1,x54281),f72(a1))+~P1(f319(f319(f226(a1),f2(a1)),x54281))
% 22.40/22.30 [7443]~P41(x74431)+P1(f319(f55(a1),x74431))+~P1(f319(f55(a906),f319(f302(a1,a906,a97),x74431)))
% 22.40/22.30 [9760]E(x97601,f181(f913(f912(a906,a906),a904)))+~P1(f319(f55(f912(a906,a906)),x97601))+P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),f181(f913(f912(a906,a906),a904))),x97601)),a28))
% 22.40/22.30 [10192]E(x101921,f2(a906))+E(x101921,f319(a104,f2(a906)))+~P1(f319(f319(f226(a906),x101921),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.30 [10341]E(x103411,f2(a91))+E(f319(f319(f74(a1),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(a24,f319(f319(f30(a91),x103411),f319(f96(a91),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))),f72(a1)),f319(a24,x103411))+E(f39(a91,x103411,f319(f96(a91),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f2(a91))
% 22.40/22.30 [10273]E(x102731,f2(a91))+~E(f39(a91,x102731,f319(f96(a91),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f2(a91))+E(f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(a24,f319(f319(f30(a91),x102731),f319(f96(a91),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))),f319(a24,x102731))
% 22.40/22.30 [4770]~P59(x47701,x47702)+P44(x47701,x47702)+~P45(a904)
% 22.40/22.30 [4699]~P146(x46991)+P28(x46991,x46992)+~E(x46992,f2(x46991))
% 22.40/22.30 [4700]~P4(x47001)+P13(x47001,x47002)+~E(x47002,f105(x47001))
% 22.40/22.30 [4709]~P113(x47091)+~E(x47092,f2(x47091))+E(f76(x47091,x47092),f2(x47091))
% 22.40/22.30 [4710]~P94(x47101)+~E(x47102,f2(x47101))+E(f76(x47101,x47102),f2(x47101))
% 22.40/22.30 [4718]~P146(x47182)+~P28(x47182,x47181)+E(x47181,f2(x47182))
% 22.40/22.30 [4763]~P113(x47632)+~E(f76(x47632,x47631),f2(x47632))+E(x47631,f2(x47632))
% 22.40/22.30 [4777]~P68(x47772)+~P68(x47771)+P68(f913(x47771,x47772))
% 22.40/22.30 [4778]~P68(x47782)+~P68(x47781)+P68(f912(x47781,x47782))
% 22.40/22.30 [4779]~P68(x47792)+~P68(x47791)+P68(f914(x47791,x47792))
% 22.40/22.30 [4780]~P6(x47802)+~P6(x47801)+P6(f187(x47801,x47802))
% 22.40/22.30 [4781]~P71(x47812)+~P71(x47811)+P71(f913(x47811,x47812))
% 22.40/22.30 [4782]~P71(x47822)+~P71(x47821)+P71(f912(x47821,x47822))
% 22.40/22.30 [4783]~P71(x47832)+~P71(x47831)+P71(f914(x47831,x47832))
% 22.40/22.30 [4784]~P109(x47842)+~P109(x47841)+P109(f912(x47841,x47842))
% 22.40/22.30 [4905]~P4(x49051)+~P13(x49051,x49052)+P13(x49051,f144(x49051,x49052))
% 22.40/22.30 [5147]~P6(x51472)+~P6(x51471)+P6(f39(a1,x51471,x51472))
% 22.40/22.30 [4720]~P83(x47201)+~E(x47202,f2(x47201))+E(f319(f73(x47201),x47202),x47202)
% 22.40/22.30 [4735]~P141(x47351)+~E(x47352,f2(a1))+E(f319(f95(x47351),x47352),f2(x47351))
% 22.40/22.30 [4736]~P97(x47361)+~E(x47362,f2(a1))+E(f319(f95(x47361),x47362),f2(x47361))
% 22.40/22.30 [4760]~P66(x47601)+~E(f2(x47601),x47602)+E(f319(f73(x47601),x47602),f2(x47601))
% 22.40/22.30 [4761]~P66(x47611)+~E(x47612,f2(x47611))+E(f319(f73(x47611),x47612),f2(x47611))
% 22.40/22.30 [4762]~P92(x47621)+~E(x47622,f2(x47621))+E(f319(f69(x47621),x47622),f2(x47621))
% 22.40/22.30 [4786]~P83(x47862)+E(x47861,f2(x47862))+~E(f319(f73(x47862),x47861),x47861)
% 22.40/22.30 [4788]E(x47881,f319(a97,x47882))+~E(x47881,f2(a906))+~E(x47882,f319(f92(a1),x47881))
% 22.40/22.30 [4789]E(f319(a97,x47891),x47892)+~E(x47892,f2(a906))+~E(x47891,f319(f92(a1),x47892))
% 22.40/22.30 [4791]~P97(x47912)+E(x47911,f2(a1))+~E(f319(f95(x47912),x47911),f2(x47912))
% 22.40/22.30 [4795]~P66(x47952)+E(x47951,f2(x47952))+~E(f319(f73(x47952),x47951),f2(x47952))
% 22.40/22.30 [4796]~P92(x47962)+E(x47961,f2(x47962))+~E(f319(f69(x47962),x47961),f2(x47962))
% 22.40/22.30 [4797]~P66(x47971)+E(f2(x47971),x47972)+~E(f319(f73(x47971),x47972),f2(x47971))
% 22.40/22.30 [4978]~P4(x49781)+~P13(x49781,x49782)+P13(x49781,f319(f163(x49781),x49782))
% 22.40/22.30 [5005]~P1(x50052)+~P1(x50051)+P1(f319(f319(a317,x50051),x50052))
% 22.40/22.30 [5039]~E(f72(a906),f2(a906))+E(f319(f29(x50391),x50392),f2(a906))+~P1(f319(f55(x50391),x50392))
% 22.40/22.30 [5076]~P116(x50761)+~P145(x50761)+E(f319(f319(f236(x50761),f2(x50761)),f319(a104,x50762)),f2(x50761))
% 22.40/22.30 [5115]~P4(x51151)+P13(x51151,f131(x51151,x51152))+~P1(f319(f55(x51151),x51152))
% 22.40/22.30 [5116]~P4(x51161)+P13(x51161,f716(x51162,x51161))+~P1(f319(f55(x51161),x51162))
% 22.40/22.30 [5139]~P4(x51391)+E(f319(f164(x51391),f131(x51391,x51392)),x51392)+~P1(f319(f55(x51391),x51392))
% 22.40/22.30 [5140]~P4(x51401)+E(f319(f164(x51401),f716(x51402,x51401)),x51402)+~P1(f319(f55(x51401),x51402))
% 22.40/22.30 [5169]P1(x51691)+P1(x51692)+~P1(f319(f319(a318,x51692),x51691))
% 22.40/22.30 [5182]E(x51821,f181(f913(x51822,a904)))+~E(f319(f29(x51822),x51821),f2(a906))+~P1(f319(f55(x51822),x51821))
% 22.40/22.30 [5187]P1(x51871)+~P1(x51872)+~P1(f319(f319(a322,x51872),x51871))
% 22.40/22.30 [5241]~P81(x52411)+E(f319(f69(x52411),x52412),x52412)+P1(f319(f319(f226(x52411),x52412),f2(x52411)))
% 22.40/22.30 [5242]~P5(x52422)+~P40(x52422,x52422,x52421)+E(f319(x52421,f88(x52422,x52421)),f88(x52422,x52421))
% 22.40/22.30 [5243]~P5(x52432)+~P40(x52432,x52432,x52431)+E(f319(x52431,f87(x52432,x52431)),f87(x52432,x52431))
% 22.40/22.30 [5304]~P71(x53042)+~P1(f319(f50(x53042),x53041))+P1(f319(x53041,f717(x53041,x53042)))
% 22.40/22.30 [5305]~P71(x53052)+~P1(f319(f50(x53052),x53051))+P1(f319(x53051,f724(x53051,x53052)))
% 22.40/22.30 [5345]E(x53451,f105(x53452))+P1(f319(f129(x53452),f106(x53452,x53451)))+~P1(f319(f129(x53452),x53451))
% 22.40/22.30 [5350]~P4(x53501)+~P1(f319(f55(x53501),x53502))+P1(f319(f129(x53501),f131(x53501,x53502)))
% 22.40/22.30 [5351]~P4(x53511)+~P1(f319(f55(x53511),x53512))+P1(f319(f129(x53511),f716(x53512,x53511)))
% 22.40/22.30 [5356]~P141(x53561)+E(f319(f92(x53561),f319(a97,x53562)),f319(f95(x53561),x53562))+P1(f319(f319(f226(a1),x53562),f2(a1)))
% 22.40/22.30 [5377]P7(x53772,x53771)+E(f319(x53771,f510(x53771)),f319(x53771,f514(x53771)))+P1(f319(f319(x53771,f510(x53771)),f514(x53771)))
% 22.40/22.30 [5389]E(f319(f92(a1),f430(x53891,x53892)),x53891)+P1(f319(x53892,f319(a97,x53891)))+~P1(f319(x53892,f2(a906)))
% 22.40/22.30 [5402]~P71(x54021)+~P1(f319(x54022,f730(x54022,x54021)))+P1(f319(f51(x54021),x54022))
% 22.40/22.30 [5403]~P71(x54031)+~P1(f319(x54032,f740(x54032,x54031)))+P1(f319(f51(x54031),x54032))
% 22.40/22.30 [5438]~P113(x54381)+~E(f76(x54381,x54382),f319(f73(x54381),f72(x54381)))+P1(f319(f319(f226(x54381),x54382),f2(x54381)))
% 22.40/22.30 [5512]~E(x55122,f2(a1))+E(f208(x55121,x55122),f319(f319(f244(a1,a1),f2(a1)),f72(a1)))+P1(f319(f319(f226(a1),x55122),f2(a1)))
% 22.40/22.30 [5513]~E(x55131,f2(a1))+E(f208(x55131,x55132),f319(f319(f244(a1,a1),f2(a1)),f72(a1)))+P1(f319(f319(f226(a1),x55132),f2(a1)))
% 22.40/22.30 [5566]E(f319(f92(a1),f430(x55661,x55662)),x55661)+P1(f319(x55662,f319(a97,x55661)))+P1(f319(f319(f226(a1),x55661),f2(a1)))
% 22.40/22.30 [5633]~P113(x56331)+E(f76(x56331,x56332),f319(f73(x56331),f72(x56331)))+~P1(f319(f319(f226(x56331),x56332),f2(x56331)))
% 22.40/22.30 [5634]~P92(x56341)+E(f319(f69(x56341),x56342),f319(f73(x56341),x56342))+~P1(f319(f319(f225(x56341),x56342),f2(x56341)))
% 22.40/22.30 [5635]~P92(x56351)+E(f319(f69(x56351),x56352),f319(f73(x56351),x56352))+~P1(f319(f319(f226(x56351),x56352),f2(x56351)))
% 22.40/22.30 [5636]~P81(x56361)+E(f319(f69(x56361),x56362),f319(f73(x56361),x56362))+~P1(f319(f319(f226(x56361),x56362),f2(x56361)))
% 22.40/22.30 [5738]~P1(f319(x57381,f430(x57382,x57381)))+P1(f319(x57381,f319(a97,x57382)))+~P1(f319(x57381,f2(a906)))
% 22.40/22.30 [5745]E(x57451,f2(a906))+E(f319(a104,f329(x57452,x57451)),x57451)+~P1(f319(f319(f226(a906),x57451),f319(a104,x57452)))
% 22.40/22.30 [5749]P7(x57491,x57492)+~E(f319(x57492,f510(x57492)),f319(x57492,f514(x57492)))+~P1(f319(f319(x57492,f510(x57492)),f514(x57492)))
% 22.40/22.30 [5768]~P4(x57681)+P13(x57681,x57682)+P1(f319(f319(f225(a906),f699(x57682,x57681)),f700(x57682,x57681)))
% 22.40/22.30 [5769]~P4(x57691)+P13(x57691,x57692)+P1(f319(f319(f225(a906),f707(x57692,x57691)),f711(x57692,x57691)))
% 22.40/22.30 [5855]~P92(x58551)+~E(x58552,f2(x58551))+P1(f319(f319(f225(x58551),f319(f69(x58551),x58552)),f2(x58551)))
% 22.40/22.30 [5948]~P1(f319(x59481,f430(x59482,x59481)))+P1(f319(x59481,f319(a97,x59482)))+P1(f319(f319(f226(a1),x59482),f2(a1)))
% 22.40/22.30 [5973]~P1(f319(x59731,f319(a97,x59732)))+P1(f319(x59731,f2(a906)))+~P1(f319(f319(f226(a1),x59732),f2(a1)))
% 22.40/22.30 [6313]~P113(x63131)+~P1(f319(f319(f226(x63131),x63132),f2(x63131)))+P1(f319(f319(f226(x63131),f76(x63131,x63132)),f2(x63131)))
% 22.40/22.30 [6427]~P113(x64271)+P1(f319(f319(f225(x64271),f319(f95(x64271),x64272)),f2(x64271)))+~P1(f319(f319(f225(a1),x64272),f2(a1)))
% 22.40/22.30 [6428]~P113(x64281)+P1(f319(f319(f226(x64281),f319(f95(x64281),x64282)),f2(x64281)))+~P1(f319(f319(f226(a1),x64282),f2(a1)))
% 22.40/22.30 [6437]~P92(x64372)+E(x64371,f2(x64372))+~P1(f319(f319(f225(x64372),f319(f69(x64372),x64371)),f2(x64372)))
% 22.40/22.30 [6516]~P141(x65161)+~P1(f319(f319(f321(x65161),x65162),f102(x65161)))+P1(f319(f319(f321(x65161),f319(f73(x65161),x65162)),f102(x65161)))
% 22.40/22.30 [6548]~P113(x65481)+~P1(f319(f319(f226(x65481),f76(x65481,x65482)),f2(x65481)))+P1(f319(f319(f226(x65481),x65482),f2(x65481)))
% 22.40/22.30 [6721]~P113(x67212)+~P1(f319(f319(f225(x67212),f319(f95(x67212),x67211)),f2(x67212)))+P1(f319(f319(f225(a1),x67211),f2(a1)))
% 22.40/22.30 [6722]~P113(x67222)+~P1(f319(f319(f226(x67222),f319(f95(x67222),x67221)),f2(x67222)))+P1(f319(f319(f226(a1),x67221),f2(a1)))
% 22.40/22.30 [6809]~P5(x68091)+~P40(x68091,x68091,x68092)+P1(f319(f319(f225(x68091),f319(x68092,f88(x68091,x68092))),f88(x68091,x68092)))
% 22.40/22.30 [6810]~P5(x68101)+~P40(x68101,x68101,x68102)+P1(f319(f319(f225(x68101),f319(x68102,f87(x68101,x68102))),f87(x68101,x68102)))
% 22.40/22.30 [7222]~P83(x72221)+~P1(f319(f319(f225(x72221),x72222),f2(x72221)))+P1(f319(f319(f225(x72221),f319(f319(f74(x72221),x72222),x72222)),f2(x72221)))
% 22.40/22.30 [7224]~P113(x72241)+~P1(f319(f319(f226(x72241),x72242),f2(x72241)))+P1(f319(f319(f226(x72241),f319(f319(f74(x72241),x72242),x72242)),f2(x72241)))
% 22.40/22.30 [7225]~P83(x72251)+~P1(f319(f319(f226(x72251),x72252),f2(x72251)))+P1(f319(f319(f226(x72251),f319(f319(f74(x72251),x72252),x72252)),f2(x72251)))
% 22.40/22.30 [7776]~P83(x77761)+~P1(f319(f319(f225(x77761),f319(f319(f74(x77761),x77762),x77762)),f2(x77761)))+P1(f319(f319(f225(x77761),x77762),f2(x77761)))
% 22.40/22.30 [7777]~P113(x77771)+~P1(f319(f319(f226(x77771),f319(f319(f74(x77771),x77772),x77772)),f2(x77771)))+P1(f319(f319(f226(x77771),x77772),f2(x77771)))
% 22.40/22.30 [7778]~P83(x77781)+~P1(f319(f319(f226(x77781),f319(f319(f74(x77781),x77782),x77782)),f2(x77781)))+P1(f319(f319(f226(x77781),x77782),f2(x77781)))
% 22.40/22.30 [4832]~E(x48322,f2(a906))+~E(x48321,f2(a906))+E(f319(f319(f74(a906),x48321),x48322),f2(a906))
% 22.40/22.30 [4833]~E(x48332,f72(a906))+~E(x48331,f72(a906))+E(f319(f319(f75(a906),x48331),x48332),f72(a906))
% 22.40/22.30 [4834]~E(x48342,f72(a1))+~E(x48341,f72(a1))+E(f319(f319(f75(a1),x48341),x48342),f72(a1))
% 22.40/22.30 [4889]~P120(x48892)+E(x48891,f2(x48892))+E(f319(f319(f282(x48892),x48891),x48891),f72(x48892))
% 22.40/22.30 [4890]~P69(x48902)+E(x48901,f2(x48902))+E(f319(f319(f30(x48902),x48901),x48901),f72(x48902))
% 22.40/22.30 [4891]~P121(x48912)+E(x48911,f2(x48912))+E(f319(f319(f282(x48912),x48911),x48911),f72(x48912))
% 22.40/22.30 [4909]~P83(x49091)+~E(x49092,f2(x49091))+E(f319(f319(f74(x49091),x49092),x49092),f2(x49091))
% 22.40/22.30 [4912]~P140(x49121)+~E(x49122,f72(x49121))+E(f319(f319(f75(x49121),x49122),x49122),f72(x49121))
% 22.40/22.30 [4913]~P121(x49131)+~E(x49132,f2(x49131))+E(f319(f319(f282(x49131),x49132),x49132),f2(x49131))
% 22.40/22.30 [4956]~E(x49562,f2(a906))+~E(x49561,f2(a906))+E(f319(f73(a1),f319(f92(a1),x49561)),f319(f92(a1),x49562))
% 22.40/22.30 [4975]E(x49751,f72(a906))+E(x49752,f2(a906))+~E(f319(f319(f75(a906),x49752),x49751),x49752)
% 22.40/22.30 [4987]E(x49871,f2(a906))+E(x49872,f2(a906))+~E(f319(f319(f75(a906),x49872),x49871),f2(a906))
% 22.40/22.30 [5014]~E(x50142,f2(a906))+~E(x50141,f319(a104,f2(a906)))+E(f319(f319(f74(a906),x50141),x50142),f319(a104,f2(a906)))
% 22.40/22.30 [5015]~E(x50151,f2(a906))+~E(x50152,f319(a104,f2(a906)))+E(f319(f319(f74(a906),x50151),x50152),f319(a104,f2(a906)))
% 22.40/22.30 [5022]E(x50221,f72(a1))+E(x50222,f319(f96(a1),a89))+~E(f319(f319(f75(a1),x50221),x50222),f72(a1))
% 22.40/22.30 [5023]E(x50231,f72(a1))+E(x50232,f319(f96(a1),a89))+~E(f319(f319(f75(a1),x50232),x50231),f72(a1))
% 22.40/22.30 [5024]E(x50241,f72(a1))+E(x50241,f319(f96(a1),a89))+~E(f319(f319(f75(a1),x50242),x50241),f72(a1))
% 22.40/22.30 [5026]E(x50261,f72(a1))+E(x50261,f319(f96(a1),a89))+~E(f319(f319(f75(a1),x50261),x50262),f72(a1))
% 22.40/22.30 [5048]~P83(x50482)+E(x50481,f2(x50482))+~E(f319(f319(f74(x50482),x50481),x50481),f2(x50482))
% 22.40/22.30 [5054]~E(x50541,f319(f96(a1),a89))+~E(x50542,f319(f96(a1),a89))+E(f319(f319(f75(a1),x50541),x50542),f72(a1))
% 22.40/22.30 [5065]E(x50651,f2(a906))+E(x50652,f2(a906))+~E(f319(f319(f74(a906),x50652),x50651),f319(a104,f2(a906)))
% 22.40/22.30 [5075]~P72(x50751)+~P98(x50751)+E(f319(f319(f282(x50751),x50752),f319(f96(x50751),a77)),f2(x50751))
% 22.40/22.30 [5081]~P140(x50811)+~E(x50812,f319(f73(x50811),f72(x50811)))+E(f319(f319(f75(x50811),x50812),x50812),f72(x50811))
% 22.40/22.30 [5086]~P6(x50862)+~P6(x50861)+P6(f319(f319(f74(a1),x50861),x50862))
% 22.40/22.30 [5087]~P6(x50872)+~P6(x50871)+P6(f319(f319(f75(a1),x50871),x50872))
% 22.40/22.30 [5088]~P6(x50882)+~P6(x50881)+P6(f319(f319(f30(a1),x50881),x50882))
% 22.40/22.30 [5090]~E(x50902,f2(a1))+E(x50901,f2(a1))+E(f40(x50901,x50902),f319(f319(f244(a1,a1),f2(a1)),x50901))
% 22.40/22.30 [5113]~E(x51132,f319(a104,f2(a906)))+~E(x51131,f319(a104,f2(a906)))+E(f319(f319(f75(a906),x51131),x51132),f319(a104,f2(a906)))
% 22.40/22.30 [5130]E(x51301,f2(a906))+E(x51302,f319(a104,f2(a906)))+~E(f319(f319(f236(a906),x51302),x51301),f319(a104,f2(a906)))
% 22.40/22.30 [5131]E(x51311,f2(a906))+E(x51311,f319(a104,f2(a906)))+~E(f319(f319(f74(a906),x51312),x51311),f319(a104,f2(a906)))
% 22.40/22.30 [5132]E(x51321,f2(a906))+E(x51321,f319(a104,f2(a906)))+~E(f319(f319(f74(a906),x51321),x51322),f319(a104,f2(a906)))
% 22.40/22.30 [5141]~P72(x51411)+~P98(x51411)+E(f319(f319(f282(x51411),x51412),f319(f96(x51411),a89)),f319(f73(x51411),x51412))
% 22.40/22.30 [5161]E(x51611,f319(a97,x51612))+~E(x51611,f2(a906))+P1(f319(f319(f225(a1),f2(a1)),x51612))
% 22.40/22.30 [5162]E(f319(a97,x51621),x51622)+~E(x51622,f2(a906))+P1(f319(f319(f225(a1),f2(a1)),x51621))
% 22.40/22.30 [5178]E(x51781,f319(a104,f2(a906)))+E(x51782,f319(a104,f2(a906)))+~E(f319(f319(f74(a906),x51781),x51782),f319(a104,f2(a906)))
% 22.40/22.30 [5189]~E(x51891,f319(a97,x51892))+E(x51891,f2(a906))+P1(f319(f319(f225(a1),f2(a1)),x51892))
% 22.40/22.30 [5190]~E(f319(a97,x51902),x51901)+E(x51901,f2(a906))+P1(f319(f319(f225(a1),f2(a1)),x51902))
% 22.40/22.30 [5216]~P101(x52161)+E(f319(f57(x52161,f94(x52161)),x52162),f12(x52161,x52162))+~P1(f319(f55(x52161),x52162))
% 22.40/22.30 [5217]~P101(x52171)+E(f319(f57(x52171,f93(x52171)),x52172),f15(x52171,x52172))+~P1(f319(f55(x52171),x52172))
% 22.40/22.30 [5218]~P4(x52181)+E(f319(f57(x52181,f180(x52181)),x52182),f16(x52181,x52182))+~P1(f319(f55(x52181),x52182))
% 22.40/22.30 [5219]~P4(x52191)+E(f319(f57(x52191,f230(x52191)),x52192),f17(x52191,x52192))+~P1(f319(f55(x52191),x52192))
% 22.40/22.30 [5299]E(x52991,x52992)+~E(f319(f319(f3(a906),x52992),x52991),f2(a906))+~E(f319(f319(f3(a906),x52991),x52992),f2(a906))
% 22.40/22.30 [5316]P6(x53161)+~P41(x53162)+~P1(f319(f319(f321(a1),x53161),x53162))
% 22.40/22.30 [5346]~P113(x53461)+~E(f76(x53461,x53462),f72(x53461))+P1(f319(f319(f226(x53461),f2(x53461)),x53462))
% 22.40/22.30 [5357]~P98(x53571)+E(f319(f92(x53571),f319(f96(a906),x53572)),f319(f96(x53571),x53572))+P1(f319(a186,f319(f96(a1),x53572)))
% 22.40/22.30 [5362]~P44(x53621,x53622)+P45(a904)+P1(f319(f55(f912(x53621,x53621)),x53622))
% 22.40/22.30 [5430]~P4(x54301)+E(f319(f57(x54301,f180(x54301)),x54302),f13(x54301,f180(x54301),x54302))+~P1(f319(f55(x54301),x54302))
% 22.40/22.30 [5431]~P4(x54311)+E(f319(f57(x54311,f230(x54311)),x54312),f14(x54311,f230(x54311),x54312))+~P1(f319(f55(x54311),x54312))
% 22.40/22.30 [5445]E(x54451,x54452)+P1(f319(f319(f226(a906),x54452),x54451))+P1(f319(f319(f226(a906),x54451),x54452))
% 22.40/22.30 [5446]E(x54461,x54462)+P1(f319(f319(f226(a1),x54462),x54461))+P1(f319(f319(f226(a1),x54461),x54462))
% 22.40/22.30 [5499]~P98(x54991)+E(f319(f92(x54991),f319(f96(a906),x54992)),f2(x54991))+~P1(f319(a186,f319(f96(a1),x54992)))
% 22.40/22.30 [5502]~E(x55022,f319(a97,x55021))+E(x55021,f319(f92(a1),x55022))+~P1(f319(f319(f225(a1),f2(a1)),x55021))
% 22.40/22.30 [5503]~E(f319(a97,x55031),x55032)+E(x55031,f319(f92(a1),x55032))+~P1(f319(f319(f225(a1),f2(a1)),x55031))
% 22.40/22.30 [5504]~E(x55041,f319(a97,x55042))+E(f319(f92(a1),x55041),x55042)+~P1(f319(f319(f225(a1),f2(a1)),x55042))
% 22.40/22.30 [5514]E(x55141,f319(a97,x55142))+~E(x55142,f319(f92(a1),x55141))+~P1(f319(f319(f225(a1),f2(a1)),x55142))
% 22.40/22.30 [5515]E(f319(a97,x55151),x55152)+~E(x55151,f319(f92(a1),x55152))+~P1(f319(f319(f225(a1),f2(a1)),x55151))
% 22.40/22.30 [5546]~P119(x55462)+E(x55461,f2(x55462))+~P1(f319(f319(f279(x55462),f2(x55462)),x55461))
% 22.40/22.30 [5557]~P92(x55572)+E(x55571,f2(x55572))+P1(f319(f319(f226(x55572),f2(x55572)),f319(f69(x55572),x55571)))
% 22.40/22.30 [5620]~P113(x56201)+E(f76(x56201,x56202),f72(x56201))+~P1(f319(f319(f226(x56201),f2(x56201)),x56202))
% 22.40/22.30 [5626]~P98(x56261)+E(f319(f92(x56261),f319(f96(a906),x56262)),f2(x56261))+P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x56262)))
% 22.40/22.30 [5637]~P92(x56371)+E(f319(f69(x56371),x56372),x56372)+~P1(f319(f319(f225(x56371),f2(x56371)),x56372))
% 22.40/22.30 [5638]~P92(x56381)+E(f319(f69(x56381),x56382),x56382)+~P1(f319(f319(f226(x56381),f2(x56381)),x56382))
% 22.40/22.30 [5647]E(x56471,f2(a906))+~E(f131(a906,f319(f294(a906,x56472),x56471)),f105(a906))+P1(f319(f319(f225(a906),x56471),x56472))
% 22.40/22.30 [5657]~P76(x56571)+E(f319(f319(f8(x56571,x56571),f7(x56571)),f319(f164(x56571),x56572)),f319(f157(x56571),x56572))+~P1(f319(f129(x56571),x56572))
% 22.40/22.30 [5660]~P141(x56601)+E(f319(f92(x56601),f319(a97,x56602)),f319(f95(x56601),x56602))+~P1(f319(f319(f225(a1),f2(a1)),x56602))
% 22.40/22.30 [5687]E(x56871,x56872)+P1(f319(f319(f226(a906),x56871),x56872))+~P1(f319(f319(f225(a906),x56871),x56872))
% 22.40/22.30 [5688]E(x56881,x56882)+P1(f319(f319(f226(a1),x56881),x56882))+~P1(f319(f319(f225(a1),x56881),x56882))
% 22.40/22.30 [5691]E(x56911,f72(a1))+~E(f319(f319(f75(a1),x56912),x56911),f72(a1))+~P1(f319(f319(f226(a1),f2(a1)),x56912))
% 22.40/22.30 [5692]E(x56921,f72(a1))+~E(f319(f319(f75(a1),x56921),x56922),f72(a1))+~P1(f319(f319(f226(a1),f2(a1)),x56921))
% 22.40/22.30 [5735]~P41(x57352)+P1(f319(f319(f225(a1),f2(a1)),x57351))+~P1(f319(f319(f321(a1),x57351),x57352))
% 22.40/22.30 [5755]~P59(x57551,x57552)+P37(x57551,x57552)+~P1(f319(f55(f912(x57551,x57551)),x57552))
% 22.40/22.30 [5757]~P59(x57571,x57572)+P44(x57571,x57572)+~P1(f319(f55(f912(x57571,x57571)),x57572))
% 22.40/22.30 [5799]E(x57991,f181(f913(x57992,a904)))+~P1(f319(f55(x57992),x57991))+P1(f319(f319(f226(a906),f2(a906)),f319(f29(x57992),x57991)))
% 22.40/22.30 [5826]~P1(f319(x58261,x58262))+P1(f319(x58261,f2(a906)))+P1(f319(f319(f226(a906),f354(x58262,x58261)),x58262))
% 22.40/22.30 [5849]E(x58491,f2(a906))+~E(f319(f157(a906),x58492),f2(a906))+~P1(f319(f319(f321(a906),x58491),f319(f164(a906),x58492)))
% 22.40/22.30 [5917]E(x59171,x59172)+~P1(f319(f319(f225(a906),x59172),x59171))+~P1(f319(f319(f225(a906),x59171),x59172))
% 22.40/22.30 [5918]E(x59181,x59182)+~P1(f319(f319(f225(a1),x59182),x59181))+~P1(f319(f319(f225(a1),x59181),x59182))
% 22.40/22.30 [5922]E(x59221,x59222)+~P1(f319(f319(f279(a906),x59222),x59221))+~P1(f319(f319(f279(a906),x59221),x59222))
% 22.40/22.30 [5924]E(f319(f29(x59241),x59242),f2(a906))+~P1(f319(f55(x59241),x59242))+P1(f319(f319(f321(x59241),f372(x59242,x59241)),x59242))
% 22.40/22.30 [5933]E(f44(x59331,x59332),f40(x59331,x59332))+P1(f319(f319(f225(a1),f2(a1)),x59331))+~P1(f319(f319(f226(a1),f2(a1)),x59332))
% 22.40/22.30 [5960]~P1(f319(x59601,f423(x59601)))+P1(f319(x59601,f319(a97,x59602)))+~P1(f319(f319(f225(a1),f2(a1)),x59602))
% 22.40/22.30 [5963]P1(f319(f319(f225(a906),x59631),f849(x59632)))+~P1(f319(f55(a906),x59632))+~P1(f319(f319(f321(a906),x59631),x59632))
% 22.40/22.30 [5964]P1(f319(f319(f226(a906),x59641),f886(x59642)))+~P1(f319(f55(a906),x59642))+~P1(f319(f319(f321(a906),x59641),x59642))
% 22.40/22.30 [5995]E(x59951,x59952)+~P1(f319(f319(f226(a906),x59951),f319(a104,x59952)))+P1(f319(f319(f226(a906),x59951),x59952))
% 22.40/22.30 [6027]E(x60271,f319(a104,x60272))+~P1(f319(f319(f225(a906),x60271),f319(a104,x60272)))+P1(f319(f319(f225(a906),x60271),x60272))
% 22.40/22.30 [6042]P1(f319(x60421,f424(x60421)))+~P1(f319(x60421,f319(a97,x60422)))+~P1(f319(f319(f225(a1),f2(a1)),x60422))
% 22.40/22.30 [6057]~P1(f319(x60571,x60572))+~P1(f319(f319(f225(a1),f2(a1)),x60572))+P1(f319(x60571,f319(f92(a1),f432(x60571))))
% 22.40/22.30 [6068]~P92(x60682)+~E(x60681,f2(x60682))+~P1(f319(f319(f226(x60682),f2(x60682)),f319(f69(x60682),x60681)))
% 22.40/22.30 [6092]~P59(x60921,x60922)+P37(x60921,f319(f278(x60921,x60921),x60922))+~P1(f319(f55(f912(x60921,x60921)),x60922))
% 22.40/22.30 [6102]~P98(x61021)+E(f319(f92(x61021),f319(f96(a906),x61022)),f319(f96(x61021),x61022))+~P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x61022)))
% 22.40/22.30 [6105]E(f319(a104,x61051),x61052)+~P1(f319(f319(f226(a906),x61051),x61052))+P1(f319(f319(f226(a906),f319(a104,x61051)),x61052))
% 22.40/22.30 [6120]E(f319(f319(f30(a1),x61201),x61202),f2(a1))+~P1(f319(f319(f225(a1),x61201),f2(a1)))+~P1(f319(f319(f226(a1),x61202),x61201))
% 22.40/22.30 [6131]E(f39(a1,x61311,x61312),x61311)+~P1(f319(f319(f225(a1),x61311),f2(a1)))+~P1(f319(f319(f226(a1),x61312),x61311))
% 22.40/22.30 [6145]E(f41(x61451,x61452),f40(x61451,x61452))+~P1(f319(f319(f225(a1),f2(a1)),x61451))+~P1(f319(f319(f225(a1),f2(a1)),x61452))
% 22.40/22.30 [6155]E(f319(f319(f30(a1),x61551),x61552),f2(a1))+~P1(f319(f319(f225(a1),f2(a1)),x61551))+~P1(f319(f319(f226(a1),x61551),x61552))
% 22.40/22.30 [6164]E(f39(a906,f319(f96(a906),x61641),f319(f96(a906),x61642)),f319(f96(a906),x61641))+P1(f319(a186,f319(f96(a1),x61641)))+~P1(f319(a186,f319(f96(a1),x61642)))
% 22.40/22.30 [6166]E(f39(a1,x61661,x61662),x61661)+~P1(f319(f319(f225(a1),f2(a1)),x61661))+~P1(f319(f319(f226(a1),x61661),x61662))
% 22.40/22.30 [6167]E(x61671,x61672)+~P1(f319(f319(f226(a906),x61671),f319(a104,x61672)))+~P1(f319(f319(f225(a906),x61672),x61671))
% 22.40/22.30 [6181]~P83(x61811)+~P1(f319(f319(f225(x61811),x61812),f2(x61811)))+P1(f319(f319(f225(x61811),x61812),f319(f73(x61811),x61812)))
% 22.40/22.30 [6182]~P113(x61821)+~P1(f319(f319(f226(x61821),x61822),f2(x61821)))+P1(f319(f319(f226(x61821),x61822),f319(f73(x61821),x61822)))
% 22.40/22.30 [6191]~P5(x61911)+E(f319(f319(f58(x61911,x61911,f94(x61911)),f234(x61911)),x61912),f32(x61911,x61912))+~P1(f319(f55(x61911),x61912))
% 22.40/22.30 [6192]~P5(x61921)+E(f319(f319(f58(x61921,x61921,f93(x61921)),f181(x61921)),x61922),f31(x61921,x61922))+~P1(f319(f55(x61921),x61922))
% 22.40/22.30 [6209]~P113(x62091)+~P1(f319(f319(f225(a1),f2(a1)),x62092))+P1(f319(f319(f225(x62091),f2(x62091)),f319(f95(x62091),x62092)))
% 22.40/22.30 [6210]~P126(x62101)+~P1(f319(f319(f226(a906),f2(a906)),x62102))+P1(f319(f319(f226(x62101),f2(x62101)),f319(f92(x62101),x62102)))
% 22.40/22.30 [6211]~P113(x62111)+~P1(f319(f319(f226(a1),f2(a1)),x62112))+P1(f319(f319(f226(x62111),f2(x62111)),f319(f95(x62111),x62112)))
% 22.40/22.30 [6214]~P6(x62142)+~P6(x62141)+E(f319(f302(a906,a1,f92(a1)),f295(a906,f319(a97,x62141),f319(a97,x62142))),f295(a1,x62141,x62142))
% 22.40/22.30 [6220]P1(f319(x62201,x62202))+~P1(f319(f319(f225(a1),f2(a1)),x62202))+~P1(f319(x62201,f319(f92(a1),f433(x62201))))
% 22.40/22.30 [6252]E(f319(f319(f74(a906),f319(f96(a906),x62521)),f319(f96(a906),x62522)),f319(f96(a906),x62521))+P1(f319(f319(f226(a1),x62521),a77))+~P1(f319(f319(f226(a1),x62522),a77))
% 22.40/22.30 [6258]~P113(x62581)+P1(f319(f319(f226(x62581),f2(x62581)),f76(x62581,x62582)))+~P1(f319(f319(f226(x62581),f2(x62581)),x62582))
% 22.40/22.30 [6271]~P65(x62711)+~P1(f319(f319(f225(x62711),x62712),f2(x62711)))+P1(f319(f319(f225(x62711),f2(x62711)),f319(f73(x62711),x62712)))
% 22.40/22.30 [6272]~P65(x62721)+~P1(f319(f319(f226(x62721),x62722),f2(x62721)))+P1(f319(f319(f226(x62721),f2(x62721)),f319(f73(x62721),x62722)))
% 22.40/22.30 [6275]E(x62751,f234(f913(x62752,a904)))+~E(f319(f29(x62752),x62751),f319(f29(x62752),f234(f913(x62752,a904))))+~P1(f319(f55(x62752),f234(f913(x62752,a904))))
% 22.40/22.30 [6297]~P1(f319(f319(f226(a906),f2(a906)),x62972))+~P1(f319(f319(f279(a906),x62971),x62972))+P1(f319(f319(f225(a906),x62971),x62972))
% 22.40/22.30 [6304]~P83(x63041)+P1(f319(f319(f225(x63041),x63042),f2(x63041)))+~P1(f319(f319(f225(x63041),x63042),f319(f73(x63041),x63042)))
% 22.40/22.30 [6305]~P113(x63051)+P1(f319(f319(f226(x63051),x63052),f2(x63051)))+~P1(f319(f319(f226(x63051),x63052),f319(f73(x63051),x63052)))
% 22.40/22.30 [6315]~P98(x63151)+P1(f319(f319(f321(x63151),f319(f96(x63151),x63152)),f178(x63151)))+~P1(f319(f319(f225(a1),a77),x63152))
% 22.40/22.30 [6344]E(x63441,f2(a906))+~P1(f319(f319(f226(a906),x63441),f319(a104,x63442)))+P1(f319(f319(f226(a906),f329(x63442,x63441)),x63442))
% 22.40/22.30 [6367]~P113(x63671)+~P1(f319(f319(f226(x63671),f2(x63671)),f76(x63671,x63672)))+P1(f319(f319(f226(x63671),f2(x63671)),x63672))
% 22.40/22.30 [6369]~E(f319(f96(a906),x63692),f319(f96(a906),x63691))+P1(f319(f319(f225(a1),f319(f96(a1),x63691)),f2(a1)))+~P1(f319(a186,f319(f96(a1),x63692)))
% 22.40/22.30 [6398]E(f319(f243(a1,a1),f44(x63981,x63982)),f319(f319(f30(a1),x63981),x63982))+~P1(f319(f319(f226(a1),x63981),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x63982))
% 22.40/22.30 [6435]E(f319(f248(a1,a1),f44(x64351,x64352)),f39(a1,x64351,x64352))+~P1(f319(f319(f226(a1),x64351),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x64352))
% 22.40/22.30 [6438]~P113(x64382)+~P1(f319(f319(f225(x64382),f2(x64382)),f319(f95(x64382),x64381)))+P1(f319(f319(f225(a1),f2(a1)),x64381))
% 22.40/22.30 [6439]~P126(x64392)+~P1(f319(f319(f226(x64392),f2(x64392)),f319(f92(x64392),x64391)))+P1(f319(f319(f226(a906),f2(a906)),x64391))
% 22.40/22.30 [6440]~P113(x64402)+~P1(f319(f319(f226(x64402),f2(x64402)),f319(f95(x64402),x64401)))+P1(f319(f319(f226(a1),f2(a1)),x64401))
% 22.40/22.30 [6443]E(f319(f243(a1,a1),f41(x64431,x64432)),f319(f319(f30(a1),x64431),x64432))+~P1(f319(f319(f225(a1),f2(a1)),x64432))+~P1(f319(f319(f226(a1),f2(a1)),x64431))
% 22.40/22.30 [6456]E(f319(f248(a1,a1),f41(x64561,x64562)),f39(a1,x64561,x64562))+~P1(f319(f319(f225(a1),f2(a1)),x64562))+~P1(f319(f319(f226(a1),f2(a1)),x64561))
% 22.40/22.30 [6472]~P65(x64721)+P1(f319(f319(f225(x64721),x64722),f2(x64721)))+~P1(f319(f319(f225(x64721),f2(x64721)),f319(f73(x64721),x64722)))
% 22.40/22.30 [6473]~P65(x64731)+P1(f319(f319(f226(x64731),x64732),f2(x64731)))+~P1(f319(f319(f226(x64731),f2(x64731)),f319(f73(x64731),x64732)))
% 22.40/22.30 [6496]~P5(x64961)+~P40(x64961,x64961,x64962)+P1(f319(f319(f225(x64961),f88(x64961,x64962)),f319(x64962,f88(x64961,x64962))))
% 22.40/22.30 [6497]~P5(x64971)+~P40(x64971,x64971,x64972)+P1(f319(f319(f225(x64971),f87(x64971,x64972)),f319(x64972,f87(x64971,x64972))))
% 22.40/22.30 [6501]P1(f319(f43(x65011,x65012),f44(x65011,x65012)))+~P1(f319(f319(f226(a1),x65011),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x65012))
% 22.40/22.30 [6515]~P1(f319(f319(f226(a906),f2(a906)),x65151))+~P1(f319(f319(f279(a906),x65152),x65151))+~P1(f319(f319(f226(a906),x65151),x65152))
% 22.40/22.30 [6528]P1(f319(f43(x65281,x65282),f41(x65281,x65282)))+~P1(f319(f319(f225(a1),f2(a1)),x65281))+~P1(f319(f319(f226(a1),f2(a1)),x65282))
% 22.40/22.30 [6571]~P65(x65711)+P1(f319(f319(f225(x65711),f319(f73(x65711),x65712)),f2(x65711)))+~P1(f319(f319(f225(x65711),f2(x65711)),x65712))
% 22.40/22.30 [6572]~P65(x65721)+P1(f319(f319(f226(x65721),f319(f73(x65721),x65722)),f2(x65721)))+~P1(f319(f319(f226(x65721),f2(x65721)),x65722))
% 22.40/22.30 [6589]E(f319(f319(f3(a906),f319(a97,x65891)),f319(a97,x65892)),f319(a97,f187(x65891,x65892)))+~P1(f319(f319(f225(a1),f2(a1)),x65892))+~P1(f319(f319(f225(a1),f2(a1)),x65891))
% 22.40/22.30 [6607]P1(f319(f319(f225(a1),f2(a1)),f187(x66071,x66072)))+~P1(f319(f319(f225(a1),f2(a1)),x66072))+~P1(f319(f319(f225(a1),f2(a1)),x66071))
% 22.40/22.30 [6640]~P1(f319(x66401,x66402))+P1(f319(x66401,f2(a906)))+P1(f319(x66401,f319(f319(f74(a906),f354(x66402,x66401)),f72(a906))))
% 22.40/22.30 [6728]E(f319(f96(a906),x67281),f319(f96(a906),x67282))+~P1(f319(f319(f225(a1),f319(f96(a1),x67282)),f2(a1)))+~P1(f319(a186,f319(f96(a1),x67281)))
% 22.40/22.30 [6740]~E(x67401,f2(a906))+~E(f666(x67402,x67401),f2(a906))+E(f319(f134(a906,a906,f74(a906),x67401),x67402),f2(a906))
% 22.40/22.30 [6764]~P1(f319(f55(x67641),f680(x67642,x67641)))+~P1(f319(f55(f913(x67641,a904)),x67642))+P1(f319(f55(x67641),f31(f913(x67641,a904),x67642)))
% 22.40/22.30 [6770]E(x67701,x67702)+P1(f319(f319(f226(a1),x67701),x67702))+~P1(f319(f319(f226(a1),x67701),f319(f319(f74(a1),x67702),f72(a1))))
% 22.40/22.30 [6771]P1(f319(f319(f225(a906),f319(a97,x67711)),f319(a97,x67712)))+~P1(f319(f319(f225(a1),f2(a1)),x67712))+~P1(f319(f319(f225(a1),x67711),x67712))
% 22.40/22.30 [6772]P1(f319(f319(f225(a906),f319(a97,x67721)),f319(a97,x67722)))+~P1(f319(f319(f226(a1),f2(a1)),x67721))+~P1(f319(f319(f225(a1),x67721),x67722))
% 22.40/22.30 [6774]P1(f319(f319(f226(a906),f319(a97,x67741)),f319(a97,x67742)))+~P1(f319(f319(f225(a1),f2(a1)),x67741))+~P1(f319(f319(f226(a1),x67741),x67742))
% 22.40/22.30 [6775]P1(f319(f319(f226(a906),f319(a97,x67751)),f319(a97,x67752)))+~P1(f319(f319(f226(a1),f2(a1)),x67752))+~P1(f319(f319(f226(a1),x67751),x67752))
% 22.40/22.30 [6787]E(f39(a906,f319(a97,x67871),f319(a97,x67872)),f319(a97,f39(a1,x67871,x67872)))+~P1(f319(f319(f225(a1),f2(a1)),x67872))+~P1(f319(f319(f225(a1),f2(a1)),x67871))
% 22.40/22.30 [6814]~P65(x68141)+~P1(f319(f319(f225(x68141),f319(f73(x68141),x68142)),f2(x68141)))+P1(f319(f319(f225(x68141),f2(x68141)),x68142))
% 22.40/22.30 [6815]~P65(x68151)+~P1(f319(f319(f226(x68151),f319(f73(x68151),x68152)),f2(x68151)))+P1(f319(f319(f226(x68151),f2(x68151)),x68152))
% 22.40/22.30 [6830]~P1(f319(f319(f226(a1),a77),x68302))+~P1(f319(f319(f226(a1),x68301),x68302))+P1(f319(f319(f226(a906),f319(f96(a906),x68301)),f319(f96(a906),x68302)))
% 22.40/22.30 [6916]~P1(f319(f319(f225(a1),f2(a1)),x69161))+P1(f319(f319(f226(a906),f319(a97,x69161)),x69162))+~P1(f319(f319(f226(a1),x69161),f319(f92(a1),x69162)))
% 22.40/22.30 [6921]P1(f319(x69211,x69212))+~P1(f319(x69211,f319(a22,f799(x69211,x69212))))+~P1(f319(f319(f321(a906),x69212),f234(f913(a906,a904))))
% 22.40/22.30 [6931]E(x69311,f2(a1))+E(f39(a1,x69312,x69311),f2(a1))+E(f319(f319(f3(a1),f319(f73(a1),f319(f319(f30(a1),x69312),x69311))),f72(a1)),f319(f319(f30(a1),x69312),f319(f73(a1),x69311)))
% 22.40/22.30 [6943]~P1(f319(f319(f225(a1),f2(a1)),x69431))+~P1(f319(f319(f226(a906),f319(a97,x69431)),x69432))+P1(f319(f319(f226(a1),x69431),f319(f92(a1),x69432)))
% 22.40/22.30 [6979]~P1(f319(f319(f225(a906),f319(a97,x69791)),f319(a97,x69792)))+~P1(f319(f319(f225(a1),f2(a1)),x69792))+P1(f319(f319(f225(a1),x69791),x69792))
% 22.40/22.30 [6980]~P1(f319(f319(f225(a906),f319(a97,x69801)),f319(a97,x69802)))+~P1(f319(f319(f226(a1),f2(a1)),x69801))+P1(f319(f319(f225(a1),x69801),x69802))
% 22.40/22.30 [7009]P1(f319(f319(f225(a1),x70091),x70092))+~P1(f319(f319(f225(a906),f319(f96(a906),x70091)),f319(f96(a906),x70092)))+P1(f319(f319(f225(a1),x70091),a77))
% 22.40/22.30 [7034]P1(f319(f319(f225(a1),f2(a1)),f39(a1,x70341,x70342)))+~P1(f319(f319(f225(a1),f2(a1)),x70342))+~P1(f319(f319(f225(a1),f2(a1)),x70341))
% 22.40/22.30 [7133]P1(f319(f319(f226(a1),a77),x71331))+~P1(f319(f319(f226(a1),x71332),x71331))+~P1(f319(f319(f226(a906),f319(f96(a906),x71332)),f319(f96(a906),x71331)))
% 22.40/22.30 [7186]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),x71861),x71862)),f39(a1,x71861,x71862)),f44(x71861,x71862))+~P1(f319(f319(f226(a1),x71861),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x71862))
% 22.40/22.30 [7205]E(f319(f319(f244(a1,a1),f319(f319(f30(a1),x72051),x72052)),f39(a1,x72051,x72052)),f41(x72051,x72052))+~P1(f319(f319(f225(a1),f2(a1)),x72052))+~P1(f319(f319(f225(a1),f2(a1)),x72051))
% 22.40/22.30 [7257]~P100(x72572)+E(x72571,f105(x72572))+E(f319(f134(x72572,x72572,f75(x72572),f319(f133(x72572),x72571)),f319(f163(x72572),x72571)),f319(f57(x72572,f75(x72572)),f319(f164(x72572),x72571)))
% 22.40/22.30 [7373]~E(x73731,f2(a906))+E(f319(f134(a906,a906,f74(a906),x73731),x73732),f2(a906))+P1(f319(f319(f321(a906),f666(x73732,x73731)),f319(f164(a906),x73732)))
% 22.40/22.30 [7421]~P1(f319(f319(f225(a1),x74211),f2(a1)))+P1(f319(f319(f225(a1),f319(f319(f30(a1),x74211),x74212)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x74212))
% 22.40/22.30 [7422]~P1(f319(f319(f226(a1),x74222),f2(a1)))+P1(f319(f319(f225(a1),f319(f319(f30(a1),x74221),x74222)),f2(a1)))+~P1(f319(f319(f225(a1),f2(a1)),x74221))
% 22.40/22.30 [7423]~P1(f319(f319(f226(a1),x74232),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x74231),x74232)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x74231))
% 22.40/22.30 [7425]~P1(f319(f319(f226(a1),x74251),f2(a1)))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x74251),x74252)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x74252))
% 22.40/22.30 [7433]P1(f319(f319(f321(f913(x74331,a904)),f680(x74332,x74331)),x74332))+~P1(f319(f55(f913(x74331,a904)),x74332))+P1(f319(f55(x74331),f31(f913(x74331,a904),x74332)))
% 22.40/22.30 [7516]P25(x75161,x75161,x75162,f234(f913(x75161,a904)))+~E(f319(f302(x75161,x75161,x75162),f234(f913(x75161,a904))),f234(f913(x75161,a904)))+~P1(f319(f55(x75161),f234(f913(x75161,a904))))
% 22.40/22.30 [7635]~P25(x76351,x76351,x76352,f234(f913(x76351,a904)))+E(f319(f302(x76351,x76351,x76352),f234(f913(x76351,a904))),f234(f913(x76351,a904)))+~P1(f319(f55(x76351),f234(f913(x76351,a904))))
% 22.40/22.30 [7769]E(f319(f319(f30(a1),x77691),x77692),f319(f96(a1),a89))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),x77691),x77692)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x77691))
% 22.40/22.30 [7825]~P1(f319(f319(f226(a1),x78252),f2(a1)))+~P1(f319(f319(f226(a1),f319(f319(f30(a1),x78251),x78252)),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x78251))
% 22.40/22.30 [7830]E(f319(f319(f74(a1),x78301),x78302),f39(a1,x78301,x78302))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),x78301),x78302)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x78301))
% 22.40/22.30 [7833]P1(f319(f319(f226(a1),x78331),f2(a1)))+~P1(f319(f319(f226(a1),f319(f319(f30(a1),x78331),x78332)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x78332))
% 22.40/22.30 [8516]~P4(x85161)+P13(x85161,x85162)+~P1(f319(f319(f225(x85161),f319(f319(f156(x85161),x85162),f699(x85162,x85161))),f319(f319(f156(x85161),x85162),f700(x85162,x85161))))
% 22.40/22.30 [8517]~P4(x85171)+P13(x85171,x85172)+~P1(f319(f319(f225(x85171),f319(f319(f156(x85171),x85172),f707(x85172,x85171))),f319(f319(f156(x85171),x85172),f711(x85172,x85171))))
% 22.40/22.30 [5792]E(x57921,f2(a1))+~E(f39(a1,x57922,x57921),f2(a1))+E(f319(f319(f30(a1),x57922),f319(f73(a1),x57921)),f319(f73(a1),f319(f319(f30(a1),x57922),x57921)))
% 22.40/22.30 [5810]~P41(x58102)+~P41(x58101)+P41(f319(f319(f93(f913(a1,a904)),x58101),x58102))
% 22.40/22.30 [5811]~P41(x58112)+~P41(x58111)+P41(f319(f319(f94(f913(a1,a904)),x58111),x58112))
% 22.40/22.30 [5829]~P72(x58291)+~P98(x58291)+E(f319(f73(x58291),f319(f319(f282(x58291),f72(x58291)),x58292)),f319(f319(f282(x58291),f319(f96(x58291),a89)),x58292))
% 22.40/22.30 [5952]E(x59521,f2(a1))+~E(f39(a1,x59522,x59521),f2(a1))+E(f319(f319(f30(a1),f319(f73(a1),x59522)),x59521),f319(f73(a1),f319(f319(f30(a1),x59522),x59521)))
% 22.40/22.30 [6086]~P4(x60861)+P13(x60861,x60862)+P1(f319(f319(f226(a906),f700(x60862,x60861)),f319(f182(f907(x60861)),x60862)))
% 22.40/22.30 [6087]~P4(x60871)+P13(x60871,x60872)+P1(f319(f319(f226(a906),f711(x60872,x60871)),f319(f182(f907(x60871)),x60872)))
% 22.40/22.30 [6246]~P98(x62461)+~E(f319(f96(x62461),x62462),f2(x62461))+P28(x62461,f319(f96(x62461),f319(f319(f74(a1),x62462),f319(f73(a1),a77))))
% 22.40/22.30 [6247]~P98(x62471)+~E(f319(f96(x62471),x62472),f2(x62471))+P28(x62471,f319(f96(x62471),f319(f319(f74(a1),a77),f319(f73(a1),x62472))))
% 22.40/22.30 [6249]E(f319(a45,f41(f319(f73(a1),x62491),f319(f73(a1),x62492))),f40(x62491,x62492))+P1(f319(f319(f225(a1),f2(a1)),x62491))+P1(f319(f319(f226(a1),f2(a1)),x62492))
% 22.40/22.30 [6375]~E(x63752,f2(a906))+~E(x63751,f2(a906))+P1(f319(f319(f225(a1),f319(f92(a1),x63751)),f319(f73(a1),f319(f92(a1),x63752))))
% 22.40/22.30 [6404]E(f319(f319(f74(a906),f319(f96(a906),x64041)),f319(f96(a906),x64042)),f319(f96(a906),f319(f319(f74(a1),x64041),x64042)))+P1(f319(f319(f226(a1),x64041),a77))+P1(f319(f319(f226(a1),x64042),a77))
% 22.40/22.30 [6537]~P83(x65371)+~P1(f319(f319(f225(x65371),f2(x65371)),x65372))+P1(f319(f319(f225(x65371),f319(f73(x65371),x65372)),x65372))
% 22.40/22.30 [6538]~P83(x65381)+~P1(f319(f319(f226(x65381),f2(x65381)),x65382))+P1(f319(f319(f226(x65381),f319(f73(x65381),x65382)),x65382))
% 22.40/22.30 [6714]E(f319(f319(f3(a906),f319(a97,x67141)),f319(a97,x67142)),f319(a97,f319(f319(f3(a1),x67141),x67142)))+~P1(f319(f319(f225(a1),f2(a1)),x67142))+~P1(f319(f319(f225(a1),x67142),x67141))
% 22.40/22.30 [6748]E(f319(a97,f39(a1,f319(f96(a1),x67481),f319(f96(a1),x67482))),f39(a906,f319(f96(a906),x67481),f319(f96(a906),x67482)))+P1(f319(a186,f319(f96(a1),x67481)))+P1(f319(a186,f319(f96(a1),x67482)))
% 22.40/22.30 [6765]~P83(x67651)+P1(f319(f319(f225(x67651),f2(x67651)),x67652))+~P1(f319(f319(f225(x67651),f319(f73(x67651),x67652)),x67652))
% 22.40/22.30 [6766]~P83(x67661)+P1(f319(f319(f226(x67661),f2(x67661)),x67662))+~P1(f319(f319(f226(x67661),f319(f73(x67661),x67662)),x67662))
% 22.40/22.30 [6779]~P83(x67791)+~P1(f319(f319(f225(x67791),f2(x67791)),x67792))+P1(f319(f319(f225(x67791),f2(x67791)),f319(f319(f74(x67791),x67792),x67792)))
% 22.40/22.30 [6781]~P83(x67811)+~P1(f319(f319(f226(x67811),f2(x67811)),x67812))+P1(f319(f319(f226(x67811),f2(x67811)),f319(f319(f74(x67811),x67812),x67812)))
% 22.40/22.30 [6793]E(f319(f319(f74(a906),f319(a97,x67931)),f319(a97,x67932)),f319(a97,f319(f319(f74(a1),x67931),x67932)))+~P1(f319(f319(f225(a1),f2(a1)),x67932))+~P1(f319(f319(f225(a1),f2(a1)),x67931))
% 22.40/22.30 [6805]E(x68051,f2(a906))+P1(f319(f319(f226(a906),f2(a906)),x68052))+~P1(f319(f319(f226(a906),f2(a906)),f319(f319(f236(a906),x68052),x68051)))
% 22.40/22.30 [6840]~P98(x68401)+E(f319(f96(x68401),x68402),f2(x68401))+~P28(x68401,f319(f96(x68401),f319(f319(f74(a1),a77),f319(f73(a1),x68402))))
% 22.40/22.30 [6841]~P98(x68411)+E(f319(f96(x68411),x68412),f2(x68411))+~P28(x68411,f319(f96(x68411),f319(f319(f74(a1),x68412),f319(f73(a1),a77))))
% 22.40/22.30 [6894]~P1(f319(f55(x68941),x68942))+~P1(f319(f55(x68941),f234(f913(x68941,a904))))+P1(f319(f55(x68941),f319(f73(f913(x68941,a904)),x68942)))
% 22.40/22.30 [6917]~P1(f319(f319(f226(a1),f2(a1)),x69172))+~P1(f319(f319(f225(a1),x69172),x69171))+P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x69171),x69172)))
% 22.40/22.30 [6918]~P1(f319(f319(f225(a1),x69181),f2(a1)))+~P1(f319(f319(f226(a1),x69182),f2(a1)))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f30(a1),x69181),x69182)))
% 22.40/22.30 [6953]~P1(f319(f319(f225(a1),f2(a1)),x69532))+~P1(f319(f319(f225(a1),f2(a1)),x69531))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f74(a1),x69531),x69532)))
% 22.40/22.30 [6954]~P1(f319(f319(f225(a1),f2(a1)),x69542))+~P1(f319(f319(f225(a1),f2(a1)),x69541))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f75(a1),x69541),x69542)))
% 22.40/22.30 [6955]~P1(f319(f319(f225(a1),f2(a1)),x69552))+~P1(f319(f319(f225(a1),f2(a1)),x69551))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f30(a1),x69551),x69552)))
% 22.40/22.30 [6956]~P1(f319(f319(f225(a1),f2(a1)),x69561))+~P1(f319(f319(f226(a1),f2(a1)),x69562))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f30(a1),x69561),x69562)))
% 22.40/22.30 [6957]~P1(f319(f319(f226(a906),f2(a906)),x69572))+~P1(f319(f319(f226(a906),f2(a906)),x69571))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f75(a906),x69571),x69572)))
% 22.40/22.30 [7021]E(x70211,f2(a1))+E(f39(a1,x70212,x70211),f2(a1))+E(f319(f319(f3(a1),f319(f73(a1),f319(f319(f30(a1),x70212),x70211))),f72(a1)),f319(f319(f30(a1),f319(f73(a1),x70212)),x70211))
% 22.40/22.30 [7079]P1(f319(f319(f226(a906),f2(a906)),x70791))+P1(f319(f319(f226(a906),f2(a906)),x70792))+~P1(f319(f319(f226(a906),f2(a906)),f319(f319(f74(a906),x70792),x70791)))
% 22.40/22.30 [7083]~P83(x70831)+P1(f319(f319(f225(x70831),f2(x70831)),x70832))+~P1(f319(f319(f225(x70831),f2(x70831)),f319(f319(f74(x70831),x70832),x70832)))
% 22.40/22.30 [7084]~P83(x70841)+P1(f319(f319(f226(x70841),f2(x70841)),x70842))+~P1(f319(f319(f226(x70841),f2(x70841)),f319(f319(f74(x70841),x70842),x70842)))
% 22.40/22.30 [7134]~P1(f319(f55(x71341),x71342))+P1(f319(f55(x71341),f234(f913(x71341,a904))))+~P1(f319(f55(x71341),f319(f73(f913(x71341,a904)),x71342)))
% 22.40/22.30 [7197]P1(f319(f319(f225(a1),x71971),f2(a1)))+~P1(f319(f319(f226(a1),x71972),f2(a1)))+~P1(f319(f319(f225(a1),f2(a1)),f319(f319(f30(a1),x71971),x71972)))
% 22.40/22.30 [7203]~P1(f319(f319(f226(a1),f2(a1)),x72031))+P1(f319(f319(f225(a1),x72031),x72032))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x72032),x72031)))
% 22.40/22.30 [7204]~P1(f319(f319(f225(a1),f2(a1)),x72042))+P1(f319(f319(f225(a1),x72041),x72042))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x72042),x72041)))
% 22.40/22.30 [7234]P1(f319(f319(f225(a1),f2(a1)),x72341))+~P1(f319(f319(f226(a1),f2(a1)),x72342))+~P1(f319(f319(f225(a1),f2(a1)),f319(f319(f30(a1),x72341),x72342)))
% 22.40/22.30 [7235]P1(f319(f319(f226(a1),f2(a1)),x72351))+~P1(f319(f319(f225(a1),f2(a1)),x72352))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f30(a1),x72352),x72351)))
% 22.40/22.30 [7666]~P1(f319(f55(x76662),f234(f913(x76662,a904))))+~P1(f319(f55(x76661),f234(f913(x76661,a904))))+P1(f319(f55(f912(x76661,x76662)),f234(f913(f912(x76661,x76662),a904))))
% 22.40/22.30 [7667]~P1(f319(f55(x76672),f234(f913(x76672,a904))))+~P1(f319(f55(x76671),f234(f913(x76671,a904))))+P1(f319(f55(f914(x76671,x76672)),f234(f913(f914(x76671,x76672),a904))))
% 22.40/22.30 [7734]~P1(f319(f319(f226(a906),f319(a104,f2(a906))),x77341))+~P1(f319(f319(f226(a906),f319(a104,f2(a906))),x77342))+P1(f319(f319(f226(a906),x77341),f319(f319(f75(a906),x77342),x77341)))
% 22.40/22.30 [7735]~P1(f319(f319(f226(a906),f319(a104,f2(a906))),x77351))+~P1(f319(f319(f226(a906),f319(a104,f2(a906))),x77352))+P1(f319(f319(f226(a906),x77351),f319(f319(f75(a906),x77351),x77352)))
% 22.40/22.30 [7768]E(f319(f29(x77681),f234(f913(x77681,a904))),f319(a104,f2(a906)))+P1(f319(f55(x77682),f234(f913(x77682,a904))))+~P1(f319(f55(f913(x77682,x77681)),f234(f913(f913(x77682,x77681),a904))))
% 22.40/22.30 [7897]~P1(f319(f319(f225(a906),f319(a104,f2(a906))),x78971))+~P1(f319(f319(f225(a906),f319(a104,f2(a906))),x78972))+P1(f319(f319(f225(a906),f319(a104,f2(a906))),f319(f319(f75(a906),x78971),x78972)))
% 22.40/22.30 [7898]~P1(f319(f319(f226(a906),f319(a104,f2(a906))),x78982))+~P1(f319(f319(f226(a906),f319(a104,f2(a906))),x78981))+P1(f319(f319(f226(a906),f319(a104,f2(a906))),f319(f319(f75(a906),x78981),x78982)))
% 22.40/22.30 [8233]~P111(x82331)+P40(a906,x82331,x82332)+~P1(f319(f319(f225(x82331),f319(x82332,f894(x82332,x82331))),f319(x82332,f319(a104,f894(x82332,x82331)))))
% 22.40/22.30 [8566]E(x85661,f105(x85662))+~P1(f319(f129(x85662),x85661))+E(f169(x85662,f319(f319(f10(a904,a904,x85662),a314),f319(f319(f9(x85662,x85662,a904),a316),f136(x85662,x85661))),x85661),f106(x85662,x85661))
% 22.40/22.30 [8664]~P41(x86642)+~P41(x86641)+E(f319(f302(a906,a1,f92(a1)),f319(f319(f93(f913(a906,a904)),f319(f302(a1,a906,a97),x86641)),f319(f302(a1,a906,a97),x86642))),f319(f319(f93(f913(a1,a904)),x86641),x86642))
% 22.40/22.30 [8665]~P41(x86652)+~P41(x86651)+E(f319(f302(a906,a1,f92(a1)),f319(f319(f94(f913(a906,a904)),f319(f302(a1,a906,a97),x86651)),f319(f302(a1,a906,a97),x86652))),f319(f319(f94(f913(a1,a904)),x86651),x86652))
% 22.40/22.30 [9404]~P98(x94041)+~E(f319(f96(x94041),x94042),f72(x94041))+P28(x94041,f319(f96(x94041),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),f319(f73(a1),x94042))))
% 22.40/22.30 [9629]~P98(x96291)+E(f319(f96(x96291),x96292),f72(x96291))+~P28(x96291,f319(f96(x96291),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),f319(f73(a1),x96292))))
% 22.40/22.30 [10383]E(x103831,f2(a1))+E(x103832,f2(a1))+E(f319(f250(a1,a1,a1,a1,f25(a1),f319(f75(a1),f76(a1,x103832))),f319(f319(f319(f86(f912(a1,a1)),f319(f319(a316,f76(a1,x103831)),f76(a1,x103832))),f47(x103831,x103832)),f319(f319(f249(a1,a1,f912(a1,a1)),f319(f319(f20(a1,f913(a1,f912(a1,a1)),f913(a1,f912(a1,a1))),f319(f319(f10(f913(a1,f913(f912(a1,a1),f912(a1,a1))),f913(f913(a1,f912(a1,a1)),f913(a1,f912(a1,a1))),a1),f20(a1,f912(a1,a1),f912(a1,a1))),f319(f319(f10(f912(a1,a1),f913(a1,f913(f912(a1,a1),f912(a1,a1))),a1),f319(f9(a1,f912(a1,a1),f913(f912(a1,a1),f912(a1,a1))),f319(f319(f10(a904,f913(f912(a1,a1),f913(f912(a1,a1),f912(a1,a1))),a1),f86(f912(a1,a1))),f319(f319(f9(a1,a1,a904),a316),f2(a1))))),f319(f319(f9(a1,a1,f912(a1,a1)),f319(f319(f10(a1,f913(a1,f912(a1,a1)),a1),f244(a1,a1)),f73(a1))),f2(a1))))),f319(f319(f9(a1,f913(a1,a1),f913(a1,f912(a1,a1))),f319(f319(f10(f913(a1,f912(a1,a1)),f913(f913(a1,a1),f913(a1,f912(a1,a1))),a1),f10(a1,f912(a1,a1),a1)),f319(f319(f10(a1,f913(a1,f912(a1,a1)),a1),f244(a1,a1)),f319(f319(f9(a1,a1,a1),f319(f319(f10(a1,f913(a1,a1),a1),f3(a1)),f73(a1))),f72(a1))))),f319(f3(a1),f319(f69(a1),x103832))))),f47(x103831,x103832)))),f40(x103831,x103832))
% 22.40/22.30 [10384]E(x103841,f2(a1))+E(x103842,f2(a1))+E(f319(f250(a1,a1,a1,a1,f25(a1),f319(f75(a1),f76(a1,x103842))),f319(f319(f319(f86(f912(a1,a1)),f319(f319(a318,f319(f319(a317,f319(f319(f226(a1),f2(a1)),x103842)),f319(f319(f225(a1),f2(a1)),x103841))),f319(f319(a317,f319(f319(f226(a1),x103842),f2(a1))),f319(f319(f226(a1),x103841),f2(a1))))),f47(x103841,x103842)),f319(f319(f249(a1,a1,f912(a1,a1)),f319(f319(f20(a1,f913(a1,f912(a1,a1)),f913(a1,f912(a1,a1))),f319(f319(f10(f913(a1,f913(f912(a1,a1),f912(a1,a1))),f913(f913(a1,f912(a1,a1)),f913(a1,f912(a1,a1))),a1),f20(a1,f912(a1,a1),f912(a1,a1))),f319(f319(f10(f912(a1,a1),f913(a1,f913(f912(a1,a1),f912(a1,a1))),a1),f319(f9(a1,f912(a1,a1),f913(f912(a1,a1),f912(a1,a1))),f319(f319(f10(a904,f913(f912(a1,a1),f913(f912(a1,a1),f912(a1,a1))),a1),f86(f912(a1,a1))),f319(f319(f9(a1,a1,a904),a316),f2(a1))))),f319(f319(f9(a1,a1,f912(a1,a1)),f319(f319(f10(a1,f913(a1,f912(a1,a1)),a1),f244(a1,a1)),f73(a1))),f2(a1))))),f319(f319(f9(a1,f913(a1,a1),f913(a1,f912(a1,a1))),f319(f319(f10(f913(a1,f912(a1,a1)),f913(f913(a1,a1),f913(a1,f912(a1,a1))),a1),f10(a1,f912(a1,a1),a1)),f319(f319(f10(a1,f913(a1,f912(a1,a1)),a1),f244(a1,a1)),f319(f319(f9(a1,a1,a1),f319(f319(f10(a1,f913(a1,a1),a1),f3(a1)),f73(a1))),f72(a1))))),f319(f3(a1),f319(f69(a1),x103842))))),f47(x103841,x103842)))),f40(x103841,x103842))
% 22.40/22.30 [5818]~P113(x58181)+~P98(x58181)+E(f319(f69(x58181),f319(f319(f236(x58181),f319(f96(x58181),a89)),x58182)),f72(x58181))
% 22.40/22.30 [6316]~P141(x63161)+~P1(f319(f319(f226(a1),x63162),f2(a1)))+E(f319(f73(x63161),f319(f92(x63161),f319(a97,f319(f73(a1),x63162)))),f319(f95(x63161),x63162))
% 22.40/22.30 [6521]P1(f319(f319(f225(a91),x65211),f72(a91)))+E(f319(f319(f74(a91),f72(a91)),f264(x65211,f319(f319(f30(a91),x65212),x65211))),f264(x65211,x65212))+P1(f319(f319(f226(a91),x65212),x65211))
% 22.40/22.30 [7124]~P97(x71241)+~P1(f319(f319(f321(x71241),x71242),f102(x71241)))+~E(f319(f319(f74(x71241),f319(f319(f74(x71241),f72(x71241)),x71242)),x71242),f2(x71241))
% 22.40/22.30 [7236]~P1(f319(f319(f225(a1),x72362),f2(a1)))+~P1(f319(f319(f226(a1),x72361),f2(a1)))+E(f319(f243(a1,a1),f319(a45,f41(f319(f73(a1),x72361),f319(f73(a1),x72362)))),f319(f319(f30(a1),x72361),x72362))
% 22.40/22.30 [7253]~P1(f319(f319(f225(a1),x72532),f2(a1)))+~P1(f319(f319(f226(a1),x72531),f2(a1)))+E(f319(f248(a1,a1),f319(a45,f41(f319(f73(a1),x72531),f319(f73(a1),x72532)))),f39(a1,x72531,x72532))
% 22.40/22.30 [7259]~P1(f319(f319(f226(a1),x72592),f2(a1)))+E(f319(f243(a1,a1),f319(a45,f44(f319(f73(a1),x72591),f319(f73(a1),x72592)))),f319(f319(f30(a1),x72591),x72592))+~P1(f319(f319(f226(a1),f2(a1)),x72591))
% 22.40/22.30 [7277]~P1(f319(f319(f226(a1),x72772),f2(a1)))+E(f319(f248(a1,a1),f319(a45,f44(f319(f73(a1),x72771),f319(f73(a1),x72772)))),f39(a1,x72771,x72772))+~P1(f319(f319(f226(a1),f2(a1)),x72771))
% 22.40/22.30 [7329]E(f319(f319(f30(a1),f319(f319(f236(a1),x73291),x73292)),x73291),f319(f319(f236(a1),x73291),f319(f319(f3(a906),x73292),f319(a104,f2(a906)))))+~P1(f319(f319(f226(a906),f2(a906)),x73292))+~P1(f319(f319(f226(a1),f2(a1)),x73291))
% 22.40/22.30 [7429]~P1(f319(f319(f226(a906),f2(a906)),x74291))+~P1(f319(f319(f226(a906),f2(a906)),x74292))+P1(f319(f319(f226(a906),f319(f319(f3(a906),x74291),x74292)),x74291))
% 22.40/22.30 [7430]~P1(f319(f319(f226(a906),f2(a906)),x74301))+~P1(f319(f319(f226(a906),f72(a906)),x74302))+P1(f319(f319(f226(a906),f319(f319(f30(a906),x74301),x74302)),x74301))
% 22.40/22.30 [7431]~P1(f319(f319(f226(a1),f2(a1)),x74311))+~P1(f319(f319(f226(a1),f72(a1)),x74312))+P1(f319(f319(f226(a1),f319(f319(f30(a1),x74311),x74312)),x74311))
% 22.40/22.30 [7562]E(x75621,f2(a906))+~E(x75622,f2(a1))+~P1(f319(f319(f226(a1),f2(a1)),f319(f319(f236(a1),f319(f69(a1),x75622)),x75621)))
% 22.40/22.30 [7926]~P1(f319(x79261,x79262))+P1(f319(x79261,f2(a906)))+E(f319(a104,f229(a906,f319(f319(f10(a906,a904,a906),x79261),a104))),f229(a906,x79261))
% 22.40/22.30 [7977]~E(x79772,f105(f907(x79771)))+E(f319(f182(f907(f907(x79771))),f171(x79771,x79772)),f2(a906))+~P13(a906,f319(f160(a906),f319(f319(f146(f907(x79771),a906),f182(f907(x79771))),x79772)))
% 22.40/22.30 [8219]P1(f319(x82191,x82192))+~P1(f319(x82191,f319(a99,f528(x82191,x82192))))+~P1(f319(f319(f321(f913(f912(a906,a906),a904)),x82192),a90))
% 22.40/22.30 [8237]E(x82371,f105(f907(x82372)))+E(f319(f182(f907(x82372)),f319(f319(f156(f907(x82372)),x82371),f2(a906))),f319(f182(f907(f907(x82372))),f171(x82372,x82371)))+~P13(a906,f319(f160(a906),f319(f319(f146(f907(x82372),a906),f182(f907(x82372))),x82371)))
% 22.40/22.30 [8375]~P38(x83751,x83752)+~P39(x83751,x83752)+P38(x83751,f319(f319(f3(f913(f912(x83751,x83751),a904)),x83752),f299(x83751,f181(f913(f912(x83751,x83751),a904)))))
% 22.40/22.30 [8944]~P1(f319(f55(x89441),f319(f254(x89441),x89442)))+~P1(f319(f55(x89441),f234(f913(x89441,a904))))+P1(f319(f55(x89441),f319(f254(x89441),f319(f319(f10(a904,a904,x89441),a314),x89442))))
% 22.40/22.30 [9013]E(f319(f319(f244(a906,a906),f319(a104,f319(f319(f30(a906),f319(f319(f3(a906),x90131),x90132)),x90132))),f39(a906,f319(f319(f3(a906),x90131),x90132),x90132)),f79(f912(a906,a906),f42(x90131,x90132)))+~P1(f319(f319(f226(a906),f2(a906)),x90132))+~P1(f319(f319(f225(a906),x90132),x90131))
% 22.40/22.30 [9296]~P1(f319(f55(x92961),f319(f254(x92961),x92962)))+P1(f319(f55(x92961),f234(f913(x92961,a904))))+~P1(f319(f55(x92961),f319(f254(x92961),f319(f319(f10(a904,a904,x92961),a314),x92962))))
% 22.40/22.30 [10044]P27(x100441,x100442)+~P37(x100441,f319(f243(f913(f912(x100441,x100441),a904),f913(f912(x100441,x100441),a904)),x100442))+~P1(f319(f319(f225(f913(f912(x100441,x100441),a904)),f319(f319(f281(x100441,x100441,x100441),f319(f243(f913(f912(x100441,x100441),a904),f913(f912(x100441,x100441),a904)),x100442)),f319(f248(f913(f912(x100441,x100441),a904),f913(f912(x100441,x100441),a904)),x100442))),f319(f243(f913(f912(x100441,x100441),a904),f913(f912(x100441,x100441),a904)),x100442)))
% 22.40/22.30 [7359]~P1(f319(f319(f226(a906),f2(a906)),x73592))+P1(f319(f319(f226(a906),x73591),x73592))+E(f319(a104,f319(f319(f30(a906),f319(f319(f3(a906),x73591),x73592)),x73592)),f319(f319(f30(a906),x73591),x73592))
% 22.40/22.30 [7489]~P1(f319(f319(f226(a906),f2(a906)),x74892))+~P1(f319(f319(f225(a906),x74892),x74891))+E(f319(a104,f319(f319(f30(a906),f319(f319(f3(a906),x74891),x74892)),x74892)),f319(f319(f30(a906),x74891),x74892))
% 22.40/22.30 [8541]~P98(x85411)+~P97(x85411)+~P28(x85411,f319(f96(x85411),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x85412)),x85412)))
% 22.40/22.30 [9193]E(x91931,f2(a906))+E(f319(f319(f249(a906,a906,f912(a906,a906)),f319(f319(f10(a906,f913(a906,f912(a906,a906)),a906),f244(a906,a906)),a104)),f79(f912(a906,a906),f42(f319(f319(f3(a906),x91932),x91931),x91931))),f79(f912(a906,a906),f42(x91932,x91931)))+P1(f319(f319(f226(a906),x91932),x91931))
% 22.40/22.30 [9383]~P38(x93831,x93832)+~P53(x93831,x93832)+P1(f319(f319(f225(f913(f912(x93831,x93831),a904)),f319(f319(f281(x93831,x93831,x93831),f319(f278(x93831,x93831),x93832)),x93832)),x93832))
% 22.40/22.30 [9649]P1(f319(x96492,f633(x96492,x96491)))+P1(f319(x96491,f633(x96492,x96491)))+E(f319(f254(a1),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),x96491)),f319(f254(a1),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),x96492)))
% 22.40/22.30 [9653]~P1(f319(x96532,f633(x96532,x96531)))+~P1(f319(x96531,f633(x96532,x96531)))+E(f319(f254(a1),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),x96531)),f319(f254(a1),f319(f319(f20(a1,a904,a904),f319(f319(f10(a904,f913(a904,a904),a1),a317),f319(f225(a1),f2(a1)))),x96532)))
% 22.40/22.30 [10188]~P1(f319(f319(f279(a906),x101882),x101881))+P1(f319(f319(f279(a906),x101881),x101882))+P1(f319(f319(f321(a906),x101881),f286(a906,f319(f319(f20(a906,f913(a906,a904),f913(a906,a904)),f319(f319(f10(f913(a906,f913(a904,a904)),f913(f913(a906,a904),f913(a906,a904)),a906),f20(a906,a904,a904)),f319(f319(f10(f913(a906,a904),f913(a906,f913(a904,a904)),a906),f319(f10(a904,f913(a904,a904),a906),a317)),f279(a906)))),f319(f319(f10(f913(a906,a904),f913(a906,a904),a906),f319(f10(a904,a904,a906),a314)),f319(f9(a906,a906,a904),f279(a906)))),x101882)))
% 22.40/22.30 [10189]~P1(f319(f319(f279(a906),x101892),x101891))+P1(f319(f319(f279(a906),x101891),x101892))+P1(f319(f319(f321(a906),x101892),f290(a906,f319(f319(f20(a906,f913(a906,a904),f913(a906,a904)),f319(f319(f10(f913(a906,f913(a904,a904)),f913(f913(a906,a904),f913(a906,a904)),a906),f20(a906,a904,a904)),f319(f319(f10(f913(a906,a904),f913(a906,f913(a904,a904)),a906),f319(f10(a904,f913(a904,a904),a906),a317)),f279(a906)))),f319(f319(f10(f913(a906,a904),f913(a906,a904),a906),f319(f10(a904,a904,a906),a314)),f319(f9(a906,a906,a904),f279(a906)))),x101891)))
% 22.40/22.30 [7934]~P73(x79341)+~P98(x79341)+E(f319(f319(f282(x79341),x79342),f319(f96(x79341),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),x79342)
% 22.40/22.30 [9403]~P98(x94031)+~E(f319(f96(x94031),x94032),f72(x94031))+P28(x94031,f319(f96(x94031),f319(f319(f74(a1),x94032),f319(f73(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))))
% 22.40/22.30 [9630]~P98(x96301)+E(f319(f96(x96301),x96302),f72(x96301))+~P28(x96301,f319(f96(x96301),f319(f319(f74(a1),x96302),f319(f73(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))))
% 22.40/22.30 [10067]~P140(x100671)+~E(x100672,f72(x100671))+E(f319(f319(f236(x100671),x100672),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f72(x100671))
% 22.40/22.30 [10068]~P140(x100681)+~E(x100682,f2(x100681))+E(f319(f319(f236(x100681),x100682),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f2(x100681))
% 22.40/22.30 [10071]~P140(x100711)+~E(x100712,f319(f73(x100711),f72(x100711)))+E(f319(f319(f236(x100711),x100712),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f72(x100711))
% 22.40/22.30 [10209]~P113(x102092)+E(x102091,f2(x102092))+P1(f319(f319(f226(x102092),f2(x102092)),f319(f319(f236(x102092),x102091),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.30 [10259]~P113(x102592)+~E(x102591,f2(x102592))+~P1(f319(f319(f226(x102592),f2(x102592)),f319(f319(f236(x102592),x102591),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.30 [10279]P1(f319(f319(f225(a1),x102791),f2(a1)))+P1(f319(f319(f226(a1),x102792),x102791))+E(f319(f37(x102791),f41(x102792,f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102791))),f41(x102792,x102791))
% 22.40/22.30 [10280]~P1(f319(f319(f226(a1),f2(a1)),x102801))+P1(f319(f319(f226(a1),x102802),x102801))+E(f319(f37(x102801),f41(x102802,f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102801))),f41(x102802,x102801))
% 22.40/22.30 [10281]P1(f319(f319(f225(a1),x102811),f2(a1)))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f74(a1),x102812),x102811)))+E(f319(f37(x102811),f44(x102812,f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102811))),f44(x102812,x102811))
% 22.40/22.30 [10282]~P1(f319(f319(f226(a1),f2(a1)),x102821))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f74(a1),x102822),x102821)))+E(f319(f37(x102821),f44(x102822,f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102821))),f44(x102822,x102821))
% 22.40/22.30 [10283]~P146(x102831)+~P1(f319(f319(f225(a1),f2(a1)),x102832))+E(f319(f92(x102831),f319(a97,f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x102832))),f319(f319(f74(x102831),f319(f92(x102831),f319(a97,x102832))),f319(f92(x102831),f319(a97,x102832))))
% 22.40/22.30 [5148]~P147(x51481,x51483,x51482)+~E(x51483,f2(a1))+P1(f319(x51481,x51482))
% 22.40/22.30 [5277]~P4(x52771)+~P13(x52771,x52773)+P13(x52771,f162(x52771,x52772,x52773))
% 22.40/22.30 [5278]~P4(x52781)+~P13(x52781,x52783)+P13(x52781,f169(x52781,x52782,x52783))
% 22.40/22.30 [4842]~P66(x48422)+~E(x48423,f319(f73(x48422),x48421))+E(x48421,f319(f73(x48422),x48423))
% 22.40/22.30 [4844]~P66(x48441)+~E(f319(f73(x48441),x48443),x48442)+E(f319(f73(x48441),x48442),x48443)
% 22.40/22.30 [4923]~P4(x49233)+E(x49231,x49232)+~E(f319(f296(x49233),x49231),f319(f296(x49233),x49232))
% 22.40/22.30 [4924]~P4(x49243)+E(x49241,x49242)+~E(f319(f274(x49243),x49241),f319(f274(x49243),x49242))
% 22.40/22.30 [4925]~P4(x49253)+E(x49251,x49252)+~E(f319(f275(x49253),x49251),f319(f275(x49253),x49252))
% 22.40/22.30 [4926]~P4(x49263)+E(x49261,x49262)+~E(f319(f293(x49263),x49261),f319(f293(x49263),x49262))
% 22.40/22.30 [4927]~P63(x49273)+E(x49271,x49272)+~E(f319(f73(x49273),x49271),f319(f73(x49273),x49272))
% 22.40/22.30 [4928]~P66(x49283)+E(x49281,x49282)+~E(f319(f73(x49283),x49281),f319(f73(x49283),x49282))
% 22.40/22.30 [4929]~P108(x49293)+E(x49291,x49292)+~E(f319(f92(x49293),x49291),f319(f92(x49293),x49292))
% 22.40/22.30 [4930]~P97(x49303)+E(x49301,x49302)+~E(f319(f95(x49303),x49301),f319(f95(x49303),x49302))
% 22.40/22.30 [5030]~P71(x50301)+~P1(f319(x50302,x50303))+P1(f319(f50(x50301),x50302))
% 22.40/22.30 [5067]~P71(x50673)+P1(f319(x50671,x50672))+~P1(f319(f51(x50673),x50671))
% 22.40/22.30 [5168]~P148(x51681,x51682,x51683)+~E(x51682,f2(a1))+P1(f319(x51681,f2(a1)))
% 22.40/22.30 [5204]~P117(x52042)+~P1(f319(x52041,x52043))+P1(f319(x52041,f229(x52042,x52041)))
% 22.40/22.30 [5211]~E(x52111,f2(a906))+E(f327(x52111,x52112,x52113),f181(f913(x52113,a904)))+~E(f319(f29(x52113),x52112),f319(a104,x52111))
% 22.40/22.30 [5361]~E(x53612,f2(a906))+E(f319(f243(a906,a906),x53611),f2(a906))+~P1(f319(f42(x53613,x53612),x53611))
% 22.40/22.30 [5399]P1(f319(x53991,x53992))+~E(x53993,f319(f92(a1),x53992))+~P1(f319(x53991,f319(a97,x53993)))
% 22.40/22.30 [5882]~E(x58823,f2(a906))+~P1(f319(x58821,x58822))+P1(f319(x58821,f39(a906,x58822,x58823)))
% 22.40/22.30 [5943]~P117(x59431)+~P1(f319(x59432,x59433))+~P1(f319(f319(f226(x59431),x59433),f229(x59431,x59432)))
% 22.40/22.30 [6117]~P109(x61172)+~P109(x61171)+E(f123(x61171,x61172,f124(x61171,x61173),f124(x61172,x61173)),f124(f912(x61171,x61172),x61173))
% 22.40/22.30 [6296]~E(x62963,f2(a906))+P1(f319(x62961,x62962))+~P1(f319(x62961,f39(a906,x62962,x62963)))
% 22.40/22.30 [6309]~P5(x63091)+~P1(f319(f319(f225(x63091),x63092),f319(x63093,x63092)))+P1(f319(f319(f225(x63091),x63092),f88(x63091,x63093)))
% 22.40/22.30 [6791]E(x67911,f181(f913(x67912,a904)))+~P1(f319(f55(x67912),x67911))+P1(f319(f56(x67912,x67913,x67911),f845(x67913,x67911,x67912)))
% 22.40/22.30 [6978]E(x69781,f2(a906))+~P1(f319(x69782,f445(x69781,x69783,x69782)))+P1(f319(x69782,f39(a906,x69783,x69781)))
% 22.40/22.30 [7089]~P5(x70891)+~P1(f319(f319(f225(x70891),x70892),f860(x70893,x70892,x70891)))+P1(f319(f319(f225(x70891),x70892),f32(x70891,x70893)))
% 22.40/22.30 [7091]~P1(f319(x70911,x70912))+~P1(f319(x70911,f445(x70913,x70912,x70911)))+P1(f319(x70911,f39(a906,x70912,x70913)))
% 22.40/22.30 [7192]E(x71921,f105(x71922))+E(f319(f319(f143(x71922),f682(x71923,x71921,x71922)),f684(x71923,x71921,x71922)),x71921)+~P1(f319(f319(f321(f907(x71922)),x71921),f153(x71922,x71923)))
% 22.40/22.30 [7223]~P141(x72231)+~P1(f319(f319(f321(x72231),x72232),f102(x72231)))+P1(f319(f319(f321(x72231),f319(f319(f236(x72231),x72232),x72233)),f102(x72231)))
% 22.40/22.30 [7534]P37(x75341,x75342)+~P1(f319(f319(f321(x75341),x75343),f593(x75342,x75341)))+P1(f319(f319(f321(x75341),f604(x75342,x75341,x75343)),f593(x75342,x75341)))
% 22.40/22.30 [7796]E(x77961,f105(x77962))+~P1(f319(f319(f321(f907(x77962)),x77961),f153(x77962,x77963)))+P1(f319(f319(f321(f907(x77962)),f684(x77963,x77961,x77962)),f153(x77962,x77963)))
% 22.40/22.30 [7847]E(x78471,f2(a906))+E(f319(f319(f74(a906),f319(f319(f75(a906),x78471),f446(x78471,x78472,x78473))),f445(x78471,x78472,x78473)),x78472)+P1(f319(x78473,f39(a906,x78472,x78471)))
% 22.40/22.30 [7892]~P1(f319(x78923,x78922))+E(f319(f319(f74(a906),f319(f319(f75(a906),x78921),f446(x78921,x78922,x78923))),f445(x78921,x78922,x78923)),x78922)+P1(f319(x78923,f39(a906,x78922,x78921)))
% 22.40/22.30 [8029]P1(f319(f319(f226(a1),x80291),f439(x80292,x80293,x80291)))+P1(f319(f319(x80293,f319(f319(f30(a1),x80292),x80291)),f39(a1,x80292,x80291)))+~P1(f319(f319(f226(a1),x80291),f2(a1)))
% 22.40/22.30 [8292]P1(f319(f319(x82922,f319(f319(f30(a1),x82921),x82923)),f39(a1,x82921,x82923)))+~P1(f319(f319(f226(a1),x82923),f2(a1)))+P1(f319(f319(f225(a1),f439(x82921,x82922,x82923)),f2(a1)))
% 22.40/22.30 [8471]E(f319(f319(f74(a1),f319(f319(f75(a1),x84711),f442(x84712,x84713,x84711))),f439(x84712,x84713,x84711)),x84712)+P1(f319(f319(x84713,f319(f319(f30(a1),x84712),x84711)),f39(a1,x84712,x84711)))+~P1(f319(f319(f226(a1),x84711),f2(a1)))
% 22.40/22.30 [8710]~P1(f319(f319(x87101,f442(x87102,x87101,x87103)),f439(x87102,x87101,x87103)))+P1(f319(f319(x87101,f319(f319(f30(a1),x87102),x87103)),f39(a1,x87102,x87103)))+~P1(f319(f319(f226(a1),x87103),f2(a1)))
% 22.40/22.30 [8958]~P4(x89581)+~P13(x89581,x89583)+P13(x89581,f141(x89581,x89581,f7(x89581),x89582,x89583))
% 22.40/22.30 [9464]~P127(x94642)+E(x94641,f2(x94642))+~P1(f319(f319(f225(x94642),f319(f319(f74(x94642),f319(f319(f75(x94642),x94643),x94643)),f319(f319(f75(x94642),x94641),x94641))),f2(x94642)))
% 22.40/22.30 [9465]~P127(x94652)+E(x94651,f2(x94652))+~P1(f319(f319(f225(x94652),f319(f319(f74(x94652),f319(f319(f75(x94652),x94651),x94651)),f319(f319(f75(x94652),x94653),x94653))),f2(x94652)))
% 22.40/22.30 [10372]~P113(x103721)+~P1(f319(f319(f226(x103721),x103722),f2(x103721)))+P1(f319(f319(f226(x103721),f319(f319(f236(x103721),x103722),f319(a104,f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103723)))),f2(x103721)))
% 22.40/22.30 [10378]~P113(x103782)+E(x103781,f2(x103782))+~P1(f319(f319(f225(x103782),f319(f319(f74(x103782),f319(f319(f236(x103782),x103783),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103782),x103781),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))),f2(x103782)))
% 22.40/22.30 [10379]~P113(x103792)+E(x103791,f2(x103792))+~P1(f319(f319(f225(x103792),f319(f319(f74(x103792),f319(f319(f236(x103792),x103791),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103792),x103793),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))),f2(x103792)))
% 22.40/22.30 [4878]~E(x48782,x48783)+~P66(x48781)+E(f319(f319(f3(x48781),x48782),x48783),f2(x48781))
% 22.40/22.30 [4879]~E(x48792,x48793)+~P67(x48791)+E(f319(f319(f3(x48791),x48792),x48793),f2(x48791))
% 22.40/22.30 [4892]~P143(x48921)+~E(x48923,f2(x48921))+E(f319(f319(f74(x48921),x48922),x48923),x48922)
% 22.40/22.30 [4910]~P142(x49101)+~E(x49103,f2(x49101))+E(f319(f319(f75(x49101),x49102),x49103),f2(x49101))
% 22.40/22.30 [4911]~P142(x49111)+~E(x49112,f2(x49111))+E(f319(f319(f75(x49111),x49112),x49113),f2(x49111))
% 22.40/22.30 [4932]~E(x49323,f105(x49321))+~E(x49322,f105(x49321))+E(f319(f319(f126(x49321),x49322),x49323),f105(x49321))
% 22.40/22.30 [5020]~P143(x50202)+E(x50201,f2(x50202))+~E(f319(f319(f74(x50202),x50203),x50201),x50203)
% 22.40/22.30 [5021]~P66(x50211)+~E(x50212,f319(f73(x50211),x50213))+E(f319(f319(f74(x50211),x50212),x50213),f2(x50211))
% 22.40/22.30 [5028]E(x50281,f105(x50282))+E(x50283,f2(a906))+~E(f319(f319(f167(x50282),x50283),x50281),f105(x50282))
% 22.40/22.30 [5034]~P66(x50343)+E(x50341,x50342)+~E(f319(f319(f3(x50343),x50341),x50342),f2(x50343))
% 22.40/22.30 [5035]~P67(x50353)+E(x50351,x50352)+~E(f319(f319(f3(x50353),x50351),x50352),f2(x50353))
% 22.40/22.30 [5049]~P140(x50492)+E(x50491,f2(x50492))+~E(f319(f319(f236(x50492),x50491),x50493),f2(x50492))
% 22.40/22.30 [5050]~P105(x50502)+E(x50501,f234(x50502))+~E(f319(f319(f94(x50502),x50503),x50501),f234(x50502))
% 22.40/22.30 [5051]~P105(x50512)+E(x50511,f234(x50512))+~E(f319(f319(f94(x50512),x50511),x50513),f234(x50512))
% 22.40/22.30 [5052]~P103(x50522)+E(x50521,f181(x50522))+~E(f319(f319(f93(x50522),x50523),x50521),f181(x50522))
% 22.40/22.30 [5053]~P103(x50532)+E(x50531,f181(x50532))+~E(f319(f319(f93(x50532),x50531),x50533),f181(x50532))
% 22.40/22.30 [5122]~P66(x51222)+E(x51221,f319(f73(x51222),x51223))+~E(f319(f319(f74(x51222),x51221),x51223),f2(x51222))
% 22.40/22.30 [5123]~P66(x51231)+E(f319(f73(x51231),x51232),x51233)+~E(f319(f319(f74(x51231),x51232),x51233),f2(x51231))
% 22.40/22.30 [5125]~E(x51252,x51253)+~P2(x51251)+P1(f319(f319(f225(x51251),x51252),x51253))
% 22.40/22.30 [5127]~E(x51272,x51273)+~P111(x51271)+P1(f319(f319(f225(x51271),x51272),x51273))
% 22.40/22.30 [5228]~P118(x52281)+~E(x52282,f319(f73(x52281),x52283))+E(f319(f319(f75(x52281),x52282),x52282),f319(f319(f75(x52281),x52283),x52283))
% 22.40/22.30 [5236]~P4(x52361)+~P13(x52361,x52363)+P13(x52361,f319(f319(f167(x52361),x52362),x52363))
% 22.40/22.30 [5237]~P4(x52371)+~P13(x52371,x52373)+P13(x52371,f319(f319(f130(x52371),x52372),x52373))
% 22.40/22.30 [5275]E(x52751,x52752)+E(x52753,f2(a906))+~E(f319(f319(f75(a906),x52753),x52751),f319(f319(f75(a906),x52753),x52752))
% 22.40/22.30 [5276]E(x52761,x52762)+E(x52763,f2(a906))+~E(f319(f319(f75(a906),x52761),x52763),f319(f319(f75(a906),x52762),x52763))
% 22.40/22.30 [5354]~E(x53542,x53543)+~P111(x53541)+E(f295(x53541,x53542,x53543),f319(f319(f301(x53541),x53542),f181(f913(x53541,a904))))
% 22.40/22.30 [5396]~E(x53961,x53962)+~P4(x53963)+~P1(f319(f319(f226(x53963),x53961),x53962))
% 22.40/22.30 [5397]~E(x53971,x53972)+~P111(x53973)+~P1(f319(f319(f226(x53973),x53971),x53972))
% 22.40/22.30 [5410]~P111(x54101)+E(f319(f294(x54101,x54102),x54103),f181(f913(x54101,a904)))+P1(f319(f319(f226(x54101),x54102),x54103))
% 22.40/22.30 [5458]~P111(x54581)+E(f297(x54581,x54582,x54583),f181(f913(x54581,a904)))+P1(f319(f319(f226(x54581),x54582),x54583))
% 22.40/22.30 [5459]~P111(x54591)+E(f295(x54591,x54592,x54593),f181(f913(x54591,a904)))+P1(f319(f319(f225(x54591),x54592),x54593))
% 22.40/22.30 [5460]~P111(x54601)+E(f181(f913(x54601,a904)),f297(x54601,x54602,x54603))+P1(f319(f319(f226(x54601),x54602),x54603))
% 22.40/22.30 [5461]~P111(x54611)+E(f181(f913(x54611,a904)),f295(x54611,x54612,x54613))+P1(f319(f319(f225(x54611),x54612),x54613))
% 22.40/22.30 [5468]~P106(x54681)+~E(f319(f319(f93(x54681),x54682),x54683),x54683)+P1(f319(f319(f225(x54681),x54682),x54683))
% 22.40/22.30 [5469]~P107(x54691)+~E(f319(f319(f94(x54691),x54692),x54693),x54692)+P1(f319(f319(f225(x54691),x54692),x54693))
% 22.40/22.30 [5470]~P4(x54701)+~E(f319(f319(f180(x54701),x54702),x54703),x54703)+P1(f319(f319(f225(x54701),x54702),x54703))
% 22.40/22.30 [5471]~P4(x54711)+~E(f319(f319(f230(x54711),x54712),x54713),x54712)+P1(f319(f319(f225(x54711),x54712),x54713))
% 22.40/22.30 [5490]~P4(x54901)+P13(x54901,x54902)+~P13(x54901,f319(f319(f143(x54901),x54903),x54902))
% 22.40/22.30 [5491]~P4(x54911)+P13(x54911,x54912)+~P13(x54911,f319(f319(f126(x54911),x54913),x54912))
% 22.40/22.30 [5492]~P4(x54921)+P13(x54921,x54922)+~P13(x54921,f319(f319(f126(x54921),x54922),x54923))
% 22.40/22.30 [5497]~P69(x54971)+~E(f39(x54971,x54973,x54972),f2(x54971))+P1(f319(f319(f279(x54971),x54972),x54973))
% 22.40/22.30 [5559]~P4(x55591)+P1(f319(f319(f225(x55591),x55593),x55592))+P1(f319(f319(f225(x55591),x55592),x55593))
% 22.40/22.30 [5564]~P4(x55641)+P1(f319(f319(f226(x55641),x55643),x55642))+P1(f319(f319(f225(x55641),x55642),x55643))
% 22.40/22.30 [5600]~P106(x56001)+E(f319(f319(f93(x56001),x56002),x56003),x56002)+~P1(f319(f319(f225(x56001),x56003),x56002))
% 22.40/22.30 [5602]~P106(x56021)+E(f319(f319(f93(x56021),x56022),x56023),x56023)+~P1(f319(f319(f225(x56021),x56022),x56023))
% 22.40/22.30 [5603]~P107(x56031)+E(f319(f319(f94(x56031),x56032),x56033),x56033)+~P1(f319(f319(f225(x56031),x56033),x56032))
% 22.40/22.30 [5605]~P107(x56051)+E(f319(f319(f94(x56051),x56052),x56053),x56052)+~P1(f319(f319(f225(x56051),x56052),x56053))
% 22.40/22.30 [5606]~P4(x56061)+E(f319(f319(f180(x56061),x56062),x56063),x56062)+~P1(f319(f319(f225(x56061),x56063),x56062))
% 22.40/22.30 [5608]~P4(x56081)+E(f319(f319(f180(x56081),x56082),x56083),x56083)+~P1(f319(f319(f225(x56081),x56082),x56083))
% 22.40/22.30 [5609]~P4(x56091)+E(f319(f319(f230(x56091),x56092),x56093),x56093)+~P1(f319(f319(f225(x56091),x56093),x56092))
% 22.40/22.30 [5611]~P4(x56111)+E(f319(f319(f230(x56111),x56112),x56113),x56112)+~P1(f319(f319(f225(x56111),x56112),x56113))
% 22.40/22.30 [5618]~P120(x56182)+E(x56181,f2(x56182))+E(f319(f319(f282(x56182),f319(f73(x56182),x56183)),f319(f73(x56182),x56181)),f319(f319(f282(x56182),x56183),x56181))
% 22.40/22.30 [5625]~P69(x56251)+E(f39(x56251,x56252,x56253),f2(x56251))+~P1(f319(f319(f279(x56251),x56253),x56252))
% 22.40/22.30 [5671]~P111(x56711)+E(f319(f294(x56711,x56712),x56713),f181(f913(x56711,a904)))+~P1(f319(f319(f225(x56711),x56713),x56712))
% 22.40/22.30 [5706]~P111(x57061)+E(f298(x57061,x57062,x57063),f181(f913(x57061,a904)))+~P1(f319(f319(f225(x57061),x57063),x57062))
% 22.40/22.30 [5707]~P111(x57071)+E(f297(x57071,x57072,x57073),f181(f913(x57071,a904)))+~P1(f319(f319(f225(x57071),x57073),x57072))
% 22.40/22.30 [5708]~P111(x57081)+E(f295(x57081,x57082,x57083),f181(f913(x57081,a904)))+~P1(f319(f319(f226(x57081),x57083),x57082))
% 22.40/22.30 [5751]~P117(x57511)+~P1(f319(x57512,x57513))+P1(f319(f319(f225(x57511),f229(x57511,x57512)),x57513))
% 22.40/22.30 [5761]~E(f319(f319(f3(a906),x57611),x57613),x57612)+E(x57611,f319(f319(f74(a906),x57612),x57613))+~P1(f319(f319(f225(a906),x57613),x57611))
% 22.40/22.30 [5762]~E(x57621,f319(f319(f74(a906),x57623),x57622))+E(f319(f319(f3(a906),x57621),x57622),x57623)+~P1(f319(f319(f225(a906),x57622),x57621))
% 22.40/22.30 [5807]~P1(f319(x58071,x58073))+P1(f319(x58071,f330(x58071,x58072)))+~P1(f319(f319(f225(a906),x58073),x58072))
% 22.40/22.30 [5808]~P1(f319(x58081,x58083))+P1(f319(x58081,f338(x58081,x58082)))+~P1(f319(f319(f226(a906),x58083),x58082))
% 22.40/22.30 [5816]~P111(x58161)+~E(f319(f294(x58161,x58162),x58163),f181(f913(x58161,a904)))+~P1(f319(f319(f226(x58161),x58162),x58163))
% 22.40/22.30 [5821]~P2(x58211)+~P1(f319(f319(f226(x58211),x58212),x58213))+P1(f319(f319(f225(x58211),x58212),x58213))
% 22.40/22.30 [5823]~P111(x58231)+~P1(f319(f319(f226(x58231),x58232),x58233))+P1(f319(f319(f225(x58231),x58232),x58233))
% 22.40/22.30 [5936]~P111(x59361)+~E(f297(x59361,x59362,x59363),f181(f913(x59361,a904)))+~P1(f319(f319(f226(x59361),x59362),x59363))
% 22.40/22.30 [5937]~P111(x59371)+~E(f295(x59371,x59372,x59373),f181(f913(x59371,a904)))+~P1(f319(f319(f225(x59371),x59372),x59373))
% 22.40/22.30 [5938]~P111(x59381)+~E(f181(f913(x59381,a904)),f297(x59381,x59382,x59383))+~P1(f319(f319(f226(x59381),x59382),x59383))
% 22.40/22.30 [5939]~P111(x59391)+~E(f181(f913(x59391,a904)),f295(x59391,x59392,x59393))+~P1(f319(f319(f225(x59391),x59392),x59393))
% 22.40/22.30 [5950]P1(f319(x59501,x59502))+~P1(f319(x59501,f339(x59501,x59503)))+~P1(f319(f319(f225(a906),x59502),x59503))
% 22.40/22.30 [5951]P1(f319(x59511,x59512))+~P1(f319(x59511,f343(x59511,x59513)))+~P1(f319(f319(f226(a906),x59512),x59513))
% 22.40/22.30 [5959]~E(x59591,f319(a104,x59593))+P1(f319(f319(f226(a906),x59591),f319(a104,x59592)))+~P1(f319(f319(f226(a906),x59593),x59592))
% 22.40/22.30 [5978]E(x59781,x59782)+~E(f319(f319(f75(a906),x59783),x59781),f319(f319(f75(a906),x59783),x59782))+~P1(f319(f319(f226(a906),f2(a906)),x59783))
% 22.40/22.30 [6034]E(f319(x60341,f331(x60341,x60342,x60343)),f72(a906))+~E(f319(f319(f8(x60343,a906),x60341),x60342),f72(a906))+~P1(f319(f55(x60343),x60342))
% 22.40/22.30 [6049]~P5(x60491)+P1(f319(f319(f225(x60491),x60492),f31(x60491,x60493)))+~P1(f319(f319(f321(x60491),x60492),x60493))
% 22.40/22.30 [6072]~P2(x60721)+~P1(f319(f319(f226(x60721),x60723),x60722))+~P1(f319(f319(f225(x60721),x60722),x60723))
% 22.40/22.30 [6076]~P2(x60761)+~P1(f319(f319(f226(x60761),x60763),x60762))+~P1(f319(f319(f226(x60761),x60762),x60763))
% 22.40/22.30 [6079]~P4(x60791)+~P1(f319(f319(f226(x60791),x60793),x60792))+~P1(f319(f319(f225(x60791),x60792),x60793))
% 22.40/22.30 [6080]~P4(x60801)+~P1(f319(f319(f226(x60801),x60803),x60802))+~P1(f319(f319(f226(x60801),x60802),x60803))
% 22.40/22.30 [6081]~P111(x60811)+~P1(f319(f319(f226(x60811),x60813),x60812))+~P1(f319(f319(f226(x60811),x60812),x60813))
% 22.40/22.30 [6109]~E(f319(x61092,f332(x61092,x61093,x61091)),f2(a906))+E(f319(f319(f8(x61091,a906),x61092),x61093),f2(a906))+~P1(f319(f55(x61091),x61093))
% 22.40/22.30 [6110]~E(f319(x61102,f890(x61102,x61103,x61101)),f72(a906))+E(f319(f319(f11(x61101,a906),x61102),x61103),f72(a906))+~P1(f319(f55(x61101),x61103))
% 22.40/22.30 [6124]~P3(x61241)+~P1(f319(f319(f226(x61241),x61243),x61242))+P1(f319(f319(f321(x61241),x61242),f319(f296(x61241),x61243)))
% 22.40/22.30 [6125]~P3(x61251)+~P1(f319(f319(f225(x61251),x61253),x61252))+P1(f319(f319(f321(x61251),x61252),f319(f275(x61251),x61253)))
% 22.40/22.30 [6126]~P3(x61261)+~P1(f319(f319(f226(x61261),x61262),x61263))+P1(f319(f319(f321(x61261),x61262),f319(f274(x61261),x61263)))
% 22.40/22.30 [6127]~P3(x61271)+~P1(f319(f319(f225(x61271),x61272),x61273))+P1(f319(f319(f321(x61271),x61272),f319(f293(x61271),x61273)))
% 22.40/22.30 [6128]~P115(x61281)+~P1(f319(f319(f279(x61281),x61282),x61283))+P1(f319(f319(f279(x61281),x61282),f319(f73(x61281),x61283)))
% 22.40/22.30 [6140]E(f319(x61401,f333(x61401,x61402,x61403)),f319(a104,f2(a906)))+~E(f319(f319(f8(x61403,a906),x61401),x61402),f319(a104,f2(a906)))+~P1(f319(f55(x61403),x61402))
% 22.40/22.30 [6221]~P5(x62211)+~P1(f319(f319(f321(x62211),x62213),x62212))+P1(f319(f319(f225(x62211),f32(x62211,x62212)),x62213))
% 22.40/22.30 [6242]~P1(f319(f319(f225(a906),x62421),x62423))+P1(f319(f319(f225(a906),x62421),x62422))+~P1(f319(f319(f225(a906),x62423),x62422))
% 22.40/22.30 [6243]~P1(f319(f319(f225(a1),x62431),x62433))+P1(f319(f319(f225(a1),x62431),x62432))+~P1(f319(f319(f225(a1),x62433),x62432))
% 22.40/22.30 [6244]~P1(f319(f319(f279(a906),x62441),x62443))+P1(f319(f319(f279(a906),x62441),x62442))+~P1(f319(f319(f279(a906),x62443),x62442))
% 22.40/22.30 [6266]~P3(x62661)+~P1(f319(f319(f321(x62661),x62663),f319(f275(x62661),x62662)))+P1(f319(f319(f225(x62661),x62662),x62663))
% 22.40/22.30 [6267]~P3(x62671)+~P1(f319(f319(f321(x62671),x62672),f319(f293(x62671),x62673)))+P1(f319(f319(f225(x62671),x62672),x62673))
% 22.40/22.30 [6268]~P3(x62681)+~P1(f319(f319(f321(x62681),x62683),f319(f296(x62681),x62682)))+P1(f319(f319(f226(x62681),x62682),x62683))
% 22.40/22.30 [6269]~P3(x62691)+~P1(f319(f319(f321(x62691),x62692),f319(f274(x62691),x62693)))+P1(f319(f319(f226(x62691),x62692),x62693))
% 22.40/22.30 [6270]~P115(x62701)+~P1(f319(f319(f279(x62701),x62702),f319(f73(x62701),x62703)))+P1(f319(f319(f279(x62701),x62702),x62703))
% 22.40/22.30 [6341]~P1(f319(x63411,x63412))+P1(f319(x63411,f773(x63411)))+~P1(f319(f319(f321(x63413),x63412),f234(f913(x63413,a904))))
% 22.40/22.30 [6447]~P111(x64471)+~P40(a906,x64471,x64472)+P1(f319(f319(f225(x64471),f319(x64472,x64473)),f319(x64472,f319(a104,x64473))))
% 22.40/22.30 [6482]~P74(x64821)+P1(f319(f319(f226(x64821),f2(x64821)),f362(x64823,x64822,x64821)))+P1(f319(f319(f225(x64821),x64822),x64823))
% 22.40/22.30 [6483]~P75(x64831)+P1(f319(f319(f226(x64831),f2(x64831)),f449(x64833,x64832,x64831)))+P1(f319(f319(f225(x64831),x64832),x64833))
% 22.40/22.30 [6554]~P65(x65541)+~P1(f319(f319(f225(x65541),x65543),f319(f73(x65541),x65542)))+P1(f319(f319(f225(x65541),x65542),f319(f73(x65541),x65543)))
% 22.40/22.30 [6556]~P65(x65561)+~P1(f319(f319(f226(x65561),x65563),f319(f73(x65561),x65562)))+P1(f319(f319(f226(x65561),x65562),f319(f73(x65561),x65563)))
% 22.40/22.30 [6568]~P1(f319(f319(f226(a906),x65681),x65683))+~P1(f319(f319(f226(a906),x65683),x65682))+P1(f319(f319(f226(a906),f319(a104,x65681)),x65682))
% 22.40/22.30 [6595]~P126(x65951)+P1(f319(f319(f225(x65951),f319(f92(x65951),x65952)),f319(f92(x65951),x65953)))+~P1(f319(f319(f225(a906),x65952),x65953))
% 22.40/22.30 [6596]~P113(x65961)+P1(f319(f319(f225(x65961),f319(f95(x65961),x65962)),f319(f95(x65961),x65963)))+~P1(f319(f319(f225(a1),x65962),x65963))
% 22.40/22.30 [6598]~P113(x65981)+P1(f319(f319(f226(x65981),f319(f95(x65981),x65982)),f319(f95(x65981),x65983)))+~P1(f319(f319(f226(a1),x65982),x65983))
% 22.40/22.30 [6599]~P126(x65991)+P1(f319(f319(f226(x65991),f319(f92(x65991),x65992)),f319(f92(x65991),x65993)))+~P1(f319(f319(f226(a906),x65992),x65993))
% 22.40/22.30 [6605]~P4(x66051)+E(f319(f319(f93(f913(x66051,a904)),f319(f274(x66051),x66052)),f319(f294(x66051,x66052),x66053)),f319(f274(x66051),x66053))+~P1(f319(f319(f225(x66051),x66052),x66053))
% 22.40/22.30 [6631]~P63(x66311)+~P1(f319(f319(f225(x66311),x66313),x66312))+P1(f319(f319(f225(x66311),f319(f73(x66311),x66312)),f319(f73(x66311),x66313)))
% 22.40/22.30 [6633]~P65(x66331)+~P1(f319(f319(f225(x66331),x66333),x66332))+P1(f319(f319(f225(x66331),f319(f73(x66331),x66332)),f319(f73(x66331),x66333)))
% 22.40/22.30 [6634]~P65(x66341)+~P1(f319(f319(f226(x66341),x66343),x66342))+P1(f319(f319(f226(x66341),f319(f73(x66341),x66342)),f319(f73(x66341),x66343)))
% 22.40/22.30 [6670]~P4(x66701)+E(f319(f319(f93(f913(x66701,a904)),f319(f274(x66701),x66702)),f295(x66701,x66702,x66703)),f319(f293(x66701),x66703))+~P1(f319(f319(f225(x66701),x66702),x66703))
% 22.40/22.30 [6671]~P4(x66711)+E(f319(f319(f93(f913(x66711,a904)),f319(f293(x66711),x66712)),f298(x66711,x66712,x66713)),f319(f274(x66711),x66713))+~P1(f319(f319(f226(x66711),x66712),x66713))
% 22.40/22.30 [6672]~P4(x66721)+E(f319(f319(f93(f913(x66721,a904)),f319(f293(x66721),x66722)),f297(x66721,x66722,x66723)),f319(f293(x66721),x66723))+~P1(f319(f319(f225(x66721),x66722),x66723))
% 22.40/22.31 [6709]~P4(x67091)+E(f319(f319(f93(f913(x67091,a904)),f319(f294(x67091,x67092),x67093)),f319(f275(x67091),x67093)),f319(f275(x67091),x67092))+~P1(f319(f319(f225(x67091),x67092),x67093))
% 22.40/22.31 [6777]~P5(x67771)+~P1(f319(f319(f225(x67771),f319(x67772,x67773)),x67773))+P1(f319(f319(f225(x67771),f87(x67771,x67772)),x67773))
% 22.40/22.31 [6869]~P4(x68691)+E(f319(f319(f93(f913(x68691,a904)),f298(x68691,x68692,x68693)),f319(f275(x68691),x68693)),f319(f296(x68691),x68692))+~P1(f319(f319(f226(x68691),x68692),x68693))
% 22.40/22.31 [6870]~P4(x68701)+E(f319(f319(f93(f913(x68701,a904)),f297(x68701,x68702,x68703)),f319(f296(x68701),x68703)),f319(f296(x68701),x68702))+~P1(f319(f319(f225(x68701),x68702),x68703))
% 22.40/22.31 [6871]~P4(x68711)+E(f319(f319(f93(f913(x68711,a904)),f295(x68711,x68712,x68713)),f319(f296(x68711),x68713)),f319(f275(x68711),x68712))+~P1(f319(f319(f225(x68711),x68712),x68713))
% 22.40/22.31 [6885]P1(f319(x68851,x68852))+~P1(f319(f319(f225(a906),x68852),x68853))+P1(f319(f319(f321(a906),f339(x68851,x68853)),f295(a906,f2(a906),x68853)))
% 22.40/22.31 [6919]E(x69191,x69192)+~E(f319(f319(f156(x69193),x69191),f611(x69193,x69192,x69191)),f319(f319(f156(x69193),x69192),f611(x69193,x69192,x69191)))+~E(f319(f182(f907(x69193)),x69191),f319(f182(f907(x69193)),x69192))
% 22.40/22.31 [6924]~E(x69243,f319(f319(f30(a906),x69241),x69242))+~P1(f319(f319(f226(a906),f2(a906)),x69242))+P1(f319(f319(f226(a906),x69241),f319(f319(f75(a906),x69242),f319(a104,x69243))))
% 22.40/22.31 [6938]~P1(f319(x69381,x69383))+~P1(f319(f319(f225(a906),x69383),x69382))+P1(f319(f319(f321(a906),f330(x69381,x69382)),f295(a906,f2(a906),x69382)))
% 22.40/22.31 [6976]~P1(f319(x69761,x69763))+P1(f319(x69761,f340(x69761,x69762)))+~P1(f319(f319(f321(a906),x69763),f295(a906,f2(a906),x69762)))
% 22.40/22.31 [6994]~P126(x69943)+~P1(f319(f319(f225(x69943),f319(f92(x69943),x69941)),f319(f92(x69943),x69942)))+P1(f319(f319(f225(a906),x69941),x69942))
% 22.40/22.31 [6995]~P113(x69953)+~P1(f319(f319(f225(x69953),f319(f95(x69953),x69951)),f319(f95(x69953),x69952)))+P1(f319(f319(f225(a1),x69951),x69952))
% 22.40/22.31 [6997]~P126(x69973)+~P1(f319(f319(f226(x69973),f319(f92(x69973),x69971)),f319(f92(x69973),x69972)))+P1(f319(f319(f226(a906),x69971),x69972))
% 22.40/22.31 [6998]~P113(x69983)+~P1(f319(f319(f226(x69983),f319(f95(x69983),x69981)),f319(f95(x69983),x69982)))+P1(f319(f319(f226(a1),x69981),x69982))
% 22.40/22.31 [7015]~P126(x70151)+~P1(f319(f319(f226(x70151),f72(x70151)),x70152))+P1(f319(f319(f226(x70151),f72(x70151)),f319(f319(f236(x70151),x70152),f319(a104,x70153))))
% 22.40/22.31 [7017]~P63(x70171)+~P1(f319(f319(f225(x70171),f319(f73(x70171),x70173)),f319(f73(x70171),x70172)))+P1(f319(f319(f225(x70171),x70172),x70173))
% 22.40/22.31 [7018]~P65(x70181)+~P1(f319(f319(f225(x70181),f319(f73(x70181),x70183)),f319(f73(x70181),x70182)))+P1(f319(f319(f225(x70181),x70182),x70183))
% 22.40/22.31 [7019]~P65(x70191)+~P1(f319(f319(f226(x70191),f319(f73(x70191),x70193)),f319(f73(x70191),x70192)))+P1(f319(f319(f226(x70191),x70192),x70193))
% 22.40/22.31 [7043]P1(f319(x70431,x70432))+~P1(f319(x70431,f342(x70431,x70433)))+~P1(f319(f319(f321(a906),x70432),f295(a906,f2(a906),x70433)))
% 22.40/22.31 [7064]~P74(x70641)+P1(f319(f319(f226(x70641),f362(x70643,x70642,x70641)),f72(x70641)))+P1(f319(f319(f225(x70641),x70642),x70643))
% 22.40/22.31 [7086]~E(f39(a906,x70863,x70862),f39(a906,x70861,x70862))+E(f319(f319(f74(a906),x70861),f319(f319(f75(a906),x70862),f451(x70861,x70862,x70863))),x70863)+~P1(f319(f319(f225(a906),x70861),x70863))
% 22.40/22.31 [7140]E(f319(f319(f8(x71401,a906),x71402),x71403),f2(a906))+~P1(f319(f55(x71401),x71403))+P1(f319(f319(f321(x71401),f332(x71402,x71403,x71401)),x71403))
% 22.40/22.31 [7141]E(f319(f319(f11(x71411,a906),x71412),x71413),f72(a906))+~P1(f319(f55(x71411),x71413))+P1(f319(f319(f321(x71411),f890(x71412,x71413,x71411)),x71413))
% 22.40/22.31 [7163]~P4(x71631)+~P1(f319(f319(f225(x71631),x71633),x71632))+P1(f319(f319(f225(f913(x71631,a904)),f319(f296(x71631),x71632)),f319(f296(x71631),x71633)))
% 22.40/22.31 [7164]~P4(x71641)+~P1(f319(f319(f225(x71641),x71642),x71643))+P1(f319(f319(f225(f913(x71641,a904)),f319(f274(x71641),x71642)),f319(f274(x71641),x71643)))
% 22.40/22.31 [7165]~P111(x71651)+~P1(f319(f319(f225(x71651),x71653),x71652))+P1(f319(f319(f225(f913(x71651,a904)),f319(f275(x71651),x71652)),f319(f275(x71651),x71653)))
% 22.40/22.31 [7166]~P111(x71661)+~P1(f319(f319(f225(x71661),x71662),x71663))+P1(f319(f319(f225(f913(x71661,a904)),f319(f293(x71661),x71662)),f319(f293(x71661),x71663)))
% 22.40/22.31 [7167]~P4(x71671)+~P1(f319(f319(f226(x71671),x71672),x71673))+P1(f319(f319(f226(f913(x71671,a904)),f319(f274(x71671),x71672)),f319(f274(x71671),x71673)))
% 22.40/22.31 [7178]~P5(x71781)+P1(f319(f319(f225(x71781),x71782),f32(x71781,x71783)))+P1(f319(f319(f321(x71781),f860(x71783,x71782,x71781)),x71783))
% 22.40/22.31 [7184]~P65(x71841)+P1(f319(f319(f225(x71841),f319(f319(f3(x71841),x71842),x71843)),f2(x71841)))+~P1(f319(f319(f225(x71841),x71842),x71843))
% 22.40/22.31 [7185]~P65(x71851)+P1(f319(f319(f226(x71851),f319(f319(f3(x71851),x71852),x71853)),f2(x71851)))+~P1(f319(f319(f226(x71851),x71852),x71853))
% 22.40/22.31 [7226]P1(f319(x72261,x72262))+P1(f319(f319(f225(a906),f342(x72261,x72263)),x72263))+~P1(f319(f319(f321(a906),x72262),f295(a906,f2(a906),x72263)))
% 22.40/22.31 [7266]~E(f319(f319(f8(x72661,a906),x72662),x72663),f72(a906))+~P1(f319(f55(x72661),x72663))+P1(f319(f319(f321(x72661),f331(x72662,x72663,x72661)),x72663))
% 22.40/22.31 [7267]~P1(f319(x72671,x72673))+P1(f319(f319(f225(a906),f340(x72671,x72672)),x72672))+~P1(f319(f319(f321(a906),x72673),f295(a906,f2(a906),x72672)))
% 22.40/22.31 [7306]~P5(x73061)+P1(f319(f319(f321(x73061),f766(x73063,x73062,x73061)),x73062))+P1(f319(f319(f225(x73061),f31(x73061,x73062)),x73063))
% 22.40/22.31 [7340]~E(f319(f319(f8(x73401,a906),x73402),x73403),f319(a104,f2(a906)))+~P1(f319(f55(x73401),x73403))+P1(f319(f319(f321(x73401),f333(x73402,x73403,x73401)),x73403))
% 22.40/22.31 [7351]E(x73511,f2(a906))+P1(f319(x73512,f39(a906,x73513,x73511)))+P1(f319(f319(f226(a906),f445(x73511,x73513,x73512)),x73511))
% 22.40/22.31 [7453]~P1(f319(x74531,x74532))+P1(f319(x74531,f39(a906,x74532,x74533)))+P1(f319(f319(f226(a906),f445(x74533,x74532,x74531)),x74533))
% 22.40/22.31 [7566]E(x75661,f105(x75662))+~P1(f319(f319(f321(f907(x75662)),x75661),f153(x75662,x75663)))+P1(f319(f319(f321(x75662),f682(x75663,x75661,x75662)),x75663))
% 22.40/22.31 [7589]~P4(x75891)+E(f319(f319(f93(f913(x75891,a904)),f319(f319(f301(x75891),x75892),f181(f913(x75891,a904)))),f298(x75891,x75892,x75893)),f319(f294(x75891,x75892),x75893))+~P1(f319(f319(f226(x75891),x75892),x75893))
% 22.40/22.31 [7610]~P4(x76101)+E(f319(f319(f93(f913(x76101,a904)),f319(f319(f301(x76101),x76102),f181(f913(x76101,a904)))),f297(x76101,x76102,x76103)),f295(x76101,x76102,x76103))+~P1(f319(f319(f225(x76101),x76102),x76103))
% 22.40/22.31 [7714]~P4(x77141)+P1(f319(f319(f225(x77141),x77142),x77143))+~P1(f319(f319(f225(f913(x77141,a904)),f319(f296(x77141),x77143)),f319(f296(x77141),x77142)))
% 22.40/22.31 [7715]~P111(x77151)+P1(f319(f319(f225(x77151),x77152),x77153))+~P1(f319(f319(f225(f913(x77151,a904)),f319(f275(x77151),x77153)),f319(f275(x77151),x77152)))
% 22.40/22.31 [7716]~P4(x77161)+P1(f319(f319(f225(x77161),x77162),x77163))+~P1(f319(f319(f225(f913(x77161,a904)),f319(f274(x77161),x77162)),f319(f274(x77161),x77163)))
% 22.40/22.31 [7717]~P111(x77171)+P1(f319(f319(f225(x77171),x77172),x77173))+~P1(f319(f319(f225(f913(x77171,a904)),f319(f293(x77171),x77172)),f319(f293(x77171),x77173)))
% 22.40/22.31 [7718]~P4(x77181)+P1(f319(f319(f226(x77181),x77182),x77183))+~P1(f319(f319(f226(f913(x77181,a904)),f319(f274(x77181),x77182)),f319(f274(x77181),x77183)))
% 22.40/22.31 [7741]~P65(x77411)+~P1(f319(f319(f225(x77411),f319(f319(f3(x77411),x77412),x77413)),f2(x77411)))+P1(f319(f319(f225(x77411),x77412),x77413))
% 22.40/22.31 [7742]~P65(x77421)+~P1(f319(f319(f226(x77421),f319(f319(f3(x77421),x77422),x77423)),f2(x77421)))+P1(f319(f319(f226(x77421),x77422),x77423))
% 22.40/22.31 [7899]E(x78991,f2(a906))+~E(f319(f134(a906,a906,f74(a906),x78992),x78993),f2(a906))+~P1(f319(f319(f321(a906),x78991),f319(f164(a906),x78993)))
% 22.40/22.31 [7903]~P5(x79031)+~P1(f319(f319(f225(x79031),f766(x79033,x79032,x79031)),x79033))+P1(f319(f319(f225(x79031),f31(x79031,x79032)),x79033))
% 22.40/22.31 [8050]P1(f319(f319(f225(a1),f2(a1)),f440(x80501,x80502,x80503)))+P1(f319(f319(x80502,f319(f319(f30(a1),x80501),x80503)),f39(a1,x80501,x80503)))+~P1(f319(f319(f226(a1),f2(a1)),x80503))
% 22.40/22.31 [8136]E(x81361,x81362)+~E(f319(f182(f907(x81363)),x81361),f319(f182(f907(x81363)),x81362))+~P1(f319(f319(f249(x81363,x81363,a904),a316),f653(x81363,x81361,x81362)))
% 22.40/22.31 [8208]~P37(x82082,x82083)+E(x82081,f181(f913(x82082,a904)))+~P1(f319(f319(f225(f913(x82082,a904)),x82081),f319(f277(x82082,x82082,x82083),x82081)))
% 22.40/22.31 [8239]~P75(x82391)+~P1(f319(f319(f225(x82391),x82392),f319(f319(f74(x82391),x82393),f449(x82393,x82392,x82391))))+P1(f319(f319(f225(x82391),x82392),x82393))
% 22.40/22.31 [8274]P54(x82741,x82742,x82743)+P1(f319(f319(f321(x82741),f567(x82743,x82742,x82741)),x82742))+P1(f319(f319(f321(f912(x82741,x82741)),f568(x82743,x82742,x82741)),x82743))
% 22.40/22.31 [8295]P1(f319(f319(x82952,f319(f319(f30(a1),x82951),x82953)),f39(a1,x82951,x82953)))+~P1(f319(f319(f226(a1),f2(a1)),x82953))+P1(f319(f319(f226(a1),f440(x82951,x82952,x82953)),x82953))
% 22.40/22.31 [8318]E(f319(f302(a906,a906,f319(f319(f9(a906,a906,a906),f3(a906)),x83181)),f319(f294(a906,x83182),x83183)),f181(f913(a906,a904)))+P1(f319(f319(f226(a906),x83181),x83183))+P1(f319(f319(f226(a906),x83182),x83183))
% 22.40/22.31 [8429]E(f319(f302(a906,a906,f319(f319(f9(a906,a906,a906),f3(a906)),x84291)),f319(f294(a906,x84292),x84293)),f319(f319(f301(a906),f2(a906)),f181(f913(a906,a904))))+P1(f319(f319(f226(a906),x84291),x84293))+~P1(f319(f319(f226(a906),x84292),x84293))
% 22.40/22.31 [8440]~P4(x84401)+E(f141(x84401,x84401,f7(x84401),x84402,x84403),x84403)+~P1(f319(f319(f321(x84401),x84402),f319(f164(x84401),x84403)))
% 22.40/22.31 [8453]P25(x84531,x84531,x84532,x84533)+~P1(f319(f55(x84531),x84533))+~P1(f319(f319(f225(f913(x84531,a904)),x84533),f319(f302(x84531,x84531,x84532),x84533)))
% 22.40/22.31 [8478]E(f319(f319(f74(a1),f319(f319(f75(a1),x84781),f441(x84782,x84783,x84781))),f440(x84782,x84783,x84781)),x84782)+P1(f319(f319(x84783,f319(f319(f30(a1),x84782),x84781)),f39(a1,x84782,x84781)))+~P1(f319(f319(f226(a1),f2(a1)),x84781))
% 22.40/22.31 [8717]~P1(f319(f319(x87171,f441(x87172,x87171,x87173)),f440(x87172,x87171,x87173)))+P1(f319(f319(x87171,f319(f319(f30(a1),x87172),x87173)),f39(a1,x87172,x87173)))+~P1(f319(f319(f226(a1),f2(a1)),x87173))
% 22.40/22.31 [9605]~P1(f319(f55(x96051),x96052))+~P1(f319(f319(f321(x96051),x96053),x96052))+P1(f319(f319(f226(a906),f319(f29(x96051),f319(f319(f3(f913(x96051,a904)),x96052),f319(f319(f301(x96051),x96053),f181(f913(x96051,a904)))))),f319(f29(x96051),x96052)))
% 22.40/22.31 [10204]P54(x102041,x102042,x102043)+~P1(f319(f319(f249(x102041,x102041,a904),f319(f319(f9(x102041,f913(x102041,a904),f913(x102041,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x102041,a904),f913(x102041,a904)),x102041),f10(a904,a904,x102041)),f319(f319(f10(a904,f913(a904,a904),x102041),a317),f319(f319(f9(x102041,f913(x102041,a904),a904),f321(x102041)),x102042)))),f319(f319(f9(x102041,f913(x102041,a904),a904),f321(x102041)),x102042))),f568(x102043,x102042,x102041)))+P1(f319(f319(f321(x102041),f567(x102043,x102042,x102041)),x102042))
% 22.40/22.31 [5581]~P120(x55812)+E(x55811,f2(x55812))+E(f319(f319(f282(x55812),x55813),f319(f73(x55812),x55811)),f319(f73(x55812),f319(f319(f282(x55812),x55813),x55811)))
% 22.40/22.31 [5722]~E(x57223,f181(f913(x57221,a904)))+~E(x57222,f181(f913(x57221,a904)))+E(f319(f319(f93(f913(x57221,a904)),x57222),x57223),f181(f913(x57221,a904)))
% 22.40/22.31 [5781]~E(x57813,f2(a906))+~P1(f319(x57811,f2(a906)))+P1(f319(x57811,f319(f319(f30(a906),x57812),x57813)))
% 22.40/22.31 [5928]~P75(x59282)+E(x59281,f2(x59282))+E(f319(f319(f282(x59282),f319(f69(x59282),x59283)),f319(f69(x59282),x59281)),f319(f69(x59282),f319(f319(f282(x59282),x59283),x59281)))
% 22.40/22.31 [6096]~P1(f319(f55(x60961),x60963))+E(f319(f29(x60961),f319(f319(f301(x60961),x60962),x60963)),f319(a104,f319(f29(x60961),x60963)))+P1(f319(f319(f321(x60961),x60962),x60963))
% 22.40/22.31 [6170]~E(x61702,f2(a906))+P1(f319(x61701,f2(a906)))+~P1(f319(x61701,f319(f319(f30(a906),x61703),x61702)))
% 22.40/22.31 [6187]~P1(f319(f55(x61871),x61873))+E(f319(f29(x61871),f319(f319(f301(x61871),x61872),x61873)),f319(f29(x61871),x61873))+~P1(f319(f319(f321(x61871),x61872),x61873))
% 22.40/22.31 [6223]~P1(f319(f55(x62231),x62233))+E(f319(f29(x62231),f319(f319(f301(x62231),x62232),x62233)),f319(f319(f74(a906),f72(a906)),f319(f29(x62231),x62233)))+P1(f319(f319(f321(x62231),x62232),x62233))
% 22.40/22.31 [6230]~P70(x62301)+E(f319(f319(f30(x62301),x62302),f319(f73(x62301),x62303)),f319(f73(x62301),f319(f319(f30(x62301),x62302),x62303)))+~P1(f319(f319(f279(x62301),x62303),x62302))
% 22.40/22.31 [6342]E(f319(f319(f74(a906),x63421),f334(x63421,x63422,x63423)),x63422)+~P1(f319(x63423,f2(a906)))+P1(f319(x63423,f319(f319(f3(a906),x63422),x63421)))
% 22.40/22.31 [6343]E(f319(f319(f74(a906),x63431),f335(x63431,x63432,x63433)),x63432)+~P1(f319(x63433,f2(a906)))+P1(f319(x63433,f319(f319(f3(a906),x63432),x63431)))
% 22.40/22.31 [6366]~P70(x63661)+E(f319(f319(f30(x63661),f319(f73(x63661),x63662)),x63663),f319(f73(x63661),f319(f319(f30(x63661),x63662),x63663)))+~P1(f319(f319(f279(x63661),x63663),x63662))
% 22.40/22.31 [6390]~P5(x63901)+~P1(f319(f55(x63901),x63903))+E(f319(f319(f58(x63901,x63901,f93(x63901)),x63902),x63903),f319(f319(f93(x63901),x63902),f31(x63901,x63903)))
% 22.40/22.31 [6391]~P5(x63911)+~P1(f319(f55(x63911),x63913))+E(f319(f319(f58(x63911,x63911,f94(x63911)),x63912),x63913),f319(f319(f94(x63911),x63912),f32(x63911,x63913)))
% 22.40/22.31 [6397]~P98(x63971)+~E(f319(f96(x63971),x63972),f319(f96(x63971),x63973))+P28(x63971,f319(f96(x63971),f319(f319(f74(a1),x63972),f319(f73(a1),x63973))))
% 22.40/22.31 [6405]~P141(x64051)+E(f319(f319(f3(x64051),f319(f92(x64051),x64052)),f319(f92(x64051),x64053)),f319(f92(x64051),f319(f319(f3(a906),x64052),x64053)))+~P1(f319(f319(f225(a906),x64053),x64052))
% 22.40/22.31 [6411]~P115(x64111)+~P1(f319(f319(f279(x64111),x64112),x64113))+P1(f319(f319(f279(x64111),f319(f73(x64111),x64112)),x64113))
% 22.40/22.31 [6493]E(f319(f319(f74(a906),x64931),f334(x64931,x64932,x64933)),x64932)+P1(f319(f319(f226(a906),x64932),x64931))+P1(f319(x64933,f319(f319(f3(a906),x64932),x64931)))
% 22.40/22.31 [6494]E(f319(f319(f74(a906),x64941),f335(x64941,x64942,x64943)),x64942)+P1(f319(f319(f226(a906),x64942),x64941))+P1(f319(x64943,f319(f319(f3(a906),x64942),x64941)))
% 22.40/22.31 [6512]~P113(x65121)+E(f319(f319(f75(x65121),f319(f69(x65121),x65122)),x65123),f319(f69(x65121),f319(f319(f75(x65121),x65122),x65123)))+~P1(f319(f319(f225(x65121),f2(x65121)),x65123))
% 22.40/22.31 [6513]~P74(x65131)+E(f319(f319(f282(x65131),f319(f69(x65131),x65132)),x65133),f319(f69(x65131),f319(f319(f282(x65131),x65132),x65133)))+~P1(f319(f319(f226(x65131),f2(x65131)),x65133))
% 22.40/22.31 [6522]~P101(x65221)+~P1(f319(f55(x65221),x65223))+E(f319(f319(f58(x65221,x65221,f94(x65221)),x65222),x65223),f12(x65221,f319(f319(f301(x65221),x65222),x65223)))
% 22.40/22.31 [6523]~P101(x65231)+~P1(f319(f55(x65231),x65233))+E(f319(f319(f58(x65231,x65231,f93(x65231)),x65232),x65233),f15(x65231,f319(f319(f301(x65231),x65232),x65233)))
% 22.40/22.31 [6524]~P4(x65241)+~P1(f319(f55(x65241),x65243))+E(f319(f319(f58(x65241,x65241,f180(x65241)),x65242),x65243),f16(x65241,f319(f319(f301(x65241),x65242),x65243)))
% 22.40/22.31 [6525]~P4(x65251)+~P1(f319(f55(x65251),x65253))+E(f319(f319(f58(x65251,x65251,f230(x65251)),x65252),x65253),f17(x65251,f319(f319(f301(x65251),x65252),x65253)))
% 22.40/22.31 [6570]E(x65701,f105(x65702))+~E(f171(x65702,x65703),f105(f907(x65702)))+~P1(f319(f319(f321(f907(x65702)),x65701),f319(f164(f907(x65702)),x65703)))
% 22.40/22.31 [6613]~P1(f319(f129(x66131),x66133))+P1(f319(f319(f321(x66131),x66132),f319(f164(x66131),x66133)))+P1(f319(f129(x66131),f319(f319(f143(x66131),x66132),x66133)))
% 22.40/22.31 [6624]~P100(x66241)+~P1(f319(f55(x66241),x66243))+E(f319(f57(x66241,f75(x66241)),f319(f319(f301(x66241),x66242),x66243)),f319(f319(f58(x66241,x66241,f75(x66241)),x66242),x66243))
% 22.40/22.31 [6644]~P4(x66441)+~P1(f319(f55(x66441),x66443))+E(f13(x66441,f180(x66441),f319(f319(f301(x66441),x66442),x66443)),f319(f319(f58(x66441,x66441,f180(x66441)),x66442),x66443))
% 22.40/22.31 [6645]~P4(x66451)+~P1(f319(f55(x66451),x66453))+E(f14(x66451,f230(x66451),f319(f319(f301(x66451),x66452),x66453)),f319(f319(f58(x66451,x66451,f230(x66451)),x66452),x66453))
% 22.40/22.31 [6647]P1(f319(x66471,f2(a906)))+~P1(f319(f319(f226(a906),x66472),x66473))+~P1(f319(x66471,f319(f319(f3(a906),x66472),x66473)))
% 22.40/22.31 [6667]~P92(x66671)+P1(f319(f319(f225(x66671),x66672),x66673))+~P1(f319(f319(f225(x66671),f319(f69(x66671),x66672)),x66673))
% 22.40/22.31 [6668]~P113(x66681)+P1(f319(f319(f226(x66681),x66682),x66683))+~P1(f319(f319(f226(x66681),f319(f69(x66681),x66682)),x66683))
% 22.40/22.31 [6669]~P115(x66691)+P1(f319(f319(f279(x66691),x66692),x66693))+~P1(f319(f319(f279(x66691),f319(f73(x66691),x66692)),x66693))
% 22.40/22.31 [6686]E(x66861,f105(x66862))+E(f319(f133(x66862),f319(f319(f130(x66862),x66863),x66861)),f319(f319(f156(x66862),x66861),x66863))+~P1(f319(f319(f226(a906),x66863),f319(f182(f907(x66862)),x66861)))
% 22.40/22.31 [6742]~P1(f319(x67421,x67423))+P1(f319(x67421,f346(x67421,x67422)))+~P1(f319(f319(f321(a906),x67423),f319(f294(a906,f2(a906)),x67422)))
% 22.40/22.31 [6762]P1(f319(x67621,x67622))+~P1(f319(f319(f226(a906),x67622),x67623))+P1(f319(f319(f321(a906),f343(x67621,x67623)),f319(f294(a906,f2(a906)),x67623)))
% 22.40/22.31 [6778]~P126(x67781)+~P1(f319(f319(f225(x67781),f72(x67781)),x67782))+P1(f319(f319(f225(x67781),f72(x67781)),f319(f319(f236(x67781),x67782),x67783)))
% 22.40/22.31 [6780]~P126(x67801)+~P1(f319(f319(f225(x67801),f2(x67801)),x67802))+P1(f319(f319(f225(x67801),f2(x67801)),f319(f319(f236(x67801),x67802),x67803)))
% 22.40/22.31 [6782]~P126(x67821)+~P1(f319(f319(f226(x67821),f2(x67821)),x67822))+P1(f319(f319(f226(x67821),f2(x67821)),f319(f319(f236(x67821),x67822),x67823)))
% 22.40/22.31 [6808]~P1(f319(x68081,x68083))+~P1(f319(f319(f226(a906),x68083),x68082))+P1(f319(f319(f321(a906),f338(x68081,x68082)),f319(f294(a906,f2(a906)),x68082)))
% 22.40/22.31 [6818]P1(f319(f55(x68181),x68182))+~P1(f319(f55(x68181),x68183))+~P1(f319(f319(f225(f913(x68181,a904)),x68182),x68183))
% 22.40/22.31 [6825]~P1(f319(f319(f279(a906),x68251),x68252))+~P1(f319(f319(f279(a906),x68251),x68253))+P1(f319(f319(f279(a906),x68251),f319(f319(f3(a906),x68252),x68253)))
% 22.40/22.31 [6826]P1(f319(x68261,x68262))+~P1(f319(x68261,f344(x68261,x68263)))+~P1(f319(f319(f321(a906),x68262),f319(f294(a906,f2(a906)),x68263)))
% 22.40/22.31 [6837]E(x68371,f2(a906))+P1(f319(x68372,f426(x68371,x68373,x68372)))+~P1(f319(x68372,f319(f319(f30(a906),x68373),x68371)))
% 22.40/22.31 [6845]~P127(x68452)+E(x68451,f2(x68452))+~E(f319(f319(f74(x68452),f319(f319(f75(x68452),x68453),x68453)),f319(f319(f75(x68452),x68451),x68451)),f2(x68452))
% 22.40/22.31 [6846]~P127(x68462)+E(x68461,f2(x68462))+~E(f319(f319(f74(x68462),f319(f319(f75(x68462),x68461),x68461)),f319(f319(f75(x68462),x68463),x68463)),f2(x68462))
% 22.40/22.31 [6886]E(x68861,f2(a906))+~P1(f319(x68862,f427(x68861,x68863,x68862)))+P1(f319(x68862,f319(f319(f30(a906),x68863),x68861)))
% 22.40/22.31 [6891]~P4(x68911)+~P13(x68911,x68913)+P13(x68911,f319(f319(f140(x68911,x68911,f7(x68911)),x68912),x68913))
% 22.40/22.31 [6932]P1(f319(x69321,f426(x69322,x69323,x69321)))+P1(f319(x69321,f2(a906)))+~P1(f319(x69321,f319(f319(f30(a906),x69323),x69322)))
% 22.40/22.31 [6937]~P98(x69371)+E(f319(f96(x69371),x69372),f319(f96(x69371),x69373))+~P28(x69371,f319(f96(x69371),f319(f319(f74(a1),x69372),f319(f73(a1),x69373))))
% 22.40/22.31 [7001]E(x70011,f2(a1))+E(x70012,f2(a1))+~P1(f319(f43(x70012,x70012),f319(f319(f244(a1,a1),x70013),x70011)))
% 22.40/22.31 [7002]E(x70021,f72(a1))+E(x70022,f2(a1))+~P1(f319(f43(x70022,x70022),f319(f319(f244(a1,a1),x70021),x70023)))
% 22.40/22.31 [7016]P1(f319(x70161,x70162))+P1(f319(f319(f226(a906),f344(x70161,x70163)),x70163))+~P1(f319(f319(f321(a906),x70162),f319(f294(a906,f2(a906)),x70163)))
% 22.40/22.31 [7039]~P1(f319(x70391,f334(x70393,x70392,x70391)))+~P1(f319(x70391,f2(a906)))+P1(f319(x70391,f319(f319(f3(a906),x70392),x70393)))
% 22.40/22.31 [7040]~P1(f319(x70401,f335(x70403,x70402,x70401)))+~P1(f319(x70401,f2(a906)))+P1(f319(x70401,f319(f319(f3(a906),x70402),x70403)))
% 22.40/22.31 [7041]~P1(f319(x70411,f427(x70413,x70412,x70411)))+~P1(f319(x70411,f2(a906)))+P1(f319(x70411,f319(f319(f30(a906),x70412),x70413)))
% 22.40/22.31 [7060]~P1(f319(x70601,x70603))+P1(f319(f319(f226(a906),f346(x70601,x70602)),x70602))+~P1(f319(f319(f321(a906),x70603),f319(f294(a906,f2(a906)),x70602)))
% 22.40/22.31 [7061]E(f319(f319(f3(a906),f319(f319(f3(a906),x70611),x70612)),f319(f319(f3(a906),x70613),x70612)),f319(f319(f3(a906),x70611),x70613))+~P1(f319(f319(f225(a906),x70612),x70611))+~P1(f319(f319(f225(a906),x70612),x70613))
% 22.40/22.31 [7099]~P65(x70991)+~P1(f319(f319(f225(x70991),f319(f73(x70991),x70993)),x70992))+P1(f319(f319(f225(x70991),f319(f73(x70991),x70992)),x70993))
% 22.40/22.31 [7101]~P92(x71011)+~P1(f319(f319(f225(x71011),f319(f69(x71011),x71012)),x71013))+P1(f319(f319(f225(x71011),f319(f73(x71011),x71012)),x71013))
% 22.40/22.31 [7103]~P65(x71031)+~P1(f319(f319(f226(x71031),f319(f73(x71031),x71033)),x71032))+P1(f319(f319(f226(x71031),f319(f73(x71031),x71032)),x71033))
% 22.40/22.31 [7104]~P113(x71041)+~P1(f319(f319(f226(x71041),f319(f69(x71041),x71042)),x71043))+P1(f319(f319(f226(x71041),f319(f73(x71041),x71042)),x71043))
% 22.40/22.31 [7135]~P1(f319(x71353,f334(x71352,x71351,x71353)))+P1(f319(f319(f226(a906),x71351),x71352))+P1(f319(x71353,f319(f319(f3(a906),x71351),x71352)))
% 22.40/22.31 [7136]~P1(f319(x71363,f335(x71362,x71361,x71363)))+P1(f319(f319(f226(a906),x71361),x71362))+P1(f319(x71363,f319(f319(f3(a906),x71361),x71362)))
% 22.40/22.31 [7188]~E(f704(x71883,x71882,x71881),f688(x71883,x71882,x71881))+E(f319(f319(f94(f913(x71881,a904)),x71882),f31(f913(x71881,a904),x71883)),f181(f913(x71881,a904)))+P1(f319(f319(f321(f913(x71881,a904)),x71882),x71883))
% 22.40/22.31 [7195]~P1(f319(f55(x71951),x71953))+P1(f319(f55(x71951),f32(f913(x71951,a904),x71952)))+~P1(f319(f319(f321(f913(x71951,a904)),x71953),x71952))
% 22.40/22.31 [7255]~P4(x72551)+E(f319(f319(f93(f913(x72551,a904)),f319(f294(x72551,x72552),x72553)),f319(f319(f301(x72551),x72553),f181(f913(x72551,a904)))),f295(x72551,x72552,x72553))+~P1(f319(f319(f225(x72551),x72552),x72553))
% 22.40/22.31 [7256]E(x72561,f2(a906))+P1(f319(f319(f226(a906),f429(x72561,x72563,x72562)),x72561))+P1(f319(x72562,f319(f319(f30(a906),x72563),x72561)))
% 22.40/22.31 [7285]P1(f319(f319(f226(a906),f319(f182(f907(x72851)),x72852)),f775(x72853,x72851)))+~P1(f319(f55(f907(x72851)),x72853))+~P1(f319(f319(f321(f907(x72851)),x72852),x72853))
% 22.40/22.31 [7291]E(x72911,x72912)+~P1(f319(f319(f225(f913(x72913,a904)),x72911),x72912))+P1(f319(f319(f226(f913(x72913,a904)),x72911),x72912))
% 22.40/22.31 [7303]E(x73031,x73032)+~E(f319(f182(f907(x73033)),x73031),f319(f182(f907(x73033)),x73032))+P1(f319(f319(f226(a906),f611(x73033,x73031,x73032)),f319(f182(f907(x73033)),x73032)))
% 22.40/22.31 [7352]P8(x73521,x73522,x73523)+~E(f319(f256(x73521,x73521),x73523),x73522)+~E(f319(f319(f281(x73521,x73521,x73521),f319(f278(x73521,x73521),x73523)),x73523),x73523)
% 22.40/22.31 [7428]~P1(f319(x74281,f2(a906)))+P1(f319(f319(f226(a906),f429(x74283,x74282,x74281)),x74283))+P1(f319(x74281,f319(f319(f30(a906),x74282),x74283)))
% 22.40/22.31 [7438]~P4(x74381)+E(f319(f319(f93(f913(x74381,a904)),f298(x74381,x74382,x74383)),f319(f319(f301(x74381),x74383),f181(f913(x74381,a904)))),f297(x74381,x74382,x74383))+~P1(f319(f319(f226(x74381),x74382),x74383))
% 22.40/22.31 [7523]~P1(f319(f55(x75231),x75233))+P1(f319(f319(f225(a906),f319(f29(x75231),x75232)),f319(f29(x75231),x75233)))+~P1(f319(f319(f225(f913(x75231,a904)),x75232),x75233))
% 22.40/22.31 [7524]~P1(f319(f55(x75241),x75243))+P1(f319(f319(f226(a906),f319(f29(x75241),x75242)),f319(f29(x75241),x75243)))+~P1(f319(f319(f226(f913(x75241,a904)),x75242),x75243))
% 22.40/22.31 [7654]E(x76541,x76542)+~P1(f319(f319(f225(f913(x76543,a904)),x76542),x76541))+~P1(f319(f319(f225(f913(x76543,a904)),x76541),x76542))
% 22.40/22.31 [7657]~P4(x76571)+P13(x76571,x76572)+~P13(x76571,f319(f319(f140(x76571,x76571,f7(x76571)),x76573),x76572))
% 22.40/22.31 [7723]~P1(f319(f319(f226(a906),x77233),x77232))+~P1(f319(f319(f226(a906),x77233),x77231))+P1(f319(f319(f226(a906),f319(f319(f3(a906),x77231),x77232)),f319(f319(f3(a906),x77231),x77233)))
% 22.40/22.31 [7724]~P1(f319(f319(f225(a906),x77242),x77241))+~P1(f319(f319(f226(a906),x77241),x77243))+P1(f319(f319(f226(a906),f319(f319(f3(a906),x77241),x77242)),f319(f319(f3(a906),x77243),x77242)))
% 22.40/22.31 [7739]~P1(f319(f319(f226(a1),x77392),f2(a1)))+~P1(f319(f319(f225(a1),x77393),x77391))+P1(f319(f319(f225(a1),f319(f319(f30(a1),x77391),x77392)),f319(f319(f30(a1),x77393),x77392)))
% 22.40/22.31 [7756]~P1(f319(f319(f226(a906),f2(a906)),x77563))+~P1(f319(f319(f225(a906),x77563),x77562))+P1(f319(f319(f225(a906),f319(f319(f30(a906),x77561),x77562)),f319(f319(f30(a906),x77561),x77563)))
% 22.40/22.31 [7757]~P1(f319(f319(f226(a1),f2(a1)),x77572))+~P1(f319(f319(f225(a1),x77571),x77573))+P1(f319(f319(f225(a1),f319(f319(f30(a1),x77571),x77572)),f319(f319(f30(a1),x77573),x77572)))
% 22.40/22.31 [7761]~P1(f319(f319(f226(a906),f2(a906)),x77612))+~P1(f319(f319(f226(a906),x77611),x77613))+P1(f319(f319(f226(a906),f319(f319(f75(a906),x77611),x77612)),f319(f319(f75(a906),x77613),x77612)))
% 22.40/22.31 [7762]~P1(f319(f319(f226(a906),f2(a906)),x77621))+~P1(f319(f319(f226(a906),x77622),x77623))+P1(f319(f319(f226(a906),f319(f319(f75(a906),x77621),x77622)),f319(f319(f75(a906),x77621),x77623)))
% 22.40/22.31 [7763]~P1(f319(f319(f226(a1),f2(a1)),x77631))+~P1(f319(f319(f226(a1),x77632),x77633))+P1(f319(f319(f226(a1),f319(f319(f75(a1),x77631),x77632)),f319(f319(f75(a1),x77631),x77633)))
% 22.40/22.31 [7810]E(x78101,f2(a906))+E(f319(f319(f74(a906),f319(f319(f75(a906),x78101),f427(x78101,x78102,x78103))),f429(x78101,x78102,x78103)),x78102)+P1(f319(x78103,f319(f319(f30(a906),x78102),x78101)))
% 22.40/22.31 [7870]E(f319(f319(f74(a906),f319(f319(f75(a906),x78701),f427(x78701,x78702,x78703))),f429(x78701,x78702,x78703)),x78702)+~P1(f319(x78703,f2(a906)))+P1(f319(x78703,f319(f319(f30(a906),x78702),x78701)))
% 22.40/22.31 [7890]~P1(f319(f55(x78901),x78903))+P1(f319(f319(f321(x78901),f899(x78902,x78903,x78901)),x78903))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f11(x78901,a906),x78902),x78903)))
% 22.40/22.31 [7891]~P1(f319(f55(x78911),x78913))+P1(f319(f319(f321(x78911),f364(x78912,x78913,x78911)),x78913))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f11(x78911,a906),x78912),x78913)))
% 22.40/22.31 [8177]E(x81771,f181(f913(x81772,a904)))+E(x81771,f319(f319(f301(x81772),x81773),f181(f913(x81772,a904))))+~P1(f319(f319(f225(f913(x81772,a904)),x81771),f319(f319(f301(x81772),x81773),f181(f913(x81772,a904)))))
% 22.40/22.31 [8209]~P1(f319(f319(f226(a906),f72(a906)),x82093))+P1(f319(f319(f225(a906),x82091),x82092))+~P1(f319(f319(f279(a906),f319(f319(f236(a906),x82093),x82091)),f319(f319(f236(a906),x82093),x82092)))
% 22.40/22.31 [8211]~P1(f319(f319(f226(a906),f2(a906)),x82113))+P1(f319(f319(f225(a906),x82111),x82112))+~P1(f319(f319(f225(a906),f319(f319(f75(a906),x82113),x82111)),f319(f319(f75(a906),x82113),x82112)))
% 22.40/22.31 [8212]~P1(f319(f319(f226(a906),f2(a906)),x82123))+P1(f319(f319(f225(a906),x82121),x82122))+~P1(f319(f319(f225(a906),f319(f319(f75(a906),x82121),x82123)),f319(f319(f75(a906),x82122),x82123)))
% 22.40/22.31 [8214]~P1(f319(f319(f226(a906),f2(a906)),x82143))+P1(f319(f319(f226(a906),x82141),x82142))+~P1(f319(f319(f226(a906),f319(f319(f236(a906),x82143),x82141)),f319(f319(f236(a906),x82143),x82142)))
% 22.40/22.31 [8255]~E(f319(f319(f94(f913(x82551,a904)),f688(x82553,x82552,x82551)),f704(x82553,x82552,x82551)),f181(f913(x82551,a904)))+E(f319(f319(f94(f913(x82551,a904)),x82552),f31(f913(x82551,a904),x82553)),f181(f913(x82551,a904)))+P1(f319(f319(f321(f913(x82551,a904)),x82552),x82553))
% 22.40/22.31 [8269]E(x82691,f105(x82692))+~E(f319(f134(f907(x82692),f907(x82692),f126(x82692),f105(x82692)),x82693),f105(x82692))+~P1(f319(f319(f321(f907(x82692)),x82691),f319(f164(f907(x82692)),x82693)))
% 22.40/22.31 [8323]E(x83231,f181(f913(f913(x83232,a904),a904)))+P1(f319(f319(f321(f913(x83232,a904)),f867(x83233,x83231,x83232)),x83231))+P1(f319(f319(f225(f913(x83232,a904)),f32(f913(x83232,a904),x83231)),x83233))
% 22.40/22.31 [8328]~P76(x83281)+~P82(x83281)+E(f319(f319(f8(a1,x83281),f319(f319(f10(a906,x83281,a1),x83282),a97)),f319(f302(a906,a1,f92(a1)),x83283)),f319(f319(f8(a906,x83281),x83282),x83283))
% 22.40/22.31 [8329]~P76(x83291)+~P82(x83291)+E(f319(f319(f11(a1,x83291),f319(f319(f10(a906,x83291,a1),x83292),a97)),f319(f302(a906,a1,f92(a1)),x83293)),f319(f319(f11(a906,x83291),x83292),x83293))
% 22.40/22.31 [8371]~P1(f319(f55(x83711),x83713))+~P1(f319(f319(f226(a906),f2(a906)),f319(x83712,f899(x83712,x83713,x83711))))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f11(x83711,a906),x83712),x83713)))
% 22.40/22.31 [8372]~P1(f319(f55(x83721),x83723))+~P1(f319(f319(f226(a906),f2(a906)),f319(x83722,f364(x83722,x83723,x83721))))+P1(f319(f319(f226(a906),f2(a906)),f319(f319(f11(x83721,a906),x83722),x83723)))
% 22.40/22.31 [8409]~P73(x84092)+E(x84091,f72(x84092))+E(f319(f319(f282(x84092),f319(f319(f3(x84092),f319(f319(f236(x84092),x84091),x84093)),f72(x84092))),f319(f319(f3(x84092),x84091),f72(x84092))),f319(f319(f8(a906,x84092),f319(f236(x84092),x84091)),f319(f294(a906,f2(a906)),x84093)))
% 22.40/22.31 [8464]E(x84641,f2(a906))+~P1(f319(x84643,f319(f319(f30(a906),x84642),x84641)))+P1(f319(f319(f226(a906),x84642),f319(f319(f75(a906),x84641),f319(a104,f426(x84641,x84642,x84643)))))
% 22.40/22.31 [8482]P1(f319(x84821,f2(a906)))+~P1(f319(x84821,f319(f319(f30(a906),x84822),x84823)))+P1(f319(f319(f226(a906),x84822),f319(f319(f75(a906),x84823),f319(a104,f426(x84823,x84822,x84821)))))
% 22.40/22.31 [8518]E(x85181,f2(a906))+~P1(f319(x85183,f319(f319(f30(a906),x85182),x85181)))+P1(f319(f319(f225(a906),f319(f319(f75(a906),x85181),f426(x85181,x85182,x85183))),x85182))
% 22.40/22.31 [8552]P1(f319(x85521,f2(a906)))+~P1(f319(x85521,f319(f319(f30(a906),x85523),x85522)))+P1(f319(f319(f225(a906),f319(f319(f75(a906),x85522),f426(x85522,x85523,x85521))),x85523))
% 22.40/22.31 [8560]~P4(x85601)+E(f319(f319(f140(x85601,x85601,f7(x85601)),x85602),x85603),f141(x85601,x85601,f7(x85601),x85602,x85603))+P1(f319(f319(f321(x85601),x85602),f319(f164(x85601),x85603)))
% 22.40/22.31 [8594]~E(f319(x85943,f579(x85942,x85943,x85941)),f319(x85943,f581(x85942,x85943,x85941)))+~P61(x85941,f319(x85943,f580(x85942,x85943,x85941)))+P61(x85941,f319(f319(f33(x85942,f913(x85941,f913(x85941,a904))),f234(f913(x85942,a904))),x85943))
% 22.40/22.31 [8603]E(x86031,f181(f913(f913(x86032,a904),a904)))+~P1(f319(f319(f225(f913(x86032,a904)),f867(x86033,x86031,x86032)),x86033))+P1(f319(f319(f225(f913(x86032,a904)),f32(f913(x86032,a904),x86031)),x86033))
% 22.40/22.31 [8667]~P75(x86671)+~P1(f319(f319(f226(x86671),x86672),x86673))+P1(f319(f319(f226(x86671),x86672),f319(f319(f282(x86671),f319(f319(f74(x86671),x86672),x86673)),f319(f319(f74(x86671),f72(x86671)),f72(x86671)))))
% 22.40/22.31 [8725]~P1(f319(f319(x87251,f479(x87251,x87253,x87252)),f483(x87251,x87253,x87252)))+P1(f319(f319(x87251,x87252),x87253))+~P1(f319(f307(f912(a1,a1),a46),f319(f319(f244(a1,a1),x87252),x87253)))
% 22.40/22.31 [8726]~P1(f319(f319(x87261,f484(x87261,x87263,x87262)),f485(x87261,x87263,x87262)))+P1(f319(f319(x87261,x87262),x87263))+~P1(f319(f307(f912(a1,a1),a52),f319(f319(f244(a1,a1),x87262),x87263)))
% 22.40/22.31 [8727]~P1(f319(f319(x87271,f488(x87271,x87273,x87272)),f492(x87271,x87273,x87272)))+P1(f319(f319(x87271,x87272),x87273))+~P1(f319(f307(f912(a1,a1),a214),f319(f319(f244(a1,a1),x87272),x87273)))
% 22.40/22.31 [8728]~P1(f319(f319(x87281,f493(x87281,x87283,x87282)),f495(x87281,x87283,x87282)))+P1(f319(f319(x87281,x87282),x87283))+~P1(f319(f307(f912(a906,a906),a212),f319(f319(f244(a906,a906),x87282),x87283)))
% 22.40/22.31 [8729]~P1(f319(f319(x87291,f667(x87291,x87293,x87292)),f669(x87291,x87293,x87292)))+P1(f319(f319(x87291,x87292),x87293))+~P1(f319(f307(f912(a1,a1),a174),f319(f319(f244(a1,a1),x87292),x87293)))
% 22.40/22.31 [8730]~P1(f319(f319(x87301,f762(x87301,x87303,x87302)),f763(x87301,x87303,x87302)))+P1(f319(f319(x87301,x87302),x87303))+~P1(f319(f307(f912(a1,a1),a125),f319(f319(f244(a1,a1),x87302),x87303)))
% 22.40/22.31 [9003]P1(f319(f319(x90031,x90032),x90033))+P1(f319(f307(f912(a906,a906),a212),f319(f319(f244(a906,a906),f493(x90031,x90033,x90032)),f495(x90031,x90033,x90032))))+~P1(f319(f307(f912(a906,a906),a212),f319(f319(f244(a906,a906),x90032),x90033)))
% 22.40/22.31 [9004]P1(f319(f319(x90041,x90042),x90043))+P1(f319(f307(f912(a1,a1),a46),f319(f319(f244(a1,a1),f479(x90041,x90043,x90042)),f483(x90041,x90043,x90042))))+~P1(f319(f307(f912(a1,a1),a46),f319(f319(f244(a1,a1),x90042),x90043)))
% 22.40/22.31 [9005]P1(f319(f319(x90051,x90052),x90053))+P1(f319(f307(f912(a1,a1),a52),f319(f319(f244(a1,a1),f484(x90051,x90053,x90052)),f485(x90051,x90053,x90052))))+~P1(f319(f307(f912(a1,a1),a52),f319(f319(f244(a1,a1),x90052),x90053)))
% 22.40/22.31 [9006]P1(f319(f319(x90061,x90062),x90063))+P1(f319(f307(f912(a1,a1),a214),f319(f319(f244(a1,a1),f488(x90061,x90063,x90062)),f492(x90061,x90063,x90062))))+~P1(f319(f307(f912(a1,a1),a214),f319(f319(f244(a1,a1),x90062),x90063)))
% 22.40/22.31 [9007]P1(f319(f319(x90071,x90072),x90073))+P1(f319(f307(f912(a1,a1),a174),f319(f319(f244(a1,a1),f667(x90071,x90073,x90072)),f669(x90071,x90073,x90072))))+~P1(f319(f307(f912(a1,a1),a174),f319(f319(f244(a1,a1),x90072),x90073)))
% 22.40/22.31 [9008]P1(f319(f319(x90081,x90082),x90083))+P1(f319(f307(f912(a1,a1),a125),f319(f319(f244(a1,a1),f762(x90081,x90083,x90082)),f763(x90081,x90083,x90082))))+~P1(f319(f307(f912(a1,a1),a125),f319(f319(f244(a1,a1),x90082),x90083)))
% 22.40/22.31 [9342]~P1(f319(f55(x93421),x93423))+P1(f319(f319(f321(f912(f913(x93421,a904),f913(x93421,a904))),f319(f319(f244(f913(x93421,a904),f913(x93421,a904)),x93422),x93423)),f306(x93421)))+~P1(f319(f319(f226(f913(x93421,a904)),x93422),x93423))
% 22.40/22.31 [9424]~P61(x94241,f319(x94243,f580(x94242,x94243,x94241)))+P61(x94241,f319(f319(f33(x94242,f913(x94241,f913(x94241,a904))),f234(f913(x94242,a904))),x94243))+~E(f319(f319(f94(f913(x94241,a904)),f241(x94241,x94241,f319(x94243,f579(x94242,x94243,x94241)))),f242(x94241,x94241,f319(x94243,f581(x94242,x94243,x94241)))),f181(f913(x94241,a904)))
% 22.40/22.31 [9621]P54(x96211,x96212,x96213)+P1(f319(f319(f321(f912(x96211,x96211)),f568(x96213,x96212,x96211)),x96213))+~P1(f319(f319(f321(f912(x96211,x96211)),f319(f319(f244(x96211,x96211),f567(x96213,x96212,x96211)),f567(x96213,x96212,x96211))),x96213))
% 22.40/22.31 [10216]P54(x102161,x102162,x102163)+~P1(f319(f319(f249(x102161,x102161,a904),f319(f319(f9(x102161,f913(x102161,a904),f913(x102161,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x102161,a904),f913(x102161,a904)),x102161),f10(a904,a904,x102161)),f319(f319(f10(a904,f913(a904,a904),x102161),a317),f319(f319(f9(x102161,f913(x102161,a904),a904),f321(x102161)),x102162)))),f319(f319(f9(x102161,f913(x102161,a904),a904),f321(x102161)),x102162))),f568(x102163,x102162,x102161)))+~P1(f319(f319(f321(f912(x102161,x102161)),f319(f319(f244(x102161,x102161),f567(x102163,x102162,x102161)),f567(x102163,x102162,x102161))),x102163))
% 22.40/22.31 [5763]~P69(x57632)+E(x57631,f2(x57632))+E(f319(f319(f30(x57632),f319(f319(f75(x57632),x57633),x57631)),x57631),x57633)
% 22.40/22.31 [5764]~P69(x57642)+E(x57641,f2(x57642))+E(f319(f319(f30(x57642),f319(f319(f75(x57642),x57641),x57643)),x57641),x57643)
% 22.40/22.31 [6569]~P76(x65691)+~E(f319(x65692,f2(a906)),f2(x65691))+E(f319(f319(f8(a906,x65691),x65692),f319(f294(a906,f319(a104,f2(a906))),x65693)),f319(f319(f8(a906,x65691),x65692),f319(f294(a906,f2(a906)),x65693)))
% 22.40/22.31 [6702]~P69(x67022)+E(x67021,f2(x67022))+E(f319(f319(f30(x67022),f319(f319(f74(x67022),x67023),x67021)),x67021),f319(f319(f74(x67022),f319(f319(f30(x67022),x67023),x67021)),f72(x67022)))
% 22.40/22.31 [6703]~P69(x67032)+E(x67031,f2(x67032))+E(f319(f319(f30(x67032),f319(f319(f74(x67032),x67031),x67033)),x67031),f319(f319(f74(x67032),f319(f319(f30(x67032),x67033),x67031)),f72(x67032)))
% 22.40/22.31 [6922]~P1(f319(x69223,f2(a1)))+P1(f319(f319(f225(a906),x69221),x69222))+P1(f319(x69223,f319(f92(a1),f319(f319(f3(a906),x69222),x69221))))
% 22.40/22.31 [7022]P1(f319(f319(f226(a906),x70222),x70221))+P1(f319(f319(f225(a906),x70221),x70222))+P1(f319(x70223,f319(f92(a1),f319(f319(f3(a906),x70222),x70221))))
% 22.40/22.31 [7097]E(f319(f319(f74(a906),f319(f96(a906),x70971)),f319(f319(f74(a906),f319(f96(a906),x70972)),x70973)),f319(f319(f74(a906),f319(f96(a906),x70971)),x70973))+P1(f319(a186,f319(f96(a1),x70971)))+~P1(f319(a186,f319(f96(a1),x70972)))
% 22.40/22.31 [7175]~E(x71752,f319(f319(f30(a906),x71753),x71751))+~P1(f319(f319(f226(a906),f2(a906)),x71751))+P1(f319(f319(f225(a906),f319(f319(f75(a906),x71751),x71752)),x71753))
% 22.40/22.31 [7288]~P1(f319(f55(x72881),x72883))+~P1(f319(f55(x72881),x72882))+P1(f319(f55(x72881),f319(f319(f93(f913(x72881,a904)),x72882),x72883)))
% 22.40/22.31 [7337]~P38(x73371,x73373)+~P38(x73371,x73372)+P38(x73371,f319(f319(f94(f913(f912(x73371,x73371),a904)),x73372),x73373))
% 22.40/22.31 [7338]~P53(x73381,x73383)+~P53(x73381,x73382)+P53(x73381,f319(f319(f93(f913(f912(x73381,x73381),a904)),x73382),x73383))
% 22.40/22.31 [7339]~P53(x73391,x73393)+~P53(x73391,x73392)+P53(x73391,f319(f319(f94(f913(f912(x73391,x73391),a904)),x73392),x73393))
% 22.40/22.31 [7572]~P4(x75721)+~P1(f319(f55(x75721),x75722))+E(f131(x75721,f319(f319(f3(f913(x75721,a904)),x75722),f319(f319(f301(x75721),x75723),f181(f913(x75721,a904))))),f162(x75721,x75723,f131(x75721,x75722)))
% 22.40/22.31 [7633]P1(f319(x76331,f2(a1)))+~P1(f319(f319(f226(a906),x76332),x76333))+~P1(f319(x76331,f319(f92(a1),f319(f319(f3(a906),x76332),x76333))))
% 22.40/22.31 [7651]~P1(f319(f55(x76511),x76512))+E(f319(f29(x76511),f319(f319(f3(f913(x76511,a904)),x76512),f319(f319(f301(x76511),x76513),f181(f913(x76511,a904))))),f319(f29(x76511),x76512))+P1(f319(f319(f321(x76511),x76513),x76512))
% 22.40/22.31 [7779]~P126(x77791)+~P1(f319(f319(f226(x77791),f72(x77791)),x77792))+P1(f319(f319(f226(x77791),f72(x77791)),f319(f319(f75(x77791),x77792),f319(f319(f236(x77791),x77792),x77793))))
% 22.40/22.31 [7820]~P1(f319(f55(x78201),x78203))+E(f319(f319(f3(a906),f319(f29(x78201),x78202)),f319(f29(x78201),x78203)),f319(f29(x78201),f319(f319(f3(f913(x78201,a904)),x78202),x78203)))+~P1(f319(f319(f225(f913(x78201,a904)),x78203),x78202))
% 22.40/22.31 [7878]~P1(f319(f319(f225(a906),x78782),x78783))+~P1(f319(f319(f225(a906),x78781),f319(f319(f3(a906),x78783),x78782)))+P1(f319(f319(f225(a906),f319(f319(f74(a906),x78781),x78782)),x78783))
% 22.40/22.31 [7935]P1(f319(f55(x79351),x79352))+~P1(f319(f55(x79351),x79353))+~P1(f319(f55(x79351),f319(f319(f3(f913(x79351,a904)),x79352),x79353)))
% 22.40/22.31 [7941]~P1(f319(f55(x79411),x79412))+E(f319(f29(x79411),f319(f319(f3(f913(x79411,a904)),x79412),f319(f319(f301(x79411),x79413),f181(f913(x79411,a904))))),f319(f319(f3(a906),f319(f29(x79411),x79412)),f72(a906)))+~P1(f319(f319(f321(x79411),x79413),x79412))
% 22.40/22.31 [8012]P61(x80121,x80122)+~P61(x80121,x80123)+~P1(f319(f319(f225(f913(x80121,f913(x80121,a904))),x80122),x80123))
% 22.40/22.31 [8049]~P1(f319(f319(f225(a906),x80493),x80492))+P1(f319(f319(f225(a906),x80491),f319(f319(f3(a906),x80492),x80493)))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),x80491),x80493)),x80492))
% 22.40/22.31 [8067]P37(x80671,x80672)+~P37(x80671,x80673)+~P1(f319(f319(f225(f913(f912(x80671,x80671),a904)),x80672),x80673))
% 22.40/22.31 [8068]P59(x80681,x80682)+~P59(x80681,x80683)+~P1(f319(f319(f225(f913(f912(x80681,x80681),a904)),x80682),x80683))
% 22.40/22.31 [8069]P39(x80691,x80692)+~P39(x80691,x80693)+~P1(f319(f319(f225(f913(f912(x80691,x80691),a904)),x80692),x80693))
% 22.40/22.31 [8303]~P126(x83031)+~P1(f319(f319(f226(x83031),f72(x83031)),x83032))+P1(f319(f319(f226(x83031),f319(f319(f236(x83031),x83032),x83033)),f319(f319(f75(x83031),x83032),f319(f319(f236(x83031),x83032),x83033))))
% 22.40/22.31 [8390]~P1(f319(x83901,f2(a1)))+~P1(f319(x83901,f319(f319(f3(a1),f319(f92(a1),x83902)),f319(f92(a1),x83903))))+P1(f319(x83901,f319(f92(a1),f319(f319(f3(a906),x83902),x83903))))
% 22.40/22.31 [8405]~P1(f319(f319(f225(a906),x84053),x84052))+P1(f319(x84051,f319(f319(f3(a1),f319(f92(a1),x84052)),f319(f92(a1),x84053))))+~P1(f319(x84051,f319(f92(a1),f319(f319(f3(a906),x84052),x84053))))
% 22.40/22.31 [8426]P1(f319(f319(f226(a906),x84261),x84262))+~P1(f319(x84263,f319(f319(f3(a1),f319(f92(a1),x84261)),f319(f92(a1),x84262))))+P1(f319(x84263,f319(f92(a1),f319(f319(f3(a906),x84261),x84262))))
% 22.40/22.31 [8475]~P127(x84752)+E(x84751,f2(x84752))+P1(f319(f319(f226(x84752),f2(x84752)),f319(f319(f74(x84752),f319(f319(f75(x84752),x84753),x84753)),f319(f319(f75(x84752),x84751),x84751))))
% 22.40/22.31 [8476]~P127(x84762)+E(x84761,f2(x84762))+P1(f319(f319(f226(x84762),f2(x84762)),f319(f319(f74(x84762),f319(f319(f75(x84762),x84761),x84761)),f319(f319(f75(x84762),x84763),x84763))))
% 22.40/22.31 [8579]~P1(f319(f319(f226(a906),f2(a906)),x85791))+~P1(f319(f319(f226(a1),x85792),x85793))+P1(f319(f319(f226(a1),f319(f319(f75(a1),f319(f92(a1),x85791)),x85792)),f319(f319(f75(a1),f319(f92(a1),x85791)),x85793)))
% 22.40/22.31 [8635]E(f319(f319(f94(f913(x86351,a904)),x86352),f31(f913(x86351,a904),x86353)),f181(f913(x86351,a904)))+P1(f319(f319(f321(f913(x86351,a904)),x86352),x86353))+P1(f319(f319(f321(f913(x86351,a904)),f688(x86353,x86352,x86351)),f319(f319(f301(f913(x86351,a904)),x86352),x86353)))
% 22.40/22.31 [8636]E(f319(f319(f94(f913(x86361,a904)),x86362),f31(f913(x86361,a904),x86363)),f181(f913(x86361,a904)))+P1(f319(f319(f321(f913(x86361,a904)),x86362),x86363))+P1(f319(f319(f321(f913(x86361,a904)),f704(x86363,x86362,x86361)),f319(f319(f301(f913(x86361,a904)),x86362),x86363)))
% 22.40/22.31 [8666]E(x86661,x86662)+~E(f319(f182(f907(x86663)),x86661),f319(f182(f907(x86663)),x86662))+P1(f319(f319(f321(f912(x86663,x86663)),f653(x86663,x86661,x86662)),f319(f164(f912(x86663,x86663)),f319(f319(f173(x86663,x86663),x86662),x86661))))
% 22.40/22.31 [8908]E(f299(x89081,x89082),f299(x89081,x89083))+~P1(f319(f319(f225(f913(f912(x89081,x89081),a904)),x89083),f299(x89081,x89082)))+~P1(f319(f319(f225(f913(f912(x89081,x89081),a904)),x89082),x89083))
% 22.40/22.31 [8980]~P54(x89801,f234(f913(x89801,a904)),x89803)+P1(f319(f319(f225(f913(f912(f907(x89801),f907(x89801)),a904)),f149(x89801,x89802)),f150(x89801,x89803)))+~P1(f319(f319(f225(f913(f912(x89801,x89801),a904)),x89802),x89803))
% 22.40/22.31 [9175]P37(x91751,x91752)+~P1(f319(f319(f321(x91751),x91753),f593(x91752,x91751)))+P1(f319(f319(f321(f912(x91751,x91751)),f319(f319(f244(x91751,x91751),f604(x91752,x91751,x91753)),x91753)),x91752))
% 22.40/22.31 [9204]~P1(f319(f55(x92041),x92042))+P1(f319(f55(f913(x92041,a904)),f319(f319(f54(x92041),x92042),x92043)))+~P1(f319(f319(f225(f913(f912(x92041,x92041),a904)),x92043),f319(f319(f246(x92041,x92041),x92042),f319(f18(f913(x92041,a904),x92041),x92042))))
% 22.40/22.31 [9247]P54(x92471,x92472,x92473)+P1(f319(f319(f321(x92471),f535(x92473,x92472,x92471)),x92472))+~P1(f319(f319(f225(f913(f912(x92471,x92471),a904)),x92473),f319(f319(f246(x92471,x92471),x92472),f319(f18(f913(x92471,a904),x92471),x92472))))
% 22.40/22.31 [9248]P54(x92481,x92482,x92483)+P1(f319(f319(f321(x92481),f548(x92482,x92483,x92481)),x92482))+~P1(f319(f319(f225(f913(f912(x92481,x92481),a904)),x92483),f319(f319(f246(x92481,x92481),x92482),f319(f18(f913(x92481,a904),x92481),x92482))))
% 22.40/22.31 [9286]~P75(x92861)+~P1(f319(f319(f226(x92861),x92862),x92863))+P1(f319(f319(f226(x92861),f319(f319(f282(x92861),f319(f319(f74(x92861),x92862),x92863)),f319(f319(f74(x92861),f72(x92861)),f72(x92861)))),x92863))
% 22.40/22.31 [9316]~P74(x93161)+P1(f319(f319(f225(x93161),x93162),x93163))+~P1(f319(f319(f225(x93161),f319(f319(f75(x93161),f362(x93163,x93162,x93161)),x93162)),x93163))
% 22.40/22.31 [9455]E(f319(f182(f907(f907(x94551))),f319(f128(f907(x94551),f319(f319(f10(a906,a904,f907(x94551)),f319(f226(a906),x94552)),f182(f907(x94551)))),f171(x94551,x94553))),f319(f182(f907(x94551)),f319(f319(f156(f907(x94551)),x94553),x94552)))+~P13(a906,f319(f160(a906),f319(f319(f146(f907(x94551),a906),f182(f907(x94551))),x94553)))+~P1(f319(f319(f226(a906),x94552),f319(f182(f907(f907(x94551))),x94553)))
% 22.40/22.31 [9568]~P37(x95681,x95682)+P27(x95681,f319(f319(f244(f913(f912(x95681,x95681),a904),f913(f912(x95681,x95681),a904)),x95682),x95683))+~P1(f319(f319(f225(f913(f912(x95681,x95681),a904)),f319(f319(f281(x95681,x95681,x95681),x95682),x95683)),x95682))
% 22.40/22.31 [9573]E(f319(f319(f146(f907(x95731),x95731),f319(f319(f9(f907(x95731),a906,x95731),f156(x95731)),x95732)),f319(f128(f907(x95731),f319(f319(f10(a906,a904,f907(x95731)),f319(f226(a906),x95732)),f182(f907(x95731)))),f171(x95731,x95733))),f319(f319(f156(f907(x95731)),x95733),x95732))+~P13(a906,f319(f160(a906),f319(f319(f146(f907(x95731),a906),f182(f907(x95731))),x95733)))+~P1(f319(f319(f226(a906),x95732),f319(f182(f907(f907(x95731))),x95733)))
% 22.40/22.31 [9718]P54(x97181,x97182,x97183)+~P1(f319(f319(f321(f912(x97181,x97181)),f319(f319(f244(x97181,x97181),f535(x97183,x97182,x97181)),f535(x97183,x97182,x97181))),x97183))+~P1(f319(f319(f225(f913(f912(x97181,x97181),a904)),x97183),f319(f319(f246(x97181,x97181),x97182),f319(f18(f913(x97181,a904),x97181),x97182))))
% 22.40/22.31 [9719]P54(x97191,x97192,x97193)+~P1(f319(f319(f321(f912(x97191,x97191)),f319(f319(f244(x97191,x97191),f548(x97192,x97193,x97191)),f548(x97192,x97193,x97191))),x97193))+~P1(f319(f319(f225(f913(f912(x97191,x97191),a904)),x97193),f319(f319(f246(x97191,x97191),x97192),f319(f18(f913(x97191,a904),x97191),x97192))))
% 22.40/22.31 [9916]~P141(x99161)+~P123(x99161)+E(f319(f319(f282(x99161),f319(f95(x99161),f319(f319(f66(f912(a1,a1),a1,x99162,f243(a1,a1)),f205(x99162)),x99163))),f319(f95(x99161),f319(f319(f66(f912(a1,a1),a1,x99162,f248(a1,a1)),f205(x99162)),x99163))),f215(x99162,x99161,x99163))
% 22.40/22.31 [10087]~E(x100873,f2(a906))+~E(f319(f182(f907(x100871)),f319(f319(f156(f907(x100871)),x100872),f702(x100873,x100871,x100872))),x100873)+E(f319(f319(f146(a906,f907(x100871)),f319(f319(f9(a906,f907(a906),f907(x100871)),f319(f319(f10(f913(a906,x100871),f913(f907(a906),f907(x100871)),a906),f146(a906,x100871)),f319(f9(a906,a906,x100871),f319(f319(f10(f907(x100871),f913(a906,x100871),a906),f156(x100871)),f319(f156(f907(x100871)),x100872))))),f131(a906,f319(f294(a906,f2(a906)),f319(f182(f907(f907(x100871))),x100872))))),f131(a906,f319(f294(a906,f2(a906)),x100873))),f171(x100871,x100872))
% 22.40/22.31 [10088]E(x100881,f105(f907(x100882)))+~E(f319(f182(f907(x100882)),f319(f319(f156(f907(x100882)),x100881),f702(x100883,x100882,x100881))),x100883)+E(f319(f319(f146(a906,f907(x100882)),f319(f319(f9(a906,f907(a906),f907(x100882)),f319(f319(f10(f913(a906,x100882),f913(f907(a906),f907(x100882)),a906),f146(a906,x100882)),f319(f9(a906,a906,x100882),f319(f319(f10(f907(x100882),f913(a906,x100882),a906),f156(x100882)),f319(f156(f907(x100882)),x100881))))),f131(a906,f319(f294(a906,f2(a906)),f319(f182(f907(f907(x100882))),x100881))))),f131(a906,f319(f294(a906,f2(a906)),x100883))),f171(x100882,x100881))
% 22.40/22.31 [10089]~E(x100893,f2(a906))+E(f319(f319(f146(a906,f907(x100891)),f319(f319(f9(a906,f907(a906),f907(x100891)),f319(f319(f10(f913(a906,x100891),f913(f907(a906),f907(x100891)),a906),f146(a906,x100891)),f319(f9(a906,a906,x100891),f319(f319(f10(f907(x100891),f913(a906,x100891),a906),f156(x100891)),f319(f156(f907(x100891)),x100892))))),f131(a906,f319(f294(a906,f2(a906)),f319(f182(f907(f907(x100891))),x100892))))),f131(a906,f319(f294(a906,f2(a906)),x100893))),f171(x100891,x100892))+P1(f319(f319(f226(a906),f702(x100893,x100891,x100892)),f319(f182(f907(f907(x100891))),x100892)))
% 22.40/22.31 [10090]E(x100901,f105(f907(x100902)))+E(f319(f319(f146(a906,f907(x100902)),f319(f319(f9(a906,f907(a906),f907(x100902)),f319(f319(f10(f913(a906,x100902),f913(f907(a906),f907(x100902)),a906),f146(a906,x100902)),f319(f9(a906,a906,x100902),f319(f319(f10(f907(x100902),f913(a906,x100902),a906),f156(x100902)),f319(f156(f907(x100902)),x100901))))),f131(a906,f319(f294(a906,f2(a906)),f319(f182(f907(f907(x100902))),x100901))))),f131(a906,f319(f294(a906,f2(a906)),x100903))),f171(x100902,x100901))+P1(f319(f319(f226(a906),f702(x100903,x100902,x100901)),f319(f182(f907(f907(x100902))),x100901)))
% 22.40/22.31 [7817]E(f319(f319(f74(a906),f319(f96(a906),x78171)),f319(f319(f74(a906),f319(f96(a906),x78172)),x78173)),f319(f319(f74(a906),f319(f96(a906),f319(f319(f74(a1),x78171),x78172))),x78173))+P1(f319(a186,f319(f96(a1),x78171)))+P1(f319(a186,f319(f96(a1),x78172)))
% 22.40/22.31 [8571]~P1(f319(f55(x85711),x85712))+~P1(f319(f319(f321(x85711),x85713),x85712))+E(f319(a104,f319(f29(x85711),f319(f319(f3(f913(x85711,a904)),x85712),f319(f319(f301(x85711),x85713),f181(f913(x85711,a904)))))),f319(f29(x85711),x85712))
% 22.40/22.31 [8584]~P1(f319(f55(x85841),x85842))+~P1(f319(f319(f321(x85841),x85843),x85842))+E(f319(f319(f74(a906),f72(a906)),f319(f29(x85841),f319(f319(f3(f913(x85841,a904)),x85842),f319(f319(f301(x85841),x85843),f181(f913(x85841,a904)))))),f319(f29(x85841),x85842))
% 22.40/22.31 [8674]~P4(x86741)+~P1(f319(f55(x86741),x86743))+E(f319(f319(f140(x86741,x86741,f7(x86741)),x86742),f131(x86741,f319(f319(f3(f913(x86741,a904)),x86743),f319(f319(f301(x86741),x86742),f181(f913(x86741,a904)))))),f131(x86741,f319(f319(f301(x86741),x86742),x86743)))
% 22.40/22.31 [8833]~P1(f319(f55(x88331),x88333))+~P1(f319(f55(x88331),x88332))+E(f319(f319(f74(a906),f319(f29(x88331),f319(f319(f93(f913(x88331,a904)),x88332),x88333))),f319(f29(x88331),f319(f319(f94(f913(x88331,a904)),x88332),x88333))),f319(f319(f74(a906),f319(f29(x88331),x88332)),f319(f29(x88331),x88333)))
% 22.40/22.31 [10048]~P25(x100481,f913(f913(x100481,a904),a904),f319(f319(f9(x100481,f913(f912(x100481,x100481),a904),f913(f913(x100481,a904),a904)),f319(f319(f10(f913(x100481,a904),f913(f913(f912(x100481,x100481),a904),f913(f913(x100481,a904),a904)),x100481),f54(x100481)),f319(f319(f9(x100481,f913(x100481,a904),f913(x100481,a904)),f301(x100481)),f181(f913(x100481,a904))))),x100483),x100482)+~P1(f319(f55(x100481),x100482))+E(f319(f29(f913(x100481,a904)),f319(f319(f54(x100481),x100482),x100483)),f319(f29(x100481),x100482))
% 22.40/22.31 [10367]~P40(f913(x103671,a904),f913(x103671,a904),x103672)+~P1(f319(f319(f225(f913(x103671,a904)),x103673),f319(x103672,f87(f913(x103671,a904),f319(f319(f9(f913(x103671,a904),f913(x103671,a904),f913(x103671,a904)),f319(f319(f10(f913(x103671,a904),f913(f913(x103671,a904),f913(x103671,a904)),f913(x103671,a904)),f93(f913(x103671,a904))),f319(f319(f9(f913(x103671,a904),f913(x103671,a904),f913(x103671,a904)),f319(f319(f10(f913(x103671,a904),f913(f913(x103671,a904),f913(x103671,a904)),f913(x103671,a904)),f93(f913(x103671,a904))),x103672)),x103673))),f88(f913(x103671,a904),x103672))))))+P1(f319(f319(f225(f913(x103671,a904)),f87(f913(x103671,a904),f319(f319(f9(f913(x103671,a904),f913(x103671,a904),f913(x103671,a904)),f319(f319(f10(f913(x103671,a904),f913(f913(x103671,a904),f913(x103671,a904)),f913(x103671,a904)),f93(f913(x103671,a904))),f319(f319(f9(f913(x103671,a904),f913(x103671,a904),f913(x103671,a904)),f319(f319(f10(f913(x103671,a904),f913(f913(x103671,a904),f913(x103671,a904)),f913(x103671,a904)),f93(f913(x103671,a904))),x103672)),x103673))),f88(f913(x103671,a904),x103672)))),f319(x103672,f87(f913(x103671,a904),f319(f319(f9(f913(x103671,a904),f913(x103671,a904),f913(x103671,a904)),f319(f319(f10(f913(x103671,a904),f913(f913(x103671,a904),f913(x103671,a904)),f913(x103671,a904)),f93(f913(x103671,a904))),f319(f319(f9(f913(x103671,a904),f913(x103671,a904),f913(x103671,a904)),f319(f319(f10(f913(x103671,a904),f913(f913(x103671,a904),f913(x103671,a904)),f913(x103671,a904)),f93(f913(x103671,a904))),x103672)),x103673))),f88(f913(x103671,a904),x103672))))))
% 22.40/22.31 [8222]~P98(x82221)+P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x82223)))+E(f319(f319(f236(x82221),x82222),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x82223)),x82223))),f72(x82221))
% 22.40/22.31 [9561]~P98(x95611)+~P1(f319(f319(f225(a1),f2(a1)),f319(f96(a1),x95613)))+E(f319(f319(f236(x95611),x95612),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x95613)),x95613))),f319(f319(f82(x95611,x95611),f319(f319(f236(x95611),x95612),f319(f96(a906),x95613))),f319(f319(f20(x95611,x95611,x95611),f319(f319(f10(x95611,f913(x95611,x95611),x95611),f75(x95611)),f319(f75(x95611),x95612))),f7(x95611))))
% 22.40/22.31 [9979]~P1(f319(f129(x99791),x99793))+~P1(f319(f319(f321(x99791),x99792),f319(f164(x99791),x99793)))+E(f319(f319(f130(x99791),f319(f182(f907(x99791)),f169(x99791,f319(f319(f10(a904,a904,x99791),a314),f319(f319(f9(x99791,x99791,a904),a316),x99792)),f319(f160(x99791),x99793)))),f319(f160(x99791),x99793)),f319(f319(f143(x99791),x99792),f319(f160(x99791),f169(x99791,f319(f319(f10(a904,a904,x99791),a314),f319(f319(f9(x99791,x99791,a904),a316),x99792)),x99793))))
% 22.40/22.31 [10033]P1(f319(f319(f225(f913(f912(x100331,x100331),a904)),f299(x100331,x100332)),x100333))+~P1(f319(f319(f225(f913(f912(x100331,x100331),a904)),f299(x100331,f181(f913(f912(x100331,x100331),a904)))),x100333))+~P1(f319(f319(f225(f913(f912(x100331,x100331),a904)),f319(f319(f281(x100331,x100331,x100331),f319(f319(f94(f913(f912(x100331,x100331),a904)),f299(x100331,x100332)),x100333)),x100332)),x100333))
% 22.40/22.31 [9888]~P1(f319(f55(x98881),f319(f254(x98881),x98883)))+~P1(f319(f55(x98881),f319(f254(x98881),x98882)))+P1(f319(f55(x98881),f319(f254(x98881),f319(f319(f20(x98881,a904,a904),f319(f319(f10(a904,f913(a904,a904),x98881),a318),x98882)),x98883))))
% 22.40/22.31 [10146]P1(f319(f319(f225(f913(f912(x101461,x101461),a904)),f319(f319(f281(x101461,x101461,x101461),x101462),f299(x101461,x101462))),x101463))+~P1(f319(f319(f225(f913(f912(x101461,x101461),a904)),x101462),x101463))+~P1(f319(f319(f225(f913(f912(x101461,x101461),a904)),f319(f319(f281(x101461,x101461,x101461),f319(f319(f94(f913(f912(x101461,x101461),a904)),f319(f319(f281(x101461,x101461,x101461),x101462),f299(x101461,x101462))),x101463)),x101462)),x101463))
% 22.40/22.31 [10107]~P1(f319(f129(x101071),x101073))+~P1(f319(f319(f321(x101071),x101072),f319(f164(x101071),x101073)))+E(f319(f160(x101071),f319(f163(x101071),f319(f319(f130(x101071),f319(f182(f907(x101071)),f169(x101071,f319(f319(f10(a904,a904,x101071),a314),f319(f319(f9(x101071,x101071,a904),a316),x101072)),x101073))),x101073))),f169(x101071,f319(f319(f10(a904,a904,x101071),a314),f319(f319(f9(x101071,x101071,a904),a316),x101072)),f319(f160(x101071),x101073)))
% 22.40/22.31 [10302]~P113(x103022)+E(x103021,f2(x103022))+~E(f319(f319(f74(x103022),f319(f319(f236(x103022),x103023),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103022),x103021),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f2(x103022))
% 22.40/22.31 [10303]~P113(x103032)+E(x103031,f2(x103032))+~E(f319(f319(f74(x103032),f319(f319(f236(x103032),x103031),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103032),x103033),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f2(x103032))
% 22.40/22.31 [10337]~P113(x103372)+E(x103371,f2(x103372))+P1(f319(f319(f226(x103372),f2(x103372)),f319(f319(f74(x103372),f319(f319(f236(x103372),x103373),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103372),x103371),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))))
% 22.40/22.31 [10338]~P113(x103382)+E(x103381,f2(x103382))+P1(f319(f319(f226(x103382),f2(x103382)),f319(f319(f74(x103382),f319(f319(f236(x103382),x103381),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103382),x103383),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))))
% 22.40/22.31 [10363]~P113(x103631)+P1(f319(f319(f225(x103631),f2(x103631)),x103632))+~P1(f319(f319(f225(x103631),f2(x103631)),f319(f319(f236(x103631),x103632),f319(a104,f319(f319(f75(a906),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),x103633)))))
% 22.40/22.31 [5592]~P14(x55921,x55924,x55923)+P14(x55921,x55922,x55923)+~P14(x55921,x55922,x55924)
% 22.40/22.31 [5059]~E(x50592,f84(x50593,x50591))+P1(f319(x50591,x50592))+~P1(f319(x50591,x50594))
% 22.40/22.31 [5310]E(f62(x53103,x53102,x53104),x53102)+E(x53101,f729(x53102,x53103,x53104))+~P1(f319(x53104,x53101))
% 22.40/22.31 [6625]E(f62(x66251,x66252,x66253),f79(x66251,x66253))+~E(f765(x66252,x66251,x66253,x66254),x66254)+~P1(f319(x66253,x66254))
% 22.40/22.31 [6838]~P37(x68382,x68384)+~P37(x68381,x68383)+P37(f912(x68381,x68382),f312(x68381,x68382,x68383,x68384))
% 22.40/22.31 [6839]~P38(x68392,x68394)+~P38(x68391,x68393)+P38(f912(x68391,x68392),f312(x68391,x68392,x68393,x68394))
% 22.40/22.31 [5249]~P7(x52494,x52491)+~E(f319(x52491,x52492),f319(x52491,x52493))+P1(f319(f319(x52491,x52492),x52493))
% 22.40/22.31 [5407]~P7(x54074,x54071)+E(f319(x54071,x54072),f319(x54071,x54073))+~P1(f319(f319(x54071,x54072),x54073))
% 22.40/22.31 [5408]~P16(x54084,x54081)+E(f319(x54081,x54082),f319(x54081,x54083))+~P1(f319(f319(x54081,x54082),x54083))
% 22.40/22.31 [5500]~P19(x55003,x55004,x55001)+E(f319(x55001,x55002),f319(f57(x55003,x55004),x55002))+~P1(f319(f55(x55003),x55002))
% 22.40/22.31 [5501]~P9(x55013,x55014,x55011)+E(f319(x55011,x55012),f319(f57(x55013,x55014),x55012))+~P1(f319(f55(x55013),x55012))
% 22.40/22.31 [5627]~P7(x56274,x56271)+~P1(f319(f319(x56271,x56273),x56272))+P1(f319(f319(x56271,x56272),x56273))
% 22.40/22.31 [5628]~P52(x56284,x56281)+~P1(f319(f319(x56281,x56283),x56282))+P1(f319(f319(x56281,x56282),x56283))
% 22.40/22.31 [5629]~P16(x56294,x56291)+~P1(f319(f319(x56291,x56293),x56292))+P1(f319(f319(x56291,x56292),x56293))
% 22.40/22.31 [5630]~P16(x56303,x56301)+P1(f319(f319(x56301,x56302),x56302))+~P1(f319(f319(x56301,x56304),x56302))
% 22.40/22.31 [5631]~P16(x56313,x56311)+P1(f319(f319(x56311,x56312),x56312))+~P1(f319(f319(x56311,x56312),x56314))
% 22.40/22.31 [5703]E(x57031,x57032)+~E(f319(f243(x57033,x57034),x57031),f319(f243(x57033,x57034),x57032))+~E(f319(f248(x57033,x57034),x57031),f319(f248(x57033,x57034),x57032))
% 22.40/22.31 [5731]E(x57311,x57312)+~P1(f319(f42(x57313,x57314),x57312))+~P1(f319(f42(x57313,x57314),x57311))
% 22.40/22.31 [5927]~P76(x59272)+E(f224(x59271,x59272,x59273,x59274),f2(x59272))+P1(f319(f55(x59271),x59274))
% 22.40/22.31 [5976]~P7(x59763,x59762)+~P1(f319(x59761,x59764))+P1(f319(x59761,f809(x59761,x59762,x59763)))
% 22.40/22.31 [6067]~P1(f319(f307(x60671,x60672),x60674))+P1(f319(f307(x60671,x60672),x60673))+~P1(f319(f319(x60672,x60673),x60674))
% 22.40/22.31 [6874]~P29(x68741,x68743,x68744)+P1(f319(x68741,x68742))+~P1(f319(f319(f321(a1),x68742),f295(a1,x68743,x68744)))
% 22.40/22.31 [7057]~P7(x70571,x70573)+~P1(f319(x70572,x70574))+P1(f319(f319(f321(x70571),f809(x70572,x70573,x70571)),f262(x70571,x70573)))
% 22.40/22.31 [7929]E(x79291,f2(a906))+~P1(f319(x79292,x79293))+P1(f319(x79292,f759(x79292,x79293,x79291,x79294)))
% 22.40/22.31 [8007]~P4(x80072)+~P1(f319(f129(x80071),x80074))+P1(f319(f129(x80071),f142(x80071,x80072,x80073,x80074)))
% 22.40/22.31 [8048]E(f62(x80481,x80482,x80483),f79(x80481,x80483))+~P1(f319(x80483,x80484))+P1(f319(x80483,f765(x80482,x80481,x80483,x80484)))
% 22.40/22.31 [8228]~P1(f319(f55(x82282),x82284))+~P1(f319(f55(x82281),x82283))+P1(f319(f55(f914(x82281,x82282)),f305(x82281,x82282,x82283,x82284)))
% 22.40/22.31 [8229]~P1(f319(f129(x82292),x82294))+~P1(f319(f129(x82291),x82293))+P1(f319(f129(f912(x82291,x82292)),f53(x82291,x82292,x82293,x82294)))
% 22.40/22.31 [8232]P1(f319(f319(f321(f907(x82321)),f319(f319(f126(x82321),x82322),x82323)),f153(x82321,x82324)))+~P1(f319(f319(f321(f907(x82321)),x82323),f153(x82321,x82324)))+~P1(f319(f319(f321(f907(x82321)),x82322),f153(x82321,x82324)))
% 22.40/22.31 [8506]E(x85061,f2(a906))+P1(f319(x85062,x85063))+~P1(f319(x85062,f761(x85062,x85063,x85061,x85064)))
% 22.40/22.31 [8544]~P4(x85443)+~P1(f319(f129(x85441),f142(x85441,x85443,x85444,x85442)))+P1(f319(f129(x85441),x85442))
% 22.40/22.31 [8822]~P1(f319(f319(f321(f912(x88221,x88221)),f319(f319(f244(x88221,x88221),x88222),x88224)),f299(x88221,x88223)))+P1(f319(f319(f321(x88221),x88222),f308(x88221,x88223)))+~P1(f319(f319(f321(x88221),x88224),f308(x88221,x88223)))
% 22.40/22.31 [5231]~P76(x52312)+E(f319(f319(f8(x52311,x52312),x52313),x52314),f2(x52312))+P1(f319(f55(x52311),x52314))
% 22.40/22.31 [5234]~P82(x52342)+E(f319(f319(f11(x52341,x52342),x52343),x52344),f72(x52342))+P1(f319(f55(x52341),x52344))
% 22.40/22.31 [5371]~P79(x53713)+E(x53711,x53712)+~E(f319(f319(f74(x53713),x53714),x53711),f319(f319(f74(x53713),x53714),x53712))
% 22.40/22.31 [5372]~P80(x53723)+E(x53721,x53722)+~E(f319(f319(f74(x53723),x53724),x53721),f319(f319(f74(x53723),x53724),x53722))
% 22.40/22.31 [5374]~P79(x53743)+E(x53741,x53742)+~E(f319(f319(f74(x53743),x53741),x53744),f319(f319(f74(x53743),x53742),x53744))
% 22.40/22.31 [5495]~P5(x54953)+E(x54951,f181(f913(x54952,a904)))+E(f319(f319(f33(x54952,x54953),x54951),f319(f18(x54953,x54952),x54954)),x54954)
% 22.40/22.31 [5496]~P5(x54963)+E(x54961,f181(f913(x54962,a904)))+E(f319(f319(f34(x54962,x54963),x54961),f319(f18(x54963,x54962),x54964)),x54964)
% 22.40/22.31 [5717]~P111(x57173)+E(x57171,x57172)+~E(f295(x57173,x57174,x57171),f319(f319(f301(x57173),x57172),f181(f913(x57173,a904))))
% 22.40/22.31 [5718]~P111(x57183)+E(x57181,x57182)+~E(f295(x57183,x57181,x57182),f319(f319(f301(x57183),x57184),f181(f913(x57183,a904))))
% 22.40/22.31 [5779]~P35(x57793,x57791,x57794)+P35(x57793,x57791,f319(f319(f143(x57793),x57792),x57794))+P1(f319(x57791,x57792))
% 22.40/22.31 [5881]~P31(x58811,x58812,x58814)+~P1(f319(x58812,x58813))+P31(x58811,x58812,f319(f319(f143(x58811),x58813),x58814))
% 22.40/22.31 [6024]P1(f319(x60241,x60242))+~P1(f319(f240(x60243,x60241),x60244))+~P1(f319(f319(f321(x60243),x60242),x60244))
% 22.40/22.31 [6033]~P31(x60331,x60332,x60334)+~P31(x60331,x60332,x60333)+P31(x60331,x60332,f319(f319(f126(x60331),x60333),x60334))
% 22.40/22.31 [6046]P33(x60461,x60462,x60463)+~P33(x60461,x60462,f319(f319(f143(x60461),x60464),x60463))+P1(f319(x60462,x60464))
% 22.40/22.31 [6047]P35(x60471,x60472,x60473)+~P35(x60471,x60472,f319(f319(f143(x60471),x60474),x60473))+P1(f319(x60472,x60474))
% 22.40/22.31 [6121]P33(x61211,x61212,x61213)+P33(x61211,x61212,x61214)+~P33(x61211,x61212,f319(f319(f126(x61211),x61214),x61213))
% 22.40/22.31 [6141]~P76(x61411)+E(f319(f319(f8(a906,x61411),x61412),f319(f294(a906,x61413),f319(a104,x61414))),f2(x61411))+~P1(f319(f319(f226(a906),x61414),x61413))
% 22.40/22.31 [6146]~P70(x61461)+~E(f39(x61461,x61462,x61463),f39(x61461,x61464,x61463))+E(f39(x61461,f319(f73(x61461),x61462),x61463),f39(x61461,f319(f73(x61461),x61464),x61463))
% 22.40/22.31 [6212]P1(f319(x62121,x62122))+~E(f319(f128(x62123,x62121),x62124),x62124)+~P1(f319(f319(f321(x62123),x62122),f319(f164(x62123),x62124)))
% 22.40/22.31 [6232]~E(f319(f319(f74(a906),x62323),x62322),f319(f319(f74(a906),x62321),x62324))+~P1(f319(f319(f226(a906),x62323),x62324))+P1(f319(f319(f226(a906),x62321),x62322))
% 22.40/22.31 [6238]P33(x62381,x62382,x62383)+~P1(f319(x62382,x62384))+~P1(f319(f319(f321(x62381),x62384),f319(f164(x62381),x62383)))
% 22.40/22.31 [6241]~P69(x62411)+E(f39(x62411,f39(x62411,x62412,x62413),x62414),f39(x62411,x62412,x62414))+~P1(f319(f319(f279(x62411),x62414),x62413))
% 22.40/22.31 [6282]~P31(x62823,x62821,x62824)+P1(f319(x62821,x62822))+~P1(f319(f319(f321(x62823),x62822),f319(f164(x62823),x62824)))
% 22.40/22.31 [6284]~E(f319(f128(x62841,x62842),x62843),f105(x62841))+~P1(f319(x62842,x62844))+~P1(f319(f319(f321(x62841),x62844),f319(f164(x62841),x62843)))
% 22.40/22.31 [6285]~E(f169(x62853,x62851,x62854),x62854)+P1(f319(x62851,x62852))+~P1(f319(f319(f321(x62853),x62852),f319(f164(x62853),x62854)))
% 22.40/22.31 [6308]~E(x63084,f181(f913(x63082,a904)))+~E(x63083,f181(f913(x63081,a904)))+E(f305(x63081,x63082,x63083,x63084),f181(f913(f914(x63081,x63082),a904)))
% 22.40/22.31 [6454]P1(f319(x64541,x64542))+~P1(f319(f152(x64543,x64541),x64544))+~P1(f319(f319(f321(x64543),x64542),f319(f164(x64543),x64544)))
% 22.40/22.31 [6594]~P30(x65941,x65943,x65944)+P1(f319(x65941,x65942))+~P1(f319(f319(f321(a906),x65942),f319(f294(a906,x65943),x65944)))
% 22.40/22.31 [6730]~P76(x67301)+E(f319(f319(f8(a906,x67301),x67302),f295(a906,x67303,f319(a104,x67304))),f2(x67301))+~P1(f319(f319(f226(a906),f319(a104,x67304)),x67303))
% 22.40/22.31 [6877]~P4(x68771)+E(f319(f319(f3(f913(x68771,a904)),f319(f294(x68771,x68772),x68773)),f319(f294(x68771,x68772),x68774)),f319(f294(x68771,x68774),x68773))+~P1(f319(f319(f225(x68771),x68772),x68774))
% 22.40/22.31 [6941]~E(x69413,x69414)+E(x69411,f2(a906))+P1(f319(f319(f321(x69412),x69413),f319(f164(x69412),f161(x69412,x69411,x69414))))
% 22.40/22.31 [7220]~P1(f319(f319(f321(f907(x72201)),x72204),f153(x72201,x72203)))+P1(f319(f319(f321(x72201),x72202),x72203))+~P1(f319(f319(f321(x72201),x72202),f319(f164(x72201),x72204)))
% 22.40/22.31 [7227]~P37(x72271,x72272)+P1(f319(f319(f321(x72271),f594(x72272,x72271,x72273)),x72273))+~P1(f319(f319(f321(x72271),x72274),x72273))
% 22.40/22.31 [7282]~P76(x72821)+E(f319(f319(f319(f59(x72821,x72822,f74(x72821)),x72823),f2(x72821)),x72824),f319(f319(f8(x72822,x72821),x72823),x72824))+~P1(f319(f55(x72822),x72824))
% 22.40/22.31 [7284]~P82(x72841)+E(f319(f319(f319(f59(x72841,x72842,f75(x72841)),x72843),f72(x72841)),x72844),f319(f319(f11(x72842,x72841),x72843),x72844))+~P1(f319(f55(x72842),x72844))
% 22.40/22.31 [7312]P25(x73121,x73122,x73123,x73124)+~E(f319(f29(x73122),f319(f302(x73121,x73122,x73123),x73124)),f319(f29(x73121),x73124))+~P1(f319(f55(x73121),x73124))
% 22.40/22.31 [7495]~P76(x74951)+E(f319(f319(f74(x74951),f319(x74952,x74953)),f319(f319(f8(a906,x74951),x74952),f297(a906,x74953,x74954))),f319(f319(f8(a906,x74951),x74952),f295(a906,x74953,x74954)))+~P1(f319(f319(f225(a906),x74953),x74954))
% 22.40/22.31 [7504]~P76(x75041)+~P25(x75042,x75041,x75043,x75044)+E(f319(f319(f8(x75041,x75041),f25(x75041)),f319(f302(x75042,x75041,x75043),x75044)),f319(f319(f8(x75042,x75041),x75043),x75044))
% 22.40/22.31 [7505]~P82(x75051)+~P25(x75052,x75051,x75053,x75054)+E(f319(f319(f11(x75051,x75051),f25(x75051)),f319(f302(x75052,x75051,x75053),x75054)),f319(f319(f11(x75052,x75051),x75053),x75054))
% 22.40/22.31 [7554]E(f319(f29(f914(x75541,x75542)),f305(x75541,x75542,x75543,x75544)),f319(f319(f74(a906),f319(f29(x75541),x75543)),f319(f29(x75542),x75544)))+~P1(f319(f55(x75542),x75544))+~P1(f319(f55(x75541),x75543))
% 22.40/22.31 [7634]E(x76341,x76342)+P1(f319(f319(f321(x76343),x76341),f319(f164(x76343),f162(x76343,x76342,x76344))))+~P1(f319(f319(f321(x76343),x76341),f319(f164(x76343),x76344)))
% 22.40/22.31 [7772]~P1(f319(f319(f225(f913(x77721,a904)),x77724),f319(x77723,x77724)))+~P1(f319(f319(f321(x77721),x77722),x77724))+P1(f319(f319(f321(x77721),x77722),f88(f913(x77721,a904),x77723)))
% 22.40/22.31 [7856]~P76(x78561)+E(f319(f319(f74(x78561),f319(f319(f8(a906,x78561),x78562),f319(f294(a906,x78563),x78564))),f319(x78562,x78564)),f319(f319(f8(a906,x78561),x78562),f319(f294(a906,x78563),f319(a104,x78564))))+P1(f319(f319(f226(a906),x78564),x78563))
% 22.40/22.31 [7909]~P25(x79091,x79092,x79093,f234(f913(x79091,a904)))+~P1(f319(f55(x79092),x79094))+P1(f319(f55(x79091),f319(f303(x79091,x79092,x79093),x79094)))
% 22.40/22.31 [8022]P1(f319(f319(f321(f907(x80221)),f319(f319(f143(x80221),x80222),x80223)),f153(x80221,x80224)))+~P1(f319(f319(f321(f907(x80221)),x80223),f153(x80221,x80224)))+~P1(f319(f319(f321(x80221),x80222),x80224))
% 22.40/22.31 [8103]~E(f319(f302(x81033,x81031,x81034),f234(f913(x81033,a904))),f234(f913(x81031,a904)))+P1(f319(f55(x81031),x81032))+~P1(f319(f55(x81033),f319(f303(x81033,x81031,x81034),x81032)))
% 22.40/22.31 [8199]~P25(x81991,x81993,x81994,x81992)+P1(f319(f55(x81991),x81992))+~P1(f319(f55(x81993),f319(f302(x81991,x81993,x81994),x81992)))
% 22.40/22.31 [8221]~E(x82212,x82213)+P1(f319(f319(f321(f912(x82211,x82211)),f319(f319(f244(x82211,x82211),x82212),x82213)),f255(x82211,x82214)))+~P1(f319(f319(f321(x82211),x82212),x82214))
% 22.40/22.31 [8256]~P76(x82561)+E(f319(f319(f74(x82561),f319(f319(f8(a906,x82561),x82562),f295(a906,x82563,x82564))),f319(x82562,f319(a104,x82564))),f319(f319(f8(a906,x82561),x82562),f295(a906,x82563,f319(a104,x82564))))+P1(f319(f319(f226(a906),f319(a104,x82564)),x82563))
% 22.40/22.31 [8315]P1(f319(x83151,x83152))+~P1(f319(x83151,f319(f319(f156(x83153),x83154),f652(x83151,x83154,x83153))))+~P1(f319(f319(f321(x83153),x83152),f319(f164(x83153),x83154)))
% 22.40/22.31 [8452]~P1(f319(f319(f321(x84521),x84522),f308(x84521,x84524)))+P1(f319(f319(f321(f907(x84521)),f319(f319(f143(x84521),x84522),x84523)),f308(f907(x84521),f149(x84521,x84524))))+~P1(f319(f319(f321(f907(x84521)),x84523),f308(f907(x84521),f149(x84521,x84524))))
% 22.40/22.31 [8467]~P25(x84672,x84673,x84674,f868(x84674,x84673,x84672,x84671))+P25(x84672,x84673,x84674,f32(f913(x84672,a904),x84671))+E(x84671,f181(f913(f913(x84672,a904),a904)))
% 22.40/22.31 [8738]E(x87381,x87382)+~P1(f319(f319(f321(f912(x87383,x87383)),f319(f319(f244(x87383,x87383),x87381),x87382)),f299(x87383,x87384)))+P1(f319(f319(f321(x87383),x87381),f319(f256(x87383,x87383),x87384)))
% 22.40/22.31 [9020]E(x90201,f2(a906))+P1(f319(x90202,x90203))+P1(f319(f319(f321(x90204),f761(x90202,x90203,x90201,x90204)),f319(f164(x90204),f161(x90204,x90201,x90203))))
% 22.40/22.31 [9032]E(x90321,f2(a906))+~P1(f319(x90323,x90324))+P1(f319(f319(f321(x90322),f759(x90323,x90324,x90321,x90322)),f319(f164(x90322),f161(x90322,x90321,x90324))))
% 22.40/22.31 [9034]~P26(x90341,x90342,x90343,f234(f913(x90341,a904)),f234(f913(x90342,a904)))+~P1(f319(f55(x90342),x90344))+P1(f319(f55(x90341),f319(f303(x90341,x90342,x90343),x90344)))
% 22.40/22.31 [9036]P25(x90362,x90363,x90364,f32(f913(x90362,a904),x90361))+E(x90361,f181(f913(f913(x90362,a904),a904)))+P1(f319(f319(f321(f913(x90362,a904)),f868(x90364,x90363,x90362,x90361)),x90361))
% 22.40/22.31 [9152]~P26(x91523,x91521,x91524,f234(f913(x91523,a904)),f234(f913(x91521,a904)))+P1(f319(f55(x91521),x91522))+~P1(f319(f55(x91523),f319(f303(x91523,x91521,x91524),x91522)))
% 22.40/22.31 [9165]P1(f319(f55(x91651),x91652))+~P1(f319(f55(x91654),f319(f302(x91651,x91654,x91653),x91652)))+P1(f319(f319(f321(x91651),f569(x91653,x91654,x91652,x91651)),x91652))
% 22.40/22.31 [9260]~P5(x92602)+E(f319(f319(f58(x92601,x92602,f319(f319(f10(x92602,f913(x92602,x92602),x92601),f93(x92602)),x92603)),f181(x92602)),x92604),f319(f319(f33(x92601,x92602),x92604),x92603))+~P1(f319(f55(x92601),x92604))
% 22.40/22.31 [9261]~P5(x92612)+E(f319(f319(f58(x92611,x92612,f319(f319(f10(x92612,f913(x92612,x92612),x92611),f94(x92612)),x92613)),f234(x92612)),x92614),f319(f319(f34(x92611,x92612),x92614),x92613))+~P1(f319(f55(x92611),x92614))
% 22.40/22.31 [9305]~P1(f319(f319(f279(a906),x93052),x93054))+~P1(f319(f319(f279(a906),x93053),x93051))+P1(f319(f319(f225(f913(a906,a904)),f288(a906,f279(a906),x93051,x93052)),f288(a906,f279(a906),x93053,x93054)))
% 22.40/22.31 [9345]P1(f319(x93451,x93452))+~P1(f319(x93451,f319(f319(f156(x93453),x93454),f689(x93452,x93451,x93454,x93453))))+~P1(f319(f319(f321(x93453),x93452),f319(f164(x93453),x93454)))
% 22.40/22.31 [9367]E(x93671,x93672)+~P1(f319(f319(f321(f912(x93673,x93673)),f319(f319(f244(x93673,x93673),x93671),x93672)),f299(x93673,x93674)))+P1(f319(f319(f321(f912(x93673,x93673)),f319(f319(f244(x93673,x93673),x93671),x93672)),f319(f319(f281(x93673,x93673,x93673),x93674),f299(x93673,x93674))))
% 22.40/22.31 [9425]~E(f319(f182(f907(x94251)),x94252),f319(f182(f907(x94251)),x94253))+~P1(f319(f319(f321(f912(f907(x94251),f907(x94251))),f319(f319(f244(f907(x94251),f907(x94251)),x94252),x94253)),f139(x94251,x94254)))+P1(f319(f319(f321(f912(f907(x94251),f907(x94251))),f319(f319(f244(f907(x94251),f907(x94251)),x94252),x94253)),f137(x94251,x94254)))
% 22.40/22.31 [9540]P1(f319(f319(f279(a906),x95401),x95402))+~P1(f319(f319(f279(a906),x95403),x95401))+~P1(f319(f319(f225(f913(a906,a904)),f288(a906,f279(a906),x95403,x95401)),f288(a906,f279(a906),x95404,x95402)))
% 22.40/22.31 [9541]P1(f319(f319(f279(a906),x95411),x95412))+~P1(f319(f319(f279(a906),x95412),x95413))+~P1(f319(f319(f225(f913(a906,a904)),f288(a906,f279(a906),x95412,x95413)),f288(a906,f279(a906),x95411,x95414)))
% 22.40/22.31 [9667]P31(x96671,f319(f319(f20(x96671,a904,a904),f319(f319(f10(a904,f913(a904,a904),x96671),a318),f319(f319(f10(a904,a904,x96671),a314),x96672))),f319(a316,x96673)),x96674)+~P1(f319(x96672,x96673))+~P35(x96671,x96672,f319(f319(f143(x96671),x96673),x96674))
% 22.40/22.31 [9846]~P31(x98461,f319(f319(f20(x98461,a904,a904),f319(f319(f10(a904,f913(a904,a904),x98461),a318),f319(f319(f10(a904,a904,x98461),a314),x98462))),f319(a316,x98463)),x98464)+~P1(f319(x98462,x98463))+P35(x98461,x98462,f319(f319(f143(x98461),x98463),x98464))
% 22.40/22.31 [9850]~P35(x98501,x98502,x98504)+~P31(x98501,f319(f319(f20(x98501,a904,a904),f319(f319(f10(a904,f913(a904,a904),x98501),a318),f319(f319(f10(a904,a904,x98501),a314),x98502))),f319(a316,x98503)),x98504)+P35(x98501,x98502,f319(f319(f143(x98501),x98503),x98504))
% 22.40/22.31 [9889]~P67(x98891)+E(f319(f319(f8(a906,x98891),f319(f319(f20(a906,x98891,x98891),f319(f319(f10(x98891,f913(x98891,x98891),a906),f3(x98891)),x98892)),f319(f319(f10(a906,x98891,a906),x98892),f319(f319(f9(a906,a906,a906),f74(a906)),f72(a906))))),f295(a906,x98893,x98894)),f2(x98891))+P1(f319(f319(f225(a906),x98893),x98894))
% 22.40/22.31 [10102]~P37(x101022,x101024)+~P25(x101022,x101021,x101023,f234(f913(x101022,a904)))+P37(x101021,f319(f302(f912(x101022,x101022),f912(x101021,x101021),f250(x101022,x101021,x101022,x101021,x101023,x101023)),x101024))
% 22.40/22.31 [10315]~E(f319(f182(f907(x103151)),x103153),f319(f182(f907(x103151)),x103152))+P1(f319(f319(f321(f912(f907(x103151),f907(x103151))),f319(f319(f244(f907(x103151),f907(x103151)),x103152),x103153)),f150(x103151,x103154)))+~P1(f319(f319(f249(x103151,x103151,a904),f319(f319(f9(x103151,f913(f912(x103151,x103151),a904),f913(x103151,a904)),f319(f319(f10(f913(x103151,f913(f913(f912(x103151,x103151),a904),a904)),f913(f913(f912(x103151,x103151),a904),f913(x103151,a904)),x103151),f9(x103151,f913(f912(x103151,x103151),a904),a904)),f319(f319(f10(f913(x103151,f912(x103151,x103151)),f913(x103151,f913(f913(f912(x103151,x103151),a904),a904)),x103151),f319(f10(f912(x103151,x103151),f913(f913(f912(x103151,x103151),a904),a904),x103151),f321(f912(x103151,x103151)))),f244(x103151,x103151)))),x103154)),f654(x103154,x103153,x103152,x103151)))
% 22.40/22.31 [6193]~P69(x61931)+~E(x61932,f2(x61931))+E(f319(f319(f30(x61931),f319(f319(f75(x61931),x61932),x61933)),f319(f319(f75(x61931),x61932),x61934)),f2(x61931))
% 22.40/22.31 [6235]E(x62351,f105(x62352))+E(x62353,f319(f319(f3(a906),f319(f182(f907(x62352)),x62351)),f72(a906)))+E(f136(x62352,f319(f319(f151(x62352,x62351),x62353),x62354)),f136(x62352,x62351))
% 22.40/22.31 [6273]E(x62731,x62732)+P1(f319(x62733,x62732))+~P1(f319(f319(f319(f301(x62734),x62731),x62733),x62732))
% 22.40/22.31 [6289]~P76(x62891)+~P1(f319(f129(x62892),x62894))+E(f319(f157(x62891),f319(f319(f146(x62892,x62891),x62893),x62894)),f319(f319(f8(x62892,x62891),x62893),f319(f164(x62892),x62894)))
% 22.40/22.31 [6301]~P82(x63012)+~P1(f319(f55(x63011),x63014))+E(f319(f319(f11(x63011,x63012),f319(f18(x63012,x63011),x63013)),x63014),f319(f319(f236(x63012),x63013),f319(f29(x63011),x63014)))
% 22.40/22.31 [6355]~P72(x63552)+E(x63551,f2(x63552))+E(f319(f319(f282(x63552),f319(f319(f75(x63552),x63553),x63551)),f319(f319(f75(x63552),x63554),x63551)),f319(f319(f282(x63552),x63553),x63554))
% 22.40/22.31 [6356]~P72(x63562)+E(x63561,f2(x63562))+E(f319(f319(f282(x63562),f319(f319(f75(x63562),x63561),x63563)),f319(f319(f75(x63562),x63561),x63564)),f319(f319(f282(x63562),x63563),x63564))
% 22.40/22.31 [6357]~P69(x63572)+E(x63571,f2(x63572))+E(f319(f319(f30(x63572),f319(f319(f75(x63572),x63573),x63571)),f319(f319(f75(x63572),x63574),x63571)),f319(f319(f30(x63572),x63573),x63574))
% 22.40/22.31 [6359]~P69(x63592)+E(x63591,f2(x63592))+E(f319(f319(f30(x63592),f319(f319(f75(x63592),x63591),x63593)),f319(f319(f75(x63592),x63591),x63594)),f319(f319(f30(x63592),x63593),x63594))
% 22.40/22.31 [6424]P1(f319(x64241,x64242))+~E(x64243,f319(f319(f74(a906),x64244),x64242))+~P1(f319(x64241,f319(f319(f3(a906),x64243),x64244)))
% 22.40/22.31 [6511]~P1(f319(x65112,x65113))+~P1(f319(f152(x65111,x65112),x65114))+P1(f319(f152(x65111,x65112),f319(f319(f143(x65111),x65113),x65114)))
% 22.40/22.31 [6552]E(x65521,f105(x65522))+~E(x65523,f319(f319(f3(a906),f319(f182(f907(x65522)),x65521)),f72(a906)))+E(f136(x65522,f319(f319(f151(x65522,x65521),x65523),x65524)),x65524)
% 22.40/22.31 [6574]~P106(x65741)+~P1(f319(f319(f225(x65741),x65742),x65744))+P1(f319(f319(f225(x65741),x65742),f319(f319(f93(x65741),x65743),x65744)))
% 22.40/22.31 [6575]~P106(x65751)+~P1(f319(f319(f225(x65751),x65752),x65753))+P1(f319(f319(f225(x65751),x65752),f319(f319(f93(x65751),x65753),x65754)))
% 22.40/22.31 [6577]~P4(x65771)+~P1(f319(f319(f225(x65771),x65772),x65774))+P1(f319(f319(f225(x65771),x65772),f319(f319(f180(x65771),x65773),x65774)))
% 22.40/22.31 [6579]~P4(x65791)+~P1(f319(f319(f225(x65791),x65792),x65793))+P1(f319(f319(f225(x65791),x65792),f319(f319(f180(x65791),x65793),x65794)))
% 22.40/22.31 [6580]~P106(x65801)+~P1(f319(f319(f226(x65801),x65802),x65804))+P1(f319(f319(f226(x65801),x65802),f319(f319(f93(x65801),x65803),x65804)))
% 22.40/22.31 [6581]~P106(x65811)+~P1(f319(f319(f226(x65811),x65812),x65813))+P1(f319(f319(f226(x65811),x65812),f319(f319(f93(x65811),x65813),x65814)))
% 22.40/22.31 [6583]~P4(x65831)+~P1(f319(f319(f226(x65831),x65832),x65834))+P1(f319(f319(f226(x65831),x65832),f319(f319(f180(x65831),x65833),x65834)))
% 22.40/22.31 [6585]~P4(x65851)+~P1(f319(f319(f226(x65851),x65852),x65853))+P1(f319(f319(f226(x65851),x65852),f319(f319(f180(x65851),x65853),x65854)))
% 22.40/22.31 [6673]~E(f319(f319(f156(x66731),x66732),x66733),x66734)+E(f319(f319(f151(x66731,x66732),x66733),x66734),x66732)+~P1(f319(f319(f226(a906),x66733),f319(f182(f907(x66731)),x66732)))
% 22.40/22.31 [6716]P1(f319(x67161,x67162))+~P1(f319(x67163,x67162))+~P1(f319(f319(f225(f913(x67164,a904)),x67163),x67161))
% 22.40/22.31 [6749]~E(f319(f319(f151(x67491,x67492),x67493),x67494),x67492)+E(f319(f319(f156(x67491),x67492),x67493),x67494)+~P1(f319(f319(f226(a906),x67493),f319(f182(f907(x67491)),x67492)))
% 22.40/22.31 [6763]~P1(f319(f152(x67631,x67632),x67634))+~P1(f319(f152(x67631,x67632),x67633))+P1(f319(f152(x67631,x67632),f319(f319(f126(x67631),x67633),x67634)))
% 22.40/22.31 [6873]E(x68731,f181(f913(x68732,a904)))+E(x68733,f181(f913(x68734,a904)))+~E(f319(f319(f246(x68734,x68732),x68733),f319(f18(f913(x68732,a904),x68734),x68731)),f181(f913(f912(x68734,x68732),a904)))
% 22.40/22.31 [6888]E(x68881,x68882)+P1(f319(f319(f321(x68883),x68881),x68884))+~P1(f319(f319(f321(x68883),x68881),f319(f319(f301(x68883),x68882),x68884)))
% 22.40/22.31 [6905]~P4(x69051)+P1(f319(f319(f225(x69051),x69052),x69053))+~P1(f319(f319(f225(x69051),x69052),f319(f319(f230(x69051),x69054),x69053)))
% 22.40/22.31 [6907]~P4(x69071)+P1(f319(f319(f225(x69071),x69072),x69073))+~P1(f319(f319(f225(x69071),x69072),f319(f319(f230(x69071),x69073),x69074)))
% 22.40/22.31 [6909]~P107(x69091)+P1(f319(f319(f225(x69091),x69092),x69093))+~P1(f319(f319(f225(x69091),x69092),f319(f319(f94(x69091),x69094),x69093)))
% 22.40/22.31 [6911]~P107(x69111)+P1(f319(f319(f225(x69111),x69112),x69113))+~P1(f319(f319(f225(x69111),x69112),f319(f319(f94(x69111),x69113),x69114)))
% 22.40/22.31 [6912]~P4(x69121)+P1(f319(f319(f226(x69121),x69122),x69123))+~P1(f319(f319(f226(x69121),x69122),f319(f319(f230(x69121),x69124),x69123)))
% 22.40/22.31 [6913]~P4(x69131)+P1(f319(f319(f226(x69131),x69132),x69133))+~P1(f319(f319(f226(x69131),x69132),f319(f319(f230(x69131),x69133),x69134)))
% 22.40/22.31 [6933]~E(f319(f319(f156(x69331),x69333),x69334),x69332)+P1(f319(f319(f321(x69331),x69332),f319(f164(x69331),x69333)))+~P1(f319(f319(f226(a906),x69334),f319(f182(f907(x69331)),x69333)))
% 22.40/22.31 [6942]~P4(x69421)+~P13(x69421,f319(f319(f143(x69421),x69422),f319(f319(f143(x69421),x69423),x69424)))+P1(f319(f319(f225(x69421),x69422),x69423))
% 22.40/22.31 [7087]~P31(x70872,x70871,x70873)+P1(f319(x70871,f319(f319(f156(x70872),x70873),x70874)))+~P1(f319(f319(f226(a906),x70874),f319(f182(f907(x70872)),x70873)))
% 22.40/22.31 [7105]E(x71051,f2(a1))+E(f319(f319(f30(a1),x71052),x71051),x71053)+~P1(f319(f43(x71052,x71051),f319(f319(f244(a1,a1),x71053),x71054)))
% 22.40/22.31 [7127]E(f39(a1,x71272,x71271),x71273)+E(x71271,f2(a1))+~P1(f319(f43(x71272,x71271),f319(f319(f244(a1,a1),x71274),x71273)))
% 22.40/22.31 [7244]P1(f319(f319(f321(x72441),x72442),x72443))+~P1(f319(f319(f321(x72441),x72442),x72444))+~P1(f319(f319(f226(f913(x72441,a904)),x72444),x72443))
% 22.40/22.31 [7245]P1(f319(f319(f321(x72451),x72452),x72453))+~P1(f319(f319(f321(x72451),x72452),x72454))+~P1(f319(f319(f225(f913(x72451,a904)),x72454),x72453))
% 22.40/22.31 [7356]P33(x73561,x73562,x73563)+~P1(f319(x73562,f319(f319(f156(x73561),x73563),x73564)))+~P1(f319(f319(f226(a906),x73564),f319(f182(f907(x73561)),x73563)))
% 22.40/22.31 [7461]~P3(x74612)+~P1(f319(f319(f226(f913(x74611,x74612)),x74613),x74614))+P1(f319(f319(f225(f913(x74611,x74612)),x74613),x74614))
% 22.40/22.31 [7543]~P14(x75431,x75432,x75434)+P14(x75431,x75432,f319(f319(f301(f905(x75431)),x75433),x75434))+~P14(x75431,x75432,f319(f319(f301(f905(x75431)),x75433),f181(f913(f905(x75431),a904))))
% 22.40/22.31 [7585]~P1(f319(f319(f321(x75851),x75852),x75854))+P1(f319(f319(f321(x75851),x75852),f31(f913(x75851,a904),x75853)))+~P1(f319(f319(f321(f913(x75851,a904)),x75854),x75853))
% 22.40/22.31 [7587]~P119(x75871)+~P1(f319(f319(f225(a906),x75873),x75874))+P1(f319(f319(f279(x75871),f319(f319(f236(x75871),x75872),x75873)),f319(f319(f236(x75871),x75872),x75874)))
% 22.40/22.31 [7613]~P90(x76131)+~P1(f319(f319(f225(x76131),x76133),x76134))+P1(f319(f319(f225(x76131),f319(f319(f74(x76131),x76132),x76133)),f319(f319(f74(x76131),x76132),x76134)))
% 22.40/22.31 [7614]~P91(x76141)+~P1(f319(f319(f225(x76141),x76143),x76144))+P1(f319(f319(f225(x76141),f319(f319(f74(x76141),x76142),x76143)),f319(f319(f74(x76141),x76142),x76144)))
% 22.40/22.31 [7615]~P90(x76151)+~P1(f319(f319(f225(x76151),x76152),x76154))+P1(f319(f319(f225(x76151),f319(f319(f74(x76151),x76152),x76153)),f319(f319(f74(x76151),x76154),x76153)))
% 22.40/22.31 [7616]~P91(x76161)+~P1(f319(f319(f225(x76161),x76162),x76164))+P1(f319(f319(f225(x76161),f319(f319(f74(x76161),x76162),x76163)),f319(f319(f74(x76161),x76164),x76163)))
% 22.40/22.31 [7617]~P89(x76171)+~P1(f319(f319(f226(x76171),x76173),x76174))+P1(f319(f319(f226(x76171),f319(f319(f74(x76171),x76172),x76173)),f319(f319(f74(x76171),x76172),x76174)))
% 22.40/22.31 [7618]~P90(x76181)+~P1(f319(f319(f226(x76181),x76183),x76184))+P1(f319(f319(f226(x76181),f319(f319(f74(x76181),x76182),x76183)),f319(f319(f74(x76181),x76182),x76184)))
% 22.40/22.31 [7619]~P89(x76191)+~P1(f319(f319(f226(x76191),x76192),x76194))+P1(f319(f319(f226(x76191),f319(f319(f74(x76191),x76192),x76193)),f319(f319(f74(x76191),x76194),x76193)))
% 22.40/22.31 [7620]~P90(x76201)+~P1(f319(f319(f226(x76201),x76202),x76204))+P1(f319(f319(f226(x76201),f319(f319(f74(x76201),x76202),x76203)),f319(f319(f74(x76201),x76204),x76203)))
% 22.40/22.31 [7621]~P119(x76211)+~P1(f319(f319(f279(x76211),x76212),x76214))+P1(f319(f319(f279(x76211),f319(f319(f236(x76211),x76212),x76213)),f319(f319(f236(x76211),x76214),x76213)))
% 22.40/22.31 [7628]~P124(x76281)+~P99(x76281)+E(f319(f319(f3(x76281),f319(f319(f75(x76281),x76282),f319(f96(x76281),x76283))),f319(f319(f75(x76281),x76284),f319(f96(x76281),x76283))),f319(f319(f75(x76281),f319(f319(f3(x76281),x76282),x76284)),f319(f96(x76281),x76283)))
% 22.40/22.31 [7629]~P139(x76291)+~P99(x76291)+E(f319(f319(f74(x76291),f319(f319(f75(x76291),x76292),f319(f96(x76291),x76293))),f319(f319(f75(x76291),x76294),f319(f96(x76291),x76293))),f319(f319(f75(x76291),f319(f319(f74(x76291),x76292),x76294)),f319(f96(x76291),x76293)))
% 22.40/22.31 [7665]~P76(x76651)+E(f319(f319(f74(x76651),f319(x76652,x76653)),f319(f319(f8(a906,x76651),x76652),f295(a906,f319(a104,x76653),x76654))),f319(f319(f8(a906,x76651),x76652),f295(a906,x76653,x76654)))+~P1(f319(f319(f225(a906),x76653),x76654))
% 22.40/22.31 [7676]~P25(x76762,x76761,x76763,f319(f164(x76762),x76764))+~P1(f319(f129(x76762),x76764))+P1(f319(f129(x76761),f319(f319(f146(x76762,x76761),x76763),x76764)))
% 22.40/22.31 [7721]~P1(f319(f319(f225(a906),x77212),x77214))+~P1(f319(f319(f225(a906),x77211),x77213))+P1(f319(f319(f225(a906),f319(f319(f74(a906),x77211),x77212)),f319(f319(f74(a906),x77213),x77214)))
% 22.40/22.31 [7722]~P1(f319(f319(f225(a906),x77222),x77224))+~P1(f319(f319(f225(a906),x77221),x77223))+P1(f319(f319(f225(a906),f319(f319(f75(a906),x77221),x77222)),f319(f319(f75(a906),x77223),x77224)))
% 22.40/22.31 [7725]~P1(f319(f319(f226(a906),x77252),x77254))+~P1(f319(f319(f226(a906),x77251),x77253))+P1(f319(f319(f226(a906),f319(f319(f74(a906),x77251),x77252)),f319(f319(f74(a906),x77253),x77254)))
% 22.40/22.31 [7726]~P1(f319(f319(f225(a1),x77262),x77264))+~P1(f319(f319(f226(a1),x77261),x77263))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x77261),x77262)),f319(f319(f74(a1),x77263),x77264)))
% 22.40/22.31 [7774]P1(f319(f319(f321(x77741),x77742),x77743))+~P1(f319(f319(f321(x77741),x77742),f32(f913(x77741,a904),x77744)))+~P1(f319(f319(f321(f913(x77741,a904)),x77743),x77744))
% 22.40/22.31 [7790]~P1(f319(x77901,f650(x77901,x77903,x77902)))+P1(f319(x77901,f319(f319(f156(x77902),x77903),x77904)))+~P1(f319(f319(f226(a906),x77904),f319(f182(f907(x77902)),x77903)))
% 22.40/22.31 [7795]P1(f319(x77951,x77952))+~P1(f319(f319(f321(x77954),x77952),f319(f164(x77954),x77953)))+P1(f319(f319(f226(a906),f652(x77951,x77953,x77954)),f319(f182(f907(x77954)),x77953)))
% 22.40/22.31 [7841]~P3(x78411)+~P1(f319(f319(f226(f913(x78412,x78411)),x78414),x78413))+~P1(f319(f319(f225(f913(x78412,x78411)),x78413),x78414))
% 22.40/22.31 [7888]~P1(f319(x78884,x78882))+~P1(f319(f319(f321(x78881),x78882),x78883))+P1(f319(f319(f321(x78881),x78882),f319(f319(f94(f913(x78881,a904)),x78883),f319(f254(x78881),x78884))))
% 22.40/22.31 [8030]~P1(f319(f319(f321(x80301),x80303),x80304))+~P1(f319(f319(f226(f913(x80301,a904)),x80302),x80304))+P1(f319(f319(f226(f913(x80301,a904)),x80302),f319(f319(f301(x80301),x80303),x80304)))
% 22.40/22.31 [8032]E(f319(f319(f94(f913(x80321,a904)),x80322),x80323),f181(f913(x80321,a904)))+~E(f319(f319(f94(f913(x80321,a904)),f31(f913(x80321,a904),x80324)),x80323),f181(f913(x80321,a904)))+~P1(f319(f319(f321(f913(x80321,a904)),x80322),x80324))
% 22.40/22.31 [8099]P1(f319(f319(f321(x80991),x80992),x80993))+~P1(f319(f319(f225(f913(x80991,a904)),x80993),f319(f319(f301(x80991),x80992),x80994)))+P1(f319(f319(f225(f913(x80991,a904)),x80993),x80994))
% 22.40/22.31 [8116]P1(f319(f319(f321(x81162),f650(x81161,x81163,x81162)),f319(f164(x81162),x81163)))+P1(f319(x81161,f319(f319(f156(x81162),x81163),x81164)))+~P1(f319(f319(f226(a906),x81164),f319(f182(f907(x81162)),x81163)))
% 22.40/22.31 [8124]~P1(f319(f319(f225(f913(x81241,a904)),x81242),x81244))+P1(f319(f319(f225(f913(x81241,a904)),x81242),x81243))+~P1(f319(f319(f225(f913(x81241,a904)),x81244),x81243))
% 22.40/22.31 [8125]~P1(f319(f319(f226(f913(x81251,a904)),x81252),x81254))+~P1(f319(f319(f225(f913(x81251,a904)),x81254),x81253))+P1(f319(f319(f226(f913(x81251,a904)),x81252),x81253))
% 22.40/22.31 [8126]~P1(f319(f319(f225(f913(x81261,a904)),x81262),x81264))+~P1(f319(f319(f226(f913(x81261,a904)),x81264),x81263))+P1(f319(f319(f226(f913(x81261,a904)),x81262),x81263))
% 22.40/22.31 [8127]~P1(f319(f319(f226(f913(x81271,a904)),x81272),x81274))+P1(f319(f319(f226(f913(x81271,a904)),x81272),x81273))+~P1(f319(f319(f226(f913(x81271,a904)),x81274),x81273))
% 22.40/22.31 [8176]~P1(f319(f319(f321(x81761),x81764),x81763))+~P1(f319(f319(f226(f913(x81761,a904)),x81762),f319(f319(f301(x81761),x81764),x81763)))+P1(f319(f319(f226(f913(x81761,a904)),x81762),x81763))
% 22.40/22.31 [8185]~P90(x81851)+P1(f319(f319(f225(x81851),x81852),x81853))+~P1(f319(f319(f225(x81851),f319(f319(f74(x81851),x81854),x81852)),f319(f319(f74(x81851),x81854),x81853)))
% 22.40/22.31 [8187]~P90(x81871)+P1(f319(f319(f225(x81871),x81872),x81873))+~P1(f319(f319(f225(x81871),f319(f319(f74(x81871),x81872),x81874)),f319(f319(f74(x81871),x81873),x81874)))
% 22.40/22.31 [8189]~P90(x81891)+P1(f319(f319(f226(x81891),x81892),x81893))+~P1(f319(f319(f226(x81891),f319(f319(f74(x81891),x81894),x81892)),f319(f319(f74(x81891),x81894),x81893)))
% 22.40/22.31 [8191]~P90(x81911)+P1(f319(f319(f226(x81911),x81912),x81913))+~P1(f319(f319(f226(x81911),f319(f319(f74(x81911),x81912),x81914)),f319(f319(f74(x81911),x81913),x81914)))
% 22.40/22.31 [8240]P1(f319(x82401,x82402))+~E(f319(f319(f130(x82403),f319(f182(f907(x82403)),f169(x82403,x82401,x82404))),x82404),f105(x82403))+~P1(f319(f319(f321(x82403),x82402),f319(f164(x82403),x82404)))
% 22.40/22.31 [8356]P1(f319(x83561,x83562))+~P1(f319(f319(f321(x83563),x83562),f319(f164(x83563),x83564)))+P1(f319(f319(f226(a906),f319(f182(f907(x83563)),f319(f128(x83563,x83561),x83564))),f319(f182(f907(x83563)),x83564)))
% 22.40/22.31 [8838]~P1(f319(x88381,f743(x88381,x88383,x88382,x88384)))+P1(f319(x88381,f319(f319(f156(x88382),x88383),x88384)))+~P1(f319(f319(f226(a906),x88384),f319(f182(f907(x88382)),x88383)))
% 22.40/22.31 [8857]~P25(x88574,x88573,x88571,f234(f913(x88574,a904)))+E(f319(x88571,f613(x88572,x88571,x88573,x88574)),x88572)+~P1(f319(f319(f321(x88573),x88572),f319(f302(x88574,x88573,x88571),f234(f913(x88574,a904)))))
% 22.40/22.31 [8932]E(f169(x89321,x89322,x89323),f319(f319(f167(x89321),x89324),x89323))+P1(f319(f319(f226(a906),f713(x89322,x89323,x89321,x89324)),x89324))+P1(f319(f319(f226(a906),x89324),f319(f182(f907(x89321)),x89323)))
% 22.40/22.31 [8935]E(f169(x89351,x89352,x89353),f319(f319(f167(x89351),x89354),x89353))+P1(f319(f319(f226(a906),f713(x89352,x89353,x89351,x89354)),x89354))+P1(f319(x89352,f319(f319(f156(x89351),x89353),x89354)))
% 22.40/22.31 [8974]P1(f319(x89741,x89742))+~P1(f319(f319(f321(x89744),x89742),f319(f164(x89744),x89743)))+P1(f319(f319(f226(a906),f689(x89742,x89741,x89743,x89744)),f319(f182(f907(x89744)),x89743)))
% 22.40/22.31 [8976]E(f169(x89761,x89762,x89763),f319(f319(f167(x89761),x89764),x89763))+P1(f319(f319(f226(a906),x89764),f319(f182(f907(x89761)),x89763)))+P1(f319(f319(f226(a906),f713(x89762,x89763,x89761,x89764)),f319(f182(f907(x89761)),x89763)))
% 22.40/22.31 [8982]E(f169(x89821,x89822,x89823),f319(f319(f167(x89821),x89824),x89823))+P1(f319(x89822,f319(f319(f156(x89821),x89823),x89824)))+P1(f319(f319(f226(a906),f713(x89822,x89823,x89821,x89824)),f319(f182(f907(x89821)),x89823)))
% 22.40/22.31 [9010]~P126(x90104)+P1(f319(f319(f321(x90101),f385(x90102,x90103,x90101,x90104)),x90103))+P1(f319(f319(f226(x90104),f2(x90104)),f319(f319(f11(x90101,x90104),x90102),x90103)))
% 22.40/22.31 [9011]~P126(x90114)+P1(f319(f319(f321(x90111),f386(x90112,x90113,x90111,x90114)),x90113))+P1(f319(f319(f225(x90114),f2(x90114)),f319(f319(f11(x90111,x90114),x90112),x90113)))
% 22.40/22.31 [9038]~P1(f319(f55(x90381),x90384))+P1(f319(f319(f321(x90381),f532(x90382,x90383,x90384,x90381)),x90384))+P1(f319(f55(f912(x90381,x90383)),f319(f319(f246(x90381,x90383),x90384),x90382)))
% 22.40/22.31 [9071]P1(f319(f319(f321(x90712),f743(x90711,x90713,x90712,x90714)),f319(f164(x90712),x90713)))+P1(f319(x90711,f319(f319(f156(x90712),x90713),x90714)))+~P1(f319(f319(f226(a906),x90714),f319(f182(f907(x90712)),x90713)))
% 22.40/22.31 [9189]P1(f319(f319(f225(a906),x91894),f319(f182(f907(x91892)),f169(x91892,x91893,x91891))))+P1(f319(f319(f226(a906),f715(x91891,x91892,x91893,x91894)),x91894))+~P1(f319(f319(f225(a906),x91894),f319(f182(f907(x91892)),x91891)))
% 22.40/22.31 [9349]E(f169(x93491,x93492,x93493),f319(f319(f167(x93491),x93494),x93493))+~P1(f319(x93492,f319(f319(f156(x93491),x93493),f713(x93492,x93493,x93491,x93494))))+P1(f319(f319(f226(a906),x93494),f319(f182(f907(x93491)),x93493)))
% 22.40/22.31 [9357]E(f169(x93571,x93572,x93573),f319(f319(f167(x93571),x93574),x93573))+~P1(f319(x93572,f319(f319(f156(x93571),x93573),f713(x93572,x93573,x93571,x93574))))+P1(f319(x93572,f319(f319(f156(x93571),x93573),x93574)))
% 22.40/22.31 [9361]~P1(f319(f55(x93611),x93613))+~P1(f319(f55(x93612),f319(x93614,f532(x93614,x93612,x93613,x93611))))+P1(f319(f55(f912(x93611,x93612)),f319(f319(f246(x93611,x93612),x93613),x93614)))
% 22.40/22.31 [9369]~P126(x93691)+~P1(f319(f319(f225(x93691),f2(x93691)),f319(x93693,f386(x93693,x93694,x93692,x93691))))+P1(f319(f319(f225(x93691),f2(x93691)),f319(f319(f11(x93692,x93691),x93693),x93694)))
% 22.40/22.31 [9370]~P126(x93701)+~P1(f319(f319(f226(x93701),f2(x93701)),f319(x93703,f385(x93703,x93704,x93702,x93701))))+P1(f319(f319(f226(x93701),f2(x93701)),f319(f319(f11(x93702,x93701),x93703),x93704)))
% 22.40/22.31 [9378]~E(f319(f182(f907(x93784)),x93782),f319(f182(f907(x93784)),x93783))+P1(f319(f319(f321(f912(f907(x93784),f907(x93784))),f319(f319(f244(f907(x93784),f907(x93784)),x93783),x93782)),f150(x93784,x93781)))+P1(f319(f319(f226(a906),f635(x93781,x93782,x93783,x93784)),f319(f182(f907(x93784)),x93783)))
% 22.40/22.31 [9434]~P1(f319(x94343,f319(f319(f156(x94342),x94344),f715(x94344,x94342,x94343,x94341))))+P1(f319(f319(f225(a906),x94341),f319(f182(f907(x94342)),f169(x94342,x94343,x94344))))+~P1(f319(f319(f225(a906),x94341),f319(f182(f907(x94342)),x94344)))
% 22.40/22.31 [9518]E(f319(f319(f167(x95181),f651(x95182,x95183,x95184,x95181)),x95183),f319(f319(f167(x95181),f651(x95182,x95183,x95184,x95181)),x95184))+~P1(f319(f319(f321(f912(f907(x95181),f907(x95181))),f319(f319(f244(f907(x95181),f907(x95181)),x95184),x95183)),f139(x95181,x95182)))+P1(f319(f319(f226(a906),f319(f182(f907(x95181)),x95184)),f319(f182(f907(x95181)),x95183)))
% 22.40/22.31 [9570]~P1(f319(f319(f226(a906),f2(a906)),x95703))+~P1(f319(f319(f226(a906),x95704),x95701))+P1(f319(f319(f226(a906),f319(f319(f74(a906),f319(f319(f75(a906),x95701),f39(a906,x95702,x95703))),x95704)),f319(f319(f75(a906),x95701),x95703)))
% 22.40/22.31 [9786]~P3(x97862)+~P1(f319(f319(f225(x97862),f319(x97863,f550(x97864,x97863,x97861,x97862))),f319(x97864,f550(x97864,x97863,x97861,x97862))))+P1(f319(f319(f225(f913(x97861,x97862)),x97863),x97864))
% 22.40/22.31 [9787]~P3(x97872)+~P1(f319(f319(f225(x97872),f319(x97873,f656(x97871,x97874,x97873,x97872))),f319(x97874,f656(x97871,x97874,x97873,x97872))))+P1(f319(f319(f225(f913(x97871,x97872)),x97873),x97874))
% 22.40/22.31 [9894]~P67(x98941)+E(f319(f319(f8(a906,x98941),f319(f319(f20(a906,x98941,x98941),f319(f319(f10(x98941,f913(x98941,x98941),a906),f3(x98941)),x98942)),f319(f319(f10(a906,x98941,a906),x98942),f319(f319(f9(a906,a906,a906),f74(a906)),f72(a906))))),f295(a906,x98943,x98944)),f319(f319(f3(x98941),f319(x98942,x98943)),f319(x98942,f319(f319(f74(a906),x98944),f72(a906)))))+~P1(f319(f319(f225(a906),x98943),x98944))
% 22.40/22.31 [9978]~P37(x99783,f319(f319(f281(x99783,x99783,x99783),x99782),f299(x99783,x99782)))+~P1(f319(f319(f321(f912(x99783,x99783)),f319(f319(f244(x99783,x99783),f319(x99781,f319(a104,f825(x99782,x99781,x99783)))),f319(x99781,f825(x99782,x99781,x99783)))),f299(x99783,x99782)))+E(f319(x99781,f319(f319(f74(a906),f824(x99782,x99781,x99783)),x99784)),f319(x99781,f824(x99782,x99781,x99783)))
% 22.40/22.31 [6936]E(f319(f319(f126(x69361),x69362),x69363),x69364)+~E(x69363,f319(f319(f130(x69361),f319(f182(f907(x69361)),x69362)),x69364))+~E(f319(f319(f167(x69361),f319(f182(f907(x69361)),x69362)),x69364),x69362)
% 22.40/22.31 [6990]~P73(x69902)+E(x69901,f2(x69902))+E(f319(f319(f282(x69902),f319(f319(f236(x69902),x69903),x69904)),f319(f319(f236(x69902),x69901),x69904)),f319(f319(f236(x69902),f319(f319(f282(x69902),x69903),x69901)),x69904))
% 22.40/22.31 [7142]~P107(x71421)+~P1(f319(f319(f225(x71421),x71423),x71424))+P1(f319(f319(f225(x71421),f319(f319(f94(x71421),x71422),x71423)),x71424))
% 22.40/22.31 [7143]~P107(x71431)+~P1(f319(f319(f225(x71431),x71432),x71434))+P1(f319(f319(f225(x71431),f319(f319(f94(x71431),x71432),x71433)),x71434))
% 22.40/22.31 [7145]~P4(x71451)+~P1(f319(f319(f225(x71451),x71453),x71454))+P1(f319(f319(f225(x71451),f319(f319(f230(x71451),x71452),x71453)),x71454))
% 22.40/22.31 [7147]~P4(x71471)+~P1(f319(f319(f225(x71471),x71472),x71474))+P1(f319(f319(f225(x71471),f319(f319(f230(x71471),x71472),x71473)),x71474))
% 22.40/22.31 [7148]~P107(x71481)+~P1(f319(f319(f226(x71481),x71483),x71484))+P1(f319(f319(f226(x71481),f319(f319(f94(x71481),x71482),x71483)),x71484))
% 22.40/22.31 [7149]~P107(x71491)+~P1(f319(f319(f226(x71491),x71492),x71494))+P1(f319(f319(f226(x71491),f319(f319(f94(x71491),x71492),x71493)),x71494))
% 22.40/22.31 [7151]~P4(x71511)+~P1(f319(f319(f226(x71511),x71513),x71514))+P1(f319(f319(f226(x71511),f319(f319(f230(x71511),x71512),x71513)),x71514))
% 22.40/22.31 [7153]~P4(x71531)+~P1(f319(f319(f226(x71531),x71532),x71534))+P1(f319(f319(f226(x71531),f319(f319(f230(x71531),x71532),x71533)),x71534))
% 22.40/22.31 [7176]~P1(f319(x71763,x71764))+~P1(f319(x71762,x71764))+P1(f319(f319(f319(f94(f913(x71761,a904)),x71762),x71763),x71764))
% 22.40/22.31 [7299]P14(x72991,x72992,x72993)+~P14(x72991,x72992,x72994)+~P1(f319(f319(f225(f913(f905(x72991),a904)),x72993),x72994))
% 22.40/22.31 [7432]~P69(x74321)+E(f319(f319(f30(x74321),f319(f319(f236(x74321),x74322),x74323)),f319(f319(f236(x74321),x74324),x74323)),f319(f319(f236(x74321),f319(f319(f30(x74321),x74322),x74324)),x74323))+~P1(f319(f319(f279(x74321),x74324),x74322))
% 22.40/22.31 [7655]~P76(x76551)+E(f319(f319(f74(x76551),f319(x76552,x76553)),f319(f319(f8(a906,x76551),x76552),f319(f294(a906,f319(a104,x76553)),x76554))),f319(f319(f8(a906,x76551),x76552),f319(f294(a906,x76553),x76554)))+~P1(f319(f319(f226(a906),x76553),x76554))
% 22.40/22.31 [7673]E(x76731,x76732)+P1(f319(f319(f164(x76733),x76734),x76732))+~P1(f319(f319(f164(x76733),f319(f319(f143(x76733),x76731),x76734)),x76732))
% 22.40/22.31 [7684]~P4(x76841)+P1(f319(f319(f225(x76841),x76842),x76843))+~P1(f319(f319(f225(x76841),f319(f319(f180(x76841),x76844),x76842)),x76843))
% 22.40/22.31 [7686]~P4(x76861)+P1(f319(f319(f225(x76861),x76862),x76863))+~P1(f319(f319(f225(x76861),f319(f319(f180(x76861),x76862),x76864)),x76863))
% 22.40/22.31 [7688]~P106(x76881)+P1(f319(f319(f225(x76881),x76882),x76883))+~P1(f319(f319(f225(x76881),f319(f319(f93(x76881),x76884),x76882)),x76883))
% 22.40/22.31 [7690]~P106(x76901)+P1(f319(f319(f225(x76901),x76902),x76903))+~P1(f319(f319(f225(x76901),f319(f319(f93(x76901),x76902),x76904)),x76903))
% 22.40/22.31 [7691]~P4(x76911)+P1(f319(f319(f226(x76911),x76912),x76913))+~P1(f319(f319(f226(x76911),f319(f319(f180(x76911),x76914),x76912)),x76913))
% 22.40/22.31 [7692]~P4(x76921)+P1(f319(f319(f226(x76921),x76922),x76923))+~P1(f319(f319(f226(x76921),f319(f319(f180(x76921),x76922),x76924)),x76923))
% 22.40/22.31 [7765]~P1(f319(f319(f321(x77651),x77652),x77654))+P1(f319(f319(f321(x77651),x77652),x77653))+P1(f319(f319(f321(x77651),x77652),f319(f319(f3(f913(x77651,a904)),x77654),x77653)))
% 22.40/22.31 [7848]P1(f319(x78481,x78482))+P1(f319(x78483,x78482))+~P1(f319(f319(f319(f93(f913(x78484,a904)),x78483),x78481),x78482))
% 22.40/22.31 [7859]~P1(f319(f319(f321(x78591),x78592),x78594))+~P1(f319(f319(f321(x78591),x78592),x78593))+P1(f319(f319(f321(x78591),x78592),f319(f319(f94(f913(x78591,a904)),x78593),x78594)))
% 22.40/22.31 [7910]~P106(x79101)+~P1(f319(f55(x79101),x79104))+E(f319(f319(f58(x79101,x79101,f93(x79101)),x79102),f319(f319(f301(x79101),x79103),x79104)),f319(f319(f93(x79101),x79103),f319(f319(f58(x79101,x79101,f93(x79101)),x79102),x79104)))
% 22.40/22.31 [7911]~P107(x79111)+~P1(f319(f55(x79111),x79114))+E(f319(f319(f58(x79111,x79111,f94(x79111)),x79112),f319(f319(f301(x79111),x79113),x79114)),f319(f319(f94(x79111),x79113),f319(f319(f58(x79111,x79111,f94(x79111)),x79112),x79114)))
% 22.40/22.31 [7912]~P4(x79121)+~P1(f319(f55(x79121),x79124))+E(f319(f319(f58(x79121,x79121,f180(x79121)),x79122),f319(f319(f301(x79121),x79123),x79124)),f319(f319(f180(x79121),x79123),f319(f319(f58(x79121,x79121,f180(x79121)),x79122),x79124)))
% 22.40/22.31 [7913]~P4(x79131)+~P1(f319(f55(x79131),x79134))+E(f319(f319(f58(x79131,x79131,f230(x79131)),x79132),f319(f319(f301(x79131),x79133),x79134)),f319(f319(f230(x79131),x79133),f319(f319(f58(x79131,x79131,f230(x79131)),x79132),x79134)))
% 22.40/22.31 [7914]~P124(x79141)+~P99(x79141)+E(f319(f319(f3(x79141),f319(f319(f75(x79141),f319(f96(x79141),x79142)),x79143)),f319(f319(f75(x79141),f319(f96(x79141),x79142)),x79144)),f319(f319(f75(x79141),f319(f96(x79141),x79142)),f319(f319(f3(x79141),x79143),x79144)))
% 22.40/22.31 [7915]~P139(x79151)+~P99(x79151)+E(f319(f319(f74(x79151),f319(f319(f75(x79151),f319(f96(x79151),x79152)),x79153)),f319(f319(f75(x79151),f319(f96(x79151),x79152)),x79154)),f319(f319(f75(x79151),f319(f96(x79151),x79152)),f319(f319(f74(x79151),x79153),x79154)))
% 22.40/22.31 [8027]E(x80271,x80272)+P1(f319(f319(f321(x80273),x80271),f319(f164(x80273),x80274)))+~P1(f319(f319(f321(x80273),x80271),f319(f164(x80273),f319(f319(f143(x80273),x80272),x80274))))
% 22.40/22.31 [8196]P56(x81961,x81962,x81963)+~P56(x81961,x81962,x81964)+~P1(f319(f319(f225(f913(f912(x81961,x81962),a904)),x81963),x81964))
% 22.40/22.31 [8242]P1(f319(f319(f321(x82421),x82422),x82423))+P1(f319(f319(f321(x82421),x82422),x82424))+~P1(f319(f319(f321(x82421),x82422),f319(f319(f93(f913(x82421,a904)),x82424),x82423)))
% 22.40/22.31 [8252]~P54(x82521,x82524,x82523)+~P1(f319(f319(f321(x82521),x82522),x82524))+P1(f319(f319(f321(f912(x82521,x82521)),f319(f319(f244(x82521,x82521),x82522),x82522)),x82523))
% 22.40/22.31 [8264]~P1(f319(f55(x82642),x82644))+~P1(f319(f55(x82641),x82643))+P1(f319(f55(f912(x82641,x82642)),f319(f319(f246(x82641,x82642),x82643),f319(f18(f913(x82642,a904),x82641),x82644))))
% 22.40/22.31 [8265]~P1(f319(f319(f321(x82651),x82652),x82654))+~P1(f319(f319(f225(f913(x82651,a904)),x82653),x82654))+P1(f319(f319(f225(f913(x82651,a904)),f319(f319(f301(x82651),x82652),x82653)),x82654))
% 22.40/22.31 [8272]~P82(x82722)+~P146(x82722)+E(f319(f319(f11(x82721,x82722),f319(f319(f10(a906,x82722,x82721),f92(x82722)),x82723)),x82724),f319(f92(x82722),f319(f319(f11(x82721,a906),x82723),x82724)))
% 22.40/22.31 [8273]~P82(x82732)+~P141(x82732)+E(f319(f319(f11(x82731,x82732),f319(f319(f10(a1,x82732,x82731),f95(x82732)),x82733)),x82734),f319(f95(x82732),f319(f319(f11(x82731,a1),x82733),x82734)))
% 22.40/22.31 [8298]E(f319(f319(f3(f913(x82981,a904)),x82982),f319(f319(f3(f913(x82981,a904)),x82983),x82984)),x82984)+~P1(f319(f319(f225(f913(x82981,a904)),x82982),x82983))+~P1(f319(f319(f225(f913(x82981,a904)),x82984),x82982))
% 22.40/22.31 [8391]~P1(f319(f55(x83911),x83914))+E(f319(f319(f3(a906),f319(f319(f8(x83911,a906),x83912),x83913)),f319(f319(f8(x83911,a906),x83912),x83914)),f319(f319(f8(x83911,a906),x83912),f319(f319(f3(f913(x83911,a904)),x83913),x83914)))+~P1(f319(f319(f225(f913(x83911,a904)),x83914),x83913))
% 22.40/22.31 [8540]~P8(x85401,x85404,x85403)+~P1(f319(f319(f321(x85401),x85402),x85404))+P1(f319(f319(f321(x85401),x85402),f319(f277(x85401,x85401,x85403),f319(f319(f301(x85401),x85402),f181(f913(x85401,a904))))))
% 22.40/22.31 [8601]~P1(f319(f319(f225(f913(x86011,a904)),x86012),x86013))+~P1(f319(f319(f225(f913(x86011,a904)),x86012),x86014))+P1(f319(f319(f225(f913(x86011,a904)),x86012),f319(f319(f94(f913(x86011,a904)),x86013),x86014)))
% 22.40/22.31 [8705]E(x87051,f181(f913(x87052,a904)))+P1(f319(f55(x87053),x87054))+~P1(f319(f55(f912(x87053,x87052)),f319(f319(f246(x87053,x87052),x87054),f319(f18(f913(x87052,a904),x87053),x87051))))
% 22.40/22.31 [8706]E(x87061,f181(f913(x87062,a904)))+P1(f319(f55(x87063),x87064))+~P1(f319(f55(f912(x87062,x87063)),f319(f319(f246(x87062,x87063),x87061),f319(f18(f913(x87063,a904),x87062),x87064))))
% 22.40/22.31 [8775]P1(f319(f319(f321(x87751),x87752),f308(x87751,x87753)))+~P1(f319(f319(f321(x87751),x87754),f308(x87751,x87753)))+~P1(f319(f319(f321(f912(x87751,x87751)),f319(f319(f244(x87751,x87751),x87752),x87754)),x87753))
% 22.40/22.31 [8830]~P37(x88301,x88304)+P1(f319(f319(f321(f912(x88301,x88301)),f319(f319(f244(x88301,x88301),x88303),x88302)),f299(x88301,x88304)))+P37(x88301,f319(f319(f301(f912(x88301,x88301)),f319(f319(f244(x88301,x88301),x88302),x88303)),x88304))
% 22.40/22.31 [8831]~P59(x88311,x88314)+P1(f319(f319(f321(f912(x88311,x88311)),f319(f319(f244(x88311,x88311),x88313),x88312)),f299(x88311,x88314)))+P59(x88311,f319(f319(f301(f912(x88311,x88311)),f319(f319(f244(x88311,x88311),x88312),x88313)),x88314))
% 22.40/22.31 [8913]~E(x89132,x89133)+~P1(f319(f319(f321(x89131),x89132),f319(f164(x89131),x89134)))+P1(f319(f319(f321(f912(x89131,x89131)),f319(f319(f244(x89131,x89131),x89132),x89133)),f319(f164(f912(x89131,x89131)),f319(f319(f173(x89131,x89131),x89134),x89134))))
% 22.40/22.31 [8942]~P40(f913(x89421,a904),f913(x89421,a904),x89423)+~P1(f319(f319(f321(x89421),x89422),f88(f913(x89421,a904),x89423)))+P1(f319(f319(f321(x89421),x89422),f319(x89423,f319(f319(f93(f913(x89421,a904)),x89424),f88(f913(x89421,a904),x89423)))))
% 22.40/22.31 [9009]~E(x90093,x90094)+P1(f319(f319(f249(x90091,x90091,a904),a316),x90092))+~P1(f319(f319(f321(f912(x90091,x90091)),x90092),f319(f164(f912(x90091,x90091)),f319(f319(f173(x90091,x90091),x90093),x90094))))
% 22.40/22.31 [9055]P1(f319(f319(f321(f912(f907(x90551),f907(x90551))),f319(f319(f244(f907(x90551),f907(x90551)),x90552),x90553)),f139(x90551,x90554)))+~E(f319(f319(f167(x90551),f319(f182(f907(x90551)),x90552)),x90553),x90552)+~P1(f319(f319(f226(a906),f319(f182(f907(x90551)),x90552)),f319(f182(f907(x90551)),x90553)))
% 22.40/22.31 [9058]~P53(x90581,x90584)+~P1(f319(f319(f321(f912(x90581,x90581)),f319(f319(f244(x90581,x90581),x90583),x90582)),x90584))+P1(f319(f319(f321(f912(x90581,x90581)),f319(f319(f244(x90581,x90581),x90582),x90583)),x90584))
% 22.40/22.31 [9150]~P1(f319(f55(x91501),x91504))+P1(f319(f319(f321(x91501),f466(x91502,x91503,x91504,x91501)),x91504))+P1(f319(f55(x91503),f319(f319(f33(x91501,f913(x91503,a904)),x91504),x91502)))
% 22.40/22.31 [9151]~P1(f319(f55(x91511),x91514))+P1(f319(f319(f321(x91511),f578(x91512,x91513,x91514,x91511)),x91514))+P1(f319(f55(x91513),f319(f319(f33(x91511,f913(x91513,a904)),x91514),x91512)))
% 22.40/22.31 [9230]P1(f319(f319(f321(f912(x92301,x92301)),x92302),f319(f319(f281(x92301,x92301,x92301),x92303),f299(x92301,x92303))))+~P1(f319(f319(f226(a906),f2(a906)),x92304))+~P1(f319(f319(f321(f912(x92301,x92301)),x92302),f319(f319(f175(f912(x92301,x92301),a904),x92304),x92303)))
% 22.40/22.31 [9239]~P37(x92391,x92392)+~P1(f319(f319(f321(f912(x92391,x92391)),f319(f319(f244(x92391,x92391),x92394),x92393)),x92392))+~P1(f319(f319(f321(f912(x92391,x92391)),f319(f319(f244(x92391,x92391),x92393),x92394)),x92392))
% 22.40/22.31 [9368]~P1(f319(f55(x93681),x93684))+E(f319(f319(f8(x93681,a906),f319(f319(f10(f913(x93682,a904),a906,x93681),f29(x93682)),x93683)),x93684),f319(f29(f912(x93681,x93682)),f319(f319(f246(x93681,x93682),x93684),x93683)))+P1(f319(f319(f321(x93681),f536(x93683,x93682,x93684,x93681)),x93684))
% 22.40/22.31 [9372]~P1(f319(f129(x93721),x93722))+P1(f319(f129(x93721),f319(f319(f151(x93721,x93722),x93723),x93724)))+P1(f319(f319(f321(x93721),x93724),f319(f319(f3(f913(x93721,a904)),f319(f164(x93721),x93722)),f319(f319(f301(x93721),f319(f319(f156(x93721),x93722),x93723)),f181(f913(x93721,a904))))))
% 22.40/22.31 [9390]~P1(f319(f55(x93902),x93903))+~P1(f319(f55(x93901),f319(x93904,f466(x93904,x93901,x93903,x93902))))+P1(f319(f55(x93901),f319(f319(f33(x93902,f913(x93901,a904)),x93903),x93904)))
% 22.40/22.31 [9391]~P1(f319(f55(x93912),x93913))+~P1(f319(f55(x93911),f319(x93914,f578(x93914,x93911,x93913,x93912))))+P1(f319(f55(x93911),f319(f319(f33(x93912,f913(x93911,a904)),x93913),x93914)))
% 22.40/22.31 [9472]~P1(f319(f319(f321(f912(x94721,x94721)),x94722),f319(f319(f281(x94721,x94721,x94721),x94724),f299(x94721,x94724))))+P1(f319(f319(f321(f912(x94721,x94721)),x94722),f319(f319(f281(x94721,x94721,x94721),x94723),f299(x94721,x94723))))+~P1(f319(f319(f225(f913(f912(x94721,x94721),a904)),x94724),x94723))
% 22.40/22.31 [9480]E(f319(f319(f167(x94801),f651(x94804,x94803,x94802,x94801)),x94803),f319(f319(f167(x94801),f651(x94804,x94803,x94802,x94801)),x94802))+~P1(f319(f319(f321(f912(f907(x94801),f907(x94801))),f319(f319(f244(f907(x94801),f907(x94801)),x94802),x94803)),f139(x94801,x94804)))+E(f319(f319(f167(x94801),f319(f182(f907(x94801)),x94802)),x94803),x94802)
% 22.40/22.31 [9500]~P1(f319(f55(x95001),x95004))+E(f319(f319(f8(x95001,a906),f319(f319(f10(f913(x95002,a904),a906,x95001),f29(x95002)),x95003)),x95004),f319(f29(f912(x95001,x95002)),f319(f319(f246(x95001,x95002),x95004),x95003)))+~P1(f319(f55(x95002),f319(x95003,f536(x95003,x95002,x95004,x95001))))
% 22.40/22.31 [9505]~E(f319(f182(f907(x95051)),x95053),f319(f182(f907(x95051)),x95052))+P1(f319(f319(f321(f912(f907(x95051),f907(x95051))),f319(f319(f244(f907(x95051),f907(x95051)),x95052),x95053)),f150(x95051,x95054)))+P1(f319(f319(f321(f912(x95051,x95051)),f654(x95054,x95053,x95052,x95051)),f319(f164(f912(x95051,x95051)),f319(f319(f173(x95051,x95051),x95052),x95053))))
% 22.40/22.31 [9579]~P1(f319(f319(f321(f912(f907(x95791),f907(x95791))),f319(f319(f244(f907(x95791),f907(x95791)),x95792),x95793)),f139(x95791,x95794)))+E(f319(f319(f167(x95791),f319(f182(f907(x95791)),x95792)),x95793),x95792)+P1(f319(f319(f226(a906),f651(x95794,x95793,x95792,x95791)),f319(f319(f230(a906),f319(f182(f907(x95791)),x95792)),f319(f182(f907(x95791)),x95793))))
% 22.40/22.31 [9603]~P1(f319(f319(f321(f912(f907(x96031),f907(x96031))),f319(f319(f244(f907(x96031),f907(x96031)),x96032),x96033)),f139(x96031,x96034)))+P1(f319(f319(f226(a906),f319(f182(f907(x96031)),x96032)),f319(f182(f907(x96031)),x96033)))+P1(f319(f319(f226(a906),f651(x96034,x96033,x96032,x96031)),f319(f319(f230(a906),f319(f182(f907(x96031)),x96032)),f319(f182(f907(x96031)),x96033))))
% 22.40/22.31 [10038]~P1(f319(f319(f321(f912(f907(x100381),f907(x100381))),f319(f319(f244(f907(x100381),f907(x100381)),x100382),x100383)),f139(x100381,x100384)))+E(f319(f319(f167(x100381),f319(f182(f907(x100381)),x100382)),x100383),x100382)+P1(f319(f319(f321(f912(x100381,x100381)),f319(f319(f244(x100381,x100381),f319(f319(f156(x100381),x100382),f651(x100384,x100383,x100382,x100381))),f319(f319(f156(x100381),x100383),f651(x100384,x100383,x100382,x100381)))),x100384))
% 22.40/22.31 [10039]~P1(f319(f319(f321(f912(f907(x100391),f907(x100391))),f319(f319(f244(f907(x100391),f907(x100391)),x100392),x100393)),f139(x100391,x100394)))+P1(f319(f319(f226(a906),f319(f182(f907(x100391)),x100392)),f319(f182(f907(x100391)),x100393)))+P1(f319(f319(f321(f912(x100391,x100391)),f319(f319(f244(x100391,x100391),f319(f319(f156(x100391),x100392),f651(x100394,x100393,x100392,x100391))),f319(f319(f156(x100391),x100393),f651(x100394,x100393,x100392,x100391)))),x100394))
% 22.40/22.31 [10082]~E(f319(f182(f907(x100821)),x100822),f319(f182(f907(x100821)),x100823))+P1(f319(f319(f321(f912(f907(x100821),f907(x100821))),f319(f319(f244(f907(x100821),f907(x100821)),x100822),x100823)),f150(x100821,x100824)))+~P1(f319(f319(f321(f912(x100821,x100821)),f319(f319(f244(x100821,x100821),f319(f319(f156(x100821),x100822),f635(x100824,x100823,x100822,x100821))),f319(f319(f156(x100821),x100823),f635(x100824,x100823,x100822,x100821)))),x100824))
% 22.40/22.31 [10226]~P76(x102261)+~P1(f319(f55(x102262),x102264))+E(f319(f157(x102261),f319(f319(f146(x102262,x102261),x102263),f84(f907(x102262),f319(f319(f20(f907(x102262),a904,a904),f319(f319(f10(a904,f913(a904,a904),f907(x102262)),a317),f319(f319(f9(f907(x102262),f913(x102262,a904),a904),f319(f319(f10(f913(x102262,a904),f913(f913(x102262,a904),a904),f907(x102262)),a316),f164(x102262))),x102264))),f129(x102262))))),f224(x102262,x102261,x102263,x102264))
% 22.40/22.31 [7506]~P72(x75062)+E(x75061,f2(x75062))+E(f319(f319(f282(x75062),f319(f319(f74(x75062),x75063),f319(f319(f75(x75062),x75064),x75061))),x75061),f319(f319(f74(x75062),x75064),f319(f319(f282(x75062),x75063),x75061)))
% 22.40/22.31 [7507]~P69(x75072)+E(x75071,f2(x75072))+E(f319(f319(f30(x75072),f319(f319(f74(x75072),x75073),f319(f319(f75(x75072),x75074),x75071))),x75071),f319(f319(f74(x75072),x75074),f319(f319(f30(x75072),x75073),x75071)))
% 22.40/22.31 [7508]~P69(x75082)+E(x75081,f2(x75082))+E(f319(f319(f30(x75082),f319(f319(f74(x75082),x75083),f319(f319(f75(x75082),x75081),x75084))),x75081),f319(f319(f74(x75082),x75084),f319(f319(f30(x75082),x75083),x75081)))
% 22.40/22.31 [7729]~P73(x77292)+E(x77291,f2(x77292))+E(f319(f319(f282(x77292),f319(f319(f3(x77292),x77293),f319(f319(f75(x77292),x77291),x77294))),x77291),f319(f319(f3(x77292),f319(f319(f282(x77292),x77293),x77291)),x77294))
% 22.40/22.31 [7730]~P72(x77302)+E(x77301,f2(x77302))+E(f319(f319(f282(x77302),f319(f319(f74(x77302),x77303),f319(f319(f75(x77302),x77304),x77301))),x77301),f319(f319(f74(x77302),f319(f319(f282(x77302),x77303),x77301)),x77304))
% 22.40/22.31 [7731]~P73(x77312)+E(x77311,f2(x77312))+E(f319(f319(f282(x77312),f319(f319(f74(x77312),x77313),f319(f319(f75(x77312),x77311),x77314))),x77311),f319(f319(f74(x77312),f319(f319(f282(x77312),x77313),x77311)),x77314))
% 22.40/22.31 [8424]~P1(f319(f152(x84241,x84243),x84244))+~P1(f319(f152(x84241,x84242),x84244))+P1(f319(f152(x84241,f319(f319(f94(f913(x84241,a904)),x84242),x84243)),x84244))
% 22.40/22.31 [8788]~E(f319(f319(f281(x87881,x87881,x87881),x87882),x87884),f181(f913(f912(x87881,x87881),a904)))+~E(f319(f319(f281(x87881,x87881,x87881),x87882),x87883),f181(f913(f912(x87881,x87881),a904)))+E(f319(f319(f281(x87881,x87881,x87881),x87882),f319(f319(f93(f913(f912(x87881,x87881),a904)),x87883),x87884)),f181(f913(f912(x87881,x87881),a904)))
% 22.40/22.31 [8914]~P1(f319(f319(f225(f913(x89141,a904)),x89143),x89144))+~P1(f319(f319(f225(f913(x89141,a904)),x89142),x89144))+P1(f319(f319(f225(f913(x89141,a904)),f319(f319(f93(f913(x89141,a904)),x89142),x89143)),x89144))
% 22.40/22.31 [9297]~P1(f319(f55(x92971),x92974))+~P1(f319(f55(x92971),x92973))+E(f319(f319(f3(a906),f319(f319(f74(a906),f319(f319(f8(x92971,a906),x92972),x92973)),f319(f319(f8(x92971,a906),x92972),x92974))),f319(f319(f8(x92971,a906),x92972),f319(f319(f94(f913(x92971,a904)),x92973),x92974))),f319(f319(f8(x92971,a906),x92972),f319(f319(f93(f913(x92971,a904)),x92973),x92974)))
% 22.40/22.31 [9386]~P1(f319(f319(f321(x93861),x93863),x93862))+~P1(f319(f319(f225(f913(x93861,a904)),x93862),f319(f319(f301(x93861),x93863),x93864)))+P1(f319(f319(f225(f913(x93861,a904)),f319(f319(f3(f913(x93861,a904)),x93862),f319(f319(f301(x93861),x93863),f181(f913(x93861,a904))))),x93864))
% 22.40/22.31 [9555]~P1(f319(f319(f321(x95551),x95553),x95552))+P1(f319(f319(f225(f913(x95551,a904)),x95552),f319(f319(f301(x95551),x95553),x95554)))+~P1(f319(f319(f225(f913(x95551,a904)),f319(f319(f3(f913(x95551,a904)),x95552),f319(f319(f301(x95551),x95553),f181(f913(x95551,a904))))),x95554))
% 22.40/22.31 [9656]~P1(f319(f319(f225(a906),x96561),x96563))+~P1(f319(f319(f226(a906),x96562),x96564))+P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),f319(f319(f244(a906,a906),x96561),x96562)),f319(f319(f244(a906,a906),x96563),x96564))),a26))
% 22.40/22.31 [9657]~P1(f319(f319(f225(a906),x96572),x96574))+~P1(f319(f319(f225(a906),x96571),x96573))+P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),f319(f319(f244(a906,a906),x96571),x96572)),f319(f319(f244(a906,a906),x96573),x96574))),a64))
% 22.40/22.31 [9976]~P1(f319(f319(f321(f907(x99761)),x99764),f153(x99761,x99763)))+~P1(f319(f319(f321(f907(x99761)),x99764),f153(x99761,x99762)))+P1(f319(f152(x99761,f319(f319(f94(f913(x99761,a904)),f319(f319(f9(x99761,f913(x99761,a904),a904),f321(x99761)),x99762)),f319(f319(f9(x99761,f913(x99761,a904),a904),f321(x99761)),x99763))),x99764))
% 22.40/22.31 [10057]~P25(x100571,f913(f913(x100571,a904),a904),f319(f319(f9(x100571,f913(f912(x100571,x100571),a904),f913(f913(x100571,a904),a904)),f319(f319(f10(f913(x100571,a904),f913(f913(f912(x100571,x100571),a904),f913(f913(x100571,a904),a904)),x100571),f54(x100571)),f319(f319(f9(x100571,f913(x100571,a904),f913(x100571,a904)),f301(x100571)),f181(f913(x100571,a904))))),x100573),x100572)+~P1(f319(f319(f321(x100571),x100574),x100572))+E(f319(f319(f3(f913(f913(x100571,a904),a904)),f319(f319(f54(x100571),x100572),x100573)),f319(f319(f54(x100571),f319(f319(f301(x100571),x100574),f181(f913(x100571,a904)))),x100573)),f319(f319(f54(x100571),f319(f319(f3(f913(x100571,a904)),x100572),f319(f319(f301(x100571),x100574),f181(f913(x100571,a904))))),x100573))
% 22.40/22.31 [10172]~P54(x101721,x101722,x101724)+~P1(f319(f319(f321(f912(x101721,x101721)),x101723),x101724))+P1(f319(f319(f249(x101721,x101721,a904),f319(f319(f9(x101721,f913(x101721,a904),f913(x101721,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x101721,a904),f913(x101721,a904)),x101721),f10(a904,a904,x101721)),f319(f319(f10(a904,f913(a904,a904),x101721),a317),f319(f319(f9(x101721,f913(x101721,a904),a904),f321(x101721)),x101722)))),f319(f319(f9(x101721,f913(x101721,a904),a904),f321(x101721)),x101722))),x101723))
% 22.40/22.31 [10185]P1(f319(f55(x101851),x101852))+~P1(f319(f55(x101853),f319(f302(x101851,x101853,x101854),x101852)))+~P1(f319(f55(x101851),f319(f254(x101851),f319(f319(f20(x101851,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101851),a317),f319(f319(f9(x101851,f913(x101851,a904),a904),f321(x101851)),x101852))),f319(f319(f9(x101851,x101853,a904),f319(f319(f10(x101853,f913(x101853,a904),x101851),a316),x101854)),f319(x101854,f569(x101854,x101853,x101852,x101851)))))))
% 22.40/22.31 [8180]~P73(x81802)+E(x81801,f2(x81802))+E(f319(f319(f282(x81802),f319(f319(f3(x81802),f319(f319(f75(x81802),x81801),x81803)),x81804)),x81801),f319(f319(f3(x81802),x81803),f319(f319(f282(x81802),x81804),x81801)))
% 22.40/22.31 [8181]~P73(x81812)+E(x81811,f2(x81812))+E(f319(f319(f282(x81812),f319(f319(f74(x81812),f319(f319(f75(x81812),x81811),x81813)),x81814)),x81811),f319(f319(f74(x81812),x81813),f319(f319(f282(x81812),x81814),x81811)))
% 22.40/22.31 [9085]~E(f319(f319(f281(x90851,x90851,x90851),x90853),x90854),f181(f913(f912(x90851,x90851),a904)))+~E(f319(f319(f281(x90851,x90851,x90851),x90852),x90854),f181(f913(f912(x90851,x90851),a904)))+E(f319(f319(f281(x90851,x90851,x90851),f319(f319(f93(f913(f912(x90851,x90851),a904)),x90852),x90853)),x90854),f181(f913(f912(x90851,x90851),a904)))
% 22.40/22.31 [9879]~P1(f319(f152(x98791,x98793),x98794))+~P1(f319(f152(x98791,x98792),x98794))+P1(f319(f152(x98791,f319(f319(f20(x98791,a904,a904),f319(f319(f10(a904,f913(a904,a904),x98791),a317),x98792)),x98793)),x98794))
% 22.40/22.31 [10112]P1(f319(x101121,f551(x101122,x101123,x101121,x101124)))+~P1(f319(f55(x101124),f319(f254(x101124),x101121)))+P1(f319(f55(x101123),f319(f254(x101123),f319(f319(f10(f913(x101124,a904),a904,x101123),f80(x101124)),f319(f319(f10(f913(x101124,a904),f913(x101124,a904),x101123),f319(f20(x101124,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101124),a317),x101121))),x101122)))))
% 22.40/22.31 [10131]~P1(f319(f55(x101312),f319(f254(x101312),x101313)))+~P1(f319(f55(x101311),f319(f254(x101311),f319(f319(f9(x101311,x101312,a904),x101314),f551(x101314,x101311,x101313,x101312)))))+P1(f319(f55(x101311),f319(f254(x101311),f319(f319(f10(f913(x101312,a904),a904,x101311),f80(x101312)),f319(f319(f10(f913(x101312,a904),f913(x101312,a904),x101311),f319(f20(x101312,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101312),a317),x101313))),x101314)))))
% 22.40/22.31 [10197]~P1(f319(f55(x101971),x101974))+P1(f319(f319(f321(x101971),f784(x101972,x101973,x101974,x101971)),x101974))+P1(f319(f55(x101973),f319(f254(x101973),f319(f319(f10(f913(x101971,a904),a904,x101973),f80(x101971)),f319(f319(f10(f913(x101971,a904),f913(x101971,a904),x101973),f319(f20(x101971,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101971),a317),f319(f319(f9(x101971,f913(x101971,a904),a904),f321(x101971)),x101974)))),x101972)))))
% 22.40/22.31 [10203]~P1(f319(f55(x102032),x102033))+~P1(f319(f55(x102031),f319(f254(x102031),f319(f319(f9(x102031,x102032,a904),x102034),f784(x102034,x102031,x102033,x102032)))))+P1(f319(f55(x102031),f319(f254(x102031),f319(f319(f10(f913(x102032,a904),a904,x102031),f80(x102032)),f319(f319(f10(f913(x102032,a904),f913(x102032,a904),x102031),f319(f20(x102032,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102032),a317),f319(f319(f9(x102032,f913(x102032,a904),a904),f321(x102032)),x102033)))),x102034)))))
% 22.40/22.31 [5136]~E(x51362,x51364)+E(f161(x51361,x51362,x51363),f161(x51361,x51364,x51365))+~E(x51362,f2(a906))
% 22.40/22.31 [5388]E(x53881,x53882)+~E(f161(x53884,x53883,x53881),f161(x53884,x53885,x53882))+E(x53883,f2(a906))
% 22.40/22.31 [6652]E(x66521,x66522)+~E(f319(x66523,x66521),f319(x66523,x66522))+~P25(x66524,x66525,x66523,f234(f913(x66524,a904)))
% 22.40/22.31 [7538]E(x75381,x75382)+~P25(x75383,x75384,x75385,f234(f913(x75383,a904)))+~E(f319(f302(x75383,x75384,x75385),x75381),f319(f302(x75383,x75384,x75385),x75382))
% 22.40/22.31 [7783]P25(x77832,x77833,f487(x77834,x77833,x77832,x77831),x77831)+~E(f319(f302(x77833,x77832,x77835),x77834),x77831)+E(x77831,f181(f913(x77832,a904)))
% 22.40/22.31 [8309]~P1(f319(f319(x83093,x83092),x83095))+~P1(f319(f319(x83093,x83094),x83092))+P1(f319(f319(f321(x83091),x83092),f288(x83091,x83093,x83094,x83095)))
% 22.40/22.31 [8310]~P1(f319(f319(x83103,x83102),x83105))+~P1(f319(f319(x83103,x83104),x83102))+P1(f319(f319(f321(x83101),x83102),f291(x83101,x83103,x83104,x83105)))
% 22.40/22.31 [8608]~P25(x86081,x86082,x86083,x86084)+P26(x86081,x86082,x86083,x86084,x86085)+~E(f319(f302(x86081,x86082,x86083),x86084),x86085)
% 22.40/22.31 [8745]~P26(x87451,x87453,x87454,x87452,x87455)+~P1(f319(f55(x87453),x87455))+P1(f319(f55(x87451),x87452))
% 22.40/22.31 [8746]~P26(x87463,x87461,x87464,x87465,x87462)+~P1(f319(f55(x87463),x87465))+P1(f319(f55(x87461),x87462))
% 22.40/22.31 [8871]~P25(x88711,x88713,x88715,f234(f913(x88711,a904)))+~P25(x88713,x88712,x88714,f234(f913(x88713,a904)))+P25(x88711,x88712,f319(f66(x88713,x88712,x88711,x88714),x88715),f234(f913(x88711,a904)))
% 22.40/22.31 [9449]P1(f319(f319(f321(f912(x94491,x94491)),f319(f319(f244(x94491,x94491),x94492),x94493)),f299(x94491,x94494)))+~P1(f319(f319(f321(f912(x94491,x94491)),f319(f319(f244(x94491,x94491),x94492),x94495)),f299(x94491,x94494)))+~P1(f319(f319(f321(f912(x94491,x94491)),f319(f319(f244(x94491,x94491),x94495),x94493)),f299(x94491,x94494)))
% 22.40/22.31 [9487]~P4(x94872)+~P1(f319(f129(x94871),x94875))+P1(f319(f129(x94871),f141(x94871,x94872,x94873,x94874,x94875)))
% 22.40/22.31 [5463]~E(x54632,f105(x54631))+E(f319(f319(f126(x54631),x54632),x54633),f319(f319(f143(x54631),x54634),x54635))+~E(x54633,f319(f319(f143(x54631),x54634),x54635))
% 22.40/22.31 [5464]~E(x54642,f105(x54641))+E(f319(f319(f126(x54641),x54642),x54643),f319(f319(f143(x54641),x54644),x54645))+~E(f319(f319(f143(x54641),x54644),x54645),x54643)
% 22.40/22.31 [6611]~E(f319(f182(f907(x66111)),x66115),f319(f182(f907(x66112)),x66114))+E(f319(f319(f146(f912(x66111,x66112),x66112),f248(x66111,x66112)),x66113),x66114)+~E(f319(f319(f173(x66111,x66112),x66115),x66114),x66113)
% 22.40/22.31 [6612]~E(f319(f182(f907(x66121)),x66124),f319(f182(f907(x66122)),x66125))+E(f319(f319(f146(f912(x66121,x66122),x66121),f243(x66121,x66122)),x66123),x66124)+~E(f319(f319(f173(x66121,x66122),x66124),x66125),x66123)
% 22.40/22.31 [7088]~P4(x70881)+~P13(x70881,f319(f319(f146(x70882,x70881),x70883),x70885))+P13(x70881,f319(f319(f146(x70882,x70881),x70883),f319(f128(x70882,x70884),x70885)))
% 22.40/22.31 [7228]~P4(x72281)+P13(x72281,f319(f319(f146(x72282,x72281),x72283),f162(x72282,x72284,x72285)))+~P13(x72281,f319(f319(f146(x72282,x72281),x72283),x72285))
% 22.40/22.31 [7251]~P56(x72513,x72512,x72515)+~P56(x72511,x72513,x72514)+P56(x72511,x72512,f319(f319(f281(x72511,x72513,x72512),x72514),x72515))
% 22.40/22.31 [7345]E(x73451,x73452)+~P25(x73453,x73454,x73455,f234(f913(x73453,a904)))+~E(f319(f319(f146(x73453,x73454),x73455),x73451),f319(f319(f146(x73453,x73454),x73455),x73452))
% 22.40/22.31 [7493]~P1(f319(f319(f225(a906),x74931),f319(x74933,x74935)))+P1(f319(f319(f225(a906),x74931),f147(x74932,x74933,x74934)))+~P1(f319(f319(f321(x74932),x74935),f319(f164(x74932),x74934)))
% 22.40/22.31 [7494]~P1(f319(f319(f226(a906),x74941),f319(x74943,x74945)))+P1(f319(f319(f226(a906),x74941),f147(x74942,x74943,x74944)))+~P1(f319(f319(f321(x74942),x74945),f319(f164(x74942),x74944)))
% 22.40/22.31 [7879]P1(f319(x78791,x78792))+~P1(f319(x78791,x78793))+~P1(f319(f319(f321(x78794),x78792),f319(f164(x78794),f161(x78794,x78795,x78793))))
% 22.40/22.31 [7880]P1(f319(x78801,x78802))+~P1(f319(x78801,x78803))+~P1(f319(f319(f321(x78804),x78803),f319(f164(x78804),f161(x78804,x78805,x78802))))
% 22.40/22.31 [7885]~P111(x78851)+P1(f319(f319(f225(f913(x78851,a904)),f295(x78851,x78852,x78853)),f295(x78851,x78854,x78855)))+P1(f319(f319(f225(x78851),x78852),x78853))
% 22.40/22.31 [7908]~P5(x79081)+P1(f319(f319(f225(x79081),f319(f319(f34(x79082,x79081),x79083),x79084)),f319(x79084,x79085)))+~P1(f319(f319(f321(x79082),x79085),x79083))
% 22.40/22.31 [7978]~P25(x79781,x79782,x79784,x79783)+E(f319(f71(x79781,x79782,x79783,x79784),f319(x79784,x79785)),x79785)+~P1(f319(f319(f321(x79781),x79785),x79783))
% 22.40/22.31 [7979]~P25(x79791,x79792,x79794,x79793)+E(f319(f85(x79791,x79792,x79793,x79794),f319(x79794,x79795)),x79795)+~P1(f319(f319(f321(x79791),x79795),x79793))
% 22.40/22.31 [8171]~P1(f319(x81711,x81715))+P1(f319(x81711,f891(x81711,x81712,x81713,x81714)))+~P1(f319(f319(f321(x81714),x81715),x81713))
% 22.40/22.31 [8172]~P1(f319(x81721,x81725))+P1(f319(x81721,f891(x81721,x81722,x81723,x81724)))+~P1(f319(f319(f321(x81724),x81725),x81722))
% 22.40/22.31 [8262]P1(f319(f55(x82621),x82622))+~P1(f319(f55(x82623),x82624))+~P1(f319(f319(f225(f913(x82621,a904)),x82622),f319(f302(x82623,x82621,x82625),x82624)))
% 22.40/22.31 [8428]E(x84281,x84282)+~P25(x84283,x84284,x84285,f319(f319(f93(f913(x84283,a904)),f319(f164(x84283),x84281)),f319(f164(x84283),x84282)))+~E(f319(f319(f146(x84283,x84284),x84285),x84281),f319(f319(f146(x84283,x84284),x84285),x84282))
% 22.40/22.31 [8477]~P111(x84771)+~P1(f319(f319(f226(f913(x84771,a904)),f295(x84771,x84774,x84775)),f295(x84771,x84772,x84773)))+P1(f319(f319(f225(x84771),x84772),x84773))
% 22.40/22.31 [8539]~P25(x85391,x85394,x85395,f234(f913(x85391,a904)))+~P1(f319(f319(f321(x85394),f319(x85395,x85392)),f319(f302(x85391,x85394,x85395),x85393)))+P1(f319(f319(f321(x85391),x85392),x85393))
% 22.40/22.31 [8614]P1(f319(x86141,x86142))+~P1(f319(x86141,f902(x86141,x86143,x86144,x86145)))+~P1(f319(f319(f321(x86145),x86142),x86144))
% 22.40/22.31 [8615]P1(f319(x86151,x86152))+~P1(f319(x86151,f902(x86151,x86153,x86154,x86155)))+~P1(f319(f319(f321(x86155),x86152),x86153))
% 22.40/22.31 [8911]~P25(x89112,x89113,x89111,x89114)+E(f319(x89111,f319(f71(x89112,x89113,x89114,x89111),x89115)),x89115)+~P1(f319(f319(f321(x89113),x89115),f319(f302(x89112,x89113,x89111),x89114)))
% 22.40/22.31 [9025]E(x90251,f105(x90252))+E(f319(f319(f143(x90252),x90253),f670(x90254,x90253,x90255,x90251,x90252)),x90251)+~E(f319(f319(f126(x90252),x90251),x90255),f319(f319(f143(x90252),x90253),x90254))
% 22.40/22.31 [9026]E(x90261,f105(x90262))+E(f319(f319(f143(x90262),x90263),f671(x90264,x90261,x90265,x90263,x90262)),x90261)+~E(f319(f319(f126(x90262),x90261),x90264),f319(f319(f143(x90262),x90263),x90265))
% 22.40/22.31 [9043]E(f319(f319(f143(x90432),x90433),f670(x90434,x90433,x90431,x90435,x90432)),x90435)+~E(f319(f319(f126(x90432),x90435),x90431),f319(f319(f143(x90432),x90433),x90434))+E(x90431,f319(f319(f143(x90432),x90433),x90434))
% 22.40/22.31 [9044]E(f319(f319(f143(x90441),x90442),f671(x90444,x90445,x90443,x90442,x90441)),x90445)+~E(f319(f319(f126(x90441),x90445),x90444),f319(f319(f143(x90441),x90442),x90443))+E(f319(f319(f143(x90441),x90442),x90443),x90444)
% 22.40/22.31 [9121]~E(f319(f302(x91213,x91212,x91214),f234(f913(x91213,a904))),f234(f913(x91212,a904)))+~E(f319(f302(x91211,x91213,x91215),f234(f913(x91211,a904))),f234(f913(x91213,a904)))+E(f319(f302(x91211,x91212,f319(f66(x91213,x91212,x91211,x91214),x91215)),f234(f913(x91211,a904))),f234(f913(x91212,a904)))
% 22.40/22.31 [9497]E(x94971,f105(x94972))+~E(f319(f319(f126(x94972),x94971),x94973),f319(f319(f143(x94972),x94975),x94974))+E(f319(f319(f126(x94972),f671(x94973,x94971,x94974,x94975,x94972)),x94973),x94974)
% 22.40/22.31 [9498]E(x94981,f105(x94982))+~E(f319(f319(f126(x94982),x94981),x94985),f319(f319(f143(x94982),x94984),x94983))+E(f319(f319(f126(x94982),f670(x94983,x94984,x94985,x94981,x94982)),x94985),x94983)
% 22.40/22.31 [9506]E(f319(f319(f126(x95062),f670(x95064,x95063,x95061,x95065,x95062)),x95061),x95064)+~E(f319(f319(f126(x95062),x95065),x95061),f319(f319(f143(x95062),x95063),x95064))+E(x95061,f319(f319(f143(x95062),x95063),x95064))
% 22.40/22.31 [9507]~E(f319(f319(f126(x95071),x95075),x95074),f319(f319(f143(x95071),x95072),x95073))+E(f319(f319(f126(x95071),f671(x95074,x95075,x95073,x95072,x95071)),x95074),x95073)+E(f319(f319(f143(x95071),x95072),x95073),x95074)
% 22.40/22.31 [9508]E(f319(f319(f126(x95081),x95085),f674(x95083,x95082,x95084,x95085,x95081)),x95082)+E(f319(f319(f126(x95081),x95082),f673(x95083,x95082,x95084,x95085,x95081)),x95085)+~E(f319(f319(f126(x95081),x95085),x95084),f319(f319(f126(x95081),x95082),x95083))
% 22.40/22.31 [9538]~P4(x95381)+P13(x95381,f319(f319(f146(x95382,x95381),x95383),f141(x95382,x95381,x95383,x95384,x95385)))+~P13(x95381,f319(f319(f146(x95382,x95381),x95383),x95385))
% 22.40/22.31 [9552]~P60(x95525,x95521,x95524,x95523)+P1(f319(f319(x95521,x95522),f526(x95523,x95524,x95521,x95525,x95522)))+~P1(f319(f319(f321(x95525),x95522),x95524))
% 22.40/22.31 [9553]~P60(x95535,x95531,x95534,x95533)+P1(f319(f319(x95531,x95532),f789(x95533,x95534,x95531,x95535,x95532)))+~P1(f319(f319(f321(x95535),x95532),x95534))
% 22.40/22.31 [9668]~P1(f319(f319(f321(f912(x96681,x96681)),f319(f319(f244(x96681,x96681),x96685),x96683)),f299(x96681,x96684)))+P1(f319(f319(f321(f912(x96681,x96681)),f319(f319(f244(x96681,x96681),x96682),x96683)),f319(f319(f281(x96681,x96681,x96681),x96684),f299(x96681,x96684))))+~P1(f319(f319(f321(f912(x96681,x96681)),f319(f319(f244(x96681,x96681),x96682),x96685)),f319(f319(f281(x96681,x96681,x96681),x96684),f299(x96681,x96684))))
% 22.40/22.31 [9669]~P1(f319(f319(f321(f912(x96691,x96691)),f319(f319(f244(x96691,x96691),x96692),x96695)),f299(x96691,x96694)))+P1(f319(f319(f321(f912(x96691,x96691)),f319(f319(f244(x96691,x96691),x96692),x96693)),f319(f319(f281(x96691,x96691,x96691),x96694),f299(x96691,x96694))))+~P1(f319(f319(f321(f912(x96691,x96691)),f319(f319(f244(x96691,x96691),x96695),x96693)),f319(f319(f281(x96691,x96691,x96691),x96694),f299(x96691,x96694))))
% 22.40/22.31 [9671]P1(f319(f319(f321(f912(f907(x96711),f907(x96711))),f319(f319(f244(f907(x96711),f907(x96711)),x96712),x96713)),f150(x96711,f299(x96711,x96714))))+~P1(f319(f319(f321(f912(f907(x96711),f907(x96711))),f319(f319(f244(f907(x96711),f907(x96711)),x96712),x96715)),f150(x96711,f299(x96711,x96714))))+~P1(f319(f319(f321(f912(f907(x96711),f907(x96711))),f319(f319(f244(f907(x96711),f907(x96711)),x96715),x96713)),f150(x96711,f299(x96711,x96714))))
% 22.40/22.31 [9675]E(f319(f319(f126(x96751),x96752),f673(x96753,x96752,x96754,x96755,x96751)),x96755)+E(f319(f319(f126(x96751),f674(x96753,x96752,x96754,x96755,x96751)),x96753),x96754)+~E(f319(f319(f126(x96751),x96752),x96753),f319(f319(f126(x96751),x96755),x96754))
% 22.40/22.31 [9676]E(f319(f319(f126(x96761),x96762),f674(x96763,x96764,x96765,x96762,x96761)),x96764)+E(f319(f319(f126(x96761),f673(x96763,x96764,x96765,x96762,x96761)),x96765),x96763)+~E(f319(f319(f126(x96761),x96762),x96765),f319(f319(f126(x96761),x96764),x96763))
% 22.40/22.31 [9736]P1(f319(f319(f321(f912(x97361,x97361)),f319(f319(f244(x97361,x97361),x97362),x97363)),f319(f319(f281(x97361,x97361,x97361),x97364),f299(x97361,x97364))))+~P1(f319(f319(f321(f912(x97361,x97361)),f319(f319(f244(x97361,x97361),x97362),x97365)),f319(f319(f281(x97361,x97361,x97361),x97364),f299(x97361,x97364))))+~P1(f319(f319(f321(f912(x97361,x97361)),f319(f319(f244(x97361,x97361),x97365),x97363)),f319(f319(f281(x97361,x97361,x97361),x97364),f299(x97361,x97364))))
% 22.40/22.31 [9767]P34(x97671,x97672,x97673,x97674,x97675)+~E(f319(f182(f907(x97671)),x97674),f319(f182(f907(x97672)),x97675))+~P1(f319(f319(f249(x97671,x97672,a904),x97673),f690(x97675,x97674,x97673,x97672,x97671)))
% 22.40/22.31 [9768]P34(x97681,x97682,x97683,x97684,x97685)+~E(f319(f182(f907(x97681)),x97684),f319(f182(f907(x97682)),x97685))+~P1(f319(f319(f249(x97681,x97682,a904),x97683),f691(x97683,x97685,x97684,x97682,x97681)))
% 22.40/22.31 [9773]E(f319(f319(f126(x97731),f673(x97732,x97733,x97734,x97735,x97731)),x97734),x97732)+~E(f319(f319(f126(x97731),x97733),x97732),f319(f319(f126(x97731),x97735),x97734))+E(f319(f319(f126(x97731),f674(x97732,x97733,x97734,x97735,x97731)),x97732),x97734)
% 22.40/22.31 [9793]~P4(x97932)+E(f319(f319(f140(x97931,x97932,x97933),x97934),x97935),f319(f319(f143(x97931),x97934),x97935))+P1(f319(f319(f321(x97931),f734(x97934,x97933,x97935,x97931,x97932)),f319(f164(x97931),x97935)))
% 22.40/22.31 [9797]~P60(x97971,x97974,x97973,x97972)+~P1(f319(f319(f321(x97971),x97975),x97973))+P1(f319(f319(f321(x97971),f526(x97972,x97973,x97974,x97971,x97975)),x97972))
% 22.40/22.31 [9798]~P60(x97981,x97984,x97983,x97982)+~P1(f319(f319(f321(x97981),x97985),x97983))+P1(f319(f319(f321(x97981),f789(x97982,x97983,x97984,x97981,x97985)),x97982))
% 22.40/22.31 [9929]~P1(f319(f319(f321(f912(f913(x99291,a904),f913(x99291,a904))),f319(f319(f244(f913(x99291,a904),f913(x99291,a904)),x99294),x99293)),f311(x99291,x99292)))+~P1(f319(f319(f321(x99291),x99295),x99294))+P1(f319(f319(f321(x99291),f597(x99292,x99293,x99294,x99291,x99295)),x99293))
% 22.40/22.31 [9938]~P4(x99382)+E(f319(f319(f140(x99381,x99382,x99383),x99384),x99385),f319(f319(f143(x99381),x99384),x99385))+~P1(f319(f319(f225(x99382),f319(x99383,x99384)),f319(x99383,f734(x99384,x99383,x99385,x99381,x99382))))
% 22.40/22.31 [9985]~P25(x99853,x99854,x99855,f234(f913(x99853,a904)))+P1(f319(x99851,x99852))+~P1(f319(x99851,f319(f85(x99853,x99854,f234(f913(x99853,a904)),x99855),f803(x99852,x99851,x99855,x99854,x99853))))
% 22.40/22.31 [10097]P34(x100971,x100972,x100973,x100974,x100975)+~E(f319(f182(f907(x100971)),x100974),f319(f182(f907(x100972)),x100975))+~P1(f319(f319(x100973,f319(f319(f156(x100971),x100974),f692(x100975,x100974,x100973,x100972,x100971))),f319(f319(f156(x100972),x100975),f692(x100975,x100974,x100973,x100972,x100971))))
% 22.40/22.31 [10098]P34(x100981,x100982,x100983,x100984,x100985)+~E(f319(f182(f907(x100981)),x100984),f319(f182(f907(x100982)),x100985))+~P1(f319(f319(x100983,f319(f319(f156(x100981),x100984),f727(x100983,x100985,x100982,x100984,x100981))),f319(f319(f156(x100982),x100985),f727(x100983,x100985,x100982,x100984,x100981))))
% 22.40/22.31 [6682]~P18(x66822,x66825,x66821)+~P1(f319(f55(x66822),x66824))+E(f319(x66821,f319(f319(f301(x66822),x66823),x66824)),f319(f319(f58(x66822,x66822,x66825),x66823),x66824))
% 22.40/22.31 [6683]~E(x66833,x66834)+~E(x66832,x66835)+E(f319(f319(f301(x66831),x66832),f319(f319(f301(x66831),x66833),f181(f913(x66831,a904)))),f319(f319(f301(x66831),x66834),f319(f319(f301(x66831),x66835),f181(f913(x66831,a904)))))
% 22.40/22.31 [6693]P1(f319(x66932,x66935))+E(f169(x66931,x66932,f319(f319(f126(x66931),x66933),x66934)),f169(x66931,x66932,x66933))+~P1(f319(f319(f321(x66931),x66935),f319(f164(x66931),x66933)))
% 22.40/22.31 [6733]E(f319(x67331,x67332),f234(f913(x67333,a904)))+~E(f319(f319(f34(x67334,f913(x67333,a904)),x67335),x67331),f234(f913(x67333,a904)))+~P1(f319(f319(f321(x67334),x67332),x67335))
% 22.40/22.31 [6734]E(f319(x67341,x67342),f181(f913(x67343,a904)))+~E(f319(f319(f33(x67344,f913(x67343,a904)),x67345),x67341),f181(f913(x67343,a904)))+~P1(f319(f319(f321(x67344),x67342),x67345))
% 22.40/22.31 [7238]~E(x72382,x72384)+~P143(x72381)+E(f319(f319(f74(x72381),f319(f319(f75(x72381),x72382),x72383)),f319(f319(f75(x72381),x72384),x72385)),f319(f319(f74(x72381),f319(f319(f75(x72381),x72382),x72385)),f319(f319(f75(x72381),x72384),x72383)))
% 22.40/22.31 [7298]~P5(x72981)+~P1(f319(f319(f321(x72984),x72983),x72985))+P1(f319(f319(f225(x72981),f319(x72982,x72983)),f319(f319(f33(x72984,x72981),x72985),x72982)))
% 22.40/22.31 [7350]~P3(x73501)+P1(f319(f319(f225(x73501),f319(x73502,x73503)),f319(x73504,x73503)))+~P1(f319(f319(f225(f913(x73505,x73501)),x73502),x73504))
% 22.40/22.31 [7462]E(x74621,x74622)+E(x74623,x74621)+~E(f319(f319(f301(x74624),x74621),f319(f319(f301(x74624),x74625),f181(f913(x74624,a904)))),f319(f319(f301(x74624),x74622),f319(f319(f301(x74624),x74623),f181(f913(x74624,a904)))))
% 22.40/22.31 [7463]E(x74631,x74632)+E(x74633,x74631)+~E(f319(f319(f301(x74634),x74633),f319(f319(f301(x74634),x74632),f181(f913(x74634,a904)))),f319(f319(f301(x74634),x74635),f319(f319(f301(x74634),x74631),f181(f913(x74634,a904)))))
% 22.40/22.31 [7464]E(x74641,x74642)+E(x74641,x74643)+~E(f319(f319(f301(x74644),x74643),f319(f319(f301(x74644),x74642),f181(f913(x74644,a904)))),f319(f319(f301(x74644),x74645),f319(f319(f301(x74644),x74641),f181(f913(x74644,a904)))))
% 22.40/22.31 [7465]E(x74651,x74652)+E(x74651,x74653)+~E(f319(f319(f301(x74654),x74651),f319(f319(f301(x74654),x74655),f181(f913(x74654,a904)))),f319(f319(f301(x74654),x74652),f319(f319(f301(x74654),x74653),f181(f913(x74654,a904)))))
% 22.40/22.31 [7984]P25(x79841,x79842,x79843,x79844)+~P25(x79841,x79842,x79843,x79845)+~P1(f319(f319(f225(f913(x79841,a904)),x79844),x79845))
% 22.40/22.31 [8013]~E(f319(x80133,x80135),x80134)+~P25(x80131,x80132,x80133,f234(f913(x80131,a904)))+E(f319(f85(x80131,x80132,f234(f913(x80131,a904)),x80133),x80134),x80135)
% 22.40/22.31 [8155]E(x81551,x81552)+~E(f319(f302(x81553,x81554,x81555),x81551),f319(f302(x81553,x81554,x81555),x81552))+~P25(x81553,x81554,x81555,f319(f319(f93(f913(x81553,a904)),x81551),x81552))
% 22.40/22.31 [8231]P1(f319(x82312,x82314))+E(f319(f319(f130(x82311),f319(f182(f907(x82311)),f169(x82311,x82312,x82313))),x82313),f319(f319(f143(x82311),x82314),x82315))+~E(f319(f319(f126(x82311),f169(x82311,x82312,x82313)),f319(f319(f143(x82311),x82314),x82315)),x82313)
% 22.40/22.31 [8260]~P25(x82601,x82602,x82603,x82605)+~P25(x82601,x82602,x82603,x82604)+P25(x82601,x82602,x82603,f319(f319(f94(f913(x82601,a904)),x82604),x82605))
% 22.40/22.31 [8365]~P76(x83651)+E(f319(f319(f74(x83651),f319(x83652,x83653)),f319(f157(x83651),f319(f319(f146(x83654,x83651),x83652),f162(x83654,x83653,x83655)))),f319(f157(x83651),f319(f319(f146(x83654,x83651),x83652),x83655)))+~P1(f319(f319(f321(x83654),x83653),f319(f164(x83654),x83655)))
% 22.40/22.31 [8451]~P4(x84511)+~P13(x84511,f319(f319(f146(x84512,x84511),x84513),x84515))+P13(x84511,f319(f319(f146(x84512,x84511),x84513),f319(f319(f140(x84512,x84511,x84513),x84514),x84515)))
% 22.40/22.31 [8535]~P5(x85351)+P1(f319(f319(f225(x85351),f319(f319(f33(x85352,x85351),x85353),x85354)),f319(f319(f33(x85352,x85351),x85355),x85354)))+~P1(f319(f319(f225(f913(x85352,a904)),x85353),x85355))
% 22.40/22.31 [8536]~P5(x85361)+P1(f319(f319(f225(x85361),f319(f319(f34(x85362,x85361),x85363),x85364)),f319(f319(f34(x85362,x85361),x85365),x85364)))+~P1(f319(f319(f225(f913(x85362,a904)),x85365),x85363))
% 22.40/22.31 [8572]~P4(x85723)+P1(f319(f129(x85721),x85722))+~P1(f319(f129(x85721),f319(f319(f140(x85721,x85723,x85724),x85725),x85722)))
% 22.40/22.31 [8716]~P4(x87161)+~P1(f319(f319(f321(x87162),x87163),f319(f164(x87162),x87164)))+~P1(f319(f129(x87162),f319(f319(f140(x87162,x87161,x87165),x87163),x87164)))
% 22.40/22.31 [8800]~P4(x88001)+P13(x88001,f319(f319(f146(x88002,x88001),x88003),x88004))+~P13(x88001,f319(f319(f146(x88002,x88001),x88003),f319(f319(f140(x88002,x88001,x88003),x88005),x88004)))
% 22.40/22.31 [8848]~P25(x88482,x88481,x88484,x88483)+E(f319(f302(x88481,x88482,f85(x88482,x88481,x88483,x88484)),f319(f302(x88482,x88481,x88484),x88485)),x88485)+~P1(f319(f319(f225(f913(x88482,a904)),x88485),x88483))
% 22.40/22.31 [8899]~P4(x88992)+E(f319(f319(f140(x88991,x88992,x88993),x88994),x88995),f141(x88991,x88992,x88993,x88994,x88995))+P1(f319(f319(f321(x88992),f319(x88993,x88994)),f319(f302(x88991,x88992,x88993),f319(f164(x88991),x88995))))
% 22.40/22.31 [8985]~P4(x89852)+E(f141(x89851,x89852,x89853,x89854,x89855),x89855)+~P1(f319(f319(f321(x89852),f319(x89853,x89854)),f319(f302(x89851,x89852,x89853),f319(f164(x89851),x89855))))
% 22.40/22.31 [9002]~P25(x90022,x90021,x90023,x90025)+P1(f319(f319(f226(f913(x90021,a904)),f319(f302(x90022,x90021,x90023),x90024)),f319(f302(x90022,x90021,x90023),x90025)))+~P1(f319(f319(f226(f913(x90022,a904)),x90024),x90025))
% 22.40/22.31 [9158]~P25(x91581,x91582,x91583,f234(f913(x91581,a904)))+~P1(f319(f319(f225(f913(x91582,a904)),x91584),f319(f302(x91581,x91582,x91583),x91585)))+P1(f319(f319(f225(f913(x91581,a904)),f319(f303(x91581,x91582,x91583),x91584)),x91585))
% 22.40/22.31 [9179]~E(f319(f302(x91793,x91791,x91794),f234(f913(x91793,a904))),f234(f913(x91791,a904)))+P1(f319(f319(f225(f913(x91791,a904)),x91792),f319(f302(x91793,x91791,x91794),x91795)))+~P1(f319(f319(f225(f913(x91793,a904)),f319(f303(x91793,x91791,x91794),x91792)),x91795))
% 22.40/22.31 [9290]~P25(x92901,x92904,x92905,f234(f913(x92901,a904)))+~P1(f319(f319(f225(f913(x92904,a904)),f319(f302(x92901,x92904,x92905),x92902)),f319(f302(x92901,x92904,x92905),x92903)))+P1(f319(f319(f225(f913(x92901,a904)),x92902),x92903))
% 22.40/22.31 [9417]~P88(x94171)+~E(f319(x94173,f710(x94173,x94174,x94175,x94172,x94171)),f2(x94171))+E(f319(f157(x94171),f319(f319(f146(x94172,x94171),x94173),f319(f128(x94172,x94174),x94175))),f319(f157(x94171),f319(f319(f146(x94172,x94171),x94173),x94175)))
% 22.40/22.31 [9444]~P26(x94441,x94442,x94443,f234(f913(x94441,a904)),f234(f913(x94442,a904)))+~P1(f319(f319(f225(f913(x94442,a904)),x94444),f319(f302(x94441,x94442,x94443),x94445)))+P1(f319(f319(f225(f913(x94441,a904)),f319(f303(x94441,x94442,x94443),x94444)),x94445))
% 22.40/22.31 [9473]~P26(x94733,x94731,x94734,f234(f913(x94733,a904)),f234(f913(x94731,a904)))+P1(f319(f319(f225(f913(x94731,a904)),x94732),f319(f302(x94733,x94731,x94734),x94735)))+~P1(f319(f319(f225(f913(x94733,a904)),f319(f303(x94733,x94731,x94734),x94732)),x94735))
% 22.40/22.31 [9596]~P17(x95961,x95962,x95963)+~P1(f319(f55(x95961),x95965))+P1(f319(f60(x95961,x95962,x95963,x95964,x95965),f319(f319(f58(x95961,x95962,x95963),x95964),x95965)))
% 22.40/22.31 [9688]~P26(x96882,x96881,x96884,f234(f913(x96882,a904)),f234(f913(x96881,a904)))+~P26(x96881,x96883,x96885,f234(f913(x96881,a904)),f234(f913(x96883,a904)))+E(f319(f66(x96881,x96882,x96883,f85(x96882,x96881,f234(f913(x96882,a904)),x96884)),f85(x96881,x96883,f234(f913(x96881,a904)),x96885)),f85(x96882,x96883,f234(f913(x96882,a904)),f319(f66(x96881,x96883,x96882,x96885),x96884)))
% 22.40/22.31 [9689]P1(f319(x96891,f634(x96892,x96891,x96893,x96894,x96895)))+~P1(f319(f319(f225(f913(x96895,a904)),x96894),x96893))+P1(f319(f319(f225(f913(x96895,a904)),f319(f319(f94(f913(x96895,a904)),x96894),f319(f254(x96895),x96891))),f319(f319(f94(f913(x96895,a904)),x96893),f319(f254(x96895),x96892))))
% 22.40/22.31 [9704]~P88(x97041)+~P1(f319(x97044,f710(x97043,x97044,x97045,x97042,x97041)))+E(f319(f157(x97041),f319(f319(f146(x97042,x97041),x97043),f319(f128(x97042,x97044),x97045))),f319(f157(x97041),f319(f319(f146(x97042,x97041),x97043),x97045)))
% 22.40/22.31 [9795]~P5(x97955)+P1(f319(f319(f321(x97951),f472(x97952,x97953,x97951,x97954,x97955)),x97953))+P1(f319(f319(f225(x97955),x97954),f319(f319(f34(x97951,x97955),x97953),x97952)))
% 22.40/22.31 [9799]~P88(x97991)+E(f319(f157(x97991),f319(f319(f146(x97992,x97991),x97993),f319(f128(x97992,x97994),x97995))),f319(f157(x97991),f319(f319(f146(x97992,x97991),x97993),x97995)))+P1(f319(f319(f321(x97992),f710(x97993,x97994,x97995,x97992,x97991)),f319(f164(x97992),x97995)))
% 22.40/22.31 [9806]~P1(f319(x98065,f634(x98065,x98063,x98064,x98062,x98061)))+~P1(f319(f319(f225(f913(x98061,a904)),x98062),x98064))+P1(f319(f319(f225(f913(x98061,a904)),f319(f319(f94(f913(x98061,a904)),x98062),f319(f254(x98061),x98063))),f319(f319(f94(f913(x98061,a904)),x98064),f319(f254(x98061),x98065))))
% 22.40/22.31 [9823]~P25(x98235,x98233,x98234,f234(f913(x98235,a904)))+P1(f319(x98231,x98232))+P1(f319(f319(f321(x98233),f803(x98232,x98231,x98234,x98233,x98235)),f319(f302(x98235,x98233,x98234),f234(f913(x98235,a904)))))
% 22.40/22.31 [9847]P34(x98471,x98472,x98473,x98474,x98475)+~E(f319(f182(f907(x98472)),x98475),f319(f182(f907(x98471)),x98474))+P1(f319(f319(f226(a906),f692(x98475,x98474,x98473,x98472,x98471)),f319(f182(f907(x98471)),x98474)))
% 22.40/22.31 [9848]P34(x98481,x98482,x98483,x98484,x98485)+~E(f319(f182(f907(x98482)),x98485),f319(f182(f907(x98481)),x98484))+P1(f319(f319(f226(a906),f727(x98483,x98485,x98482,x98484,x98481)),f319(f182(f907(x98481)),x98484)))
% 22.40/22.31 [9881]P1(f319(f319(f321(x98811),f634(x98812,x98813,x98814,x98815,x98811)),x98815))+~P1(f319(f319(f225(f913(x98811,a904)),x98815),x98814))+P1(f319(f319(f225(f913(x98811,a904)),f319(f319(f94(f913(x98811,a904)),x98815),f319(f254(x98811),x98813))),f319(f319(f94(f913(x98811,a904)),x98814),f319(f254(x98811),x98812))))
% 22.40/22.31 [9939]~P5(x99391)+~P1(f319(f319(f225(x99391),x99392),f319(x99395,f472(x99395,x99394,x99393,x99392,x99391))))+P1(f319(f319(f225(x99391),x99392),f319(f319(f34(x99393,x99391),x99394),x99395)))
% 22.40/22.31 [9974]~P82(x99741)+~P1(f319(f55(x99742),x99745))+E(f319(f319(f319(f59(x99741,x99742,f75(x99741)),f319(f319(f20(x99742,x99741,x99741),f319(f319(f10(x99741,f913(x99741,x99741),x99742),f75(x99741)),x99743)),x99744)),f72(x99741)),x99745),f319(f319(f75(x99741),f319(f319(f319(f59(x99741,x99742,f75(x99741)),x99743),f72(x99741)),x99745)),f319(f319(f319(f59(x99741,x99742,f75(x99741)),x99744),f72(x99741)),x99745)))
% 22.40/22.31 [10024]~P1(f319(f319(f321(f912(f913(x100241,a904),f913(x100241,a904))),f319(f319(f244(f913(x100241,a904),f913(x100241,a904)),x100245),x100244)),f311(x100241,x100243)))+~P1(f319(f319(f321(x100241),x100242),x100245))+P1(f319(f319(f321(f912(x100241,x100241)),f319(f319(f244(x100241,x100241),x100242),f597(x100243,x100244,x100245,x100241,x100242))),x100243))
% 22.40/22.31 [10126]~P1(f319(f319(f321(f912(f907(x101261),f907(x101261))),f319(f319(f244(f907(x101261),f907(x101261)),f319(f319(f126(x101261),x101265),x101262)),f319(f319(f126(x101261),x101265),x101263))),f139(x101261,x101264)))+P1(f319(f319(f321(f912(f907(x101261),f907(x101261))),f319(f319(f244(f907(x101261),f907(x101261)),x101262),x101263)),f139(x101261,x101264)))+P1(f319(f319(f321(f912(x101261,x101261)),f319(f319(f244(x101261,x101261),f679(x101264,x101263,x101262,x101265,x101261)),f679(x101264,x101263,x101262,x101265,x101261))),x101264))
% 22.40/22.31 [7353]~E(x73533,x73535)+E(f319(f319(f156(x73531),f319(f319(f151(x73531,x73532),x73533),x73534)),x73535),x73534)+~P1(f319(f319(f226(a906),x73533),f319(f182(f907(x73531)),x73532)))
% 22.40/22.31 [7459]~E(f319(f319(f126(x74591),x74592),x74594),f319(f319(f126(x74591),x74593),x74595))+E(f319(f319(f167(x74591),f319(f182(f907(x74591)),x74592)),x74593),x74592)+P1(f319(f319(f225(a906),f319(f182(f907(x74591)),x74593)),f319(f182(f907(x74591)),x74592)))
% 22.40/22.31 [7949]~E(f319(f319(f126(x79491),x79492),x79494),f319(f319(f126(x79491),x79493),x79495))+E(f319(f319(f167(x79491),f319(f182(f907(x79491)),x79492)),x79493),x79492)+~P1(f319(f319(f225(a906),f319(f182(f907(x79491)),x79492)),f319(f182(f907(x79491)),x79493)))
% 22.40/22.31 [7973]~P1(f319(f55(x79731),f319(x79734,x79735)))+~P1(f319(f319(f321(x79732),x79735),x79733))+P1(f319(f55(x79731),f319(f319(f34(x79732,f913(x79731,a904)),x79733),x79734)))
% 22.40/22.31 [8138]~P54(x81381,x81383,x81385)+~P54(x81381,x81382,x81384)+P54(x81381,f319(f319(f93(f913(x81381,a904)),x81382),x81383),f319(f319(f93(f913(f912(x81381,x81381),a904)),x81384),x81385))
% 22.40/22.31 [8139]~P54(x81391,x81393,x81395)+~P54(x81391,x81392,x81394)+P54(x81391,f319(f319(f94(f913(x81391,a904)),x81392),x81393),f319(f319(f94(f913(f912(x81391,x81391),a904)),x81394),x81395))
% 22.40/22.31 [8490]E(f319(f319(f244(x84901,x84902),f319(f319(f156(x84901),x84903),x84904)),f319(f319(f156(x84902),x84905),x84904)),f319(f319(f156(f912(x84901,x84902)),f319(f319(f173(x84901,x84902),x84903),x84905)),x84904))+~P1(f319(f319(f226(a906),x84904),f319(f182(f907(x84901)),x84903)))+~P1(f319(f319(f226(a906),x84904),f319(f182(f907(x84902)),x84905)))
% 22.40/22.31 [8646]~P54(x86461,x86463,x86464)+P1(f319(f319(f321(x86461),x86462),x86463))+~P1(f319(f319(f321(f912(x86461,x86461)),f319(f319(f244(x86461,x86461),x86465),x86462)),x86464))
% 22.40/22.31 [8647]~P54(x86471,x86473,x86474)+P1(f319(f319(f321(x86471),x86472),x86473))+~P1(f319(f319(f321(f912(x86471,x86471)),f319(f319(f244(x86471,x86471),x86472),x86475)),x86474))
% 22.40/22.31 [8648]~P8(x86481,x86483,x86484)+P1(f319(f319(f321(x86481),x86482),x86483))+~P1(f319(f319(f321(f912(x86481,x86481)),f319(f319(f244(x86481,x86481),x86485),x86482)),x86484))
% 22.40/22.31 [8649]~P8(x86491,x86493,x86494)+P1(f319(f319(f321(x86491),x86492),x86493))+~P1(f319(f319(f321(f912(x86491,x86491)),f319(f319(f244(x86491,x86491),x86492),x86495)),x86494))
% 22.40/22.31 [8925]~P8(x89251,x89255,x89252)+E(f319(f277(x89251,x89251,x89252),f319(f319(f301(x89251),x89253),f181(f913(x89251,a904)))),f319(f277(x89251,x89251,x89252),f319(f319(f301(x89251),x89254),f181(f913(x89251,a904)))))+~P1(f319(f319(f321(f912(x89251,x89251)),f319(f319(f244(x89251,x89251),x89253),x89254)),x89252))
% 22.40/22.31 [9118]P1(f319(x91181,x91182))+~P1(f319(f319(f321(x91183),x91182),x91185))+P1(f319(f319(f321(x91183),f902(x91181,x91184,x91185,x91183)),f319(f319(f93(f913(x91183,a904)),x91185),x91184)))
% 22.40/22.31 [9119]P1(f319(x91191,x91192))+~P1(f319(f319(f321(x91193),x91192),x91194))+P1(f319(f319(f321(x91193),f902(x91191,x91194,x91195,x91193)),f319(f319(f93(f913(x91193,a904)),x91195),x91194)))
% 22.40/22.31 [9127]~P1(f319(x91272,x91275))+~P1(f319(f319(f321(x91271),x91275),x91274))+P1(f319(f319(f321(x91271),f891(x91272,x91273,x91274,x91271)),f319(f319(f93(f913(x91271,a904)),x91274),x91273)))
% 22.40/22.31 [9128]~P1(f319(x91282,x91285))+~P1(f319(f319(f321(x91281),x91285),x91283))+P1(f319(f319(f321(x91281),f891(x91282,x91283,x91284,x91281)),f319(f319(f93(f913(x91281,a904)),x91284),x91283)))
% 22.40/22.31 [9143]~P1(f319(f319(f225(f913(x91431,a904)),x91433),x91435))+~P1(f319(f319(f225(f913(x91431,a904)),x91432),x91434))+P1(f319(f319(f225(f913(x91431,a904)),f319(f319(f93(f913(x91431,a904)),x91432),x91433)),f319(f319(f93(f913(x91431,a904)),x91434),x91435)))
% 22.40/22.31 [9144]~P1(f319(f319(f225(f913(x91441,a904)),x91443),x91445))+~P1(f319(f319(f225(f913(x91441,a904)),x91442),x91444))+P1(f319(f319(f225(f913(x91441,a904)),f319(f319(f94(f913(x91441,a904)),x91442),x91443)),f319(f319(f94(f913(x91441,a904)),x91444),x91445)))
% 22.40/22.31 [9145]~P1(f319(f319(f225(f913(x91451,a904)),x91455),x91453))+~P1(f319(f319(f225(f913(x91451,a904)),x91452),x91454))+P1(f319(f319(f225(f913(x91451,a904)),f319(f319(f3(f913(x91451,a904)),x91452),x91453)),f319(f319(f3(f913(x91451,a904)),x91454),x91455)))
% 22.40/22.31 [9234]P1(f319(f319(f321(f912(x92341,x92341)),f319(f319(f244(x92341,x92341),x92342),x92343)),f313(x92341,x92344,x92345)))+~P1(f319(f319(f225(a906),f319(x92344,x92342)),f319(x92344,x92343)))+~P1(f319(f319(f321(f912(x92341,x92341)),f319(f319(f244(x92341,x92341),x92342),x92343)),x92345))
% 22.40/22.31 [9431]P1(f319(f319(f321(f912(x94311,x94311)),f319(f319(f244(x94311,x94311),x94312),x94313)),f299(x94311,x94314)))+~P1(f319(f319(f321(f912(x94311,x94311)),f319(f319(f244(x94311,x94311),x94312),x94315)),f299(x94311,x94314)))+~P1(f319(f319(f321(f912(x94311,x94311)),f319(f319(f244(x94311,x94311),x94315),x94313)),x94314))
% 22.40/22.31 [9432]P1(f319(f319(f321(f912(x94321,x94321)),f319(f319(f244(x94321,x94321),x94322),x94323)),f299(x94321,x94324)))+~P1(f319(f319(f321(f912(x94321,x94321)),f319(f319(f244(x94321,x94321),x94325),x94323)),f299(x94321,x94324)))+~P1(f319(f319(f321(f912(x94321,x94321)),f319(f319(f244(x94321,x94321),x94322),x94325)),x94324))
% 22.40/22.31 [9528]E(x95281,x95282)+E(f319(a104,f618(x95283,x95284,x95281,x95282,x95285)),x95284)+~P1(f319(f319(f321(f912(x95285,x95285)),f319(f319(f244(x95285,x95285),x95282),x95281)),f319(f319(f175(f912(x95285,x95285),a904),x95284),x95283)))
% 22.40/22.31 [9529]E(x95291,x95292)+E(f319(a104,f620(x95293,x95294,x95291,x95292,x95295)),x95294)+~P1(f319(f319(f321(f912(x95295,x95295)),f319(f319(f244(x95295,x95295),x95292),x95291)),f319(f319(f175(f912(x95295,x95295),a904),x95294),x95293)))
% 22.40/22.31 [9530]E(x95301,f2(a906))+E(f319(a104,f618(x95302,x95301,x95303,x95304,x95305)),x95301)+~P1(f319(f319(f321(f912(x95305,x95305)),f319(f319(f244(x95305,x95305),x95304),x95303)),f319(f319(f175(f912(x95305,x95305),a904),x95301),x95302)))
% 22.40/22.31 [9531]E(x95311,f2(a906))+E(f319(a104,f620(x95312,x95311,x95313,x95314,x95315)),x95311)+~P1(f319(f319(f321(f912(x95315,x95315)),f319(f319(f244(x95315,x95315),x95314),x95313)),f319(f319(f175(f912(x95315,x95315),a904),x95311),x95312)))
% 22.40/22.31 [9551]P1(f319(f319(f321(f912(x95511,x95511)),f319(f319(f244(x95511,x95511),x95512),x95513)),f319(f319(f281(x95511,x95511,x95511),x95514),f299(x95511,x95514))))+~P1(f319(f319(f321(f912(x95511,x95511)),f319(f319(f244(x95511,x95511),x95512),x95515)),x95514))+~P1(f319(f319(f321(f912(x95511,x95511)),f319(f319(f244(x95511,x95511),x95515),x95513)),x95514))
% 22.40/22.31 [9556]~P1(f319(f319(f321(f912(x95561,x95561)),f319(f319(f244(x95561,x95561),x95562),x95565)),f299(x95561,x95564)))+P1(f319(f319(f321(f912(x95561,x95561)),f319(f319(f244(x95561,x95561),x95562),x95563)),f319(f319(f281(x95561,x95561,x95561),x95564),f299(x95561,x95564))))+~P1(f319(f319(f321(f912(x95561,x95561)),f319(f319(f244(x95561,x95561),x95565),x95563)),x95564))
% 22.40/22.31 [9590]~P8(x95901,x95905,x95902)+~P1(f319(f319(f321(f912(x95901,x95901)),f319(f319(f244(x95901,x95901),x95903),x95904)),x95902))+P1(f319(f319(f225(f913(x95901,a904)),f319(f277(x95901,x95901,x95902),f319(f319(f301(x95901),x95903),f181(f913(x95901,a904))))),f319(f277(x95901,x95901,x95902),f319(f319(f301(x95901),x95904),f181(f913(x95901,a904))))))
% 22.40/22.31 [9661]P1(f319(f319(f321(f912(x96611,x96611)),f319(f319(f244(x96611,x96611),x96612),x96613)),f319(f319(f281(x96611,x96611,x96611),x96614),f299(x96611,x96614))))+~P1(f319(f319(f321(f912(x96611,x96611)),f319(f319(f244(x96611,x96611),x96612),x96615)),f319(f319(f281(x96611,x96611,x96611),x96614),f299(x96611,x96614))))+~P1(f319(f319(f321(f912(x96611,x96611)),f319(f319(f244(x96611,x96611),x96615),x96613)),x96614))
% 22.40/22.31 [9662]P1(f319(f319(f321(f912(x96621,x96621)),f319(f319(f244(x96621,x96621),x96622),x96623)),f319(f319(f281(x96621,x96621,x96621),x96624),f299(x96621,x96624))))+~P1(f319(f319(f321(f912(x96621,x96621)),f319(f319(f244(x96621,x96621),x96625),x96623)),f319(f319(f281(x96621,x96621,x96621),x96624),f299(x96621,x96624))))+~P1(f319(f319(f321(f912(x96621,x96621)),f319(f319(f244(x96621,x96621),x96622),x96625)),x96624))
% 22.40/22.31 [9711]~P1(f319(f60(x97111,x97111,x97114,x97112,x97113),x97115))+P1(f319(f319(f321(x97111),x97112),x97113))+P1(f319(f56(x97111,x97114,f319(f319(f301(x97111),x97112),x97113)),x97115))
% 22.40/22.31 [9756]~E(f319(f302(x97563,x97562,x97565),x97564),x97561)+E(x97561,f181(f913(x97562,a904)))+P1(f319(f319(f225(f913(x97563,a904)),f319(f302(x97562,x97563,f487(x97564,x97563,x97562,x97561)),x97561)),x97564))
% 22.40/22.31 [9809]~P5(x98095)+P1(f319(f319(f321(x98091),f474(x98092,x98093,x98094,x98091,x98095)),x98094))+P1(f319(f319(f225(x98095),f319(f319(f33(x98091,x98095),x98094),x98093)),x98092))
% 22.40/22.31 [9867]P34(x98671,x98672,x98673,x98674,x98675)+~E(f319(f182(f907(x98671)),x98674),f319(f182(f907(x98672)),x98675))+P1(f319(f319(f321(f912(x98671,x98672)),f690(x98675,x98674,x98673,x98672,x98671)),f319(f164(f912(x98671,x98672)),f319(f319(f173(x98671,x98672),x98674),x98675))))
% 22.40/22.31 [9868]P34(x98681,x98682,x98683,x98684,x98685)+~E(f319(f182(f907(x98681)),x98684),f319(f182(f907(x98682)),x98685))+P1(f319(f319(f321(f912(x98681,x98682)),f691(x98683,x98685,x98684,x98682,x98681)),f319(f164(f912(x98681,x98682)),f319(f319(f173(x98681,x98682),x98684),x98685))))
% 22.40/22.31 [10003]E(x100031,x100032)+P1(f319(f319(f321(f912(x100033,x100033)),f319(f319(f244(x100033,x100033),x100031),f619(x100034,x100035,x100032,x100031,x100033))),x100034))+~P1(f319(f319(f321(f912(x100033,x100033)),f319(f319(f244(x100033,x100033),x100031),x100032)),f319(f319(f175(f912(x100033,x100033),a904),x100035),x100034)))
% 22.40/22.31 [10004]E(x100041,f2(a906))+P1(f319(f319(f321(f912(x100042,x100042)),f319(f319(f244(x100042,x100042),x100043),f619(x100044,x100041,x100045,x100043,x100042))),x100044))+~P1(f319(f319(f321(f912(x100042,x100042)),f319(f319(f244(x100042,x100042),x100043),x100045)),f319(f319(f175(f912(x100042,x100042),a904),x100041),x100044)))
% 22.40/22.31 [10040]~P5(x100401)+~P1(f319(f319(f225(x100401),f319(x100404,f474(x100405,x100404,x100403,x100402,x100401))),x100405))+P1(f319(f319(f225(x100401),f319(f319(f33(x100402,x100401),x100403),x100404)),x100405))
% 22.40/22.31 [10064]E(x100641,x100642)+P1(f319(f319(f321(f912(x100643,x100643)),f319(f319(f244(x100643,x100643),f621(x100644,x100645,x100641,x100642,x100643)),x100641)),x100644))+~P1(f319(f319(f321(f912(x100643,x100643)),f319(f319(f244(x100643,x100643),x100642),x100641)),f319(f319(f175(f912(x100643,x100643),a904),x100645),x100644)))
% 22.40/22.31 [10065]E(x100651,f2(a906))+P1(f319(f319(f321(f912(x100652,x100652)),f319(f319(f244(x100652,x100652),f621(x100653,x100651,x100654,x100655,x100652)),x100654)),x100653))+~P1(f319(f319(f321(f912(x100652,x100652)),f319(f319(f244(x100652,x100652),x100655),x100654)),f319(f319(f175(f912(x100652,x100652),a904),x100651),x100653)))
% 22.40/22.31 [10075]E(x100751,x100752)+P1(f319(f319(f321(f912(x100753,x100753)),f319(f319(f244(x100753,x100753),x100751),f621(x100754,x100755,x100752,x100751,x100753))),f319(f319(f175(f912(x100753,x100753),a904),f620(x100754,x100755,x100752,x100751,x100753)),x100754)))+~P1(f319(f319(f321(f912(x100753,x100753)),f319(f319(f244(x100753,x100753),x100751),x100752)),f319(f319(f175(f912(x100753,x100753),a904),x100755),x100754)))
% 22.40/22.31 [10076]E(x100761,f2(a906))+P1(f319(f319(f321(f912(x100762,x100762)),f319(f319(f244(x100762,x100762),x100763),f621(x100764,x100761,x100765,x100763,x100762))),f319(f319(f175(f912(x100762,x100762),a904),f620(x100764,x100761,x100765,x100763,x100762)),x100764)))+~P1(f319(f319(f321(f912(x100762,x100762)),f319(f319(f244(x100762,x100762),x100763),x100765)),f319(f319(f175(f912(x100762,x100762),a904),x100761),x100764)))
% 22.40/22.31 [10118]E(x101181,x101182)+P1(f319(f319(f321(f912(x101183,x101183)),f319(f319(f244(x101183,x101183),f619(x101184,x101185,x101181,x101182,x101183)),x101181)),f319(f319(f175(f912(x101183,x101183),a904),f618(x101184,x101185,x101181,x101182,x101183)),x101184)))+~P1(f319(f319(f321(f912(x101183,x101183)),f319(f319(f244(x101183,x101183),x101182),x101181)),f319(f319(f175(f912(x101183,x101183),a904),x101185),x101184)))
% 22.40/22.31 [10119]E(x101191,f2(a906))+P1(f319(f319(f321(f912(x101192,x101192)),f319(f319(f244(x101192,x101192),f619(x101193,x101191,x101194,x101195,x101192)),x101194)),f319(f319(f175(f912(x101192,x101192),a904),f618(x101193,x101191,x101194,x101195,x101192)),x101193)))+~P1(f319(f319(f321(f912(x101192,x101192)),f319(f319(f244(x101192,x101192),x101195),x101194)),f319(f319(f175(f912(x101192,x101192),a904),x101191),x101193)))
% 22.40/22.31 [10155]~P76(x101552)+~P1(f319(f55(x101551),x101555))+E(f319(f319(f8(x101551,x101552),f319(f319(f9(x101551,x101552,x101552),f319(f319(f20(x101551,x101552,f913(x101552,x101552)),f319(f319(f10(a904,f913(x101552,f913(x101552,x101552)),x101551),f86(x101552)),f319(f319(f9(x101551,f913(x101551,a904),a904),f321(x101551)),x101553))),x101554)),f2(x101552))),x101555),f319(f319(f8(x101551,x101552),x101554),f319(f319(f94(f913(x101551,a904)),x101555),x101553)))
% 22.40/22.31 [8713]~P76(x87131)+~P1(f319(f55(x87134),x87135))+E(f319(f319(f74(x87131),f319(x87132,x87133)),f319(f319(f8(x87134,x87131),x87132),f319(f319(f3(f913(x87134,a904)),x87135),f319(f319(f301(x87134),x87133),f181(f913(x87134,a904)))))),f319(f319(f8(x87134,x87131),x87132),f319(f319(f301(x87134),x87133),x87135)))
% 22.40/22.31 [8714]~P82(x87141)+~P1(f319(f55(x87144),x87145))+E(f319(f319(f75(x87141),f319(x87142,x87143)),f319(f319(f11(x87144,x87141),x87142),f319(f319(f3(f913(x87144,a904)),x87145),f319(f319(f301(x87144),x87143),f181(f913(x87144,a904)))))),f319(f319(f11(x87144,x87141),x87142),f319(f319(f301(x87144),x87143),x87145)))
% 22.40/22.31 [9050]~P4(x90502)+~P13(x90502,f319(f160(x90502),f319(f319(f146(x90501,x90502),x90504),x90505)))+E(f319(f128(x90501,f319(f319(f10(x90502,a904,x90501),f319(f226(x90502),x90503)),x90504)),x90505),f169(x90501,f319(f319(f10(x90502,a904,x90501),f319(f226(x90502),x90503)),x90504),x90505))
% 22.40/22.31 [9075]~P76(x90751)+E(f319(f319(f74(x90751),f319(f319(f8(a906,x90751),x90752),f295(a906,x90753,x90754))),f319(f319(f8(a906,x90751),x90752),f295(a906,f319(f319(f74(a906),x90754),f72(a906)),f319(f319(f74(a906),x90754),x90755)))),f319(f319(f8(a906,x90751),x90752),f295(a906,x90753,f319(f319(f74(a906),x90754),x90755))))+~P1(f319(f319(f225(a906),x90753),f319(f319(f74(a906),x90754),f72(a906))))
% 22.40/22.31 [9076]~P1(f319(f319(f321(x90761),x90764),x90765))+~P1(f319(f319(f225(f913(x90761,a904)),f319(f164(x90761),x90762)),x90765))+P1(f319(f319(f225(f913(x90761,a904)),f319(f164(x90761),f319(f319(f151(x90761,x90762),x90763),x90764))),x90765))
% 22.40/22.31 [9298]~P5(x92982)+~P1(f319(f55(x92981),x92985))+E(f319(f319(f58(x92981,x92982,f319(f319(f10(x92982,f913(x92982,x92982),x92981),f93(x92982)),x92983)),x92984),x92985),f319(f319(f93(x92982),x92984),f319(f319(f33(x92981,x92982),x92985),x92983)))
% 22.40/22.31 [9299]~P5(x92992)+~P1(f319(f55(x92991),x92995))+E(f319(f319(f58(x92991,x92992,f319(f319(f10(x92992,f913(x92992,x92992),x92991),f94(x92992)),x92993)),x92994),x92995),f319(f319(f94(x92992),x92994),f319(f319(f34(x92991,x92992),x92995),x92993)))
% 22.40/22.31 [9347]E(f319(x93471,x93472),f319(x93471,x93473))+P1(f319(f319(f226(a906),f319(x93471,x93472)),f319(x93471,x93473)))+~P1(f319(f319(f321(f912(x93474,x93474)),f319(f319(f244(x93474,x93474),x93472),x93473)),f145(x93474,f319(f319(f143(f913(x93474,a906)),x93471),x93475))))
% 22.40/22.31 [9381]~E(f319(x93814,x93812),f319(x93814,x93813))+~P1(f319(f319(f321(f912(x93811,x93811)),f319(f319(f244(x93811,x93811),x93812),x93813)),f145(x93811,x93815)))+P1(f319(f319(f321(f912(x93811,x93811)),f319(f319(f244(x93811,x93811),x93812),x93813)),f145(x93811,f319(f319(f143(f913(x93811,a906)),x93814),x93815))))
% 22.40/22.31 [9402]~P25(x94021,x94022,x94023,x94025)+P25(x94021,x94022,x94023,f319(f319(f301(x94021),x94024),x94025))+P1(f319(f319(f321(x94022),f319(x94023,x94024)),f319(f302(x94021,x94022,x94023),f319(f319(f3(f913(x94021,a904)),x94025),f319(f319(f301(x94021),x94024),f181(f913(x94021,a904)))))))
% 22.40/22.31 [9407]P1(f319(x94072,x94075))+~P1(f319(f319(f321(x94071),x94075),f319(f164(x94071),x94073)))+E(f319(f319(f130(x94071),f319(f182(f907(x94071)),f169(x94071,x94072,f319(f319(f126(x94071),x94073),x94074)))),f319(f319(f126(x94071),x94073),x94074)),f319(f319(f126(x94071),f319(f319(f130(x94071),f319(f182(f907(x94071)),f169(x94071,x94072,x94073))),x94073)),x94074))
% 22.40/22.31 [9413]~P1(f319(f319(f321(f912(x94131,x94131)),f319(f319(f244(x94131,x94131),x94132),x94133)),f145(x94131,x94135)))+~P1(f319(f319(f225(a906),f319(x94134,x94132)),f319(x94134,x94133)))+P1(f319(f319(f321(f912(x94131,x94131)),f319(f319(f244(x94131,x94131),x94132),x94133)),f145(x94131,f319(f319(f143(f913(x94131,a906)),x94134),x94135))))
% 22.40/22.31 [9478]P1(f319(f319(f321(f912(x94784,x94784)),f319(f319(f244(x94784,x94784),x94782),x94783)),f145(x94784,x94785)))+P1(f319(f319(f226(a906),f319(x94781,x94782)),f319(x94781,x94783)))+~P1(f319(f319(f321(f912(x94784,x94784)),f319(f319(f244(x94784,x94784),x94782),x94783)),f145(x94784,f319(f319(f143(f913(x94784,a906)),x94781),x94785))))
% 22.40/22.31 [9623]~P1(f319(f319(f321(f912(f907(x96231),f907(x96231))),f319(f319(f244(f907(x96231),f907(x96231)),x96232),x96234)),f150(x96231,x96235)))+~P1(f319(f319(f226(a906),x96233),f319(f182(f907(x96231)),x96232)))+P1(f319(f319(f321(f912(x96231,x96231)),f319(f319(f244(x96231,x96231),f319(f319(f156(x96231),x96232),x96233)),f319(f319(f156(x96231),x96234),x96233))),x96235))
% 22.40/22.31 [9895]E(x98951,f2(a1))+~P1(f319(f43(x98953,x98951),f319(f319(f244(a1,a1),x98954),x98955)))+P1(f319(f43(f319(f319(f75(a1),x98952),x98953),x98951),f319(f319(f244(a1,a1),f319(f319(f74(a1),f319(f319(f75(a1),x98952),x98954)),f319(f319(f30(a1),f319(f319(f75(a1),x98952),x98955)),x98951))),f39(a1,f319(f319(f75(a1),x98952),x98955),x98951))))
% 22.40/22.31 [9903]~P1(f319(f319(f226(a906),f2(a906)),x99033))+~P1(f319(f42(x99032,x99033),f319(f319(f244(a906,a906),x99034),x99035)))+P1(f319(f42(f319(f319(f75(a906),x99031),x99032),x99033),f319(f319(f244(a906,a906),f319(f319(f74(a906),f319(f319(f75(a906),x99031),x99034)),f319(f319(f30(a906),f319(f319(f75(a906),x99031),x99035)),x99033))),f39(a906,f319(f319(f75(a906),x99031),x99035),x99033))))
% 22.40/22.31 [10173]~P76(x101732)+~P1(f319(f55(x101731),x101734))+E(f319(f319(f8(x101731,x101732),x101733),f319(f254(x101731),f319(f319(f20(x101731,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101731),a317),f319(f319(f9(x101731,f913(x101731,a904),a904),f321(x101731)),x101734))),f319(f319(f9(x101731,f913(x101731,a904),a904),f321(x101731)),x101735)))),f319(f319(f8(x101731,x101732),f319(f319(f9(x101731,x101732,x101732),f319(f319(f20(x101731,x101732,f913(x101732,x101732)),f319(f319(f10(a904,f913(x101732,f913(x101732,x101732)),x101731),f86(x101732)),f319(f319(f9(x101731,f913(x101731,a904),a904),f321(x101731)),x101735))),x101733)),f2(x101732))),x101734))
% 22.40/22.31 [8344]~E(f319(f319(f126(x83441),x83442),x83445),f319(f319(f126(x83441),x83443),x83444))+E(f319(f319(f126(x83441),f319(f319(f130(x83441),f319(f182(f907(x83441)),x83442)),x83443)),x83444),x83445)+P1(f319(f319(f225(a906),f319(f182(f907(x83441)),x83443)),f319(f182(f907(x83441)),x83442)))
% 22.40/22.31 [8538]~E(f319(f319(f126(x85382),x85383),x85381),f319(f319(f126(x85382),x85384),x85385))+E(x85381,f319(f319(f126(x85382),f319(f319(f130(x85382),f319(f182(f907(x85382)),x85383)),x85384)),x85385))+~P1(f319(f319(f225(a906),f319(f182(f907(x85382)),x85383)),f319(f182(f907(x85382)),x85384)))
% 22.40/22.31 [8629]~E(f319(f319(f74(a906),f319(f319(f75(a906),x86293),x86294)),x86291),f319(f319(f74(a906),f319(f319(f75(a906),x86292),x86294)),x86295))+~P1(f319(f319(f225(a906),x86293),x86292))+E(x86291,f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x86292),x86293)),x86294)),x86295))
% 22.40/22.31 [8630]~E(f319(f319(f74(a906),f319(f319(f75(a906),x86301),x86303)),x86304),f319(f319(f74(a906),f319(f319(f75(a906),x86302),x86303)),x86305))+~P1(f319(f319(f225(a906),x86302),x86301))+E(f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x86301),x86302)),x86303)),x86304),x86305)
% 22.40/22.31 [8791]E(f319(f319(f74(a906),f319(f319(f75(a906),x87911),x87912)),x87913),f319(f319(f74(a906),f319(f319(f75(a906),x87914),x87912)),x87915))+~P1(f319(f319(f225(a906),x87914),x87911))+~E(x87915,f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x87911),x87914)),x87912)),x87913))
% 22.40/22.31 [8792]E(f319(f319(f74(a906),f319(f319(f75(a906),x87921),x87922)),x87923),f319(f319(f74(a906),f319(f319(f75(a906),x87924),x87922)),x87925))+~P1(f319(f319(f225(a906),x87924),x87921))+~E(f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x87921),x87924)),x87922)),x87923),x87925)
% 22.40/22.31 [9687]~P72(x96872)+~P1(f319(f55(x96871),x96875))+E(f319(f319(f11(x96871,x96872),f319(f319(f20(x96871,x96872,x96872),f319(f319(f10(x96872,f913(x96872,x96872),x96871),f282(x96872)),x96873)),x96874)),x96875),f319(f319(f282(x96872),f319(f319(f11(x96871,x96872),x96873),x96875)),f319(f319(f11(x96871,x96872),x96874),x96875)))
% 22.40/22.31 [9829]~E(f622(x98295,x98294,x98293,x98292,x98291),f623(x98295,x98294,x98293,x98292,x98291))+P1(f319(f319(f321(f912(x98291,x98291)),f319(f319(f244(x98291,x98291),x98292),x98293)),f299(x98291,x98294)))+~P1(f319(f319(f321(f912(x98291,x98291)),f319(f319(f244(x98291,x98291),x98292),x98293)),f299(x98291,f319(f319(f93(f913(f912(x98291,x98291),a904)),x98294),x98295))))
% 22.40/22.31 [9830]~E(f624(x98305,x98304,x98303,x98302,x98301),f625(x98305,x98304,x98303,x98302,x98301))+P1(f319(f319(f321(f912(x98301,x98301)),f319(f319(f244(x98301,x98301),x98302),x98303)),f299(x98301,x98304)))+~P1(f319(f319(f321(f912(x98301,x98301)),f319(f319(f244(x98301,x98301),x98302),x98303)),f299(x98301,f319(f319(f93(f913(f912(x98301,x98301),a904)),x98304),x98305))))
% 22.40/22.31 [10032]P1(f319(f319(f321(f912(x100321,x100321)),f319(f319(f244(x100321,x100321),x100322),f623(x100325,x100324,x100323,x100322,x100321))),f299(x100321,x100324)))+P1(f319(f319(f321(f912(x100321,x100321)),f319(f319(f244(x100321,x100321),x100322),x100323)),f299(x100321,x100324)))+~P1(f319(f319(f321(f912(x100321,x100321)),f319(f319(f244(x100321,x100321),x100322),x100323)),f299(x100321,f319(f319(f93(f913(f912(x100321,x100321),a904)),x100324),x100325))))
% 22.40/22.31 [10094]P1(f319(f319(f321(f912(x100941,x100941)),f319(f319(f244(x100941,x100941),f625(x100945,x100944,x100943,x100942,x100941)),x100943)),f299(x100941,x100944)))+P1(f319(f319(f321(f912(x100941,x100941)),f319(f319(f244(x100941,x100941),x100942),x100943)),f299(x100941,x100944)))+~P1(f319(f319(f321(f912(x100941,x100941)),f319(f319(f244(x100941,x100941),x100942),x100943)),f299(x100941,f319(f319(f93(f913(f912(x100941,x100941),a904)),x100944),x100945))))
% 22.40/22.31 [10124]P1(f319(f319(f321(f912(x101241,x101241)),f319(f319(f244(x101241,x101241),x101242),x101243)),f299(x101241,x101244)))+P1(f319(f319(f321(f912(x101241,x101241)),f319(f319(f244(x101241,x101241),f623(x101245,x101244,x101243,x101242,x101241)),f622(x101245,x101244,x101243,x101242,x101241))),x101245))+~P1(f319(f319(f321(f912(x101241,x101241)),f319(f319(f244(x101241,x101241),x101242),x101243)),f299(x101241,f319(f319(f93(f913(f912(x101241,x101241),a904)),x101244),x101245))))
% 22.40/22.31 [10125]P1(f319(f319(f321(f912(x101251,x101251)),f319(f319(f244(x101251,x101251),x101252),x101253)),f299(x101251,x101254)))+P1(f319(f319(f321(f912(x101251,x101251)),f319(f319(f244(x101251,x101251),f624(x101255,x101254,x101253,x101252,x101251)),f625(x101255,x101254,x101253,x101252,x101251))),x101255))+~P1(f319(f319(f321(f912(x101251,x101251)),f319(f319(f244(x101251,x101251),x101252),x101253)),f299(x101251,f319(f319(f93(f913(f912(x101251,x101251),a904)),x101254),x101255))))
% 22.40/22.31 [10301]~P1(f319(f319(f321(f912(f907(x103011),f907(x103011))),f319(f319(f244(f907(x103011),f907(x103011)),x103014),x103015)),f150(x103011,x103012)))+~P1(f319(f319(f321(f912(x103011,x103011)),x103013),f319(f164(f912(x103011,x103011)),f319(f319(f173(x103011,x103011),x103014),x103015))))+P1(f319(f319(f249(x103011,x103011,a904),f319(f319(f9(x103011,f913(f912(x103011,x103011),a904),f913(x103011,a904)),f319(f319(f10(f913(x103011,f913(f913(f912(x103011,x103011),a904),a904)),f913(f913(f912(x103011,x103011),a904),f913(x103011,a904)),x103011),f9(x103011,f913(f912(x103011,x103011),a904),a904)),f319(f319(f10(f913(x103011,f912(x103011,x103011)),f913(x103011,f913(f913(f912(x103011,x103011),a904),a904)),x103011),f319(f10(f912(x103011,x103011),f913(f913(f912(x103011,x103011),a904),a904),x103011),f321(f912(x103011,x103011)))),f244(x103011,x103011)))),x103012)),x103013))
% 22.40/22.31 [9715]~P1(f319(f319(f225(a906),x97153),x97152))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),f319(f319(f75(a906),x97153),x97154)),x97151)),f319(f319(f74(a906),f319(f319(f75(a906),x97152),x97154)),x97155)))+P1(f319(f319(f225(a906),x97151),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x97152),x97153)),x97154)),x97155)))
% 22.40/22.31 [9716]~P1(f319(f319(f225(a906),x97163),x97162))+~P1(f319(f319(f226(a906),f319(f319(f74(a906),f319(f319(f75(a906),x97163),x97164)),x97161)),f319(f319(f74(a906),f319(f319(f75(a906),x97162),x97164)),x97165)))+P1(f319(f319(f226(a906),x97161),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x97162),x97163)),x97164)),x97165)))
% 22.40/22.31 [9740]~P1(f319(f319(f225(a906),x97401),x97404))+P1(f319(f319(f225(a906),f319(f319(f74(a906),f319(f319(f75(a906),x97401),x97402)),x97403)),f319(f319(f74(a906),f319(f319(f75(a906),x97404),x97402)),x97405)))+~P1(f319(f319(f225(a906),x97403),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x97404),x97401)),x97402)),x97405)))
% 22.40/22.31 [9741]~P1(f319(f319(f225(a906),x97411),x97414))+P1(f319(f319(f226(a906),f319(f319(f74(a906),f319(f319(f75(a906),x97411),x97412)),x97413)),f319(f319(f74(a906),f319(f319(f75(a906),x97414),x97412)),x97415)))+~P1(f319(f319(f226(a906),x97413),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x97414),x97411)),x97412)),x97415)))
% 22.40/22.31 [9865]~P1(f319(f319(f225(a906),x98652),x98651))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),f319(f319(f75(a906),x98651),x98653)),x98654)),f319(f319(f74(a906),f319(f319(f75(a906),x98652),x98653)),x98655)))+P1(f319(f319(f225(a906),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x98651),x98652)),x98653)),x98654)),x98655))
% 22.40/22.31 [9866]~P1(f319(f319(f225(a906),x98662),x98661))+~P1(f319(f319(f226(a906),f319(f319(f74(a906),f319(f319(f75(a906),x98661),x98663)),x98664)),f319(f319(f74(a906),f319(f319(f75(a906),x98662),x98663)),x98665)))+P1(f319(f319(f226(a906),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x98661),x98662)),x98663)),x98664)),x98665))
% 22.40/22.31 [9926]~P1(f319(f319(f225(a906),x99264),x99261))+P1(f319(f319(f225(a906),f319(f319(f74(a906),f319(f319(f75(a906),x99261),x99262)),x99263)),f319(f319(f74(a906),f319(f319(f75(a906),x99264),x99262)),x99265)))+~P1(f319(f319(f225(a906),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x99261),x99264)),x99262)),x99263)),x99265))
% 22.40/22.31 [9927]~P1(f319(f319(f225(a906),x99274),x99271))+P1(f319(f319(f226(a906),f319(f319(f74(a906),f319(f319(f75(a906),x99271),x99272)),x99273)),f319(f319(f74(a906),f319(f319(f75(a906),x99274),x99272)),x99275)))+~P1(f319(f319(f226(a906),f319(f319(f74(a906),f319(f319(f75(a906),f319(f319(f3(a906),x99271),x99274)),x99272)),x99273)),x99275))
% 22.40/22.31 [10113]~P11(x101131,x101132,x101135,x101133)+~P1(f319(f319(f321(f912(x101131,x101131)),x101134),x101135))+P1(f319(f319(f249(x101131,x101131,a904),f319(f319(f9(x101131,f913(x101131,x101132),f913(x101131,a904)),f319(f319(f10(f913(x101132,a904),f913(f913(x101131,x101132),f913(x101131,a904)),x101131),f10(x101132,a904,x101131)),f319(f319(f10(x101132,f913(x101132,a904),x101131),a316),x101133))),x101133)),x101134))
% 22.40/22.31 [10135]~P111(x101351)+~P40(x101351,f913(x101352,a904),x101353)+P40(x101351,f913(x101352,a904),f319(f319(f9(x101351,f913(x101352,a904),f913(x101352,a904)),f319(f319(f10(f913(x101352,a904),f913(f913(x101352,a904),f913(x101352,a904)),x101351),f93(f913(x101352,a904))),f319(f319(f9(x101351,f913(x101352,a904),f913(x101352,a904)),f319(f319(f10(f913(x101352,a904),f913(f913(x101352,a904),f913(x101352,a904)),x101351),f93(f913(x101352,a904))),x101353)),x101354))),x101355))
% 22.40/22.31 [8502]~P20(x85026,x85021,x85022,x85024)+E(f319(f66(x85021,x85021,x85021,f319(x85022,x85023)),f319(x85024,x85025)),f319(f66(x85021,x85021,x85021,f319(x85024,x85025)),f319(x85022,x85023)))+~P1(f319(f55(x85026),x85025))
% 22.40/22.31 [8937]~P25(x89371,x89373,x89375,x89376)+~P25(x89373,x89372,x89374,f319(f302(x89371,x89373,x89375),x89376))+P25(x89371,x89372,f319(f66(x89373,x89372,x89371,x89374),x89375),x89376)
% 22.40/22.31 [9515]~P1(f319(f319(x95154,x95152),x95156))+~P1(f319(f319(x95153,x95155),x95152))+P1(f319(f319(f321(x95151),x95152),f289(x95151,x95153,x95154,x95155,x95156)))
% 22.40/22.31 [9516]~P1(f319(f319(x95163,x95162),x95166))+~P1(f319(f319(x95164,x95165),x95162))+P1(f319(f319(f321(x95161),x95162),f292(x95161,x95163,x95164,x95165,x95166)))
% 22.40/22.31 [9624]E(x96241,x96242)+E(x96243,x96244)+~P1(f319(f319(f321(f912(f907(x96245),f907(x96245))),f319(f319(f244(f907(x96245),f907(x96245)),f319(f319(f143(x96245),x96243),x96241)),f319(f319(f143(x96245),x96244),x96242))),f149(x96245,x96246)))
% 22.40/22.31 [9638]~E(x96382,x96384)+P1(f319(f319(f321(f912(f907(x96381),f907(x96381))),f319(f319(f244(f907(x96381),f907(x96381)),f319(f319(f143(x96381),x96382),x96383)),f319(f319(f143(x96381),x96384),x96385))),f137(x96381,x96386)))+~P1(f319(f319(f321(f912(f907(x96381),f907(x96381))),f319(f319(f244(f907(x96381),f907(x96381)),x96383),x96385)),f137(x96381,x96386)))
% 22.40/22.31 [9639]~E(x96392,x96394)+P1(f319(f319(f321(f912(f907(x96391),f907(x96391))),f319(f319(f244(f907(x96391),f907(x96391)),f319(f319(f143(x96391),x96392),x96393)),f319(f319(f143(x96391),x96394),x96395))),f139(x96391,x96396)))+~P1(f319(f319(f321(f912(f907(x96391),f907(x96391))),f319(f319(f244(f907(x96391),f907(x96391)),x96393),x96395)),f139(x96391,x96396)))
% 22.40/22.31 [9640]~E(x96402,x96404)+P1(f319(f319(f321(f912(f907(x96401),f907(x96401))),f319(f319(f244(f907(x96401),f907(x96401)),f319(f319(f143(x96401),x96402),x96403)),f319(f319(f143(x96401),x96404),x96405))),f149(x96401,x96406)))+~P1(f319(f319(f321(f912(f907(x96401),f907(x96401))),f319(f319(f244(f907(x96401),f907(x96401)),x96403),x96405)),f149(x96401,x96406)))
% 22.40/22.31 [9641]~E(x96412,x96414)+P1(f319(f319(f321(f912(f907(x96411),f907(x96411))),f319(f319(f244(f907(x96411),f907(x96411)),f319(f319(f126(x96411),x96412),x96413)),f319(f319(f126(x96411),x96414),x96415))),f149(x96411,x96416)))+~P1(f319(f319(f321(f912(f907(x96411),f907(x96411))),f319(f319(f244(f907(x96411),f907(x96411)),x96413),x96415)),f149(x96411,x96416)))
% 22.40/22.31 [9642]~E(x96423,x96425)+P1(f319(f319(f321(f912(f907(x96421),f907(x96421))),f319(f319(f244(f907(x96421),f907(x96421)),f319(f319(f126(x96421),x96422),x96423)),f319(f319(f126(x96421),x96424),x96425))),f149(x96421,x96426)))+~P1(f319(f319(f321(f912(f907(x96421),f907(x96421))),f319(f319(f244(f907(x96421),f907(x96421)),x96422),x96424)),f149(x96421,x96426)))
% 22.40/22.31 [9705]E(x97051,x97052)+P1(f319(f319(f321(f912(f907(x97053),f907(x97053))),f319(f319(f244(f907(x97053),f907(x97053)),x97051),x97052)),f149(x97053,x97054)))+~P1(f319(f319(f321(f912(f907(x97053),f907(x97053))),f319(f319(f244(f907(x97053),f907(x97053)),f319(f319(f143(x97053),x97055),x97051)),f319(f319(f143(x97053),x97056),x97052))),f149(x97053,x97054)))
% 22.40/22.31 [9869]~E(x98693,x98695)+P1(f319(f319(f321(f912(f907(x98691),f907(x98691))),f319(f319(f244(f907(x98691),f907(x98691)),f319(f319(f126(x98691),x98692),f319(f319(f143(x98691),x98693),f105(x98691)))),f319(f319(f126(x98691),x98694),f319(f319(f143(x98691),x98695),f105(x98691))))),f149(x98691,x98696)))+~P1(f319(f319(f321(f912(f907(x98691),f907(x98691))),f319(f319(f244(f907(x98691),f907(x98691)),x98692),x98694)),f149(x98691,x98696)))
% 22.40/22.31 [9930]E(x99301,x99302)+E(x99303,x99304)+~P1(f319(f319(f321(f912(f907(x99305),f907(x99305))),f319(f319(f244(f907(x99305),f907(x99305)),f319(f319(f126(x99305),x99303),f319(f319(f143(x99305),x99301),f105(x99305)))),f319(f319(f126(x99305),x99304),f319(f319(f143(x99305),x99302),f105(x99305))))),f149(x99305,x99306)))
% 22.40/22.31 [9953]E(x99531,x99532)+~P1(f319(f319(f321(f912(f907(x99533),f907(x99533))),f319(f319(f244(f907(x99533),f907(x99533)),f319(f319(f126(x99533),x99531),f319(f319(f143(x99533),x99535),f105(x99533)))),f319(f319(f126(x99533),x99532),f319(f319(f143(x99533),x99536),f105(x99533))))),f149(x99533,x99534)))+P1(f319(f319(f321(f912(f907(x99533),f907(x99533))),f319(f319(f244(f907(x99533),f907(x99533)),x99531),x99532)),f149(x99533,x99534)))
% 22.40/22.31 [9995]~P1(f319(f319(f321(f912(f913(x99951,a904),f913(x99951,a904))),f319(f319(f244(f913(x99951,a904),f913(x99951,a904)),x99952),x99954)),f311(x99951,x99956)))+~P1(f319(f319(f321(f912(f913(x99951,a904),f913(x99951,a904))),f319(f319(f244(f913(x99951,a904),f913(x99951,a904)),x99953),x99955)),f311(x99951,x99956)))+P1(f319(f319(f321(f912(f913(x99951,a904),f913(x99951,a904))),f319(f319(f244(f913(x99951,a904),f913(x99951,a904)),f319(f319(f93(f913(x99951,a904)),x99952),x99953)),f319(f319(f93(f913(x99951,a904)),x99954),x99955))),f311(x99951,x99956)))
% 22.40/22.31 [5771]~E(f319(f319(f126(x57711),x57716),x57713),x57715)+E(f319(f319(f126(x57711),x57712),x57713),f319(f319(f143(x57711),x57714),x57715))+~E(x57712,f319(f319(f143(x57711),x57714),x57716))
% 22.40/22.31 [5772]~E(f319(f319(f126(x57721),x57726),x57723),x57725)+E(f319(f319(f126(x57721),x57722),x57723),f319(f319(f126(x57721),x57724),x57725))+~E(x57722,f319(f319(f126(x57721),x57724),x57726))
% 22.40/22.31 [5774]E(f319(f319(f126(x57741),x57742),x57743),f319(f319(f143(x57741),x57744),x57745))+~E(f319(f319(f143(x57741),x57744),x57746),x57742)+~E(x57745,f319(f319(f126(x57741),x57746),x57743))
% 22.40/22.31 [5776]~E(f319(f319(f126(x57761),x57762),x57766),x57764)+E(f319(f319(f126(x57761),x57762),x57763),f319(f319(f126(x57761),x57764),x57765))+~E(x57763,f319(f319(f126(x57761),x57766),x57765))
% 22.40/22.31 [6920]E(f319(x69201,x69202),f319(x69203,x69202))+~E(f319(f319(f146(x69204,x69205),x69201),x69206),f319(f319(f146(x69204,x69205),x69203),x69206))+~P1(f319(f319(f321(x69204),x69202),f319(f164(x69204),x69206)))
% 22.40/22.31 [7300]~P20(x73004,x73005,x73006,x73001)+E(f319(f319(x73001,x73002),x73003),f319(f319(f58(x73004,x73005,x73006),x73003),x73002))+~P1(f319(f55(x73004),x73002))
% 22.40/22.31 [7371]~E(x73712,f319(x73714,x73716))+~P1(f319(f319(f321(x73713),x73716),x73715))+P1(f319(f319(f321(x73711),x73712),f319(f302(x73713,x73711,x73714),x73715)))
% 22.40/22.31 [7372]~E(f319(x73724,x73722),x73726)+~P1(f319(f319(f321(x73723),x73726),x73725))+P1(f319(f319(f321(x73721),x73722),f319(f303(x73721,x73723,x73724),x73725)))
% 22.40/22.31 [7803]~P32(x78031,x78032,x78034,x78036)+P32(x78031,x78032,f319(f319(f143(x78031),x78033),x78034),f319(f319(f143(x78031),x78035),x78036))+~P1(f319(f319(x78032,x78033),x78035))
% 22.40/22.31 [8801]~P58(x88014,x88015,x88011,x88012,x88016)+E(f319(x88011,f319(x88012,x88013)),x88013)+~P1(f319(f319(f321(x88015),x88013),x88016))
% 22.40/22.31 [9308]~P26(x93082,x93081,x93085,x93084,x93083)+E(f319(f85(x93081,x93082,x93083,f85(x93082,x93081,x93084,x93085)),x93086),f319(x93085,x93086))+~P1(f319(f319(f321(x93082),x93086),x93084))
% 22.40/22.31 [9319]~P25(x93191,x93192,x93193,x93196)+P25(x93191,x93192,f68(x93191,x93192,x93193,x93194,x93195),x93196)+P1(f319(f319(f321(x93192),x93195),f319(f302(x93191,x93192,x93193),x93196)))
% 22.40/22.31 [9627]E(x96271,x96272)+E(f319(f182(f907(x96273)),x96274),f319(f182(f907(x96273)),x96275))+~P1(f319(f319(f321(f912(f907(x96273),f907(x96273))),f319(f319(f244(f907(x96273),f907(x96273)),f319(f319(f143(x96273),x96271),x96274)),f319(f319(f143(x96273),x96272),x96275))),f137(x96273,x96276)))
% 22.40/22.31 [9699]~P17(x96991,x96992,x96993)+E(f319(f319(f58(x96991,x96992,x96993),x96994),x96995),x96996)+~P1(f319(f60(x96991,x96992,x96993,x96994,x96995),x96996))
% 22.40/22.31 [9706]E(f319(f182(f907(x97061)),x97062),f319(f182(f907(x97061)),x97063))+P1(f319(f319(f321(f912(f907(x97061),f907(x97061))),f319(f319(f244(f907(x97061),f907(x97061)),x97062),x97063)),f137(x97061,x97064)))+~P1(f319(f319(f321(f912(f907(x97061),f907(x97061))),f319(f319(f244(f907(x97061),f907(x97061)),f319(f319(f143(x97061),x97065),x97062)),f319(f319(f143(x97061),x97066),x97063))),f137(x97061,x97064)))
% 22.40/22.31 [9734]~P1(f319(f319(f321(f912(x97341,x97341)),f319(f319(f244(x97341,x97341),x97342),x97344)),f299(x97341,x97346)))+P1(f319(f319(f321(f912(f907(x97341),f907(x97341))),f319(f319(f244(f907(x97341),f907(x97341)),f319(f319(f143(x97341),x97342),x97343)),f319(f319(f143(x97341),x97344),x97345))),f299(f907(x97341),f149(x97341,x97346))))+~P1(f319(f319(f321(f912(f907(x97341),f907(x97341))),f319(f319(f244(f907(x97341),f907(x97341)),x97343),x97345)),f299(f907(x97341),f149(x97341,x97346))))
% 22.40/22.31 [9935]~P1(f319(x99352,x99356))+~E(f319(f128(x99351,x99352),x99353),f319(f319(f143(x99351),x99354),x99355))+~P1(f319(f319(f321(x99351),x99356),f319(f164(x99351),f733(x99355,x99354,x99353,x99352,x99351))))
% 22.40/22.31 [9936]~P1(f319(x99364,x99366))+~E(f319(f319(f143(x99361),x99362),x99363),f319(f128(x99361,x99364),x99365))+~P1(f319(f319(f321(x99361),x99366),f319(f164(x99361),f737(x99365,x99364,x99363,x99362,x99361))))
% 22.40/22.31 [10217]~P76(x102172)+E(f319(f319(f8(x102171,x102172),f319(f319(f10(f913(x102173,a904),x102172,x102171),f319(f8(x102173,x102172),x102174)),f319(f319(f10(f913(x102173,a904),f913(x102173,a904),x102171),f254(x102173)),f319(f319(f10(f913(x102173,a904),f913(x102173,a904),x102171),f319(f20(x102173,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102173),a317),f319(f319(f9(x102173,f913(x102173,a904),a904),f321(x102173)),x102175)))),f319(f9(x102173,x102171,a904),f319(f319(f10(x102171,f913(x102171,a904),x102173),a316),x102176)))))),f319(f302(x102173,x102171,x102176),x102175)),f319(f319(f8(x102173,x102172),x102174),x102175))+~P1(f319(f55(x102173),x102175))
% 22.40/22.31 [6975]~P4(x69753)+P1(f319(x69752,x69755))+E(f319(f128(x69751,x69752),f319(f319(f140(x69751,x69753,x69754),x69755),x69756)),f319(f128(x69751,x69752),x69756))
% 22.40/22.31 [6977]P1(f319(x69771,x69772))+~E(f158(x69773,x69771,x69774),f319(f319(f244(f907(x69773),f907(x69773)),x69775),x69776))+~P1(f319(f319(f321(x69773),x69772),f319(f164(x69773),x69775)))
% 22.40/22.31 [7020]~P1(f319(x70202,x70206))+~E(f158(x70201,x70202,x70203),f319(f319(f244(f907(x70201),f907(x70201)),x70204),x70205))+~P1(f319(f319(f321(x70201),x70206),f319(f164(x70201),x70205)))
% 22.40/22.31 [7672]~P15(x76721,x76722,x76723)+~P1(f319(f55(x76721),x76726))+E(f319(f319(f58(x76721,x76722,x76723),x76724),f319(f319(f301(x76721),x76725),x76726)),f319(f319(f58(x76721,x76722,x76723),f319(f319(x76723,x76725),x76724)),x76726))
% 22.40/22.31 [7720]~P4(x77202)+~P1(f319(f319(f225(x77202),f319(x77203,x77204)),f319(x77203,x77205)))+E(f319(f319(f140(x77201,x77202,x77203),x77204),f319(f319(f143(x77201),x77205),x77206)),f319(f319(f143(x77201),x77204),f319(f319(f143(x77201),x77205),x77206)))
% 22.40/22.31 [7831]E(x78311,x78312)+~E(f319(f319(f246(x78313,x78314),x78311),f319(f18(f913(x78314,a904),x78313),x78315)),f319(f319(f246(x78313,x78314),x78312),f319(f18(f913(x78314,a904),x78313),x78315)))+~P1(f319(f319(f321(x78314),x78316),x78315))
% 22.40/22.31 [7900]~P15(x79001,x79002,x79003)+~P1(f319(f55(x79001),x79006))+E(f319(f319(f58(x79001,x79002,x79003),x79004),f319(f319(f301(x79001),x79005),x79006)),f319(f319(x79003,x79005),f319(f319(f58(x79001,x79002,x79003),x79004),x79006)))
% 22.40/22.31 [8014]~P17(x80141,x80142,x80143)+~P1(f319(f55(x80141),x80146))+E(f319(f319(f58(x80141,x80142,x80143),f319(f319(x80143,x80144),x80145)),x80146),f319(f319(x80143,x80144),f319(f319(f58(x80141,x80142,x80143),x80145),x80146)))
% 22.40/22.31 [8078]~P21(x80782,x80785,x80786,x80781)+~P1(f319(f55(x80782),x80784))+E(f319(x80781,f319(f319(f301(x80782),x80783),x80784)),f319(f66(x80785,x80785,x80785,f319(x80781,x80784)),f319(x80786,x80783)))
% 22.40/22.31 [8109]~P4(x81092)+P1(f319(f319(f225(x81092),f319(x81093,x81094)),f319(x81093,x81095)))+E(f319(f319(f140(x81091,x81092,x81093),x81094),f319(f319(f143(x81091),x81095),x81096)),f319(f319(f143(x81091),x81095),f319(f319(f140(x81091,x81092,x81093),x81094),x81096)))
% 22.40/22.31 [8253]~E(f319(f182(f907(x82531)),x82535),f319(f182(f907(x82532)),x82536))+~E(f319(f182(f907(x82531)),x82533),f319(f182(f907(x82532)),x82534))+E(f319(f319(f126(f912(x82531,x82532)),f319(f319(f173(x82531,x82532),x82533),x82534)),f319(f319(f173(x82531,x82532),x82535),x82536)),f319(f319(f173(x82531,x82532),f319(f319(f126(x82531),x82533),x82535)),f319(f319(f126(x82532),x82534),x82536)))
% 22.40/22.31 [8362]~E(x83622,f319(f302(x83623,x83621,x83624),x83626))+P1(f319(f319(f225(f913(x83621,a904)),x83622),f319(f302(x83623,x83621,x83624),x83625)))+~P1(f319(f319(f225(f913(x83623,a904)),x83626),x83625))
% 22.40/22.31 [8462]~P4(x84625)+E(f319(x84621,x84622),f319(x84621,x84623))+E(f319(f319(f140(x84624,x84625,x84621),x84622),f319(f319(f140(x84624,x84625,x84621),x84623),x84626)),f319(f319(f140(x84624,x84625,x84621),x84623),f319(f319(f140(x84624,x84625,x84621),x84622),x84626)))
% 22.40/22.31 [8638]~P1(f319(f319(f321(x86382),x86384),f319(x86386,x86383)))+~P1(f319(f319(f321(x86381),x86383),x86385))+P1(f319(f319(f321(f912(x86381,x86382)),f319(f319(f244(x86381,x86382),x86383),x86384)),f319(f319(f246(x86381,x86382),x86385),x86386)))
% 22.40/22.31 [9116]~P76(x91162)+~P25(x91164,x91161,x91165,x91166)+E(f319(f319(f8(x91161,x91162),x91163),f319(f302(x91164,x91161,x91165),x91166)),f319(f319(f8(x91164,x91162),f319(f66(x91161,x91162,x91164,x91163),x91165)),x91166))
% 22.40/22.31 [9117]~P82(x91172)+~P25(x91174,x91171,x91175,x91176)+E(f319(f319(f11(x91171,x91172),x91173),f319(f302(x91174,x91171,x91175),x91176)),f319(f319(f11(x91174,x91172),f319(f66(x91171,x91172,x91174,x91173),x91175)),x91176))
% 22.40/22.31 [9160]~P34(x91602,x91605,x91601,x91603,x91606)+P1(f319(f319(x91601,f319(f319(f156(x91602),x91603),x91604)),f319(f319(f156(x91605),x91606),x91604)))+~P1(f319(f319(f226(a906),x91604),f319(f182(f907(x91605)),x91606)))
% 22.40/22.31 [9161]~P34(x91612,x91615,x91611,x91613,x91616)+P1(f319(f319(x91611,f319(f319(f156(x91612),x91613),x91614)),f319(f319(f156(x91615),x91616),x91614)))+~P1(f319(f319(f226(a906),x91614),f319(f182(f907(x91612)),x91613)))
% 22.40/22.31 [9170]~E(f319(f302(x91701,x91702,x91703),x91704),x91706)+E(f319(f302(x91701,x91702,x91703),f319(f302(x91702,x91701,f85(x91701,x91702,x91704,x91703)),x91705)),x91705)+~P1(f319(f319(f225(f913(x91702,a904)),x91705),x91706))
% 22.40/22.31 [9376]~P20(x93763,x93761,x93766,x93762)+~P1(f319(f55(x93763),x93764))+E(f319(f66(x93761,x93761,x93761,f319(x93762,f319(f319(f3(f913(x93763,a904)),x93764),f319(f319(f301(x93763),x93765),f181(f913(x93763,a904)))))),f319(x93766,x93765)),f319(x93762,f319(f319(f301(x93763),x93765),x93764)))
% 22.40/22.31 [9389]~P1(f319(f319(f321(x93895),x93893),x93896))+P1(f319(f319(f321(x93891),f319(x93892,x93893)),f88(f913(x93891,a904),x93894)))+~P1(f319(f319(f225(f913(x93891,a904)),f319(f302(x93895,x93891,x93892),x93896)),f319(x93894,f319(f302(x93895,x93891,x93892),x93896))))
% 22.40/22.31 [10015]~E(f319(f302(x100152,x100154,x100156),f234(f913(x100152,a904))),f234(f913(x100154,a904)))+~E(f319(f302(x100151,x100153,x100155),f234(f913(x100151,a904))),f234(f913(x100153,a904)))+E(f319(f302(f912(x100151,x100152),f912(x100153,x100154),f250(x100151,x100153,x100152,x100154,x100155,x100156)),f234(f913(f912(x100151,x100152),a904))),f234(f913(f912(x100153,x100154),a904)))
% 22.40/22.31 [10055]~P25(x100553,x100554,x100555,f319(x100556,f529(x100556,x100555,x100554,x100553,x100552,x100551)))+P25(x100553,x100554,x100555,f319(f319(f34(x100552,f913(x100553,a904)),x100551),x100556))+E(x100551,f181(f913(x100552,a904)))
% 22.40/22.31 [10101]P25(x101016,x101015,x101014,f319(f319(f34(x101012,f913(x101016,a904)),x101011),x101013))+E(x101011,f181(f913(x101012,a904)))+P1(f319(f319(f321(x101012),f529(x101013,x101014,x101015,x101016,x101012,x101011)),x101011))
% 22.40/22.31 [10104]P1(f319(f319(f321(x101041),f590(x101042,x101043,x101044,x101045,x101046,x101041)),x101046))+P1(f319(f319(f225(f913(f912(x101041,x101044),a904)),f319(f319(f246(x101041,x101044),x101046),x101043)),f319(f319(f246(x101041,x101044),x101045),x101042)))+~P1(f319(f319(f225(f913(x101041,a904)),x101046),x101045))
% 22.40/22.31 [10233]~P1(f319(f319(f225(f913(x102332,a904)),f319(x102334,f590(x102336,x102334,x102332,x102335,x102333,x102331))),f319(x102336,f590(x102336,x102334,x102332,x102335,x102333,x102331))))+~P1(f319(f319(f225(f913(x102331,a904)),x102333),x102335))+P1(f319(f319(f225(f913(f912(x102331,x102332),a904)),f319(f319(f246(x102331,x102332),x102333),x102334)),f319(f319(f246(x102331,x102332),x102335),x102336)))
% 22.40/22.31 [7853]~P1(f319(x78531,x78535))+~P1(f319(x78536,x78534))+P1(f319(x78531,f319(f248(x78532,x78533),f319(f319(f244(x78532,x78533),x78534),x78535))))
% 22.40/22.31 [7854]~P1(f319(x78541,x78544))+~P1(f319(x78546,x78545))+P1(f319(x78541,f319(f243(x78542,x78543),f319(f319(f244(x78542,x78543),x78544),x78545))))
% 22.40/22.31 [7905]~P1(f319(f319(x79054,x79056),x79055))+~P1(f319(f319(f321(x79051),x79056),x79053))+P1(f319(f319(f319(f33(x79051,f913(x79052,a904)),x79053),x79054),x79055))
% 22.40/22.31 [8203]~P1(f319(f319(f321(x82031),x82032),f319(x82035,x82036)))+~P1(f319(f319(f321(x82033),x82036),x82034))+P1(f319(f319(f321(x82031),x82032),f319(f319(f33(x82033,f913(x82031,a904)),x82034),x82035)))
% 22.40/22.31 [8247]P1(f319(f319(x82471,x82472),x82473))+~P1(f319(f319(x82474,x82472),x82473))+~P1(f319(f319(f225(f913(x82475,f913(x82476,a904))),x82474),x82471))
% 22.40/22.31 [8385]P1(f319(f319(x83851,x83852),x83853))+~P1(f319(f319(f321(x83854),x83852),x83855))+~P1(f319(f319(f319(f34(x83854,f913(x83856,a904)),x83855),x83851),x83853))
% 22.40/22.31 [8515]P1(f319(f319(f321(x85151),x85152),f319(x85153,x85154)))+~P1(f319(f319(f321(x85155),x85154),x85156))+~P1(f319(f319(f321(x85151),x85152),f319(f319(f34(x85155,f913(x85151,a904)),x85156),x85153)))
% 22.40/22.31 [8781]~P11(x87814,x87815,x87816,x87811)+E(f319(x87811,x87812),f319(x87811,x87813))+~P1(f319(f319(f321(f912(x87814,x87814)),f319(f319(f244(x87814,x87814),x87812),x87813)),x87816))
% 22.40/22.31 [8815]P1(f319(f319(f225(f913(x88151,a904)),x88152),f319(x88153,x88154)))+~P1(f319(f319(f321(x88155),x88154),x88156))+~P1(f319(f319(f225(f913(x88151,a904)),x88152),f319(f319(f34(x88155,f913(x88151,a904)),x88156),x88153)))
% 22.40/22.31 [8850]~P56(x88503,x88504,f319(f278(x88504,x88503),x88505))+E(x88501,f181(f913(x88502,a904)))+E(f319(f319(f34(x88502,f913(x88503,a904)),x88501),f319(f319(f10(f913(x88504,a904),f913(x88503,a904),x88502),f277(x88504,x88503,x88505)),x88506)),f319(f277(x88504,x88503,x88505),f319(f319(f34(x88502,f913(x88504,a904)),x88501),x88506)))
% 22.40/22.31 [8928]P1(f319(f319(f321(x89281),x89282),f319(f277(x89283,x89281,x89284),x89285)))+~P1(f319(f319(f321(x89283),x89286),x89285))+~P1(f319(f319(f321(f912(x89283,x89281)),f319(f319(f244(x89283,x89281),x89286),x89282)),x89284))
% 22.40/22.31 [9236]P1(f319(f319(f225(f913(x92361,a904)),f319(f277(x92362,x92361,x92363),x92364)),f319(f277(x92362,x92361,x92365),x92366)))+~P1(f319(f319(f225(f913(x92362,a904)),x92364),x92366))+~P1(f319(f319(f225(f913(f912(x92362,x92361),a904)),x92363),x92365))
% 22.40/22.31 [9433]~P1(f319(f319(f321(x94332),x94336),x94334))+~P1(f319(f319(f225(f913(x94331,a904)),x94333),x94335))+P1(f319(f319(f225(f913(f912(x94331,x94332),a904)),f319(f319(f246(x94331,x94332),x94333),f319(f18(f913(x94332,a904),x94331),x94334))),f319(f319(f246(x94331,x94332),x94335),f319(f18(f913(x94332,a904),x94331),x94334))))
% 22.40/22.31 [9441]~P34(x94411,x94412,x94413,x94415,x94416)+P1(f319(f319(f249(x94411,x94412,a904),x94413),x94414))+~P1(f319(f319(f321(f912(x94411,x94412)),x94414),f319(f164(f912(x94411,x94412)),f319(f319(f173(x94411,x94412),x94415),x94416))))
% 22.40/22.31 [9577]~E(x95773,x95775)+P1(f319(f319(f321(f912(f907(x95771),f907(x95771))),f319(f319(f244(f907(x95771),f907(x95771)),f319(f319(f143(x95771),x95772),x95773)),f319(f319(f143(x95771),x95774),x95775))),f149(x95771,x95776)))+~P1(f319(f319(f321(f912(x95771,x95771)),f319(f319(f244(x95771,x95771),x95772),x95774)),x95776))
% 22.40/22.31 [9583]~E(f319(f182(f907(x95831)),x95833),f319(f182(f907(x95831)),x95835))+P1(f319(f319(f321(f912(f907(x95831),f907(x95831))),f319(f319(f244(f907(x95831),f907(x95831)),f319(f319(f143(x95831),x95832),x95833)),f319(f319(f143(x95831),x95834),x95835))),f137(x95831,x95836)))+~P1(f319(f319(f321(f912(x95831,x95831)),f319(f319(f244(x95831,x95831),x95832),x95834)),x95836))
% 22.40/22.31 [9619]P1(f319(f319(f321(f912(x96191,x96191)),f319(f319(f244(x96191,x96191),x96192),x96193)),f319(f319(f175(f912(x96191,x96191),a904),f319(a104,x96194)),x96195)))+~P1(f319(f319(f321(f912(x96191,x96191)),f319(f319(f244(x96191,x96191),x96196),x96193)),x96195))+~P1(f319(f319(f321(f912(x96191,x96191)),f319(f319(f244(x96191,x96191),x96192),x96196)),f319(f319(f175(f912(x96191,x96191),a904),x96194),x96195)))
% 22.40/22.31 [9620]P1(f319(f319(f321(f912(x96201,x96201)),f319(f319(f244(x96201,x96201),x96202),x96203)),f319(f319(f175(f912(x96201,x96201),a904),f319(a104,x96204)),x96205)))+~P1(f319(f319(f321(f912(x96201,x96201)),f319(f319(f244(x96201,x96201),x96202),x96206)),x96205))+~P1(f319(f319(f321(f912(x96201,x96201)),f319(f319(f244(x96201,x96201),x96206),x96203)),f319(f319(f175(f912(x96201,x96201),a904),x96204),x96205)))
% 22.40/22.31 [9622]~P1(f319(f319(f321(x96224),x96225),x96226))+P1(f319(f319(f225(f913(x96221,a904)),x96222),x96223))+~P1(f319(f319(f225(f913(f912(x96221,x96224),a904)),f319(f319(f246(x96221,x96224),x96222),f319(f18(f913(x96224,a904),x96221),x96226))),f319(f319(f246(x96221,x96224),x96223),f319(f18(f913(x96224,a904),x96221),x96226))))
% 22.40/22.31 [9677]E(x96771,x96772)+~P1(f319(f319(f321(f912(f907(x96773),f907(x96773))),f319(f319(f244(f907(x96773),f907(x96773)),f319(f319(f143(x96773),x96771),x96775)),f319(f319(f143(x96773),x96772),x96776))),f137(x96773,x96774)))+P1(f319(f319(f321(f912(x96773,x96773)),f319(f319(f244(x96773,x96773),x96771),x96772)),x96774))
% 22.40/22.31 [9678]E(x96781,x96782)+~P1(f319(f319(f321(f912(f907(x96783),f907(x96783))),f319(f319(f244(f907(x96783),f907(x96783)),f319(f319(f143(x96783),x96781),x96785)),f319(f319(f143(x96783),x96782),x96786))),f139(x96783,x96784)))+P1(f319(f319(f321(f912(x96783,x96783)),f319(f319(f244(x96783,x96783),x96781),x96782)),x96784))
% 22.40/22.31 [9679]E(x96791,x96792)+~P1(f319(f319(f321(f912(f907(x96793),f907(x96793))),f319(f319(f244(f907(x96793),f907(x96793)),f319(f319(f143(x96793),x96791),x96795)),f319(f319(f143(x96793),x96792),x96796))),f149(x96793,x96794)))+P1(f319(f319(f321(f912(x96793,x96793)),f319(f319(f244(x96793,x96793),x96791),x96792)),x96794))
% 22.40/22.31 [9714]P1(f319(f319(f321(f912(f907(x97141),f907(x97141))),f319(f319(f244(f907(x97141),f907(x97141)),f319(f319(f143(x97141),x97142),x97143)),f319(f319(f143(x97141),x97144),x97145))),f150(x97141,x97146)))+~P1(f319(f319(f321(f912(f907(x97141),f907(x97141))),f319(f319(f244(f907(x97141),f907(x97141)),x97143),x97145)),f150(x97141,x97146)))+~P1(f319(f319(f321(f912(x97141,x97141)),f319(f319(f244(x97141,x97141),x97142),x97144)),x97146))
% 22.40/22.31 [9738]P1(f319(x97381,x97382))+~P1(f319(x97381,f570(x97381,x97383,x97384,x97385,x97386)))+~P1(f319(f319(f321(x97386),x97382),f319(f319(f33(x97385,f913(x97386,a904)),x97384),x97383)))
% 22.40/22.31 [9743]~P1(f319(f319(f321(f912(f907(x97431),f907(x97431))),f319(f319(f244(f907(x97431),f907(x97431)),f319(f319(f143(x97431),x97432),x97435)),f319(f319(f143(x97431),x97433),x97436))),f137(x97431,x97434)))+P1(f319(f319(f321(f912(f907(x97431),f907(x97431))),f319(f319(f244(f907(x97431),f907(x97431)),x97435),x97436)),f137(x97431,x97434)))+P1(f319(f319(f321(f912(x97431,x97431)),f319(f319(f244(x97431,x97431),x97432),x97433)),x97434))
% 22.40/22.31 [9744]~P1(f319(f319(f321(f912(f907(x97441),f907(x97441))),f319(f319(f244(f907(x97441),f907(x97441)),f319(f319(f143(x97441),x97442),x97445)),f319(f319(f143(x97441),x97443),x97446))),f139(x97441,x97444)))+P1(f319(f319(f321(f912(f907(x97441),f907(x97441))),f319(f319(f244(f907(x97441),f907(x97441)),x97445),x97446)),f139(x97441,x97444)))+P1(f319(f319(f321(f912(x97441,x97441)),f319(f319(f244(x97441,x97441),x97442),x97443)),x97444))
% 22.40/22.31 [9745]~P1(f319(f319(f321(f912(f907(x97451),f907(x97451))),f319(f319(f244(f907(x97451),f907(x97451)),f319(f319(f143(x97451),x97452),x97455)),f319(f319(f143(x97451),x97453),x97456))),f149(x97451,x97454)))+P1(f319(f319(f321(f912(f907(x97451),f907(x97451))),f319(f319(f244(f907(x97451),f907(x97451)),x97455),x97456)),f149(x97451,x97454)))+P1(f319(f319(f321(f912(x97451,x97451)),f319(f319(f244(x97451,x97451),x97452),x97453)),x97454))
% 22.40/22.31 [9841]P1(f319(x98411,x98412))+P1(f319(f319(f321(x98413),f557(x98411,x98414,x98415,x98413,x98416)),x98415))+~P1(f319(f319(f321(x98416),x98412),f319(f319(f33(x98413,f913(x98416,a904)),x98415),x98414)))
% 22.40/22.31 [9852]~E(x98522,x98524)+P1(f319(f319(f321(f912(f907(x98521),f907(x98521))),f319(f319(f244(f907(x98521),f907(x98521)),f319(f319(f126(x98521),x98522),f319(f319(f143(x98521),x98523),f105(x98521)))),f319(f319(f126(x98521),x98524),f319(f319(f143(x98521),x98525),f105(x98521))))),f149(x98521,x98526)))+~P1(f319(f319(f321(f912(x98521,x98521)),f319(f319(f244(x98521,x98521),x98523),x98525)),x98526))
% 22.40/22.31 [9943]E(x99431,x99432)+~P1(f319(f319(f321(f912(f907(x99433),f907(x99433))),f319(f319(f244(f907(x99433),f907(x99433)),f319(f319(f126(x99433),x99435),f319(f319(f143(x99433),x99431),f105(x99433)))),f319(f319(f126(x99433),x99436),f319(f319(f143(x99433),x99432),f105(x99433))))),f149(x99433,x99434)))+P1(f319(f319(f321(f912(x99433,x99433)),f319(f319(f244(x99433,x99433),x99431),x99432)),x99434))
% 22.40/22.31 [9972]~P1(f319(f319(f321(f912(f907(x99721),f907(x99721))),f319(f319(f244(f907(x99721),f907(x99721)),f319(f319(f126(x99721),x99725),f319(f319(f143(x99721),x99722),f105(x99721)))),f319(f319(f126(x99721),x99726),f319(f319(f143(x99721),x99723),f105(x99721))))),f149(x99721,x99724)))+P1(f319(f319(f321(f912(f907(x99721),f907(x99721))),f319(f319(f244(f907(x99721),f907(x99721)),x99725),x99726)),f149(x99721,x99724)))+P1(f319(f319(f321(f912(x99721,x99721)),f319(f319(f244(x99721,x99721),x99722),x99723)),x99724))
% 22.40/22.31 [9996]P1(f319(x99961,x99962))+P1(f319(f319(f321(x99963),f570(x99961,x99964,x99965,x99966,x99963)),f319(x99964,f557(x99961,x99964,x99965,x99966,x99963))))+~P1(f319(f319(f321(x99963),x99962),f319(f319(f33(x99966,f913(x99963,a904)),x99965),x99964)))
% 22.40/22.31 [10108]P1(f319(f319(f321(x101081),f829(x101082,x101083,x101084,x101085,x101086,x101081)),x101085))+~P1(f319(f319(f225(f913(x101081,a904)),x101086),x101085))+P1(f319(f319(f225(f913(x101084,a904)),f319(f319(f34(x101081,f913(x101084,a904)),x101085),x101083)),f319(f319(f34(x101081,f913(x101084,a904)),x101085),x101082)))
% 22.40/22.31 [10234]~P1(f319(f319(f225(f913(x102341,a904)),f319(x102344,f829(x102345,x102344,x102341,x102343,x102346,x102342))),f319(x102345,f829(x102345,x102344,x102341,x102343,x102346,x102342))))+~P1(f319(f319(f225(f913(x102342,a904)),x102346),x102343))+P1(f319(f319(f225(f913(x102341,a904)),f319(f319(f34(x102342,f913(x102341,a904)),x102343),x102344)),f319(f319(f34(x102342,f913(x102341,a904)),x102343),x102345)))
% 22.40/22.31 [8950]~P17(x89503,x89504,x89501)+~P1(f319(f55(x89503),x89506))+E(f319(f319(x89501,x89502),f319(f319(f58(x89503,x89504,x89501),x89505),f319(f319(f3(f913(x89503,a904)),x89506),f319(f319(f301(x89503),x89502),f181(f913(x89503,a904)))))),f319(f319(f58(x89503,x89504,x89501),x89505),f319(f319(f301(x89503),x89502),x89506)))
% 22.40/22.31 [9245]~P1(f319(f319(f321(x92455),x92453),x92456))+P1(f319(f319(f225(f913(x92451,a904)),f319(x92452,x92453)),x92454))+~P1(f319(f319(f225(f913(x92451,a904)),f319(f319(f33(x92455,f913(x92451,a904)),x92456),x92452)),x92454))
% 22.40/22.31 [9915]~P8(x99151,x99155,x99154)+P1(f319(f319(f321(f912(x99151,x99151)),f319(f319(f244(x99151,x99151),x99152),x99153)),x99154))+~P1(f319(f319(f321(x99151),x99156),f319(f319(f94(f913(x99151,a904)),f319(f277(x99151,x99151,x99154),f319(f319(f301(x99151),x99152),f181(f913(x99151,a904))))),f319(f277(x99151,x99151,x99154),f319(f319(f301(x99151),x99153),f181(f913(x99151,a904)))))))
% 22.40/22.31 [8675]~P124(x86752)+~E(f319(f319(f74(x86752),f319(f319(f75(x86752),x86754),x86755)),x86751),f319(f319(f74(x86752),f319(f319(f75(x86752),x86753),x86755)),x86756))+E(x86751,f319(f319(f74(x86752),f319(f319(f75(x86752),f319(f319(f3(x86752),x86753),x86754)),x86755)),x86756))
% 22.40/22.31 [8676]~P124(x86761)+~E(f319(f319(f74(x86761),f319(f319(f75(x86761),x86762),x86764)),x86765),f319(f319(f74(x86761),f319(f319(f75(x86761),x86763),x86764)),x86766))+E(f319(f319(f74(x86761),f319(f319(f75(x86761),f319(f319(f3(x86761),x86762),x86763)),x86764)),x86765),x86766)
% 22.40/22.31 [8853]~P124(x88531)+E(f319(f319(f74(x88531),f319(f319(f75(x88531),x88532),x88533)),x88534),f319(f319(f74(x88531),f319(f319(f75(x88531),x88535),x88533)),x88536))+~E(x88536,f319(f319(f74(x88531),f319(f319(f75(x88531),f319(f319(f3(x88531),x88532),x88535)),x88533)),x88534))
% 22.40/22.31 [8854]~P124(x88541)+E(f319(f319(f74(x88541),f319(f319(f75(x88541),x88542),x88543)),x88544),f319(f319(f74(x88541),f319(f319(f75(x88541),x88545),x88543)),x88546))+~E(f319(f319(f74(x88541),f319(f319(f75(x88541),f319(f319(f3(x88541),x88542),x88545)),x88543)),x88544),x88546)
% 22.40/22.31 [9181]~P1(f319(f319(x91814,x91815),x91816))+~P1(f319(f319(x91813,x91815),x91816))+P1(f319(f319(f319(f319(f94(f913(x91811,f913(x91812,a904))),x91813),x91814),x91815),x91816))
% 22.40/22.31 [9450]P1(f319(f319(x94501,x94502),x94503))+P1(f319(f319(x94504,x94502),x94503))+~P1(f319(f319(f319(f319(f93(f913(x94505,f913(x94506,a904))),x94504),x94501),x94502),x94503))
% 22.40/22.31 [9758]~P125(x97581)+~P1(f319(f319(f225(x97581),f319(f319(f74(x97581),f319(f319(f75(x97581),x97584),x97585)),x97582)),f319(f319(f74(x97581),f319(f319(f75(x97581),x97583),x97585)),x97586)))+P1(f319(f319(f225(x97581),x97582),f319(f319(f74(x97581),f319(f319(f75(x97581),f319(f319(f3(x97581),x97583),x97584)),x97585)),x97586)))
% 22.40/22.31 [9759]~P125(x97591)+~P1(f319(f319(f226(x97591),f319(f319(f74(x97591),f319(f319(f75(x97591),x97594),x97595)),x97592)),f319(f319(f74(x97591),f319(f319(f75(x97591),x97593),x97595)),x97596)))+P1(f319(f319(f226(x97591),x97592),f319(f319(f74(x97591),f319(f319(f75(x97591),f319(f319(f3(x97591),x97593),x97594)),x97595)),x97596)))
% 22.40/22.31 [9791]~P125(x97911)+P1(f319(f319(f225(x97911),f319(f319(f74(x97911),f319(f319(f75(x97911),x97912),x97913)),x97914)),f319(f319(f74(x97911),f319(f319(f75(x97911),x97915),x97913)),x97916)))+~P1(f319(f319(f225(x97911),x97914),f319(f319(f74(x97911),f319(f319(f75(x97911),f319(f319(f3(x97911),x97915),x97912)),x97913)),x97916)))
% 22.40/22.31 [9792]~P125(x97921)+P1(f319(f319(f226(x97921),f319(f319(f74(x97921),f319(f319(f75(x97921),x97922),x97923)),x97924)),f319(f319(f74(x97921),f319(f319(f75(x97921),x97925),x97923)),x97926)))+~P1(f319(f319(f226(x97921),x97924),f319(f319(f74(x97921),f319(f319(f75(x97921),f319(f319(f3(x97921),x97925),x97922)),x97923)),x97926)))
% 22.40/22.31 [9907]~P125(x99071)+~P1(f319(f319(f225(x99071),f319(f319(f74(x99071),f319(f319(f75(x99071),x99072),x99074)),x99075)),f319(f319(f74(x99071),f319(f319(f75(x99071),x99073),x99074)),x99076)))+P1(f319(f319(f225(x99071),f319(f319(f74(x99071),f319(f319(f75(x99071),f319(f319(f3(x99071),x99072),x99073)),x99074)),x99075)),x99076))
% 22.40/22.31 [9908]~P125(x99081)+~P1(f319(f319(f226(x99081),f319(f319(f74(x99081),f319(f319(f75(x99081),x99082),x99084)),x99085)),f319(f319(f74(x99081),f319(f319(f75(x99081),x99083),x99084)),x99086)))+P1(f319(f319(f226(x99081),f319(f319(f74(x99081),f319(f319(f75(x99081),f319(f319(f3(x99081),x99082),x99083)),x99084)),x99085)),x99086))
% 22.40/22.31 [9955]~P125(x99551)+P1(f319(f319(f225(x99551),f319(f319(f74(x99551),f319(f319(f75(x99551),x99552),x99553)),x99554)),f319(f319(f74(x99551),f319(f319(f75(x99551),x99555),x99553)),x99556)))+~P1(f319(f319(f225(x99551),f319(f319(f74(x99551),f319(f319(f75(x99551),f319(f319(f3(x99551),x99552),x99555)),x99553)),x99554)),x99556))
% 22.40/22.31 [9956]~P125(x99561)+P1(f319(f319(f226(x99561),f319(f319(f74(x99561),f319(f319(f75(x99561),x99562),x99563)),x99564)),f319(f319(f74(x99561),f319(f319(f75(x99561),x99565),x99563)),x99566)))+~P1(f319(f319(f226(x99561),f319(f319(f74(x99561),f319(f319(f75(x99561),f319(f319(f3(x99561),x99562),x99565)),x99563)),x99564)),x99566))
% 22.40/22.31 [10095]~P76(x100952)+~P1(f319(f55(x100951),x100956))+E(f319(f319(f8(x100951,x100952),f319(f319(f20(x100951,x100952,x100952),f319(f319(f20(x100951,x100952,f913(x100952,x100952)),f319(f319(f10(a904,f913(x100952,f913(x100952,x100952)),x100951),f86(x100952)),x100953)),x100954)),x100955)),x100956),f319(f319(f74(x100952),f319(f319(f8(x100951,x100952),x100954),f319(f319(f94(f913(x100951,a904)),x100956),f319(f254(x100951),x100953)))),f319(f319(f8(x100951,x100952),x100955),f319(f319(f94(f913(x100951,a904)),x100956),f319(f73(f913(x100951,a904)),f319(f254(x100951),x100953))))))
% 22.40/22.31 [10151]P1(f319(f319(f321(x101512),x101514),x101516))+P1(f319(f319(f321(x101512),x101515),x101516))+E(f319(f303(x101511,x101512,f319(f319(f9(x101511,x101512,x101512),f319(f319(f9(x101511,x101512,f913(x101512,x101512)),f319(f319(f10(a904,f913(x101512,f913(x101512,x101512)),x101511),f86(x101512)),f319(f319(f9(x101511,f913(x101511,a904),a904),f321(x101511)),x101513))),x101514)),x101515)),x101516),f181(f913(x101511,a904)))
% 22.40/22.31 [10152]P1(f319(f319(f321(x101522),x101525),x101526))+~P1(f319(f319(f321(x101522),x101524),x101526))+E(f319(f303(x101521,x101522,f319(f319(f9(x101521,x101522,x101522),f319(f319(f9(x101521,x101522,f913(x101522,x101522)),f319(f319(f10(a904,f913(x101522,f913(x101522,x101522)),x101521),f86(x101522)),f319(f319(f9(x101521,f913(x101521,a904),a904),f321(x101521)),x101523))),x101524)),x101525)),x101526),x101523)
% 22.40/22.31 [10153]P1(f319(f319(f321(x101532),x101534),x101536))+~P1(f319(f319(f321(x101532),x101535),x101536))+E(f319(f303(x101531,x101532,f319(f319(f9(x101531,x101532,x101532),f319(f319(f9(x101531,x101532,f913(x101532,x101532)),f319(f319(f10(a904,f913(x101532,f913(x101532,x101532)),x101531),f86(x101532)),f319(f319(f9(x101531,f913(x101531,a904),a904),f321(x101531)),x101533))),x101534)),x101535)),x101536),f319(f73(f913(x101531,a904)),x101533))
% 22.40/22.31 [10154]~P1(f319(f319(f321(x101542),x101544),x101546))+~P1(f319(f319(f321(x101542),x101545),x101546))+E(f319(f303(x101541,x101542,f319(f319(f9(x101541,x101542,x101542),f319(f319(f9(x101541,x101542,f913(x101542,x101542)),f319(f319(f10(a904,f913(x101542,f913(x101542,x101542)),x101541),f86(x101542)),f319(f319(f9(x101541,f913(x101541,a904),a904),f321(x101541)),x101543))),x101544)),x101545)),x101546),f234(f913(x101541,a904)))
% 22.40/22.31 [8707]E(x87071,x87072)+~P58(x87074,x87075,x87073,x87076,x87077)+~E(f319(x87073,x87071),f319(x87073,x87072))
% 22.40/22.31 [8737]~P10(x87376,x87375,x87377,x87374,x87371)+E(f319(f319(x87371,x87372),x87373),x87374)+P1(f319(f55(x87375),x87373))
% 22.40/22.31 [9606]P43(x96061,x96062,x96063,x96064,x96065,f319(f319(x96063,x96066),x96067))+~E(f319(f319(x96063,x96066),x96067),x96064)+~E(x96065,f181(f913(x96061,a904)))
% 22.40/22.31 [9811]~P1(f319(x98116,x98113))+~P1(f319(f319(f321(f912(x98112,x98112)),f319(f319(f244(x98112,x98112),x98114),x98115)),f319(x98117,x98113)))+P1(f319(f319(f321(f912(f912(x98111,x98112),f912(x98111,x98112))),f319(f319(f244(f912(x98111,x98112),f912(x98111,x98112)),f319(f319(f244(x98111,x98112),x98113),x98114)),f319(f319(f244(x98111,x98112),x98113),x98115))),f272(x98111,x98112,x98116,x98117)))
% 22.40/22.31 [10220]~P43(x102202,x102207,x102203,x102206,x102201,f319(f319(x102203,x102205),x102204))+E(f319(f319(x102203,f419(x102204,x102205,x102201,x102206,x102203,x102207,x102202)),f420(x102204,x102205,x102201,x102206,x102203,x102207,x102202)),f319(f319(x102203,x102205),x102204))+E(x102201,f181(f913(x102202,a904)))
% 22.40/22.31 [10221]~P43(x102217,x102216,x102211,x102214,x102215,f319(f319(x102211,x102212),x102213))+E(f319(f319(x102211,f419(x102213,x102212,x102215,x102214,x102211,x102216,x102217)),f420(x102213,x102212,x102215,x102214,x102211,x102216,x102217)),f319(f319(x102211,x102212),x102213))+E(f319(f319(x102211,x102212),x102213),x102214)
% 22.40/22.31 [9284]~P34(x92841,x92842,x92843,x92845,x92847)+P34(x92841,x92842,x92843,f319(f319(f143(x92841),x92844),x92845),f319(f319(f143(x92842),x92846),x92847))+~P1(f319(f319(x92843,x92844),x92846))
% 22.40/22.31 [9300]P34(x93001,x93002,x93003,x93004,x93005)+~P34(x93001,x93002,x93003,f319(f319(f126(x93001),x93006),x93004),f319(f319(f126(x93002),x93007),x93005))+~E(f319(f182(f907(x93001)),x93006),f319(f182(f907(x93002)),x93007))
% 22.40/22.31 [9301]P34(x93011,x93012,x93013,x93014,x93015)+~P34(x93011,x93012,x93013,f319(f319(f126(x93011),x93014),x93016),f319(f319(f126(x93012),x93015),x93017))+~E(f319(f182(f907(x93011)),x93014),f319(f182(f907(x93012)),x93015))
% 22.40/22.31 [9519]~P34(x95191,x95192,x95193,x95195,x95197)+~P34(x95191,x95192,x95193,x95194,x95196)+P34(x95191,x95192,x95193,f319(f319(f126(x95191),x95194),x95195),f319(f319(f126(x95192),x95196),x95197))
% 22.40/22.31 [9892]~P1(f319(f60(x98921,x98924,x98925,x98926,x98923),x98927))+P1(f319(f60(x98921,x98924,x98925,x98926,f319(f319(f301(x98921),x98922),x98923)),f319(f319(x98925,x98922),x98927)))+P1(f319(f319(f321(x98921),x98922),x98923))
% 22.40/22.31 [10251]~P43(x102512,x102517,x102516,x102515,x102511,f319(f319(x102516,x102514),x102513))+E(x102511,f181(f913(x102512,a904)))+P1(f319(f319(f321(x102512),f419(x102513,x102514,x102511,x102515,x102516,x102517,x102512)),x102511))
% 22.40/22.31 [10252]~P43(x102525,x102527,x102521,x102524,x102526,f319(f319(x102521,x102522),x102523))+E(f319(f319(x102521,x102522),x102523),x102524)+P1(f319(f319(f321(x102525),f419(x102523,x102522,x102526,x102524,x102521,x102527,x102525)),x102526))
% 22.40/22.31 [10385]E(f319(f319(f244(x103851,x103852),x103853),x103854),f319(f319(f244(x103851,x103852),x103855),x103856))+P1(f319(f319(f321(f912(f912(x103851,x103852),f912(x103851,x103852))),f319(f319(f244(f912(x103851,x103852),f912(x103851,x103852)),f319(f319(f244(x103851,x103852),f832(x103857,x103854,x103853,x103856,x103855,x103852,x103851)),f833(x103857,x103854,x103853,x103856,x103855,x103852,x103851))),f319(f319(f244(x103851,x103852),x103853),x103854))),f299(f912(x103851,x103852),x103857)))+~P1(f319(f319(f321(f912(f912(x103851,x103852),f912(x103851,x103852))),f319(f319(f244(f912(x103851,x103852),f912(x103851,x103852)),f319(f319(f244(x103851,x103852),x103855),x103856)),f319(f319(f244(x103851,x103852),x103853),x103854))),f299(f912(x103851,x103852),x103857)))
% 22.40/22.31 [8977]~P22(x89774,x89775,x89776,x89777,x89771)+~P1(f319(f55(x89775),x89773))+E(f319(f319(x89771,x89772),x89773),f319(f319(f319(f59(x89774,x89775,x89776),x89772),x89777),x89773))
% 22.40/22.31 [8978]~P10(x89784,x89785,x89786,x89787,x89781)+~P1(f319(f55(x89785),x89783))+E(f319(f319(x89781,x89782),x89783),f319(f319(f319(f59(x89784,x89785,x89786),x89782),x89787),x89783))
% 22.40/22.31 [9785]~P24(x97853,x97854,x97855,x97857,x97856,x97851)+~P1(f319(f55(x97854),x97852))+E(f319(x97851,x97852),f319(f319(f319(f59(x97853,x97854,x97855),x97856),x97857),x97852))
% 22.40/22.31 [9951]P43(x99511,x99512,x99513,x99514,x99515,f319(f319(x99513,x99516),x99517))+~P43(x99511,x99512,x99513,x99514,f319(f319(f3(f913(x99511,a904)),x99515),f319(f319(f301(x99511),x99516),f181(f913(x99511,a904)))),x99517)+~P1(f319(f319(f321(x99511),x99516),x99515))
% 22.40/22.31 [10297]P1(f319(f319(x102977,f779(x102974,x102975,x102971,x102976,x102973,x102972,x102977)),f780(x102974,x102975,x102971,x102976,x102973,x102972,x102977)))+~P1(f319(f319(x102977,f319(f248(x102972,x102973),x102976)),f319(f243(x102972,x102973),x102976)))+P1(f319(x102971,f319(f319(f249(x102972,x102973,x102974),x102975),x102976)))
% 22.40/22.31 [10308]~P43(x103082,x103083,x103084,x103085,x103081,f319(f319(x103084,x103087),x103086))+P43(x103082,x103083,x103084,x103085,f319(f319(f3(f913(x103082,a904)),x103081),f319(f319(f301(x103082),f419(x103086,x103087,x103081,x103085,x103084,x103083,x103082)),f181(f913(x103082,a904)))),f420(x103086,x103087,x103081,x103085,x103084,x103083,x103082))+E(x103081,f181(f913(x103082,a904)))
% 22.40/22.31 [10309]~P43(x103095,x103096,x103091,x103094,x103097,f319(f319(x103091,x103092),x103093))+P43(x103095,x103096,x103091,x103094,f319(f319(f3(f913(x103095,a904)),x103097),f319(f319(f301(x103095),f419(x103093,x103092,x103097,x103094,x103091,x103096,x103095)),f181(f913(x103095,a904)))),f420(x103093,x103092,x103097,x103094,x103091,x103096,x103095))+E(f319(f319(x103091,x103092),x103093),x103094)
% 22.40/22.31 [10342]~P1(f319(x103421,f319(f319(x103425,f780(x103424,x103425,x103421,x103426,x103423,x103422,x103427)),f779(x103424,x103425,x103421,x103426,x103423,x103422,x103427))))+~P1(f319(f319(x103427,f319(f248(x103422,x103423),x103426)),f319(f243(x103422,x103423),x103426)))+P1(f319(x103421,f319(f319(f249(x103422,x103423,x103424),x103425),x103426)))
% 22.40/22.31 [9591]P1(f319(f319(f225(f913(f912(x95911,x95912),a904)),f319(f319(f281(x95911,x95913,x95912),x95914),x95915)),f319(f319(f281(x95911,x95913,x95912),x95916),x95917)))+~P1(f319(f319(f225(f913(f912(x95913,x95912),a904)),x95915),x95917))+~P1(f319(f319(f225(f913(f912(x95911,x95913),a904)),x95914),x95916))
% 22.40/22.31 [10376]E(f319(f319(f244(x103761,x103762),x103763),x103764),f319(f319(f244(x103761,x103762),x103765),x103766))+~P1(f319(f319(f321(f912(f912(x103761,x103762),f912(x103761,x103762))),f319(f319(f244(f912(x103761,x103762),f912(x103761,x103762)),f319(f319(f244(x103761,x103762),x103763),x103764)),f319(f319(f244(x103761,x103762),x103765),x103766))),f299(f912(x103761,x103762),x103767)))+P1(f319(f319(f321(f912(f912(x103761,x103762),f912(x103761,x103762))),f319(f319(f244(f912(x103761,x103762),f912(x103761,x103762)),f319(f319(f244(x103761,x103762),x103763),x103764)),f319(f319(f244(x103761,x103762),f832(x103767,x103766,x103765,x103764,x103763,x103762,x103761)),f833(x103767,x103766,x103765,x103764,x103763,x103762,x103761)))),x103767))
% 22.40/22.31 [9961]~P1(f319(f319(f321(x99611),x99616),x99615))+P1(f319(f60(x99611,x99612,x99613,x99614,x99615),f319(f319(x99613,x99616),x99617)))+~P1(f319(f60(x99611,x99612,x99613,x99614,f319(f319(f3(f913(x99611,a904)),x99615),f319(f319(f301(x99611),x99616),f181(f913(x99611,a904))))),x99617))
% 22.40/22.31 [10392]~P145(x103921)+~P25(f912(x103922,x103923),x103921,f319(f249(x103922,x103923,x103921),f319(f319(f9(x103922,f913(x103923,x103921),f913(x103923,x103921)),f319(f319(f10(f913(x103921,x103921),f913(f913(x103923,x103921),f913(x103923,x103921)),x103922),f10(x103921,x103921,x103923)),f319(f319(f10(x103921,f913(x103921,x103921),x103922),f75(x103921)),x103924))),x103925)),f319(f319(f246(x103922,x103923),x103926),f319(f18(f913(x103923,a904),x103922),x103927)))+E(f319(f319(f8(x103921,x103921),f25(x103921)),f319(f254(x103921),f319(f319(f10(f913(x103922,a904),a904,x103921),f80(x103922)),f319(f319(f10(f913(x103922,f913(x103923,a904)),f913(x103922,a904),x103921),f319(f10(f913(x103923,a904),a904,x103922),f80(x103923))),f319(f319(f9(x103921,f913(x103922,f913(x103923,a904)),f913(x103922,f913(x103923,a904))),f319(f319(f10(f913(x103922,f913(f913(x103923,a904),f913(x103923,a904))),f913(f913(x103922,f913(x103923,a904)),f913(x103922,f913(x103923,a904))),x103921),f20(x103922,f913(x103923,a904),f913(x103923,a904))),f319(f319(f10(f913(x103922,f913(x103923,f913(a904,a904))),f913(x103922,f913(f913(x103923,a904),f913(x103923,a904))),x103921),f319(f10(f913(x103923,f913(a904,a904)),f913(f913(x103923,a904),f913(x103923,a904)),x103922),f20(x103923,a904,a904))),f319(f319(f10(f913(x103922,f913(x103923,a904)),f913(x103922,f913(x103923,f913(a904,a904))),x103921),f319(f10(f913(x103923,a904),f913(x103923,f913(a904,a904)),x103922),f319(f10(a904,f913(a904,a904),x103923),a317))),f319(f319(f9(x103921,f913(x103922,f913(x103923,x103921)),f913(x103922,f913(x103923,a904))),f319(f319(f10(f913(f913(x103923,x103921),f913(x103923,a904)),f913(f913(x103922,f913(x103923,x103921)),f913(x103922,f913(x103923,a904))),x103921),f10(f913(x103923,x103921),f913(x103923,a904),x103922)),f319(f319(f10(f913(x103921,a904),f913(f913(x103923,x103921),f913(x103923,a904)),x103921),f10(x103921,a904,x103923)),a316))),f319(f319(f9(x103922,f913(x103923,x103921),f913(x103923,x103921)),f319(f319(f10(f913(x103921,x103921),f913(f913(x103923,x103921),f913(x103923,x103921)),x103922),f10(x103921,x103921,x103923)),f319(f319(f10(x103921,f913(x103921,x103921),x103922),f75(x103921)),x103924))),x103925)))))),f319(f319(f9(x103922,f913(x103923,a904),f913(x103923,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x103923,a904),f913(x103923,a904)),x103922),f10(a904,a904,x103923)),f319(f319(f10(a904,f913(a904,a904),x103922),a317),f319(f319(f9(x103922,f913(x103922,a904),a904),f321(x103922)),x103926)))),f319(f319(f9(x103923,f913(x103923,a904),a904),f321(x103923)),x103927))))))),f319(f319(f75(x103921),f319(f319(f8(x103922,x103921),x103924),x103926)),f319(f319(f8(x103923,x103921),x103925),x103927)))
% 22.40/22.31 [9595]~P26(x95951,x95953,x95955,x95956,x95958)+~P26(x95953,x95952,x95954,x95958,x95957)+P26(x95951,x95952,f319(f66(x95953,x95952,x95951,x95954),x95955),x95956,x95957)
% 22.40/22.31 [9628]P26(x96281,x96282,x96283,x96284,x96285)+~P26(x96286,x96281,x96287,x96288,x96284)+~P26(x96286,x96282,f319(f66(x96281,x96282,x96286,x96283),x96287),x96288,x96285)
% 22.40/22.31 [9783]~P1(f319(f319(x97834,x97836),x97838))+~P1(f319(f319(x97835,x97838),x97837))+P1(f319(f319(f245(x97831,x97832,x97833,x97834,x97835),x97836),x97837))
% 22.40/22.31 [9352]~P20(x93528,x93521,x93523,x93525)+~P1(f319(f55(x93528),x93526))+E(f319(f66(x93521,x93521,x93522,f319(x93523,x93524)),f319(f66(x93521,x93521,x93522,f319(x93525,x93526)),x93527)),f319(f66(x93521,x93521,x93522,f319(x93525,x93526)),f319(f66(x93521,x93521,x93522,f319(x93523,x93524)),x93527)))
% 22.40/22.31 [9769]~P23(x97697,x97692,x97695,x97698,x97696,x97691)+~P1(f319(f55(x97692),x97694))+E(f319(x97691,f319(f319(f301(x97692),x97693),x97694)),f319(f319(x97695,f319(x97696,x97693)),f319(x97691,x97694)))
% 22.40/22.31 [9904]~P25(x99042,x99044,x99046,x99048)+~P25(x99041,x99043,x99045,x99047)+P25(f912(x99041,x99042),f912(x99043,x99044),f250(x99041,x99043,x99042,x99044,x99045,x99046),f319(f319(f246(x99041,x99042),x99047),f319(f18(f913(x99042,a904),x99041),x99048)))
% 22.40/22.31 [9539]P1(f319(f319(f321(f912(x95391,x95392)),f319(f319(f244(x95391,x95392),x95393),x95394)),f319(f319(f281(x95391,x95395,x95392),x95396),x95397)))+~P1(f319(f319(f321(f912(x95391,x95395)),f319(f319(f244(x95391,x95395),x95393),x95398)),x95396))+~P1(f319(f319(f321(f912(x95395,x95392)),f319(f319(f244(x95395,x95392),x95398),x95394)),x95397))
% 22.40/22.31 [9746]~P1(f319(f319(f225(f913(f912(x97463,x97462),a904)),x97465),f319(f319(f246(x97463,x97462),x97468),f319(f18(f913(x97462,a904),x97463),x97467))))+~P1(f319(f319(f225(f913(f912(x97461,x97463),a904)),x97464),f319(f319(f246(x97461,x97463),x97466),f319(f18(f913(x97463,a904),x97461),x97468))))+P1(f319(f319(f225(f913(f912(x97461,x97462),a904)),f319(f319(f281(x97461,x97463,x97462),x97464),x97465)),f319(f319(f246(x97461,x97462),x97466),f319(f18(f913(x97462,a904),x97461),x97467))))
% 22.40/22.31 [9805]~E(x98053,x98055)+P1(f319(f319(f321(f912(f912(x98051,x98052),f912(x98051,x98052))),f319(f319(f244(f912(x98051,x98052),f912(x98051,x98052)),f319(f319(f244(x98051,x98052),x98053),x98054)),f319(f319(f244(x98051,x98052),x98055),x98056))),f312(x98051,x98052,x98057,x98058)))+~P1(f319(f319(f321(f912(x98052,x98052)),f319(f319(f244(x98052,x98052),x98054),x98056)),x98058))
% 22.40/22.31 [9928]E(x99281,x99282)+~P1(f319(f319(f321(f912(f912(x99283,x99285),f912(x99283,x99285))),f319(f319(f244(f912(x99283,x99285),f912(x99283,x99285)),f319(f319(f244(x99283,x99285),x99281),x99286)),f319(f319(f244(x99283,x99285),x99282),x99287))),f312(x99283,x99285,x99284,x99288)))+P1(f319(f319(f321(f912(x99283,x99283)),f319(f319(f244(x99283,x99283),x99281),x99282)),x99284))
% 22.40/22.31 [9942]~P1(f319(f319(f321(f912(f912(x99421,x99425),f912(x99421,x99425))),f319(f319(f244(f912(x99421,x99425),f912(x99421,x99425)),f319(f319(f244(x99421,x99425),x99422),x99426)),f319(f319(f244(x99421,x99425),x99423),x99427))),f312(x99421,x99425,x99424,x99428)))+P1(f319(f319(f321(f912(x99421,x99421)),f319(f319(f244(x99421,x99421),x99422),x99423)),x99424))+P1(f319(f319(f321(f912(x99425,x99425)),f319(f319(f244(x99425,x99425),x99426),x99427)),x99428))
% 22.40/22.31 [9842]~P24(x98427,x98425,x98421,x98428,x98422,x98424)+~P1(f319(f55(x98425),x98426))+E(f319(f319(x98421,f319(x98422,x98423)),f319(x98424,f319(f319(f3(f913(x98425,a904)),x98426),f319(f319(f301(x98425),x98423),f181(f913(x98425,a904)))))),f319(x98424,f319(f319(f301(x98425),x98423),x98426)))
% 22.40/22.31 [9307]~P1(f319(f319(f319(x93075,x93078),x93076),x93077))+~P1(f319(f319(f321(x93071),x93078),x93074))+P1(f319(f319(f319(f319(f33(x93071,f913(x93072,f913(x93073,a904))),x93074),x93075),x93076),x93077))
% 22.40/22.31 [9527]P1(f319(f319(f319(x95271,x95272),x95273),x95274))+~P1(f319(f319(f321(x95275),x95272),x95276))+~P1(f319(f319(f319(f319(f34(x95275,f913(x95277,f913(x95278,a904))),x95276),x95271),x95273),x95274))
% 22.40/22.31 [9739]~P22(x97393,x97392,x97394,x97398,x97391)+~P1(f319(f55(x97392),x97397))+E(f319(f319(x97391,f319(f319(f20(x97392,x97393,x97393),f319(f319(f10(x97393,f913(x97393,x97393),x97392),x97394),x97395)),x97396)),x97397),f319(f319(x97394,f319(f319(x97391,x97395),x97397)),f319(f319(x97391,x97396),x97397)))
% 22.40/22.31 [10021]~E(f319(f302(x100212,x100214,x100216),x100218),x1002110)+~E(f319(f302(x100211,x100213,x100215),x100217),x100219)+E(f319(f302(f912(x100211,x100212),f912(x100213,x100214),f250(x100211,x100213,x100212,x100214,x100215,x100216)),f319(f319(f246(x100211,x100212),x100217),f319(f18(f913(x100212,a904),x100211),x100218))),f319(f319(f246(x100213,x100214),x100219),f319(f18(f913(x100214,a904),x100213),x1002110)))
% 22.40/22.31 [4980]~P49(x49801,x49802)+~P51(x49801,x49802)+~P52(x49801,x49802)+P7(x49801,x49802)
% 22.40/22.31 [4936]~P4(x49362)+~P13(x49362,x49361)+P13(x49362,f106(x49362,x49361))+E(x49361,f105(x49362))
% 22.40/22.31 [4937]~P4(x49372)+~P13(x49372,x49371)+P13(x49372,f698(x49371,x49372))+E(x49371,f105(x49372))
% 22.40/22.31 [5180]~P5(x51802)+E(f12(x51802,x51801),f32(x51802,x51801))+E(x51801,f181(f913(x51802,a904)))+~P1(f319(f55(x51802),x51801))
% 22.40/22.31 [5181]~P5(x51812)+E(f15(x51812,x51811),f31(x51812,x51811))+E(x51811,f181(f913(x51812,a904)))+~P1(f319(f55(x51812),x51811))
% 22.40/22.31 [5343]~P4(x53432)+~P13(x53432,x53431)+E(x53431,f105(x53432))+E(f319(f319(f143(x53432),f718(x53431,x53432)),f698(x53431,x53432)),x53431)
% 22.40/22.31 [6152]~P101(x61522)+E(x61521,f181(f913(x61522,a904)))+P1(f319(f319(f225(x61522),f12(x61522,x61521)),f15(x61522,x61521)))+~P1(f319(f55(x61522),x61521))
% 22.40/22.31 [6161]~P41(x61612)+~P41(x61611)+E(x61611,x61612)+~E(f319(f302(a1,a906,a97),x61611),f319(f302(a1,a906,a97),x61612))
% 22.40/22.31 [9162]~P113(x91621)+~P1(f319(f319(f321(x91621),x91622),f102(x91621)))+P1(f319(f319(f226(x91621),f319(f319(f74(x91621),f319(f319(f74(x91621),f72(x91621)),x91622)),x91622)),f2(x91621)))+~P1(f319(f319(f226(x91621),x91622),f2(x91621)))
% 22.40/22.31 [9410]~P113(x94101)+~P1(f319(f319(f321(x94101),x94102),f102(x94101)))+~P1(f319(f319(f226(x94101),f319(f319(f74(x94101),f319(f319(f74(x94101),f72(x94101)),x94102)),x94102)),f2(x94101)))+P1(f319(f319(f226(x94101),x94102),f2(x94101)))
% 22.40/22.31 [4995]~P116(x49952)+~P145(x49952)+E(x49951,f2(a906))+E(f319(f319(f236(x49952),f2(x49952)),x49951),f2(x49952))
% 22.40/22.31 [4998]~P116(x49981)+~P145(x49981)+~E(x49982,f2(a906))+E(f319(f319(f236(x49981),f2(x49981)),x49982),f72(x49981))
% 22.40/22.31 [5166]~P140(x51662)+E(x51661,f72(x51662))+E(x51661,f319(f73(x51662),f72(x51662)))+~E(f319(f319(f75(x51662),x51661),x51661),f72(x51662))
% 22.40/22.31 [5418]~P94(x54182)+E(x54181,f2(x54182))+E(f76(x54182,x54181),f319(f73(x54182),f72(x54182)))+P1(f319(f319(f226(x54182),f2(x54182)),x54181))
% 22.40/22.31 [5658]~P94(x56582)+E(f76(x56582,x56581),f72(x56582))+E(x56581,f2(x56582))+~P1(f319(f319(f226(x56582),f2(x56582)),x56581))
% 22.40/22.31 [5667]E(x56671,x56672)+~E(f319(f96(a906),x56671),f319(f96(a906),x56672))+P1(f319(a186,f319(f96(a1),x56672)))+P1(f319(a186,f319(f96(a1),x56671)))
% 22.40/22.31 [5720]~P97(x57201)+~E(x57202,f2(x57201))+E(f319(f319(f74(x57201),x57202),x57202),f2(x57201))+~P1(f319(f319(f321(x57201),x57202),f102(x57201)))
% 22.40/22.31 [5760]E(x57601,f2(a1))+~E(f319(f319(f30(a1),x57602),x57601),f2(a1))+P1(f319(f319(f226(a1),x57601),x57602))+P1(f319(f319(f226(a1),x57602),x57601))
% 22.40/22.31 [5790]E(x57901,f2(a1))+~E(f319(f319(f30(a1),x57902),x57901),f2(a1))+P1(f319(f319(f225(a1),x57902),f2(a1)))+P1(f319(f319(f226(a1),x57902),x57901))
% 22.40/22.31 [5824]E(x58241,f2(a1))+~E(f319(f319(f30(a1),x58242),x58241),f2(a1))+P1(f319(f319(f225(a1),f2(a1)),x58242))+P1(f319(f319(f226(a1),x58241),x58242))
% 22.40/22.31 [5859]~P97(x58592)+E(x58591,f2(x58592))+~E(f319(f319(f74(x58592),x58591),x58591),f2(x58592))+~P1(f319(f319(f321(x58592),x58591),f102(x58592)))
% 22.40/22.31 [5925]E(f319(f96(a906),x59251),f319(f96(a906),x59252))+~E(f319(f96(a1),x59252),f2(a1))+P1(f319(a186,f319(f96(a1),x59252)))+~P1(f319(a186,f319(f96(a1),x59251)))
% 22.40/22.31 [5955]~E(f319(f96(a906),x59552),f319(f96(a906),x59551))+E(f319(f96(a1),x59551),f2(a1))+P1(f319(a186,f319(f96(a1),x59551)))+~P1(f319(a186,f319(f96(a1),x59552)))
% 22.40/22.31 [5965]~P4(x59652)+E(x59651,f181(f913(x59652,a904)))+~P1(f319(f55(x59652),x59651))+P1(f319(f319(f321(x59652),f16(x59652,x59651)),x59651))
% 22.40/22.31 [5966]~P4(x59662)+E(x59661,f181(f913(x59662,a904)))+~P1(f319(f55(x59662),x59661))+P1(f319(f319(f321(x59662),f17(x59662,x59661)),x59661))
% 22.40/22.31 [6129]~P113(x61291)+~P98(x61291)+P1(f319(f319(f225(x61291),f2(x61291)),f319(f96(x61291),x61292)))+~P1(f319(f319(f225(a1),a77),x61292))
% 22.40/22.31 [6130]~P113(x61301)+~P98(x61301)+P1(f319(f319(f226(x61301),f2(x61301)),f319(f96(x61301),x61302)))+~P1(f319(f319(f226(a1),a77),x61302))
% 22.40/22.31 [6151]~P113(x61511)+~P98(x61511)+E(f319(f69(x61511),f319(f96(x61511),x61512)),f319(f96(x61511),x61512))+P1(f319(f319(f226(x61511),f319(f96(x61511),x61512)),f2(x61511)))
% 22.40/22.31 [6185]E(x61851,x61852)+~E(f319(a97,x61851),f319(a97,x61852))+~P1(f319(f319(f225(a1),f2(a1)),x61852))+~P1(f319(f319(f225(a1),f2(a1)),x61851))
% 22.40/22.31 [6382]~P98(x63822)+~P113(x63822)+~P1(f319(f319(f225(x63822),f2(x63822)),f319(f96(x63822),x63821)))+P1(f319(f319(f225(a1),a77),x63821))
% 22.40/22.31 [6383]~P98(x63832)+~P113(x63832)+~P1(f319(f319(f226(x63832),f2(x63832)),f319(f96(x63832),x63831)))+P1(f319(f319(f226(a1),a77),x63831))
% 22.40/22.31 [6388]~P113(x63881)+~P98(x63881)+P1(f319(f319(f225(x63881),f319(f96(x63881),x63882)),f2(x63881)))+~P1(f319(f319(f225(a1),x63882),a77))
% 22.40/22.31 [6389]~P113(x63891)+~P98(x63891)+P1(f319(f319(f226(x63891),f319(f96(x63891),x63892)),f2(x63891)))+~P1(f319(f319(f226(a1),x63892),a77))
% 22.40/22.31 [6707]~P98(x67072)+~P113(x67072)+~P1(f319(f319(f225(x67072),f319(f96(x67072),x67071)),f2(x67072)))+P1(f319(f319(f225(a1),x67071),a77))
% 22.40/22.31 [6708]~P98(x67082)+~P113(x67082)+~P1(f319(f319(f226(x67082),f319(f96(x67082),x67081)),f2(x67082)))+P1(f319(f319(f226(a1),x67081),a77))
% 22.40/22.31 [6801]~P113(x68011)+~P98(x68011)+E(f319(f69(x68011),f319(f96(x68011),x68012)),f319(f73(x68011),f319(f96(x68011),x68012)))+~P1(f319(f319(f226(x68011),f319(f96(x68011),x68012)),f2(x68011)))
% 22.40/22.31 [6822]E(f319(f96(a906),x68221),f319(f96(a906),x68222))+~E(f319(f96(a1),x68222),f2(a1))+~P1(f319(f319(f225(a1),f319(f96(a1),x68221)),f2(a1)))+~P1(f319(a186,f319(f96(a1),x68221)))
% 22.40/22.31 [7678]~P4(x76782)+E(x76781,f181(f913(x76782,a904)))+~P1(f319(f55(x76782),x76781))+P1(f319(f319(f225(x76782),f14(x76782,f230(x76782),x76781)),f13(x76782,f180(x76782),x76781)))
% 22.40/22.31 [7990]~P41(x79902)+~P6(x79901)+P1(f319(f319(f321(a1),x79901),x79902))+~P1(f319(f319(f321(a906),f319(a97,x79901)),f319(f302(a1,a906,a97),x79902)))
% 22.40/22.31 [5961]~P141(x59612)+E(x59611,f2(a1))+E(f319(f73(x59612),f319(f95(x59612),f319(f73(a1),x59611))),f319(f95(x59612),x59611))+~P1(f319(f319(f226(a1),x59611),f2(a1)))
% 22.40/22.31 [6371]~P83(x63712)+E(x63711,f181(f913(x63712,a904)))+E(f17(x63712,f319(f302(x63712,x63712,f73(x63712)),x63711)),f319(f73(x63712),f16(x63712,x63711)))+~P1(f319(f55(x63712),x63711))
% 22.40/22.31 [6372]~P83(x63722)+E(x63721,f181(f913(x63722,a904)))+E(f16(x63722,f319(f302(x63722,x63722,f73(x63722)),x63721)),f319(f73(x63722),f17(x63722,x63721)))+~P1(f319(f55(x63722),x63721))
% 22.40/22.31 [6495]E(x64951,f2(a1))+E(f319(a45,f44(f319(f73(a1),x64951),f319(f73(a1),x64952))),f40(x64951,x64952))+P1(f319(f319(f225(a1),f2(a1)),x64952))+~P1(f319(f319(f225(a1),f2(a1)),x64951))
% 22.40/22.31 [8760]~P41(x87602)+~P41(x87601)+P1(f319(f319(f226(f913(a906,a904)),f319(f302(a1,a906,a97),x87601)),f319(f302(a1,a906,a97),x87602)))+~P1(f319(f319(f226(f913(a1,a904)),x87601),x87602))
% 22.40/22.31 [8997]~E(f720(x89972,x89971),f721(x89972,x89971))+~P1(f319(f129(x89971),f722(x89972,x89971)))+~P1(f319(f129(f907(x89971)),x89972))+P1(f319(f129(x89971),f319(f134(f907(x89971),f907(x89971),f126(x89971),f105(x89971)),x89972)))
% 22.40/22.31 [9086]~P41(x90862)+~P41(x90861)+~P1(f319(f319(f225(f913(a906,a904)),f319(f302(a1,a906,a97),x90861)),f319(f302(a1,a906,a97),x90862)))+P1(f319(f319(f225(f913(a1,a904)),x90861),x90862))
% 22.40/22.31 [9087]~P41(x90872)+~P41(x90871)+~P1(f319(f319(f226(f913(a906,a904)),f319(f302(a1,a906,a97),x90871)),f319(f302(a1,a906,a97),x90872)))+P1(f319(f319(f226(f913(a1,a904)),x90871),x90872))
% 22.40/22.31 [9093]~E(f720(x90932,x90931),f721(x90932,x90931))+~P1(f319(f129(f907(x90931)),x90932))+P1(f319(f129(x90931),f319(f134(f907(x90931),f907(x90931),f126(x90931),f105(x90931)),x90932)))+P1(f319(f319(f321(f907(x90931)),f722(x90932,x90931)),f319(f164(f907(x90931)),x90932)))
% 22.40/22.31 [9134]~P1(f319(f129(x91341),f722(x91342,x91341)))+~P1(f319(f129(f907(x91341)),x91342))+P1(f319(f129(x91341),f319(f134(f907(x91341),f907(x91341),f126(x91341),f105(x91341)),x91342)))+P1(f319(f319(f321(f907(x91341)),f721(x91342,x91341)),f319(f164(f907(x91341)),x91342)))
% 22.40/22.31 [9135]~P1(f319(f129(x91351),f722(x91352,x91351)))+~P1(f319(f129(f907(x91351)),x91352))+P1(f319(f129(x91351),f319(f134(f907(x91351),f907(x91351),f126(x91351),f105(x91351)),x91352)))+P1(f319(f319(f321(f907(x91351)),f720(x91352,x91351)),f319(f164(f907(x91351)),x91352)))
% 22.40/22.31 [9200]~P1(f319(f129(f907(x92001)),x92002))+P1(f319(f129(x92001),f319(f134(f907(x92001),f907(x92001),f126(x92001),f105(x92001)),x92002)))+P1(f319(f319(f321(f907(x92001)),f721(x92002,x92001)),f319(f164(f907(x92001)),x92002)))+P1(f319(f319(f321(f907(x92001)),f722(x92002,x92001)),f319(f164(f907(x92001)),x92002)))
% 22.40/22.31 [9201]~P1(f319(f129(f907(x92011)),x92012))+P1(f319(f129(x92011),f319(f134(f907(x92011),f907(x92011),f126(x92011),f105(x92011)),x92012)))+P1(f319(f319(f321(f907(x92011)),f720(x92012,x92011)),f319(f164(f907(x92011)),x92012)))+P1(f319(f319(f321(f907(x92011)),f722(x92012,x92011)),f319(f164(f907(x92011)),x92012)))
% 22.40/22.31 [9215]~E(f319(f319(f94(f913(x92151,a904)),f319(f164(x92151),f721(x92152,x92151))),f319(f164(x92151),f720(x92152,x92151))),f181(f913(x92151,a904)))+~P1(f319(f129(x92151),f722(x92152,x92151)))+~P1(f319(f129(f907(x92151)),x92152))+P1(f319(f129(x92151),f319(f134(f907(x92151),f907(x92151),f126(x92151),f105(x92151)),x92152)))
% 22.40/22.31 [9288]~E(f319(f319(f94(f913(x92881,a904)),f319(f164(x92881),f721(x92882,x92881))),f319(f164(x92881),f720(x92882,x92881))),f181(f913(x92881,a904)))+~P1(f319(f129(f907(x92881)),x92882))+P1(f319(f129(x92881),f319(f134(f907(x92881),f907(x92881),f126(x92881),f105(x92881)),x92882)))+P1(f319(f319(f321(f907(x92881)),f722(x92882,x92881)),f319(f164(f907(x92881)),x92882)))
% 22.40/22.31 [9566]E(x95661,f2(a1))+E(x95662,f2(a1))+E(f319(f319(f82(a1,f912(a1,a1)),f319(f319(a210,x95662),x95661)),f319(f319(f20(a1,a1,f912(a1,a1)),f319(f319(f10(a1,f913(a1,f912(a1,a1)),a1),f244(a1,a1)),f319(f30(a1),x95662))),f319(f30(a1),x95661))),f208(x95662,x95661))+P1(f319(f319(f226(a1),x95661),f2(a1)))
% 22.40/22.31 [8436]~P98(x84362)+~P113(x84362)+~P1(f319(f319(f225(x84362),f319(f96(x84362),x84361)),f72(x84362)))+P1(f319(f319(f225(a1),x84361),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))
% 22.40/22.31 [8437]~P98(x84372)+~P113(x84372)+~P1(f319(f319(f226(x84372),f319(f96(x84372),x84371)),f72(x84372)))+P1(f319(f319(f226(a1),x84371),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))
% 22.40/22.31 [8718]~P113(x87181)+~P98(x87181)+P1(f319(f319(f225(x87181),f319(f96(x87181),x87182)),f72(x87181)))+~P1(f319(f319(f225(a1),x87182),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))
% 22.40/22.31 [8719]~P113(x87191)+~P98(x87191)+P1(f319(f319(f226(x87191),f319(f96(x87191),x87192)),f72(x87191)))+~P1(f319(f319(f226(a1),x87192),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)))
% 22.40/22.31 [8922]~P98(x89222)+~P113(x89222)+~P1(f319(f319(f225(x89222),f72(x89222)),f319(f96(x89222),x89221)))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),x89221))
% 22.40/22.31 [8923]~P98(x89232)+~P113(x89232)+~P1(f319(f319(f226(x89232),f72(x89232)),f319(f96(x89232),x89231)))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),x89231))
% 22.40/22.31 [9277]~P113(x92771)+~P98(x92771)+P1(f319(f319(f225(x92771),f72(x92771)),f319(f96(x92771),x92772)))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),x92772))
% 22.40/22.31 [9278]~P113(x92781)+~P98(x92781)+P1(f319(f319(f226(x92781),f72(x92781)),f319(f96(x92781),x92782)))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77)),x92782))
% 22.40/22.31 [9408]~P97(x94081)+~P98(x94081)+~P28(x94081,f319(f96(x94081),x94082))+P28(x94081,f319(f96(x94081),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x94082)),x94082)),a89)))
% 22.40/22.31 [9631]~P97(x96311)+~P98(x96311)+P28(x96311,f319(f96(x96311),x96312))+~P28(x96311,f319(f96(x96311),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),x96312)),x96312)),a89)))
% 22.40/22.31 [10128]~P140(x101282)+E(x101281,f72(x101282))+E(x101281,f319(f73(x101282),f72(x101282)))+~E(f319(f319(f236(x101282),x101281),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f72(x101282))
% 22.40/22.31 [10213]~P74(x102131)+~P98(x102131)+~P1(f319(f319(f226(x102131),f2(x102131)),x102132))+P1(f319(f319(f226(x102131),f2(x102131)),f319(f319(f282(x102131),x102132),f319(f96(x102131),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.31 [10260]~P74(x102601)+~P98(x102601)+P1(f319(f319(f226(x102601),f2(x102601)),x102602))+~P1(f319(f319(f226(x102601),f2(x102601)),f319(f319(f282(x102601),x102602),f319(f96(x102601),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.31 [10349]~P141(x103492)+E(x103491,f2(a1))+P1(f319(f319(f226(a1),x103491),f2(a1)))+E(f319(f319(f249(a1,a1,x103492),f319(f319(f9(a1,f913(a1,f913(x103492,x103492)),f913(a1,x103492)),f319(f319(f10(f913(f913(x103492,x103492),x103492),f913(f913(a1,f913(x103492,x103492)),f913(a1,x103492)),a1),f10(f913(x103492,x103492),x103492,a1)),f319(f319(f10(x103492,f913(f913(x103492,x103492),x103492),a1),f82(x103492,x103492)),f95(x103492)))),f319(f319(f9(a1,f913(x103492,x103492),f913(x103492,x103492)),f319(f319(f10(f913(x103492,f913(x103492,x103492)),f913(f913(x103492,x103492),f913(x103492,x103492)),a1),f20(x103492,x103492,x103492)),f319(f319(f9(a1,f913(x103492,x103492),f913(x103492,f913(x103492,x103492))),f319(f319(f10(f913(x103492,f913(x103492,x103492)),f913(f913(x103492,x103492),f913(x103492,f913(x103492,x103492))),a1),f10(x103492,f913(x103492,x103492),x103492)),f319(f319(f10(a904,f913(x103492,f913(x103492,x103492)),a1),f86(x103492)),f319(f319(f9(a1,a1,a904),a316),f2(a1))))),f319(f319(f20(x103492,x103492,x103492),f74(x103492)),f7(x103492))))),f319(f319(f9(x103492,x103492,x103492),f319(f319(f10(x103492,f913(x103492,x103492),x103492),f74(x103492)),f319(f319(f20(x103492,x103492,x103492),f74(x103492)),f7(x103492)))),f72(x103492))))),f40(x103491,f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f95(x103492),x103491))
% 22.40/22.31 [5298]~P111(x52981)+~P111(x52982)+~P50(x52981,x52982,x52983)+P40(x52981,x52982,x52983)
% 22.40/22.31 [5427]~P38(x54271,x54273)+~P53(x54271,x54273)+~P54(x54271,x54272,x54273)+P8(x54271,x54272,x54273)
% 22.40/22.31 [5191]~P5(x51913)+~P40(x51913,x51913,x51911)+E(f319(x51911,x51912),x51912)+~E(x51912,f88(x51913,x51911))
% 22.40/22.31 [5192]~P5(x51923)+~P40(x51923,x51923,x51921)+E(f319(x51921,x51922),x51922)+~E(x51922,f87(x51923,x51921))
% 22.40/22.31 [4964]~P97(x49643)+~P98(x49643)+E(x49641,x49642)+~E(f319(f96(x49643),x49641),f319(f96(x49643),x49642))
% 22.40/22.31 [5437]~P51(x54371,x54372)+~P52(x54371,x54372)+P16(x54371,x54372)+~P1(f319(f319(x54372,x54373),x54373))
% 22.40/22.31 [5940]P16(x59402,x59401)+E(f319(x59401,f796(x59401)),f319(x59401,f797(x59401)))+P1(f319(f319(x59401,f796(x59401)),f797(x59401)))+~P1(f319(f319(x59401,x59403),x59403))
% 22.40/22.31 [6139]~P1(f319(x61391,x61392))+~P1(f319(x61391,x61393))+~P1(f319(f319(f225(a906),x61393),f354(x61392,x61391)))+P1(f319(x61391,f2(a906)))
% 22.40/22.31 [6204]P16(x62041,x62042)+P1(f319(f319(x62042,f796(x62042)),f796(x62042)))+P1(f319(f319(x62042,f796(x62042)),f797(x62042)))+~P1(f319(f319(x62042,x62043),x62043))
% 22.40/22.31 [6205]P16(x62051,x62052)+P1(f319(f319(x62052,f796(x62052)),f797(x62052)))+P1(f319(f319(x62052,f797(x62052)),f797(x62052)))+~P1(f319(f319(x62052,x62053),x62053))
% 22.40/22.31 [6562]P148(x65622,x65621,x65623)+E(x65621,f2(a1))+P1(f319(f319(f225(a1),f2(a1)),f851(x65623,x65621,x65622)))+P1(f319(f319(f226(a1),x65621),f2(a1)))
% 22.40/22.31 [6563]P147(x65632,x65631,x65633)+E(x65631,f2(a1))+P1(f319(f319(f225(a1),f2(a1)),f855(x65633,x65631,x65632)))+P1(f319(f319(f226(a1),x65631),f2(a1)))
% 22.40/22.31 [6684]P147(x66841,x66842,x66843)+~P1(f319(x66841,x66843))+P1(f319(f319(f225(a1),f2(a1)),f855(x66843,x66842,x66841)))+P1(f319(f319(f226(a1),x66842),f2(a1)))
% 22.40/22.31 [6713]P148(x67131,x67132,x67133)+P1(f319(f319(f225(a1),f2(a1)),f851(x67133,x67132,x67131)))+~P1(f319(x67131,f2(a1)))+P1(f319(f319(f226(a1),x67132),f2(a1)))
% 22.40/22.31 [6743]P148(x67432,x67431,x67433)+E(x67431,f2(a1))+~P1(f319(x67432,f852(x67433,x67431,x67432)))+P1(f319(f319(f226(a1),x67431),f2(a1)))
% 22.40/22.31 [6744]P147(x67442,x67441,x67443)+E(x67441,f2(a1))+~P1(f319(x67442,f855(x67443,x67441,x67442)))+P1(f319(f319(f226(a1),x67441),f2(a1)))
% 22.40/22.31 [6848]~P4(x68481)+~P5(x68481)+~P1(f319(f319(f226(x68481),x68482),f31(x68481,x68483)))+P1(f319(f319(f226(x68481),x68482),f387(x68483,x68482,x68481)))
% 22.40/22.31 [6857]P147(x68571,x68572,x68573)+~P1(f319(x68571,x68573))+~P1(f319(x68571,f855(x68573,x68572,x68571)))+P1(f319(f319(f226(a1),x68572),f2(a1)))
% 22.40/22.31 [6884]P148(x68841,x68842,x68843)+~P1(f319(x68841,f852(x68843,x68842,x68841)))+~P1(f319(x68841,f2(a1)))+P1(f319(f319(f226(a1),x68842),f2(a1)))
% 22.40/22.31 [7131]P148(x71312,x71311,x71313)+E(x71311,f2(a1))+P1(f319(f319(f225(a1),f2(a1)),f851(x71313,x71311,x71312)))+P1(f319(f319(f226(a1),x71311),f850(x71313,x71311,x71312)))
% 22.40/22.31 [7132]P147(x71322,x71321,x71323)+E(x71321,f2(a1))+P1(f319(f319(f225(a1),f2(a1)),f855(x71323,x71321,x71322)))+P1(f319(f319(f226(a1),x71321),f854(x71323,x71321,x71322)))
% 22.40/22.31 [7250]P147(x72501,x72502,x72503)+~P1(f319(x72501,x72503))+P1(f319(f319(f225(a1),f2(a1)),f855(x72503,x72502,x72501)))+P1(f319(f319(f226(a1),x72502),f854(x72503,x72502,x72501)))
% 22.40/22.31 [7269]P148(x72691,x72692,x72693)+P1(f319(f319(f225(a1),f2(a1)),f851(x72693,x72692,x72691)))+P1(f319(f319(f226(a1),x72692),f850(x72693,x72692,x72691)))+~P1(f319(x72691,f2(a1)))
% 22.40/22.31 [7301]P148(x73012,x73011,x73013)+E(x73011,f2(a1))+~P1(f319(x73012,f852(x73013,x73011,x73012)))+P1(f319(f319(f226(a1),x73011),f850(x73013,x73011,x73012)))
% 22.40/22.31 [7302]P147(x73022,x73021,x73023)+E(x73021,f2(a1))+~P1(f319(x73022,f855(x73023,x73021,x73022)))+P1(f319(f319(f226(a1),x73021),f854(x73023,x73021,x73022)))
% 22.40/22.31 [7346]P148(x73462,x73461,x73463)+E(x73461,f2(a1))+P1(f319(f319(f225(a1),f2(a1)),f851(x73463,x73461,x73462)))+~P1(f319(x73462,f853(x73463,x73461,x73462)))
% 22.40/22.31 [7347]P147(x73472,x73471,x73473)+E(x73471,f2(a1))+P1(f319(f319(f225(a1),f2(a1)),f855(x73473,x73471,x73472)))+~P1(f319(x73472,f854(x73473,x73471,x73472)))
% 22.40/22.31 [7440]P147(x74401,x74402,x74403)+~P1(f319(x74401,x74403))+~P1(f319(x74401,f855(x74403,x74402,x74401)))+P1(f319(f319(f226(a1),x74402),f854(x74403,x74402,x74401)))
% 22.40/22.31 [7449]P148(x74491,x74492,x74493)+~P1(f319(x74491,f852(x74493,x74492,x74491)))+P1(f319(f319(f226(a1),x74492),f850(x74493,x74492,x74491)))+~P1(f319(x74491,f2(a1)))
% 22.40/22.31 [7452]P147(x74521,x74522,x74523)+~P1(f319(x74521,x74523))+P1(f319(f319(f225(a1),f2(a1)),f855(x74523,x74522,x74521)))+~P1(f319(x74521,f854(x74523,x74522,x74521)))
% 22.40/22.31 [7468]P148(x74681,x74682,x74683)+P1(f319(f319(f225(a1),f2(a1)),f851(x74683,x74682,x74681)))+~P1(f319(x74681,f853(x74683,x74682,x74681)))+~P1(f319(x74681,f2(a1)))
% 22.40/22.31 [7469]~P111(x74692)+~P111(x74691)+P50(x74691,x74692,x74693)+P1(f319(f319(f226(x74691),f428(x74693,x74691,x74692)),f436(x74693,x74691,x74692)))
% 22.40/22.31 [7491]P148(x74912,x74911,x74913)+E(x74911,f2(a1))+~P1(f319(x74912,f852(x74913,x74911,x74912)))+~P1(f319(x74912,f853(x74913,x74911,x74912)))
% 22.40/22.31 [7492]P147(x74922,x74921,x74923)+E(x74921,f2(a1))+~P1(f319(x74922,f855(x74923,x74921,x74922)))+~P1(f319(x74922,f854(x74923,x74921,x74922)))
% 22.40/22.31 [7577]P147(x75771,x75772,x75773)+~P1(f319(x75771,x75773))+~P1(f319(x75771,f855(x75773,x75772,x75771)))+~P1(f319(x75771,f854(x75773,x75772,x75771)))
% 22.40/22.31 [7595]P148(x75951,x75952,x75953)+~P1(f319(x75951,f852(x75953,x75952,x75951)))+~P1(f319(x75951,f853(x75953,x75952,x75951)))+~P1(f319(x75951,f2(a1)))
% 22.40/22.31 [7638]P148(x76382,x76381,x76383)+E(x76381,f2(a1))+P1(f319(f319(f225(a1),f2(a1)),f851(x76383,x76381,x76382)))+P1(f319(f319(f225(a1),f850(x76383,x76381,x76382)),f2(a1)))
% 22.40/22.31 [7639]P147(x76392,x76391,x76393)+E(x76391,f2(a1))+P1(f319(f319(f225(a1),f2(a1)),f855(x76393,x76391,x76392)))+P1(f319(f319(f225(a1),f854(x76393,x76391,x76392)),f2(a1)))
% 22.40/22.31 [7640]~P93(x76401)+~P1(f319(f319(f225(x76401),x76403),f2(x76401)))+~P1(f319(f319(f225(x76401),x76402),f2(x76401)))+P1(f319(f319(f225(x76401),f319(f319(f74(x76401),x76402),x76403)),f2(x76401)))
% 22.40/22.31 [7641]~P141(x76411)+~P1(f319(f319(f321(x76411),x76413),f102(x76411)))+~P1(f319(f319(f321(x76411),x76412),f102(x76411)))+P1(f319(f319(f321(x76411),f319(f319(f3(x76411),x76412),x76413)),f102(x76411)))
% 22.40/22.31 [7642]~P141(x76421)+~P1(f319(f319(f321(x76421),x76423),f102(x76421)))+~P1(f319(f319(f321(x76421),x76422),f102(x76421)))+P1(f319(f319(f321(x76421),f319(f319(f74(x76421),x76422),x76423)),f102(x76421)))
% 22.40/22.31 [7643]~P146(x76431)+~P1(f319(f319(f321(x76431),x76433),f178(x76431)))+~P1(f319(f319(f321(x76431),x76432),f178(x76431)))+P1(f319(f319(f321(x76431),f319(f319(f74(x76431),x76432),x76433)),f178(x76431)))
% 22.40/22.31 [7644]~P141(x76441)+~P1(f319(f319(f321(x76441),x76443),f102(x76441)))+~P1(f319(f319(f321(x76441),x76442),f102(x76441)))+P1(f319(f319(f321(x76441),f319(f319(f75(x76441),x76442),x76443)),f102(x76441)))
% 22.40/22.31 [7645]~P146(x76451)+~P1(f319(f319(f321(x76451),x76453),f178(x76451)))+~P1(f319(f319(f321(x76451),x76452),f178(x76451)))+P1(f319(f319(f321(x76451),f319(f319(f75(x76451),x76452),x76453)),f178(x76451)))
% 22.40/22.31 [7646]~P93(x76461)+~P1(f319(f319(f225(x76461),x76463),f2(x76461)))+~P1(f319(f319(f226(x76461),x76462),f2(x76461)))+P1(f319(f319(f226(x76461),f319(f319(f74(x76461),x76462),x76463)),f2(x76461)))
% 22.40/22.31 [7647]~P93(x76471)+~P1(f319(f319(f225(x76471),x76472),f2(x76471)))+~P1(f319(f319(f226(x76471),x76473),f2(x76471)))+P1(f319(f319(f226(x76471),f319(f319(f74(x76471),x76472),x76473)),f2(x76471)))
% 22.40/22.31 [7648]~P93(x76481)+~P1(f319(f319(f226(x76481),x76483),f2(x76481)))+~P1(f319(f319(f226(x76481),x76482),f2(x76481)))+P1(f319(f319(f226(x76481),f319(f319(f74(x76481),x76482),x76483)),f2(x76481)))
% 22.40/22.31 [7674]P148(x76743,x76741,x76742)+E(x76741,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x76741),f852(x76742,x76741,x76743))),f851(x76742,x76741,x76743)),x76742)+P1(f319(f319(f226(a1),x76741),f2(a1)))
% 22.40/22.31 [7675]P147(x76753,x76751,x76752)+E(x76751,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x76751),f856(x76752,x76751,x76753))),f855(x76752,x76751,x76753)),x76752)+P1(f319(f319(f226(a1),x76751),f2(a1)))
% 22.40/22.31 [7754]P147(x77541,x77542,x77543)+~P1(f319(x77541,x77543))+P1(f319(f319(f225(a1),f2(a1)),f855(x77543,x77542,x77541)))+P1(f319(f319(f225(a1),f854(x77543,x77542,x77541)),f2(a1)))
% 22.40/22.31 [7784]P148(x77841,x77842,x77843)+P1(f319(f319(f225(a1),f2(a1)),f851(x77843,x77842,x77841)))+~P1(f319(x77841,f2(a1)))+P1(f319(f319(f225(a1),f850(x77843,x77842,x77841)),f2(a1)))
% 22.40/22.31 [7793]P147(x77933,x77931,x77932)+~P1(f319(x77933,x77932))+E(f319(f319(f74(a1),f319(f319(f75(a1),x77931),f856(x77932,x77931,x77933))),f855(x77932,x77931,x77933)),x77932)+P1(f319(f319(f226(a1),x77931),f2(a1)))
% 22.40/22.31 [7799]P148(x77992,x77991,x77993)+E(x77991,f2(a1))+~P1(f319(x77992,f852(x77993,x77991,x77992)))+P1(f319(f319(f225(a1),f850(x77993,x77991,x77992)),f2(a1)))
% 22.40/22.31 [7800]P147(x78002,x78001,x78003)+E(x78001,f2(a1))+~P1(f319(x78002,f855(x78003,x78001,x78002)))+P1(f319(f319(f225(a1),f854(x78003,x78001,x78002)),f2(a1)))
% 22.40/22.31 [7804]P148(x78043,x78041,x78042)+E(f319(f319(f74(a1),f319(f319(f75(a1),x78041),f852(x78042,x78041,x78043))),f851(x78042,x78041,x78043)),x78042)+~P1(f319(x78043,f2(a1)))+P1(f319(f319(f226(a1),x78041),f2(a1)))
% 22.40/22.31 [7860]P147(x78601,x78602,x78603)+~P1(f319(x78601,x78603))+~P1(f319(x78601,f855(x78603,x78602,x78601)))+P1(f319(f319(f225(a1),f854(x78603,x78602,x78601)),f2(a1)))
% 22.40/22.31 [7865]P148(x78651,x78652,x78653)+~P1(f319(x78651,f852(x78653,x78652,x78651)))+~P1(f319(x78651,f2(a1)))+P1(f319(f319(f225(a1),f850(x78653,x78652,x78651)),f2(a1)))
% 22.40/22.31 [7936]~P127(x79361)+~P1(f319(f319(f225(x79361),f319(f319(f75(x79361),x79363),x79362)),f2(x79361)))+P1(f319(f319(f225(x79361),x79362),f2(x79361)))+P1(f319(f319(f225(x79361),x79363),f2(x79361)))
% 22.40/22.31 [7937]~P74(x79371)+~P1(f319(f319(f225(x79371),f319(f319(f282(x79371),x79373),x79372)),f2(x79371)))+P1(f319(f319(f225(x79371),x79372),f2(x79371)))+P1(f319(f319(f225(x79371),x79373),f2(x79371)))
% 22.40/22.31 [7938]~P74(x79381)+~P1(f319(f319(f226(x79381),f319(f319(f282(x79381),x79383),x79382)),f2(x79381)))+P1(f319(f319(f226(x79381),x79382),f2(x79381)))+P1(f319(f319(f226(x79381),x79383),f2(x79381)))
% 22.40/22.31 [8043]P148(x80433,x80431,x80432)+E(x80431,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x80431),f852(x80432,x80431,x80433))),f851(x80432,x80431,x80433)),x80432)+P1(f319(f319(f226(a1),x80431),f850(x80432,x80431,x80433)))
% 22.40/22.31 [8044]P147(x80443,x80441,x80442)+E(x80441,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x80441),f856(x80442,x80441,x80443))),f855(x80442,x80441,x80443)),x80442)+P1(f319(f319(f226(a1),x80441),f854(x80442,x80441,x80443)))
% 22.40/22.31 [8056]P148(x80563,x80561,x80562)+E(x80561,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x80561),f853(x80562,x80561,x80563))),f850(x80562,x80561,x80563)),x80562)+P1(f319(f319(f225(a1),f2(a1)),f851(x80562,x80561,x80563)))
% 22.40/22.31 [8057]P147(x80573,x80571,x80572)+E(x80571,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x80571),f857(x80572,x80571,x80573))),f854(x80572,x80571,x80573)),x80572)+P1(f319(f319(f225(a1),f2(a1)),f855(x80572,x80571,x80573)))
% 22.40/22.31 [8097]P147(x80973,x80971,x80972)+~P1(f319(x80973,x80972))+E(f319(f319(f74(a1),f319(f319(f75(a1),x80971),f856(x80972,x80971,x80973))),f855(x80972,x80971,x80973)),x80972)+P1(f319(f319(f226(a1),x80971),f854(x80972,x80971,x80973)))
% 22.40/22.31 [8106]P148(x81063,x81061,x81062)+E(f319(f319(f74(a1),f319(f319(f75(a1),x81061),f852(x81062,x81061,x81063))),f851(x81062,x81061,x81063)),x81062)+P1(f319(f319(f226(a1),x81061),f850(x81062,x81061,x81063)))+~P1(f319(x81063,f2(a1)))
% 22.40/22.31 [8112]P147(x81123,x81121,x81122)+~P1(f319(x81123,x81122))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81121),f857(x81122,x81121,x81123))),f854(x81122,x81121,x81123)),x81122)+P1(f319(f319(f225(a1),f2(a1)),f855(x81122,x81121,x81123)))
% 22.40/22.31 [8118]P148(x81183,x81181,x81182)+E(f319(f319(f74(a1),f319(f319(f75(a1),x81181),f853(x81182,x81181,x81183))),f850(x81182,x81181,x81183)),x81182)+P1(f319(f319(f225(a1),f2(a1)),f851(x81182,x81181,x81183)))+~P1(f319(x81183,f2(a1)))
% 22.40/22.31 [8129]P148(x81293,x81291,x81292)+E(x81291,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81291),f852(x81292,x81291,x81293))),f851(x81292,x81291,x81293)),x81292)+~P1(f319(x81293,f853(x81292,x81291,x81293)))
% 22.40/22.31 [8130]P147(x81303,x81301,x81302)+E(x81301,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81301),f856(x81302,x81301,x81303))),f855(x81302,x81301,x81303)),x81302)+~P1(f319(x81303,f854(x81302,x81301,x81303)))
% 22.40/22.31 [8131]P148(x81313,x81311,x81312)+E(x81311,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81311),f853(x81312,x81311,x81313))),f850(x81312,x81311,x81313)),x81312)+~P1(f319(x81313,f852(x81312,x81311,x81313)))
% 22.40/22.31 [8132]P147(x81323,x81321,x81322)+E(x81321,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81321),f857(x81322,x81321,x81323))),f854(x81322,x81321,x81323)),x81322)+~P1(f319(x81323,f855(x81322,x81321,x81323)))
% 22.40/22.31 [8194]P147(x81943,x81941,x81942)+~P1(f319(x81943,x81942))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81941),f856(x81942,x81941,x81943))),f855(x81942,x81941,x81943)),x81942)+~P1(f319(x81943,f854(x81942,x81941,x81943)))
% 22.40/22.31 [8195]P147(x81953,x81951,x81952)+~P1(f319(x81953,x81952))+E(f319(f319(f74(a1),f319(f319(f75(a1),x81951),f857(x81952,x81951,x81953))),f854(x81952,x81951,x81953)),x81952)+~P1(f319(x81953,f855(x81952,x81951,x81953)))
% 22.40/22.31 [8206]P148(x82063,x82061,x82062)+E(f319(f319(f74(a1),f319(f319(f75(a1),x82061),f852(x82062,x82061,x82063))),f851(x82062,x82061,x82063)),x82062)+~P1(f319(x82063,f853(x82062,x82061,x82063)))+~P1(f319(x82063,f2(a1)))
% 22.40/22.31 [8207]P148(x82073,x82071,x82072)+E(f319(f319(f74(a1),f319(f319(f75(a1),x82071),f853(x82072,x82071,x82073))),f850(x82072,x82071,x82073)),x82072)+~P1(f319(x82073,f852(x82072,x82071,x82073)))+~P1(f319(x82073,f2(a1)))
% 22.40/22.31 [8306]P148(x83063,x83061,x83062)+E(x83061,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83061),f852(x83062,x83061,x83063))),f851(x83062,x83061,x83063)),x83062)+P1(f319(f319(f225(a1),f850(x83062,x83061,x83063)),f2(a1)))
% 22.40/22.31 [8307]P147(x83073,x83071,x83072)+E(x83071,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83071),f856(x83072,x83071,x83073))),f855(x83072,x83071,x83073)),x83072)+P1(f319(f319(f225(a1),f854(x83072,x83071,x83073)),f2(a1)))
% 22.40/22.31 [8343]P147(x83433,x83431,x83432)+~P1(f319(x83433,x83432))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83431),f856(x83432,x83431,x83433))),f855(x83432,x83431,x83433)),x83432)+P1(f319(f319(f225(a1),f854(x83432,x83431,x83433)),f2(a1)))
% 22.40/22.31 [8348]P148(x83483,x83481,x83482)+E(f319(f319(f74(a1),f319(f319(f75(a1),x83481),f852(x83482,x83481,x83483))),f851(x83482,x83481,x83483)),x83482)+~P1(f319(x83483,f2(a1)))+P1(f319(f319(f225(a1),f850(x83482,x83481,x83483)),f2(a1)))
% 22.40/22.31 [8480]P148(x84803,x84801,x84802)+E(x84801,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84801),f853(x84802,x84801,x84803))),f850(x84802,x84801,x84803)),x84802)+E(f319(f319(f74(a1),f319(f319(f75(a1),x84801),f852(x84802,x84801,x84803))),f851(x84802,x84801,x84803)),x84802)
% 22.40/22.31 [8481]P147(x84813,x84811,x84812)+E(x84811,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x84811),f857(x84812,x84811,x84813))),f854(x84812,x84811,x84813)),x84812)+E(f319(f319(f74(a1),f319(f319(f75(a1),x84811),f856(x84812,x84811,x84813))),f855(x84812,x84811,x84813)),x84812)
% 22.40/22.31 [8501]P147(x85013,x85011,x85012)+~P1(f319(x85013,x85012))+E(f319(f319(f74(a1),f319(f319(f75(a1),x85011),f857(x85012,x85011,x85013))),f854(x85012,x85011,x85013)),x85012)+E(f319(f319(f74(a1),f319(f319(f75(a1),x85011),f856(x85012,x85011,x85013))),f855(x85012,x85011,x85013)),x85012)
% 22.40/22.31 [8508]P148(x85083,x85081,x85082)+E(f319(f319(f74(a1),f319(f319(f75(a1),x85081),f853(x85082,x85081,x85083))),f850(x85082,x85081,x85083)),x85082)+E(f319(f319(f74(a1),f319(f319(f75(a1),x85081),f852(x85082,x85081,x85083))),f851(x85082,x85081,x85083)),x85082)+~P1(f319(x85083,f2(a1)))
% 22.40/22.31 [9174]~P127(x91741)+~E(x91743,f2(x91741))+~E(x91742,f2(x91741))+P1(f319(f319(f225(x91741),f319(f319(f74(x91741),f319(f319(f75(x91741),x91742),x91742)),f319(f319(f75(x91741),x91743),x91743))),f2(x91741)))
% 22.40/22.31 [10362]~P113(x103621)+~E(x103623,f2(x103621))+~E(x103622,f2(x103621))+P1(f319(f319(f225(x103621),f319(f319(f74(x103621),f319(f319(f236(x103621),x103622),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103621),x103623),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))),f2(x103621)))
% 22.40/22.31 [4914]~E(x49143,x49141)+~P120(x49142)+E(x49141,f2(x49142))+E(f319(f319(f282(x49142),x49143),x49141),f72(x49142))
% 22.40/22.31 [4965]~P103(x49651)+~E(x49653,f181(x49651))+~E(x49652,f181(x49651))+E(f319(f319(f93(x49651),x49652),x49653),f181(x49651))
% 22.40/22.31 [4966]~P105(x49661)+~E(x49663,f234(x49661))+~E(x49662,f234(x49661))+E(f319(f319(f94(x49661),x49662),x49663),f234(x49661))
% 22.40/22.31 [5060]~P120(x50603)+E(x50601,x50602)+E(x50602,f2(x50603))+~E(f319(f319(f282(x50603),x50601),x50602),f72(x50603))
% 22.40/22.31 [5078]~P129(x50782)+E(x50781,f2(x50782))+E(x50783,f2(x50782))+~E(f319(f319(f75(x50782),x50783),x50781),f2(x50782))
% 22.40/22.31 [5079]~P142(x50792)+E(x50791,f2(x50792))+E(x50793,f2(x50792))+~E(f319(f319(f75(x50792),x50793),x50791),f2(x50792))
% 22.40/22.31 [5456]~P118(x54563)+E(x54561,x54562)+E(x54561,f319(f73(x54563),x54562))+~E(f319(f319(f75(x54563),x54561),x54561),f319(f319(f75(x54563),x54562),x54562))
% 22.40/22.31 [5494]~P63(x54941)+E(f319(f73(x54941),x54942),x54943)+~E(f319(f319(f93(x54941),x54942),x54943),f234(x54941))+~E(f319(f319(f94(x54941),x54942),x54943),f181(x54941))
% 22.40/22.31 [5575]~P113(x55753)+E(x55751,x55752)+P1(f319(f319(f226(x55753),x55752),x55751))+P1(f319(f319(f226(x55753),x55751),x55752))
% 22.40/22.31 [5576]~P4(x55763)+E(x55761,x55762)+P1(f319(f319(f226(x55763),x55762),x55761))+P1(f319(f319(f226(x55763),x55761),x55762))
% 22.40/22.31 [5577]~E(x55772,x55773)+~P4(x55771)+P1(f319(f319(f226(x55771),x55772),x55773))+P1(f319(f319(f225(x55771),x55772),x55773))
% 22.40/22.31 [5840]~P111(x58403)+E(x58401,x58402)+~P1(f319(f319(f225(x58403),x58402),x58401))+P1(f319(f319(f226(x58403),x58402),x58401))
% 22.40/22.31 [5842]~P4(x58423)+E(x58421,x58422)+~P1(f319(f319(f225(x58423),x58421),x58422))+P1(f319(f319(f226(x58423),x58421),x58422))
% 22.40/22.31 [5848]~P111(x58483)+E(x58481,x58482)+~P1(f319(f319(f225(x58483),x58481),x58482))+P1(f319(f319(f226(x58483),x58481),x58482))
% 22.40/22.31 [5958]P147(x59581,x59582,x59583)+~P1(f319(x59581,x59583))+P1(f319(f319(f226(a1),x59582),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x59582))
% 22.40/22.31 [6008]P148(x60081,x60082,x60083)+~P1(f319(x60081,f2(a1)))+P1(f319(f319(f226(a1),x60082),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x60082))
% 22.40/22.31 [6013]~P101(x60131)+E(f319(f319(f93(x60131),x60132),f12(x60131,x60133)),x60132)+~P1(f319(f55(x60131),x60133))+~P1(f319(f319(f321(x60131),x60132),x60133))
% 22.40/22.31 [6014]~P101(x60141)+E(f319(f319(f94(x60141),x60142),f15(x60141,x60143)),x60142)+~P1(f319(f55(x60141),x60143))+~P1(f319(f319(f321(x60141),x60142),x60143))
% 22.40/22.31 [6050]~P101(x60501)+E(f319(f319(f93(x60501),x60502),f15(x60501,x60503)),f15(x60501,x60503))+~P1(f319(f55(x60501),x60503))+~P1(f319(f319(f321(x60501),x60502),x60503))
% 22.40/22.31 [6051]~P101(x60511)+E(f319(f319(f94(x60511),x60512),f12(x60511,x60513)),f12(x60511,x60513))+~P1(f319(f55(x60511),x60513))+~P1(f319(f319(f321(x60511),x60512),x60513))
% 22.40/22.31 [6052]~P4(x60521)+E(f319(f319(f180(x60521),x60522),f16(x60521,x60523)),f16(x60521,x60523))+~P1(f319(f55(x60521),x60523))+~P1(f319(f319(f321(x60521),x60522),x60523))
% 22.40/22.31 [6053]~P4(x60531)+E(f319(f319(f230(x60531),x60532),f17(x60531,x60533)),f17(x60531,x60533))+~P1(f319(f55(x60531),x60533))+~P1(f319(f319(f321(x60531),x60532),x60533))
% 22.40/22.31 [6091]E(x60911,x60912)+~P111(x60913)+~P1(f319(f319(f225(x60913),x60912),x60911))+~P1(f319(f319(f225(x60913),x60911),x60912))
% 22.40/22.31 [6233]~P2(x62331)+P1(f319(f319(f226(x62331),x62333),x62332))+~P1(f319(f319(f225(x62331),x62333),x62332))+P1(f319(f319(f225(x62331),x62332),x62333))
% 22.40/22.31 [6263]~P4(x62631)+~P1(f319(f55(x62631),x62633))+P1(f319(f319(f225(x62631),x62632),f16(x62631,x62633)))+~P1(f319(f319(f321(x62631),x62632),x62633))
% 22.40/22.31 [6306]~P4(x63061)+E(f319(f319(f180(x63061),x63062),f14(x63061,f230(x63061),x63063)),x63062)+~P1(f319(f55(x63061),x63063))+~P1(f319(f319(f321(x63061),x63062),x63063))
% 22.40/22.31 [6307]~P4(x63071)+E(f319(f319(f230(x63071),x63072),f13(x63071,f180(x63071),x63073)),x63072)+~P1(f319(f55(x63071),x63073))+~P1(f319(f319(f321(x63071),x63072),x63073))
% 22.40/22.31 [6446]E(x64461,x64462)+~E(f319(f319(f3(a906),x64461),x64463),f319(f319(f3(a906),x64462),x64463))+~P1(f319(f319(f225(a906),x64463),x64461))+~P1(f319(f319(f225(a906),x64463),x64462))
% 22.40/22.31 [6474]~P4(x64741)+~P1(f319(f55(x64741),x64742))+~P1(f319(f319(f321(x64741),x64743),x64742))+P1(f319(f319(f225(x64741),f17(x64741,x64742)),x64743))
% 22.40/22.31 [6541]P148(x65412,x65411,x65413)+E(x65411,f2(a1))+P1(f319(f319(f226(a1),x65411),f850(x65413,x65411,x65412)))+P1(f319(f319(f226(a1),f2(a1)),x65411))
% 22.40/22.31 [6542]P147(x65422,x65421,x65423)+E(x65421,f2(a1))+P1(f319(f319(f226(a1),x65421),f854(x65423,x65421,x65422)))+P1(f319(f319(f226(a1),f2(a1)),x65421))
% 22.40/22.31 [6543]~P4(x65431)+E(f319(f319(f180(x65431),x65432),f13(x65431,f180(x65431),x65433)),f13(x65431,f180(x65431),x65433))+~P1(f319(f55(x65431),x65433))+~P1(f319(f319(f321(x65431),x65432),x65433))
% 22.40/22.31 [6544]~P4(x65441)+E(f319(f319(f230(x65441),x65442),f14(x65441,f230(x65441),x65443)),f14(x65441,f230(x65441),x65443))+~P1(f319(f55(x65441),x65443))+~P1(f319(f319(f321(x65441),x65442),x65443))
% 22.40/22.31 [6549]~P1(f319(x65491,x65492))+P1(f319(x65491,f450(x65492,x65491,x65493)))+P1(f319(x65491,f2(a906)))+~P1(f319(f319(f226(a906),x65492),x65493))
% 22.40/22.31 [6606]~P1(f319(x66061,x66062))+~P1(f319(f55(x66063),x66062))+P1(f319(x66061,f859(x66061,x66062,x66063)))+P1(f319(x66061,f181(f913(x66063,a904))))
% 22.40/22.31 [6619]~P113(x66191)+~P98(x66191)+P1(f319(f319(f225(x66191),f319(f96(x66191),x66192)),f319(f96(x66191),x66193)))+~P1(f319(f319(f225(a1),x66192),x66193))
% 22.40/22.31 [6620]~P113(x66201)+~P98(x66201)+P1(f319(f319(f226(x66201),f319(f96(x66201),x66202)),f319(f96(x66201),x66203)))+~P1(f319(f319(f226(a1),x66202),x66203))
% 22.40/22.31 [6623]~P1(f319(x66231,x66233))+~P1(f319(f55(x66232),x66233))+P1(f319(f55(x66232),f859(x66231,x66233,x66232)))+P1(f319(x66231,f181(f913(x66232,a904))))
% 22.40/22.31 [6654]P147(x66541,x66542,x66543)+~P1(f319(x66541,x66543))+P1(f319(f319(f226(a1),x66542),f854(x66543,x66542,x66541)))+P1(f319(f319(f226(a1),f2(a1)),x66542))
% 22.40/22.31 [6690]P148(x66901,x66902,x66903)+P1(f319(f319(f226(a1),x66902),f850(x66903,x66902,x66901)))+~P1(f319(x66901,f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x66902))
% 22.40/22.31 [6724]~P3(x67241)+~P99(x67241)+E(f319(f319(f180(x67241),f319(f96(x67241),x67242)),f319(f96(x67241),x67243)),f319(f96(x67241),x67242))+P1(f319(f319(f225(x67241),f319(f96(x67241),x67242)),f319(f96(x67241),x67243)))
% 22.40/22.31 [6725]~P3(x67251)+~P99(x67251)+E(f319(f319(f230(x67251),f319(f96(x67251),x67252)),f319(f96(x67251),x67253)),f319(f96(x67251),x67253))+P1(f319(f319(f225(x67251),f319(f96(x67251),x67252)),f319(f96(x67251),x67253)))
% 22.40/22.31 [6784]P148(x67842,x67841,x67843)+E(x67841,f2(a1))+~P1(f319(x67842,f853(x67843,x67841,x67842)))+P1(f319(f319(f226(a1),f2(a1)),x67841))
% 22.40/22.31 [6785]P147(x67852,x67851,x67853)+E(x67851,f2(a1))+~P1(f319(x67852,f854(x67853,x67851,x67852)))+P1(f319(f319(f226(a1),f2(a1)),x67851))
% 22.40/22.31 [6789]P1(f319(x67891,x67892))+~P1(f319(f55(x67893),x67892))+P1(f319(x67891,f376(x67891,x67892,x67893)))+~P1(f319(x67891,f181(f913(x67893,a904))))
% 22.40/22.31 [6813]P1(f319(x68131,x68132))+P1(f319(f55(x68133),f376(x68131,x68132,x68133)))+~P1(f319(f55(x68133),x68132))+~P1(f319(x68131,f181(f913(x68133,a904))))
% 22.40/22.31 [6878]P147(x68781,x68782,x68783)+~P1(f319(x68781,x68783))+~P1(f319(x68781,f854(x68783,x68782,x68781)))+P1(f319(f319(f226(a1),f2(a1)),x68782))
% 22.40/22.31 [6903]P148(x69031,x69032,x69033)+~P1(f319(x69031,f853(x69033,x69032,x69031)))+~P1(f319(x69031,f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x69032))
% 22.40/22.31 [7007]~P98(x70073)+~P113(x70073)+~P1(f319(f319(f225(x70073),f319(f96(x70073),x70071)),f319(f96(x70073),x70072)))+P1(f319(f319(f225(a1),x70071),x70072))
% 22.40/22.31 [7008]~P98(x70083)+~P113(x70083)+~P1(f319(f319(f226(x70083),f319(f96(x70083),x70081)),f319(f96(x70083),x70082)))+P1(f319(f319(f226(a1),x70081),x70082))
% 22.40/22.31 [7035]~P4(x70351)+~P13(x70351,x70353)+P13(x70351,f319(f319(f143(x70351),x70352),x70353))+~P1(f319(f319(f225(x70351),x70352),f701(x70353,x70352,x70351)))
% 22.40/22.31 [7036]~P4(x70361)+~P13(x70361,x70363)+P13(x70361,f319(f319(f143(x70361),x70362),x70363))+~P1(f319(f319(f225(x70361),x70362),f703(x70363,x70362,x70361)))
% 22.40/22.31 [7037]~P4(x70371)+~P13(x70371,x70373)+P13(x70371,f319(f319(f143(x70371),x70372),x70373))+~P1(f319(f319(f225(x70371),x70372),f742(x70372,x70373,x70371)))
% 22.40/22.31 [7125]P148(x71252,x71251,x71253)+E(x71251,f2(a1))+P1(f319(f319(f226(a1),x71251),f2(a1)))+P1(f319(f319(f226(a1),f851(x71253,x71251,x71252)),x71251))
% 22.40/22.31 [7126]P147(x71262,x71261,x71263)+E(x71261,f2(a1))+P1(f319(f319(f226(a1),x71261),f2(a1)))+P1(f319(f319(f226(a1),f855(x71263,x71261,x71262)),x71261))
% 22.40/22.31 [7161]P148(x71612,x71611,x71613)+E(x71611,f2(a1))+P1(f319(f319(f225(a1),f850(x71613,x71611,x71612)),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x71611))
% 22.40/22.31 [7162]P147(x71622,x71621,x71623)+E(x71621,f2(a1))+P1(f319(f319(f225(a1),f854(x71623,x71621,x71622)),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x71621))
% 22.40/22.31 [7187]~P4(x71871)+~P13(x71871,x71873)+E(f319(f319(f140(x71871,x71871,f7(x71871)),x71872),f162(x71871,x71872,x71873)),x71873)+~P1(f319(f319(f321(x71871),x71872),f319(f164(x71871),x71873)))
% 22.40/22.31 [7233]P147(x72331,x72332,x72333)+~P1(f319(x72331,x72333))+P1(f319(f319(f226(a1),x72332),f2(a1)))+P1(f319(f319(f226(a1),f855(x72333,x72332,x72331)),x72332))
% 22.40/22.31 [7239]~P3(x72391)+~P99(x72391)+E(f319(f319(f180(x72391),f319(f96(x72391),x72392)),f319(f96(x72391),x72393)),f319(f96(x72391),x72393))+~P1(f319(f319(f225(x72391),f319(f96(x72391),x72392)),f319(f96(x72391),x72393)))
% 22.40/22.31 [7240]~P3(x72401)+~P99(x72401)+E(f319(f319(f230(x72401),f319(f96(x72401),x72402)),f319(f96(x72401),x72403)),f319(f96(x72401),x72402))+~P1(f319(f319(f225(x72401),f319(f96(x72401),x72402)),f319(f96(x72401),x72403)))
% 22.40/22.31 [7254]P148(x72541,x72542,x72543)+~P1(f319(x72541,f2(a1)))+P1(f319(f319(f226(a1),x72542),f2(a1)))+P1(f319(f319(f226(a1),f851(x72543,x72542,x72541)),x72542))
% 22.40/22.31 [7262]P147(x72621,x72622,x72623)+~P1(f319(x72621,x72623))+P1(f319(f319(f225(a1),f854(x72623,x72622,x72621)),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x72622))
% 22.40/22.31 [7286]P148(x72861,x72862,x72863)+~P1(f319(x72861,f2(a1)))+P1(f319(f319(f225(a1),f850(x72863,x72862,x72861)),f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x72862))
% 22.40/22.31 [7313]~P1(f319(x73131,x73132))+P1(f319(x73131,f2(a906)))+~P1(f319(f319(f226(a906),x73132),x73133))+P1(f319(f319(f226(a906),f450(x73132,x73131,x73133)),x73133))
% 22.40/22.31 [7330]~P4(x73301)+~P13(x73301,x73303)+P13(x73301,f319(f319(f143(x73301),x73302),x73303))+P1(f319(f319(f321(x73301),f701(x73303,x73302,x73301)),f319(f164(x73301),x73303)))
% 22.40/22.31 [7331]~P4(x73311)+~P13(x73311,x73313)+P13(x73311,f319(f319(f143(x73311),x73312),x73313))+P1(f319(f319(f321(x73311),f703(x73313,x73312,x73311)),f319(f164(x73311),x73313)))
% 22.40/22.31 [7332]~P4(x73321)+~P13(x73321,x73323)+P13(x73321,f319(f319(f143(x73321),x73322),x73323))+P1(f319(f319(f321(x73321),f742(x73322,x73323,x73321)),f319(f164(x73321),x73323)))
% 22.40/22.31 [7444]~P4(x74441)+~P5(x74441)+~P1(f319(f319(f226(x74441),x74443),f31(x74441,x74442)))+P1(f319(f319(f321(x74441),f387(x74442,x74443,x74441)),x74442))
% 22.40/22.31 [7593]~P4(x75931)+~P5(x75931)+~P1(f319(f319(f226(x75931),f32(x75931,x75933)),x75932))+P1(f319(f319(f321(x75931),f394(x75932,x75933,x75931)),x75933))
% 22.40/22.31 [7594]~P4(x75941)+~P5(x75941)+~P1(f319(f319(f226(x75941),f32(x75941,x75943)),x75942))+P1(f319(f319(f226(x75941),f394(x75942,x75943,x75941)),x75942))
% 22.40/22.31 [7605]P148(x76052,x76051,x76053)+E(x76051,f2(a1))+P1(f319(f319(f226(a1),x76051),f850(x76053,x76051,x76052)))+P1(f319(f319(f226(a1),f851(x76053,x76051,x76052)),x76051))
% 22.40/22.31 [7606]P147(x76062,x76061,x76063)+E(x76061,f2(a1))+P1(f319(f319(f226(a1),x76061),f854(x76063,x76061,x76062)))+P1(f319(f319(f226(a1),f855(x76063,x76061,x76062)),x76061))
% 22.40/22.31 [7693]P148(x76933,x76931,x76932)+E(x76931,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x76931),f853(x76932,x76931,x76933))),f850(x76932,x76931,x76933)),x76932)+P1(f319(f319(f226(a1),f2(a1)),x76931))
% 22.40/22.31 [7694]P147(x76943,x76941,x76942)+E(x76941,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x76941),f857(x76942,x76941,x76943))),f854(x76942,x76941,x76943)),x76942)+P1(f319(f319(f226(a1),f2(a1)),x76941))
% 22.40/22.31 [7696]~P127(x76961)+~P1(f319(f319(f225(x76961),x76963),f2(x76961)))+P1(f319(f319(f225(x76961),f319(f319(f75(x76961),x76962),x76963)),f2(x76961)))+~P1(f319(f319(f225(x76961),f2(x76961)),x76962))
% 22.40/22.31 [7697]~P127(x76971)+~P1(f319(f319(f225(x76971),x76972),f2(x76971)))+P1(f319(f319(f225(x76971),f319(f319(f75(x76971),x76972),x76973)),f2(x76971)))+~P1(f319(f319(f225(x76971),f2(x76971)),x76973))
% 22.40/22.31 [7699]~P135(x76991)+~P1(f319(f319(f225(x76991),x76993),f2(x76991)))+P1(f319(f319(f225(x76991),f319(f319(f75(x76991),x76992),x76993)),f2(x76991)))+~P1(f319(f319(f225(x76991),f2(x76991)),x76992))
% 22.40/22.31 [7701]~P135(x77011)+~P1(f319(f319(f225(x77011),x77012),f2(x77011)))+P1(f319(f319(f225(x77011),f319(f319(f75(x77011),x77012),x77013)),f2(x77011)))+~P1(f319(f319(f225(x77011),f2(x77011)),x77013))
% 22.40/22.31 [7702]~P74(x77021)+~P1(f319(f319(f225(x77021),x77023),f2(x77021)))+P1(f319(f319(f225(x77021),f319(f319(f282(x77021),x77022),x77023)),f2(x77021)))+~P1(f319(f319(f225(x77021),f2(x77021)),x77022))
% 22.40/22.31 [7703]~P74(x77031)+~P1(f319(f319(f225(x77031),x77032),f2(x77031)))+P1(f319(f319(f225(x77031),f319(f319(f282(x77031),x77032),x77033)),f2(x77031)))+~P1(f319(f319(f225(x77031),f2(x77031)),x77033))
% 22.40/22.31 [7704]~P75(x77041)+~P1(f319(f319(f225(x77041),x77042),f2(x77041)))+P1(f319(f319(f225(x77041),f319(f319(f282(x77041),x77042),x77043)),f2(x77041)))+~P1(f319(f319(f226(x77041),f2(x77041)),x77043))
% 22.40/22.31 [7705]~P75(x77051)+~P1(f319(f319(f226(x77051),x77053),f2(x77051)))+P1(f319(f319(f225(x77051),f319(f319(f282(x77051),x77052),x77053)),f2(x77051)))+~P1(f319(f319(f225(x77051),f2(x77051)),x77052))
% 22.40/22.31 [7707]~P131(x77071)+~P1(f319(f319(f226(x77071),x77073),f2(x77071)))+P1(f319(f319(f226(x77071),f319(f319(f75(x77071),x77072),x77073)),f2(x77071)))+~P1(f319(f319(f226(x77071),f2(x77071)),x77072))
% 22.40/22.31 [7708]~P131(x77081)+~P1(f319(f319(f226(x77081),x77082),f2(x77081)))+P1(f319(f319(f226(x77081),f319(f319(f75(x77081),x77082),x77083)),f2(x77081)))+~P1(f319(f319(f226(x77081),f2(x77081)),x77083))
% 22.40/22.31 [7709]~P74(x77091)+~P1(f319(f319(f226(x77091),x77093),f2(x77091)))+P1(f319(f319(f226(x77091),f319(f319(f282(x77091),x77092),x77093)),f2(x77091)))+~P1(f319(f319(f226(x77091),f2(x77091)),x77092))
% 22.40/22.31 [7710]~P74(x77101)+~P1(f319(f319(f226(x77101),x77102),f2(x77101)))+P1(f319(f319(f226(x77101),f319(f319(f282(x77101),x77102),x77103)),f2(x77101)))+~P1(f319(f319(f226(x77101),f2(x77101)),x77103))
% 22.40/22.31 [7711]~P75(x77111)+~P1(f319(f319(f226(x77111),x77113),f2(x77111)))+P1(f319(f319(f226(x77111),f319(f319(f282(x77111),x77112),x77113)),f2(x77111)))+~P1(f319(f319(f226(x77111),f2(x77111)),x77112))
% 22.40/22.31 [7712]~P75(x77121)+~P1(f319(f319(f226(x77121),x77122),f2(x77121)))+P1(f319(f319(f226(x77121),f319(f319(f282(x77121),x77122),x77123)),f2(x77121)))+~P1(f319(f319(f226(x77121),f2(x77121)),x77123))
% 22.40/22.31 [7727]P147(x77271,x77272,x77273)+~P1(f319(x77271,x77273))+P1(f319(f319(f226(a1),x77272),f854(x77273,x77272,x77271)))+P1(f319(f319(f226(a1),f855(x77273,x77272,x77271)),x77272))
% 22.40/22.31 [7740]P148(x77401,x77402,x77403)+P1(f319(f319(f226(a1),x77402),f850(x77403,x77402,x77401)))+~P1(f319(x77401,f2(a1)))+P1(f319(f319(f226(a1),f851(x77403,x77402,x77401)),x77402))
% 22.40/22.31 [7791]P148(x77912,x77911,x77913)+E(x77911,f2(a1))+~P1(f319(x77912,f853(x77913,x77911,x77912)))+P1(f319(f319(f226(a1),f851(x77913,x77911,x77912)),x77911))
% 22.40/22.31 [7792]P147(x77922,x77921,x77923)+E(x77921,f2(a1))+~P1(f319(x77922,f854(x77923,x77921,x77922)))+P1(f319(f319(f226(a1),f855(x77923,x77921,x77922)),x77921))
% 22.40/22.31 [7801]P147(x78013,x78011,x78012)+~P1(f319(x78013,x78012))+E(f319(f319(f74(a1),f319(f319(f75(a1),x78011),f857(x78012,x78011,x78013))),f854(x78012,x78011,x78013)),x78012)+P1(f319(f319(f226(a1),f2(a1)),x78011))
% 22.40/22.31 [7816]P148(x78163,x78161,x78162)+E(f319(f319(f74(a1),f319(f319(f75(a1),x78161),f853(x78162,x78161,x78163))),f850(x78162,x78161,x78163)),x78162)+~P1(f319(x78163,f2(a1)))+P1(f319(f319(f226(a1),f2(a1)),x78161))
% 22.40/22.31 [7844]~P1(f319(x78441,x78443))+~P1(f319(f55(x78442),x78443))+P1(f319(f319(f321(x78442),f863(x78441,x78443,x78442)),f859(x78441,x78443,x78442)))+P1(f319(x78441,f181(f913(x78442,a904))))
% 22.40/22.31 [7855]P147(x78551,x78552,x78553)+~P1(f319(x78551,x78553))+~P1(f319(x78551,f854(x78553,x78552,x78551)))+P1(f319(f319(f226(a1),f855(x78553,x78552,x78551)),x78552))
% 22.40/22.31 [7861]P148(x78611,x78612,x78613)+~P1(f319(x78611,f853(x78613,x78612,x78611)))+~P1(f319(x78611,f2(a1)))+P1(f319(f319(f226(a1),f851(x78613,x78612,x78611)),x78612))
% 22.40/22.31 [7967]~P127(x79671)+~P1(f319(f319(f225(x79671),f319(f319(f75(x79671),x79673),x79672)),f2(x79671)))+P1(f319(f319(f225(x79671),x79672),f2(x79671)))+P1(f319(f319(f225(x79671),f2(x79671)),x79672))
% 22.40/22.31 [7968]~P127(x79681)+~P1(f319(f319(f225(x79681),f319(f319(f75(x79681),x79682),x79683)),f2(x79681)))+P1(f319(f319(f225(x79681),x79682),f2(x79681)))+P1(f319(f319(f225(x79681),f2(x79681)),x79682))
% 22.40/22.31 [7969]~P74(x79691)+~P1(f319(f319(f225(x79691),f319(f319(f282(x79691),x79693),x79692)),f2(x79691)))+P1(f319(f319(f225(x79691),x79692),f2(x79691)))+P1(f319(f319(f225(x79691),f2(x79691)),x79692))
% 22.40/22.31 [7970]~P74(x79701)+~P1(f319(f319(f225(x79701),f319(f319(f282(x79701),x79702),x79703)),f2(x79701)))+P1(f319(f319(f225(x79701),x79702),f2(x79701)))+P1(f319(f319(f225(x79701),f2(x79701)),x79702))
% 22.40/22.31 [7971]~P74(x79711)+~P1(f319(f319(f226(x79711),f319(f319(f282(x79711),x79713),x79712)),f2(x79711)))+P1(f319(f319(f226(x79711),x79712),f2(x79711)))+P1(f319(f319(f226(x79711),f2(x79711)),x79712))
% 22.40/22.31 [7972]~P74(x79721)+~P1(f319(f319(f226(x79721),f319(f319(f282(x79721),x79722),x79723)),f2(x79721)))+P1(f319(f319(f226(x79721),x79722),f2(x79721)))+P1(f319(f319(f226(x79721),f2(x79721)),x79722))
% 22.40/22.31 [7991]~P127(x79911)+~P1(f319(f319(f225(x79911),f319(f319(f75(x79911),x79912),x79913)),f2(x79911)))+P1(f319(f319(f225(x79911),f2(x79911)),x79912))+P1(f319(f319(f225(x79911),f2(x79911)),x79913))
% 22.40/22.31 [7992]~P74(x79921)+~P1(f319(f319(f225(x79921),f319(f319(f282(x79921),x79922),x79923)),f2(x79921)))+P1(f319(f319(f225(x79921),f2(x79921)),x79922))+P1(f319(f319(f225(x79921),f2(x79921)),x79923))
% 22.40/22.31 [7993]~P74(x79931)+~P1(f319(f319(f226(x79931),f319(f319(f282(x79931),x79932),x79933)),f2(x79931)))+P1(f319(f319(f226(x79931),f2(x79931)),x79932))+P1(f319(f319(f226(x79931),f2(x79931)),x79933))
% 22.40/22.31 [8015]P148(x80152,x80151,x80153)+E(x80151,f2(a1))+P1(f319(f319(f225(a1),f850(x80153,x80151,x80152)),f2(a1)))+P1(f319(f319(f226(a1),f851(x80153,x80151,x80152)),x80151))
% 22.40/22.31 [8016]P147(x80162,x80161,x80163)+E(x80161,f2(a1))+P1(f319(f319(f225(a1),f854(x80163,x80161,x80162)),f2(a1)))+P1(f319(f319(f226(a1),f855(x80163,x80161,x80162)),x80161))
% 22.40/22.31 [8023]~P126(x80231)+~P1(f319(f319(f226(x80231),x80232),f72(x80231)))+P1(f319(f319(f226(x80231),f319(f319(f236(x80231),x80232),f319(a104,x80233))),f72(x80231)))+~P1(f319(f319(f226(x80231),f2(x80231)),x80232))
% 22.40/22.31 [8072]~P4(x80721)+~E(x80723,f105(x80721))+~P13(x80721,f319(f160(x80721),x80723))+E(f319(f134(x80721,x80721,f319(f9(x80721,x80721,x80721),f180(x80721)),x80722),f319(f160(x80721),x80723)),x80722)
% 22.40/22.31 [8075]P147(x80751,x80752,x80753)+~P1(f319(x80751,x80753))+P1(f319(f319(f225(a1),f854(x80753,x80752,x80751)),f2(a1)))+P1(f319(f319(f226(a1),f855(x80753,x80752,x80751)),x80752))
% 22.40/22.31 [8081]P148(x80811,x80812,x80813)+~P1(f319(x80811,f2(a1)))+P1(f319(f319(f225(a1),f850(x80813,x80812,x80811)),f2(a1)))+P1(f319(f319(f226(a1),f851(x80813,x80812,x80811)),x80812))
% 22.40/22.31 [8301]P148(x83013,x83011,x83012)+E(x83011,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83011),f853(x83012,x83011,x83013))),f850(x83012,x83011,x83013)),x83012)+P1(f319(f319(f226(a1),f851(x83012,x83011,x83013)),x83011))
% 22.40/22.31 [8302]P147(x83023,x83021,x83022)+E(x83021,f2(a1))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83021),f857(x83022,x83021,x83023))),f854(x83022,x83021,x83023)),x83022)+P1(f319(f319(f226(a1),f855(x83022,x83021,x83023)),x83021))
% 22.40/22.31 [8334]P147(x83343,x83341,x83342)+~P1(f319(x83343,x83342))+E(f319(f319(f74(a1),f319(f319(f75(a1),x83341),f857(x83342,x83341,x83343))),f854(x83342,x83341,x83343)),x83342)+P1(f319(f319(f226(a1),f855(x83342,x83341,x83343)),x83341))
% 22.40/22.31 [8335]~P76(x83351)+~P82(x83351)+~P41(x83353)+E(f319(f319(f8(a906,x83351),f319(f319(f10(a1,x83351,a906),x83352),f92(a1))),f319(f302(a1,a906,a97),x83353)),f319(f319(f8(a1,x83351),x83352),x83353))
% 22.40/22.31 [8336]~P76(x83361)+~P82(x83361)+~P41(x83363)+E(f319(f319(f11(a906,x83361),f319(f319(f10(a1,x83361,a906),x83362),f92(a1))),f319(f302(a1,a906,a97),x83363)),f319(f319(f11(a1,x83361),x83362),x83363))
% 22.40/22.31 [8345]P148(x83453,x83451,x83452)+E(f319(f319(f74(a1),f319(f319(f75(a1),x83451),f853(x83452,x83451,x83453))),f850(x83452,x83451,x83453)),x83452)+~P1(f319(x83453,f2(a1)))+P1(f319(f319(f226(a1),f851(x83452,x83451,x83453)),x83451))
% 22.40/22.31 [8367]~E(x83672,f2(a906))+~E(f319(f243(a906,a906),x83673),f2(a906))+~E(x83671,f319(f319(f74(a906),f319(f319(f75(a906),f319(f243(a906,a906),x83673)),x83672)),f319(f248(a906,a906),x83673)))+P1(f319(f42(x83671,x83672),x83673))
% 22.40/22.31 [8425]P1(f319(x84251,x84252))+~P1(f319(f319(f321(x84253),f384(x84251,x84252,x84253)),f376(x84251,x84252,x84253)))+~P1(f319(f55(x84253),x84252))+~P1(f319(x84251,f181(f913(x84253,a904))))
% 22.40/22.31 [8970]~P111(x89701)+~P111(x89702)+P50(x89701,x89702,x89703)+~P1(f319(f319(f226(x89702),f319(x89703,f428(x89703,x89701,x89702))),f319(x89703,f436(x89703,x89701,x89702))))
% 22.40/22.31 [9051]P1(f319(x90511,x90512))+~P1(f319(f55(x90513),x90512))+~P1(f319(x90511,f319(f319(f301(x90513),f384(x90511,x90512,x90513)),f376(x90511,x90512,x90513))))+~P1(f319(x90511,f181(f913(x90513,a904))))
% 22.40/22.31 [9283]P1(f319(f319(f225(a1),x92831),f2(a1)))+~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f75(a1),x92833),x92831)),x92832)),f2(a1)))+~P1(f319(f319(f225(a1),f2(a1)),x92832))+~P1(f319(f319(f226(a1),f2(a1)),x92833))
% 22.40/22.31 [5910]~P101(x59102)+E(x59101,f181(f913(x59102,a904)))+~P1(f319(f55(x59102),x59101))+E(f12(x59102,f319(f319(f301(x59102),x59103),x59101)),f319(f319(f94(x59102),x59103),f12(x59102,x59101)))
% 22.40/22.31 [5911]~P101(x59112)+E(x59111,f181(f913(x59112,a904)))+~P1(f319(f55(x59112),x59111))+E(f15(x59112,f319(f319(f301(x59112),x59113),x59111)),f319(f319(f93(x59112),x59113),f15(x59112,x59111)))
% 22.40/22.31 [5912]~P4(x59122)+E(x59121,f181(f913(x59122,a904)))+~P1(f319(f55(x59122),x59121))+E(f16(x59122,f319(f319(f301(x59122),x59123),x59121)),f319(f319(f180(x59122),x59123),f16(x59122,x59121)))
% 22.40/22.31 [5913]~P4(x59132)+E(x59131,f181(f913(x59132,a904)))+~P1(f319(f55(x59132),x59131))+E(f17(x59132,f319(f319(f301(x59132),x59133),x59131)),f319(f319(f230(x59132),x59133),f17(x59132,x59131)))
% 22.40/22.31 [6229]~P127(x62291)+~E(x62293,f2(x62291))+~E(x62292,f2(x62291))+E(f319(f319(f74(x62291),f319(f319(f75(x62291),x62292),x62292)),f319(f319(f75(x62291),x62293),x62293)),f2(x62291))
% 22.40/22.31 [6299]~P100(x62992)+E(x62991,f181(f913(x62992,a904)))+~P1(f319(f55(x62992),x62991))+E(f319(f57(x62992,f75(x62992)),f319(f319(f301(x62992),x62993),x62991)),f319(f319(f75(x62992),x62993),f319(f57(x62992,f75(x62992)),x62991)))
% 22.40/22.31 [6425]~P4(x64252)+E(x64251,f181(f913(x64252,a904)))+~P1(f319(f55(x64252),x64251))+E(f13(x64252,f180(x64252),f319(f319(f301(x64252),x64253),x64251)),f319(f319(f180(x64252),x64253),f13(x64252,f180(x64252),x64251)))
% 22.40/22.31 [6426]~P4(x64262)+E(x64261,f181(f913(x64262,a904)))+~P1(f319(f55(x64262),x64261))+E(f14(x64262,f230(x64262),f319(f319(f301(x64262),x64263),x64261)),f319(f319(f230(x64262),x64263),f14(x64262,f230(x64262),x64261)))
% 22.40/22.31 [6935]~P77(x69351)+~P1(f319(f55(x69351),x69353))+E(f319(f57(x69351,f75(x69351)),f319(f319(f301(x69351),x69352),x69353)),f319(f319(f58(x69351,x69351,f75(x69351)),x69352),x69353))+P1(f319(f319(f321(x69351),x69352),x69353))
% 22.40/22.31 [7014]~E(f319(f319(f74(a1),x70142),f319(f319(f75(a1),x70143),x70141)),x70143)+~P1(f319(f319(f226(a1),f2(a1)),x70143))+P1(f319(f319(f225(a1),f72(a1)),x70141))+~P1(f319(f319(f226(a1),x70142),x70143))
% 22.40/22.31 [7042]~E(f319(f319(f74(a1),x70422),f319(f319(f75(a1),x70423),x70421)),x70423)+P1(f319(f319(f225(a1),x70421),f72(a1)))+~P1(f319(f319(f225(a1),f2(a1)),x70422))+~P1(f319(f319(f226(a1),f2(a1)),x70423))
% 22.40/22.31 [7059]E(x70591,f2(a906))+~P1(f319(f42(x70593,x70591),x70592))+~P1(f319(f319(f226(a906),f2(a906)),x70591))+P1(f319(f319(f226(a906),f319(f248(a906,a906),x70592)),x70591))
% 22.40/22.31 [7092]~P138(x70921)+~P1(f319(f319(f225(x70921),x70922),f2(x70921)))+~P1(f319(f319(f225(x70921),x70923),f2(x70921)))+E(f319(f319(f75(x70921),f319(f69(x70921),x70922)),f319(f69(x70921),x70923)),f319(f69(x70921),f319(f319(f75(x70921),x70922),x70923)))
% 22.40/22.31 [7138]~P138(x71381)+~P1(f319(f319(f225(x71381),x71382),f2(x71381)))+E(f319(f319(f75(x71381),f319(f69(x71381),x71382)),f319(f69(x71381),x71383)),f319(f69(x71381),f319(f319(f75(x71381),x71382),x71383)))+~P1(f319(f319(f225(x71381),f2(x71381)),x71383))
% 22.40/22.31 [7139]~P138(x71391)+~P1(f319(f319(f225(x71391),x71393),f2(x71391)))+E(f319(f319(f75(x71391),f319(f69(x71391),x71392)),f319(f69(x71391),x71393)),f319(f69(x71391),f319(f319(f75(x71391),x71392),x71393)))+~P1(f319(f319(f225(x71391),f2(x71391)),x71392))
% 22.40/22.31 [7194]~P138(x71941)+E(f319(f319(f75(x71941),f319(f69(x71941),x71942)),f319(f69(x71941),x71943)),f319(f69(x71941),f319(f319(f75(x71941),x71942),x71943)))+~P1(f319(f319(f225(x71941),f2(x71941)),x71942))+~P1(f319(f319(f225(x71941),f2(x71941)),x71943))
% 22.40/22.31 [7211]~P125(x72111)+~P1(f319(f319(f225(x72111),x72113),f2(x72111)))+~P1(f319(f319(f225(x72111),x72112),f2(x72111)))+P1(f319(f319(f225(x72111),f2(x72111)),f319(f319(f75(x72111),x72112),x72113)))
% 22.40/22.31 [7212]~P127(x72121)+~P1(f319(f319(f225(x72121),x72123),f2(x72121)))+~P1(f319(f319(f225(x72121),x72122),f2(x72121)))+P1(f319(f319(f225(x72121),f2(x72121)),f319(f319(f75(x72121),x72122),x72123)))
% 22.40/22.31 [7213]~P74(x72131)+~P1(f319(f319(f225(x72131),x72133),f2(x72131)))+~P1(f319(f319(f225(x72131),x72132),f2(x72131)))+P1(f319(f319(f225(x72131),f2(x72131)),f319(f319(f282(x72131),x72132),x72133)))
% 22.40/22.31 [7214]~P75(x72141)+~P1(f319(f319(f226(x72141),x72143),f2(x72141)))+~P1(f319(f319(f225(x72141),x72142),f2(x72141)))+P1(f319(f319(f225(x72141),f2(x72141)),f319(f319(f282(x72141),x72142),x72143)))
% 22.40/22.31 [7215]~P127(x72151)+~P1(f319(f319(f226(x72151),x72153),f2(x72151)))+~P1(f319(f319(f226(x72151),x72152),f2(x72151)))+P1(f319(f319(f226(x72151),f2(x72151)),f319(f319(f75(x72151),x72152),x72153)))
% 22.40/22.31 [7216]~P74(x72161)+~P1(f319(f319(f226(x72161),x72163),f2(x72161)))+~P1(f319(f319(f226(x72161),x72162),f2(x72161)))+P1(f319(f319(f226(x72161),f2(x72161)),f319(f319(f282(x72161),x72162),x72163)))
% 22.40/22.31 [7217]~P75(x72171)+~P1(f319(f319(f226(x72171),x72173),f2(x72171)))+~P1(f319(f319(f226(x72171),x72172),f2(x72171)))+P1(f319(f319(f226(x72171),f2(x72171)),f319(f319(f282(x72171),x72172),x72173)))
% 22.40/22.31 [7218]~P126(x72181)+~P1(f319(f319(f226(a906),f2(a906)),x72183))+~P1(f319(f319(f226(x72181),f72(x72181)),x72182))+P1(f319(f319(f226(x72181),f72(x72181)),f319(f319(f236(x72181),x72182),x72183)))
% 22.40/22.31 [7315]~P125(x73151)+~P1(f319(f319(f225(x73151),f2(x73151)),x73153))+~P1(f319(f319(f225(x73151),f2(x73151)),x73152))+P1(f319(f319(f225(x73151),f2(x73151)),f319(f319(f75(x73151),x73152),x73153)))
% 22.40/22.31 [7316]~P127(x73161)+~P1(f319(f319(f225(x73161),f2(x73161)),x73163))+~P1(f319(f319(f225(x73161),f2(x73161)),x73162))+P1(f319(f319(f225(x73161),f2(x73161)),f319(f319(f75(x73161),x73162),x73163)))
% 22.40/22.31 [7317]~P135(x73171)+~P1(f319(f319(f225(x73171),f2(x73171)),x73173))+~P1(f319(f319(f225(x73171),f2(x73171)),x73172))+P1(f319(f319(f225(x73171),f2(x73171)),f319(f319(f75(x73171),x73172),x73173)))
% 22.40/22.31 [7318]~P74(x73181)+~P1(f319(f319(f225(x73181),f2(x73181)),x73183))+~P1(f319(f319(f225(x73181),f2(x73181)),x73182))+P1(f319(f319(f225(x73181),f2(x73181)),f319(f319(f282(x73181),x73182),x73183)))
% 22.40/22.31 [7319]~P75(x73191)+~P1(f319(f319(f226(x73191),f2(x73191)),x73193))+~P1(f319(f319(f225(x73191),f2(x73191)),x73192))+P1(f319(f319(f225(x73191),f2(x73191)),f319(f319(f282(x73191),x73192),x73193)))
% 22.40/22.31 [7320]~P126(x73201)+~P1(f319(f319(f226(x73201),f72(x73201)),x73203))+~P1(f319(f319(f226(x73201),f72(x73201)),x73202))+P1(f319(f319(f226(x73201),f72(x73201)),f319(f319(f75(x73201),x73202),x73203)))
% 22.40/22.31 [7323]~P93(x73231)+~P1(f319(f319(f226(x73231),f2(x73231)),x73233))+~P1(f319(f319(f226(x73231),f2(x73231)),x73232))+P1(f319(f319(f226(x73231),f2(x73231)),f319(f319(f74(x73231),x73232),x73233)))
% 22.40/22.31 [7324]~P131(x73241)+~P1(f319(f319(f226(x73241),f2(x73241)),x73243))+~P1(f319(f319(f226(x73241),f2(x73241)),x73242))+P1(f319(f319(f226(x73241),f2(x73241)),f319(f319(f75(x73241),x73242),x73243)))
% 22.40/22.31 [7325]~P74(x73251)+~P1(f319(f319(f226(x73251),f2(x73251)),x73253))+~P1(f319(f319(f226(x73251),f2(x73251)),x73252))+P1(f319(f319(f226(x73251),f2(x73251)),f319(f319(f282(x73251),x73252),x73253)))
% 22.40/22.31 [7326]~P75(x73261)+~P1(f319(f319(f226(x73261),f2(x73261)),x73263))+~P1(f319(f319(f226(x73261),f2(x73261)),x73262))+P1(f319(f319(f226(x73261),f2(x73261)),f319(f319(f282(x73261),x73262),x73263)))
% 22.40/22.31 [7400]~P101(x74001)+~P1(f319(f55(x74001),x74003))+E(f12(x74001,f319(f319(f301(x74001),x74002),x74003)),x74002)+~E(f319(f319(f3(f913(x74001,a904)),x74003),f319(f319(f301(x74001),x74002),f181(f913(x74001,a904)))),f181(f913(x74001,a904)))
% 22.40/22.31 [7401]~P101(x74011)+~P1(f319(f55(x74011),x74013))+E(f15(x74011,f319(f319(f301(x74011),x74012),x74013)),x74012)+~E(f319(f319(f3(f913(x74011,a904)),x74013),f319(f319(f301(x74011),x74012),f181(f913(x74011,a904)))),f181(f913(x74011,a904)))
% 22.40/22.31 [7402]~P4(x74021)+~P1(f319(f55(x74021),x74023))+E(f16(x74021,f319(f319(f301(x74021),x74022),x74023)),x74022)+~E(f319(f319(f3(f913(x74021,a904)),x74023),f319(f319(f301(x74021),x74022),f181(f913(x74021,a904)))),f181(f913(x74021,a904)))
% 22.40/22.31 [7403]~P4(x74031)+~P1(f319(f55(x74031),x74033))+E(f17(x74031,f319(f319(f301(x74031),x74032),x74033)),x74032)+~E(f319(f319(f3(f913(x74031,a904)),x74033),f319(f319(f301(x74031),x74032),f181(f913(x74031,a904)))),f181(f913(x74031,a904)))
% 22.40/22.31 [7405]~P127(x74051)+P1(f319(f319(f225(x74051),x74052),f2(x74051)))+P1(f319(f319(f225(x74051),f2(x74051)),x74053))+~P1(f319(f319(f225(x74051),f2(x74051)),f319(f319(f75(x74051),x74053),x74052)))
% 22.40/22.31 [7406]~P127(x74061)+P1(f319(f319(f225(x74061),x74062),f2(x74061)))+P1(f319(f319(f225(x74061),f2(x74061)),x74063))+~P1(f319(f319(f225(x74061),f2(x74061)),f319(f319(f75(x74061),x74062),x74063)))
% 22.40/22.31 [7407]~P74(x74071)+P1(f319(f319(f225(x74071),x74072),f2(x74071)))+P1(f319(f319(f225(x74071),f2(x74071)),x74073))+~P1(f319(f319(f225(x74071),f2(x74071)),f319(f319(f282(x74071),x74073),x74072)))
% 22.40/22.31 [7408]~P74(x74081)+P1(f319(f319(f225(x74081),x74082),f2(x74081)))+P1(f319(f319(f225(x74081),f2(x74081)),x74083))+~P1(f319(f319(f225(x74081),f2(x74081)),f319(f319(f282(x74081),x74082),x74083)))
% 22.40/22.31 [7409]~P127(x74091)+P1(f319(f319(f225(x74091),x74092),f2(x74091)))+P1(f319(f319(f225(x74091),f2(x74091)),x74092))+~P1(f319(f319(f225(x74091),f2(x74091)),f319(f319(f75(x74091),x74093),x74092)))
% 22.40/22.31 [7410]~P127(x74101)+P1(f319(f319(f225(x74101),x74102),f2(x74101)))+P1(f319(f319(f225(x74101),f2(x74101)),x74102))+~P1(f319(f319(f225(x74101),f2(x74101)),f319(f319(f75(x74101),x74102),x74103)))
% 22.40/22.31 [7411]~P74(x74111)+P1(f319(f319(f225(x74111),x74112),f2(x74111)))+P1(f319(f319(f225(x74111),f2(x74111)),x74112))+~P1(f319(f319(f225(x74111),f2(x74111)),f319(f319(f282(x74111),x74113),x74112)))
% 22.40/22.31 [7412]~P74(x74121)+P1(f319(f319(f225(x74121),x74122),f2(x74121)))+P1(f319(f319(f225(x74121),f2(x74121)),x74122))+~P1(f319(f319(f225(x74121),f2(x74121)),f319(f319(f282(x74121),x74122),x74123)))
% 22.40/22.31 [7413]~P74(x74131)+P1(f319(f319(f226(x74131),x74132),f2(x74131)))+P1(f319(f319(f226(x74131),f2(x74131)),x74133))+~P1(f319(f319(f226(x74131),f2(x74131)),f319(f319(f282(x74131),x74133),x74132)))
% 22.40/22.31 [7414]~P74(x74141)+P1(f319(f319(f226(x74141),x74142),f2(x74141)))+P1(f319(f319(f226(x74141),f2(x74141)),x74143))+~P1(f319(f319(f226(x74141),f2(x74141)),f319(f319(f282(x74141),x74142),x74143)))
% 22.40/22.31 [7415]~P74(x74151)+P1(f319(f319(f226(x74151),x74152),f2(x74151)))+P1(f319(f319(f226(x74151),f2(x74151)),x74152))+~P1(f319(f319(f226(x74151),f2(x74151)),f319(f319(f282(x74151),x74153),x74152)))
% 22.40/22.31 [7416]~P74(x74161)+P1(f319(f319(f226(x74161),x74162),f2(x74161)))+P1(f319(f319(f226(x74161),f2(x74161)),x74162))+~P1(f319(f319(f226(x74161),f2(x74161)),f319(f319(f282(x74161),x74162),x74163)))
% 22.40/22.31 [7484]~P1(f319(f319(f279(a906),x74841),x74843))+P1(f319(f319(f279(a906),x74841),x74842))+~P1(f319(f319(f225(a906),x74842),x74843))+~P1(f319(f319(f279(a906),x74841),f319(f319(f3(a906),x74843),x74842)))
% 22.40/22.31 [7485]~P1(f319(f319(f279(a906),x74851),x74853))+P1(f319(f319(f279(a906),x74851),x74852))+~P1(f319(f319(f225(a906),x74853),x74852))+~P1(f319(f319(f279(a906),x74851),f319(f319(f3(a906),x74852),x74853)))
% 22.40/22.31 [7499]~E(f319(f319(f94(f913(x74991,a904)),f319(f164(x74991),x74992)),f319(f164(x74991),x74993)),f181(f913(x74991,a904)))+~P1(f319(f129(x74991),x74993))+~P1(f319(f129(x74991),x74992))+P1(f319(f129(x74991),f319(f319(f126(x74991),x74992),x74993)))
% 22.40/22.31 [7500]~P4(x75001)+~P1(f319(f55(x75001),x75003))+E(f13(x75001,f180(x75001),f319(f319(f301(x75001),x75002),x75003)),x75002)+~E(f319(f319(f3(f913(x75001,a904)),x75003),f319(f319(f301(x75001),x75002),f181(f913(x75001,a904)))),f181(f913(x75001,a904)))
% 22.40/22.31 [7501]~P4(x75011)+~P1(f319(f55(x75011),x75013))+E(f14(x75011,f230(x75011),f319(f319(f301(x75011),x75012),x75013)),x75012)+~E(f319(f319(f3(f913(x75011,a904)),x75013),f319(f319(f301(x75011),x75012),f181(f913(x75011,a904)))),f181(f913(x75011,a904)))
% 22.40/22.31 [7514]~P92(x75141)+~P1(f319(f319(f225(x75141),x75142),x75143))+~P1(f319(f319(f225(x75141),f319(f73(x75141),x75142)),x75143))+P1(f319(f319(f225(x75141),f319(f69(x75141),x75142)),x75143))
% 22.40/22.31 [7515]~P113(x75151)+~P1(f319(f319(f226(x75151),x75152),x75153))+~P1(f319(f319(f226(x75151),f319(f73(x75151),x75152)),x75153))+P1(f319(f319(f226(x75151),f319(f69(x75151),x75152)),x75153))
% 22.40/22.31 [7582]~P131(x75821)+P1(f319(f319(f226(x75821),f2(x75821)),x75822))+~P1(f319(f319(f226(x75821),f2(x75821)),x75823))+~P1(f319(f319(f226(x75821),f2(x75821)),f319(f319(f75(x75821),x75823),x75822)))
% 22.40/22.31 [7583]~P131(x75831)+P1(f319(f319(f226(x75831),f2(x75831)),x75832))+~P1(f319(f319(f226(x75831),f2(x75831)),x75833))+~P1(f319(f319(f226(x75831),f2(x75831)),f319(f319(f75(x75831),x75832),x75833)))
% 22.40/22.31 [7876]E(x78761,x78762)+~P1(f319(f55(x78763),x78761))+~P1(f319(f319(f225(a906),f319(f29(x78763),x78761)),f319(f29(x78763),x78762)))+~P1(f319(f319(f225(f913(x78763,a904)),x78762),x78761))
% 22.40/22.31 [8020]~P1(f319(f319(f226(a1),x80201),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x80202))+~P1(f319(f319(f225(a1),x80202),x80203))+P1(f319(f319(f225(a1),f319(f319(f30(a1),x80201),x80202)),f319(f319(f30(a1),x80201),x80203)))
% 22.40/22.31 [8031]~P1(f319(f319(f225(a1),f2(a1)),x80311))+~P1(f319(f319(f226(a1),f2(a1)),x80313))+~P1(f319(f319(f225(a1),x80313),x80312))+P1(f319(f319(f225(a1),f319(f319(f30(a1),x80311),x80312)),f319(f319(f30(a1),x80311),x80313)))
% 22.40/22.31 [8160]E(f319(x81601,f452(x81602,x81601,x81603)),x81602)+~P1(f319(f319(f225(a1),x81602),f319(x81601,x81603)))+P1(f319(f319(f226(a906),f453(x81602,x81601,x81603)),x81603))+~P1(f319(f319(f225(a1),f319(x81601,f2(a906))),x81602))
% 22.40/22.31 [8161]E(f319(x81611,f454(x81612,x81611,x81613)),x81612)+~P1(f319(f319(f225(a1),x81612),f319(x81611,x81613)))+P1(f319(f319(f226(a906),f455(x81612,x81611,x81613)),x81613))+~P1(f319(f319(f225(a1),f319(x81611,f2(a906))),x81612))
% 22.40/22.31 [8263]~P1(f319(f55(x82631),x82633))+~P1(f319(f319(f226(a906),f319(f29(x82631),x82632)),f319(f29(x82631),x82633)))+~P1(f319(f319(f225(f913(x82631,a904)),x82632),x82633))+P1(f319(f319(f226(f913(x82631,a904)),x82632),x82633))
% 22.40/22.31 [8290]E(f319(f319(f74(a1),f395(x82903,x82901,x82902)),f396(x82903,x82901,x82902)),x82901)+E(f319(f319(f3(a1),x82901),x82902),x82901)+~P1(f319(f319(f226(a1),f2(a1)),x82902))+~P1(f319(f319(f321(a1),f319(f319(f3(a1),x82901),f72(a1))),x82903))
% 22.40/22.31 [8291]E(f319(f319(f3(a1),f403(x82913,x82911,x82912)),f404(x82913,x82911,x82912)),x82911)+E(f319(f319(f74(a1),x82911),x82912),x82911)+~P1(f319(f319(f226(a1),f2(a1)),x82912))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x82911),f72(a1))),x82913))
% 22.40/22.31 [8340]~P1(f319(f319(f225(a906),x83403),x83401))+P1(f319(f319(f225(a906),x83401),x83402))+~P1(f319(f319(f225(a906),x83403),x83402))+~P1(f319(f319(f225(a906),f319(f319(f3(a906),x83401),x83403)),f319(f319(f3(a906),x83402),x83403)))
% 22.40/22.31 [8341]~P1(f319(f319(f225(a906),x83413),x83411))+P1(f319(f319(f226(a906),x83411),x83412))+~P1(f319(f319(f225(a906),x83413),x83412))+~P1(f319(f319(f226(a906),f319(f319(f3(a906),x83411),x83413)),f319(f319(f3(a906),x83412),x83413)))
% 22.40/22.31 [8360]~P4(x83602)+E(x83601,f105(x83602))+~P13(x83602,f319(f160(x83602),x83601))+E(f319(f134(x83602,x83602,f319(f9(x83602,x83602,x83602),f180(x83602)),x83603),f319(f160(x83602),x83601)),f319(f319(f180(x83602),f319(f319(f156(x83602),x83601),f2(a906))),x83603))
% 22.40/22.31 [8407]~P5(x84071)+~P40(x84071,x84071,x84073)+P1(f319(f319(f225(x84071),x84072),f88(x84071,x84073)))+~P1(f319(f319(f225(x84071),x84072),f319(x84073,f319(f319(f93(x84071),x84072),f88(x84071,x84073)))))
% 22.40/22.31 [8430]E(f319(f319(f3(a1),x84301),x84302),x84301)+~P1(f319(f319(f226(a1),f2(a1)),x84302))+P1(f319(f319(f321(a1),f395(x84303,x84301,x84302)),x84303))+~P1(f319(f319(f321(a1),f319(f319(f3(a1),x84301),f72(a1))),x84303))
% 22.40/22.31 [8431]E(f319(f319(f74(a1),x84311),x84312),x84311)+~P1(f319(f319(f226(a1),f2(a1)),x84312))+P1(f319(f319(f321(a1),f403(x84313,x84311,x84312)),x84313))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x84311),f72(a1))),x84313))
% 22.40/22.31 [8499]~P1(f319(f319(f225(a1),x84991),f319(x84992,x84993)))+P1(f319(f319(f226(a906),f453(x84991,x84992,x84993)),x84993))+P1(f319(f319(f225(a906),f452(x84991,x84992,x84993)),x84993))+~P1(f319(f319(f225(a1),f319(x84992,f2(a906))),x84991))
% 22.40/22.31 [8500]~P1(f319(f319(f225(a1),x85001),f319(x85002,x85003)))+P1(f319(f319(f226(a906),f455(x85001,x85002,x85003)),x85003))+P1(f319(f319(f225(a906),f454(x85001,x85002,x85003)),x85003))+~P1(f319(f319(f225(a1),f319(x85002,f2(a906))),x85001))
% 22.40/22.31 [8575]E(f319(f319(f3(a1),x85751),x85752),x85751)+~P1(f319(f319(f226(a1),f2(a1)),x85752))+P1(f319(f319(f321(a1),f396(x85753,x85751,x85752)),f295(a1,f72(a1),x85752)))+~P1(f319(f319(f321(a1),f319(f319(f3(a1),x85751),f72(a1))),x85753))
% 22.40/22.31 [8576]E(f319(f319(f74(a1),x85761),x85762),x85761)+~P1(f319(f319(f226(a1),f2(a1)),x85762))+P1(f319(f319(f321(a1),f404(x85763,x85761,x85762)),f295(a1,f72(a1),x85762)))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x85761),f72(a1))),x85763))
% 22.40/22.31 [8708]~P126(x87081)+~P1(f319(f319(f226(x87081),x87082),f72(x87081)))+~P1(f319(f319(f226(x87081),f2(x87081)),x87082))+P1(f319(f319(f226(x87081),f319(f319(f75(x87081),x87082),f319(f319(f236(x87081),x87082),x87083))),f319(f319(f236(x87081),x87082),x87083)))
% 22.40/22.31 [8795]~P1(f319(x87951,x87952))+P1(f319(x87951,f2(a906)))+~P1(f319(f319(f226(a906),x87952),x87953))+~P1(f319(x87951,f39(a906,f319(a104,f450(x87952,x87951,x87953)),x87953)))
% 22.40/22.31 [8951]E(f495(x89511,x89512,x89513),f2(a906))+P1(f319(f319(x89511,x89513),x89512))+P1(f319(f319(x89511,f495(x89511,x89512,x89513)),f39(a906,f493(x89511,x89512,x89513),f495(x89511,x89512,x89513))))+~P1(f319(f307(f912(a906,a906),a212),f319(f319(f244(a906,a906),x89513),x89512)))
% 22.40/22.31 [8990]~P25(x89901,x89901,x89902,x89903)+E(f319(f302(x89901,x89901,x89902),x89903),x89903)+~P1(f319(f55(x89901),x89903))+~P1(f319(f319(f225(f913(x89901,a904)),f319(f302(x89901,x89901,x89902),x89903)),x89903))
% 22.40/22.31 [9064]~P5(x90641)+~P40(x90641,x90641,x90643)+P1(f319(f319(f225(x90641),f319(f319(f93(x90641),x90642),f88(x90641,x90643))),f319(x90643,f319(f319(f93(x90641),x90642),f88(x90641,x90643)))))+~P1(f319(f319(f225(x90641),x90642),f319(x90643,f319(f319(f93(x90641),x90642),f88(x90641,x90643)))))
% 22.40/22.31 [9197]P1(f319(f319(x91971,x91972),x91973))+P1(f319(f319(f226(a1),f762(x91971,x91973,x91972)),f763(x91971,x91973,x91972)))+P1(f319(f319(x91971,f762(x91971,x91973,x91972)),f319(f319(f74(a1),f763(x91971,x91973,x91972)),f72(a1))))+~P1(f319(f307(f912(a1,a1),a125),f319(f319(f244(a1,a1),x91972),x91973)))
% 22.40/22.31 [9214]P1(f319(f319(x92141,x92142),x92143))+~P1(f319(f319(f226(a1),f492(x92141,x92143,x92142)),f2(a1)))+P1(f319(f319(x92141,f319(f73(a1),f488(x92141,x92143,x92142))),f319(f73(a1),f492(x92141,x92143,x92142))))+~P1(f319(f307(f912(a1,a1),a214),f319(f319(f244(a1,a1),x92142),x92143)))
% 22.40/22.31 [9416]P1(f319(f319(x94161,x94162),x94163))+P1(f319(f319(x94161,f319(f319(f74(a1),f667(x94161,x94163,x94162)),f72(a1))),f669(x94161,x94163,x94162)))+~P1(f319(f319(f225(a1),f667(x94161,x94163,x94162)),f669(x94161,x94163,x94162)))+~P1(f319(f307(f912(a1,a1),a174),f319(f319(f244(a1,a1),x94162),x94163)))
% 22.40/22.31 [9874]~P71(x98742)+~P71(x98741)+~P1(f319(f50(f912(x98741,x98742)),x98743))+P1(f319(f50(x98741),f319(f319(f10(f913(x98742,a904),a904,x98741),f50(x98742)),f319(f319(f10(f913(x98742,f912(x98741,x98742)),f913(x98742,a904),x98741),f319(f10(f912(x98741,x98742),a904,x98742),x98743)),f244(x98741,x98742)))))
% 22.40/22.31 [9875]~P71(x98752)+~P71(x98751)+~P1(f319(f51(f912(x98751,x98752)),x98753))+P1(f319(f51(x98751),f319(f319(f10(f913(x98752,a904),a904,x98751),f51(x98752)),f319(f319(f10(f913(x98752,f912(x98751,x98752)),f913(x98752,a904),x98751),f319(f10(f912(x98751,x98752),a904,x98752),x98753)),f244(x98751,x98752)))))
% 22.40/22.31 [9983]~P71(x99832)+~P71(x99831)+P1(f319(f50(f912(x99831,x99832)),x99833))+~P1(f319(f50(x99831),f319(f319(f10(f913(x99832,a904),a904,x99831),f50(x99832)),f319(f319(f10(f913(x99832,f912(x99831,x99832)),f913(x99832,a904),x99831),f319(f10(f912(x99831,x99832),a904,x99832),x99833)),f244(x99831,x99832)))))
% 22.40/22.31 [9984]~P71(x99842)+~P71(x99841)+P1(f319(f51(f912(x99841,x99842)),x99843))+~P1(f319(f51(x99841),f319(f319(f10(f913(x99842,a904),a904,x99841),f51(x99842)),f319(f319(f10(f913(x99842,f912(x99841,x99842)),f913(x99842,a904),x99841),f319(f10(f912(x99841,x99842),a904,x99842),x99843)),f244(x99841,x99842)))))
% 22.40/22.31 [10116]E(f319(x101161,f452(x101162,x101161,x101163)),x101162)+~P1(f319(f319(f225(a1),x101162),f319(x101161,x101163)))+~P1(f319(f319(f225(a1),f319(f69(a1),f319(f319(f3(a1),f319(x101161,f319(f319(f74(a906),f453(x101162,x101161,x101163)),f72(a906)))),f319(x101161,f453(x101162,x101161,x101163))))),f72(a1)))+~P1(f319(f319(f225(a1),f319(x101161,f2(a906))),x101162))
% 22.40/22.31 [10117]E(f319(x101171,f454(x101172,x101171,x101173)),x101172)+~P1(f319(f319(f225(a1),x101172),f319(x101171,x101173)))+~P1(f319(f319(f225(a1),f319(f69(a1),f319(f319(f3(a1),f319(x101171,f319(f319(f74(a906),f455(x101172,x101171,x101173)),f72(a906)))),f319(x101171,f455(x101172,x101171,x101173))))),f72(a1)))+~P1(f319(f319(f225(a1),f319(x101171,f2(a906))),x101172))
% 22.40/22.31 [10120]~P1(f319(f319(f225(a1),x101201),f319(x101202,x101203)))+~P1(f319(f319(f225(a1),f319(f69(a1),f319(f319(f3(a1),f319(x101202,f319(f319(f74(a906),f453(x101201,x101202,x101203)),f72(a906)))),f319(x101202,f453(x101201,x101202,x101203))))),f72(a1)))+P1(f319(f319(f225(a906),f452(x101201,x101202,x101203)),x101203))+~P1(f319(f319(f225(a1),f319(x101202,f2(a906))),x101201))
% 22.40/22.31 [10121]~P1(f319(f319(f225(a1),x101211),f319(x101212,x101213)))+~P1(f319(f319(f225(a1),f319(f69(a1),f319(f319(f3(a1),f319(x101212,f319(f319(f74(a906),f455(x101211,x101212,x101213)),f72(a906)))),f319(x101212,f455(x101211,x101212,x101213))))),f72(a1)))+P1(f319(f319(f225(a906),f454(x101211,x101212,x101213)),x101213))+~P1(f319(f319(f225(a1),f319(x101212,f2(a906))),x101211))
% 22.40/22.31 [10176]E(x101761,x101762)+~E(f319(f134(f907(x101763),f907(x101763),f126(x101763),f105(x101763)),x101761),f319(f134(f907(x101763),f907(x101763),f126(x101763),f105(x101763)),x101762))+~E(f319(f182(f907(f907(x101763))),x101761),f319(f182(f907(f907(x101763))),x101762))+~P1(f319(f319(f249(f907(x101763),f907(x101763),a904),f319(f319(f9(f907(x101763),f913(f907(x101763),a906),f913(f907(x101763),a904)),f319(f319(f10(f913(a906,a904),f913(f913(f907(x101763),a906),f913(f907(x101763),a904)),f907(x101763)),f10(a906,a904,f907(x101763))),f319(f319(f10(a906,f913(a906,a904),f907(x101763)),a316),f182(f907(x101763))))),f182(f907(x101763)))),f694(x101762,x101761,x101763)))
% 22.40/22.31 [10177]E(x101771,x101772)+~E(f319(f134(f907(x101773),f907(x101773),f126(x101773),f105(x101773)),x101771),f319(f134(f907(x101773),f907(x101773),f126(x101773),f105(x101773)),x101772))+~E(f319(f182(f907(f907(x101773))),x101771),f319(f182(f907(f907(x101773))),x101772))+~P1(f319(f319(f249(f907(x101773),f907(x101773),a904),f319(f319(f9(f907(x101773),f913(f907(x101773),a906),f913(f907(x101773),a904)),f319(f319(f10(f913(a906,a904),f913(f913(f907(x101773),a906),f913(f907(x101773),a904)),f907(x101773)),f10(a906,a904,f907(x101773))),f319(f319(f10(a906,f913(a906,a904),f907(x101773)),a316),f182(f907(x101773))))),f182(f907(x101773)))),f695(x101771,x101772,x101773)))
% 22.40/22.31 [6925]~E(f72(a906),f2(a906))+~P1(f319(f55(x69251),x69253))+~P1(f319(f55(x69251),x69252))+E(f319(f319(f74(a906),f319(f29(x69251),x69252)),f319(f29(x69251),x69253)),f319(f29(x69251),f319(f319(f93(f913(x69251,a904)),x69252),x69253)))
% 22.40/22.31 [7333]~P107(x73331)+~P1(f319(f55(x73331),x73332))+~P1(f319(f319(f321(x73331),x73333),x73332))+P1(f319(f319(f225(x73331),f319(f57(x73331,f94(x73331)),x73332)),x73333))
% 22.40/22.31 [7334]~P4(x73341)+~P1(f319(f55(x73341),x73342))+~P1(f319(f319(f321(x73341),x73343),x73342))+P1(f319(f319(f225(x73341),f319(f57(x73341,f230(x73341)),x73342)),x73343))
% 22.40/22.31 [7576]~P1(f319(f55(x75761),x75763))+~P1(f319(f55(x75761),x75762))+~E(f319(f319(f94(f913(x75761,a904)),x75762),x75763),f181(f913(x75761,a904)))+E(f319(f319(f74(a906),f319(f29(x75761),x75762)),f319(f29(x75761),x75763)),f319(f29(x75761),f319(f319(f93(f913(x75761,a904)),x75762),x75763)))
% 22.40/22.31 [8346]~P37(x83461,x83463)+~P37(x83461,x83462)+~E(f319(f319(f94(f913(x83461,a904)),f319(f256(x83461,x83461),x83462)),f319(f276(x83461,x83461),x83463)),f181(f913(x83461,a904)))+P37(x83461,f319(f319(f93(f913(f912(x83461,x83461),a904)),x83462),x83463))
% 22.40/22.31 [8439]E(x84391,f319(f319(f30(a906),x84392),x84393))+~P1(f319(f319(f226(a906),f2(a906)),x84393))+~P1(f319(f319(f226(a906),x84392),f319(f319(f75(a906),x84393),f319(a104,x84391))))+~P1(f319(f319(f225(a906),f319(f319(f75(a906),x84393),x84391)),x84392))
% 22.40/22.31 [8573]~P1(f319(f55(x85731),x85732))+~P1(f319(f55(x85731),x85733))+E(f319(f319(f74(a906),f319(f29(x85731),x85732)),f319(f29(x85731),x85733)),f319(f29(x85731),f319(f319(f93(f913(x85731,a904)),x85732),x85733)))+P1(f319(f319(f321(x85731),f347(x85733,x85732,x85731)),f319(f319(f94(f913(x85731,a904)),x85732),x85733)))
% 22.40/22.31 [8964]~P127(x89642)+~E(x89641,f2(x89642))+~E(x89643,f2(x89642))+~P1(f319(f319(f226(x89642),f2(x89642)),f319(f319(f74(x89642),f319(f319(f75(x89642),x89643),x89643)),f319(f319(f75(x89642),x89641),x89641))))
% 22.40/22.31 [9499]~P37(x94991,x94993)+~P37(x94991,x94992)+P37(x94991,f319(f319(f93(f913(f912(x94991,x94991),a904)),x94992),x94993))+~P1(f319(f319(f225(f913(f912(x94991,x94991),a904)),f319(f319(f281(x94991,x94991,x94991),x94992),x94993)),x94992))
% 22.40/22.31 [9625]~P1(f319(x96251,x96253))+~P1(f319(f55(x96252),x96253))+P1(f319(x96251,f181(f913(x96252,a904))))+~P1(f319(x96251,f319(f319(f3(f913(x96252,a904)),f859(x96251,x96253,x96252)),f319(f319(f301(x96252),f863(x96251,x96253,x96252)),f181(f913(x96252,a904))))))
% 22.40/22.31 [8749]~P1(f319(f319(f226(a1),f2(a1)),x87493))+P1(f319(f319(f225(a1),f2(a1)),x87491))+~P1(f319(f319(f226(a1),x87492),x87493))+~P1(f319(f319(f225(a1),f2(a1)),f319(f319(f74(a1),f319(f319(f75(a1),x87493),x87491)),x87492)))
% 22.40/22.31 [8768]~P101(x87681)+~P1(f319(f55(x87681),x87682))+E(f319(f319(f3(f913(x87681,a904)),x87682),f319(f319(f301(x87681),x87683),f181(f913(x87681,a904)))),f181(f913(x87681,a904)))+E(f319(f319(f94(x87681),x87683),f12(x87681,f319(f319(f3(f913(x87681,a904)),x87682),f319(f319(f301(x87681),x87683),f181(f913(x87681,a904)))))),f12(x87681,f319(f319(f301(x87681),x87683),x87682)))
% 22.40/22.31 [8769]~P101(x87691)+~P1(f319(f55(x87691),x87692))+E(f319(f319(f3(f913(x87691,a904)),x87692),f319(f319(f301(x87691),x87693),f181(f913(x87691,a904)))),f181(f913(x87691,a904)))+E(f319(f319(f93(x87691),x87693),f15(x87691,f319(f319(f3(f913(x87691,a904)),x87692),f319(f319(f301(x87691),x87693),f181(f913(x87691,a904)))))),f15(x87691,f319(f319(f301(x87691),x87693),x87692)))
% 22.40/22.31 [8770]~P4(x87701)+~P1(f319(f55(x87701),x87702))+E(f319(f319(f3(f913(x87701,a904)),x87702),f319(f319(f301(x87701),x87703),f181(f913(x87701,a904)))),f181(f913(x87701,a904)))+E(f319(f319(f180(x87701),x87703),f16(x87701,f319(f319(f3(f913(x87701,a904)),x87702),f319(f319(f301(x87701),x87703),f181(f913(x87701,a904)))))),f16(x87701,f319(f319(f301(x87701),x87703),x87702)))
% 22.40/22.31 [8771]~P4(x87711)+~P1(f319(f55(x87711),x87712))+E(f319(f319(f3(f913(x87711,a904)),x87712),f319(f319(f301(x87711),x87713),f181(f913(x87711,a904)))),f181(f913(x87711,a904)))+E(f319(f319(f230(x87711),x87713),f17(x87711,f319(f319(f3(f913(x87711,a904)),x87712),f319(f319(f301(x87711),x87713),f181(f913(x87711,a904)))))),f17(x87711,f319(f319(f301(x87711),x87713),x87712)))
% 22.40/22.31 [8842]~P4(x88421)+~P1(f319(f55(x88421),x88422))+E(f319(f319(f3(f913(x88421,a904)),x88422),f319(f319(f301(x88421),x88423),f181(f913(x88421,a904)))),f181(f913(x88421,a904)))+E(f319(f319(f180(x88421),x88423),f13(x88421,f180(x88421),f319(f319(f3(f913(x88421,a904)),x88422),f319(f319(f301(x88421),x88423),f181(f913(x88421,a904)))))),f13(x88421,f180(x88421),f319(f319(f301(x88421),x88423),x88422)))
% 22.40/22.31 [8843]~P4(x88431)+~P1(f319(f55(x88431),x88432))+E(f319(f319(f3(f913(x88431,a904)),x88432),f319(f319(f301(x88431),x88433),f181(f913(x88431,a904)))),f181(f913(x88431,a904)))+E(f319(f319(f230(x88431),x88433),f14(x88431,f230(x88431),f319(f319(f3(f913(x88431,a904)),x88432),f319(f319(f301(x88431),x88433),f181(f913(x88431,a904)))))),f14(x88431,f230(x88431),f319(f319(f301(x88431),x88433),x88432)))
% 22.40/22.31 [9219]~P5(x92191)+~P40(x92191,x92191,x92192)+P1(f319(f319(f225(x92191),f87(x92191,x92192)),x92193))+~P1(f319(f319(f225(x92191),f319(x92192,f319(f319(f94(x92191),f87(x92191,x92192)),x92193))),x92193))
% 22.40/22.31 [9435]E(x94351,x94352)+~E(f319(f134(f907(x94353),f907(x94353),f126(x94353),f105(x94353)),x94351),f319(f134(f907(x94353),f907(x94353),f126(x94353),f105(x94353)),x94352))+~E(f319(f182(f907(f907(x94353))),x94351),f319(f182(f907(f907(x94353))),x94352))+P1(f319(f319(f321(f912(f907(x94353),f907(x94353))),f694(x94352,x94351,x94353)),f319(f164(f912(f907(x94353),f907(x94353))),f319(f319(f173(f907(x94353),f907(x94353)),x94351),x94352))))
% 22.40/22.31 [9436]E(x94361,x94362)+~E(f319(f134(f907(x94363),f907(x94363),f126(x94363),f105(x94363)),x94361),f319(f134(f907(x94363),f907(x94363),f126(x94363),f105(x94363)),x94362))+~E(f319(f182(f907(f907(x94363))),x94361),f319(f182(f907(f907(x94363))),x94362))+P1(f319(f319(f321(f912(f907(x94363),f907(x94363))),f695(x94361,x94362,x94363)),f319(f164(f912(f907(x94363),f907(x94363))),f319(f319(f173(f907(x94363),f907(x94363)),x94362),x94361))))
% 22.40/22.31 [10318]~P102(x103182)+E(x103181,f181(f913(x103182,a904)))+~P1(f319(f55(x103182),x103181))+E(f12(x103182,f319(f254(x103182),f319(f319(f10(f913(x103182,a904),a904,x103182),f80(x103182)),f319(f319(f9(x103182,f913(x103182,a904),f913(x103182,a904)),f319(f319(f10(f913(x103182,f913(a904,a904)),f913(f913(x103182,a904),f913(x103182,a904)),x103182),f20(x103182,a904,a904)),f319(f319(f10(f913(x103182,a904),f913(x103182,f913(a904,a904)),x103182),f319(f10(a904,f913(a904,a904),x103182),a317)),f319(f319(f9(x103182,f913(x103182,x103182),f913(x103182,a904)),f319(f319(f10(f913(x103182,a904),f913(f913(x103182,x103182),f913(x103182,a904)),x103182),f10(x103182,a904,x103182)),a316)),f319(f93(x103182),x103183))))),f319(f319(f9(x103182,f913(x103182,a904),a904),f321(x103182)),x103181))))),f319(f319(f93(x103182),x103183),f12(x103182,x103181)))
% 22.40/22.31 [10319]~P102(x103192)+E(x103191,f181(f913(x103192,a904)))+~P1(f319(f55(x103192),x103191))+E(f15(x103192,f319(f254(x103192),f319(f319(f10(f913(x103192,a904),a904,x103192),f80(x103192)),f319(f319(f9(x103192,f913(x103192,a904),f913(x103192,a904)),f319(f319(f10(f913(x103192,f913(a904,a904)),f913(f913(x103192,a904),f913(x103192,a904)),x103192),f20(x103192,a904,a904)),f319(f319(f10(f913(x103192,a904),f913(x103192,f913(a904,a904)),x103192),f319(f10(a904,f913(a904,a904),x103192),a317)),f319(f319(f9(x103192,f913(x103192,x103192),f913(x103192,a904)),f319(f319(f10(f913(x103192,a904),f913(f913(x103192,x103192),f913(x103192,a904)),x103192),f10(x103192,a904,x103192)),a316)),f319(f94(x103192),x103193))))),f319(f319(f9(x103192,f913(x103192,a904),a904),f321(x103192)),x103191))))),f319(f319(f94(x103192),x103193),f15(x103192,x103191)))
% 22.40/22.31 [10320]~P85(x103202)+E(x103201,f181(f913(x103202,a904)))+~P1(f319(f55(x103202),x103201))+E(f16(x103202,f319(f254(x103202),f319(f319(f10(f913(x103202,a904),a904,x103202),f80(x103202)),f319(f319(f9(x103202,f913(x103202,a904),f913(x103202,a904)),f319(f319(f10(f913(x103202,f913(a904,a904)),f913(f913(x103202,a904),f913(x103202,a904)),x103202),f20(x103202,a904,a904)),f319(f319(f10(f913(x103202,a904),f913(x103202,f913(a904,a904)),x103202),f319(f10(a904,f913(a904,a904),x103202),a317)),f319(f319(f9(x103202,f913(x103202,x103202),f913(x103202,a904)),f319(f319(f10(f913(x103202,a904),f913(f913(x103202,x103202),f913(x103202,a904)),x103202),f10(x103202,a904,x103202)),a316)),f319(f74(x103202),x103203))))),f319(f319(f9(x103202,f913(x103202,a904),a904),f321(x103202)),x103201))))),f319(f319(f74(x103202),x103203),f16(x103202,x103201)))
% 22.40/22.31 [10321]~P85(x103212)+E(x103211,f181(f913(x103212,a904)))+~P1(f319(f55(x103212),x103211))+E(f17(x103212,f319(f254(x103212),f319(f319(f10(f913(x103212,a904),a904,x103212),f80(x103212)),f319(f319(f9(x103212,f913(x103212,a904),f913(x103212,a904)),f319(f319(f10(f913(x103212,f913(a904,a904)),f913(f913(x103212,a904),f913(x103212,a904)),x103212),f20(x103212,a904,a904)),f319(f319(f10(f913(x103212,a904),f913(x103212,f913(a904,a904)),x103212),f319(f10(a904,f913(a904,a904),x103212),a317)),f319(f319(f9(x103212,f913(x103212,x103212),f913(x103212,a904)),f319(f319(f10(f913(x103212,a904),f913(f913(x103212,x103212),f913(x103212,a904)),x103212),f10(x103212,a904,x103212)),a316)),f319(f74(x103212),x103213))))),f319(f319(f9(x103212,f913(x103212,a904),a904),f321(x103212)),x103211))))),f319(f319(f74(x103212),x103213),f17(x103212,x103211)))
% 22.40/22.31 [10322]~P4(x103222)+E(x103221,f181(f913(x103222,a904)))+~P1(f319(f55(x103222),x103221))+E(f14(x103222,f230(x103222),f319(f254(x103222),f319(f319(f10(f913(x103222,a904),a904,x103222),f80(x103222)),f319(f319(f9(x103222,f913(x103222,a904),f913(x103222,a904)),f319(f319(f10(f913(x103222,f913(a904,a904)),f913(f913(x103222,a904),f913(x103222,a904)),x103222),f20(x103222,a904,a904)),f319(f319(f10(f913(x103222,a904),f913(x103222,f913(a904,a904)),x103222),f319(f10(a904,f913(a904,a904),x103222),a317)),f319(f319(f9(x103222,f913(x103222,x103222),f913(x103222,a904)),f319(f319(f10(f913(x103222,a904),f913(f913(x103222,x103222),f913(x103222,a904)),x103222),f10(x103222,a904,x103222)),a316)),f319(f180(x103222),x103223))))),f319(f319(f9(x103222,f913(x103222,a904),a904),f321(x103222)),x103221))))),f319(f319(f180(x103222),x103223),f14(x103222,f230(x103222),x103221)))
% 22.40/22.31 [10323]~P4(x103232)+E(x103231,f181(f913(x103232,a904)))+~P1(f319(f55(x103232),x103231))+E(f13(x103232,f180(x103232),f319(f254(x103232),f319(f319(f10(f913(x103232,a904),a904,x103232),f80(x103232)),f319(f319(f9(x103232,f913(x103232,a904),f913(x103232,a904)),f319(f319(f10(f913(x103232,f913(a904,a904)),f913(f913(x103232,a904),f913(x103232,a904)),x103232),f20(x103232,a904,a904)),f319(f319(f10(f913(x103232,a904),f913(x103232,f913(a904,a904)),x103232),f319(f10(a904,f913(a904,a904),x103232),a317)),f319(f319(f9(x103232,f913(x103232,x103232),f913(x103232,a904)),f319(f319(f10(f913(x103232,a904),f913(f913(x103232,x103232),f913(x103232,a904)),x103232),f10(x103232,a904,x103232)),a316)),f319(f230(x103232),x103233))))),f319(f319(f9(x103232,f913(x103232,a904),a904),f321(x103232)),x103231))))),f319(f319(f230(x103232),x103233),f13(x103232,f180(x103232),x103231)))
% 22.40/22.31 [10256]~P113(x102561)+~E(x102563,f2(x102561))+~E(x102562,f2(x102561))+E(f319(f319(f74(x102561),f319(f319(f236(x102561),x102562),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x102561),x102563),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f2(x102561))
% 22.40/22.31 [10328]~P126(x103281)+~P1(f319(f319(f225(x103281),f2(x103281)),x103283))+P1(f319(f319(f225(x103281),x103282),x103283))+~P1(f319(f319(f225(x103281),f319(f319(f236(x103281),x103282),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103281),x103283),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))))
% 22.40/22.31 [10356]~P113(x103562)+~E(x103561,f2(x103562))+~E(x103563,f2(x103562))+~P1(f319(f319(f226(x103562),f2(x103562)),f319(f319(f74(x103562),f319(f319(f236(x103562),x103563),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89)))),f319(f319(f236(x103562),x103561),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))))
% 22.40/22.31 [6106]~P4(x61061)+~P111(x61062)+~P50(x61061,x61062,x61063)+P25(x61061,x61062,x61063,x61064)
% 22.40/22.31 [6811]~P7(x68113,x68112)+~P1(f319(x68111,x68114))+~P1(f319(f319(f321(x68113),x68114),f262(x68113,x68112)))+P1(f319(x68111,f810(x68111,x68112,x68113)))
% 22.40/22.31 [8684]P26(x86841,x86842,f814(x86843,x86842,x86844,x86841),x86844,x86843)+~E(f319(f29(x86841),x86844),f319(f29(x86842),x86843))+~P1(f319(f55(x86842),x86843))+~P1(f319(f55(x86841),x86844))
% 22.40/22.31 [9395]E(x93951,x93952)+~E(f646(x93951,x93952,x93954,x93953),f648(x93951,x93952,x93954,x93953))+P1(f319(f319(f321(f912(f907(x93953),f907(x93953))),f319(f319(f244(f907(x93953),f907(x93953)),x93952),x93951)),f139(x93953,x93954)))+P1(f319(f319(f321(f912(f907(x93953),f907(x93953))),f319(f319(f244(f907(x93953),f907(x93953)),x93951),x93952)),f139(x93953,x93954)))
% 22.40/22.31 [4950]~P72(x49502)+~E(x49504,f2(x49502))+~E(x49501,f2(x49502))+E(x49501,f319(f319(f282(x49502),x49503),x49504))
% 22.40/22.31 [4951]~P72(x49511)+~E(x49513,f2(x49511))+~E(x49514,f2(x49511))+E(f319(f319(f282(x49511),x49512),x49513),x49514)
% 22.40/22.31 [5068]~P72(x50682)+E(x50681,f2(x50682))+~E(x50683,f2(x50682))+~E(x50681,f319(f319(f282(x50682),x50684),x50683))
% 22.40/22.31 [5069]~P72(x50692)+E(x50691,f2(x50692))+~E(x50693,f2(x50692))+~E(f319(f319(f282(x50692),x50694),x50693),x50691)
% 22.40/22.31 [5256]~P120(x52562)+E(x52561,f2(x52562))+~E(f319(f319(f282(x52562),x52563),x52561),x52564)+E(x52563,f319(f319(f75(x52562),x52564),x52561))
% 22.40/22.31 [5258]~P120(x52582)+E(x52581,f2(x52582))+~E(f319(f319(f75(x52582),x52583),x52581),x52584)+E(x52583,f319(f319(f282(x52582),x52584),x52581))
% 22.40/22.31 [5259]~P72(x52592)+E(x52591,f2(x52592))+~E(f319(f319(f282(x52592),x52593),x52591),x52594)+E(x52593,f319(f319(f75(x52592),x52594),x52591))
% 22.40/22.31 [5260]~P72(x52602)+E(x52601,f2(x52602))+~E(f319(f319(f75(x52602),x52603),x52601),x52604)+E(x52603,f319(f319(f282(x52602),x52604),x52601))
% 22.40/22.31 [5261]~P120(x52612)+E(x52611,f2(x52612))+~E(x52613,f319(f319(f282(x52612),x52614),x52611))+E(f319(f319(f75(x52612),x52613),x52611),x52614)
% 22.40/22.31 [5263]~P120(x52632)+E(x52631,f2(x52632))+~E(x52633,f319(f319(f75(x52632),x52634),x52631))+E(f319(f319(f282(x52632),x52633),x52631),x52634)
% 22.40/22.31 [5264]~P72(x52642)+E(x52641,f2(x52642))+~E(x52643,f319(f319(f282(x52642),x52644),x52641))+E(f319(f319(f75(x52642),x52643),x52641),x52644)
% 22.40/22.31 [5265]~P72(x52652)+E(x52651,f2(x52652))+~E(x52653,f319(f319(f75(x52652),x52654),x52651))+E(f319(f319(f282(x52652),x52653),x52651),x52654)
% 22.40/22.31 [5289]~P72(x52892)+~E(x52891,f2(x52892))+~E(f319(f319(f75(x52892),x52891),x52894),x52893)+E(x52891,f319(f319(f282(x52892),x52893),x52894))
% 22.40/22.31 [5290]~P72(x52901)+~E(x52904,f2(x52901))+~E(x52902,f319(f319(f75(x52901),x52904),x52903))+E(f319(f319(f282(x52901),x52902),x52903),x52904)
% 22.40/22.31 [5364]~E(x53643,x53644)+~E(x53642,x53643)+~P111(x53641)+E(f295(x53641,x53642,x53643),f319(f319(f301(x53641),x53644),f181(f913(x53641,a904))))
% 22.40/22.31 [5565]~E(f106(x55652,x55651),x55653)+~E(f136(x55652,x55651),x55654)+E(x55651,f105(x55652))+E(f319(f319(f126(x55652),x55653),f319(f319(f143(x55652),x55654),f105(x55652))),x55651)
% 22.40/22.31 [6195]~P126(x61953)+E(x61951,x61952)+~E(f319(f319(f236(x61953),x61954),x61951),f319(f319(f236(x61953),x61954),x61952))+~P1(f319(f319(f226(x61953),f72(x61953)),x61954))
% 22.40/22.31 [6196]E(x61961,x61962)+~E(f319(f319(f301(x61963),x61964),x61961),f319(f319(f301(x61963),x61964),x61962))+P1(f319(f319(f321(x61963),x61964),x61962))+P1(f319(f319(f321(x61963),x61964),x61961))
% 22.40/22.31 [6239]E(f319(x62391,x62392),f72(a906))+~E(f319(f319(f11(x62393,a906),x62391),x62394),f72(a906))+~P1(f319(f55(x62393),x62394))+~P1(f319(f319(f321(x62393),x62392),x62394))
% 22.40/22.31 [6240]E(f319(x62401,x62402),f2(a906))+~E(f319(f319(f8(x62403,a906),x62401),x62404),f2(a906))+~P1(f319(f55(x62403),x62404))+~P1(f319(f319(f321(x62403),x62402),x62404))
% 22.40/22.31 [6458]~P111(x64581)+~P1(f319(f319(f225(x64581),x64584),x64583))+P1(f319(f319(f225(x64581),x64582),x64583))+~P1(f319(f319(f225(x64581),x64582),x64584))
% 22.40/22.31 [6459]~P2(x64591)+~P1(f319(f319(f225(x64591),x64592),x64594))+P1(f319(f319(f225(x64591),x64592),x64593))+~P1(f319(f319(f225(x64591),x64594),x64593))
% 22.40/22.31 [6460]~P111(x64601)+~P1(f319(f319(f226(x64601),x64604),x64603))+P1(f319(f319(f226(x64601),x64602),x64603))+~P1(f319(f319(f225(x64601),x64602),x64604))
% 22.40/22.31 [6461]~P111(x64611)+~P1(f319(f319(f226(x64611),x64612),x64614))+P1(f319(f319(f226(x64611),x64612),x64613))+~P1(f319(f319(f225(x64611),x64614),x64613))
% 22.40/22.31 [6462]~P111(x64621)+~P1(f319(f319(f226(x64621),x64624),x64623))+P1(f319(f319(f226(x64621),x64622),x64623))+~P1(f319(f319(f226(x64621),x64622),x64624))
% 22.40/22.31 [6463]~P2(x64631)+~P1(f319(f319(f226(x64631),x64632),x64634))+P1(f319(f319(f226(x64631),x64632),x64633))+~P1(f319(f319(f225(x64631),x64634),x64633))
% 22.40/22.31 [6464]~P2(x64641)+~P1(f319(f319(f226(x64641),x64644),x64643))+P1(f319(f319(f226(x64641),x64642),x64643))+~P1(f319(f319(f225(x64641),x64642),x64644))
% 22.40/22.31 [6465]~P2(x64651)+~P1(f319(f319(f226(x64651),x64652),x64654))+P1(f319(f319(f226(x64651),x64652),x64653))+~P1(f319(f319(f226(x64651),x64654),x64653))
% 22.40/22.31 [6466]~P119(x64661)+~P1(f319(f319(f279(x64661),x64662),x64664))+P1(f319(f319(f279(x64661),x64662),x64663))+~P1(f319(f319(f279(x64661),x64664),x64663))
% 22.40/22.31 [6550]~P35(x65504,x65503,x65502)+E(x65501,f747(x65502,x65503,x65504))+~P1(f319(x65503,x65501))+~P1(f319(f319(f321(x65504),x65501),f319(f164(x65504),x65502)))
% 22.40/22.31 [6551]~P35(x65514,x65513,x65512)+E(x65511,f757(x65512,x65513,x65514))+~P1(f319(x65513,x65511))+~P1(f319(f319(f321(x65514),x65511),f319(f164(x65514),x65512)))
% 22.40/22.31 [6700]~P5(x67001)+~P1(f319(f319(f225(x67001),x67002),f32(x67001,x67004)))+P1(f319(f319(f225(x67001),x67002),x67003))+~P1(f319(f319(f321(x67001),x67003),x67004))
% 22.40/22.31 [6851]~P4(x68511)+~P13(x68511,f319(f319(f143(x68511),x68512),x68514))+~P1(f319(f319(f321(x68511),x68513),f319(f164(x68511),x68514)))+P1(f319(f319(f225(x68511),x68512),x68513))
% 22.40/22.31 [6934]~P5(x69341)+~P1(f319(f319(f225(x69341),f31(x69341,x69344)),x69343))+P1(f319(f319(f225(x69341),x69342),x69343))+~P1(f319(f319(f321(x69341),x69342),x69344))
% 22.40/22.31 [7074]~P69(x70741)+P1(f319(f319(f279(x70741),x70742),f39(x70741,x70743,x70744)))+~P1(f319(f319(f279(x70741),x70742),x70744))+~P1(f319(f319(f279(x70741),x70742),x70743))
% 22.40/22.31 [7336]~P4(x73361)+E(f319(f319(f93(f913(x73361,a904)),f319(f294(x73361,x73362),x73363)),f319(f294(x73361,x73363),x73364)),f319(f294(x73361,x73362),x73364))+~P1(f319(f319(f225(x73361),x73363),x73364))+~P1(f319(f319(f225(x73361),x73362),x73363))
% 22.40/22.31 [7380]P35(x73801,x73802,x73803)+~E(f758(x73803,x73802,x73801,x73804),x73804)+~P1(f319(x73802,x73804))+~P1(f319(f319(f321(x73801),x73804),f319(f164(x73801),x73803)))
% 22.40/22.31 [7381]P35(x73811,x73812,x73813)+~E(f767(x73813,x73812,x73811,x73814),x73814)+~P1(f319(x73812,x73814))+~P1(f319(f319(f321(x73811),x73814),f319(f164(x73811),x73813)))
% 22.40/22.31 [7419]~P69(x74191)+~P1(f319(f319(f279(x74191),x74192),f39(x74191,x74193,x74194)))+P1(f319(f319(f279(x74191),x74192),x74193))+~P1(f319(f319(f279(x74191),x74192),x74194))
% 22.40/22.31 [7448]~P4(x74481)+E(f319(f319(f93(f913(x74481,a904)),f319(f294(x74481,x74482),x74483)),f295(x74481,x74483,x74484)),f295(x74481,x74482,x74484))+~P1(f319(f319(f225(x74481),x74483),x74484))+~P1(f319(f319(f225(x74481),x74482),x74483))
% 22.40/22.31 [7509]~P4(x75091)+E(f319(f319(f93(f913(x75091,a904)),f298(x75091,x75092,x75093)),f319(f294(x75091,x75093),x75094)),f298(x75091,x75092,x75094))+~P1(f319(f319(f225(x75091),x75093),x75094))+~P1(f319(f319(f226(x75091),x75092),x75093))
% 22.40/22.31 [7526]~P4(x75261)+E(f319(f319(f93(f913(x75261,a904)),f295(x75261,x75262,x75263)),f298(x75261,x75263,x75264)),f319(f294(x75261,x75262),x75264))+~P1(f319(f319(f225(x75261),x75262),x75263))+~P1(f319(f319(f226(x75261),x75263),x75264))
% 22.40/22.31 [7557]~P4(x75571)+E(f319(f319(f93(f913(x75571,a904)),f298(x75571,x75572,x75573)),f295(x75571,x75573,x75574)),f297(x75571,x75572,x75574))+~P1(f319(f319(f225(x75571),x75573),x75574))+~P1(f319(f319(f226(x75571),x75572),x75573))
% 22.40/22.31 [7558]~P4(x75581)+E(f319(f319(f93(f913(x75581,a904)),f297(x75581,x75582,x75583)),f298(x75581,x75583,x75584)),f298(x75581,x75582,x75584))+~P1(f319(f319(f225(x75581),x75582),x75583))+~P1(f319(f319(f226(x75581),x75583),x75584))
% 22.40/22.31 [7559]~P4(x75591)+E(f319(f319(f93(f913(x75591,a904)),f297(x75591,x75592,x75593)),f297(x75591,x75593,x75594)),f297(x75591,x75592,x75594))+~P1(f319(f319(f225(x75591),x75593),x75594))+~P1(f319(f319(f225(x75591),x75592),x75593))
% 22.40/22.31 [7560]~P4(x75601)+E(f319(f319(f93(f913(x75601,a904)),f295(x75601,x75602,x75603)),f297(x75601,x75603,x75604)),f295(x75601,x75602,x75604))+~P1(f319(f319(f225(x75601),x75603),x75604))+~P1(f319(f319(f225(x75601),x75602),x75603))
% 22.40/22.31 [8330]P25(x83301,x83302,f895(x83303,x83302,x83304,x83301),x83304)+~P1(f319(f55(x83302),x83303))+~P1(f319(f55(x83301),x83304))+~P1(f319(f319(f225(a906),f319(f29(x83301),x83304)),f319(f29(x83302),x83303)))
% 22.40/22.31 [8351]P35(x83511,x83512,x83513)+~P1(f319(x83512,x83514))+P1(f319(x83512,f758(x83513,x83512,x83511,x83514)))+~P1(f319(f319(f321(x83511),x83514),f319(f164(x83511),x83513)))
% 22.40/22.31 [8352]P35(x83521,x83522,x83523)+~P1(f319(x83522,x83524))+P1(f319(x83522,f767(x83523,x83522,x83521,x83524)))+~P1(f319(f319(f321(x83521),x83524),f319(f164(x83521),x83523)))
% 22.40/22.31 [8406]~P82(x84061)+~E(f319(x84063,f375(x84063,x84064,x84062,x84061)),f72(x84061))+E(f319(f319(f319(f59(x84061,x84062,f75(x84061)),x84063),f72(x84061)),x84064),f72(x84061))+~P1(f319(f55(x84062),x84064))
% 22.40/22.31 [8673]~P126(x86731)+~P1(f319(f319(f225(x86731),f2(x86731)),x86733))+P1(f319(f319(f225(x86731),x86732),x86733))+~P1(f319(f319(f225(x86731),f319(f319(f236(x86731),x86732),f319(a104,x86734))),f319(f319(f236(x86731),x86733),f319(a104,x86734))))
% 22.40/22.31 [8841]~P40(f913(x88414,a904),f913(x88414,a904),x88413)+P1(f319(x88411,x88412))+~P1(f319(x88411,f595(x88411,x88413,x88412,x88414)))+~P1(f319(f319(f321(x88414),x88412),f87(f913(x88414,a904),x88413)))
% 22.40/22.31 [8991]P35(x89911,x89912,x89913)+~P1(f319(x89912,x89914))+~P1(f319(f319(f321(x89911),x89914),f319(f164(x89911),x89913)))+P1(f319(f319(f321(x89911),f758(x89913,x89912,x89911,x89914)),f319(f164(x89911),x89913)))
% 22.40/22.31 [8992]P35(x89921,x89922,x89923)+~P1(f319(x89922,x89924))+~P1(f319(f319(f321(x89921),x89924),f319(f164(x89921),x89923)))+P1(f319(f319(f321(x89921),f767(x89923,x89922,x89921,x89924)),f319(f164(x89921),x89923)))
% 22.40/22.31 [9072]~P82(x90721)+E(f319(f319(f319(f59(x90721,x90722,f75(x90721)),x90723),f72(x90721)),x90724),f72(x90721))+~P1(f319(f55(x90722),x90724))+P1(f319(f319(f321(x90722),f375(x90723,x90724,x90722,x90721)),x90724))
% 22.40/22.31 [9567]~P1(f319(f319(f225(a1),x95674),f2(a1)))+P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f75(a1),x95671),f39(a1,x95672,x95673))),x95674)),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x95673))+~P1(f319(f319(f226(a1),x95671),x95674))
% 22.40/22.31 [10034]~P1(f319(f55(x100341),x100342))+~P1(f319(f319(f321(x100341),x100344),x100342))+~P1(f319(f319(f321(x100341),x100343),x100342))+P1(f319(f319(f226(a906),f319(f29(x100341),f319(f319(f3(f913(x100341,a904)),f319(f319(f3(f913(x100341,a904)),x100342),f319(f319(f301(x100341),x100343),f181(f913(x100341,a904))))),f319(f319(f301(x100341),x100344),f181(f913(x100341,a904)))))),f319(f29(x100341),x100342)))
% 22.40/22.31 [7046]~P107(x70461)+~P1(f319(f319(f225(x70461),x70462),x70464))+~P1(f319(f319(f225(x70461),x70462),x70463))+P1(f319(f319(f225(x70461),x70462),f319(f319(f94(x70461),x70463),x70464)))
% 22.40/22.31 [7049]~P4(x70491)+~P1(f319(f319(f225(x70491),x70492),x70494))+~P1(f319(f319(f225(x70491),x70492),x70493))+P1(f319(f319(f225(x70491),x70492),f319(f319(f230(x70491),x70493),x70494)))
% 22.40/22.31 [7050]~P4(x70501)+~P1(f319(f319(f226(x70501),x70502),x70504))+~P1(f319(f319(f226(x70501),x70502),x70503))+P1(f319(f319(f226(x70501),x70502),f319(f319(f230(x70501),x70503),x70504)))
% 22.40/22.31 [7051]~P115(x70511)+~P1(f319(f319(f279(x70511),x70512),x70514))+~P1(f319(f319(f279(x70511),x70512),x70513))+P1(f319(f319(f279(x70511),x70512),f319(f319(f3(x70511),x70513),x70514)))
% 22.40/22.31 [7071]~P73(x70712)+E(x70711,f2(x70712))+E(f319(f319(f282(x70712),f319(f319(f236(x70712),x70711),x70713)),f319(f319(f236(x70712),x70711),x70714)),f319(f319(f236(x70712),x70711),f319(f319(f3(a906),x70713),x70714)))+~P1(f319(f319(f225(a906),x70714),x70713))
% 22.40/22.31 [7119]~P4(x71191)+~P13(x71191,f319(f319(f143(x71191),x71193),x71194))+P13(x71191,f319(f319(f143(x71191),x71192),f319(f319(f143(x71191),x71193),x71194)))+~P1(f319(f319(f225(x71191),x71192),x71193))
% 22.40/22.31 [7154]~P93(x71541)+~P1(f319(f319(f225(x71541),f2(x71541)),x71544))+~P1(f319(f319(f225(x71541),x71542),x71543))+P1(f319(f319(f225(x71541),x71542),f319(f319(f74(x71541),x71543),x71544)))
% 22.40/22.31 [7155]~P93(x71551)+~P1(f319(f319(f225(x71551),f2(x71551)),x71553))+~P1(f319(f319(f225(x71551),x71552),x71554))+P1(f319(f319(f225(x71551),x71552),f319(f319(f74(x71551),x71553),x71554)))
% 22.40/22.31 [7156]~P126(x71561)+~P1(f319(f319(f226(x71561),f2(x71561)),x71563))+~P1(f319(f319(f226(x71561),x71562),x71564))+P1(f319(f319(f226(x71561),x71562),f319(f319(f74(x71561),x71563),x71564)))
% 22.40/22.31 [7157]~P93(x71571)+~P1(f319(f319(f225(x71571),x71572),x71574))+~P1(f319(f319(f226(x71571),f2(x71571)),x71573))+P1(f319(f319(f226(x71571),x71572),f319(f319(f74(x71571),x71573),x71574)))
% 22.40/22.31 [7158]~P93(x71581)+~P1(f319(f319(f225(x71581),f2(x71581)),x71583))+~P1(f319(f319(f226(x71581),x71582),x71584))+P1(f319(f319(f226(x71581),x71582),f319(f319(f74(x71581),x71583),x71584)))
% 22.40/22.31 [7198]~P4(x71981)+P1(f319(f319(f225(x71981),x71982),x71983))+P1(f319(f319(f225(x71981),x71982),x71984))+~P1(f319(f319(f225(x71981),x71982),f319(f319(f180(x71981),x71984),x71983)))
% 22.40/22.31 [7199]~P4(x71991)+P1(f319(f319(f226(x71991),x71992),x71993))+P1(f319(f319(f226(x71991),x71992),x71994))+~P1(f319(f319(f226(x71991),x71992),f319(f319(f180(x71991),x71994),x71993)))
% 22.40/22.31 [7482]~P111(x74822)+~P71(x74821)+~P1(f319(f319(f226(f913(x74821,x74822)),x74823),x74824))+P1(f319(f319(f225(f913(x74821,x74822)),x74823),x74824))
% 22.40/22.31 [7837]~P75(x78371)+~P1(f319(f319(f226(x78371),x78374),f2(x78371)))+~P1(f319(f319(f225(x78371),x78373),f319(f319(f282(x78371),x78372),x78374)))+P1(f319(f319(f225(x78371),x78372),f319(f319(f75(x78371),x78373),x78374)))
% 22.40/22.31 [7838]~P75(x78381)+~P1(f319(f319(f226(x78381),x78384),f2(x78381)))+~P1(f319(f319(f225(x78381),x78383),f319(f319(f75(x78381),x78382),x78384)))+P1(f319(f319(f225(x78381),x78382),f319(f319(f282(x78381),x78383),x78384)))
% 22.40/22.31 [7839]~P75(x78391)+~P1(f319(f319(f226(x78391),x78394),f2(x78391)))+~P1(f319(f319(f226(x78391),x78393),f319(f319(f282(x78391),x78392),x78394)))+P1(f319(f319(f226(x78391),x78392),f319(f319(f75(x78391),x78393),x78394)))
% 22.40/22.31 [7840]~P75(x78401)+~P1(f319(f319(f226(x78401),x78404),f2(x78401)))+~P1(f319(f319(f226(x78401),x78403),f319(f319(f75(x78401),x78402),x78404)))+P1(f319(f319(f226(x78401),x78402),f319(f319(f282(x78401),x78403),x78404)))
% 22.40/22.31 [7950]~P125(x79501)+~P1(f319(f319(f225(x79501),x79502),f2(x79501)))+~P1(f319(f319(f225(x79501),x79504),x79503))+P1(f319(f319(f225(x79501),f319(f319(f75(x79501),x79502),x79503)),f319(f319(f75(x79501),x79502),x79504)))
% 22.40/22.31 [7951]~P127(x79511)+~P1(f319(f319(f226(x79511),x79512),f2(x79511)))+~P1(f319(f319(f225(x79511),x79514),x79513))+P1(f319(f319(f225(x79511),f319(f319(f75(x79511),x79512),x79513)),f319(f319(f75(x79511),x79512),x79514)))
% 22.40/22.31 [7952]~P125(x79521)+~P1(f319(f319(f225(x79521),x79523),f2(x79521)))+~P1(f319(f319(f225(x79521),x79524),x79522))+P1(f319(f319(f225(x79521),f319(f319(f75(x79521),x79522),x79523)),f319(f319(f75(x79521),x79524),x79523)))
% 22.40/22.31 [7953]~P74(x79531)+~P1(f319(f319(f225(x79531),x79533),f2(x79531)))+~P1(f319(f319(f225(x79531),x79534),x79532))+P1(f319(f319(f225(x79531),f319(f319(f282(x79531),x79532),x79533)),f319(f319(f282(x79531),x79534),x79533)))
% 22.40/22.31 [7957]~P127(x79571)+~P1(f319(f319(f226(x79571),x79573),f2(x79571)))+~P1(f319(f319(f226(x79571),x79574),x79572))+P1(f319(f319(f226(x79571),f319(f319(f75(x79571),x79572),x79573)),f319(f319(f75(x79571),x79574),x79573)))
% 22.40/22.31 [7958]~P127(x79581)+~P1(f319(f319(f226(x79581),x79582),f2(x79581)))+~P1(f319(f319(f226(x79581),x79584),x79583))+P1(f319(f319(f226(x79581),f319(f319(f75(x79581),x79582),x79583)),f319(f319(f75(x79581),x79582),x79584)))
% 22.40/22.31 [7959]~P75(x79591)+~P1(f319(f319(f226(x79591),x79593),f2(x79591)))+~P1(f319(f319(f226(x79591),x79594),x79592))+P1(f319(f319(f226(x79591),f319(f319(f282(x79591),x79592),x79593)),f319(f319(f282(x79591),x79594),x79593)))
% 22.40/22.31 [7960]~P126(x79601)+~P1(f319(f319(f226(x79601),f72(x79601)),x79602))+~P1(f319(f319(f225(a906),x79603),x79604))+P1(f319(f319(f225(x79601),f319(f319(f236(x79601),x79602),x79603)),f319(f319(f236(x79601),x79602),x79604)))
% 22.40/22.31 [7961]~P126(x79611)+~P1(f319(f319(f225(x79611),f72(x79611)),x79612))+~P1(f319(f319(f225(a906),x79613),x79614))+P1(f319(f319(f225(x79611),f319(f319(f236(x79611),x79612),x79613)),f319(f319(f236(x79611),x79612),x79614)))
% 22.40/22.31 [7963]~P126(x79631)+~P1(f319(f319(f226(x79631),f72(x79631)),x79632))+~P1(f319(f319(f226(a906),x79633),x79634))+P1(f319(f319(f226(x79631),f319(f319(f236(x79631),x79632),x79633)),f319(f319(f236(x79631),x79632),x79634)))
% 22.40/22.31 [7986]P1(f319(f319(f226(a906),f2(a906)),f319(x79861,x79862)))+~P1(f319(f55(x79863),x79864))+~P1(f319(f319(f321(x79863),x79862),x79864))+~P1(f319(f319(f226(a906),f2(a906)),f319(f319(f11(x79863,a906),x79861),x79864)))
% 22.40/22.31 [7994]~P127(x79941)+~P1(f319(f319(f226(x79941),f2(x79941)),x79942))+~P1(f319(f319(f225(x79941),x79943),x79944))+P1(f319(f319(f225(x79941),f319(f319(f75(x79941),x79942),x79943)),f319(f319(f75(x79941),x79942),x79944)))
% 22.40/22.31 [7995]~P137(x79951)+~P1(f319(f319(f225(x79951),x79953),x79954))+~P1(f319(f319(f225(x79951),f2(x79951)),x79952))+P1(f319(f319(f225(x79951),f319(f319(f75(x79951),x79952),x79953)),f319(f319(f75(x79951),x79952),x79954)))
% 22.40/22.31 [7996]~P136(x79961)+~P1(f319(f319(f225(x79961),x79963),x79964))+~P1(f319(f319(f225(x79961),f2(x79961)),x79962))+P1(f319(f319(f225(x79961),f319(f319(f75(x79961),x79962),x79963)),f319(f319(f75(x79961),x79962),x79964)))
% 22.40/22.31 [7997]~P137(x79971)+~P1(f319(f319(f225(x79971),x79972),x79974))+~P1(f319(f319(f225(x79971),f2(x79971)),x79973))+P1(f319(f319(f225(x79971),f319(f319(f75(x79971),x79972),x79973)),f319(f319(f75(x79971),x79974),x79973)))
% 22.40/22.31 [7998]~P74(x79981)+~P1(f319(f319(f225(x79981),x79982),x79984))+~P1(f319(f319(f225(x79981),f2(x79981)),x79983))+P1(f319(f319(f225(x79981),f319(f319(f282(x79981),x79982),x79983)),f319(f319(f282(x79981),x79984),x79983)))
% 22.40/22.31 [7999]~P126(x79991)+~P1(f319(f319(f225(x79991),x79992),x79994))+~P1(f319(f319(f225(x79991),f2(x79991)),x79992))+P1(f319(f319(f225(x79991),f319(f319(f236(x79991),x79992),x79993)),f319(f319(f236(x79991),x79994),x79993)))
% 22.40/22.31 [8001]~P131(x80011)+~P1(f319(f319(f226(x80011),x80013),x80014))+~P1(f319(f319(f226(x80011),f2(x80011)),x80012))+P1(f319(f319(f226(x80011),f319(f319(f75(x80011),x80012),x80013)),f319(f319(f75(x80011),x80012),x80014)))
% 22.40/22.31 [8002]~P122(x80021)+~P1(f319(f319(f226(x80021),x80023),x80024))+~P1(f319(f319(f226(x80021),f2(x80021)),x80022))+P1(f319(f319(f226(x80021),f319(f319(f75(x80021),x80022),x80023)),f319(f319(f75(x80021),x80022),x80024)))
% 22.40/22.31 [8003]~P127(x80031)+~P1(f319(f319(f226(x80031),x80032),x80034))+~P1(f319(f319(f226(x80031),f2(x80031)),x80033))+P1(f319(f319(f226(x80031),f319(f319(f75(x80031),x80032),x80033)),f319(f319(f75(x80031),x80034),x80033)))
% 22.40/22.31 [8004]~P131(x80041)+~P1(f319(f319(f226(x80041),x80042),x80044))+~P1(f319(f319(f226(x80041),f2(x80041)),x80043))+P1(f319(f319(f226(x80041),f319(f319(f75(x80041),x80042),x80043)),f319(f319(f75(x80041),x80044),x80043)))
% 22.40/22.31 [8005]~P127(x80051)+~P1(f319(f319(f226(x80051),x80053),x80054))+~P1(f319(f319(f226(x80051),f2(x80051)),x80052))+P1(f319(f319(f226(x80051),f319(f319(f75(x80051),x80052),x80053)),f319(f319(f75(x80051),x80052),x80054)))
% 22.40/22.31 [8006]~P75(x80061)+~P1(f319(f319(f226(x80061),x80062),x80064))+~P1(f319(f319(f226(x80061),f2(x80061)),x80063))+P1(f319(f319(f226(x80061),f319(f319(f282(x80061),x80062),x80063)),f319(f319(f282(x80061),x80064),x80063)))
% 22.40/22.31 [8045]~P3(x80452)+P1(f319(f319(f226(f913(x80451,x80452)),x80454),x80453))+~P1(f319(f319(f225(f913(x80451,x80452)),x80454),x80453))+P1(f319(f319(f225(f913(x80451,x80452)),x80453),x80454))
% 22.40/22.31 [8083]P1(f319(f319(f321(x80831),x80832),x80833))+P1(f319(f319(f321(x80831),x80832),x80834))+~P1(f319(f319(f225(f913(x80831,a904)),x80834),x80833))+P1(f319(f319(f226(f913(x80831,a904)),x80834),f319(f319(f301(x80831),x80832),x80833)))
% 22.40/22.31 [8245]P1(f319(f319(f321(x82451),x82452),x82453))+P1(f319(f319(f321(x82451),x82452),x82454))+~P1(f319(f319(f226(f913(x82451,a904)),x82454),f319(f319(f301(x82451),x82452),x82453)))+P1(f319(f319(f225(f913(x82451,a904)),x82454),x82453))
% 22.40/22.31 [8311]~P127(x83111)+P1(f319(f319(f226(x83111),x83113),x83112))+P1(f319(f319(f226(x83111),x83112),x83113))+~P1(f319(f319(f226(x83111),f319(f319(f75(x83111),x83114),x83112)),f319(f319(f75(x83111),x83114),x83113)))
% 22.40/22.31 [8312]~P127(x83121)+P1(f319(f319(f226(x83121),x83123),x83122))+P1(f319(f319(f226(x83121),x83122),x83123))+~P1(f319(f319(f226(x83121),f319(f319(f75(x83121),x83122),x83124)),f319(f319(f75(x83121),x83123),x83124)))
% 22.40/22.31 [8321]~P127(x83211)+P1(f319(f319(f226(x83211),x83214),f2(x83211)))+P1(f319(f319(f226(x83211),x83212),x83213))+~P1(f319(f319(f226(x83211),f319(f319(f75(x83211),x83212),x83214)),f319(f319(f75(x83211),x83213),x83214)))
% 22.40/22.31 [8322]~P127(x83221)+P1(f319(f319(f226(x83221),x83224),f2(x83221)))+P1(f319(f319(f226(x83221),x83222),x83223))+~P1(f319(f319(f226(x83221),f319(f319(f75(x83221),x83224),x83222)),f319(f319(f75(x83221),x83224),x83223)))
% 22.40/22.31 [8325]~P127(x83251)+P1(f319(f319(f226(x83251),x83252),x83253))+P1(f319(f319(f226(x83251),f2(x83251)),x83254))+~P1(f319(f319(f226(x83251),f319(f319(f75(x83251),x83254),x83253)),f319(f319(f75(x83251),x83254),x83252)))
% 22.40/22.31 [8326]~P127(x83261)+P1(f319(f319(f226(x83261),x83262),x83263))+P1(f319(f319(f226(x83261),f2(x83261)),x83264))+~P1(f319(f319(f226(x83261),f319(f319(f75(x83261),x83263),x83264)),f319(f319(f75(x83261),x83262),x83264)))
% 22.40/22.31 [8338]~P127(x83381)+P1(f319(f319(f226(x83381),x83382),f2(x83381)))+P1(f319(f319(f226(x83381),f2(x83381)),x83382))+~P1(f319(f319(f226(x83381),f319(f319(f75(x83381),x83383),x83382)),f319(f319(f75(x83381),x83384),x83382)))
% 22.40/22.31 [8339]~P127(x83391)+P1(f319(f319(f226(x83391),x83392),f2(x83391)))+P1(f319(f319(f226(x83391),f2(x83391)),x83392))+~P1(f319(f319(f226(x83391),f319(f319(f75(x83391),x83392),x83393)),f319(f319(f75(x83391),x83392),x83394)))
% 22.40/22.31 [8368]~P127(x83681)+~P1(f319(f319(f226(x83681),x83684),f2(x83681)))+P1(f319(f319(f225(x83681),x83682),x83683))+~P1(f319(f319(f225(x83681),f319(f319(f75(x83681),x83684),x83683)),f319(f319(f75(x83681),x83684),x83682)))
% 22.40/22.31 [8369]~P127(x83691)+~P1(f319(f319(f226(x83691),x83694),f2(x83691)))+P1(f319(f319(f226(x83691),x83692),x83693))+~P1(f319(f319(f226(x83691),f319(f319(f75(x83691),x83694),x83693)),f319(f319(f75(x83691),x83694),x83692)))
% 22.40/22.31 [8380]~P126(x83803)+~P1(f319(f319(f226(x83803),f72(x83803)),x83804))+P1(f319(f319(f225(a906),x83801),x83802))+~P1(f319(f319(f225(x83803),f319(f319(f236(x83803),x83804),x83801)),f319(f319(f236(x83803),x83804),x83802)))
% 22.40/22.31 [8382]~P126(x83823)+~P1(f319(f319(f226(x83823),f72(x83823)),x83824))+P1(f319(f319(f226(a906),x83821),x83822))+~P1(f319(f319(f226(x83823),f319(f319(f236(x83823),x83824),x83821)),f319(f319(f236(x83823),x83824),x83822)))
% 22.40/22.31 [8392]~P127(x83921)+P1(f319(f319(f225(x83921),x83922),x83923))+~P1(f319(f319(f226(x83921),f2(x83921)),x83924))+~P1(f319(f319(f225(x83921),f319(f319(f75(x83921),x83924),x83922)),f319(f319(f75(x83921),x83924),x83923)))
% 22.40/22.31 [8393]~P131(x83931)+P1(f319(f319(f225(x83931),x83932),x83933))+~P1(f319(f319(f226(x83931),f2(x83931)),x83934))+~P1(f319(f319(f225(x83931),f319(f319(f75(x83931),x83934),x83932)),f319(f319(f75(x83931),x83934),x83933)))
% 22.40/22.31 [8394]~P131(x83941)+P1(f319(f319(f225(x83941),x83942),x83943))+~P1(f319(f319(f226(x83941),f2(x83941)),x83944))+~P1(f319(f319(f225(x83941),f319(f319(f75(x83941),x83942),x83944)),f319(f319(f75(x83941),x83943),x83944)))
% 22.40/22.31 [8395]~P127(x83951)+P1(f319(f319(f226(x83951),x83952),x83953))+~P1(f319(f319(f226(x83951),f2(x83951)),x83954))+~P1(f319(f319(f226(x83951),f319(f319(f75(x83951),x83954),x83952)),f319(f319(f75(x83951),x83954),x83953)))
% 22.40/22.31 [8396]~P131(x83961)+P1(f319(f319(f226(x83961),x83962),x83963))+~P1(f319(f319(f225(x83961),f2(x83961)),x83964))+~P1(f319(f319(f226(x83961),f319(f319(f75(x83961),x83964),x83962)),f319(f319(f75(x83961),x83964),x83963)))
% 22.40/22.31 [8397]~P132(x83971)+P1(f319(f319(f226(x83971),x83972),x83973))+~P1(f319(f319(f225(x83971),f2(x83971)),x83974))+~P1(f319(f319(f226(x83971),f319(f319(f75(x83971),x83974),x83972)),f319(f319(f75(x83971),x83974),x83973)))
% 22.40/22.31 [8398]~P126(x83981)+~P1(f319(f319(f225(x83981),f2(x83981)),x83983))+P1(f319(f319(f226(x83981),x83982),x83983))+~P1(f319(f319(f226(x83981),f319(f319(f236(x83981),x83982),x83984)),f319(f319(f236(x83981),x83983),x83984)))
% 22.40/22.31 [8399]~P131(x83991)+P1(f319(f319(f226(x83991),x83992),x83993))+~P1(f319(f319(f225(x83991),f2(x83991)),x83994))+~P1(f319(f319(f226(x83991),f319(f319(f75(x83991),x83992),x83994)),f319(f319(f75(x83991),x83993),x83994)))
% 22.40/22.31 [8400]~P132(x84001)+P1(f319(f319(f226(x84001),x84002),x84003))+~P1(f319(f319(f225(x84001),f2(x84001)),x84004))+~P1(f319(f319(f226(x84001),f319(f319(f75(x84001),x84002),x84004)),f319(f319(f75(x84001),x84003),x84004)))
% 22.40/22.31 [8442]P1(f319(f319(f321(x84421),x84422),x84423))+~P1(f319(f319(f225(f913(x84421,a904)),x84423),x84424))+~P1(f319(f319(f226(f913(x84421,a904)),x84423),x84424))+P1(f319(f319(f226(f913(x84421,a904)),x84423),f319(f319(f301(x84421),x84422),x84424)))
% 22.40/22.31 [8816]E(f319(f319(f3(a1),f388(x88161,x88162,x88163,x88164)),f389(x88161,x88162,x88163,x88164)),x88164)+~P1(f319(f319(f226(a1),f2(a1)),x88163))+~P1(f319(f319(f225(a1),x88161),x88164))+P1(f319(f319(f225(a1),x88161),f319(f319(f74(a1),x88164),x88163)))
% 22.40/22.31 [8817]E(f319(f319(f3(a1),f414(x88171,x88172,x88173,x88174)),f415(x88171,x88172,x88173,x88174)),x88174)+~P1(f319(f319(f226(a1),f2(a1)),x88173))+~P1(f319(f319(f226(a1),x88171),x88174))+P1(f319(f319(f226(a1),x88171),f319(f319(f74(a1),x88174),x88173)))
% 22.40/22.31 [8973]~E(f319(f319(f156(x89731),x89733),f668(x89734,x89733,x89731,x89732)),f319(f319(f156(x89731),x89734),f668(x89734,x89733,x89731,x89732)))+E(f319(f319(f167(x89731),x89732),x89733),f319(f319(f167(x89731),x89732),x89734))+~P1(f319(f319(f225(a906),x89732),f319(f182(f907(x89731)),x89733)))+~P1(f319(f319(f225(a906),x89732),f319(f182(f907(x89731)),x89734)))
% 22.40/22.31 [9039]~P1(f319(f319(f226(a1),f2(a1)),x90393))+~P1(f319(f319(f225(a1),x90391),x90394))+P1(f319(f319(f321(a1),f388(x90391,x90392,x90393,x90394)),x90392))+P1(f319(f319(f225(a1),x90391),f319(f319(f74(a1),x90394),x90393)))
% 22.40/22.31 [9040]~P1(f319(f319(f226(a1),f2(a1)),x90403))+~P1(f319(f319(f226(a1),x90401),x90404))+P1(f319(f319(f321(a1),f414(x90401,x90402,x90403,x90404)),x90402))+P1(f319(f319(f226(a1),x90401),f319(f319(f74(a1),x90404),x90403)))
% 22.40/22.31 [9081]~P107(x90811)+~P1(f319(f55(x90811),x90813))+~P1(f319(f319(f321(x90811),x90814),x90813))+P1(f319(f319(f225(x90811),f319(f319(f58(x90811,x90811,f94(x90811)),x90812),x90813)),f319(f319(f94(x90811),x90814),x90812)))
% 22.40/22.31 [9082]~P4(x90821)+~P1(f319(f55(x90821),x90823))+~P1(f319(f319(f321(x90821),x90824),x90823))+P1(f319(f319(f225(x90821),f319(f319(f58(x90821,x90821,f230(x90821)),x90822),x90823)),f319(f319(f230(x90821),x90824),x90822)))
% 22.40/22.31 [9126]E(f319(f319(f167(x91261),x91262),x91263),f319(f319(f167(x91261),x91262),x91264))+P1(f319(f319(f226(a906),f668(x91263,x91264,x91261,x91262)),x91262))+~P1(f319(f319(f225(a906),x91262),f319(f182(f907(x91261)),x91263)))+~P1(f319(f319(f225(a906),x91262),f319(f182(f907(x91261)),x91264)))
% 22.40/22.31 [9131]~P1(f319(f319(f226(a1),f2(a1)),x91313))+~P1(f319(f319(f225(a1),x91311),x91312))+P1(f319(f319(f321(a1),f389(x91311,x91314,x91313,x91312)),f295(a1,f72(a1),x91313)))+P1(f319(f319(f225(a1),x91311),f319(f319(f74(a1),x91312),x91313)))
% 22.40/22.31 [9132]~P1(f319(f319(f226(a1),f2(a1)),x91323))+~P1(f319(f319(f226(a1),x91321),x91322))+P1(f319(f319(f321(a1),f415(x91321,x91324,x91323,x91322)),f295(a1,f72(a1),x91323)))+P1(f319(f319(f226(a1),x91321),f319(f319(f74(a1),x91322),x91323)))
% 22.40/22.31 [9456]~P4(x94561)+~P1(f319(f55(x94561),x94564))+P1(f319(f319(f321(x94561),f380(x94562,x94563,x94564,x94561)),x94564))+P1(f319(f319(f225(x94561),f319(f319(f58(x94561,x94561,f180(x94561)),x94562),x94564)),f319(f319(f180(x94561),x94563),x94562)))
% 22.40/22.31 [9457]~P106(x94571)+~P1(f319(f55(x94571),x94574))+P1(f319(f319(f321(x94571),f382(x94572,x94573,x94574,x94571)),x94574))+P1(f319(f319(f225(x94571),f319(f319(f58(x94571,x94571,f93(x94571)),x94572),x94574)),f319(f319(f93(x94571),x94573),x94572)))
% 22.40/22.31 [9581]~P106(x95811)+~P1(f319(f55(x95811),x95813))+~P1(f319(f319(f225(x95811),f382(x95812,x95814,x95813,x95811)),x95814))+P1(f319(f319(f225(x95811),f319(f319(f58(x95811,x95811,f93(x95811)),x95812),x95813)),f319(f319(f93(x95811),x95814),x95812)))
% 22.40/22.31 [9582]~P4(x95821)+~P1(f319(f55(x95821),x95823))+~P1(f319(f319(f225(x95821),f380(x95822,x95824,x95823,x95821)),x95824))+P1(f319(f319(f225(x95821),f319(f319(f58(x95821,x95821,f180(x95821)),x95822),x95823)),f319(f319(f180(x95821),x95824),x95822)))
% 22.40/22.31 [9584]~P1(f319(f319(f225(a1),f2(a1)),x95844))+~P1(f319(f319(f226(a1),f2(a1)),x95843))+~P1(f319(f319(f226(a1),x95844),x95841))+P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f75(a1),x95841),f39(a1,x95842,x95843))),x95844)),f319(f319(f75(a1),x95841),x95843)))
% 22.40/22.31 [10007]E(x100071,x100072)+P1(f319(f319(f321(f912(f907(x100073),f907(x100073))),f319(f319(f244(f907(x100073),f907(x100073)),x100072),x100071)),f139(x100073,x100074)))+P1(f319(f319(f321(f912(f907(x100073),f907(x100073))),f319(f319(f244(f907(x100073),f907(x100073)),x100071),x100072)),f139(x100073,x100074)))+~P1(f319(f319(f321(f912(x100073,x100073)),f319(f319(f244(x100073,x100073),f646(x100071,x100072,x100074,x100073)),f648(x100071,x100072,x100074,x100073))),x100074))
% 22.40/22.31 [10008]E(x100081,x100082)+P1(f319(f319(f321(f912(f907(x100083),f907(x100083))),f319(f319(f244(f907(x100083),f907(x100083)),x100082),x100081)),f139(x100083,x100084)))+P1(f319(f319(f321(f912(f907(x100083),f907(x100083))),f319(f319(f244(f907(x100083),f907(x100083)),x100081),x100082)),f139(x100083,x100084)))+~P1(f319(f319(f321(f912(x100083,x100083)),f319(f319(f244(x100083,x100083),f648(x100081,x100082,x100084,x100083)),f646(x100081,x100082,x100084,x100083))),x100084))
% 22.40/22.31 [7548]~P106(x75481)+~P1(f319(f319(f225(x75481),x75483),x75484))+~P1(f319(f319(f225(x75481),x75482),x75484))+P1(f319(f319(f225(x75481),f319(f319(f93(x75481),x75482),x75483)),x75484))
% 22.40/22.31 [7551]~P4(x75511)+~P1(f319(f319(f225(x75511),x75513),x75514))+~P1(f319(f319(f225(x75511),x75512),x75514))+P1(f319(f319(f225(x75511),f319(f319(f180(x75511),x75512),x75513)),x75514))
% 22.40/22.31 [7552]~P4(x75521)+~P1(f319(f319(f226(x75521),x75523),x75524))+~P1(f319(f319(f226(x75521),x75522),x75524))+P1(f319(f319(f226(x75521),f319(f319(f180(x75521),x75522),x75523)),x75524))
% 22.40/22.31 [7862]~E(x78621,x78623)+E(f131(a906,f319(f294(a906,x78621),x78622)),f319(f319(f143(a906),x78623),x78624))+~E(f131(a906,f319(f294(a906,f319(f319(f74(a906),x78621),f72(a906))),x78622)),x78624)+~P1(f319(f319(f226(a906),x78621),x78622))
% 22.40/22.31 [7871]~P4(x78711)+P1(f319(f319(f225(x78711),x78712),x78713))+P1(f319(f319(f225(x78711),x78714),x78713))+~P1(f319(f319(f225(x78711),f319(f319(f230(x78711),x78714),x78712)),x78713))
% 22.40/22.31 [7872]~P4(x78721)+P1(f319(f319(f226(x78721),x78722),x78723))+P1(f319(f319(f226(x78721),x78724),x78723))+~P1(f319(f319(f226(x78721),f319(f319(f230(x78721),x78724),x78722)),x78723))
% 22.40/22.31 [8141]~P74(x81411)+~P1(f319(f319(f226(x81411),f2(x81411)),x81413))+~P1(f319(f319(f225(x81411),x81412),f319(f319(f282(x81411),x81414),x81413)))+P1(f319(f319(f225(x81411),f319(f319(f75(x81411),x81412),x81413)),x81414))
% 22.40/22.31 [8142]~P75(x81421)+~P1(f319(f319(f226(x81421),f2(x81421)),x81423))+~P1(f319(f319(f225(x81421),x81422),f319(f319(f282(x81421),x81424),x81423)))+P1(f319(f319(f225(x81421),f319(f319(f75(x81421),x81422),x81423)),x81424))
% 22.40/22.31 [8143]~P74(x81431)+~P1(f319(f319(f226(x81431),f2(x81431)),x81433))+~P1(f319(f319(f225(x81431),x81432),f319(f319(f75(x81431),x81434),x81433)))+P1(f319(f319(f225(x81431),f319(f319(f282(x81431),x81432),x81433)),x81434))
% 22.40/22.31 [8145]~P75(x81451)+~P1(f319(f319(f226(x81451),f2(x81451)),x81453))+~P1(f319(f319(f225(x81451),x81452),f319(f319(f75(x81451),x81454),x81453)))+P1(f319(f319(f225(x81451),f319(f319(f282(x81451),x81452),x81453)),x81454))
% 22.40/22.31 [8146]~P74(x81461)+~P1(f319(f319(f226(x81461),f2(x81461)),x81463))+~P1(f319(f319(f226(x81461),x81462),f319(f319(f282(x81461),x81464),x81463)))+P1(f319(f319(f226(x81461),f319(f319(f75(x81461),x81462),x81463)),x81464))
% 22.40/22.31 [8147]~P75(x81471)+~P1(f319(f319(f226(x81471),f2(x81471)),x81473))+~P1(f319(f319(f226(x81471),x81472),f319(f319(f282(x81471),x81474),x81473)))+P1(f319(f319(f226(x81471),f319(f319(f75(x81471),x81472),x81473)),x81474))
% 22.40/22.31 [8148]~P74(x81481)+~P1(f319(f319(f226(x81481),f2(x81481)),x81483))+~P1(f319(f319(f226(x81481),x81482),f319(f319(f75(x81481),x81484),x81483)))+P1(f319(f319(f226(x81481),f319(f319(f282(x81481),x81482),x81483)),x81484))
% 22.40/22.31 [8150]~P75(x81501)+~P1(f319(f319(f226(x81501),f2(x81501)),x81503))+~P1(f319(f319(f226(x81501),x81502),f319(f319(f75(x81501),x81504),x81503)))+P1(f319(f319(f226(x81501),f319(f319(f282(x81501),x81502),x81503)),x81504))
% 22.40/22.31 [8280]~P74(x82801)+~P1(f319(f319(f226(x82801),f2(x82801)),x82804))+P1(f319(f319(f225(x82801),x82802),f319(f319(f75(x82801),x82803),x82804)))+~P1(f319(f319(f225(x82801),f319(f319(f282(x82801),x82802),x82804)),x82803))
% 22.40/22.31 [8281]~P74(x82811)+~P1(f319(f319(f226(x82811),f2(x82811)),x82814))+P1(f319(f319(f225(x82811),x82812),f319(f319(f282(x82811),x82813),x82814)))+~P1(f319(f319(f225(x82811),f319(f319(f75(x82811),x82812),x82814)),x82813))
% 22.40/22.31 [8283]~P75(x82831)+~P1(f319(f319(f226(x82831),f2(x82831)),x82834))+P1(f319(f319(f225(x82831),x82832),f319(f319(f75(x82831),x82833),x82834)))+~P1(f319(f319(f225(x82831),f319(f319(f282(x82831),x82832),x82834)),x82833))
% 22.40/22.31 [8284]~P75(x82841)+~P1(f319(f319(f226(x82841),f2(x82841)),x82844))+P1(f319(f319(f225(x82841),x82842),f319(f319(f282(x82841),x82843),x82844)))+~P1(f319(f319(f225(x82841),f319(f319(f75(x82841),x82842),x82844)),x82843))
% 22.40/22.31 [8285]~P74(x82851)+~P1(f319(f319(f226(x82851),f2(x82851)),x82854))+P1(f319(f319(f226(x82851),x82852),f319(f319(f75(x82851),x82853),x82854)))+~P1(f319(f319(f226(x82851),f319(f319(f282(x82851),x82852),x82854)),x82853))
% 22.40/22.31 [8286]~P74(x82861)+~P1(f319(f319(f226(x82861),f2(x82861)),x82864))+P1(f319(f319(f226(x82861),x82862),f319(f319(f282(x82861),x82863),x82864)))+~P1(f319(f319(f226(x82861),f319(f319(f75(x82861),x82862),x82864)),x82863))
% 22.40/22.31 [8288]~P75(x82881)+~P1(f319(f319(f226(x82881),f2(x82881)),x82884))+P1(f319(f319(f226(x82881),x82882),f319(f319(f75(x82881),x82883),x82884)))+~P1(f319(f319(f226(x82881),f319(f319(f282(x82881),x82882),x82884)),x82883))
% 22.40/22.31 [8289]~P75(x82891)+~P1(f319(f319(f226(x82891),f2(x82891)),x82894))+P1(f319(f319(f226(x82891),x82892),f319(f319(f282(x82891),x82893),x82894)))+~P1(f319(f319(f226(x82891),f319(f319(f75(x82891),x82892),x82894)),x82893))
% 22.40/22.31 [8445]~P75(x84451)+~P1(f319(f319(f226(x84451),x84453),f2(x84451)))+~P1(f319(f319(f225(x84451),f319(f319(f282(x84451),x84454),x84453)),x84452))+P1(f319(f319(f225(x84451),f319(f319(f75(x84451),x84452),x84453)),x84454))
% 22.40/22.31 [8446]~P75(x84461)+~P1(f319(f319(f226(x84461),x84463),f2(x84461)))+~P1(f319(f319(f225(x84461),f319(f319(f75(x84461),x84464),x84463)),x84462))+P1(f319(f319(f225(x84461),f319(f319(f282(x84461),x84462),x84463)),x84464))
% 22.40/22.31 [8447]~P75(x84471)+~P1(f319(f319(f226(x84471),x84473),f2(x84471)))+~P1(f319(f319(f226(x84471),f319(f319(f282(x84471),x84474),x84473)),x84472))+P1(f319(f319(f226(x84471),f319(f319(f75(x84471),x84472),x84473)),x84474))
% 22.40/22.31 [8448]~P75(x84481)+~P1(f319(f319(f226(x84481),x84483),f2(x84481)))+~P1(f319(f319(f226(x84481),f319(f319(f75(x84481),x84484),x84483)),x84482))+P1(f319(f319(f226(x84481),f319(f319(f282(x84481),x84482),x84483)),x84484))
% 22.40/22.31 [8460]~P1(f319(x84601,x84604))+~P1(f319(f319(f226(a906),x84602),f319(f319(f75(a906),x84603),f319(a104,x84604))))+P1(f319(x84601,f319(f319(f30(a906),x84602),x84603)))+~P1(f319(f319(f225(a906),f319(f319(f75(a906),x84603),x84604)),x84602))
% 22.40/22.31 [8671]~P106(x86711)+~P1(f319(f55(x86711),x86714))+~P1(f319(f319(f321(x86711),x86712),x86714))+P1(f319(f319(f225(x86711),f319(f319(f93(x86711),x86712),x86713)),f319(f319(f58(x86711,x86711,f93(x86711)),x86713),x86714)))
% 22.40/22.31 [8672]~P4(x86721)+~P1(f319(f55(x86721),x86724))+~P1(f319(f319(f321(x86721),x86722),x86724))+P1(f319(f319(f225(x86721),f319(f319(f180(x86721),x86722),x86723)),f319(f319(f58(x86721,x86721,f180(x86721)),x86723),x86724)))
% 22.40/22.31 [8818]~P1(f319(f55(x88181),x88182))+E(f319(f29(x88181),f319(f319(f3(f913(x88181,a904)),x88182),f319(f319(f301(x88181),x88183),x88184))),f319(f319(f3(a906),f319(f29(x88181),f319(f319(f3(f913(x88181,a904)),x88182),x88184))),f72(a906)))+P1(f319(f319(f321(x88181),x88183),x88184))+~P1(f319(f319(f321(x88181),x88183),x88182))
% 22.40/22.31 [8895]E(f319(f319(f74(a1),f398(x88951,x88952,x88953,x88954)),f399(x88951,x88952,x88953,x88954)),x88954)+~P1(f319(f319(f226(a1),f2(a1)),x88953))+~P1(f319(f319(f225(a1),x88954),x88951))+P1(f319(f319(f225(a1),f319(f319(f3(a1),x88954),x88953)),x88951))
% 22.40/22.31 [8896]E(f319(f319(f74(a1),f416(x88961,x88962,x88963,x88964)),f417(x88961,x88962,x88963,x88964)),x88964)+~P1(f319(f319(f226(a1),f2(a1)),x88963))+~P1(f319(f319(f226(a1),x88964),x88961))+P1(f319(f319(f226(a1),f319(f319(f3(a1),x88964),x88963)),x88961))
% 22.40/22.31 [9111]~P1(f319(f319(f226(a1),f2(a1)),x91113))+~P1(f319(f319(f225(a1),x91114),x91111))+P1(f319(f319(f321(a1),f398(x91111,x91112,x91113,x91114)),x91112))+P1(f319(f319(f225(a1),f319(f319(f3(a1),x91114),x91113)),x91111))
% 22.40/22.31 [9112]~P1(f319(f319(f226(a1),f2(a1)),x91123))+~P1(f319(f319(f226(a1),x91124),x91121))+P1(f319(f319(f321(a1),f416(x91121,x91122,x91123,x91124)),x91122))+P1(f319(f319(f226(a1),f319(f319(f3(a1),x91124),x91123)),x91121))
% 22.40/22.31 [9187]~P1(f319(f319(f226(a1),f2(a1)),x91872))+~P1(f319(f319(f225(a1),x91871),x91873))+P1(f319(f319(f321(a1),f399(x91873,x91874,x91872,x91871)),f295(a1,f72(a1),x91872)))+P1(f319(f319(f225(a1),f319(f319(f3(a1),x91871),x91872)),x91873))
% 22.40/22.31 [9188]~P1(f319(f319(f226(a1),f2(a1)),x91882))+~P1(f319(f319(f226(a1),x91881),x91883))+P1(f319(f319(f321(a1),f417(x91883,x91884,x91882,x91881)),f295(a1,f72(a1),x91882)))+P1(f319(f319(f226(a1),f319(f319(f3(a1),x91881),x91882)),x91883))
% 22.40/22.31 [9205]~P1(f319(f319(f225(a1),f2(a1)),x92054))+~P1(f319(f319(f226(a1),f2(a1)),x92053))+~P1(f319(f319(f226(a1),x92054),x92051))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f74(a1),f319(f319(f75(a1),x92051),f39(a1,x92052,x92053))),x92054)))
% 22.40/22.31 [9241]E(x92411,x92412)+~P39(x92413,x92414)+~P1(f319(f319(f321(f912(x92413,x92413)),f319(f319(f244(x92413,x92413),x92412),x92411)),x92414))+~P1(f319(f319(f321(f912(x92413,x92413)),f319(f319(f244(x92413,x92413),x92411),x92412)),x92414))
% 22.40/22.31 [9279]~P107(x92791)+~P1(f319(f55(x92791),x92794))+~P1(f319(f319(f225(x92791),x92792),f378(x92793,x92792,x92794,x92791)))+P1(f319(f319(f225(x92791),f319(f319(f94(x92791),x92792),x92793)),f319(f319(f58(x92791,x92791,f94(x92791)),x92793),x92794)))
% 22.40/22.31 [9280]~P4(x92801)+~P1(f319(f55(x92801),x92804))+~P1(f319(f319(f225(x92801),x92802),f379(x92803,x92802,x92804,x92801)))+P1(f319(f319(f225(x92801),f319(f319(f230(x92801),x92802),x92803)),f319(f319(f58(x92801,x92801,f230(x92801)),x92803),x92804)))
% 22.40/22.31 [9294]~P1(f319(f319(f225(a1),x92944),f2(a1)))+~P1(f319(f319(f226(a1),f2(a1)),x92942))+~P1(f319(f319(f226(a1),x92941),x92944))+P1(f319(f319(f226(a1),f319(f319(f75(a1),x92941),x92942)),f319(f319(f74(a1),f319(f319(f75(a1),x92941),f39(a1,x92943,x92942))),x92944)))
% 22.40/22.31 [9320]P1(f319(f55(x93201),x93202))+~P1(f319(f55(x93201),x93203))+~P1(f319(f319(f321(f913(x93201,a904)),x93202),f319(f319(f54(x93201),x93203),x93204)))+~P1(f319(f319(f225(f913(f912(x93201,x93201),a904)),x93204),f319(f319(f246(x93201,x93201),x93203),f319(f18(f913(x93201,a904),x93201),x93203))))
% 22.40/22.31 [9343]~P4(x93431)+~P1(f319(f55(x93431),x93434))+P1(f319(f319(f321(x93431),f379(x93432,x93433,x93434,x93431)),x93434))+P1(f319(f319(f225(x93431),f319(f319(f230(x93431),x93433),x93432)),f319(f319(f58(x93431,x93431,f230(x93431)),x93432),x93434)))
% 22.40/22.31 [9344]~P107(x93441)+~P1(f319(f55(x93441),x93444))+P1(f319(f319(f321(x93441),f378(x93442,x93443,x93444,x93441)),x93444))+P1(f319(f319(f225(x93441),f319(f319(f94(x93441),x93443),x93442)),f319(f319(f58(x93441,x93441,f94(x93441)),x93442),x93444)))
% 22.40/22.31 [9356]~P40(f913(x93561,a904),f913(x93561,a904),x93563)+~P1(f319(f319(f321(x93561),x93562),x93564))+P1(f319(f319(f321(x93561),x93562),f88(f913(x93561,a904),x93563)))+~P1(f319(f319(f225(f913(x93561,a904)),x93564),f319(x93563,f319(f319(f93(f913(x93561,a904)),x93564),f88(f913(x93561,a904),x93563)))))
% 22.40/22.31 [9537]~P40(f913(x95373,a904),f913(x95373,a904),x95374)+P1(f319(x95371,x95372))+~P1(f319(f319(f321(x95373),x95372),f87(f913(x95373,a904),x95374)))+P1(f319(f319(f321(x95373),f595(x95371,x95374,x95372,x95373)),f319(x95374,f319(f319(f94(f913(x95373,a904)),f87(f913(x95373,a904),x95374)),f319(f254(x95373),x95371)))))
% 22.40/22.31 [9771]~P1(f319(f55(x97712),x97714))+~P1(f319(f55(x97711),x97713))+~P1(f319(f319(f225(a906),f319(f29(x97712),x97714)),f319(f29(x97711),x97713)))+P1(f319(f319(f225(f913(x97711,a904)),f319(f302(x97712,x97711,f895(x97713,x97711,x97714,x97712)),x97714)),x97713))
% 22.40/22.31 [9394]~P1(f319(f319(f321(x93941),x93942),x93944))+P1(f319(f319(f321(x93941),x93942),x93943))+~P1(f319(f319(f226(f913(x93941,a904)),x93944),f319(f319(f301(x93941),x93942),x93943)))+P1(f319(f319(f226(f913(x93941,a904)),f319(f319(f3(f913(x93941,a904)),x93944),f319(f319(f301(x93941),x93942),f181(f913(x93941,a904))))),x93943))
% 22.40/22.31 [9564]~P1(f319(f319(f321(x95641),x95642),x95644))+P1(f319(f319(f321(x95641),x95642),x95643))+P1(f319(f319(f226(f913(x95641,a904)),x95644),f319(f319(f301(x95641),x95642),x95643)))+~P1(f319(f319(f226(f913(x95641,a904)),f319(f319(f3(f913(x95641,a904)),x95644),f319(f319(f301(x95641),x95642),f181(f913(x95641,a904))))),x95643))
% 22.40/22.31 [9587]P1(f319(f319(f321(x95871),x95872),x95873))+~P1(f319(f319(f225(f913(x95871,a904)),x95874),x95873))+P1(f319(f319(f226(f913(x95871,a904)),x95874),f319(f319(f301(x95871),x95872),x95873)))+~P1(f319(f319(f226(f913(x95871,a904)),f319(f319(f3(f913(x95871,a904)),x95874),f319(f319(f301(x95871),x95872),f181(f913(x95871,a904))))),x95873))
% 22.40/22.31 [9592]~P1(f319(f319(f321(x95921),x95923),x95922))+~P1(f319(f319(f226(f913(x95921,a904)),x95922),x95924))+P1(f319(f319(f226(f913(x95921,a904)),x95922),f319(f319(f301(x95921),x95923),x95924)))+~P1(f319(f319(f226(f913(x95921,a904)),f319(f319(f3(f913(x95921,a904)),x95922),f319(f319(f301(x95921),x95923),f181(f913(x95921,a904))))),x95924))
% 22.40/22.31 [9608]~P1(f319(f319(f225(f913(x96081,a904)),x96082),x96084))+~P1(f319(f319(f226(f913(x96081,a904)),x96082),x96084))+P1(f319(f319(f226(f913(x96081,a904)),x96082),f319(f319(f301(x96081),x96083),x96084)))+~P1(f319(f319(f226(f913(x96081,a904)),f319(f319(f3(f913(x96081,a904)),x96082),f319(f319(f301(x96081),x96083),f181(f913(x96081,a904))))),x96084))
% 22.40/22.31 [9666]~P111(x96662)+~P71(x96661)+~P1(f319(f319(f225(f913(x96661,x96662)),x96663),x96664))+P1(f319(f51(x96661),f319(f319(f20(x96661,x96662,a904),f319(f319(f10(x96662,f913(x96662,a904),x96661),f225(x96662)),x96663)),x96664)))
% 22.40/22.31 [9822]~P111(x98222)+~P71(x98221)+P1(f319(f319(f225(f913(x98221,x98222)),x98223),x98224))+~P1(f319(f51(x98221),f319(f319(f20(x98221,x98222,a904),f319(f319(f10(x98222,f913(x98222,a904),x98221),f225(x98222)),x98223)),x98224)))
% 22.40/22.31 [10340]~P40(f913(x103401,a904),f913(x103401,a904),x103403)+~P1(f319(f319(f321(x103401),x103402),x103404))+P1(f319(f319(f321(x103401),x103402),f88(f913(x103401,a904),x103403)))+~P1(f319(f319(f225(f913(x103401,a904)),x103404),f319(x103403,f87(f913(x103401,a904),f319(f319(f9(f913(x103401,a904),f913(x103401,a904),f913(x103401,a904)),f319(f319(f10(f913(x103401,a904),f913(f913(x103401,a904),f913(x103401,a904)),f913(x103401,a904)),f93(f913(x103401,a904))),f319(f319(f9(f913(x103401,a904),f913(x103401,a904),f913(x103401,a904)),f319(f319(f10(f913(x103401,a904),f913(f913(x103401,a904),f913(x103401,a904)),f913(x103401,a904)),f93(f913(x103401,a904))),x103403)),x103404))),f88(f913(x103401,a904),x103403))))))
% 22.40/22.31 [9998]E(f319(f319(f156(x99981),f319(f319(f156(f907(x99981)),f171(x99981,x99982)),x99983)),x99984),f319(f319(f156(x99981),f319(f319(f156(f907(x99981)),x99982),x99984)),x99983))+~P1(f319(f319(f226(a906),x99983),f319(f182(f907(f907(x99981))),f171(x99981,x99982))))+~P13(a906,f319(f160(a906),f319(f319(f146(f907(x99981),a906),f182(f907(x99981))),x99982)))+~P1(f319(f319(f226(a906),x99984),f319(f182(f907(f907(x99981))),f319(f128(f907(x99981),f319(f319(f10(a906,a904,f907(x99981)),f319(f226(a906),x99983)),f182(f907(x99981)))),x99982))))
% 22.40/22.31 [10019]~P1(f319(f319(f321(f912(a906,a906)),x100194),x100191))+~P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),x100194),x100192)),a26))+~P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),x100191),x100193)),a27))+P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),x100191),f319(f319(f301(f912(a906,a906)),x100192),x100193))),a27))
% 22.40/22.31 [10020]~P1(f319(f319(f321(f912(a906,a906)),x100204),x100201))+~P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),x100204),x100202)),a64))+~P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),x100201),x100203)),a65))+P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),x100201),f319(f319(f301(f912(a906,a906)),x100202),x100203))),a65))
% 22.40/22.31 [9914]~P111(x99142)+~P71(x99141)+~P1(f319(f319(f226(f913(x99141,x99142)),x99143),x99144))+P1(f319(f50(x99141),f319(f319(f10(a904,a904,x99141),a314),f319(f319(f20(x99141,x99142,a904),f319(f319(f10(x99142,f913(x99142,a904),x99141),a316),x99143)),x99144))))
% 22.40/22.31 [10030]~P1(f319(f319(f321(f912(a906,a906)),x100304),x100303))+~P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),x100301),x100304)),a26))+~P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),x100302),x100303)),a28))+P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),f319(f319(f301(f912(a906,a906)),x100301),x100302)),x100303)),a28))
% 22.40/22.31 [10031]~P1(f319(f319(f321(f912(a906,a906)),x100314),x100313))+~P1(f319(f319(f321(f912(f912(a906,a906),f912(a906,a906))),f319(f319(f244(f912(a906,a906),f912(a906,a906)),x100311),x100314)),a64))+~P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),x100312),x100313)),a63))+P1(f319(f319(f321(f912(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904))),f319(f319(f244(f913(f912(a906,a906),a904),f913(f912(a906,a906),a904)),f319(f319(f301(f912(a906,a906)),x100311),x100312)),x100313)),a63))
% 22.40/22.31 [6148]~P7(x61484,x61481)+~P1(f319(f319(x61481,x61482),x61485))+P1(f319(f319(x61481,x61482),x61483))+~P1(f319(f319(x61481,x61485),x61483))
% 22.40/22.31 [6149]~P51(x61494,x61491)+~P1(f319(f319(x61491,x61492),x61495))+P1(f319(f319(x61491,x61492),x61493))+~P1(f319(f319(x61491,x61495),x61493))
% 22.40/22.31 [6150]~P16(x61504,x61501)+~P1(f319(f319(x61501,x61502),x61505))+P1(f319(f319(x61501,x61502),x61503))+~P1(f319(f319(x61501,x61505),x61503))
% 22.40/22.31 [8803]~P7(x88034,x88033)+~P1(f319(x88031,x88035))+P1(f319(x88032,f826(x88032,x88031,x88033,x88034)))+P1(f319(x88031,f822(x88032,x88031,x88033,x88034)))
% 22.40/22.31 [9047]~P7(x90474,x90473)+~P1(f319(x90472,x90475))+~P1(f319(x90471,f822(x90471,x90472,x90473,x90474)))+P1(f319(x90471,f826(x90471,x90472,x90473,x90474)))
% 22.40/22.31 [9218]~P7(x92184,x92183)+~P1(f319(x92181,x92185))+P1(f319(f319(f321(x92184),f826(x92182,x92181,x92183,x92184)),f262(x92184,x92183)))+P1(f319(x92181,f822(x92182,x92181,x92183,x92184)))
% 22.40/22.31 [9350]~P7(x93501,x93504)+~P1(f319(x93503,x93505))+~P1(f319(x93502,f822(x93502,x93503,x93504,x93501)))+P1(f319(f319(f321(x93501),f826(x93502,x93503,x93504,x93501)),f262(x93501,x93504)))
% 22.40/22.31 [9654]~P38(x96541,x96544)+P1(f319(f319(f321(f912(f907(x96541),f907(x96541))),f319(f319(f244(f907(x96541),f907(x96541)),x96542),x96543)),f139(x96541,x96544)))+~P1(f319(f319(f321(f912(f907(x96541),f907(x96541))),f319(f319(f244(f907(x96541),f907(x96541)),x96542),x96545)),f139(x96541,x96544)))+~P1(f319(f319(f321(f912(f907(x96541),f907(x96541))),f319(f319(f244(f907(x96541),f907(x96541)),x96545),x96543)),f139(x96541,x96544)))
% 22.40/22.31 [5387]~P67(x53875)+E(x53871,x53872)+~E(x53873,x53874)+~E(f319(f319(f3(x53875),x53873),x53874),f319(f319(f3(x53875),x53871),x53872))
% 22.40/22.31 [6264]~P18(x62645,x62641,x62643)+E(f319(f319(x62641,x62642),f319(x62643,x62644)),f319(x62643,x62644))+~P1(f319(f55(x62645),x62644))+~P1(f319(f319(f321(x62645),x62642),x62644))
% 22.40/22.31 [6449]~P65(x64491)+~E(f319(f319(f3(x64491),x64494),x64495),f319(f319(f3(x64491),x64492),x64493))+~P1(f319(f319(f225(x64491),x64494),x64495))+P1(f319(f319(f225(x64491),x64492),x64493))
% 22.40/22.31 [6451]~P65(x64511)+~E(f319(f319(f3(x64511),x64514),x64515),f319(f319(f3(x64511),x64512),x64513))+~P1(f319(f319(f226(x64511),x64514),x64515))+P1(f319(f319(f226(x64511),x64512),x64513))
% 22.40/22.31 [7420]~E(x74202,f319(f319(f143(x74201),x74204),x74205))+P1(f319(f319(f321(f907(x74201)),x74202),f153(x74201,x74203)))+~P1(f319(f319(f321(f907(x74201)),x74205),f153(x74201,x74203)))+~P1(f319(f319(f321(x74201),x74204),x74203))
% 22.40/22.31 [7811]~E(f319(f182(f907(x78111)),x78113),f319(f182(f907(x78112)),x78114))+~E(f319(f319(f146(f912(x78111,x78112),x78112),f248(x78111,x78112)),x78115),x78114)+~E(f319(f319(f146(f912(x78111,x78112),x78111),f243(x78111,x78112)),x78115),x78113)+E(f319(f319(f173(x78111,x78112),x78113),x78114),x78115)
% 22.40/22.31 [8137]~P111(x81371)+P1(f319(f319(f226(f913(x81371,a904)),f295(x81371,x81372,x81373)),f295(x81371,x81374,x81375)))+~P1(f319(f319(f225(x81371),x81374),x81375))+P1(f319(f319(f225(x81371),x81372),x81373))
% 22.40/22.31 [8238]~P111(x82381)+P1(f319(f319(f225(f913(x82381,a904)),f295(x82381,x82382,x82383)),f295(x82381,x82384,x82385)))+~P1(f319(f319(f225(x82381),x82383),x82385))+~P1(f319(f319(f225(x82381),x82384),x82382))
% 22.40/22.31 [8354]~P4(x83541)+P1(f319(f319(f225(x83541),x83542),x83543))+P1(f319(f319(f225(x83541),x83544),x83543))+~P1(f319(f319(f225(f913(x83541,a904)),f319(f294(x83541,x83543),x83542)),f319(f294(x83541,x83544),x83545)))
% 22.40/22.31 [8355]~P4(x83551)+P1(f319(f319(f225(x83551),x83552),x83553))+P1(f319(f319(f225(x83551),x83552),x83554))+~P1(f319(f319(f225(f913(x83551,a904)),f319(f294(x83551,x83553),x83552)),f319(f294(x83551,x83555),x83554)))
% 22.40/22.31 [8519]~P107(x85193)+~P107(x85191)+~P40(x85193,x85191,x85192)+P1(f319(f319(f225(x85191),f319(x85192,f319(f319(f94(x85193),x85194),x85195))),f319(f319(f94(x85191),f319(x85192,x85194)),f319(x85192,x85195))))
% 22.40/22.31 [8520]~P4(x85203)+~P107(x85201)+~P40(x85203,x85201,x85202)+P1(f319(f319(f225(x85201),f319(x85202,f319(f319(f230(x85203),x85204),x85205))),f319(f319(f94(x85201),f319(x85202,x85204)),f319(x85202,x85205))))
% 22.40/22.31 [8585]~P111(x85851)+~P1(f319(f319(f225(f913(x85851,a904)),f295(x85851,x85854,x85852)),f295(x85851,x85855,x85853)))+P1(f319(f319(f225(x85851),x85852),x85853))+~P1(f319(f319(f225(x85851),x85854),x85852))
% 22.40/22.31 [8586]~P111(x85861)+~P1(f319(f319(f226(f913(x85861,a904)),f295(x85861,x85864,x85862)),f295(x85861,x85865,x85863)))+P1(f319(f319(f225(x85861),x85862),x85863))+~P1(f319(f319(f225(x85861),x85864),x85862))
% 22.40/22.31 [8587]~P111(x85871)+~P1(f319(f319(f225(f913(x85871,a904)),f295(x85871,x85873,x85874)),f295(x85871,x85872,x85875)))+P1(f319(f319(f225(x85871),x85872),x85873))+~P1(f319(f319(f225(x85871),x85873),x85874))
% 22.40/22.31 [8588]~P111(x85881)+~P1(f319(f319(f226(f913(x85881,a904)),f295(x85881,x85883,x85884)),f295(x85881,x85882,x85885)))+P1(f319(f319(f225(x85881),x85882),x85883))+~P1(f319(f319(f225(x85881),x85883),x85884))
% 22.40/22.31 [6097]~P4(x60975)+~P4(x60971)+~P40(x60975,x60971,x60972)+E(f319(f319(f180(x60971),f319(x60972,x60973)),f319(x60972,x60974)),f319(x60972,f319(f319(f180(x60975),x60973),x60974)))
% 22.40/22.31 [6098]~P4(x60985)+~P4(x60981)+~P40(x60985,x60981,x60982)+E(f319(f319(f230(x60981),f319(x60982,x60983)),f319(x60982,x60984)),f319(x60982,f319(f319(f230(x60985),x60983),x60984)))
% 22.40/22.31 [6147]~P18(x61472,x61475,x61473)+E(x61471,f181(f913(x61472,a904)))+~P1(f319(f55(x61472),x61471))+E(f319(x61473,f319(f319(f301(x61472),x61474),x61471)),f319(f319(x61475,x61474),f319(x61473,x61471)))
% 22.40/22.31 [6923]~E(x69231,x69232)+~E(f319(f319(f94(f913(x69233,a904)),x69234),x69235),f181(f913(x69233,a904)))+~P1(f319(f319(f321(x69233),x69232),x69235))+~P1(f319(f319(f321(x69233),x69231),x69234))
% 22.40/22.31 [7000]~P19(x70002,x70005,x70001)+~P1(f319(f55(x70002),x70004))+E(f319(x70001,f319(f319(f301(x70002),x70003),x70004)),f319(f319(f58(x70002,x70002,x70005),x70003),x70004))+P1(f319(f319(f321(x70002),x70003),x70004))
% 22.40/22.31 [7067]~P76(x70672)+~P1(f319(f55(x70671),x70675))+E(f319(f319(f8(x70671,x70672),x70673),f319(f319(f301(x70671),x70674),x70675)),f319(f319(f74(x70672),f319(x70673,x70674)),f319(f319(f8(x70671,x70672),x70673),x70675)))+P1(f319(f319(f321(x70671),x70674),x70675))
% 22.40/22.31 [7069]~P82(x70692)+~P1(f319(f55(x70691),x70695))+E(f319(f319(f11(x70691,x70692),x70693),f319(f319(f301(x70691),x70694),x70695)),f319(f319(f75(x70692),f319(x70693,x70694)),f319(f319(f11(x70691,x70692),x70693),x70695)))+P1(f319(f319(f321(x70691),x70694),x70695))
% 22.40/22.31 [7561]~P19(x75612,x75615,x75611)+~P1(f319(f55(x75612),x75614))+E(f319(x75611,f319(f319(f301(x75612),x75613),x75614)),x75613)+~E(f319(f319(f3(f913(x75612,a904)),x75614),f319(f319(f301(x75612),x75613),f181(f913(x75612,a904)))),f181(f913(x75612,a904)))
% 22.40/22.31 [7884]~P119(x78841)+~P1(f319(f319(f279(x78841),x78842),x78844))+~P1(f319(f319(f225(a906),x78843),x78845))+P1(f319(f319(f279(x78841),f319(f319(f236(x78841),x78842),x78843)),f319(f319(f236(x78841),x78844),x78845)))
% 22.40/22.31 [7917]~P106(x79171)+~P1(f319(f319(f225(x79171),x79173),x79175))+~P1(f319(f319(f225(x79171),x79172),x79174))+P1(f319(f319(f225(x79171),f319(f319(f93(x79171),x79172),x79173)),f319(f319(f93(x79171),x79174),x79175)))
% 22.40/22.31 [7918]~P107(x79181)+~P1(f319(f319(f225(x79181),x79183),x79185))+~P1(f319(f319(f225(x79181),x79182),x79184))+P1(f319(f319(f225(x79181),f319(f319(f94(x79181),x79182),x79183)),f319(f319(f94(x79181),x79184),x79185)))
% 22.40/22.31 [7919]~P4(x79191)+~P1(f319(f319(f225(x79191),x79193),x79195))+~P1(f319(f319(f225(x79191),x79192),x79194))+P1(f319(f319(f225(x79191),f319(f319(f180(x79191),x79192),x79193)),f319(f319(f180(x79191),x79194),x79195)))
% 22.40/22.31 [7920]~P4(x79201)+~P1(f319(f319(f225(x79201),x79203),x79205))+~P1(f319(f319(f225(x79201),x79202),x79204))+P1(f319(f319(f225(x79201),f319(f319(f230(x79201),x79202),x79203)),f319(f319(f230(x79201),x79204),x79205)))
% 22.40/22.31 [7921]~P91(x79211)+~P1(f319(f319(f225(x79211),x79213),x79215))+~P1(f319(f319(f225(x79211),x79212),x79214))+P1(f319(f319(f225(x79211),f319(f319(f74(x79211),x79212),x79213)),f319(f319(f74(x79211),x79214),x79215)))
% 22.40/22.31 [7922]~P89(x79221)+~P1(f319(f319(f225(x79221),x79223),x79225))+~P1(f319(f319(f226(x79221),x79222),x79224))+P1(f319(f319(f226(x79221),f319(f319(f74(x79221),x79222),x79223)),f319(f319(f74(x79221),x79224),x79225)))
% 22.40/22.31 [7923]~P89(x79231)+~P1(f319(f319(f225(x79231),x79232),x79234))+~P1(f319(f319(f226(x79231),x79233),x79235))+P1(f319(f319(f226(x79231),f319(f319(f74(x79231),x79232),x79233)),f319(f319(f74(x79231),x79234),x79235)))
% 22.40/22.31 [7924]~P89(x79241)+~P1(f319(f319(f226(x79241),x79243),x79245))+~P1(f319(f319(f226(x79241),x79242),x79244))+P1(f319(f319(f226(x79241),f319(f319(f74(x79241),x79242),x79243)),f319(f319(f74(x79241),x79244),x79245)))
% 22.40/22.31 [8055]~P143(x80555)+E(x80551,x80552)+E(x80553,x80554)+~E(f319(f319(f74(x80555),f319(f319(f75(x80555),x80553),x80551)),f319(f319(f75(x80555),x80554),x80552)),f319(f319(f74(x80555),f319(f319(f75(x80555),x80553),x80552)),f319(f319(f75(x80555),x80554),x80551)))
% 22.40/22.31 [8258]~P4(x82584)+~P1(f319(f129(x82581),x82583))+P1(f319(f319(f321(x82581),x82582),f319(f164(x82581),x82583)))+P1(f319(f129(x82581),f319(f319(f140(x82581,x82584,x82585),x82582),x82583)))
% 22.40/22.31 [8401]~P67(x84011)+E(f319(f319(f3(x84011),f319(f319(f8(a906,x84011),x84012),f319(f294(a906,x84013),x84014))),f319(f319(f8(a906,x84011),x84012),f319(f294(a906,x84013),x84015))),f319(f319(f8(a906,x84011),x84012),f319(f294(a906,x84015),x84014)))+~P1(f319(f319(f225(a906),x84015),x84014))+~P1(f319(f319(f225(a906),x84013),x84015))
% 22.40/22.31 [8402]~P76(x84021)+E(f319(f319(f74(x84021),f319(f319(f8(a906,x84021),x84022),f319(f294(a906,x84023),x84024))),f319(f319(f8(a906,x84021),x84022),f319(f294(a906,x84024),x84025))),f319(f319(f8(a906,x84021),x84022),f319(f294(a906,x84023),x84025)))+~P1(f319(f319(f225(a906),x84024),x84025))+~P1(f319(f319(f225(a906),x84023),x84024))
% 22.40/22.31 [8731]~P73(x87312)+E(x87311,f2(x87312))+E(x87313,f2(x87312))+E(f319(f319(f282(x87312),f319(f319(f3(x87312),f319(f319(f75(x87312),x87314),x87311)),f319(f319(f75(x87312),x87315),x87313))),f319(f319(f75(x87312),x87313),x87311)),f319(f319(f3(x87312),f319(f319(f282(x87312),x87314),x87313)),f319(f319(f282(x87312),x87315),x87311)))
% 22.40/22.31 [8732]~P73(x87322)+E(x87321,f2(x87322))+E(x87323,f2(x87322))+E(f319(f319(f282(x87322),f319(f319(f74(x87322),f319(f319(f75(x87322),x87324),x87321)),f319(f319(f75(x87322),x87325),x87323))),f319(f319(f75(x87322),x87323),x87321)),f319(f319(f74(x87322),f319(f319(f282(x87322),x87324),x87323)),f319(f319(f282(x87322),x87325),x87321)))
% 22.40/22.31 [8741]~E(x87412,f319(x87413,x87411))+E(x87411,f613(x87412,x87413,x87414,x87415))+~P25(x87415,x87414,x87413,f234(f913(x87415,a904)))+~P1(f319(f319(f321(x87414),x87412),f319(f302(x87415,x87414,x87413),f234(f913(x87415,a904)))))
% 22.40/22.31 [8955]~P113(x89551)+~P1(f319(f319(f226(x89551),f319(f69(x89551),x89552)),x89554))+P1(f319(f319(f226(x89551),f319(f319(f75(x89551),f319(f69(x89551),x89552)),f319(f69(x89551),x89553))),f319(f319(f75(x89551),x89554),x89555)))+~P1(f319(f319(f226(x89551),f319(f69(x89551),x89553)),x89555))
% 22.40/22.31 [9073]~P25(x90731,x90733,x90735,x90732)+~P1(f319(f55(x90733),x90734))+P1(f319(f319(f225(a906),f319(f29(x90731),x90732)),f319(f29(x90733),x90734)))+~P1(f319(f319(f225(f913(x90733,a904)),f319(f302(x90731,x90733,x90735),x90732)),x90734))
% 22.40/22.31 [9140]~P76(x91402)+~P25(x91401,x91401,x91404,x91405)+~P1(f319(f55(x91401),x91405))+E(f319(f319(f8(x91401,x91402),f319(f66(x91401,x91402,x91401,x91403),x91404)),x91405),f319(f319(f8(x91401,x91402),x91403),f319(f302(x91401,x91401,x91404),x91405)))
% 22.40/22.31 [9141]~P82(x91412)+~P25(x91411,x91411,x91414,x91415)+~P1(f319(f55(x91411),x91415))+E(f319(f319(f11(x91411,x91412),f319(f66(x91411,x91412,x91411,x91413),x91414)),x91415),f319(f319(f11(x91411,x91412),x91413),f319(f302(x91411,x91411,x91414),x91415)))
% 22.40/22.31 [9250]~P37(x92501,x92502)+~P1(f319(f319(f321(x92501),x92503),x92504))+~P1(f319(f319(f321(x92501),x92505),x92504))+~P1(f319(f319(f321(f912(x92501,x92501)),f319(f319(f244(x92501,x92501),x92505),f594(x92502,x92501,x92504))),x92502))
% 22.40/22.31 [9293]~P25(x92932,x92933,x92935,x92931)+E(x92931,f181(f913(x92932,a904)))+E(f319(f302(x92933,x92932,f482(x92934,x92933,x92932,x92931)),x92934),x92931)+~P1(f319(f319(f225(f913(x92933,a904)),f319(f302(x92932,x92933,x92935),x92931)),x92934))
% 22.40/22.31 [9802]~P4(x98025)+~P5(x98025)+P1(f319(f319(f321(x98021),f473(x98022,x98023,x98021,x98024,x98025)),x98023))+~P1(f319(f319(f226(x98025),x98024),f319(f319(f33(x98021,x98025),x98023),x98022)))
% 22.40/22.31 [9807]~P4(x98071)+~P5(x98071)+P1(f319(f319(f226(x98071),x98072),f319(x98073,f473(x98073,x98074,x98075,x98072,x98071))))+~P1(f319(f319(f226(x98071),x98072),f319(f319(f33(x98075,x98071),x98074),x98073)))
% 22.40/22.31 [9893]~P77(x98931)+~P1(f319(f60(x98931,x98931,f75(x98931),x98932,x98933),x98935))+P1(f319(f319(f321(x98931),x98932),x98933))+P1(f319(f60(x98931,x98931,f75(x98931),x98934,f319(f319(f301(x98931),x98932),x98933)),f319(f319(f75(x98931),x98934),x98935)))
% 22.40/22.31 [10083]~P76(x100832)+~P1(f319(f55(x100831),x100835))+E(f319(f319(f8(x100831,x100832),f319(f319(f9(x100831,x100832,x100832),f319(f319(f20(x100831,x100832,f913(x100832,x100832)),f319(f319(f10(a904,f913(x100832,f913(x100832,x100832)),x100831),f86(x100832)),f319(a316,x100833))),x100834)),f2(x100832))),x100835),f2(x100832))+P1(f319(f319(f321(x100831),x100833),x100835))
% 22.40/22.31 [10084]~P82(x100842)+~P1(f319(f55(x100841),x100845))+E(f319(f319(f11(x100841,x100842),f319(f319(f9(x100841,x100842,x100842),f319(f319(f20(x100841,x100842,f913(x100842,x100842)),f319(f319(f10(a904,f913(x100842,f913(x100842,x100842)),x100841),f86(x100842)),f319(a316,x100843))),x100844)),f72(x100842))),x100845),f72(x100842))+P1(f319(f319(f321(x100841),x100843),x100845))
% 22.40/22.31 [10085]~P76(x100852)+~P1(f319(f55(x100851),x100855))+E(f319(f319(f8(x100851,x100852),f319(f319(f9(x100851,x100852,x100852),f319(f319(f20(x100851,x100852,f913(x100852,x100852)),f319(f319(f10(a904,f913(x100852,f913(x100852,x100852)),x100851),f86(x100852)),f319(a316,x100853))),x100854)),f2(x100852))),x100855),f319(x100854,x100853))+~P1(f319(f319(f321(x100851),x100853),x100855))
% 22.40/22.31 [10086]~P82(x100862)+~P1(f319(f55(x100861),x100865))+E(f319(f319(f11(x100861,x100862),f319(f319(f9(x100861,x100862,x100862),f319(f319(f20(x100861,x100862,f913(x100862,x100862)),f319(f319(f10(a904,f913(x100862,f913(x100862,x100862)),x100861),f86(x100862)),f319(a316,x100863))),x100864)),f72(x100862))),x100865),f319(x100864,x100863))+~P1(f319(f319(f321(x100861),x100863),x100865))
% 22.40/22.31 [10136]~P76(x101362)+~P1(f319(f55(x101361),x101365))+E(f319(f319(f8(x101361,x101362),f319(f319(f9(x101361,x101362,x101362),f319(f319(f20(x101361,x101362,f913(x101362,x101362)),f319(f319(f10(a904,f913(x101362,f913(x101362,x101362)),x101361),f86(x101362)),f319(f319(f9(x101361,x101361,a904),a316),x101363))),x101364)),f2(x101362))),x101365),f2(x101362))+P1(f319(f319(f321(x101361),x101363),x101365))
% 22.40/22.31 [10137]~P82(x101372)+~P1(f319(f55(x101371),x101375))+E(f319(f319(f11(x101371,x101372),f319(f319(f9(x101371,x101372,x101372),f319(f319(f20(x101371,x101372,f913(x101372,x101372)),f319(f319(f10(a904,f913(x101372,f913(x101372,x101372)),x101371),f86(x101372)),f319(f319(f9(x101371,x101371,a904),a316),x101373))),x101374)),f72(x101372))),x101375),f72(x101372))+P1(f319(f319(f321(x101371),x101373),x101375))
% 22.40/22.31 [10139]~P76(x101392)+~P1(f319(f55(x101391),x101395))+E(f319(f319(f8(x101391,x101392),f319(f319(f9(x101391,x101392,x101392),f319(f319(f20(x101391,x101392,f913(x101392,x101392)),f319(f319(f10(a904,f913(x101392,f913(x101392,x101392)),x101391),f86(x101392)),f319(f319(f9(x101391,x101391,a904),a316),x101393))),x101394)),f2(x101392))),x101395),f319(x101394,x101393))+~P1(f319(f319(f321(x101391),x101393),x101395))
% 22.40/22.31 [10140]~P82(x101402)+~P1(f319(f55(x101401),x101405))+E(f319(f319(f11(x101401,x101402),f319(f319(f9(x101401,x101402,x101402),f319(f319(f20(x101401,x101402,f913(x101402,x101402)),f319(f319(f10(a904,f913(x101402,f913(x101402,x101402)),x101401),f86(x101402)),f319(f319(f9(x101401,x101401,a904),a316),x101403))),x101404)),f72(x101402))),x101405),f319(x101404,x101403))+~P1(f319(f319(f321(x101401),x101403),x101405))
% 22.40/22.31 [7916]~P67(x79162)+~P1(f319(f55(x79161),x79164))+E(f319(f319(f8(x79161,x79162),x79163),f319(f319(f3(f913(x79161,a904)),x79164),f319(f319(f301(x79161),x79165),f181(f913(x79161,a904))))),f319(f319(f8(x79161,x79162),x79163),x79164))+P1(f319(f319(f321(x79161),x79165),x79164))
% 22.40/22.31 [8410]~P124(x84102)+~P1(f319(f55(x84101),x84104))+E(f319(f319(f8(x84101,x84102),x84103),f319(f319(f3(f913(x84101,a904)),x84104),f319(f319(f301(x84101),x84105),f181(f913(x84101,a904))))),f319(f319(f3(x84102),f319(f319(f8(x84101,x84102),x84103),x84104)),f319(x84103,x84105)))+~P1(f319(f319(f321(x84101),x84105),x84104))
% 22.40/22.31 [8411]~P67(x84112)+~P1(f319(f55(x84111),x84114))+E(f319(f319(f8(x84111,x84112),x84113),f319(f319(f3(f913(x84111,a904)),x84114),f319(f319(f301(x84111),x84115),f181(f913(x84111,a904))))),f319(f319(f3(x84112),f319(f319(f8(x84111,x84112),x84113),x84114)),f319(x84113,x84115)))+~P1(f319(f319(f321(x84111),x84115),x84114))
% 22.40/22.31 [8423]~P119(x84231)+~P1(f319(f319(f225(a906),x84233),x84235))+~P1(f319(f319(f279(x84231),f319(f319(f236(x84231),x84232),x84235)),x84234))+P1(f319(f319(f279(x84231),f319(f319(f236(x84231),x84232),x84233)),x84234))
% 22.40/22.31 [8438]~P67(x84381)+~P1(f319(f55(x84382),x84384))+E(f319(f319(f3(x84381),f319(f319(f8(x84382,x84381),x84383),x84384)),f319(f319(f8(x84382,x84381),x84383),x84385)),f319(f319(f8(x84382,x84381),x84383),f319(f319(f3(f913(x84382,a904)),x84384),x84385)))+~P1(f319(f319(f225(f913(x84382,a904)),x84385),x84384))
% 22.40/22.31 [8457]P1(f319(f55(x84571),f319(x84572,x84573)))+~P1(f319(f55(x84574),x84575))+~P1(f319(f319(f321(x84574),x84573),x84575))+~P1(f319(f55(x84571),f319(f319(f33(x84574,f913(x84571,a904)),x84575),x84572)))
% 22.40/22.31 [8569]~P106(x85695)+~P106(x85691)+~P40(x85695,x85691,x85692)+P1(f319(f319(f225(x85691),f319(f319(f93(x85691),f319(x85692,x85693)),f319(x85692,x85694))),f319(x85692,f319(f319(f93(x85695),x85693),x85694))))
% 22.40/22.31 [8570]~P4(x85705)+~P106(x85701)+~P40(x85705,x85701,x85702)+P1(f319(f319(f225(x85701),f319(f319(f93(x85701),f319(x85702,x85703)),f319(x85702,x85704))),f319(x85702,f319(f319(f180(x85705),x85703),x85704))))
% 22.40/22.31 [8907]~P8(x89071,x89075,x89074)+~E(f319(f277(x89071,x89071,x89074),f319(f319(f301(x89071),x89072),f181(f913(x89071,a904)))),f319(f277(x89071,x89071,x89074),f319(f319(f301(x89071),x89073),f181(f913(x89071,a904)))))+~P1(f319(f319(f321(x89071),x89073),x89075))+P1(f319(f319(f321(f912(x89071,x89071)),f319(f319(f244(x89071,x89071),x89072),x89073)),x89074))
% 22.40/22.31 [9203]~P1(f319(x92031,x92035))+P1(f319(x92031,f883(x92031,x92032,x92033,x92034)))+P1(f319(x92031,f871(x92031,x92032,x92033,x92034)))+~P1(f319(f319(f321(x92034),x92035),f319(f319(f93(f913(x92034,a904)),x92033),x92032)))
% 22.40/22.31 [9399]~P1(f319(x93991,x93995))+P1(f319(x93991,f871(x93991,x93992,x93993,x93994)))+P1(f319(f319(f321(x93994),f883(x93991,x93992,x93993,x93994)),x93992))+~P1(f319(f319(f321(x93994),x93995),f319(f319(f93(f913(x93994,a904)),x93993),x93992)))
% 22.40/22.31 [9400]~P1(f319(x94001,x94005))+P1(f319(x94001,f883(x94001,x94002,x94003,x94004)))+P1(f319(f319(f321(x94004),f871(x94001,x94002,x94003,x94004)),x94003))+~P1(f319(f319(f321(x94004),x94005),f319(f319(f93(f913(x94004,a904)),x94003),x94002)))
% 22.40/22.31 [9406]P1(f319(x94061,x94062))+~P1(f319(x94061,f348(x94061,x94063,x94064,x94065)))+~P1(f319(x94061,f341(x94061,x94063,x94064,x94065)))+~P1(f319(f319(f321(x94065),x94062),f319(f319(f93(f913(x94065,a904)),x94064),x94063)))
% 22.40/22.31 [9412]~P38(x94121,x94124)+~P1(f319(f319(f321(f912(x94121,x94121)),f319(f319(f244(x94121,x94121),x94122),x94125)),x94124))+P1(f319(f319(f321(f912(x94121,x94121)),f319(f319(f244(x94121,x94121),x94122),x94123)),x94124))+~P1(f319(f319(f321(f912(x94121,x94121)),f319(f319(f244(x94121,x94121),x94125),x94123)),x94124))
% 22.40/22.31 [9451]E(x94511,x94512)+~P1(f319(f319(f321(f912(x94513,x94513)),f319(f319(f244(x94513,x94513),x94511),x94512)),f299(x94513,x94515)))+P1(f319(f319(f321(x94513),x94511),x94514))+~P1(f319(f319(f225(f913(f912(x94513,x94513),a904)),x94515),f319(f319(f246(x94513,x94513),x94514),f319(f18(f913(x94513,a904),x94513),x94514))))
% 22.40/22.31 [9469]P1(f319(x94691,x94692))+~P1(f319(x94691,f341(x94691,x94694,x94695,x94693)))+P1(f319(f319(f321(x94693),f348(x94691,x94694,x94695,x94693)),x94694))+~P1(f319(f319(f321(x94693),x94692),f319(f319(f93(f913(x94693,a904)),x94695),x94694)))
% 22.40/22.31 [9470]P1(f319(x94701,x94702))+~P1(f319(x94701,f348(x94701,x94704,x94705,x94703)))+P1(f319(f319(f321(x94703),f341(x94701,x94704,x94705,x94703)),x94705))+~P1(f319(f319(f321(x94703),x94702),f319(f319(f93(f913(x94703,a904)),x94705),x94704)))
% 22.40/22.31 [9534]P1(f319(x95341,x95342))+P1(f319(f319(f321(x95343),f348(x95341,x95344,x95345,x95343)),x95344))+P1(f319(f319(f321(x95343),f341(x95341,x95344,x95345,x95343)),x95345))+~P1(f319(f319(f321(x95343),x95342),f319(f319(f93(f913(x95343,a904)),x95345),x95344)))
% 22.40/22.31 [9535]~P1(f319(x95352,x95355))+P1(f319(f319(f321(x95351),f883(x95352,x95353,x95354,x95351)),x95353))+P1(f319(f319(f321(x95351),f871(x95352,x95353,x95354,x95351)),x95354))+~P1(f319(f319(f321(x95351),x95355),f319(f319(f93(f913(x95351,a904)),x95354),x95353)))
% 22.40/22.31 [9697]~P8(x96971,x96975,x96974)+~P1(f319(f319(f321(x96971),x96973),x96975))+P1(f319(f319(f321(f912(x96971,x96971)),f319(f319(f244(x96971,x96971),x96972),x96973)),x96974))+~P1(f319(f319(f225(f913(x96971,a904)),f319(f277(x96971,x96971,x96974),f319(f319(f301(x96971),x96973),f181(f913(x96971,a904))))),f319(f277(x96971,x96971,x96974),f319(f319(f301(x96971),x96972),f181(f913(x96971,a904))))))
% 22.40/22.31 [9838]~P4(x98385)+~P5(x98385)+P1(f319(f319(f321(x98381),f475(x98382,x98383,x98384,x98381,x98385)),x98384))+~P1(f319(f319(f226(x98385),f319(f319(f34(x98381,x98385),x98384),x98383)),x98382))
% 22.40/22.31 [9871]~P91(x98715)+~P88(x98715)+P1(f319(f319(f321(x98711),f686(x98712,x98713,x98714,x98711,x98715)),f319(f164(x98711),x98714)))+P1(f319(f319(f225(x98715),f319(f157(x98715),f319(f319(f146(x98711,x98715),x98713),x98714))),f319(f157(x98715),f319(f319(f146(x98711,x98715),x98712),x98714))))
% 22.40/22.31 [9997]~P4(x99971)+~P5(x99971)+P1(f319(f319(f226(x99971),f319(x99972,f475(x99973,x99972,x99974,x99975,x99971))),x99973))+~P1(f319(f319(f226(x99971),f319(f319(f34(x99975,x99971),x99974),x99972)),x99973))
% 22.40/22.31 [10099]~P91(x100991)+~P88(x100991)+~P1(f319(f319(f225(x100991),f319(x100993,f686(x100995,x100993,x100994,x100992,x100991))),f319(x100995,f686(x100995,x100993,x100994,x100992,x100991))))+P1(f319(f319(f225(x100991),f319(f157(x100991),f319(f319(f146(x100992,x100991),x100993),x100994))),f319(f157(x100991),f319(f319(f146(x100992,x100991),x100995),x100994))))
% 22.40/22.31 [8754]~P76(x87541)+~P1(f319(f55(x87544),x87545))+~P1(f319(f319(f321(x87544),x87543),x87545))+E(f319(f319(f74(x87541),f319(x87542,x87543)),f319(f319(f8(x87544,x87541),x87542),f319(f319(f3(f913(x87544,a904)),x87545),f319(f319(f301(x87544),x87543),f181(f913(x87544,a904)))))),f319(f319(f8(x87544,x87541),x87542),x87545))
% 22.40/22.31 [8755]~P82(x87551)+~P1(f319(f55(x87554),x87555))+~P1(f319(f319(f321(x87554),x87553),x87555))+E(f319(f319(f75(x87551),f319(x87552,x87553)),f319(f319(f11(x87554,x87551),x87552),f319(f319(f3(f913(x87554,a904)),x87555),f319(f319(f301(x87554),x87553),f181(f913(x87554,a904)))))),f319(f319(f11(x87554,x87551),x87552),x87555))
% 22.40/22.31 [8808]~P19(x88081,x88084,x88085)+~P1(f319(f55(x88081),x88082))+E(f319(f319(f3(f913(x88081,a904)),x88082),f319(f319(f301(x88081),x88083),f181(f913(x88081,a904)))),f181(f913(x88081,a904)))+E(f319(f319(x88084,x88083),f319(x88085,f319(f319(f3(f913(x88081,a904)),x88082),f319(f319(f301(x88081),x88083),f181(f913(x88081,a904)))))),f319(x88085,f319(f319(f301(x88081),x88083),x88082)))
% 22.40/22.31 [9182]~P76(x91821)+~P1(f319(f55(x91822),x91825))+~P1(f319(f55(x91822),x91824))+E(f319(f319(f74(x91821),f319(f319(f8(x91822,x91821),x91823),f319(f319(f93(f913(x91822,a904)),x91824),x91825))),f319(f319(f8(x91822,x91821),x91823),f319(f319(f94(f913(x91822,a904)),x91824),x91825))),f319(f319(f74(x91821),f319(f319(f8(x91822,x91821),x91823),x91824)),f319(f319(f8(x91822,x91821),x91823),x91825)))
% 22.40/22.31 [9184]~P82(x91841)+~P1(f319(f55(x91842),x91845))+~P1(f319(f55(x91842),x91844))+E(f319(f319(f75(x91841),f319(f319(f11(x91842,x91841),x91843),f319(f319(f93(f913(x91842,a904)),x91844),x91845))),f319(f319(f11(x91842,x91841),x91843),f319(f319(f94(f913(x91842,a904)),x91844),x91845))),f319(f319(f75(x91841),f319(f319(f11(x91842,x91841),x91843),x91844)),f319(f319(f11(x91842,x91841),x91843),x91845)))
% 22.40/22.31 [9331]~P67(x93311)+~P1(f319(f55(x93312),x93315))+~P1(f319(f55(x93312),x93314))+E(f319(f319(f3(x93311),f319(f319(f74(x93311),f319(f319(f8(x93312,x93311),x93313),x93314)),f319(f319(f8(x93312,x93311),x93313),x93315))),f319(f319(f8(x93312,x93311),x93313),f319(f319(f94(f913(x93312,a904)),x93314),x93315))),f319(f319(f8(x93312,x93311),x93313),f319(f319(f93(f913(x93312,a904)),x93314),x93315)))
% 22.40/22.31 [9548]~P25(x95481,x95482,x95483,x95485)+~P25(x95481,x95482,x95483,x95484)+P25(x95481,x95482,x95483,f319(f319(f93(f913(x95481,a904)),x95484),x95485))+~E(f319(f319(f94(f913(x95482,a904)),f319(f302(x95481,x95482,x95483),f319(f319(f3(f913(x95481,a904)),x95484),x95485))),f319(f302(x95481,x95482,x95483),f319(f319(f3(f913(x95481,a904)),x95485),x95484))),f181(f913(x95482,a904)))
% 22.40/22.31 [9672]E(x96721,f2(a1))+~P1(f319(f319(f226(a1),f2(a1)),x96723))+~P1(f319(f43(x96722,x96721),f319(f319(f244(a1,a1),x96724),x96725)))+P1(f319(f43(x96722,f319(f319(f75(a1),x96721),x96723)),f319(f319(f244(a1,a1),f319(f319(f30(a1),x96724),x96723)),f319(f319(f74(a1),f319(f319(f75(a1),x96721),f39(a1,x96724,x96723))),x96725))))
% 22.40/22.31 [9680]~P1(f319(f319(f226(a906),f2(a906)),x96803))+~P1(f319(f319(f226(a906),f2(a906)),x96802))+~P1(f319(f42(x96801,x96802),f319(f319(f244(a906,a906),x96804),x96805)))+P1(f319(f42(x96801,f319(f319(f75(a906),x96802),x96803)),f319(f319(f244(a906,a906),f319(f319(f30(a906),x96804),x96803)),f319(f319(f74(a906),f319(f319(f75(a906),x96802),f39(a906,x96804,x96803))),x96805))))
% 22.40/22.31 [9735]~P82(x97351)+~P1(f319(f55(x97352),x97355))+~P1(f319(f55(x97352),x97354))+E(f319(f319(f75(x97351),f319(f319(f319(f59(x97351,x97352,f75(x97351)),x97353),f72(x97351)),f319(f319(f93(f913(x97352,a904)),x97354),x97355))),f319(f319(f319(f59(x97351,x97352,f75(x97351)),x97353),f72(x97351)),f319(f319(f94(f913(x97352,a904)),x97354),x97355))),f319(f319(f75(x97351),f319(f319(f319(f59(x97351,x97352,f75(x97351)),x97353),f72(x97351)),x97354)),f319(f319(f319(f59(x97351,x97352,f75(x97351)),x97353),f72(x97351)),x97355)))
% 22.40/22.31 [9737]~E(f319(f319(f167(x97371),x97375),x97372),f319(f319(f167(x97371),x97375),x97373))+P1(f319(f319(f321(f912(f907(x97371),f907(x97371))),f319(f319(f244(f907(x97371),f907(x97371)),x97372),x97373)),f139(x97371,x97374)))+~P1(f319(f319(f226(a906),x97375),f319(f319(f230(a906),f319(f182(f907(x97371)),x97372)),f319(f182(f907(x97371)),x97373))))+~P1(f319(f319(f321(f912(x97371,x97371)),f319(f319(f244(x97371,x97371),f319(f319(f156(x97371),x97372),x97375)),f319(f319(f156(x97371),x97373),x97375))),x97374))
% 22.40/22.31 [9860]~P91(x98605)+~P146(x98605)+P1(f319(f319(f321(x98601),f448(x98602,x98603,x98604,x98601,x98605)),x98604))+P1(f319(f319(f225(x98605),f319(f319(f8(x98601,x98605),x98603),x98604)),f319(f319(f75(x98605),f319(f92(x98605),f319(f29(x98601),x98604))),x98602)))
% 22.40/22.31 [10042]~P91(x100421)+~P146(x100421)+~P1(f319(f319(f225(x100421),f319(x100423,f448(x100425,x100423,x100424,x100422,x100421))),x100425))+P1(f319(f319(f225(x100421),f319(f319(f8(x100422,x100421),x100423),x100424)),f319(f319(f75(x100421),f319(f92(x100421),f319(f29(x100422),x100424))),x100425)))
% 22.40/22.31 [8778]E(f319(f319(f126(x87781),x87782),x87783),f319(f319(f126(x87781),x87784),x87785))+~E(f319(f319(f167(x87781),f319(f182(f907(x87781)),x87782)),x87784),x87782)+~E(f319(f319(f126(x87781),f319(f319(f130(x87781),f319(f182(f907(x87781)),x87782)),x87784)),x87785),x87783)+P1(f319(f319(f225(a906),f319(f182(f907(x87781)),x87784)),f319(f182(f907(x87781)),x87782)))
% 22.40/22.31 [8906]E(f319(f319(f126(x89061),x89062),x89063),f319(f319(f126(x89061),x89064),x89065))+~E(f319(f319(f167(x89061),f319(f182(f907(x89061)),x89062)),x89064),x89062)+~E(x89063,f319(f319(f126(x89061),f319(f319(f130(x89061),f319(f182(f907(x89061)),x89062)),x89064)),x89065))+~P1(f319(f319(f225(a906),f319(f182(f907(x89061)),x89062)),f319(f182(f907(x89061)),x89064)))
% 22.40/22.31 [10158]~P1(f319(x101585,x101584))+~P1(f319(f55(x101582),f319(f254(x101582),x101585)))+P1(f319(f55(x101581),f319(f254(x101581),f319(f319(f9(x101581,x101582,a904),x101583),x101584))))+~P1(f319(f55(x101581),f319(f254(x101581),f319(f319(f10(f913(x101582,a904),a904,x101581),f80(x101582)),f319(f319(f10(f913(x101582,a904),f913(x101582,a904),x101581),f319(f20(x101582,a904,a904),f319(f319(f10(a904,f913(a904,a904),x101582),a317),x101585))),x101583)))))
% 22.40/22.31 [10236]~P1(f319(f55(x102362),x102365))+~P1(f319(f319(f321(x102362),x102364),x102365))+P1(f319(f55(x102361),f319(f254(x102361),f319(f319(f9(x102361,x102362,a904),x102363),x102364))))+~P1(f319(f55(x102361),f319(f254(x102361),f319(f319(f10(f913(x102362,a904),a904,x102361),f80(x102362)),f319(f319(f10(f913(x102362,a904),f913(x102362,a904),x102361),f319(f20(x102362,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102362),a317),f319(f319(f9(x102362,f913(x102362,a904),a904),f321(x102362)),x102365)))),x102363)))))
% 22.40/22.31 [8567]~P20(x85675,x85671,x85676,x85672)+E(f319(f66(x85671,x85671,x85671,f319(x85672,x85673)),f319(x85672,x85674)),f319(f66(x85671,x85671,x85671,f319(x85672,x85674)),f319(x85672,x85673)))+~P1(f319(f55(x85675),x85674))+~P1(f319(f55(x85675),x85673))
% 22.40/22.31 [7974]~P25(x79741,x79742,x79744,x79743)+~E(f319(x79744,x79746),x79745)+E(f319(f71(x79741,x79742,x79743,x79744),x79745),x79746)+~P1(f319(f319(f321(x79741),x79746),x79743))
% 22.40/22.31 [7975]~P25(x79751,x79752,x79754,x79753)+~E(f319(x79754,x79756),x79755)+E(f319(f85(x79751,x79752,x79753,x79754),x79755),x79756)+~P1(f319(f319(f321(x79751),x79756),x79753))
% 22.40/22.31 [8159]~P21(x81596,x81591,x81594,x81592)+E(f319(f66(x81591,x81591,x81591,f319(x81592,x81593)),f319(x81594,x81595)),f319(x81592,x81593))+~P1(f319(f55(x81596),x81593))+~P1(f319(f319(f321(x81596),x81595),x81593))
% 22.40/22.31 [9285]E(x92851,x92852)+~E(f319(f85(x92853,x92854,x92855,x92856),x92851),f319(f85(x92853,x92854,x92855,x92856),x92852))+~P1(f319(f319(f321(x92854),x92852),f319(f302(x92853,x92854,x92856),x92855)))+~P1(f319(f319(f321(x92854),x92851),f319(f302(x92853,x92854,x92856),x92855)))
% 22.40/22.31 [9382]~P20(x93823,x93821,x93826,x93822)+E(f319(f66(x93821,x93821,x93821,f319(x93822,f319(f319(f3(f913(x93823,a904)),x93824),f319(f319(f301(x93823),x93825),f181(f913(x93823,a904)))))),f319(x93826,x93825)),f319(x93822,x93824))+~P1(f319(f55(x93823),x93824))+~P1(f319(f319(f321(x93823),x93825),x93824))
% 22.40/22.31 [7075]~P70(x70751)+~E(f39(x70751,x70753,x70754),f39(x70751,x70756,x70754))+~E(f39(x70751,x70752,x70754),f39(x70751,x70755,x70754))+E(f39(x70751,f319(f319(f3(x70751),x70752),x70753),x70754),f39(x70751,f319(f319(f3(x70751),x70755),x70756),x70754))
% 22.40/22.31 [7076]~P69(x70761)+~E(f39(x70761,x70763,x70764),f39(x70761,x70766,x70764))+~E(f39(x70761,x70762,x70764),f39(x70761,x70765,x70764))+E(f39(x70761,f319(f319(f74(x70761),x70762),x70763),x70764),f39(x70761,f319(f319(f74(x70761),x70765),x70766),x70764))
% 22.40/22.31 [7077]~P69(x70771)+~E(f39(x70771,x70773,x70774),f39(x70771,x70776,x70774))+~E(f39(x70771,x70772,x70774),f39(x70771,x70775,x70774))+E(f39(x70771,f319(f319(f75(x70771),x70772),x70773),x70774),f39(x70771,f319(f319(f75(x70771),x70775),x70776),x70774))
% 22.40/22.31 [7866]~P17(x78661,x78662,x78663)+~P1(f319(f55(x78661),x78666))+E(f319(f319(f58(x78661,x78662,x78663),x78664),f319(f319(f301(x78661),x78665),x78666)),f319(f319(f58(x78661,x78662,x78663),f319(f319(x78663,x78665),x78664)),x78666))+P1(f319(f319(f321(x78661),x78665),x78666))
% 22.40/22.31 [7932]~P5(x79321)+P1(f319(f319(f225(x79321),x79322),f319(x79323,x79324)))+~P1(f319(f319(f321(x79325),x79324),x79326))+~P1(f319(f319(f225(x79321),x79322),f319(f319(f34(x79325,x79321),x79326),x79323)))
% 22.40/22.31 [8080]~P17(x80801,x80802,x80803)+~P1(f319(f55(x80801),x80806))+E(f319(f319(f58(x80801,x80802,x80803),x80804),f319(f319(f301(x80801),x80805),x80806)),f319(f319(x80803,x80805),f319(f319(f58(x80801,x80802,x80803),x80804),x80806)))+P1(f319(f319(f321(x80801),x80805),x80806))
% 22.40/22.31 [8179]~P4(x81793)+~P1(f319(x81792,x81795))+~P13(x81793,f319(f319(f146(x81791,x81793),x81794),x81796))+E(f319(f128(x81791,x81792),f319(f319(f140(x81791,x81793,x81794),x81795),x81796)),f319(f319(f140(x81791,x81793,x81794),x81795),f319(f128(x81791,x81792),x81796)))
% 22.40/22.31 [8200]E(x82001,x82002)+E(x82003,f2(a1))+~P1(f319(f43(x82004,x82003),f319(f319(f244(a1,a1),x82005),x82002)))+~P1(f319(f43(x82004,x82003),f319(f319(f244(a1,a1),x82006),x82001)))
% 22.40/22.31 [8201]E(x82011,x82012)+E(x82013,f2(a1))+~P1(f319(f43(x82014,x82013),f319(f319(f244(a1,a1),x82012),x82015)))+~P1(f319(f43(x82014,x82013),f319(f319(f244(a1,a1),x82011),x82016)))
% 22.40/22.31 [8223]~P20(x82232,x82235,x82236,x82231)+~P1(f319(f55(x82232),x82234))+E(f319(x82231,f319(f319(f301(x82232),x82233),x82234)),f319(f66(x82235,x82235,x82235,f319(x82231,x82234)),f319(x82236,x82233)))+P1(f319(f319(f321(x82232),x82233),x82234))
% 22.40/22.31 [8441]~P21(x84415,x84411,x84416,x84412)+E(f319(f66(x84411,x84411,x84411,f319(x84412,x84413)),f319(x84412,x84414)),f319(x84412,x84413))+~P1(f319(f55(x84415),x84413))+~P1(f319(f319(f225(f913(x84415,a904)),x84414),x84413))
% 22.40/22.31 [9589]~P25(x95891,x95892,x95894,x95893)+~P1(f319(f319(f321(x95892),x95895),f319(f302(x95891,x95892,x95894),x95893)))+P1(f319(f319(f321(x95891),f319(f71(x95891,x95892,x95893,x95894),x95895)),x95896))+~P1(f319(f319(f225(f913(x95891,a904)),x95893),x95896))
% 22.40/22.31 [9999]~P76(x99992)+~E(f500(x99991,x99993,x99995,x99996,x99994,x99992),f501(x99991,x99993,x99995,x99996,x99994,x99992))+~P1(f319(f55(x99994),x99996))+E(f319(f319(f8(x99991,x99992),x99993),f319(f302(x99994,x99991,x99995),x99996)),f319(f319(f8(x99994,x99992),f319(f66(x99991,x99992,x99994,x99993),x99995)),x99996))
% 22.40/22.31 [10026]~P76(x100266)+E(f319(x100261,f500(x100262,x100263,x100261,x100264,x100265,x100266)),f319(x100261,f501(x100262,x100263,x100261,x100264,x100265,x100266)))+E(f319(f319(f8(x100262,x100266),x100263),f319(f302(x100265,x100262,x100261),x100264)),f319(f319(f8(x100265,x100266),f319(f66(x100262,x100266,x100265,x100263),x100261)),x100264))+~P1(f319(f55(x100265),x100264))
% 22.40/22.31 [10059]~P76(x100592)+~E(f319(x100593,f319(x100595,f501(x100591,x100593,x100595,x100596,x100594,x100592))),f2(x100592))+~P1(f319(f55(x100594),x100596))+E(f319(f319(f8(x100591,x100592),x100593),f319(f302(x100594,x100591,x100595),x100596)),f319(f319(f8(x100594,x100592),f319(f66(x100591,x100592,x100594,x100593),x100595)),x100596))
% 22.40/22.31 [10105]~P76(x101052)+~P1(f319(f55(x101054),x101056))+E(f319(f319(f8(x101051,x101052),x101053),f319(f302(x101054,x101051,x101055),x101056)),f319(f319(f8(x101054,x101052),f319(f66(x101051,x101052,x101054,x101053),x101055)),x101056))+P1(f319(f319(f321(x101054),f501(x101051,x101053,x101055,x101056,x101054,x101052)),x101056))
% 22.40/22.31 [10106]~P76(x101062)+~P1(f319(f55(x101064),x101066))+E(f319(f319(f8(x101061,x101062),x101063),f319(f302(x101064,x101061,x101065),x101066)),f319(f319(f8(x101064,x101062),f319(f66(x101061,x101062,x101064,x101063),x101065)),x101066))+P1(f319(f319(f321(x101064),f500(x101061,x101063,x101065,x101066,x101064,x101062)),x101066))
% 22.40/22.31 [10178]~P40(f913(f912(x101784,x101785),a904),f913(f912(x101784,x101785),a904),x101786)+~P1(f319(f319(x101781,f601(x101781,x101786,x101783,x101782,x101785,x101784)),f602(x101781,x101786,x101783,x101782,x101785,x101784)))+P1(f319(f319(x101781,x101782),x101783))+~P1(f319(f319(f321(f912(x101784,x101785)),f319(f319(f244(x101784,x101785),x101782),x101783)),f87(f913(f912(x101784,x101785),a904),x101786)))
% 22.40/22.31 [10235]~P82(x102351)+~P1(f319(f55(x102352),x102356))+E(f319(f319(f319(f59(x102351,x102352,f75(x102351)),f319(f319(f20(x102352,f913(x102353,a904),x102351),f319(f319(f9(x102352,x102351,f913(f913(x102353,a904),x102351)),f319(f319(f10(f913(x102353,x102351),f913(x102351,f913(f913(x102353,a904),x102351)),x102352),f59(x102351,x102353,f75(x102351))),x102354)),f72(x102351))),x102355)),f72(x102351)),x102356),f319(f319(f319(f59(x102351,f912(x102352,x102353),f75(x102351)),f319(f249(x102352,x102353,x102351),x102354)),f72(x102351)),f319(f319(f246(x102352,x102353),x102356),x102355)))+P1(f319(f319(f321(x102352),f533(x102354,x102355,x102353,x102356,x102352,x102351)),x102356))
% 22.40/22.31 [10257]~P82(x102571)+~P1(f319(f55(x102572),x102576))+E(f319(f319(f319(f59(x102571,x102572,f75(x102571)),f319(f319(f20(x102572,f913(x102573,a904),x102571),f319(f319(f9(x102572,x102571,f913(f913(x102573,a904),x102571)),f319(f319(f10(f913(x102573,x102571),f913(x102571,f913(f913(x102573,a904),x102571)),x102572),f59(x102571,x102573,f75(x102571))),x102574)),f72(x102571))),x102575)),f72(x102571)),x102576),f319(f319(f319(f59(x102571,f912(x102572,x102573),f75(x102571)),f319(f249(x102572,x102573,x102571),x102574)),f72(x102571)),f319(f319(f246(x102572,x102573),x102576),x102575)))+~P1(f319(f55(x102573),f319(x102575,f533(x102574,x102575,x102573,x102576,x102572,x102571))))
% 22.40/22.31 [8353]~P21(x83532,x83535,x83536,x83531)+~P1(f319(f55(x83532),x83534))+~P1(f319(f55(x83532),x83533))+E(f319(x83531,f319(f319(f93(f913(x83532,a904)),x83533),x83534)),f319(f66(x83535,x83535,x83535,f319(x83531,x83533)),f319(x83531,x83534)))
% 22.40/22.31 [8568]~P5(x85681)+P1(f319(f319(f225(x85681),f319(x85682,x85683)),x85684))+~P1(f319(f319(f321(x85685),x85683),x85686))+~P1(f319(f319(f225(x85681),f319(f319(f33(x85685,x85681),x85686),x85682)),x85684))
% 22.40/22.31 [9000]~P25(x90002,x90001,x90003,x90006)+E(f319(f319(f94(f913(x90001,a904)),f319(f302(x90002,x90001,x90003),x90004)),f319(f302(x90002,x90001,x90003),x90005)),f319(f302(x90002,x90001,x90003),f319(f319(f94(f913(x90002,a904)),x90004),x90005)))+~P1(f319(f319(f225(f913(x90002,a904)),x90005),x90006))+~P1(f319(f319(f225(f913(x90002,a904)),x90004),x90006))
% 22.40/22.31 [9001]~P25(x90012,x90011,x90013,x90016)+E(f319(f319(f3(f913(x90011,a904)),f319(f302(x90012,x90011,x90013),x90014)),f319(f302(x90012,x90011,x90013),x90015)),f319(f302(x90012,x90011,x90013),f319(f319(f3(f913(x90012,a904)),x90014),x90015)))+~P1(f319(f319(f225(f913(x90012,a904)),x90015),x90016))+~P1(f319(f319(f225(f913(x90012,a904)),x90014),x90016))
% 22.40/22.31 [9252]E(x92521,x92522)+~P56(x92523,x92524,x92525)+~P1(f319(f319(f321(f912(x92523,x92524)),f319(f319(f244(x92523,x92524),x92526),x92522)),x92525))+~P1(f319(f319(f321(f912(x92523,x92524)),f319(f319(f244(x92523,x92524),x92526),x92521)),x92525))
% 22.40/22.31 [10056]~P77(x100561)+~E(f319(x100563,f381(x100564,x100566,x100563,x100565,x100562,x100561)),f319(x100566,f381(x100564,x100566,x100563,x100565,x100562,x100561)))+~P1(f319(f55(x100562),x100565))+E(f319(f319(f319(f59(x100561,x100562,f75(x100561)),x100563),x100564),x100565),f319(f319(f319(f59(x100561,x100562,f75(x100561)),x100566),x100564),x100565))
% 22.40/22.31 [10103]~P77(x101031)+~P1(f319(f55(x101032),x101035))+E(f319(f319(f319(f59(x101031,x101032,f75(x101031)),x101033),x101034),x101035),f319(f319(f319(f59(x101031,x101032,f75(x101031)),x101036),x101034),x101035))+P1(f319(f319(f321(x101032),f381(x101034,x101033,x101036,x101035,x101032,x101031)),x101035))
% 22.40/22.31 [8790]~P77(x87901)+~P1(f319(f55(x87902),x87906))+P1(f319(f319(f321(x87902),x87905),x87906))+E(f319(f319(f319(f59(x87901,x87902,f75(x87901)),x87903),x87904),f319(f319(f301(x87902),x87905),x87906)),f319(f319(f75(x87901),f319(x87903,x87905)),f319(f319(f319(f59(x87901,x87902,f75(x87901)),x87903),x87904),x87906)))
% 22.40/22.31 [8844]~P8(x88441,x88446,x88443)+~P11(x88441,f913(x88442,a904),x88443,x88445)+~P1(f319(f319(f321(x88441),x88444),x88446))+E(f319(f319(f33(x88441,f913(x88442,a904)),f319(f277(x88441,x88441,x88443),f319(f319(f301(x88441),x88444),f181(f913(x88441,a904))))),x88445),f319(x88445,x88444))
% 22.40/22.31 [8975]~P17(x89753,x89754,x89751)+~P1(f319(f55(x89753),x89756))+~P1(f319(f319(f321(x89753),x89752),x89756))+E(f319(f319(x89751,x89752),f319(f319(f58(x89753,x89754,x89751),x89755),f319(f319(f3(f913(x89753,a904)),x89756),f319(f319(f301(x89753),x89752),f181(f913(x89753,a904)))))),f319(f319(f58(x89753,x89754,x89751),x89755),x89756))
% 22.40/22.31 [9269]~P20(x92693,x92691,x92696,x92692)+~P1(f319(f55(x92693),x92695))+~P1(f319(f55(x92693),x92694))+E(f319(f66(x92691,x92691,x92691,f319(x92692,f319(f319(f93(f913(x92693,a904)),x92694),x92695))),f319(x92692,f319(f319(f94(f913(x92693,a904)),x92694),x92695))),f319(f66(x92691,x92691,x92691,f319(x92692,x92694)),f319(x92692,x92695)))
% 22.40/22.31 [10269]~P40(f913(f912(x102694,x102695),a904),f913(f912(x102694,x102695),a904),x102696)+P1(f319(f319(x102691,x102692),x102693))+~P1(f319(f319(f321(f912(x102694,x102695)),f319(f319(f244(x102694,x102695),x102692),x102693)),f87(f913(f912(x102694,x102695),a904),x102696)))+P1(f319(f319(f321(f912(x102694,x102695)),f319(f319(f244(x102694,x102695),f601(x102691,x102696,x102693,x102692,x102695,x102694)),f602(x102691,x102696,x102693,x102692,x102695,x102694))),f319(x102696,f319(f319(f94(f913(f912(x102694,x102695),a904)),f87(f913(f912(x102694,x102695),a904),x102696)),f319(f254(f912(x102694,x102695)),f319(f249(x102694,x102695,a904),x102691))))))
% 22.40/22.31 [9612]~E(x96123,f319(f319(f151(x96121,x96122),x96125),x96126))+P1(f319(f319(f321(f912(f907(x96121),f907(x96121))),f319(f319(f244(f907(x96121),f907(x96121)),x96122),x96123)),f149(x96121,x96124)))+~P1(f319(f319(f226(a906),x96125),f319(f182(f907(x96121)),x96122)))+~P1(f319(f319(f321(f912(x96121,x96121)),f319(f319(f244(x96121,x96121),f319(f319(f156(x96121),x96122),x96125)),x96126)),x96124))
% 22.40/22.31 [10114]~P76(x101142)+~P1(f319(f55(x101141),x101146))+P1(f319(f319(f321(x101141),f537(x101144,x101145,x101143,x101146,x101141,x101142)),x101146))+E(f319(f319(f8(x101141,x101142),f319(f319(f20(x101141,f913(x101143,a904),x101142),f319(f319(f10(f913(x101143,x101142),f913(f913(x101143,a904),x101142),x101141),f8(x101143,x101142)),x101144)),x101145)),x101146),f319(f319(f8(f912(x101141,x101143),x101142),f319(f249(x101141,x101143,x101142),x101144)),f319(f319(f246(x101141,x101143),x101146),x101145)))
% 22.40/22.31 [10115]~P82(x101152)+~P1(f319(f55(x101151),x101156))+P1(f319(f319(f321(x101151),f538(x101154,x101155,x101153,x101156,x101151,x101152)),x101156))+E(f319(f319(f11(x101151,x101152),f319(f319(f20(x101151,f913(x101153,a904),x101152),f319(f319(f10(f913(x101153,x101152),f913(f913(x101153,a904),x101152),x101151),f11(x101153,x101152)),x101154)),x101155)),x101156),f319(f319(f11(f912(x101151,x101153),x101152),f319(f249(x101151,x101153,x101152),x101154)),f319(f319(f246(x101151,x101153),x101156),x101155)))
% 22.40/22.31 [10156]~P76(x101562)+~P1(f319(f55(x101561),x101566))+~P1(f319(f55(x101563),f319(x101565,f537(x101564,x101565,x101563,x101566,x101561,x101562))))+E(f319(f319(f8(x101561,x101562),f319(f319(f20(x101561,f913(x101563,a904),x101562),f319(f319(f10(f913(x101563,x101562),f913(f913(x101563,a904),x101562),x101561),f8(x101563,x101562)),x101564)),x101565)),x101566),f319(f319(f8(f912(x101561,x101563),x101562),f319(f249(x101561,x101563,x101562),x101564)),f319(f319(f246(x101561,x101563),x101566),x101565)))
% 22.40/22.31 [10157]~P82(x101572)+~P1(f319(f55(x101571),x101576))+~P1(f319(f55(x101573),f319(x101575,f538(x101574,x101575,x101573,x101576,x101571,x101572))))+E(f319(f319(f11(x101571,x101572),f319(f319(f20(x101571,f913(x101573,a904),x101572),f319(f319(f10(f913(x101573,x101572),f913(f913(x101573,a904),x101572),x101571),f11(x101573,x101572)),x101574)),x101575)),x101576),f319(f319(f11(f912(x101571,x101573),x101572),f319(f249(x101571,x101573,x101572),x101574)),f319(f319(f246(x101571,x101573),x101576),x101575)))
% 22.40/22.31 [10138]~P82(x101382)+~P1(f319(f55(x101381),x101386))+P1(f319(f319(f321(x101381),x101383),x101386))+E(f319(f319(f11(x101381,x101382),f319(f319(f9(x101381,x101382,x101382),f319(f319(f20(x101381,x101382,f913(x101382,x101382)),f319(f319(f10(a904,f913(x101382,f913(x101382,x101382)),x101381),f86(x101382)),f319(f319(f9(x101381,x101381,a904),a316),x101383))),x101384)),x101385)),x101386),f319(f319(f236(x101382),x101385),f319(f29(x101381),x101386)))
% 22.40/22.31 [10141]~P82(x101412)+~P1(f319(f55(x101411),x101416))+~P1(f319(f319(f321(x101411),x101413),x101416))+E(f319(f319(f11(x101411,x101412),f319(f319(f9(x101411,x101412,x101412),f319(f319(f20(x101411,x101412,f913(x101412,x101412)),f319(f319(f10(a904,f913(x101412,f913(x101412,x101412)),x101411),f86(x101412)),f319(f319(f9(x101411,x101411,a904),a316),x101413))),x101414)),x101415)),x101416),f319(f319(f75(x101412),f319(x101414,x101413)),f319(f319(f236(x101412),x101415),f319(f319(f3(a906),f319(f29(x101411),x101416)),f72(a906)))))
% 22.40/22.31 [10223]~P1(f319(f55(x102231),x102235))+~P1(f319(f55(x102232),x102233))+P1(f319(f319(f321(x102232),f552(x102236,x102234,x102233,x102232,x102235,x102231)),x102233))+E(f319(f319(f8(x102231,a906),f319(f319(f10(f913(x102232,a904),a906,x102231),f29(x102232)),f319(f319(f10(f913(x102232,a904),f913(x102232,a904),x102231),f254(x102232)),f319(f319(f10(f913(x102232,a904),f913(x102232,a904),x102231),f319(f20(x102232,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102232),a317),f319(f319(f9(x102232,f913(x102232,a904),a904),f321(x102232)),x102233)))),x102234)))),x102235),f319(f319(f75(a906),x102236),f319(f29(x102232),x102233)))
% 22.40/22.31 [10224]~P1(f319(f55(x102241),x102245))+~P1(f319(f55(x102242),x102243))+P1(f319(f319(f321(x102242),f553(x102246,x102244,x102243,x102242,x102245,x102241)),x102243))+E(f319(f319(f8(x102241,a906),f319(f319(f10(f913(x102242,a904),a906,x102241),f29(x102242)),f319(f319(f10(f913(x102242,a904),f913(x102242,a904),x102241),f254(x102242)),f319(f319(f10(f913(x102242,a904),f913(x102242,a904),x102241),f319(f20(x102242,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102242),a317),f319(f319(f9(x102242,f913(x102242,a904),a904),f321(x102242)),x102243)))),x102244)))),x102245),f319(f319(f8(x102242,a906),x102246),x102243))
% 22.40/22.31 [10275]~P1(f319(f55(x102752),x102753))+~P1(f319(f55(x102751),x102755))+~E(f319(f29(x102751),f319(f254(x102751),f319(f319(f20(x102751,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102751),a317),f319(f319(f9(x102751,f913(x102751,a904),a904),f321(x102751)),x102755))),f319(f319(f9(x102751,x102752,a904),x102754),f552(x102756,x102754,x102753,x102752,x102755,x102751))))),x102756)+E(f319(f319(f8(x102751,a906),f319(f319(f10(f913(x102752,a904),a906,x102751),f29(x102752)),f319(f319(f10(f913(x102752,a904),f913(x102752,a904),x102751),f254(x102752)),f319(f319(f10(f913(x102752,a904),f913(x102752,a904),x102751),f319(f20(x102752,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102752),a317),f319(f319(f9(x102752,f913(x102752,a904),a904),f321(x102752)),x102753)))),x102754)))),x102755),f319(f319(f75(a906),x102756),f319(f29(x102752),x102753)))
% 22.40/22.31 [10294]~P1(f319(f55(x102942),x102943))+~P1(f319(f55(x102941),x102945))+~E(f319(f29(x102941),f319(f254(x102941),f319(f319(f20(x102941,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102941),a317),f319(f319(f9(x102941,f913(x102941,a904),a904),f321(x102941)),x102945))),f319(f319(f9(x102941,x102942,a904),x102944),f553(x102946,x102944,x102943,x102942,x102945,x102941))))),f319(x102946,f553(x102946,x102944,x102943,x102942,x102945,x102941)))+E(f319(f319(f8(x102941,a906),f319(f319(f10(f913(x102942,a904),a906,x102941),f29(x102942)),f319(f319(f10(f913(x102942,a904),f913(x102942,a904),x102941),f254(x102942)),f319(f319(f10(f913(x102942,a904),f913(x102942,a904),x102941),f319(f20(x102942,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102942),a317),f319(f319(f9(x102942,f913(x102942,a904),a904),f321(x102942)),x102943)))),x102944)))),x102945),f319(f319(f8(x102942,a906),x102946),x102943))
% 22.40/22.31 [9933]E(x99331,x99332)+~P17(x99333,x99334,x99335)+~P1(f319(f60(x99333,x99334,x99335,x99336,x99337),x99332))+~P1(f319(f60(x99333,x99334,x99335,x99336,x99337),x99331))
% 22.40/22.31 [9702]P1(f319(x97021,x97022))+~P1(f319(f319(f321(x97027),x97022),f319(x97026,x97024)))+~P1(f319(x97021,f549(x97021,x97026,x97025,x97023,x97027)))+~P1(f319(f319(f321(x97023),x97024),x97025))
% 22.40/22.31 [10129]~P17(x101297,x101296,x101291)+E(f319(f319(x101291,x101292),f897(x101292,x101293,x101294,x101295,x101291,x101296,x101297)),x101293)+~P1(f319(f60(x101297,x101296,x101291,x101295,x101294),x101293))+~P1(f319(f319(f321(x101297),x101292),x101294))
% 22.40/22.31 [10191]~P17(x101911,x101912,x101913)+~P1(f319(f60(x101911,x101912,x101913,x101914,x101915),x101917))+P1(f319(f60(x101911,x101912,x101913,x101914,f319(f319(f3(f913(x101911,a904)),x101915),f319(f319(f301(x101911),x101916),f181(f913(x101911,a904))))),f897(x101916,x101917,x101915,x101914,x101913,x101912,x101911)))+~P1(f319(f319(f321(x101911),x101916),x101915))
% 22.40/22.31 [9339]P26(x93391,x93392,x93393,x93394,x93395)+~P26(x93391,x93392,x93393,x93396,x93397)+~E(f319(f302(x93391,x93392,x93393),x93394),x93395)+~P1(f319(f319(f225(f913(x93391,a904)),x93394),x93396))
% 22.40/22.31 [9580]~P26(x95801,x95802,x95803,x95805,x95807)+~P26(x95801,x95802,x95803,x95804,x95806)+P26(x95801,x95802,x95803,f319(f319(f93(f913(x95801,a904)),x95804),x95805),f319(f319(f93(f913(x95802,a904)),x95806),x95807))+~E(f319(f319(f94(f913(x95802,a904)),x95806),x95807),f181(f913(x95802,a904)))
% 22.40/22.31 [9585]~P77(x95851)+~P25(x95855,x95852,x95856,x95857)+~P1(f319(f55(x95855),x95857))+E(f319(f319(f319(f59(x95851,x95852,f75(x95851)),x95853),x95854),f319(f302(x95855,x95852,x95856),x95857)),f319(f319(f319(f59(x95851,x95855,f75(x95851)),f319(f66(x95852,x95851,x95855,x95853),x95856)),x95854),x95857))
% 22.40/22.31 [9723]~E(f319(f319(f301(x97231),x97235),x97236),f319(f319(f301(x97231),x97232),x97233))+~P1(f319(f60(x97231,x97231,x97234,x97232,x97233),x97237))+P1(f319(f319(f321(x97231),x97232),x97233))+P1(f319(f56(x97231,x97234,f319(f319(f301(x97231),x97235),x97236)),x97237))
% 22.40/22.31 [9821]P1(f319(x98211,x98212))+~P1(f319(f319(f321(x98213),x98212),f319(x98214,x98217)))+~P1(f319(f319(f321(x98216),x98217),x98215))+P1(f319(f319(f321(x98213),f549(x98211,x98214,x98215,x98216,x98213)),f319(f319(f33(x98216,f913(x98213,a904)),x98215),x98214)))
% 22.40/22.31 [9839]~P25(x98392,x98391,x98395,x98394)+~P25(x98391,x98393,x98396,f319(f302(x98392,x98391,x98395),x98394))+E(f319(f319(f66(x98391,x98392,x98393,f71(x98392,x98391,x98394,x98395)),f71(x98391,x98393,f319(f302(x98392,x98391,x98395),x98394),x98396)),x98397),f319(f71(x98392,x98393,x98394,f319(f66(x98391,x98393,x98392,x98396),x98395)),x98397))+~P1(f319(f319(f321(x98393),x98397),f319(f302(x98391,x98393,x98396),f319(f302(x98392,x98391,x98395),x98394))))
% 22.40/22.31 [9840]~P25(x98402,x98401,x98405,x98404)+~P25(x98401,x98403,x98406,f319(f302(x98402,x98401,x98405),x98404))+E(f319(f319(f66(x98401,x98402,x98403,f85(x98402,x98401,x98404,x98405)),f85(x98401,x98403,f319(f302(x98402,x98401,x98405),x98404),x98406)),x98407),f319(f85(x98402,x98403,x98404,f319(f66(x98401,x98403,x98402,x98406),x98405)),x98407))+~P1(f319(f319(f321(x98403),x98407),f319(f302(x98401,x98403,x98406),f319(f302(x98402,x98401,x98405),x98404))))
% 22.40/22.31 [10130]~P17(x101307,x101306,x101301)+E(f319(f319(x101301,x101302),f371(x101303,x101304,x101302,x101305,x101301,x101306,x101307)),x101303)+P1(f319(f319(f321(x101307),x101302),x101304))+~P1(f319(f60(x101307,x101306,x101301,x101305,f319(f319(f301(x101307),x101302),x101304)),x101303))
% 22.40/22.31 [10190]~P17(x101901,x101904,x101905)+P1(f319(f60(x101901,x101904,x101905,x101906,x101903),f371(x101907,x101903,x101902,x101906,x101905,x101904,x101901)))+P1(f319(f319(f321(x101901),x101902),x101903))+~P1(f319(f60(x101901,x101904,x101905,x101906,f319(f319(f301(x101901),x101902),x101903)),x101907))
% 22.40/22.31 [9911]E(x99111,f2(a1))+~P1(f319(f43(x99113,x99111),f319(f319(f244(a1,a1),x99115),x99117)))+~P1(f319(f43(x99112,x99111),f319(f319(f244(a1,a1),x99114),x99116)))+P1(f319(f43(f319(f319(f74(a1),x99112),x99113),x99111),f319(f319(f244(a1,a1),f319(f319(f74(a1),f319(f319(f74(a1),x99114),x99115)),f319(f319(f30(a1),f319(f319(f74(a1),x99116),x99117)),x99111))),f39(a1,f319(f319(f74(a1),x99116),x99117),x99111))))
% 22.40/22.31 [9913]~P1(f319(f319(f226(a906),f2(a906)),x99133))+~P1(f319(f42(x99132,x99133),f319(f319(f244(a906,a906),x99135),x99137)))+~P1(f319(f42(x99131,x99133),f319(f319(f244(a906,a906),x99134),x99136)))+P1(f319(f42(f319(f319(f74(a906),x99131),x99132),x99133),f319(f319(f244(a906,a906),f319(f319(f74(a906),f319(f319(f74(a906),x99134),x99135)),f319(f319(f30(a906),f319(f319(f74(a906),x99136),x99137)),x99133))),f39(a906,f319(f319(f74(a906),x99136),x99137),x99133))))
% 22.40/22.31 [10274]~P76(x102742)+~P1(f319(f55(x102743),x102745))+~P1(f319(f55(x102741),x102747))+E(f319(f319(f8(x102741,x102742),f319(f319(f20(x102741,f913(x102743,a904),x102742),f319(f319(f10(f913(x102743,x102742),f913(f913(x102743,a904),x102742),x102741),f8(x102743,x102742)),x102744)),f319(f319(f10(f913(x102743,a904),f913(x102743,a904),x102741),f254(x102743)),f319(f319(f10(f913(x102743,a904),f913(x102743,a904),x102741),f319(f20(x102743,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102743),a317),f319(f319(f9(x102743,f913(x102743,a904),a904),f321(x102743)),x102745)))),x102746)))),x102747),f319(f319(f8(x102743,x102742),f319(f319(f20(x102743,f913(x102741,a904),x102742),f319(f319(f10(f913(x102741,x102742),f913(f913(x102741,a904),x102742),x102743),f8(x102741,x102742)),f319(f9(x102741,x102743,x102742),x102744))),f319(f319(f10(f913(x102741,a904),f913(x102741,a904),x102743),f254(x102741)),f319(f319(f10(f913(x102741,a904),f913(x102741,a904),x102743),f319(f20(x102741,a904,a904),f319(f319(f10(a904,f913(a904,a904),x102741),a317),f319(f319(f9(x102741,f913(x102741,a904),a904),f321(x102741)),x102747)))),f319(f9(x102741,x102743,a904),x102746))))),x102745))
% 22.40/22.31 [10222]~P22(x102228,x102227,x102226,x102225,x102221)+~E(f319(x102222,f846(x102224,x102222,x102223,x102221,x102225,x102226,x102227)),f319(x102224,f846(x102224,x102222,x102223,x102221,x102225,x102226,x102227)))+E(f319(f319(x102221,x102222),x102223),f319(f319(x102221,x102224),x102223))+~P1(f319(f55(x102227),x102223))
% 22.40/22.31 [9770]~P23(x97707,x97706,x97701,x97708,x97702,x97704)+E(f319(f319(x97701,f319(x97702,x97703)),f319(x97704,x97705)),f319(x97704,x97705))+~P1(f319(f55(x97706),x97705))+~P1(f319(f319(f321(x97706),x97703),x97705))
% 22.40/22.31 [9774]~P12(x97746,x97741,x97742,x97748,x97743,x97744)+~P8(x97746,x97747,x97748)+P11(x97741,x97742,x97743,f319(x97744,x97745))+~P1(f319(f319(f321(x97746),x97745),x97747))
% 22.40/22.31 [10243]~P22(x102438,x102435,x102437,x102436,x102431)+E(f319(f319(x102431,x102432),x102433),f319(f319(x102431,x102434),x102433))+~P1(f319(f55(x102435),x102433))+P1(f319(f319(f321(x102435),f846(x102432,x102434,x102433,x102431,x102436,x102437,x102435)),x102433))
% 22.40/22.31 [10359]~P1(f319(f319(x103591,x103596),x103595))+P1(f319(f319(x103591,f830(x103591,x103594,x103595,x103596,x103593,x103592,x103597,x103598)),f835(x103591,x103594,x103595,x103596,x103593,x103592,x103597,x103598)))+P1(f319(f319(x103591,x103592),x103593))+~P1(f319(f319(f321(f912(f912(x103598,x103597),f912(x103598,x103597))),f319(f319(f244(f912(x103598,x103597),f912(x103598,x103597)),f319(f319(f244(x103598,x103597),x103592),x103593)),f319(f319(f244(x103598,x103597),x103596),x103595))),f299(f912(x103598,x103597),x103594)))
% 22.40/22.31 [10360]~P1(f319(f319(x103601,x103606),x103605))+P1(f319(f319(x103601,f836(x103601,x103604,x103603,x103602,x103605,x103606,x103607,x103608)),f837(x103601,x103604,x103603,x103602,x103605,x103606,x103607,x103608)))+P1(f319(f319(x103601,x103602),x103603))+~P1(f319(f319(f321(f912(f912(x103608,x103607),f912(x103608,x103607))),f319(f319(f244(f912(x103608,x103607),f912(x103608,x103607)),f319(f319(f244(x103608,x103607),x103606),x103605)),f319(f319(f244(x103608,x103607),x103602),x103603))),f299(f912(x103608,x103607),x103604)))
% 22.40/22.31 [10374]~P1(f319(f319(x103741,f831(x103741,x103746,x103745,x103744,x103743,x103742,x103747,x103748)),f834(x103741,x103746,x103745,x103744,x103743,x103742,x103747,x103748)))+P1(f319(f319(x103741,x103742),x103743))+~P1(f319(f319(x103741,x103744),x103745))+~P1(f319(f319(f321(f912(f912(x103748,x103747),f912(x103748,x103747))),f319(f319(f244(f912(x103748,x103747),f912(x103748,x103747)),f319(f319(f244(x103748,x103747),x103742),x103743)),f319(f319(f244(x103748,x103747),x103744),x103745))),f299(f912(x103748,x103747),x103746)))
% 22.40/22.31 [10375]~P1(f319(f319(x103751,f838(x103751,x103756,x103753,x103752,x103755,x103754,x103757,x103758)),f839(x103751,x103756,x103753,x103752,x103755,x103754,x103757,x103758)))+P1(f319(f319(x103751,x103752),x103753))+~P1(f319(f319(x103751,x103754),x103755))+~P1(f319(f319(f321(f912(f912(x103758,x103757),f912(x103758,x103757))),f319(f319(f244(f912(x103758,x103757),f912(x103758,x103757)),f319(f319(f244(x103758,x103757),x103754),x103755)),f319(f319(f244(x103758,x103757),x103752),x103753))),f299(f912(x103758,x103757),x103756)))
% 22.40/22.31 [10391]~P1(f319(f319(x103911,x103916),x103917))+P1(f319(f319(x103911,x103912),x103913))+P1(f319(f319(f321(f912(f912(x103914,x103915),f912(x103914,x103915))),f319(f319(f244(f912(x103914,x103915),f912(x103914,x103915)),f319(f319(f244(x103914,x103915),x103916),x103917)),f319(f319(f244(x103914,x103915),f836(x103911,x103918,x103913,x103912,x103917,x103916,x103915,x103914)),f837(x103911,x103918,x103913,x103912,x103917,x103916,x103915,x103914)))),f299(f912(x103914,x103915),x103918)))+~P1(f319(f319(f321(f912(f912(x103914,x103915),f912(x103914,x103915))),f319(f319(f244(f912(x103914,x103915),f912(x103914,x103915)),f319(f319(f244(x103914,x103915),x103916),x103917)),f319(f319(f244(x103914,x103915),x103912),x103913))),f299(f912(x103914,x103915),x103918)))
% 22.40/22.31 [10393]~P1(f319(f319(x103931,x103938),x103937))+P1(f319(f319(x103931,x103932),x103933))+P1(f319(f319(f321(f912(f912(x103934,x103935),f912(x103934,x103935))),f319(f319(f244(f912(x103934,x103935),f912(x103934,x103935)),f319(f319(f244(x103934,x103935),f830(x103931,x103936,x103937,x103938,x103933,x103932,x103935,x103934)),f835(x103931,x103936,x103937,x103938,x103933,x103932,x103935,x103934))),f319(f319(f244(x103934,x103935),x103938),x103937))),f299(f912(x103934,x103935),x103936)))+~P1(f319(f319(f321(f912(f912(x103934,x103935),f912(x103934,x103935))),f319(f319(f244(f912(x103934,x103935),f912(x103934,x103935)),f319(f319(f244(x103934,x103935),x103932),x103933)),f319(f319(f244(x103934,x103935),x103938),x103937))),f299(f912(x103934,x103935),x103936)))
% 22.40/22.31 [9365]~P20(x93657,x93651,x93658,x93653)+~P1(f319(f55(x93657),x93655))+~P1(f319(f55(x93657),x93654))+E(f319(f66(x93651,x93651,x93652,f319(x93653,x93654)),f319(f66(x93651,x93651,x93652,f319(x93653,x93655)),x93656)),f319(f66(x93651,x93651,x93652,f319(x93653,x93655)),f319(f66(x93651,x93651,x93652,f319(x93653,x93654)),x93656)))
% 22.40/22.31 [9374]~P34(x93741,x93742,x93743,x93744,x93747)+P34(x93741,x93742,x93743,f319(f319(f151(x93741,x93744),x93745),x93746),f319(f319(f151(x93742,x93747),x93745),x93748))+~P1(f319(f319(x93743,x93746),x93748))+~P1(f319(f319(f226(a906),x93745),f319(f182(f907(x93741)),x93744)))
% 22.40/22.31 [9375]~P34(x93751,x93752,x93753,x93754,x93757)+P34(x93751,x93752,x93753,f319(f319(f151(x93751,x93754),x93755),x93756),f319(f319(f151(x93752,x93757),x93755),x93758))+~P1(f319(f319(x93753,x93756),x93758))+~P1(f319(f319(f226(a906),x93755),f319(f182(f907(x93752)),x93757)))
% 22.40/22.31 [9458]~P25(x94582,x94582,x94585,x94586)+~P22(x94583,x94582,x94587,x94588,x94581)+~P1(f319(f55(x94582),x94586))+E(f319(f319(x94581,f319(f66(x94582,x94583,x94582,x94584),x94585)),x94586),f319(f319(x94581,x94584),f319(f302(x94582,x94582,x94585),x94586)))
% 22.40/22.31 [9724]P26(x97241,x97242,x97243,x97244,x97245)+~P26(x97242,x97246,x97247,x97245,x97248)+~P26(x97241,x97246,f319(f66(x97242,x97246,x97241,x97247),x97243),x97244,x97248)+~P1(f319(f319(f225(f913(x97242,a904)),f319(f302(x97241,x97242,x97243),x97244)),x97245))
% 22.40/22.31 [9772]~P24(x97727,x97722,x97725,x97728,x97726,x97721)+~P1(f319(f55(x97722),x97724))+E(f319(x97721,f319(f319(f301(x97722),x97723),x97724)),f319(f319(x97725,f319(x97726,x97723)),f319(x97721,x97724)))+P1(f319(f319(f321(x97722),x97723),x97724))
% 22.40/22.31 [9788]~P23(x97886,x97885,x97881,x97887,x97888,x97882)+E(f319(f319(x97881,f319(x97882,x97883)),f319(x97882,x97884)),f319(x97882,x97884))+~P1(f319(f55(x97885),x97884))+~P1(f319(f319(f225(f913(x97885,a904)),x97883),x97884))
% 22.40/22.31 [9351]P1(f319(f319(f321(f912(f907(x93511),f907(x93511))),f319(f319(f244(f907(x93511),f907(x93511)),x93512),x93513)),f149(x93511,x93514)))+~E(x93513,f319(f319(f126(x93511),x93515),f319(f319(f143(x93511),x93516),x93517)))+~E(x93512,f319(f319(f126(x93511),x93515),f319(f319(f143(x93511),x93518),x93517)))+~P1(f319(f319(f321(f912(x93511,x93511)),f319(f319(f244(x93511,x93511),x93518),x93516)),x93514))
% 22.40/22.31 [9781]~P23(x97816,x97812,x97815,x97817,x97818,x97811)+~P1(f319(f55(x97812),x97814))+~P1(f319(f55(x97812),x97813))+E(f319(x97811,f319(f319(f93(f913(x97812,a904)),x97813),x97814)),f319(f319(x97815,f319(x97811,x97813)),f319(x97811,x97814)))
% 22.40/22.31 [10346]~P25(x103464,x103462,x103465,x103468)+E(f319(f319(f34(x103461,f913(x103462,a904)),x103463),f319(f319(f10(f913(x103464,a904),f913(x103462,a904),x103461),f302(x103464,x103462,x103465)),x103466)),f319(f302(x103464,x103462,x103465),f319(f319(f34(x103461,f913(x103464,a904)),x103463),x103466)))+~P1(f319(f319(f321(x103461),x103467),x103463))+P1(f319(f319(f321(x103461),f502(x103467,x103466,x103463,x103461,x103468,x103465,x103462,x103464)),x103463))
% 22.40/22.31 [10382]~P25(x103824,x103822,x103825,x103827)+E(f319(f319(f34(x103821,f913(x103822,a904)),x103823),f319(f319(f10(f913(x103824,a904),f913(x103822,a904),x103821),f302(x103824,x103822,x103825)),x103826)),f319(f302(x103824,x103822,x103825),f319(f319(f34(x103821,f913(x103824,a904)),x103823),x103826)))+~P1(f319(f319(f321(x103821),x103828),x103823))+~P1(f319(f319(f225(f913(x103824,a904)),f319(x103826,f502(x103828,x103826,x103823,x103821,x103827,x103825,x103822,x103824))),x103827))
% 22.40/22.31 [10394]~P1(f319(f319(x103941,x103948),x103947))+P1(f319(f319(x103941,x103942),x103943))+~P1(f319(f319(f321(f912(f912(x103944,x103945),f912(x103944,x103945))),f319(f319(f244(f912(x103944,x103945),f912(x103944,x103945)),f319(f319(f244(x103944,x103945),x103942),x103943)),f319(f319(f244(x103944,x103945),x103948),x103947))),f299(f912(x103944,x103945),x103946)))+P1(f319(f319(f321(f912(f912(x103944,x103945),f912(x103944,x103945))),f319(f319(f244(f912(x103944,x103945),f912(x103944,x103945)),f319(f319(f244(x103944,x103945),f831(x103941,x103946,x103947,x103948,x103943,x103942,x103945,x103944)),f834(x103941,x103946,x103947,x103948,x103943,x103942,x103945,x103944))),f319(f319(f244(x103944,x103945),f830(x103941,x103946,x103947,x103948,x103943,x103942,x103945,x103944)),f835(x103941,x103946,x103947,x103948,x103943,x103942,x103945,x103944)))),x103946))
% 22.40/22.31 [10395]~P1(f319(f319(x103951,x103958),x103957))+P1(f319(f319(x103951,x103952),x103953))+~P1(f319(f319(f321(f912(f912(x103954,x103955),f912(x103954,x103955))),f319(f319(f244(f912(x103954,x103955),f912(x103954,x103955)),f319(f319(f244(x103954,x103955),x103958),x103957)),f319(f319(f244(x103954,x103955),x103952),x103953))),f299(f912(x103954,x103955),x103956)))+P1(f319(f319(f321(f912(f912(x103954,x103955),f912(x103954,x103955))),f319(f319(f244(f912(x103954,x103955),f912(x103954,x103955)),f319(f319(f244(x103954,x103955),f836(x103951,x103956,x103953,x103952,x103957,x103958,x103955,x103954)),f837(x103951,x103956,x103953,x103952,x103957,x103958,x103955,x103954))),f319(f319(f244(x103954,x103955),f838(x103951,x103956,x103953,x103952,x103957,x103958,x103955,x103954)),f839(x103951,x103956,x103953,x103952,x103957,x103958,x103955,x103954)))),x103956))
% 22.40/22.31 [9849]~P24(x98497,x98495,x98491,x98498,x98492,x98494)+~P1(f319(f55(x98495),x98496))+~P1(f319(f319(f321(x98495),x98493),x98496))+E(f319(f319(x98491,f319(x98492,x98493)),f319(x98494,f319(f319(f3(f913(x98495,a904)),x98496),f319(f319(f301(x98495),x98493),f181(f913(x98495,a904)))))),f319(x98494,x98496))
% 22.40/22.31 [9857]~P24(x98576,x98573,x98571,x98577,x98578,x98572)+~P1(f319(f55(x98573),x98575))+~P1(f319(f55(x98573),x98574))+E(f319(f319(x98571,f319(x98572,f319(f319(f93(f913(x98573,a904)),x98574),x98575))),f319(x98572,f319(f319(f94(f913(x98573,a904)),x98574),x98575))),f319(f319(x98571,f319(x98572,x98574)),f319(x98572,x98575)))
% 22.40/22.31 [9954]P43(x99541,x99542,x99543,x99544,x99545,f319(f319(x99543,x99546),x99547))+~P43(x99541,x99542,x99543,x99544,f319(f319(f3(f913(x99541,a904)),x99545),f319(f319(f301(x99541),x99548),f181(f913(x99541,a904)))),x99549)+~E(f319(f319(x99543,x99546),x99547),f319(f319(x99543,x99548),x99549))+~P1(f319(f319(f321(x99541),x99548),x99545))
% 22.40/22.31 [9883]~P12(x98836,x98837,x98838,x98839,x988310,x98831)+E(f319(f319(x98831,x98832),x98833),f319(f319(x98831,x98834),x98835))+~P1(f319(f319(f321(f912(x98837,x98837)),f319(f319(f244(x98837,x98837),x98833),x98835)),x988310))+~P1(f319(f319(f321(f912(x98836,x98836)),f319(f319(f244(x98836,x98836),x98832),x98834)),x98839))
% 22.40/22.31 [9460]~P101(x94602)+E(x94601,f181(f913(x94602,a904)))+~P1(f319(f55(x94602),x94601))+P1(f319(f319(f321(x94602),f12(x94602,x94601)),x94601))+~P1(f319(f319(f321(x94602),f319(f319(f94(x94602),f782(x94601,x94602)),f790(x94601,x94602))),f319(f319(f301(x94602),f782(x94601,x94602)),f319(f319(f301(x94602),f790(x94601,x94602)),f181(f913(x94602,a904))))))
% 22.40/22.31 [9461]~P101(x94612)+E(x94611,f181(f913(x94612,a904)))+~P1(f319(f55(x94612),x94611))+P1(f319(f319(f321(x94612),f15(x94612,x94611)),x94611))+~P1(f319(f319(f321(x94612),f319(f319(f93(x94612),f801(x94611,x94612)),f816(x94611,x94612))),f319(f319(f301(x94612),f801(x94611,x94612)),f319(f319(f301(x94612),f816(x94611,x94612)),f181(f913(x94612,a904))))))
% 22.40/22.31 [9496]~P77(x94962)+E(x94961,f181(f913(x94962,a904)))+~P1(f319(f55(x94962),x94961))+P1(f319(f319(f321(x94962),f319(f57(x94962,f75(x94962)),x94961)),x94961))+~P1(f319(f319(f321(x94962),f319(f319(f75(x94962),f887(x94961,x94962)),f888(x94961,x94962))),f319(f319(f301(x94962),f887(x94961,x94962)),f319(f319(f301(x94962),f888(x94961,x94962)),f181(f913(x94962,a904))))))
% 22.40/22.31 [9501]~P4(x95012)+E(x95011,f181(f913(x95012,a904)))+~P1(f319(f55(x95012),x95011))+P1(f319(f319(f321(x95012),f13(x95012,f180(x95012),x95011)),x95011))+~P1(f319(f319(f321(x95012),f319(f319(f180(x95012),f636(x95011,x95012)),f647(x95011,x95012))),f319(f319(f301(x95012),f636(x95011,x95012)),f319(f319(f301(x95012),f647(x95011,x95012)),f181(f913(x95012,a904))))))
% 22.40/22.31 [9502]~P4(x95022)+E(x95021,f181(f913(x95022,a904)))+~P1(f319(f55(x95022),x95021))+P1(f319(f319(f321(x95022),f14(x95022,f230(x95022),x95021)),x95021))+~P1(f319(f319(f321(x95022),f319(f319(f230(x95022),f655(x95021,x95022)),f672(x95021,x95022))),f319(f319(f301(x95022),f655(x95021,x95022)),f319(f319(f301(x95022),f672(x95021,x95022)),f181(f913(x95022,a904))))))
% 22.40/22.31 [6638]~P93(x66382)+E(x66381,f2(x66382))+~E(f319(f319(f74(x66382),x66383),x66381),f2(x66382))+~P1(f319(f319(f225(x66382),f2(x66382)),x66383))+~P1(f319(f319(f225(x66382),f2(x66382)),x66381))
% 22.40/22.31 [6639]~P93(x66392)+E(x66391,f2(x66392))+~E(f319(f319(f74(x66392),x66391),x66393),f2(x66392))+~P1(f319(f319(f225(x66392),f2(x66392)),x66393))+~P1(f319(f319(f225(x66392),f2(x66392)),x66391))
% 22.40/22.31 [7174]~P4(x71742)+~P13(x71742,x71741)+E(x71741,f105(x71742))+~P1(f319(f319(f321(x71742),x71743),f319(f164(x71742),f698(x71741,x71742))))+P1(f319(f319(f225(x71742),f718(x71741,x71742)),x71743))
% 22.40/22.31 [7341]~P4(x73411)+E(f17(x73411,x73412),x73413)+~P1(f319(f55(x73411),x73412))+~P1(f319(f319(f225(x73411),x73413),f875(x73413,x73412,x73411)))+~P1(f319(f319(f321(x73411),x73413),x73412))
% 22.40/22.31 [7374]~P4(x73741)+~P13(x73741,x73742)+~P13(x73741,x73743)+P13(x73741,f319(f319(f126(x73741),x73742),x73743))+P1(f319(f319(f321(x73741),f705(x73743,x73742,x73741)),f319(f164(x73741),x73742)))
% 22.40/22.31 [7375]~P4(x73751)+~P13(x73751,x73752)+~P13(x73751,x73753)+P13(x73751,f319(f319(f126(x73751),x73752),x73753))+P1(f319(f319(f321(x73751),f706(x73753,x73752,x73751)),f319(f164(x73751),x73753)))
% 22.40/22.31 [7434]~P4(x74341)+E(f16(x74341,x74342),x74343)+~P1(f319(f55(x74341),x74342))+P1(f319(f319(f321(x74341),f876(x74343,x74342,x74341)),x74342))+~P1(f319(f319(f321(x74341),x74343),x74342))
% 22.40/22.31 [7435]~P4(x74351)+E(f17(x74351,x74352),x74353)+~P1(f319(f55(x74351),x74352))+P1(f319(f319(f321(x74351),f875(x74353,x74352,x74351)),x74352))+~P1(f319(f319(f321(x74351),x74353),x74352))
% 22.40/22.31 [7989]~P4(x79891)+E(f16(x79891,x79892),x79893)+~P1(f319(f55(x79891),x79892))+~P1(f319(f319(f321(x79891),x79893),x79892))+~P1(f319(f319(f225(x79891),f876(x79893,x79892,x79891)),x79893))
% 22.40/22.31 [8304]~P4(x83041)+~P13(x83041,x83042)+~P13(x83041,x83043)+P13(x83041,f319(f319(f126(x83041),x83042),x83043))+~P1(f319(f319(f225(x83041),f705(x83043,x83042,x83041)),f706(x83043,x83042,x83041)))
% 22.40/22.31 [9096]~P101(x90962)+E(x90961,f181(f913(x90962,a904)))+~E(f319(f319(f94(x90962),f319(x90963,f861(x90961,x90963,x90962))),f319(x90963,f862(x90961,x90963,x90962))),f319(x90963,f319(f319(f94(x90962),f861(x90961,x90963,x90962)),f862(x90961,x90963,x90962))))+E(f12(x90962,f319(f302(x90962,x90962,x90963),x90961)),f319(x90963,f12(x90962,x90961)))+~P1(f319(f55(x90962),x90961))
% 22.40/22.31 [9097]~P101(x90972)+E(x90971,f181(f913(x90972,a904)))+~E(f319(f319(f93(x90972),f319(x90973,f864(x90971,x90973,x90972))),f319(x90973,f865(x90971,x90973,x90972))),f319(x90973,f319(f319(f93(x90972),f864(x90971,x90973,x90972)),f865(x90971,x90973,x90972))))+E(f15(x90972,f319(f302(x90972,x90972,x90973),x90971)),f319(x90973,f15(x90972,x90971)))+~P1(f319(f55(x90972),x90971))
% 22.40/22.31 [9098]~P4(x90982)+E(x90981,f181(f913(x90982,a904)))+~E(f319(f319(f180(x90982),f319(x90983,f823(x90981,x90983,x90982))),f319(x90983,f827(x90981,x90983,x90982))),f319(x90983,f319(f319(f180(x90982),f823(x90981,x90983,x90982)),f827(x90981,x90983,x90982))))+E(f16(x90982,f319(f302(x90982,x90982,x90983),x90981)),f319(x90983,f16(x90982,x90981)))+~P1(f319(f55(x90982),x90981))
% 22.40/22.31 [9099]~P4(x90992)+E(x90991,f181(f913(x90992,a904)))+~E(f319(f319(f230(x90992),f319(x90993,f840(x90991,x90993,x90992))),f319(x90993,f858(x90991,x90993,x90992))),f319(x90993,f319(f319(f230(x90992),f840(x90991,x90993,x90992)),f858(x90991,x90993,x90992))))+E(f17(x90992,f319(f302(x90992,x90992,x90993),x90991)),f319(x90993,f17(x90992,x90991)))+~P1(f319(f55(x90992),x90991))
% 22.40/22.31 [9163]~P4(x91632)+E(x91631,f181(f913(x91632,a904)))+~E(f319(f319(f180(x91632),f319(x91633,f496(x91631,x91633,x91632))),f319(x91633,f512(x91631,x91633,x91632))),f319(x91633,f319(f319(f180(x91632),f496(x91631,x91633,x91632)),f512(x91631,x91633,x91632))))+E(f13(x91632,f180(x91632),f319(f302(x91632,x91632,x91633),x91631)),f319(x91633,f13(x91632,f180(x91632),x91631)))+~P1(f319(f55(x91632),x91631))
% 22.40/22.31 [9164]~P4(x91642)+E(x91641,f181(f913(x91642,a904)))+~E(f319(f319(f230(x91642),f319(x91643,f524(x91641,x91643,x91642))),f319(x91643,f534(x91641,x91643,x91642))),f319(x91643,f319(f319(f230(x91642),f524(x91641,x91643,x91642)),f534(x91641,x91643,x91642))))+E(f14(x91642,f230(x91642),f319(f302(x91642,x91642,x91643),x91641)),f319(x91643,f14(x91642,f230(x91642),x91641)))+~P1(f319(f55(x91642),x91641))
% 22.40/22.31 [6656]~P77(x66562)+E(x66561,f181(f913(x66562,a904)))+~P1(f319(f55(x66562),x66561))+E(f319(f57(x66562,f75(x66562)),f319(f319(f301(x66562),x66563),x66561)),f319(f319(f75(x66562),x66563),f319(f57(x66562,f75(x66562)),x66561)))+P1(f319(f319(f321(x66562),x66563),x66561))
% 22.40/22.31 [7180]~P101(x71802)+E(f319(f319(f93(x71802),f15(x71802,x71801)),f15(x71802,x71803)),f15(x71802,x71803))+E(x71801,f181(f913(x71802,a904)))+~P1(f319(f55(x71802),x71803))+~P1(f319(f319(f225(f913(x71802,a904)),x71801),x71803))
% 22.40/22.31 [7181]~P101(x71812)+E(f319(f319(f94(x71812),f12(x71812,x71811)),f12(x71812,x71813)),f12(x71812,x71813))+E(x71811,f181(f913(x71812,a904)))+~P1(f319(f55(x71812),x71813))+~P1(f319(f319(f225(f913(x71812,a904)),x71811),x71813))
% 22.40/22.31 [7182]~P4(x71822)+E(f319(f319(f180(x71822),f16(x71822,x71821)),f16(x71822,x71823)),f16(x71822,x71823))+E(x71821,f181(f913(x71822,a904)))+~P1(f319(f55(x71822),x71823))+~P1(f319(f319(f225(f913(x71822,a904)),x71821),x71823))
% 22.40/22.31 [7183]~P4(x71832)+E(f319(f319(f230(x71832),f17(x71832,x71831)),f17(x71832,x71833)),f17(x71832,x71833))+E(x71831,f181(f913(x71832,a904)))+~P1(f319(f55(x71832),x71833))+~P1(f319(f319(f225(f913(x71832,a904)),x71831),x71833))
% 22.40/22.31 [7476]~P4(x74762)+E(x74761,f181(f913(x74762,a904)))+~P1(f319(f55(x74762),x74763))+P1(f319(f319(f225(x74762),f16(x74762,x74761)),f16(x74762,x74763)))+~P1(f319(f319(f225(f913(x74762,a904)),x74761),x74763))
% 22.40/22.31 [7477]~P4(x74772)+E(x74771,f181(f913(x74772,a904)))+~P1(f319(f55(x74772),x74773))+P1(f319(f319(f225(x74772),f17(x74772,x74773)),f17(x74772,x74771)))+~P1(f319(f319(f225(f913(x74772,a904)),x74771),x74773))
% 22.40/22.31 [7530]~P101(x75301)+E(f12(x75301,x75302),x75303)+~P1(f319(f55(x75301),x75302))+~E(f319(f319(f3(f913(x75301,a904)),x75302),f319(f319(f301(x75301),x75303),f181(f913(x75301,a904)))),f181(f913(x75301,a904)))+~P1(f319(f319(f321(x75301),x75303),x75302))
% 22.40/22.31 [7531]~P101(x75311)+E(f15(x75311,x75312),x75313)+~P1(f319(f55(x75311),x75312))+~E(f319(f319(f3(f913(x75311,a904)),x75312),f319(f319(f301(x75311),x75313),f181(f913(x75311,a904)))),f181(f913(x75311,a904)))+~P1(f319(f319(f321(x75311),x75313),x75312))
% 22.40/22.31 [7532]~P4(x75321)+E(f16(x75321,x75322),x75323)+~P1(f319(f55(x75321),x75322))+~E(f319(f319(f3(f913(x75321,a904)),x75322),f319(f319(f301(x75321),x75323),f181(f913(x75321,a904)))),f181(f913(x75321,a904)))+~P1(f319(f319(f321(x75321),x75323),x75322))
% 22.40/22.31 [7533]~P4(x75331)+E(f17(x75331,x75332),x75333)+~P1(f319(f55(x75331),x75332))+~E(f319(f319(f3(f913(x75331,a904)),x75332),f319(f319(f301(x75331),x75333),f181(f913(x75331,a904)))),f181(f913(x75331,a904)))+~P1(f319(f319(f321(x75331),x75333),x75332))
% 22.40/22.31 [7626]~P4(x76261)+E(f13(x76261,f180(x76261),x76262),x76263)+~P1(f319(f55(x76261),x76262))+~E(f319(f319(f3(f913(x76261,a904)),x76262),f319(f319(f301(x76261),x76263),f181(f913(x76261,a904)))),f181(f913(x76261,a904)))+~P1(f319(f319(f321(x76261),x76263),x76262))
% 22.40/22.31 [7627]~P4(x76271)+E(f14(x76271,f230(x76271),x76272),x76273)+~P1(f319(f55(x76271),x76272))+~E(f319(f319(f3(f913(x76271,a904)),x76272),f319(f319(f301(x76271),x76273),f181(f913(x76271,a904)))),f181(f913(x76271,a904)))+~P1(f319(f319(f321(x76271),x76273),x76272))
% 22.40/22.31 [7662]~P107(x76622)+E(x76621,f181(f913(x76622,a904)))+~P1(f319(f55(x76622),x76621))+~P1(f319(f319(f225(x76622),x76623),f877(x76623,x76621,x76622)))+P1(f319(f319(f225(x76622),x76623),f319(f57(x76622,f94(x76622)),x76621)))
% 22.40/22.31 [7663]~P4(x76632)+E(x76631,f181(f913(x76632,a904)))+~P1(f319(f55(x76632),x76631))+~P1(f319(f319(f225(x76632),x76633),f878(x76633,x76631,x76632)))+P1(f319(f319(f225(x76632),x76633),f319(f57(x76632,f230(x76632)),x76631)))
% 22.40/22.31 [7664]~P4(x76642)+E(x76641,f181(f913(x76642,a904)))+~P1(f319(f55(x76642),x76641))+~P1(f319(f319(f226(x76642),x76643),f879(x76643,x76641,x76642)))+P1(f319(f319(f226(x76642),x76643),f319(f57(x76642,f230(x76642)),x76641)))
% 22.40/22.31 [7746]~P107(x77462)+E(x77461,f181(f913(x77462,a904)))+~P1(f319(f55(x77462),x77461))+P1(f319(f319(f321(x77462),f877(x77463,x77461,x77462)),x77461))+P1(f319(f319(f225(x77462),x77463),f319(f57(x77462,f94(x77462)),x77461)))
% 22.40/22.31 [7747]~P4(x77472)+E(x77471,f181(f913(x77472,a904)))+~P1(f319(f55(x77472),x77471))+P1(f319(f319(f321(x77472),f878(x77473,x77471,x77472)),x77471))+P1(f319(f319(f225(x77472),x77473),f319(f57(x77472,f230(x77472)),x77471)))
% 22.40/22.31 [7748]~P4(x77482)+E(x77481,f181(f913(x77482,a904)))+~P1(f319(f55(x77482),x77481))+P1(f319(f319(f321(x77482),f879(x77483,x77481,x77482)),x77481))+P1(f319(f319(f226(x77482),x77483),f319(f57(x77482,f230(x77482)),x77481)))
% 22.40/22.31 [7868]~P4(x78682)+E(x78681,f181(f913(x78682,a904)))+E(f319(f319(f180(x78682),f13(x78682,f180(x78682),x78681)),f13(x78682,f180(x78682),x78683)),f13(x78682,f180(x78682),x78683))+~P1(f319(f55(x78682),x78683))+~P1(f319(f319(f225(f913(x78682,a904)),x78681),x78683))
% 22.40/22.31 [7869]~P4(x78692)+E(x78691,f181(f913(x78692,a904)))+E(f319(f319(f230(x78692),f14(x78692,f230(x78692),x78691)),f14(x78692,f230(x78692),x78693)),f14(x78692,f230(x78692),x78693))+~P1(f319(f55(x78692),x78693))+~P1(f319(f319(f225(f913(x78692,a904)),x78691),x78693))
% 22.40/22.31 [8063]~E(f373(x80631,x80633,x80632),f374(x80631,x80633,x80632))+~E(f319(f29(x80632),f369(x80631,x80633,x80632)),x80631)+E(f319(f319(f75(a906),x80631),f319(f29(f913(x80632,a904)),x80633)),f319(f29(x80632),f31(f913(x80632,a904),x80633)))+~P1(f319(f55(x80632),f31(f913(x80632,a904),x80633)))+~P1(f319(f55(f913(x80632,a904)),x80633))
% 22.40/22.31 [8243]~P4(x82432)+E(x82431,f181(f913(x82432,a904)))+~P1(f319(f55(x82432),x82433))+P1(f319(f319(f225(x82432),f319(f57(x82432,f230(x82432)),x82433)),f319(f57(x82432,f230(x82432)),x82431)))+~P1(f319(f319(f225(f913(x82432,a904)),x82431),x82433))
% 22.40/22.31 [8537]~E(f373(x85371,x85373,x85372),f374(x85371,x85373,x85372))+E(f319(f319(f75(a906),x85371),f319(f29(f913(x85372,a904)),x85373)),f319(f29(x85372),f31(f913(x85372,a904),x85373)))+P1(f319(f319(f321(f913(x85372,a904)),f369(x85371,x85373,x85372)),x85373))+~P1(f319(f55(x85372),f31(f913(x85372,a904),x85373)))+~P1(f319(f55(f913(x85372,a904)),x85373))
% 22.40/22.31 [8564]~E(f319(f29(x85642),f369(x85641,x85643,x85642)),x85641)+E(f319(f319(f75(a906),x85641),f319(f29(f913(x85642,a904)),x85643)),f319(f29(x85642),f31(f913(x85642,a904),x85643)))+P1(f319(f319(f321(f913(x85642,a904)),f374(x85641,x85643,x85642)),x85643))+~P1(f319(f55(x85642),f31(f913(x85642,a904),x85643)))+~P1(f319(f55(f913(x85642,a904)),x85643))
% 22.40/22.31 [8565]~E(f319(f29(x85652),f369(x85651,x85653,x85652)),x85651)+E(f319(f319(f75(a906),x85651),f319(f29(f913(x85652,a904)),x85653)),f319(f29(x85652),f31(f913(x85652,a904),x85653)))+P1(f319(f319(f321(f913(x85652,a904)),f373(x85651,x85653,x85652)),x85653))+~P1(f319(f55(x85652),f31(f913(x85652,a904),x85653)))+~P1(f319(f55(f913(x85652,a904)),x85653))
% 22.40/22.31 [8589]~E(f319(f29(x85892),f369(x85891,x85893,x85892)),x85891)+~E(f319(f319(f94(f913(x85892,a904)),f374(x85891,x85893,x85892)),f373(x85891,x85893,x85892)),f181(f913(x85892,a904)))+E(f319(f319(f75(a906),x85891),f319(f29(f913(x85892,a904)),x85893)),f319(f29(x85892),f31(f913(x85892,a904),x85893)))+~P1(f319(f55(f913(x85892,a904)),x85893))+~P1(f319(f55(x85892),f31(f913(x85892,a904),x85893)))
% 22.40/22.31 [8851]E(f319(f319(f75(a906),x88511),f319(f29(f913(x88512,a904)),x88513)),f319(f29(x88512),f31(f913(x88512,a904),x88513)))+P1(f319(f319(f321(f913(x88512,a904)),f369(x88511,x88513,x88512)),x88513))+P1(f319(f319(f321(f913(x88512,a904)),f374(x88511,x88513,x88512)),x88513))+~P1(f319(f55(f913(x88512,a904)),x88513))+~P1(f319(f55(x88512),f31(f913(x88512,a904),x88513)))
% 22.40/22.31 [8852]E(f319(f319(f75(a906),x88521),f319(f29(f913(x88522,a904)),x88523)),f319(f29(x88522),f31(f913(x88522,a904),x88523)))+P1(f319(f319(f321(f913(x88522,a904)),f369(x88521,x88523,x88522)),x88523))+P1(f319(f319(f321(f913(x88522,a904)),f373(x88521,x88523,x88522)),x88523))+~P1(f319(f55(f913(x88522,a904)),x88523))+~P1(f319(f55(x88522),f31(f913(x88522,a904),x88523)))
% 22.40/22.31 [8877]~E(f319(f319(f94(f913(x88772,a904)),f374(x88771,x88773,x88772)),f373(x88771,x88773,x88772)),f181(f913(x88772,a904)))+E(f319(f319(f75(a906),x88771),f319(f29(f913(x88772,a904)),x88773)),f319(f29(x88772),f31(f913(x88772,a904),x88773)))+~P1(f319(f55(f913(x88772,a904)),x88773))+P1(f319(f319(f321(f913(x88772,a904)),f369(x88771,x88773,x88772)),x88773))+~P1(f319(f55(x88772),f31(f913(x88772,a904),x88773)))
% 22.40/22.31 [9142]~P100(x91422)+E(x91421,f181(f913(x91422,a904)))+~E(f319(f319(f75(x91422),f319(x91423,f892(x91421,x91423,x91422))),f319(x91423,f893(x91421,x91423,x91422))),f319(x91423,f319(f319(f75(x91422),f892(x91421,x91423,x91422)),f893(x91421,x91423,x91422))))+~P1(f319(f55(x91422),x91421))+E(f319(f57(x91422,f75(x91422)),f319(f302(x91422,x91422,x91423),x91421)),f319(x91423,f319(f57(x91422,f75(x91422)),x91421)))
% 22.40/22.31 [10291]P1(f319(f319(x102911,x102912),x102913))+P1(f319(f319(f226(a1),f484(x102911,x102913,x102912)),f485(x102911,x102913,x102912)))+P1(f319(f319(f225(a1),f485(x102911,x102913,x102912)),f2(a1)))+P1(f319(f319(x102911,f484(x102911,x102913,x102912)),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f485(x102911,x102913,x102912))))+~P1(f319(f307(f912(a1,a1),a52),f319(f319(f244(a1,a1),x102912),x102913)))
% 22.40/22.31 [10292]P1(f319(f319(x102921,x102922),x102923))+P1(f319(f319(f225(a1),f483(x102921,x102923,x102922)),f2(a1)))+P1(f319(f319(x102921,f479(x102921,x102923,x102922)),f319(f319(f75(a1),f319(f96(a1),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f483(x102921,x102923,x102922))))+P1(f319(f319(f225(a1),f2(a1)),f319(f319(f74(a1),f479(x102921,x102923,x102922)),f483(x102921,x102923,x102922))))+~P1(f319(f307(f912(a1,a1),a46),f319(f319(f244(a1,a1),x102922),x102923)))
% 22.40/22.31 [8035]~P113(x80351)+~P1(f319(f319(f225(x80351),x80352),f72(x80351)))+~P1(f319(f319(f225(x80351),f2(x80351)),x80352))+~P1(f319(f319(f225(x80351),f2(x80351)),x80353))+P1(f319(f319(f225(x80351),f319(f319(f75(x80351),x80352),x80353)),x80353))
% 22.40/22.31 [8036]~P113(x80361)+~P1(f319(f319(f225(x80361),x80363),f72(x80361)))+~P1(f319(f319(f225(x80361),f2(x80361)),x80363))+~P1(f319(f319(f225(x80361),f2(x80361)),x80362))+P1(f319(f319(f225(x80361),f319(f319(f75(x80361),x80362),x80363)),x80362))
% 22.40/22.31 [8386]~P4(x83862)+E(x83861,f181(f913(x83862,a904)))+~P1(f319(f55(x83862),x83861))+P1(f319(f319(f225(x83862),f880(x83863,x83861,x83862)),x83863))+~P1(f319(f319(f225(x83862),f319(f57(x83862,f230(x83862)),x83861)),x83863))
% 22.40/22.31 [8387]~P4(x83872)+E(x83871,f181(f913(x83872,a904)))+~P1(f319(f55(x83872),x83871))+P1(f319(f319(f321(x83872),f880(x83873,x83871,x83872)),x83871))+~P1(f319(f319(f225(x83872),f319(f57(x83872,f230(x83872)),x83871)),x83873))
% 22.40/22.31 [8388]~P4(x83882)+E(x83881,f181(f913(x83882,a904)))+~P1(f319(f55(x83882),x83881))+P1(f319(f319(f321(x83882),f881(x83883,x83881,x83882)),x83881))+~P1(f319(f319(f226(x83882),f319(f57(x83882,f230(x83882)),x83881)),x83883))
% 22.40/22.31 [8389]~P4(x83892)+E(x83891,f181(f913(x83892,a904)))+~P1(f319(f55(x83892),x83891))+P1(f319(f319(f226(x83892),f881(x83893,x83891,x83892)),x83893))+~P1(f319(f319(f226(x83892),f319(f57(x83892,f230(x83892)),x83891)),x83893))
% 22.40/22.31 [8473]~P1(f319(x84731,x84733))+P1(f319(x84731,f400(x84731,x84732)))+P1(f319(x84731,f397(x84731,x84732)))+~P1(f319(f319(f226(a1),f2(a1)),x84732))+P1(f319(x84731,f319(f319(f3(a1),f397(x84731,x84732)),f319(f319(f75(a1),f401(x84731,x84732)),x84732))))
% 22.40/22.31 [8693]~P1(f319(x86931,x86933))+P1(f319(x86931,f397(x86931,x86932)))+~P1(f319(f319(f226(a1),f2(a1)),x86932))+P1(f319(f319(f321(a1),f400(x86931,x86932)),f295(a1,f72(a1),x86932)))+P1(f319(x86931,f319(f319(f3(a1),f397(x86931,x86932)),f319(f319(f75(a1),f401(x86931,x86932)),x86932))))
% 22.40/22.31 [8898]~P1(f319(x88981,x88983))+~P1(f319(x88981,f397(x88981,x88982)))+P1(f319(x88981,f400(x88981,x88982)))+~P1(f319(f319(f226(a1),f2(a1)),x88982))+~P1(f319(x88981,f319(f319(f3(a1),f397(x88981,x88982)),f319(f319(f75(a1),f401(x88981,x88982)),x88982))))
% 22.40/22.31 [9033]~P1(f319(x90331,x90333))+~P1(f319(x90331,f397(x90331,x90332)))+~P1(f319(f319(f226(a1),f2(a1)),x90332))+P1(f319(f319(f321(a1),f400(x90331,x90332)),f295(a1,f72(a1),x90332)))+~P1(f319(x90331,f319(f319(f3(a1),f397(x90331,x90332)),f319(f319(f75(a1),f401(x90331,x90332)),x90332))))
% 22.40/22.31 [8804]~P101(x88041)+~P1(f319(f55(x88041),x88042))+E(f319(f319(f3(f913(x88041,a904)),x88042),f319(f319(f301(x88041),x88043),f181(f913(x88041,a904)))),f181(f913(x88041,a904)))+~P1(f319(f319(f321(x88041),x88043),x88042))+E(f319(f319(f94(x88041),x88043),f12(x88041,f319(f319(f3(f913(x88041,a904)),x88042),f319(f319(f301(x88041),x88043),f181(f913(x88041,a904)))))),f12(x88041,x88042))
% 22.40/22.31 [8805]~P101(x88051)+~P1(f319(f55(x88051),x88052))+E(f319(f319(f3(f913(x88051,a904)),x88052),f319(f319(f301(x88051),x88053),f181(f913(x88051,a904)))),f181(f913(x88051,a904)))+~P1(f319(f319(f321(x88051),x88053),x88052))+E(f319(f319(f93(x88051),x88053),f15(x88051,f319(f319(f3(f913(x88051,a904)),x88052),f319(f319(f301(x88051),x88053),f181(f913(x88051,a904)))))),f15(x88051,x88052))
% 22.40/22.31 [8806]~P4(x88061)+~P1(f319(f55(x88061),x88062))+E(f319(f319(f3(f913(x88061,a904)),x88062),f319(f319(f301(x88061),x88063),f181(f913(x88061,a904)))),f181(f913(x88061,a904)))+~P1(f319(f319(f321(x88061),x88063),x88062))+E(f319(f319(f180(x88061),x88063),f16(x88061,f319(f319(f3(f913(x88061,a904)),x88062),f319(f319(f301(x88061),x88063),f181(f913(x88061,a904)))))),f16(x88061,x88062))
% 22.40/22.31 [8807]~P4(x88071)+~P1(f319(f55(x88071),x88072))+E(f319(f319(f3(f913(x88071,a904)),x88072),f319(f319(f301(x88071),x88073),f181(f913(x88071,a904)))),f181(f913(x88071,a904)))+~P1(f319(f319(f321(x88071),x88073),x88072))+E(f319(f319(f230(x88071),x88073),f17(x88071,f319(f319(f3(f913(x88071,a904)),x88072),f319(f319(f301(x88071),x88073),f181(f913(x88071,a904)))))),f17(x88071,x88072))
% 22.40/22.31 [8868]~P4(x88681)+~P1(f319(f55(x88681),x88682))+E(f319(f319(f3(f913(x88681,a904)),x88682),f319(f319(f301(x88681),x88683),f181(f913(x88681,a904)))),f181(f913(x88681,a904)))+~P1(f319(f319(f321(x88681),x88683),x88682))+E(f319(f319(f180(x88681),x88683),f13(x88681,f180(x88681),f319(f319(f3(f913(x88681,a904)),x88682),f319(f319(f301(x88681),x88683),f181(f913(x88681,a904)))))),f13(x88681,f180(x88681),x88682))
% 22.40/22.31 [8869]~P4(x88691)+~P1(f319(f55(x88691),x88692))+E(f319(f319(f3(f913(x88691,a904)),x88692),f319(f319(f301(x88691),x88693),f181(f913(x88691,a904)))),f181(f913(x88691,a904)))+~P1(f319(f319(f321(x88691),x88693),x88692))+E(f319(f319(f230(x88691),x88693),f14(x88691,f230(x88691),f319(f319(f3(f913(x88691,a904)),x88692),f319(f319(f301(x88691),x88693),f181(f913(x88691,a904)))))),f14(x88691,f230(x88691),x88692))
% 22.40/22.31 [8885]~P101(x88851)+~P1(f319(f55(x88851),x88853))+~P1(f319(f55(x88851),x88852))+E(f319(f319(f94(f913(x88851,a904)),x88852),x88853),f181(f913(x88851,a904)))+E(f319(f319(f93(x88851),f15(x88851,f319(f319(f93(f913(x88851,a904)),x88852),x88853))),f15(x88851,f319(f319(f94(f913(x88851,a904)),x88852),x88853))),f319(f319(f93(x88851),f15(x88851,x88852)),f15(x88851,x88853)))
% 22.40/22.31 [8886]~P101(x88861)+~P1(f319(f55(x88861),x88863))+~P1(f319(f55(x88861),x88862))+E(f319(f319(f94(f913(x88861,a904)),x88862),x88863),f181(f913(x88861,a904)))+E(f319(f319(f94(x88861),f12(x88861,f319(f319(f93(f913(x88861,a904)),x88862),x88863))),f12(x88861,f319(f319(f94(f913(x88861,a904)),x88862),x88863))),f319(f319(f94(x88861),f12(x88861,x88862)),f12(x88861,x88863)))
% 22.40/22.31 [8887]~P4(x88871)+~P1(f319(f55(x88871),x88873))+~P1(f319(f55(x88871),x88872))+E(f319(f319(f94(f913(x88871,a904)),x88872),x88873),f181(f913(x88871,a904)))+E(f319(f319(f180(x88871),f16(x88871,f319(f319(f93(f913(x88871,a904)),x88872),x88873))),f16(x88871,f319(f319(f94(f913(x88871,a904)),x88872),x88873))),f319(f319(f180(x88871),f16(x88871,x88872)),f16(x88871,x88873)))
% 22.40/22.31 [8888]~P4(x88881)+~P1(f319(f55(x88881),x88883))+~P1(f319(f55(x88881),x88882))+E(f319(f319(f94(f913(x88881,a904)),x88882),x88883),f181(f913(x88881,a904)))+E(f319(f319(f230(x88881),f17(x88881,f319(f319(f93(f913(x88881,a904)),x88882),x88883))),f17(x88881,f319(f319(f94(f913(x88881,a904)),x88882),x88883))),f319(f319(f230(x88881),f17(x88881,x88882)),f17(x88881,x88883)))
% 22.40/22.31 [9114]~P4(x91141)+~P1(f319(f55(x91141),x91143))+~P1(f319(f55(x91141),x91142))+E(f319(f319(f94(f913(x91141,a904)),x91142),x91143),f181(f913(x91141,a904)))+E(f319(f319(f180(x91141),f13(x91141,f180(x91141),f319(f319(f93(f913(x91141,a904)),x91142),x91143))),f13(x91141,f180(x91141),f319(f319(f94(f913(x91141,a904)),x91142),x91143))),f319(f319(f180(x91141),f13(x91141,f180(x91141),x91142)),f13(x91141,f180(x91141),x91143)))
% 22.40/22.31 [9115]~P4(x91151)+~P1(f319(f55(x91151),x91153))+~P1(f319(f55(x91151),x91152))+E(f319(f319(f94(f913(x91151,a904)),x91152),x91153),f181(f913(x91151,a904)))+E(f319(f319(f230(x91151),f14(x91151,f230(x91151),f319(f319(f93(f913(x91151,a904)),x91152),x91153))),f14(x91151,f230(x91151),f319(f319(f94(f913(x91151,a904)),x91152),x91153))),f319(f319(f230(x91151),f14(x91151,f230(x91151),x91152)),f14(x91151,f230(x91151),x91153)))
% 22.40/22.31 [10193]~P126(x101933)+E(x101931,x101932)+~P1(f319(f319(f225(x101933),f2(x101933)),x101932))+~P1(f319(f319(f225(x101933),f2(x101933)),x101931))+~E(f319(f319(f236(x101933),x101931),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))),f319(f319(f236(x101933),x101932),f319(f96(a906),f319(f319(f74(a1),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),f319(f319(f74(a1),f319(f319(f74(a1),f72(a1)),a77)),a77))),a89))))
% 22.40/22.31 [6453]E(f331(x64531,x64532,x64533),x64534)+E(f319(x64531,x64534),f2(a906))+~E(f319(f319(f8(x64533,a906),x64531),x64532),f72(a906))+~P1(f319(f55(x64533),x64532))+~P1(f319(f319(f321(x64533),x64534),x64532))
% 22.40/22.31 [6520]E(f333(x65201,x65202,x65203),x65204)+E(f319(x65201,x65204),f2(a906))+~E(f319(f319(f8(x65203,a906),x65201),x65202),f319(a104,f2(a906)))+~P1(f319(f55(x65203),x65202))+~P1(f319(f319(f321(x65203),x65204),x65202))
% 22.40/22.31 [6628]~P4(x66281)+~P5(x66281)+P1(f319(f319(f226(x66281),x66282),f31(x66281,x66283)))+~P1(f319(f319(f226(x66281),x66282),x66284))+~P1(f319(f319(f321(x66281),x66284),x66283))
% 22.40/22.31 [6804]~P4(x68041)+~P5(x68041)+~P1(f319(f319(f226(x68041),x68044),x68043))+P1(f319(f319(f226(x68041),f32(x68041,x68042)),x68043))+~P1(f319(f319(f321(x68041),x68044),x68042))
% 22.40/22.31 [7058]~P126(x70583)+E(x70581,x70582)+~E(f319(f319(f236(x70583),x70581),f319(a104,x70584)),f319(f319(f236(x70583),x70582),f319(a104,x70584)))+~P1(f319(f319(f225(x70583),f2(x70583)),x70582))+~P1(f319(f319(f225(x70583),f2(x70583)),x70581))
% 22.40/22.31 [7268]~E(f337(x72682,x72683,x72681,x72684),x72684)+~E(f319(x72682,x72684),f72(a906))+E(f319(f319(f8(x72681,a906),x72682),x72683),f72(a906))+~P1(f319(f55(x72681),x72683))+~P1(f319(f319(f321(x72681),x72684),x72683))
% 22.40/22.31 [7275]~P119(x72754)+~P129(x72754)+E(f319(x72751,f898(x72751,x72752,x72753,x72754)),f2(x72754))+~E(f319(f319(f11(x72753,x72754),x72751),x72752),f2(x72754))+~P1(f319(f55(x72753),x72752))
% 22.40/22.31 [7364]~E(f336(x73642,x73643,x73641,x73644),x73644)+~E(f319(x73642,x73644),f319(a104,f2(a906)))+E(f319(f319(f8(x73641,a906),x73642),x73643),f319(a104,f2(a906)))+~P1(f319(f55(x73641),x73643))+~P1(f319(f319(f321(x73641),x73644),x73643))
% 22.40/22.31 [8074]~E(f319(x80742,x80744),f72(a906))+~E(f319(x80742,f337(x80742,x80743,x80741,x80744)),f2(a906))+E(f319(f319(f8(x80741,a906),x80742),x80743),f72(a906))+~P1(f319(f55(x80741),x80743))+~P1(f319(f319(f321(x80741),x80744),x80743))
% 22.40/22.31 [8111]~E(f319(x81112,x81114),f319(a104,f2(a906)))+~E(f319(x81112,f336(x81112,x81113,x81111,x81114)),f2(a906))+E(f319(f319(f8(x81111,a906),x81112),x81113),f319(a104,f2(a906)))+~P1(f319(f55(x81111),x81113))+~P1(f319(f319(f321(x81111),x81114),x81113))
% 22.40/22.31 [8661]~P4(x86611)+~P13(x86611,x86614)+P13(x86611,x86612)+~E(x86612,f319(f319(f143(x86611),x86613),x86614))+~P1(f319(f319(f225(x86611),x86613),f719(x86612,x86611,x86614,x86613)))
% 22.40/22.31 [8697]E(x86971,x86972)+E(f319(f319(f3(a1),f406(x86973,x86972,x86974,x86971)),f407(x86973,x86972,x86974,x86971)),x86971)+~E(f319(f319(f74(a1),x86971),x86974),x86972)+~P1(f319(f319(f226(a1),f2(a1)),x86974))+~P1(f319(f319(f321(a1),x86972),x86973))
% 22.40/22.31 [8698]E(x86981,x86982)+E(f319(f319(f74(a1),f408(x86983,x86982,x86984,x86981)),f409(x86983,x86982,x86984,x86981)),x86981)+~E(f319(f319(f3(a1),x86981),x86984),x86982)+~P1(f319(f319(f226(a1),f2(a1)),x86984))+~P1(f319(f319(f321(a1),x86982),x86983))
% 22.40/22.31 [8883]E(f319(x88831,f457(x88832,x88831,x88833,x88834)),x88832)+P1(f319(f319(f225(a906),x88834),f458(x88832,x88831,x88833,x88834)))+~P1(f319(f319(f225(a1),x88832),f319(x88831,x88833)))+~P1(f319(f319(f226(a906),x88834),x88833))+~P1(f319(f319(f225(a1),f319(x88831,x88834)),x88832))
% 22.40/22.31 [8884]~P4(x88841)+~P13(x88841,x88843)+P13(x88841,x88842)+~E(x88842,f319(f319(f143(x88841),x88844),x88843))+P1(f319(f319(f321(x88841),f719(x88842,x88841,x88843,x88844)),f319(f164(x88841),x88843)))
% 22.40/22.31 [8902]~P119(x89024)+~P129(x89024)+~E(f319(f319(f11(x89021,x89024),x89022),x89023),f2(x89024))+~P1(f319(f55(x89021),x89023))+P1(f319(f319(f321(x89021),f898(x89022,x89023,x89021,x89024)),x89023))
% 22.40/22.31 [8943]~E(f319(x89432,x89434),f72(a906))+E(f319(f319(f8(x89431,a906),x89432),x89433),f72(a906))+~P1(f319(f55(x89431),x89433))+~P1(f319(f319(f321(x89431),x89434),x89433))+P1(f319(f319(f321(x89431),f337(x89432,x89433,x89431,x89434)),x89433))
% 22.40/22.31 [8956]E(x89561,x89562)+~E(f319(f319(f3(a1),x89562),x89564),x89561)+~P1(f319(f319(f226(a1),f2(a1)),x89564))+~P1(f319(f319(f321(a1),x89561),x89563))+P1(f319(f319(f321(a1),f408(x89563,x89561,x89564,x89562)),x89563))
% 22.40/22.31 [8957]E(x89571,x89572)+~E(f319(f319(f74(a1),x89572),x89574),x89571)+~P1(f319(f319(f226(a1),f2(a1)),x89574))+~P1(f319(f319(f321(a1),x89571),x89573))+P1(f319(f319(f321(a1),f406(x89573,x89571,x89574,x89572)),x89573))
% 22.40/22.31 [8959]~E(f319(x89592,x89594),f319(a104,f2(a906)))+E(f319(f319(f8(x89591,a906),x89592),x89593),f319(a104,f2(a906)))+~P1(f319(f55(x89591),x89593))+~P1(f319(f319(f321(x89591),x89594),x89593))+P1(f319(f319(f321(x89591),f336(x89592,x89593,x89591,x89594)),x89593))
% 22.40/22.31 [8965]P60(x89652,x89653,x89654,x89651)+E(x89651,f181(f913(x89652,a904)))+~P1(f319(f55(x89652),x89654))+~P1(f319(f55(x89652),x89651))+P1(f319(f319(f321(x89652),f787(x89653,x89651,x89654,x89652)),x89654))
% 22.40/22.31 [8966]P60(x89662,x89663,x89664,x89661)+E(x89661,f181(f913(x89662,a904)))+~P1(f319(f55(x89662),x89664))+~P1(f319(f55(x89662),x89661))+P1(f319(f319(f321(x89662),f523(x89661,x89664,x89663,x89662)),x89664))
% 22.40/22.31 [8967]P60(x89672,x89673,x89674,x89671)+E(x89671,f181(f913(x89672,a904)))+~P1(f319(f55(x89672),x89674))+~P1(f319(f55(x89672),x89671))+P1(f319(f319(f321(x89672),f788(x89671,x89674,x89673,x89672)),x89674))
% 22.40/22.31 [9045]E(x90451,x90452)+~E(f319(f319(f3(a1),x90452),x90454),x90451)+~P1(f319(f319(f226(a1),f2(a1)),x90454))+~P1(f319(f319(f321(a1),x90451),x90453))+P1(f319(f319(f321(a1),f409(x90453,x90451,x90454,x90452)),f295(a1,f72(a1),x90454)))
% 22.40/22.31 [9046]E(x90461,x90462)+~E(f319(f319(f74(a1),x90462),x90464),x90461)+~P1(f319(f319(f226(a1),f2(a1)),x90464))+~P1(f319(f319(f321(a1),x90461),x90463))+P1(f319(f319(f321(a1),f407(x90463,x90461,x90464,x90462)),f295(a1,f72(a1),x90464)))
% 22.40/22.31 [9120]P1(f319(f319(f225(a906),x91201),f457(x91202,x91203,x91204,x91201)))+~P1(f319(f319(f225(a1),x91202),f319(x91203,x91204)))+P1(f319(f319(f225(a906),x91201),f458(x91202,x91203,x91204,x91201)))+~P1(f319(f319(f226(a906),x91201),x91204))+~P1(f319(f319(f225(a1),f319(x91203,x91201)),x91202))
% 22.40/22.31 [9228]E(f319(x92281,f457(x92282,x92281,x92283,x92284)),x92282)+~P1(f319(f319(f225(a1),x92282),f319(x92281,x92283)))+P1(f319(f319(f226(a906),f458(x92282,x92281,x92283,x92284)),x92283))+~P1(f319(f319(f226(a906),x92284),x92283))+~P1(f319(f319(f225(a1),f319(x92281,x92284)),x92282))
% 22.40/22.31 [9362]~P1(f319(f319(f225(a1),x93622),f319(x93623,x93624)))+P1(f319(f319(f225(a906),x93621),f458(x93622,x93623,x93624,x93621)))+P1(f319(f319(f225(a906),f457(x93622,x93623,x93624,x93621)),x93624))+~P1(f319(f319(f226(a906),x93621),x93624))+~P1(f319(f319(f225(a1),f319(x93623,x93621)),x93622))
% 22.40/22.31 [9363]~P1(f319(f319(f225(a1),x93632),f319(x93633,x93634)))+P1(f319(f319(f225(a906),x93631),f457(x93632,x93633,x93634,x93631)))+P1(f319(f319(f226(a906),f458(x93632,x93633,x93634,x93631)),x93634))+~P1(f319(f319(f226(a906),x93631),x93634))+~P1(f319(f319(f225(a1),f319(x93633,x93631)),x93632))
% 22.40/22.31 [9475]~P1(f319(f319(f225(a1),x94751),f319(x94752,x94753)))+P1(f319(f319(f226(a906),f458(x94751,x94752,x94753,x94754)),x94753))+~P1(f319(f319(f226(a906),x94754),x94753))+~P1(f319(f319(f225(a1),f319(x94752,x94754)),x94751))+P1(f319(f319(f225(a906),f457(x94751,x94752,x94753,x94754)),x94753))
% 22.40/22.31 [9558]E(x95581,f181(f913(x95582,a904)))+~P1(f319(f55(x95582),x95584))+~P1(f319(f55(x95582),x95581))+P1(f319(f319(f321(f912(f913(x95582,a904),f913(x95582,a904))),f319(f319(f244(f913(x95582,a904),f913(x95582,a904)),x95584),x95581)),f311(x95582,x95583)))+P1(f319(f319(f321(x95582),f527(x95583,x95581,x95584,x95582)),x95584))
% 22.40/22.31 [9559]E(x95591,f181(f913(x95592,a904)))+~P1(f319(f55(x95592),x95594))+~P1(f319(f55(x95592),x95591))+P1(f319(f319(f321(f912(f913(x95592,a904),f913(x95592,a904))),f319(f319(f244(f913(x95592,a904),f913(x95592,a904)),x95594),x95591)),f311(x95592,x95593)))+P1(f319(f319(f321(x95592),f596(x95593,x95591,x95594,x95592)),x95594))
% 22.40/22.31 [10237]E(f319(x102371,f457(x102372,x102371,x102373,x102374)),x102372)+~P1(f319(f319(f225(a1),x102372),f319(x102371,x102373)))+~P1(f319(f319(f225(a1),f319(f69(a1),f319(f319(f3(a1),f319(x102371,f319(f319(f74(a906),f458(x102372,x102371,x102373,x102374)),f72(a906)))),f319(x102371,f458(x102372,x102371,x102373,x102374))))),f72(a1)))+~P1(f319(f319(f226(a906),x102374),x102373))+~P1(f319(f319(f225(a1),f319(x102371,x102374)),x102372))
% 22.40/22.31 [10238]~P1(f319(f319(f225(a1),x102382),f319(x102383,x102384)))+P1(f319(f319(f225(a906),x102381),f457(x102382,x102383,x102384,x102381)))+~P1(f319(f319(f225(a1),f319(f69(a1),f319(f319(f3(a1),f319(x102383,f319(f319(f74(a906),f458(x102382,x102383,x102384,x102381)),f72(a906)))),f319(x102383,f458(x102382,x102383,x102384,x102381))))),f72(a1)))+~P1(f319(f319(f226(a906),x102381),x102384))+~P1(f319(f319(f225(a1),f319(x102383,x102381)),x102382))
% 22.40/22.31 [10239]~P1(f319(f319(f225(a1),x102391),f319(x102392,x102393)))+~P1(f319(f319(f225(a1),f319(f69(a1),f319(f319(f3(a1),f319(x102392,f319(f319(f74(a906),f458(x102391,x102392,x102393,x102394)),f72(a906)))),f319(x102392,f458(x102391,x102392,x102393,x102394))))),f72(a1)))+~P1(f319(f319(f226(a906),x102394),x102393))+~P1(f319(f319(f225(a1),f319(x102392,x102394)),x102391))+P1(f319(f319(f225(a906),f457(x102391,x102392,x102393,x102394)),x102393))
% 22.40/22.31 [7327]~P74(x73271)+P1(f319(f319(f226(x73271),x73272),f2(x73271)))+~P1(f319(f319(f225(x73271),x73273),f2(x73271)))+P1(f319(f319(f226(x73271),f2(x73271)),x73272))+P1(f319(f319(f225(x73271),x73273),f319(f319(f282(x73271),x73274),x73272)))
% 22.40/22.31 [7328]~P74(x73281)+P1(f319(f319(f226(x73281),x73282),f2(x73281)))+~P1(f319(f319(f226(x73281),x73283),f2(x73281)))+P1(f319(f319(f226(x73281),f2(x73281)),x73282))+P1(f319(f319(f226(x73281),x73283),f319(f319(f282(x73281),x73284),x73282)))
% 22.40/22.31 [7567]~P74(x75671)+P1(f319(f319(f225(x75671),x75672),f2(x75671)))+P1(f319(f319(f226(x75671),x75673),f2(x75671)))+P1(f319(f319(f226(x75671),f2(x75671)),x75673))+~P1(f319(f319(f225(x75671),x75672),f319(f319(f282(x75671),x75674),x75673)))
% 22.40/22.31 [7568]~P74(x75681)+P1(f319(f319(f226(x75681),x75682),f2(x75681)))+P1(f319(f319(f226(x75681),x75683),f2(x75681)))+P1(f319(f319(f226(x75681),f2(x75681)),x75683))+~P1(f319(f319(f226(x75681),x75682),f319(f319(f282(x75681),x75684),x75683)))
% 22.40/22.31 [7682]E(x76821,x76822)+~E(f319(f319(f156(x76823),x76824),x76821),f319(f319(f156(x76823),x76824),x76822))+~P1(f319(f129(x76823),x76824))+~P1(f319(f319(f226(a906),x76822),f319(f182(f907(x76823)),x76824)))+~P1(f319(f319(f226(a906),x76821),f319(f182(f907(x76823)),x76824)))
% 22.40/22.31 [8037]~P74(x80371)+~P1(f319(f319(f225(x80371),x80373),f2(x80371)))+P1(f319(f319(f226(x80371),f2(x80371)),x80372))+~P1(f319(f319(f225(x80371),x80374),f319(f319(f75(x80371),x80373),x80372)))+P1(f319(f319(f225(x80371),x80373),f319(f319(f282(x80371),x80374),x80372)))
% 22.40/22.31 [8038]~P74(x80381)+~P1(f319(f319(f226(x80381),x80383),f2(x80381)))+P1(f319(f319(f226(x80381),f2(x80381)),x80382))+~P1(f319(f319(f226(x80381),x80384),f319(f319(f75(x80381),x80383),x80382)))+P1(f319(f319(f226(x80381),x80383),f319(f319(f282(x80381),x80384),x80382)))
% 22.40/22.31 [8039]~P74(x80391)+~P1(f319(f319(f226(x80391),x80392),f2(x80391)))+P1(f319(f319(f226(x80391),f2(x80391)),x80392))+~P1(f319(f319(f225(x80391),x80394),f319(f319(f75(x80391),x80393),x80392)))+P1(f319(f319(f225(x80391),x80393),f319(f319(f282(x80391),x80394),x80392)))
% 22.40/22.31 [8040]~P74(x80401)+~P1(f319(f319(f226(x80401),x80402),f2(x80401)))+P1(f319(f319(f226(x80401),f2(x80401)),x80402))+~P1(f319(f319(f225(x80401),x80404),f319(f319(f282(x80401),x80403),x80402)))+P1(f319(f319(f225(x80401),x80403),f319(f319(f75(x80401),x80404),x80402)))
% 22.40/22.31 [8041]~P74(x80411)+~P1(f319(f319(f226(x80411),x80412),f2(x80411)))+P1(f319(f319(f226(x80411),f2(x80411)),x80412))+~P1(f319(f319(f226(x80411),x80414),f319(f319(f75(x80411),x80413),x80412)))+P1(f319(f319(f226(x80411),x80413),f319(f319(f282(x80411),x80414),x80412)))
% 22.40/22.31 [8042]~P74(x80421)+~P1(f319(f319(f226(x80421),x80422),f2(x80421)))+P1(f319(f319(f226(x80421),f2(x80421)),x80422))+~P1(f319(f319(f226(x80421),x80424),f319(f319(f282(x80421),x80423),x80422)))+P1(f319(f319(f226(x80421),x80423),f319(f319(f75(x80421),x80424),x80422)))
% 22.40/22.31 [8170]~P69(x81701)+~P1(f319(f319(f279(x81701),x81703),x81704))+~P1(f319(f319(f279(x81701),x81703),x81702))+~P1(f319(f319(f279(x81701),x81702),x81704))+P1(f319(f319(f279(x81701),f319(f319(f30(x81701),x81702),x81703)),f319(f319(f30(x81701),x81704),x81703)))
% 22.40/22.31 [8183]~P4(x81831)+~P13(x81831,x81832)+~P1(f319(f319(f225(a906),x81833),x81834))+P1(f319(f319(f225(x81831),f319(f319(f156(x81831),x81832),x81833)),f319(f319(f156(x81831),x81832),x81834)))+~P1(f319(f319(f226(a906),x81834),f319(f182(f907(x81831)),x81832)))
% 22.40/22.31 [8234]~P126(x82341)+~P1(f319(f319(f225(x82341),x82342),f72(x82341)))+~P1(f319(f319(f225(x82341),f2(x82341)),x82342))+~P1(f319(f319(f225(a906),x82344),x82343))+P1(f319(f319(f225(x82341),f319(f319(f236(x82341),x82342),x82343)),f319(f319(f236(x82341),x82342),x82344)))
% 22.40/22.31 [8235]~P126(x82351)+~P1(f319(f319(f226(x82351),x82352),f72(x82351)))+~P1(f319(f319(f226(x82351),f2(x82351)),x82352))+~P1(f319(f319(f226(a906),x82354),x82353))+P1(f319(f319(f226(x82351),f319(f319(f236(x82351),x82352),x82353)),f319(f319(f236(x82351),x82352),x82354)))
% 22.40/22.31 [8236]~P126(x82361)+~P1(f319(f319(f225(x82361),f2(x82361)),x82362))+~P1(f319(f319(f226(a906),f2(a906)),x82363))+~P1(f319(f319(f226(x82361),x82362),x82364))+P1(f319(f319(f226(x82361),f319(f319(f236(x82361),x82362),x82363)),f319(f319(f236(x82361),x82364),x82363)))
% 22.40/22.31 [8254]~P4(x82541)+~P13(x82541,f319(f160(x82541),x82542))+~P1(f319(f319(f225(a906),x82544),x82543))+P1(f319(f319(f225(x82541),f319(f319(f156(x82541),x82542),x82543)),f319(f319(f156(x82541),x82542),x82544)))+~P1(f319(f319(f226(a906),x82543),f319(f182(f907(x82541)),x82542)))
% 22.40/22.31 [8479]~P69(x84791)+P1(f319(f319(f279(x84791),x84792),x84793))+~P1(f319(f319(f279(x84791),x84794),x84793))+~P1(f319(f319(f279(x84791),x84794),x84792))+~P1(f319(f319(f279(x84791),f319(f319(f30(x84791),x84792),x84794)),f319(f319(f30(x84791),x84793),x84794)))
% 22.40/22.31 [8494]~P74(x84941)+~P1(f319(f319(f225(x84941),x84942),f2(x84941)))+~P1(f319(f319(f225(x84941),x84943),x84944))+~P1(f319(f319(f226(x84941),f2(x84941)),f319(f319(f75(x84941),x84943),x84944)))+P1(f319(f319(f225(x84941),f319(f319(f282(x84941),x84942),x84943)),f319(f319(f282(x84941),x84942),x84944)))
% 22.40/22.31 [8495]~P75(x84951)+~P1(f319(f319(f226(x84951),x84952),f2(x84951)))+~P1(f319(f319(f226(x84951),x84953),x84954))+~P1(f319(f319(f226(x84951),f2(x84951)),f319(f319(f75(x84951),x84953),x84954)))+P1(f319(f319(f226(x84951),f319(f319(f282(x84951),x84952),x84953)),f319(f319(f282(x84951),x84952),x84954)))
% 22.40/22.31 [8504]~P75(x85041)+~P1(f319(f319(f225(x85041),x85044),x85043))+~P1(f319(f319(f225(x85041),f2(x85041)),x85042))+~P1(f319(f319(f226(x85041),f2(x85041)),f319(f319(f75(x85041),x85043),x85044)))+P1(f319(f319(f225(x85041),f319(f319(f282(x85041),x85042),x85043)),f319(f319(f282(x85041),x85042),x85044)))
% 22.40/22.31 [8505]~P75(x85051)+~P1(f319(f319(f226(x85051),x85054),x85053))+~P1(f319(f319(f226(x85051),f2(x85051)),x85052))+~P1(f319(f319(f226(x85051),f2(x85051)),f319(f319(f75(x85051),x85053),x85054)))+P1(f319(f319(f226(x85051),f319(f319(f282(x85051),x85052),x85053)),f319(f319(f282(x85051),x85052),x85054)))
% 22.40/22.31 [8604]P1(f319(x86041,x86042))+~P1(f319(f55(x86044),x86042))+P1(f319(x86041,f869(x86041,x86043,x86042,x86044)))+~P1(f319(x86041,f181(f913(x86044,a904))))+~P1(f319(f319(f225(f913(x86044,a904)),x86042),x86043))
% 22.40/22.31 [8613]P1(f319(x86131,x86132))+P1(f319(f55(x86133),f869(x86131,x86134,x86132,x86133)))+~P1(f319(f55(x86133),x86132))+~P1(f319(x86131,f181(f913(x86133,a904))))+~P1(f319(f319(f225(f913(x86133,a904)),x86132),x86134))
% 22.40/22.31 [8878]E(f319(f319(f74(a1),f410(x88781,x88782,x88783,x88784)),f411(x88781,x88782,x88783,x88784)),x88784)+~P1(f319(f319(f226(a1),f2(a1)),x88783))+~P1(f319(f319(f226(a1),x88782),x88784))+~P1(f319(f319(f321(a1),x88782),x88781))+P1(f319(f319(f226(a1),x88782),f319(f319(f3(a1),x88784),x88783)))
% 22.40/22.31 [9102]~P1(f319(f319(f226(a1),f2(a1)),x91023))+~P1(f319(f319(f226(a1),x91022),x91024))+~P1(f319(f319(f321(a1),x91022),x91021))+P1(f319(f319(f321(a1),f410(x91021,x91022,x91023,x91024)),x91021))+P1(f319(f319(f226(a1),x91022),f319(f319(f3(a1),x91024),x91023)))
% 22.40/22.31 [9113]P1(f319(x91131,x91132))+~P1(f319(f55(x91133),x91132))+P1(f319(f319(f321(x91133),f870(x91131,x91134,x91132,x91133)),x91134))+~P1(f319(x91131,f181(f913(x91133,a904))))+~P1(f319(f319(f225(f913(x91133,a904)),x91132),x91134))
% 22.40/22.31 [9130]E(f319(f319(f74(a1),f390(x91301,x91302,x91303,x91304)),f391(x91301,x91302,x91303,x91304)),x91304)+~P1(f319(f319(f226(a1),f2(a1)),x91303))+~P1(f319(f319(f225(a1),x91302),x91304))+P1(f319(f319(f225(a1),x91302),f319(f319(f3(a1),x91304),x91303)))+~P1(f319(f319(f321(a1),f319(f319(f3(a1),x91302),f72(a1))),x91301))
% 22.40/22.31 [9178]~P1(f319(f319(f226(a1),f2(a1)),x91783))+~P1(f319(f319(f226(a1),x91781),x91782))+~P1(f319(f319(f321(a1),x91781),x91784))+P1(f319(f319(f321(a1),f411(x91784,x91781,x91783,x91782)),f295(a1,f72(a1),x91783)))+P1(f319(f319(f226(a1),x91781),f319(f319(f3(a1),x91782),x91783)))
% 22.40/22.31 [9198]~P76(x91982)+~E(f768(x91983,x91984,x91981,x91982),f769(x91983,x91984,x91981,x91982))+~P1(f319(f55(x91981),f770(x91983,x91984,x91981,x91982)))+E(f319(f319(f8(f913(x91981,a904),x91982),f319(f8(x91981,x91982),x91983)),x91984),f319(f319(f8(x91981,x91982),x91983),f31(f913(x91981,a904),x91984)))+~P1(f319(f55(f913(x91981,a904)),x91984))
% 22.40/22.31 [9202]~P76(x92022)+~E(f319(x92023,f772(x92023,x92024,x92021,x92022)),f2(x92022))+~P1(f319(f55(x92021),f770(x92023,x92024,x92021,x92022)))+E(f319(f319(f8(f913(x92021,a904),x92022),f319(f8(x92021,x92022),x92023)),x92024),f319(f319(f8(x92021,x92022),x92023),f31(f913(x92021,a904),x92024)))+~P1(f319(f55(f913(x92021,a904)),x92024))
% 22.40/22.31 [9276]~P1(f319(f319(f226(a1),f2(a1)),x92763))+~P1(f319(f319(f225(a1),x92762),x92764))+P1(f319(f319(f321(a1),f390(x92761,x92762,x92763,x92764)),x92761))+P1(f319(f319(f225(a1),x92762),f319(f319(f3(a1),x92764),x92763)))+~P1(f319(f319(f321(a1),f319(f319(f3(a1),x92762),f72(a1))),x92761))
% 22.40/22.31 [9321]~P1(f319(f319(f226(a1),f2(a1)),x93213))+~P1(f319(f319(f225(a1),x93211),x93212))+P1(f319(f319(f321(a1),f391(x93214,x93211,x93213,x93212)),f295(a1,f72(a1),x93213)))+P1(f319(f319(f225(a1),x93211),f319(f319(f3(a1),x93212),x93213)))+~P1(f319(f319(f321(a1),f319(f319(f3(a1),x93211),f72(a1))),x93214))
% 22.40/22.31 [9341]~P76(x93412)+~E(f768(x93413,x93414,x93411,x93412),f769(x93413,x93414,x93411,x93412))+E(f319(f319(f8(f913(x93411,a904),x93412),f319(f8(x93411,x93412),x93413)),x93414),f319(f319(f8(x93411,x93412),x93413),f31(f913(x93411,a904),x93414)))+P1(f319(f319(f321(f913(x93411,a904)),f770(x93413,x93414,x93411,x93412)),x93414))+~P1(f319(f55(f913(x93411,a904)),x93414))
% 22.40/22.31 [9346]~P76(x93462)+~E(f319(x93463,f772(x93463,x93464,x93461,x93462)),f2(x93462))+E(f319(f319(f8(f913(x93461,a904),x93462),f319(f8(x93461,x93462),x93463)),x93464),f319(f319(f8(x93461,x93462),x93463),f31(f913(x93461,a904),x93464)))+P1(f319(f319(f321(f913(x93461,a904)),f770(x93463,x93464,x93461,x93462)),x93464))+~P1(f319(f55(f913(x93461,a904)),x93464))
% 22.40/22.31 [9452]~P76(x94522)+~P1(f319(f55(x94521),f770(x94523,x94524,x94521,x94522)))+E(f319(f319(f8(f913(x94521,a904),x94522),f319(f8(x94521,x94522),x94523)),x94524),f319(f319(f8(x94521,x94522),x94523),f31(f913(x94521,a904),x94524)))+P1(f319(f319(f321(f913(x94521,a904)),f769(x94523,x94524,x94521,x94522)),x94524))+~P1(f319(f55(f913(x94521,a904)),x94524))
% 22.40/22.31 [9453]~P76(x94532)+~P1(f319(f55(x94531),f770(x94533,x94534,x94531,x94532)))+E(f319(f319(f8(f913(x94531,a904),x94532),f319(f8(x94531,x94532),x94533)),x94534),f319(f319(f8(x94531,x94532),x94533),f31(f913(x94531,a904),x94534)))+P1(f319(f319(f321(f913(x94531,a904)),f768(x94533,x94534,x94531,x94532)),x94534))+~P1(f319(f55(f913(x94531,a904)),x94534))
% 22.40/22.31 [9532]~P76(x95322)+E(f319(f319(f8(f913(x95321,a904),x95322),f319(f8(x95321,x95322),x95323)),x95324),f319(f319(f8(x95321,x95322),x95323),f31(f913(x95321,a904),x95324)))+P1(f319(f319(f321(f913(x95321,a904)),f770(x95323,x95324,x95321,x95322)),x95324))+P1(f319(f319(f321(f913(x95321,a904)),f769(x95323,x95324,x95321,x95322)),x95324))+~P1(f319(f55(f913(x95321,a904)),x95324))
% 22.40/22.31 [9533]~P76(x95332)+E(f319(f319(f8(f913(x95331,a904),x95332),f319(f8(x95331,x95332),x95333)),x95334),f319(f319(f8(x95331,x95332),x95333),f31(f913(x95331,a904),x95334)))+P1(f319(f319(f321(f913(x95331,a904)),f770(x95333,x95334,x95331,x95332)),x95334))+P1(f319(f319(f321(f913(x95331,a904)),f768(x95333,x95334,x95331,x95332)),x95334))+~P1(f319(f55(f913(x95331,a904)),x95334))
% 22.40/22.31 [9549]~P76(x95492)+P1(f319(f319(f321(x95491),f772(x95493,x95494,x95491,x95492)),f769(x95493,x95494,x95491,x95492)))+~P1(f319(f55(x95491),f770(x95493,x95494,x95491,x95492)))+E(f319(f319(f8(f913(x95491,a904),x95492),f319(f8(x95491,x95492),x95493)),x95494),f319(f319(f8(x95491,x95492),x95493),f31(f913(x95491,a904),x95494)))+~P1(f319(f55(f913(x95491,a904)),x95494))
% 22.40/22.31 [9550]~P76(x95502)+P1(f319(f319(f321(x95501),f772(x95503,x95504,x95501,x95502)),f768(x95503,x95504,x95501,x95502)))+~P1(f319(f55(x95501),f770(x95503,x95504,x95501,x95502)))+E(f319(f319(f8(f913(x95501,a904),x95502),f319(f8(x95501,x95502),x95503)),x95504),f319(f319(f8(x95501,x95502),x95503),f31(f913(x95501,a904),x95504)))+~P1(f319(f55(f913(x95501,a904)),x95504))
% 22.40/22.31 [9562]P1(f319(x95621,x95622))+~P1(f319(f319(f321(x95623),f870(x95621,x95624,x95622,x95623)),f869(x95621,x95624,x95622,x95623)))+~P1(f319(f55(x95623),x95622))+~P1(f319(x95621,f181(f913(x95623,a904))))+~P1(f319(f319(f225(f913(x95623,a904)),x95622),x95624))
% 22.40/22.31 [9598]~P76(x95982)+P1(f319(f319(f321(x95981),f772(x95983,x95984,x95981,x95982)),f769(x95983,x95984,x95981,x95982)))+E(f319(f319(f8(f913(x95981,a904),x95982),f319(f8(x95981,x95982),x95983)),x95984),f319(f319(f8(x95981,x95982),x95983),f31(f913(x95981,a904),x95984)))+P1(f319(f319(f321(f913(x95981,a904)),f770(x95983,x95984,x95981,x95982)),x95984))+~P1(f319(f55(f913(x95981,a904)),x95984))
% 22.40/22.31 [9599]~P76(x95992)+P1(f319(f319(f321(x95991),f772(x95993,x95994,x95991,x95992)),f768(x95993,x95994,x95991,x95992)))+E(f319(f319(f8(f913(x95991,a904),x95992),f319(f8(x95991,x95992),x95993)),x95994),f319(f319(f8(x95991,x95992),x95993),f31(f913(x95991,a904),x95994)))+P1(f319(f319(f321(f913(x95991,a904)),f770(x95993,x95994,x95991,x95992)),x95994))+~P1(f319(f55(f913(x95991,a904)),x95994))
% 22.40/22.31 [9801]P1(f319(x98011,x98012))+~P1(f319(f55(x98013),x98012))+~P1(f319(x98011,f319(f319(f301(x98013),f870(x98011,x98014,x98012,x98013)),f869(x98011,x98014,x98012,x98013))))+~P1(f319(x98011,f181(f913(x98013,a904))))+~P1(f319(f319(f225(f913(x98013,a904)),x98012),x98014))
% 22.40/22.31 [7812]~P74(x78121)+P1(f319(f319(f226(x78121),x78122),f2(x78121)))+~P1(f319(f319(f225(x78121),f2(x78121)),x78124))+P1(f319(f319(f226(x78121),f2(x78121)),x78122))+P1(f319(f319(f225(x78121),f319(f319(f282(x78121),x78123),x78122)),x78124))
% 22.40/22.31 [7813]~P74(x78131)+P1(f319(f319(f226(x78131),x78132),f2(x78131)))+P1(f319(f319(f226(x78131),f2(x78131)),x78132))+~P1(f319(f319(f226(x78131),f2(x78131)),x78134))+P1(f319(f319(f226(x78131),f319(f319(f282(x78131),x78133),x78132)),x78134))
% 22.40/22.31 [8028]~P5(x80281)+~P40(x80281,x80281,x80284)+~E(x80283,f88(x80281,x80284))+P1(f319(f319(f225(x80281),x80282),x80283))+~P1(f319(f319(f225(x80281),x80282),f319(x80284,f319(f319(f93(x80281),x80282),x80283))))
% 22.40/22.31 [8086]~P1(f319(f319(f225(a1),x80864),f2(a1)))+~E(x80862,f319(f319(f74(a1),f319(f319(f75(a1),x80861),x80863)),x80864))+P1(f319(f319(f226(a1),f2(a1)),x80861))+~P1(f319(f319(f226(a1),x80861),x80864))+P1(f319(f43(x80862,x80861),f319(f319(f244(a1,a1),x80863),x80864)))
% 22.40/22.31 [8120]~P1(f319(x81201,x81204))+P1(f319(x81201,f405(x81202,x81201,x81203)))+~P1(f319(f319(f225(a1),f2(a1)),x81202))+~P1(f319(f319(f226(a1),f2(a1)),x81203))+P1(f319(x81201,f319(f319(f3(a1),x81204),f319(f319(f75(a1),x81202),x81203))))
% 22.40/22.31 [8121]~P1(f319(x81211,x81214))+P1(f319(x81211,f421(x81212,x81211,x81213)))+~P1(f319(f319(f225(a1),f2(a1)),x81212))+~P1(f319(f319(f226(a1),f2(a1)),x81213))+P1(f319(x81211,f319(f319(f74(a1),x81214),f319(f319(f75(a1),x81212),x81213))))
% 22.40/22.31 [8122]~P74(x81221)+P1(f319(f319(f226(x81221),x81222),f2(x81221)))+P1(f319(f319(f226(x81221),f2(x81221)),x81222))+P1(f319(f319(f225(x81221),f2(x81221)),x81223))+~P1(f319(f319(f225(x81221),f319(f319(f282(x81221),x81224),x81222)),x81223))
% 22.40/22.31 [8123]~P74(x81231)+P1(f319(f319(f226(x81231),x81232),f2(x81231)))+P1(f319(f319(f226(x81231),f2(x81231)),x81232))+P1(f319(f319(f226(x81231),f2(x81231)),x81233))+~P1(f319(f319(f226(x81231),f319(f319(f282(x81231),x81234),x81232)),x81233))
% 22.40/22.31 [8178]~E(x81781,f319(f319(f74(a1),f319(f319(f75(a1),x81782),x81783)),x81784))+~P1(f319(f319(f225(a1),f2(a1)),x81784))+~P1(f319(f319(f226(a1),f2(a1)),x81782))+~P1(f319(f319(f226(a1),x81784),x81782))+P1(f319(f43(x81781,x81782),f319(f319(f244(a1,a1),x81783),x81784)))
% 22.40/22.31 [8293]~P74(x82931)+P1(f319(f319(f226(x82931),x82932),f2(x82931)))+~P1(f319(f319(f225(x82931),f2(x82931)),x82934))+~P1(f319(f319(f225(x82931),x82933),f319(f319(f75(x82931),x82934),x82932)))+P1(f319(f319(f225(x82931),f319(f319(f282(x82931),x82933),x82932)),x82934))
% 22.40/22.31 [8294]~P74(x82941)+P1(f319(f319(f226(x82941),x82942),f2(x82941)))+~P1(f319(f319(f226(x82941),f2(x82941)),x82944))+~P1(f319(f319(f226(x82941),x82943),f319(f319(f75(x82941),x82944),x82942)))+P1(f319(f319(f226(x82941),f319(f319(f282(x82941),x82943),x82942)),x82944))
% 22.40/22.31 [8376]~P74(x83761)+P1(f319(f319(f226(x83761),x83762),f2(x83761)))+~P1(f319(f319(f225(x83761),x83763),f2(x83761)))+P1(f319(f319(f225(x83761),x83763),f319(f319(f282(x83761),x83764),x83762)))+~P1(f319(f319(f225(x83761),f319(f319(f75(x83761),x83763),x83762)),x83764))
% 22.40/22.31 [8377]~P74(x83771)+P1(f319(f319(f226(x83771),x83772),f2(x83771)))+~P1(f319(f319(f226(x83771),x83773),f2(x83771)))+P1(f319(f319(f226(x83771),x83773),f319(f319(f282(x83771),x83774),x83772)))+~P1(f319(f319(f226(x83771),f319(f319(f75(x83771),x83773),x83772)),x83774))
% 22.40/22.31 [8526]~P74(x85261)+~P1(f319(f319(f226(x85261),x85262),f2(x85261)))+P1(f319(f319(f226(x85261),f2(x85261)),x85262))+~P1(f319(f319(f225(x85261),f319(f319(f282(x85261),x85264),x85262)),x85263))+P1(f319(f319(f225(x85261),f319(f319(f75(x85261),x85263),x85262)),x85264))
% 22.40/22.31 [8527]~P74(x85271)+~P1(f319(f319(f226(x85271),x85272),f2(x85271)))+P1(f319(f319(f226(x85271),f2(x85271)),x85272))+~P1(f319(f319(f225(x85271),f319(f319(f75(x85271),x85274),x85272)),x85273))+P1(f319(f319(f225(x85271),f319(f319(f282(x85271),x85273),x85272)),x85274))
% 22.40/22.31 [8528]~P74(x85281)+~P1(f319(f319(f226(x85281),x85282),f2(x85281)))+P1(f319(f319(f226(x85281),f2(x85281)),x85282))+~P1(f319(f319(f226(x85281),f319(f319(f282(x85281),x85284),x85282)),x85283))+P1(f319(f319(f226(x85281),f319(f319(f75(x85281),x85283),x85282)),x85284))
% 22.40/22.31 [8529]~P74(x85291)+~P1(f319(f319(f226(x85291),x85292),f2(x85291)))+P1(f319(f319(f226(x85291),f2(x85291)),x85292))+~P1(f319(f319(f226(x85291),f319(f319(f75(x85291),x85294),x85292)),x85293))+P1(f319(f319(f226(x85291),f319(f319(f282(x85291),x85293),x85292)),x85294))
% 22.40/22.31 [8546]~P74(x85461)+~P1(f319(f319(f225(x85461),f2(x85461)),x85464))+P1(f319(f319(f226(x85461),f2(x85461)),x85462))+~P1(f319(f319(f225(x85461),f319(f319(f75(x85461),x85464),x85462)),x85463))+P1(f319(f319(f225(x85461),f319(f319(f282(x85461),x85463),x85462)),x85464))
% 22.40/22.31 [8547]~P74(x85471)+~P1(f319(f319(f226(x85471),f2(x85471)),x85474))+P1(f319(f319(f226(x85471),f2(x85471)),x85472))+~P1(f319(f319(f226(x85471),f319(f319(f75(x85471),x85474),x85472)),x85473))+P1(f319(f319(f226(x85471),f319(f319(f282(x85471),x85473),x85472)),x85474))
% 22.40/22.31 [8625]~P74(x86251)+~P1(f319(f319(f226(x86251),x86254),f2(x86251)))+~P1(f319(f319(f225(x86251),x86253),f319(f319(f75(x86251),x86252),x86254)))+P1(f319(f319(f225(x86251),x86252),f319(f319(f282(x86251),x86253),x86254)))+~P1(f319(f319(f225(x86251),f319(f319(f75(x86251),x86252),x86254)),x86253))
% 22.40/22.31 [8626]~P74(x86261)+~P1(f319(f319(f225(x86261),x86262),f2(x86261)))+~P1(f319(f319(f225(x86261),x86263),f319(f319(f75(x86261),x86262),x86264)))+P1(f319(f319(f225(x86261),x86262),f319(f319(f282(x86261),x86263),x86264)))+~P1(f319(f319(f225(x86261),f319(f319(f75(x86261),x86262),x86264)),x86263))
% 22.40/22.31 [8627]~P74(x86271)+~P1(f319(f319(f226(x86271),x86274),f2(x86271)))+~P1(f319(f319(f226(x86271),x86273),f319(f319(f75(x86271),x86272),x86274)))+P1(f319(f319(f226(x86271),x86272),f319(f319(f282(x86271),x86273),x86274)))+~P1(f319(f319(f226(x86271),f319(f319(f75(x86271),x86272),x86274)),x86273))
% 22.40/22.31 [8628]~P74(x86281)+~P1(f319(f319(f226(x86281),x86282),f2(x86281)))+~P1(f319(f319(f226(x86281),x86283),f319(f319(f75(x86281),x86282),x86284)))+P1(f319(f319(f226(x86281),x86282),f319(f319(f282(x86281),x86283),x86284)))+~P1(f319(f319(f226(x86281),f319(f319(f75(x86281),x86282),x86284)),x86283))
% 22.40/22.31 [8750]~P74(x87501)+~P1(f319(f319(f226(x87501),x87503),f2(x87501)))+~P1(f319(f319(f225(x87501),x87502),f319(f319(f75(x87501),x87504),x87503)))+~P1(f319(f319(f225(x87501),f319(f319(f75(x87501),x87504),x87503)),x87502))+P1(f319(f319(f225(x87501),f319(f319(f282(x87501),x87502),x87503)),x87504))
% 22.40/22.31 [8751]~P74(x87511)+~P1(f319(f319(f226(x87511),x87513),f2(x87511)))+~P1(f319(f319(f226(x87511),x87512),f319(f319(f75(x87511),x87514),x87513)))+~P1(f319(f319(f226(x87511),f319(f319(f75(x87511),x87514),x87513)),x87512))+P1(f319(f319(f226(x87511),f319(f319(f282(x87511),x87512),x87513)),x87514))
% 22.40/22.31 [8763]~P74(x87631)+~P1(f319(f319(f225(x87631),f2(x87631)),x87634))+~P1(f319(f319(f225(x87631),x87632),f319(f319(f75(x87631),x87634),x87633)))+~P1(f319(f319(f225(x87631),f319(f319(f75(x87631),x87634),x87633)),x87632))+P1(f319(f319(f225(x87631),f319(f319(f282(x87631),x87632),x87633)),x87634))
% 22.40/22.31 [8764]~P74(x87641)+~P1(f319(f319(f226(x87641),f2(x87641)),x87644))+~P1(f319(f319(f226(x87641),x87642),f319(f319(f75(x87641),x87644),x87643)))+~P1(f319(f319(f226(x87641),f319(f319(f75(x87641),x87644),x87643)),x87642))+P1(f319(f319(f226(x87641),f319(f319(f282(x87641),x87642),x87643)),x87644))
% 22.40/22.31 [8949]E(f319(f319(f3(a1),f412(x89491,x89492,x89493,x89494)),f413(x89491,x89492,x89493,x89494)),x89494)+~P1(f319(f319(f226(a1),f2(a1)),x89493))+~P1(f319(f319(f321(a1),x89492),x89491))+~P1(f319(f319(f226(a1),x89494),x89492))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x89494),x89493)),x89492))
% 22.40/22.31 [9027]~P1(f319(x90271,x90272))+~P1(f319(f319(f225(a1),f2(a1)),x90273))+~P1(f319(f319(f226(a1),f2(a1)),x90274))+~P1(f319(x90271,f319(f319(f3(a1),f405(x90273,x90271,x90274)),x90274)))+P1(f319(x90271,f319(f319(f3(a1),x90272),f319(f319(f75(a1),x90273),x90274))))
% 22.40/22.31 [9028]~P1(f319(x90281,x90282))+~P1(f319(f319(f225(a1),f2(a1)),x90283))+~P1(f319(f319(f226(a1),f2(a1)),x90284))+~P1(f319(x90281,f319(f319(f74(a1),f421(x90283,x90281,x90284)),x90284)))+P1(f319(x90281,f319(f319(f74(a1),x90282),f319(f319(f75(a1),x90283),x90284))))
% 22.40/22.31 [9172]~P1(f319(f319(f226(a1),f2(a1)),x91723))+~P1(f319(f319(f321(a1),x91722),x91721))+~P1(f319(f319(f226(a1),x91724),x91722))+P1(f319(f319(f321(a1),f412(x91721,x91722,x91723,x91724)),x91721))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x91724),x91723)),x91722))
% 22.40/22.31 [9186]E(f319(f319(f3(a1),f392(x91861,x91862,x91863,x91864)),f393(x91861,x91862,x91863,x91864)),x91864)+~P1(f319(f319(f226(a1),f2(a1)),x91863))+~P1(f319(f319(f225(a1),x91864),x91862))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x91862),f72(a1))),x91861))+P1(f319(f319(f225(a1),f319(f319(f74(a1),x91864),x91863)),x91862))
% 22.40/22.31 [9213]~P1(f319(f319(f226(a1),f2(a1)),x92132))+~P1(f319(f319(f321(a1),x92133),x92134))+~P1(f319(f319(f226(a1),x92131),x92133))+P1(f319(f319(f321(a1),f413(x92134,x92133,x92132,x92131)),f295(a1,f72(a1),x92132)))+P1(f319(f319(f226(a1),f319(f319(f74(a1),x92131),x92132)),x92133))
% 22.40/22.31 [9313]~P1(f319(f319(f226(a1),f2(a1)),x93133))+~P1(f319(f319(f225(a1),x93134),x93132))+P1(f319(f319(f321(a1),f392(x93131,x93132,x93133,x93134)),x93131))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x93132),f72(a1))),x93131))+P1(f319(f319(f225(a1),f319(f319(f74(a1),x93134),x93133)),x93132))
% 22.40/22.31 [9358]~P1(f319(f319(f226(a1),f2(a1)),x93582))+~P1(f319(f319(f225(a1),x93581),x93583))+P1(f319(f319(f321(a1),f393(x93584,x93583,x93582,x93581)),f295(a1,f72(a1),x93582)))+~P1(f319(f319(f321(a1),f319(f319(f74(a1),x93583),f72(a1))),x93584))+P1(f319(f319(f225(a1),f319(f319(f74(a1),x93581),x93582)),x93583))
% 22.40/22.31 [9665]~P37(x96651,x96653)+~P27(x96651,x96654)+P37(x96651,f319(f319(f93(f913(f912(x96651,x96651),a904)),x96652),x96653))+~P1(f319(f319(f225(f913(f912(x96651,x96651),a904)),x96652),f319(f243(f913(f912(x96651,x96651),a904),f913(f912(x96651,x96651),a904)),x96654)))+~P1(f319(f319(f225(f913(f912(x96651,x96651),a904)),x96653),f319(f248(f913(f912(x96651,x96651),a904),f913(f912(x96651,x96651),a904)),x96654)))
% 22.40/22.31 [10058]~P19(x100582,x100584,x100583)+E(x100581,f181(f913(x100582,a904)))+~P1(f319(f55(x100582),x100581))+P1(f319(f319(f321(x100582),f319(x100583,x100581)),x100581))+~P1(f319(f319(f321(x100582),f319(f319(x100584,f714(x100581,x100583,x100584,x100582)),f725(x100581,x100583,x100584,x100582))),f319(f319(f301(x100582),f714(x100581,x100583,x100584,x100582)),f319(f319(f301(x100582),f725(x100581,x100583,x100584,x100582)),f181(f913(x100582,a904))))))
% 22.40/22.31 [8653]~P5(x86531)+~P40(x86531,x86531,x86534)+~E(x86532,f87(x86531,x86534))+P1(f319(f319(f225(x86531),x86532),x86533))+~P1(f319(f319(f225(x86531),f319(x86534,f319(f319(f94(x86531),x86532),x86533))),x86533))
% 22.40/22.31 [10001]~P111(x100012)+~P71(x100011)+~P1(f319(f319(f225(f913(x100011,x100012)),x100013),x100014))+P1(f319(f319(f226(f913(x100011,x100012)),x100013),x100014))+~P1(f319(f50(x100011),f319(f319(f10(a904,a904,x100011),a314),f319(f319(f20(x100011,x100012,a904),f319(f319(f10(x100012,f913(x100012,a904),x100011),a316),x100013)),x100014))))
% 22.40/22.31 [5240]~P50(x52404,x52405,x52403)+E(x52401,x52402)+~P4(x52404)+~P111(x52405)+~E(f319(x52403,x52401),f319(x52403,x52402))
% 22.40/22.31 [9569]~P56(x95691,x95691,x95694)+P1(f319(f319(f321(f912(x95691,x95691)),f319(f319(f244(x95691,x95691),x95692),x95693)),f299(x95691,x95694)))+P1(f319(f319(f321(f912(x95691,x95691)),f319(f319(f244(x95691,x95691),x95693),x95692)),f299(x95691,x95694)))+~P1(f319(f319(f321(f912(x95691,x95691)),f319(f319(f244(x95691,x95691),x95695),x95692)),f299(x95691,x95694)))+~P1(f319(f319(f321(f912(x95691,x95691)),f319(f319(f244(x95691,x95691),x95695),x95693)),f299(x95691,x95694)))
% 22.40/22.31 [5729]E(x57291,f2(a906))+~E(f319(f29(x57292),x57295),x57291)+E(f319(f29(x57292),x57293),f319(a104,x57291))+~E(x57293,f319(f319(f301(x57292),x57294),x57295))+P1(f319(f319(f321(x57292),x57294),x57295))
% 22.40/22.31 [5852]~P73(x58522)+E(x58521,f2(x58522))+E(x58523,f2(x58522))+~E(f319(f319(f282(x58522),x58524),x58523),f319(f319(f282(x58522),x58525),x58521))+E(f319(f319(f75(x58522),x58524),x58521),f319(f319(f75(x58522),x58525),x58523))
% 22.40/22.31 [5853]~P73(x58532)+E(x58531,f2(x58532))+E(x58533,f2(x58532))+~E(f319(f319(f75(x58532),x58534),x58533),f319(f319(f75(x58532),x58535),x58531))+E(f319(f319(f282(x58532),x58534),x58531),f319(f319(f282(x58532),x58535),x58533))
% 22.40/22.31 [5926]~E(f319(f29(x59261),x59265),x59263)+~E(x59265,f181(f913(x59261,a904)))+E(f319(f29(x59261),x59262),f319(a104,x59263))+~E(x59262,f319(f319(f301(x59261),x59264),x59265))+P1(f319(f319(f321(x59261),x59264),x59265))
% 22.40/22.31 [6159]~P119(x61592)+~E(f319(x61593,x61595),f2(x61592))+E(f319(f319(f11(x61591,x61592),x61593),x61594),f2(x61592))+~P1(f319(f55(x61591),x61594))+~P1(f319(f319(f321(x61591),x61595),x61594))
% 22.40/22.31 [6533]~P4(x65333)+E(x65331,x65332)+~E(f319(f294(x65333,x65334),x65331),f319(f294(x65333,x65335),x65332))+~P1(f319(f319(f226(x65333),x65335),x65332))+~P1(f319(f319(f226(x65333),x65334),x65331))
% 22.40/22.31 [6534]~P4(x65343)+E(x65341,x65342)+~E(f319(f294(x65343,x65341),x65344),f319(f294(x65343,x65342),x65345))+~P1(f319(f319(f226(x65343),x65342),x65345))+~P1(f319(f319(f226(x65343),x65341),x65344))
% 22.40/22.31 [6696]~P111(x66961)+~P50(x66965,x66961,x66962)+~P4(x66965)+P1(f319(f319(f225(x66961),f319(x66962,x66963)),f319(x66962,x66964)))+~P1(f319(f319(f225(x66965),x66963),x66964))
% 22.40/22.31 [6697]~P111(x66971)+~P40(x66975,x66971,x66972)+~P111(x66975)+P1(f319(f319(f225(x66971),f319(x66972,x66973)),f319(x66972,x66974)))+~P1(f319(f319(f225(x66975),x66973),x66974))
% 22.40/22.32 [6698]~P111(x66981)+~P50(x66985,x66981,x66982)+~P4(x66985)+P1(f319(f319(f226(x66981),f319(x66982,x66983)),f319(x66982,x66984)))+~P1(f319(f319(f226(x66985),x66983),x66984))
% 22.40/22.32 [6699]~P111(x66991)+~P50(x66995,x66991,x66992)+~P111(x66995)+P1(f319(f319(f226(x66991),f319(x66992,x66993)),f319(x66992,x66994)))+~P1(f319(f319(f226(x66995),x66993),x66994))
% 22.40/22.32 [6945]~P4(x69451)+~P50(x69451,x69454,x69455)+~P111(x69454)+~P1(f319(f319(f225(x69454),f319(x69455,x69452)),f319(x69455,x69453)))+P1(f319(f319(f225(x69451),x69452),x69453))
% 22.40/22.32 [6946]~P4(x69461)+~P50(x69461,x69464,x69465)+~P111(x69464)+~P1(f319(f319(f226(x69464),f319(x69465,x69462)),f319(x69465,x69463)))+P1(f319(f319(f226(x69461),x69462),x69463))
% 22.40/22.32 [7584]~P4(x75841)+~P13(x75841,f319(f319(f126(x75841),x75844),x75845))+~P1(f319(f319(f321(x75841),x75843),f319(f164(x75841),x75845)))+~P1(f319(f319(f321(x75841),x75842),f319(f164(x75841),x75844)))+P1(f319(f319(f225(x75841),x75842),x75843))
% 22.40/22.32 [8663]~P111(x86631)+~P1(f319(f319(f226(f913(x86631,a904)),f295(x86631,x86635,x86632)),f295(x86631,x86634,x86633)))+~P1(f319(f319(f225(x86631),x86635),x86632))+P1(f319(f319(f226(x86631),x86632),x86633))+P1(f319(f319(f226(x86631),x86634),x86635))
% 22.40/22.32 [9701]~P40(f913(x97014,a904),f913(x97014,a904),x97015)+P1(f319(x97011,x97012))+~E(x97013,f87(f913(x97014,a904),x97015))+~P1(f319(x97011,f598(x97011,x97012,x97015,x97014,x97013)))+~P1(f319(f319(f321(x97014),x97012),x97013))
% 22.40/22.32 [10091]~P18(x100912,x100915,x100913)+E(x100911,f181(f913(x100912,a904)))+~E(f319(f319(x100915,f319(x100914,f872(x100911,x100914,x100913,x100915,x100912))),f319(x100914,f873(x100911,x100914,x100913,x100915,x100912))),f319(x100914,f319(f319(x100915,f872(x100911,x100914,x100913,x100915,x100912)),f873(x100911,x100914,x100913,x100915,x100912))))+E(f319(x100913,f319(f302(x100912,x100912,x100914),x100911)),f319(x100914,f319(x100913,x100911)))+~P1(f319(f55(x100912),x100911))
% 22.40/22.32 [6530]~P19(x65302,x65305,x65303)+E(x65301,f181(f913(x65302,a904)))+~P1(f319(f55(x65302),x65301))+E(f319(x65303,f319(f319(f301(x65302),x65304),x65301)),f319(f319(x65305,x65304),f319(x65303,x65301)))+P1(f319(f319(f321(x65302),x65304),x65301))
% 22.40/22.32 [7355]~P18(x73552,x73553,x73554)+E(f319(f319(x73553,f319(x73554,x73551)),f319(x73554,x73555)),f319(x73554,x73555))+E(x73551,f181(f913(x73552,a904)))+~P1(f319(f55(x73552),x73555))+~P1(f319(f319(f225(f913(x73552,a904)),x73551),x73555))
% 22.40/22.32 [7713]~P19(x77134,x77135,x77131)+E(f319(x77131,x77132),x77133)+~P1(f319(f55(x77134),x77132))+~E(f319(f319(f3(f913(x77134,a904)),x77132),f319(f319(f301(x77134),x77133),f181(f913(x77134,a904)))),f181(f913(x77134,a904)))+~P1(f319(f319(f321(x77134),x77133),x77132))
% 22.40/22.32 [8632]E(x86321,x86322)+~P8(x86323,x86324,x86325)+E(f319(f319(f94(f913(x86323,a904)),x86321),x86322),f181(f913(x86323,a904)))+~P1(f319(f319(f321(f913(x86323,a904)),x86322),f319(f319(f54(x86323),x86324),x86325)))+~P1(f319(f319(f321(f913(x86323,a904)),x86321),f319(f319(f54(x86323),x86324),x86325)))
% 22.40/22.32 [9445]~P76(x94452)+~E(f319(x94453,f356(x94453,x94454,x94455,x94451,x94452)),f2(x94452))+E(f319(f319(f8(x94451,x94452),x94453),x94454),f319(f319(f8(x94451,x94452),x94453),x94455))+~P1(f319(f55(x94451),x94455))+~P1(f319(f319(f225(f913(x94451,a904)),x94454),x94455))
% 22.40/22.32 [9446]~P76(x94462)+~E(f319(x94463,f363(x94463,x94464,x94465,x94461,x94462)),f2(x94462))+E(f319(f319(f8(x94461,x94462),x94463),x94464),f319(f319(f8(x94461,x94462),x94463),x94465))+~P1(f319(f55(x94461),x94465))+~P1(f319(f319(f225(f913(x94461,a904)),x94464),x94465))
% 22.40/22.32 [9447]~P82(x94472)+~E(f319(x94473,f357(x94473,x94474,x94475,x94471,x94472)),f72(x94472))+E(f319(f319(f11(x94471,x94472),x94473),x94474),f319(f319(f11(x94471,x94472),x94473),x94475))+~P1(f319(f55(x94471),x94475))+~P1(f319(f319(f225(f913(x94471,a904)),x94474),x94475))
% 22.40/22.32 [9448]~P82(x94482)+~E(f319(x94483,f358(x94483,x94484,x94485,x94481,x94482)),f72(x94482))+E(f319(f319(f11(x94481,x94482),x94483),x94484),f319(f319(f11(x94481,x94482),x94483),x94485))+~P1(f319(f55(x94481),x94485))+~P1(f319(f319(f225(f913(x94481,a904)),x94484),x94485))
% 22.40/22.32 [9902]~P40(f913(x99021,a904),f913(x99021,a904),f319(f319(f10(f913(x99021,a904),f913(x99021,a904),f913(x99021,a904)),f254(x99021)),x99024))+~P1(f319(f319(x99024,f319(f319(f93(f913(x99021,a904)),x99025),x99023)),f599(x99025,x99022,x99024,x99021,x99023)))+~E(x99023,f88(f913(x99021,a904),f319(f319(f10(f913(x99021,a904),f913(x99021,a904),f913(x99021,a904)),f254(x99021)),x99024)))+P1(f319(f319(f321(x99021),x99022),x99023))+~P1(f319(f319(f321(x99021),x99022),x99025))
% 22.40/22.32 [9906]~P40(f913(x99061,a904),f913(x99061,a904),f319(f319(f10(f913(x99061,a904),f913(x99061,a904),f913(x99061,a904)),f254(x99061)),x99065))+~E(x99063,f88(f913(x99061,a904),f319(f319(f10(f913(x99061,a904),f913(x99061,a904),f913(x99061,a904)),f254(x99061)),x99065)))+~P1(f319(f319(f321(x99061),x99062),x99064))+P1(f319(f319(f321(x99061),f599(x99064,x99062,x99065,x99061,x99063)),x99064))+P1(f319(f319(f321(x99061),x99062),x99063))
% 22.40/22.32 [9959]~P93(x99591)+~P1(f319(f55(x99592),x99595))+~P1(f319(f319(f225(x99591),f2(x99591)),f319(x99593,f350(x99593,x99594,x99595,x99592,x99591))))+P1(f319(f319(f225(x99591),f319(f319(f8(x99592,x99591),x99593),x99594)),f319(f319(f8(x99592,x99591),x99593),x99595)))+~P1(f319(f319(f225(f913(x99592,a904)),x99594),x99595))
% 22.40/22.32 [7581]E(x75811,f2(a906))+P1(f319(x75812,x75813))+~E(x75814,f319(f319(f74(a906),f319(f319(f75(a906),x75811),x75813)),x75815))+~P1(f319(f319(f226(a906),x75815),x75811))+~P1(f319(x75812,f319(f319(f30(a906),x75814),x75811)))
% 22.40/22.32 [7656]E(x76561,f2(a906))+P1(f319(x76562,x76563))+~P1(f319(x76562,f39(a906,x76564,x76561)))+~E(x76564,f319(f319(f74(a906),f319(f319(f75(a906),x76561),x76565)),x76563))+~P1(f319(f319(f226(a906),x76563),x76561))
% 22.40/22.32 [7946]~P73(x79463)+E(f319(x79461,x79462),f2(x79463))+~P1(f319(f55(x79464),x79465))+E(f319(f319(f11(x79464,x79463),x79461),f319(f319(f3(f913(x79464,a904)),x79465),f319(f319(f301(x79464),x79462),f181(f913(x79464,a904))))),f319(f319(f11(x79464,x79463),x79461),x79465))+P1(f319(f319(f321(x79464),x79462),x79465))
% 22.40/22.32 [8331]~P76(x83311)+~P1(f319(f55(x83312),x83315))+~P1(f319(f55(x83312),x83314))+~E(f319(f319(f94(f913(x83312,a904)),x83314),x83315),f181(f913(x83312,a904)))+E(f319(f319(f74(x83311),f319(f319(f8(x83312,x83311),x83313),x83314)),f319(f319(f8(x83312,x83311),x83313),x83315)),f319(f319(f8(x83312,x83311),x83313),f319(f319(f93(f913(x83312,a904)),x83314),x83315)))
% 22.40/22.32 [8333]~P82(x83331)+~P1(f319(f55(x83332),x83335))+~P1(f319(f55(x83332),x83334))+~E(f319(f319(f94(f913(x83332,a904)),x83334),x83335),f181(f913(x83332,a904)))+E(f319(f319(f75(x83331),f319(f319(f11(x83332,x83331),x83333),x83334)),f319(f319(f11(x83332,x83331),x83333),x83335)),f319(f319(f11(x83332,x83331),x83333),f319(f319(f93(f913(x83332,a904)),x83334),x83335)))
% 22.40/22.32 [8433]~P73(x84333)+E(f319(x84331,x84332),f2(x84333))+~P1(f319(f55(x84334),x84335))+E(f319(f319(f11(x84334,x84333),x84331),f319(f319(f3(f913(x84334,a904)),x84335),f319(f319(f301(x84334),x84332),f181(f913(x84334,a904))))),f319(f319(f282(x84333),f319(f319(f11(x84334,x84333),x84331),x84335)),f319(x84331,x84332)))+~P1(f319(f319(f321(x84334),x84332),x84335))
% 22.40/22.32 [9155]~P8(x91551,x91555,x91554)+~E(f319(f319(f54(x91551),f319(f319(f301(x91551),x91552),f181(f913(x91551,a904)))),x91554),f319(f319(f54(x91551),f319(f319(f301(x91551),x91553),f181(f913(x91551,a904)))),x91554))+~P1(f319(f319(f321(x91551),x91553),x91555))+~P1(f319(f319(f321(x91551),x91552),x91555))+P1(f319(f319(f321(f912(x91551,x91551)),f319(f319(f244(x91551,x91551),x91552),x91553)),x91554))
% 22.40/22.32 [9171]~P8(x91711,x91715,x91713)+E(f319(f319(f54(x91711),f319(f319(f301(x91711),x91712),f181(f913(x91711,a904)))),x91713),f319(f319(f54(x91711),f319(f319(f301(x91711),x91714),f181(f913(x91711,a904)))),x91713))+~P1(f319(f319(f321(x91711),x91714),x91715))+~P1(f319(f319(f321(x91711),x91712),x91715))+~P1(f319(f319(f321(f912(x91711,x91711)),f319(f319(f244(x91711,x91711),x91712),x91714)),x91713))
% 22.40/22.32 [9474]~P82(x94741)+~P1(f319(f55(x94742),x94745))+~P1(f319(f55(x94742),x94744))+~E(f319(f319(f94(f913(x94742,a904)),x94744),x94745),f181(f913(x94742,a904)))+E(f319(f319(f75(x94741),f319(f319(f319(f59(x94741,x94742,f75(x94741)),x94743),f72(x94741)),x94744)),f319(f319(f319(f59(x94741,x94742,f75(x94741)),x94743),f72(x94741)),x94745)),f319(f319(f319(f59(x94741,x94742,f75(x94741)),x94743),f72(x94741)),f319(f319(f93(f913(x94742,a904)),x94744),x94745)))
% 22.40/22.32 [9483]~P76(x94831)+~E(f319(x94833,f349(x94833,x94835,x94834,x94832,x94831)),f2(x94831))+~P1(f319(f55(x94832),x94834))+~P1(f319(f55(x94832),x94835))+E(f319(f319(f74(x94831),f319(f319(f8(x94832,x94831),x94833),x94834)),f319(f319(f8(x94832,x94831),x94833),x94835)),f319(f319(f8(x94832,x94831),x94833),f319(f319(f93(f913(x94832,a904)),x94834),x94835)))
% 22.40/22.32 [9484]~P76(x94841)+~E(f319(x94843,f351(x94843,x94845,x94844,x94842,x94841)),f2(x94841))+~P1(f319(f55(x94842),x94844))+~P1(f319(f55(x94842),x94845))+E(f319(f319(f74(x94841),f319(f319(f8(x94842,x94841),x94843),x94844)),f319(f319(f8(x94842,x94841),x94843),x94845)),f319(f319(f8(x94842,x94841),x94843),f319(f319(f93(f913(x94842,a904)),x94844),x94845)))
% 22.40/22.32 [9485]~P82(x94851)+~E(f319(x94853,f900(x94853,x94855,x94854,x94852,x94851)),f72(x94851))+~P1(f319(f55(x94852),x94854))+~P1(f319(f55(x94852),x94855))+E(f319(f319(f75(x94851),f319(f319(f11(x94852,x94851),x94853),x94854)),f319(f319(f11(x94852,x94851),x94853),x94855)),f319(f319(f11(x94852,x94851),x94853),f319(f319(f93(f913(x94852,a904)),x94854),x94855)))
% 22.40/22.32 [9486]~P82(x94861)+~E(f319(x94863,f901(x94863,x94865,x94864,x94862,x94861)),f72(x94861))+~P1(f319(f55(x94862),x94864))+~P1(f319(f55(x94862),x94865))+E(f319(f319(f75(x94861),f319(f319(f11(x94862,x94861),x94863),x94864)),f319(f319(f11(x94862,x94861),x94863),x94865)),f319(f319(f11(x94862,x94861),x94863),f319(f319(f93(f913(x94862,a904)),x94864),x94865)))
% 22.40/22.32 [9707]~P82(x97071)+~E(f319(x97073,f360(x97073,x97075,x97074,x97072,x97071)),f72(x97071))+~P1(f319(f55(x97072),x97074))+~P1(f319(f55(x97072),x97075))+E(f319(f319(f75(x97071),f319(f319(f319(f59(x97071,x97072,f75(x97071)),x97073),f72(x97071)),x97074)),f319(f319(f319(f59(x97071,x97072,f75(x97071)),x97073),f72(x97071)),x97075)),f319(f319(f319(f59(x97071,x97072,f75(x97071)),x97073),f72(x97071)),f319(f319(f93(f913(x97072,a904)),x97074),x97075)))
% 22.40/22.32 [9831]~P76(x98312)+E(f319(f319(f8(x98311,x98312),x98313),x98314),f319(f319(f8(x98311,x98312),x98313),x98315))+~P1(f319(f55(x98311),x98315))+~P1(f319(f319(f225(f913(x98311,a904)),x98314),x98315))+P1(f319(f319(f321(x98311),f356(x98313,x98314,x98315,x98311,x98312)),f319(f319(f3(f913(x98311,a904)),x98315),x98314)))
% 22.40/22.32 [9832]~P76(x98322)+E(f319(f319(f8(x98321,x98322),x98323),x98324),f319(f319(f8(x98321,x98322),x98323),x98325))+~P1(f319(f55(x98321),x98325))+~P1(f319(f319(f225(f913(x98321,a904)),x98324),x98325))+P1(f319(f319(f321(x98321),f363(x98323,x98324,x98325,x98321,x98322)),f319(f319(f3(f913(x98321,a904)),x98325),x98324)))
% 22.40/22.32 [9833]~P82(x98332)+E(f319(f319(f11(x98331,x98332),x98333),x98334),f319(f319(f11(x98331,x98332),x98333),x98335))+~P1(f319(f55(x98331),x98335))+~P1(f319(f319(f225(f913(x98331,a904)),x98334),x98335))+P1(f319(f319(f321(x98331),f357(x98333,x98334,x98335,x98331,x98332)),f319(f319(f3(f913(x98331,a904)),x98335),x98334)))
% 22.40/22.32 [9834]~P82(x98342)+E(f319(f319(f11(x98341,x98342),x98343),x98344),f319(f319(f11(x98341,x98342),x98343),x98345))+~P1(f319(f55(x98341),x98345))+~P1(f319(f319(f225(f913(x98341,a904)),x98344),x98345))+P1(f319(f319(f321(x98341),f358(x98343,x98344,x98345,x98341,x98342)),f319(f319(f3(f913(x98341,a904)),x98345),x98344)))
% 22.40/22.32 [9853]~P76(x98531)+~P1(f319(f55(x98532),x98534))+~P1(f319(f55(x98532),x98535))+E(f319(f319(f74(x98531),f319(f319(f8(x98532,x98531),x98533),x98534)),f319(f319(f8(x98532,x98531),x98533),x98535)),f319(f319(f8(x98532,x98531),x98533),f319(f319(f93(f913(x98532,a904)),x98534),x98535)))+P1(f319(f319(f321(x98532),f349(x98533,x98535,x98534,x98532,x98531)),f319(f319(f94(f913(x98532,a904)),x98534),x98535)))
% 22.40/22.32 [9854]~P76(x98541)+~P1(f319(f55(x98542),x98544))+~P1(f319(f55(x98542),x98545))+E(f319(f319(f74(x98541),f319(f319(f8(x98542,x98541),x98543),x98544)),f319(f319(f8(x98542,x98541),x98543),x98545)),f319(f319(f8(x98542,x98541),x98543),f319(f319(f93(f913(x98542,a904)),x98544),x98545)))+P1(f319(f319(f321(x98542),f351(x98543,x98545,x98544,x98542,x98541)),f319(f319(f94(f913(x98542,a904)),x98544),x98545)))
% 22.40/22.32 [9855]~P82(x98551)+~P1(f319(f55(x98552),x98554))+~P1(f319(f55(x98552),x98555))+E(f319(f319(f75(x98551),f319(f319(f11(x98552,x98551),x98553),x98554)),f319(f319(f11(x98552,x98551),x98553),x98555)),f319(f319(f11(x98552,x98551),x98553),f319(f319(f93(f913(x98552,a904)),x98554),x98555)))+P1(f319(f319(f321(x98552),f900(x98553,x98555,x98554,x98552,x98551)),f319(f319(f94(f913(x98552,a904)),x98554),x98555)))
% 22.40/22.32 [9856]~P82(x98561)+~P1(f319(f55(x98562),x98564))+~P1(f319(f55(x98562),x98565))+E(f319(f319(f75(x98561),f319(f319(f11(x98562,x98561),x98563),x98564)),f319(f319(f11(x98562,x98561),x98563),x98565)),f319(f319(f11(x98562,x98561),x98563),f319(f319(f93(f913(x98562,a904)),x98564),x98565)))+P1(f319(f319(f321(x98562),f901(x98563,x98565,x98564,x98562,x98561)),f319(f319(f94(f913(x98562,a904)),x98564),x98565)))
% 22.40/22.32 [9859]~P40(f913(x98593,a904),f913(x98593,a904),x98594)+P1(f319(x98591,x98592))+~E(x98595,f87(f913(x98593,a904),x98594))+~P1(f319(f319(f321(x98593),x98592),x98595))+P1(f319(f319(f321(x98593),f598(x98591,x98592,x98594,x98593,x98595)),f319(x98594,f319(f319(f94(f913(x98593,a904)),x98595),f319(f254(x98593),x98591)))))
% 22.40/22.32 [9863]~P93(x98635)+~P1(f319(f55(x98631),x98634))+P1(f319(f319(f225(x98635),f319(f319(f8(x98631,x98635),x98632),x98633)),f319(f319(f8(x98631,x98635),x98632),x98634)))+~P1(f319(f319(f225(f913(x98631,a904)),x98633),x98634))+P1(f319(f319(f321(x98631),f350(x98632,x98633,x98634,x98631,x98635)),f319(f319(f3(f913(x98631,a904)),x98634),x98633)))
% 22.40/22.32 [9920]~P82(x99201)+~P1(f319(f55(x99202),x99204))+~P1(f319(f55(x99202),x99205))+E(f319(f319(f75(x99201),f319(f319(f319(f59(x99201,x99202,f75(x99201)),x99203),f72(x99201)),x99204)),f319(f319(f319(f59(x99201,x99202,f75(x99201)),x99203),f72(x99201)),x99205)),f319(f319(f319(f59(x99201,x99202,f75(x99201)),x99203),f72(x99201)),f319(f319(f93(f913(x99202,a904)),x99204),x99205)))+P1(f319(f319(f321(x99202),f360(x99203,x99205,x99204,x99202,x99201)),f319(f319(f94(f913(x99202,a904)),x99204),x99205)))
% 22.40/22.32 [8834]~P19(x88341,x88344,x88345)+~P1(f319(f55(x88341),x88342))+E(f319(f319(f3(f913(x88341,a904)),x88342),f319(f319(f301(x88341),x88343),f181(f913(x88341,a904)))),f181(f913(x88341,a904)))+~P1(f319(f319(f321(x88341),x88343),x88342))+E(f319(f319(x88344,x88343),f319(x88345,f319(f319(f3(f913(x88341,a904)),x88342),f319(f319(f301(x88341),x88343),f181(f913(x88341,a904)))))),f319(x88345,x88342))
% 22.40/22.32 [8912]~P19(x89121,x89124,x89125)+~P1(f319(f55(x89121),x89123))+~P1(f319(f55(x89121),x89122))+E(f319(f319(f94(f913(x89121,a904)),x89122),x89123),f181(f913(x89121,a904)))+E(f319(f319(x89124,f319(x89125,f319(f319(f93(f913(x89121,a904)),x89122),x89123))),f319(x89125,f319(f319(f94(f913(x89121,a904)),x89122),x89123))),f319(f319(x89124,f319(x89125,x89122)),f319(x89125,x89123)))
% 22.40/22.32 [9104]~P40(f913(x91041,a904),f913(x91041,a904),x91044)+~E(x91043,f88(f913(x91041,a904),x91044))+P1(f319(f319(f321(x91041),x91042),x91043))+~P1(f319(f319(f321(x91041),x91042),x91045))+~P1(f319(f319(f225(f913(x91041,a904)),x91045),f319(x91044,f319(f319(f93(f913(x91041,a904)),x91045),x91043))))
% 22.40/22.32 [9488]~P1(f319(f319(f225(a1),x94884),f2(a1)))+~P1(f319(f319(f226(a1),x94883),x94885))+P1(f319(f319(f225(a1),x94881),x94882))+~P1(f319(f319(f226(a1),x94883),x94884))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f75(a1),x94883),x94882)),x94885)),f319(f319(f74(a1),f319(f319(f75(a1),x94883),x94881)),x94884)))
% 22.40/22.32 [9494]~P1(f319(f319(f225(a1),f2(a1)),x94945))+P1(f319(f319(f225(a1),x94941),x94942))+~P1(f319(f319(f226(a1),x94943),x94944))+~P1(f319(f319(f226(a1),x94945),x94944))+~P1(f319(f319(f225(a1),f319(f319(f74(a1),f319(f319(f75(a1),x94944),x94941)),x94945)),f319(f319(f74(a1),f319(f319(f75(a1),x94944),x94942)),x94943)))
% 22.40/22.32 [9604]~P73(x96045)+E(f319(x96041,f359(x96041,x96042,x96043,x96044,x96045)),f2(x96045))+~P1(f319(f55(x96044),x96043))+~P1(f319(f55(x96044),x96042))+E(f319(f319(f282(x96045),f319(f319(f75(x96045),f319(f319(f11(x96044,x96045),x96041),x96043)),f319(f319(f11(x96044,x96045),x96041),x96042))),f319(f319(f11(x96044,x96045),x96041),f319(f319(f94(f913(x96044,a904)),x96043),x96042))),f319(f319(f11(x96044,x96045),x96041),f319(f319(f93(f913(x96044,a904)),x96043),x96042)))
% 22.40/22.32 [9912]~P73(x99121)+~P1(f319(f55(x99122),x99124))+~P1(f319(f55(x99122),x99125))+E(f319(f319(f282(x99121),f319(f319(f75(x99121),f319(f319(f11(x99122,x99121),x99123),x99124)),f319(f319(f11(x99122,x99121),x99123),x99125))),f319(f319(f11(x99122,x99121),x99123),f319(f319(f94(f913(x99122,a904)),x99124),x99125))),f319(f319(f11(x99122,x99121),x99123),f319(f319(f93(f913(x99122,a904)),x99124),x99125)))+P1(f319(f319(f321(x99122),f359(x99123,x99125,x99124,x99122,x99121)),f319(f319(f94(f913(x99122,a904)),x99124),x99125)))
% 22.40/22.32 [9185]E(f319(f319(f126(x91851),x91852),x91853),f319(f319(f126(x91851),x91854),x91855))+~E(f319(f319(f167(x91851),f319(f182(f907(x91851)),x91854)),x91852),x91854)+~E(f319(f319(f167(x91851),f319(f182(f907(x91851)),x91852)),x91854),x91852)+~E(x91855,f319(f319(f126(x91851),f319(f319(f130(x91851),f319(f182(f907(x91851)),x91854)),x91852)),x91853))+~E(f319(f319(f126(x91851),f319(f319(f130(x91851),f319(f182(f907(x91851)),x91852)),x91854)),x91855),x91853)
% 22.40/22.32 [9602]~P4(x96022)+E(f319(f319(f140(x96021,x96022,x96023),x96024),f162(x96021,x96024,x96025)),x96025)+~P13(x96022,f319(f319(f146(x96021,x96022),x96023),x96025))+~P1(f319(f319(f321(x96021),x96024),f319(f164(x96021),x96025)))+~E(f319(f133(x96021),f319(f128(x96021,f319(f319(f10(x96022,a904,x96021),f319(a316,f319(x96023,x96024))),x96023)),x96025)),x96024)
% 22.40/22.32 [9977]~P77(x99771)+~P1(f319(f60(x99771,x99771,f75(x99771),x99772,x99773),x99775))+~P1(f319(f319(f321(x99771),x99774),x99773))+P1(f319(f319(f321(x99771),x99772),x99773))+P1(f319(f60(x99771,x99771,f75(x99771),x99774,f319(f319(f301(x99771),x99772),f319(f319(f3(f913(x99771,a904)),x99773),f319(f319(f301(x99771),x99774),f181(f913(x99771,a904)))))),x99775))
% 22.40/22.32 [10339]~P40(f913(x103391,a904),f913(x103391,a904),x103394)+~E(x103393,f88(f913(x103391,a904),x103394))+P1(f319(f319(f321(x103391),x103392),x103393))+~P1(f319(f319(f321(x103391),x103392),x103395))+~P1(f319(f319(f225(f913(x103391,a904)),x103395),f319(x103394,f87(f913(x103391,a904),f319(f319(f9(f913(x103391,a904),f913(x103391,a904),f913(x103391,a904)),f319(f319(f10(f913(x103391,a904),f913(f913(x103391,a904),f913(x103391,a904)),f913(x103391,a904)),f93(f913(x103391,a904))),f319(f319(f9(f913(x103391,a904),f913(x103391,a904),f913(x103391,a904)),f319(f319(f10(f913(x103391,a904),f913(f913(x103391,a904),f913(x103391,a904)),f913(x103391,a904)),f93(f913(x103391,a904))),x103394)),x103395))),x103393)))))
% 22.40/22.32 [7363]E(x73631,x73632)+~P25(x73634,x73635,x73633,x73636)+~E(f319(x73633,x73631),f319(x73633,x73632))+~P1(f319(f319(f321(x73634),x73632),x73636))+~P1(f319(f319(f321(x73634),x73631),x73636))
% 22.40/22.32 [6622]~P143(x66224)+E(x66221,x66222)+~E(x66225,x66226)+E(x66223,f2(x66224))+~E(f319(f319(f74(x66224),x66225),f319(f319(f75(x66224),x66223),x66221)),f319(f319(f74(x66224),x66226),f319(f319(f75(x66224),x66223),x66222)))
% 22.40/22.32 [7636]~P4(x76361)+~P5(x76361)+~P1(f319(f319(f226(x76361),x76362),f319(x76365,x76366)))+~P1(f319(f319(f321(x76363),x76366),x76364))+P1(f319(f319(f226(x76361),x76362),f319(f319(f33(x76363,x76361),x76364),x76365)))
% 22.40/22.32 [9973]~P25(x99732,x99731,x99733,x99734)+~P25(x99731,x99732,x99736,x99735)+P26(x99731,x99732,f817(x99733,x99734,x99735,x99736,x99732,x99731),x99735,x99734)+~P1(f319(f319(f225(f913(x99732,a904)),f319(f302(x99731,x99732,x99736),x99735)),x99734))+~P1(f319(f319(f225(f913(x99731,a904)),f319(f302(x99732,x99731,x99733),x99734)),x99735))
% 22.40/22.32 [8305]~P4(x83051)+~P5(x83051)+~P1(f319(f319(f226(x83051),f319(x83054,x83056)),x83055))+~P1(f319(f319(f321(x83052),x83056),x83053))+P1(f319(f319(f226(x83051),f319(f319(f34(x83052,x83051),x83053),x83054)),x83055))
% 22.40/22.32 [8553]~P20(x85532,x85535,x85536,x85531)+~P1(f319(f55(x85532),x85534))+~P1(f319(f55(x85532),x85533))+~E(f319(f319(f94(f913(x85532,a904)),x85533),x85534),f181(f913(x85532,a904)))+E(f319(x85531,f319(f319(f93(f913(x85532,a904)),x85533),x85534)),f319(f66(x85535,x85535,x85535,f319(x85531,x85533)),f319(x85531,x85534)))
% 22.40/22.32 [10145]~P82(x101451)+~E(f805(x101454,x101455,x101453,x101456,x101452,x101451),f806(x101454,x101455,x101453,x101456,x101452,x101451))+~P1(f319(f55(x101452),x101456))+E(f319(f319(f319(f59(x101451,x101452,f75(x101451)),f319(f319(f10(f913(x101453,a904),x101451,x101452),f319(f319(f59(x101451,x101453,f75(x101451)),x101454),f72(x101451))),x101455)),f72(x101451)),x101456),f319(f319(f319(f59(x101451,x101453,f75(x101451)),x101454),f72(x101451)),f319(f319(f33(x101452,f913(x101453,a904)),x101456),x101455)))+P1(f319(f319(f321(x101452),f804(x101454,x101455,x101453,x101456,x101452,x101451)),x101456))
% 22.40/22.32 [10171]~P82(x101711)+~E(f805(x101714,x101715,x101713,x101716,x101712,x101711),f806(x101714,x101715,x101713,x101716,x101712,x101711))+~P1(f319(f55(x101712),x101716))+E(f319(f319(f319(f59(x101711,x101712,f75(x101711)),f319(f319(f10(f913(x101713,a904),x101711,x101712),f319(f319(f59(x101711,x101713,f75(x101711)),x101714),f72(x101711))),x101715)),f72(x101711)),x101716),f319(f319(f319(f59(x101711,x101713,f75(x101711)),x101714),f72(x101711)),f319(f319(f33(x101712,f913(x101713,a904)),x101716),x101715)))+~P1(f319(f55(x101713),f319(x101715,f804(x101714,x101715,x101713,x101716,x101712,x101711))))
% 22.40/22.32 [10174]~P82(x101741)+~P1(f319(f55(x101742),x101746))+E(f319(f319(f319(f59(x101741,x101742,f75(x101741)),f319(f319(f10(f913(x101743,a904),x101741,x101742),f319(f319(f59(x101741,x101743,f75(x101741)),x101744),f72(x101741))),x101745)),f72(x101741)),x101746),f319(f319(f319(f59(x101741,x101743,f75(x101741)),x101744),f72(x101741)),f319(f319(f33(x101742,f913(x101743,a904)),x101746),x101745)))+P1(f319(f319(f321(x101742),f804(x101744,x101745,x101743,x101746,x101742,x101741)),x101746))+P1(f319(f319(f321(x101742),f806(x101744,x101745,x101743,x101746,x101742,x101741)),x101746))
% 22.40/22.32 [10175]~P82(x101751)+~P1(f319(f55(x101752),x101756))+E(f319(f319(f319(f59(x101751,x101752,f75(x101751)),f319(f319(f10(f913(x101753,a904),x101751,x101752),f319(f319(f59(x101751,x101753,f75(x101751)),x101754),f72(x101751))),x101755)),f72(x101751)),x101756),f319(f319(f319(f59(x101751,x101753,f75(x101751)),x101754),f72(x101751)),f319(f319(f33(x101752,f913(x101753,a904)),x101756),x101755)))+P1(f319(f319(f321(x101752),f804(x101754,x101755,x101753,x101756,x101752,x101751)),x101756))+P1(f319(f319(f321(x101752),f805(x101754,x101755,x101753,x101756,x101752,x101751)),x101756))
% 22.40/22.32 [10194]~P82(x101941)+~P1(f319(f55(x101942),x101946))+E(f319(f319(f319(f59(x101941,x101942,f75(x101941)),f319(f319(f10(f913(x101943,a904),x101941,x101942),f319(f319(f59(x101941,x101943,f75(x101941)),x101944),f72(x101941))),x101945)),f72(x101941)),x101946),f319(f319(f319(f59(x101941,x101943,f75(x101941)),x101944),f72(x101941)),f319(f319(f33(x101942,f913(x101943,a904)),x101946),x101945)))+P1(f319(f319(f321(x101942),f806(x101944,x101945,x101943,x101946,x101942,x101941)),x101946))+~P1(f319(f55(x101943),f319(x101945,f804(x101944,x101945,x101943,x101946,x101942,x101941))))
% 22.40/22.32 [10195]~P82(x101951)+~P1(f319(f55(x101952),x101956))+E(f319(f319(f319(f59(x101951,x101952,f75(x101951)),f319(f319(f10(f913(x101953,a904),x101951,x101952),f319(f319(f59(x101951,x101953,f75(x101951)),x101954),f72(x101951))),x101955)),f72(x101951)),x101956),f319(f319(f319(f59(x101951,x101953,f75(x101951)),x101954),f72(x101951)),f319(f319(f33(x101952,f913(x101953,a904)),x101956),x101955)))+P1(f319(f319(f321(x101952),f805(x101954,x101955,x101953,x101956,x101952,x101951)),x101956))+~P1(f319(f55(x101953),f319(x101955,f804(x101954,x101955,x101953,x101956,x101952,x101951))))
% 22.40/22.32 [10215]~P82(x102151)+~E(f319(f319(f94(f913(x102153,a904)),f319(x102155,f806(x102154,x102155,x102153,x102156,x102152,x102151))),f319(x102155,f805(x102154,x102155,x102153,x102156,x102152,x102151))),f181(f913(x102153,a904)))+~P1(f319(f55(x102152),x102156))+E(f319(f319(f319(f59(x102151,x102152,f75(x102151)),f319(f319(f10(f913(x102153,a904),x102151,x102152),f319(f319(f59(x102151,x102153,f75(x102151)),x102154),f72(x102151))),x102155)),f72(x102151)),x102156),f319(f319(f319(f59(x102151,x102153,f75(x102151)),x102154),f72(x102151)),f319(f319(f33(x102152,f913(x102153,a904)),x102156),x102155)))+P1(f319(f319(f321(x102152),f804(x102154,x102155,x102153,x102156,x102152,x102151)),x102156))
% 22.40/22.32 [10225]~P82(x102251)+~E(f319(f319(f94(f913(x102253,a904)),f319(x102255,f806(x102254,x102255,x102253,x102256,x102252,x102251))),f319(x102255,f805(x102254,x102255,x102253,x102256,x102252,x102251))),f181(f913(x102253,a904)))+~P1(f319(f55(x102252),x102256))+E(f319(f319(f319(f59(x102251,x102252,f75(x102251)),f319(f319(f10(f913(x102253,a904),x102251,x102252),f319(f319(f59(x102251,x102253,f75(x102251)),x102254),f72(x102251))),x102255)),f72(x102251)),x102256),f319(f319(f319(f59(x102251,x102253,f75(x102251)),x102254),f72(x102251)),f319(f319(f33(x102252,f913(x102253,a904)),x102256),x102255)))+~P1(f319(f55(x102253),f319(x102255,f804(x102254,x102255,x102253,x102256,x102252,x102251))))
% 22.40/22.32 [8882]E(x88821,x88822)+~P58(x88824,x88825,x88826,x88823,x88827)+~E(f319(x88823,x88821),f319(x88823,x88822))+~P1(f319(f319(f321(x88825),x88822),x88827))+~P1(f319(f319(f321(x88825),x88821),x88827))
% 22.40/22.32 [10183]~P1(f319(x101832,x101834))+~E(x101835,f319(f128(x101831,x101832),x101837))+E(f319(f128(x101831,x101832),x101833),f319(f319(f143(x101831),x101834),x101835))+~E(x101833,f319(f319(f126(x101831),x101836),f319(f319(f143(x101831),x101834),x101837)))+P1(f319(x101832,f738(x101835,x101834,x101833,x101832,x101831,x101836,x101837)))
% 22.40/22.32 [10184]~P1(f319(x101844,x101842))+~E(x101843,f319(f128(x101841,x101844),x101847))+E(f319(f319(f143(x101841),x101842),x101843),f319(f128(x101841,x101844),x101845))+~E(x101845,f319(f319(f126(x101841),x101846),f319(f319(f143(x101841),x101842),x101847)))+P1(f319(x101844,f739(x101845,x101844,x101843,x101842,x101841,x101846,x101847)))
% 22.40/22.32 [10240]~P1(f319(x102402,x102404))+~E(x102405,f319(f128(x102401,x102402),x102407))+E(f319(f128(x102401,x102402),x102403),f319(f319(f143(x102401),x102404),x102405))+~E(x102403,f319(f319(f126(x102401),x102406),f319(f319(f143(x102401),x102404),x102407)))+P1(f319(f319(f321(x102401),f738(x102405,x102404,x102403,x102402,x102401,x102406,x102407)),f319(f164(x102401),x102406)))
% 22.40/22.32 [10241]~P1(f319(x102414,x102412))+~E(x102413,f319(f128(x102411,x102414),x102417))+E(f319(f319(f143(x102411),x102412),x102413),f319(f128(x102411,x102414),x102415))+~E(x102415,f319(f319(f126(x102411),x102416),f319(f319(f143(x102411),x102412),x102417)))+P1(f319(f319(f321(x102411),f739(x102415,x102414,x102413,x102412,x102411,x102416,x102417)),f319(f164(x102411),x102416)))
% 22.40/22.32 [10246]~P8(x102461,x102467,x102466)+~P11(x102461,f913(x102465,a904),x102466,x102464)+P1(f319(f319(f321(x102461),f519(x102462,x102463,x102464,x102465,x102466,x102467,x102461)),x102467))+~P1(f319(f319(f321(f913(x102461,a904)),x102463),f319(f319(f54(x102461),x102467),x102466)))+P1(f319(f319(f321(f913(x102465,a904)),f319(f319(f33(x102461,f913(x102465,a904)),x102463),x102464)),x102462))
% 22.40/22.32 [10326]~P8(x103262,x103266,x103267)+~P11(x103262,f913(x103261,a904),x103267,x103264)+~P1(f319(f319(f321(f913(x103262,a904)),x103263),f319(f319(f54(x103262),x103266),x103267)))+~P1(f319(f319(f321(f913(x103261,a904)),f319(x103264,f519(x103265,x103263,x103264,x103261,x103267,x103266,x103262))),x103265))+P1(f319(f319(f321(f913(x103261,a904)),f319(f319(f33(x103262,f913(x103261,a904)),x103263),x103264)),x103265))
% 22.40/22.32 [8472]~P82(x84722)+~P25(x84721,x84725,x84728,x84724)+~E(x84723,f319(f66(x84725,x84722,x84721,x84726),x84728))+~E(x84727,f319(f302(x84721,x84725,x84728),x84724))+E(f319(f319(f11(x84721,x84722),x84723),x84724),f319(f319(f11(x84725,x84722),x84726),x84727))
% 22.40/22.32 [10335]~P82(x103352)+~P25(x103355,x103351,x103358,x103357)+~E(f319(x103356,f507(x103353,x103356,x103354,x103357,x103358,x103351,x103355,x103352)),f319(f319(f66(x103351,x103352,x103355,x103353),x103358),f507(x103353,x103356,x103354,x103357,x103358,x103351,x103355,x103352)))+~E(x103354,f319(f302(x103355,x103351,x103358),x103357))+E(f319(f319(f11(x103351,x103352),x103353),x103354),f319(f319(f11(x103355,x103352),x103356),x103357))
% 22.40/22.32 [10344]~P76(x103442)+~P25(x103441,x103445,x103448,x103444)+~E(x103447,f319(f302(x103441,x103445,x103448),x103444))+E(f319(f319(f8(x103441,x103442),x103443),x103444),f319(f319(f8(x103445,x103442),x103446),x103447))+P1(f319(f319(f321(x103441),f884(x103446,x103443,x103447,x103444,x103448,x103445,x103441,x103442)),x103444))
% 22.40/22.32 [10345]~P82(x103452)+~P25(x103451,x103455,x103458,x103454)+~E(x103457,f319(f302(x103451,x103455,x103458),x103454))+E(f319(f319(f11(x103451,x103452),x103453),x103454),f319(f319(f11(x103455,x103452),x103456),x103457))+P1(f319(f319(f321(x103451),f507(x103456,x103453,x103457,x103454,x103458,x103455,x103451,x103452)),x103454))
% 22.40/22.32 [10350]~P76(x103502)+~P25(x103505,x103501,x103508,x103507)+~E(x103504,f319(f302(x103505,x103501,x103508),x103507))+~E(f319(x103506,f884(x103503,x103506,x103504,x103507,x103508,x103501,x103505,x103502)),f319(x103503,f319(x103508,f884(x103503,x103506,x103504,x103507,x103508,x103501,x103505,x103502))))+E(f319(f319(f8(x103501,x103502),x103503),x103504),f319(f319(f8(x103505,x103502),x103506),x103507))
% 22.40/22.32 [9796]~P24(x97966,x97962,x97965,x97967,x97968,x97961)+~P1(f319(f55(x97962),x97964))+~P1(f319(f55(x97962),x97963))+~E(f319(f319(f94(f913(x97962,a904)),x97963),x97964),f181(f913(x97962,a904)))+E(f319(x97961,f319(f319(f93(f913(x97962,a904)),x97963),x97964)),f319(f319(x97965,f319(x97961,x97963)),f319(x97961,x97964)))
% 22.40/22.32 [10170]~P24(x101708,x101702,x101705,x101707,x101706,x101701)+~E(f319(x101706,f874(x101704,x101703,x101701,x101706,x101707,x101705,x101702)),x101707)+~P1(f319(f55(x101702),x101703))+~P1(f319(f55(x101702),x101704))+E(f319(x101701,f319(f319(f93(f913(x101702,a904)),x101703),x101704)),f319(f319(x101705,f319(x101701,x101703)),f319(x101701,x101704)))
% 22.40/22.32 [10253]~P24(x102538,x102532,x102535,x102537,x102536,x102531)+~P1(f319(f55(x102532),x102533))+~P1(f319(f55(x102532),x102534))+E(f319(x102531,f319(f319(f93(f913(x102532,a904)),x102533),x102534)),f319(f319(x102535,f319(x102531,x102533)),f319(x102531,x102534)))+P1(f319(f319(f321(x102532),f874(x102534,x102533,x102531,x102536,x102537,x102535,x102532)),f319(f319(f94(f913(x102532,a904)),x102533),x102534)))
% 22.40/22.32 [9964]~P8(x99644,x99648,x99645)+~P8(x99641,x99649,x99643)+~P12(x99641,x99644,f913(x99642,a904),x99643,x99645,x99647)+P11(x99641,f913(x99642,a904),x99643,f319(f319(f10(f913(x99644,f913(x99642,a904)),f913(x99642,a904),x99641),f319(f33(x99644,f913(x99642,a904)),f319(f277(x99644,x99644,x99645),f319(f319(f301(x99644),x99646),f181(f913(x99644,a904)))))),x99647))+~P1(f319(f319(f321(x99644),x99646),x99648))
% 22.40/22.32 [5525]~P4(x55253)+~P13(x55253,x55251)+E(x55251,f716(x55252,x55253))+~E(f319(f164(x55253),x55251),x55252)+~P1(f319(f55(x55253),x55252))+~P1(f319(f129(x55253),x55251))
% 22.40/22.32 [7354]P16(x73541,x73542)+~E(f319(x73542,f796(x73542)),f319(x73542,f797(x73542)))+~P1(f319(f319(x73542,f796(x73542)),f796(x73542)))+~P1(f319(f319(x73542,f796(x73542)),f797(x73542)))+~P1(f319(f319(x73542,f797(x73542)),f797(x73542)))+~P1(f319(f319(x73542,x73543),x73543))
% 22.40/22.32 [5149]~P129(x51492)+~P130(x51492)+~P144(x51492)+~P116(x51492)+E(x51491,f2(x51492))+~E(f319(f319(f236(x51492),x51491),x51493),f2(x51492))
% 22.40/22.32 [5150]~P129(x51502)+~P130(x51502)+~P144(x51502)+~P116(x51502)+~E(x51501,f2(a906))+~E(f319(f319(f236(x51502),x51503),x51501),f2(x51502))
% 22.40/22.32 [6604]~P93(x66041)+~E(x66043,f2(x66041))+~E(x66042,f2(x66041))+E(f319(f319(f74(x66041),x66042),x66043),f2(x66041))+~P1(f319(f319(f225(x66041),f2(x66041)),x66043))+~P1(f319(f319(f225(x66041),f2(x66041)),x66042))
% 22.40/22.32 [8954]~E(f319(f243(a906,a906),x89543),f2(a906))+~E(x89541,f319(f319(f74(a906),f319(f319(f75(a906),f319(f243(a906,a906),x89543)),x89542)),f319(f248(a906,a906),x89543)))+P1(f319(f42(x89541,x89542),x89543))+~P1(f319(f319(f225(a906),f319(f248(a906,a906),x89543)),f2(a906)))+P1(f319(f319(f226(a906),f2(a906)),x89542))+~P1(f319(f319(f226(a906),x89542),f319(f248(a906,a906),x89543)))
% 22.40/22.32 [8962]E(x89621,f2(a906))+~E(x89622,f319(f319(f74(a906),f319(f319(f75(a906),f319(f243(a906,a906),x89623)),x89621)),f319(f248(a906,a906),x89623)))+P1(f319(f42(x89622,x89621),x89623))+~P1(f319(f319(f226(a906),f2(a906)),x89621))+~P1(f319(f319(f225(a906),f2(a906)),f319(f248(a906,a906),x89623)))+~P1(f319(f319(f226(a906),f319(f248(a906,a906),x89623)),x89621))
% 22.40/22.32 [8981]~E(f319(f243(a906,a906),x89813),f2(a906))+~E(x89811,f319(f319(f74(a906),f319(f319(f75(a906),f319(f243(a906,a906),x89813)),x89812)),f319(f248(a906,a906),x89813)))+P1(f319(f42(x89811,x89812),x89813))+~P1(f319(f319(f226(a906),f2(a906)),x89812))+~P1(f319(f319(f225(a906),f2(a906)),f319(f248(a906,a906),x89813)))+~P1(f319(f319(f226(a906),f319(f248(a906,a906),x89813)),x89812))
% 22.40/22.32 [6984]~P101(x69842)+E(x69841,f181(f913(x69842,a904)))+E(x69843,f181(f913(x69842,a904)))+~P1(f319(f55(x69842),x69841))+~P1(f319(f55(x69842),x69843))+E(f12(x69842,f319(f319(f93(f913(x69842,a904)),x69843),x69841)),f319(f319(f94(x69842),f12(x69842,x69843)),f12(x69842,x69841)))
% 22.40/22.32 [6985]~P101(x69852)+E(x69851,f181(f913(x69852,a904)))+E(x69853,f181(f913(x69852,a904)))+~P1(f319(f55(x69852),x69851))+~P1(f319(f55(x69852),x69853))+E(f15(x69852,f319(f319(f93(f913(x69852,a904)),x69853),x69851)),f319(f319(f93(x69852),f15(x69852,x69853)),f15(x69852,x69851)))
% 22.40/22.32 [6986]~P4(x69862)+E(x69861,f181(f913(x69862,a904)))+E(x69863,f181(f913(x69862,a904)))+~P1(f319(f55(x69862),x69861))+~P1(f319(f55(x69862),x69863))+E(f16(x69862,f319(f319(f93(f913(x69862,a904)),x69863),x69861)),f319(f319(f180(x69862),f16(x69862,x69863)),f16(x69862,x69861)))
% 22.40/22.32 [6987]~P4(x69872)+E(x69871,f181(f913(x69872,a904)))+E(x69873,f181(f913(x69872,a904)))+~P1(f319(f55(x69872),x69871))+~P1(f319(f55(x69872),x69873))+E(f17(x69872,f319(f319(f93(f913(x69872,a904)),x69873),x69871)),f319(f319(f230(x69872),f17(x69872,x69873)),f17(x69872,x69871)))
% 22.40/22.32 [7612]~P100(x76122)+E(x76121,f181(f913(x76122,a904)))+E(x76123,f181(f913(x76122,a904)))+~P1(f319(f55(x76122),x76121))+~P1(f319(f55(x76122),x76123))+E(f319(f319(f75(x76122),f319(f57(x76122,f75(x76122)),x76123)),f319(f57(x76122,f75(x76122)),x76121)),f319(f57(x76122,f75(x76122)),f319(f319(f93(f913(x76122,a904)),x76123),x76121)))
% 22.40/22.32 [7766]~P4(x77662)+E(x77661,f181(f913(x77662,a904)))+E(x77663,f181(f913(x77662,a904)))+~P1(f319(f55(x77662),x77661))+~P1(f319(f55(x77662),x77663))+E(f319(f319(f180(x77662),f13(x77662,f180(x77662),x77663)),f13(x77662,f180(x77662),x77661)),f13(x77662,f180(x77662),f319(f319(f93(f913(x77662,a904)),x77663),x77661)))
% 22.40/22.32 [7767]~P4(x77672)+E(x77671,f181(f913(x77672,a904)))+E(x77673,f181(f913(x77672,a904)))+~P1(f319(f55(x77672),x77671))+~P1(f319(f55(x77672),x77673))+E(f319(f319(f230(x77672),f14(x77672,f230(x77672),x77673)),f14(x77672,f230(x77672),x77671)),f14(x77672,f230(x77672),f319(f319(f93(f913(x77672,a904)),x77673),x77671)))
% 22.40/22.32 [8784]~P1(f319(x87841,x87843))+P1(f319(x87841,f402(x87841,x87842)))+P1(f319(x87841,f397(x87841,x87842)))+~P1(f319(f319(f226(a1),f2(a1)),x87842))+~P1(f319(f319(f321(a1),x87843),f295(a1,f72(a1),x87842)))+P1(f319(x87841,f319(f319(f3(a1),f397(x87841,x87842)),f319(f319(f75(a1),f401(x87841,x87842)),x87842))))
% 22.40/22.32 [9095]~P1(f319(x90951,x90953))+~P1(f319(x90951,f397(x90951,x90952)))+P1(f319(x90951,f402(x90951,x90952)))+~P1(f319(f319(f226(a1),f2(a1)),x90952))+~P1(f319(f319(f321(a1),x90953),f295(a1,f72(a1),x90952)))+~P1(f319(x90951,f319(f319(f3(a1),f397(x90951,x90952)),f319(f319(f75(a1),f401(x90951,x90952)),x90952))))
% 22.40/22.32 [10387]~P102(x103872)+E(x103871,f181(f913(x103872,a904)))+E(x103873,f181(f913(x103872,a904)))+~P1(f319(f55(x103872),x103871))+~P1(f319(f55(x103872),x103873))+E(f12(x103872,f319(f254(x103872),f319(f319(f10(f913(x103872,a904),a904,x103872),f80(x103872)),f319(f319(f10(f913(x103872,f913(x103872,a904)),f913(x103872,a904),x103872),f319(f10(f913(x103872,a904),a904,x103872),f80(x103872))),f319(f319(f9(x103872,f913(x103872,f913(x103872,a904)),f913(x103872,f913(x103872,a904))),f319(f319(f10(f913(x103872,f913(f913(x103872,a904),f913(x103872,a904))),f913(f913(x103872,f913(x103872,a904)),f913(x103872,f913(x103872,a904))),x103872),f20(x103872,f913(x103872,a904),f913(x103872,a904))),f319(f319(f10(f913(x103872,f913(x103872,f913(a904,a904))),f913(x103872,f913(f913(x103872,a904),f913(x103872,a904))),x103872),f319(f10(f913(x103872,f913(a904,a904)),f913(f913(x103872,a904),f913(x103872,a904)),x103872),f20(x103872,a904,a904))),f319(f319(f10(f913(x103872,f913(x103872,a904)),f913(x103872,f913(x103872,f913(a904,a904))),x103872),f319(f10(f913(x103872,a904),f913(x103872,f913(a904,a904)),x103872),f319(f10(a904,f913(a904,a904),x103872),a317))),f319(f319(f9(x103872,f913(x103872,f913(x103872,x103872)),f913(x103872,f913(x103872,a904))),f319(f319(f10(f913(f913(x103872,x103872),f913(x103872,a904)),f913(f913(x103872,f913(x103872,x103872)),f913(x103872,f913(x103872,a904))),x103872),f10(f913(x103872,x103872),f913(x103872,a904),x103872)),f319(f319(f10(f913(x103872,a904),f913(f913(x103872,x103872),f913(x103872,a904)),x103872),f10(x103872,a904,x103872)),a316))),f93(x103872)))))),f319(f319(f9(x103872,f913(x103872,a904),f913(x103872,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x103872,a904),f913(x103872,a904)),x103872),f10(a904,a904,x103872)),f319(f319(f10(a904,f913(a904,a904),x103872),a317),f319(f319(f9(x103872,f913(x103872,a904),a904),f321(x103872)),x103873)))),f319(f319(f9(x103872,f913(x103872,a904),a904),f321(x103872)),x103871))))))),f319(f319(f93(x103872),f12(x103872,x103873)),f12(x103872,x103871)))
% 22.40/22.32 [10388]~P102(x103882)+E(x103881,f181(f913(x103882,a904)))+E(x103883,f181(f913(x103882,a904)))+~P1(f319(f55(x103882),x103881))+~P1(f319(f55(x103882),x103883))+E(f15(x103882,f319(f254(x103882),f319(f319(f10(f913(x103882,a904),a904,x103882),f80(x103882)),f319(f319(f10(f913(x103882,f913(x103882,a904)),f913(x103882,a904),x103882),f319(f10(f913(x103882,a904),a904,x103882),f80(x103882))),f319(f319(f9(x103882,f913(x103882,f913(x103882,a904)),f913(x103882,f913(x103882,a904))),f319(f319(f10(f913(x103882,f913(f913(x103882,a904),f913(x103882,a904))),f913(f913(x103882,f913(x103882,a904)),f913(x103882,f913(x103882,a904))),x103882),f20(x103882,f913(x103882,a904),f913(x103882,a904))),f319(f319(f10(f913(x103882,f913(x103882,f913(a904,a904))),f913(x103882,f913(f913(x103882,a904),f913(x103882,a904))),x103882),f319(f10(f913(x103882,f913(a904,a904)),f913(f913(x103882,a904),f913(x103882,a904)),x103882),f20(x103882,a904,a904))),f319(f319(f10(f913(x103882,f913(x103882,a904)),f913(x103882,f913(x103882,f913(a904,a904))),x103882),f319(f10(f913(x103882,a904),f913(x103882,f913(a904,a904)),x103882),f319(f10(a904,f913(a904,a904),x103882),a317))),f319(f319(f9(x103882,f913(x103882,f913(x103882,x103882)),f913(x103882,f913(x103882,a904))),f319(f319(f10(f913(f913(x103882,x103882),f913(x103882,a904)),f913(f913(x103882,f913(x103882,x103882)),f913(x103882,f913(x103882,a904))),x103882),f10(f913(x103882,x103882),f913(x103882,a904),x103882)),f319(f319(f10(f913(x103882,a904),f913(f913(x103882,x103882),f913(x103882,a904)),x103882),f10(x103882,a904,x103882)),a316))),f94(x103882)))))),f319(f319(f9(x103882,f913(x103882,a904),f913(x103882,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x103882,a904),f913(x103882,a904)),x103882),f10(a904,a904,x103882)),f319(f319(f10(a904,f913(a904,a904),x103882),a317),f319(f319(f9(x103882,f913(x103882,a904),a904),f321(x103882)),x103883)))),f319(f319(f9(x103882,f913(x103882,a904),a904),f321(x103882)),x103881))))))),f319(f319(f94(x103882),f15(x103882,x103883)),f15(x103882,x103881)))
% 22.40/22.32 [10389]~P4(x103892)+E(x103891,f181(f913(x103892,a904)))+E(x103893,f181(f913(x103892,a904)))+~P1(f319(f55(x103892),x103891))+~P1(f319(f55(x103892),x103893))+E(f14(x103892,f230(x103892),f319(f254(x103892),f319(f319(f10(f913(x103892,a904),a904,x103892),f80(x103892)),f319(f319(f10(f913(x103892,f913(x103892,a904)),f913(x103892,a904),x103892),f319(f10(f913(x103892,a904),a904,x103892),f80(x103892))),f319(f319(f9(x103892,f913(x103892,f913(x103892,a904)),f913(x103892,f913(x103892,a904))),f319(f319(f10(f913(x103892,f913(f913(x103892,a904),f913(x103892,a904))),f913(f913(x103892,f913(x103892,a904)),f913(x103892,f913(x103892,a904))),x103892),f20(x103892,f913(x103892,a904),f913(x103892,a904))),f319(f319(f10(f913(x103892,f913(x103892,f913(a904,a904))),f913(x103892,f913(f913(x103892,a904),f913(x103892,a904))),x103892),f319(f10(f913(x103892,f913(a904,a904)),f913(f913(x103892,a904),f913(x103892,a904)),x103892),f20(x103892,a904,a904))),f319(f319(f10(f913(x103892,f913(x103892,a904)),f913(x103892,f913(x103892,f913(a904,a904))),x103892),f319(f10(f913(x103892,a904),f913(x103892,f913(a904,a904)),x103892),f319(f10(a904,f913(a904,a904),x103892),a317))),f319(f319(f9(x103892,f913(x103892,f913(x103892,x103892)),f913(x103892,f913(x103892,a904))),f319(f319(f10(f913(f913(x103892,x103892),f913(x103892,a904)),f913(f913(x103892,f913(x103892,x103892)),f913(x103892,f913(x103892,a904))),x103892),f10(f913(x103892,x103892),f913(x103892,a904),x103892)),f319(f319(f10(f913(x103892,a904),f913(f913(x103892,x103892),f913(x103892,a904)),x103892),f10(x103892,a904,x103892)),a316))),f180(x103892)))))),f319(f319(f9(x103892,f913(x103892,a904),f913(x103892,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x103892,a904),f913(x103892,a904)),x103892),f10(a904,a904,x103892)),f319(f319(f10(a904,f913(a904,a904),x103892),a317),f319(f319(f9(x103892,f913(x103892,a904),a904),f321(x103892)),x103893)))),f319(f319(f9(x103892,f913(x103892,a904),a904),f321(x103892)),x103891))))))),f319(f319(f180(x103892),f14(x103892,f230(x103892),x103893)),f14(x103892,f230(x103892),x103891)))
% 22.40/22.32 [10390]~P4(x103902)+E(x103901,f181(f913(x103902,a904)))+E(x103903,f181(f913(x103902,a904)))+~P1(f319(f55(x103902),x103901))+~P1(f319(f55(x103902),x103903))+E(f13(x103902,f180(x103902),f319(f254(x103902),f319(f319(f10(f913(x103902,a904),a904,x103902),f80(x103902)),f319(f319(f10(f913(x103902,f913(x103902,a904)),f913(x103902,a904),x103902),f319(f10(f913(x103902,a904),a904,x103902),f80(x103902))),f319(f319(f9(x103902,f913(x103902,f913(x103902,a904)),f913(x103902,f913(x103902,a904))),f319(f319(f10(f913(x103902,f913(f913(x103902,a904),f913(x103902,a904))),f913(f913(x103902,f913(x103902,a904)),f913(x103902,f913(x103902,a904))),x103902),f20(x103902,f913(x103902,a904),f913(x103902,a904))),f319(f319(f10(f913(x103902,f913(x103902,f913(a904,a904))),f913(x103902,f913(f913(x103902,a904),f913(x103902,a904))),x103902),f319(f10(f913(x103902,f913(a904,a904)),f913(f913(x103902,a904),f913(x103902,a904)),x103902),f20(x103902,a904,a904))),f319(f319(f10(f913(x103902,f913(x103902,a904)),f913(x103902,f913(x103902,f913(a904,a904))),x103902),f319(f10(f913(x103902,a904),f913(x103902,f913(a904,a904)),x103902),f319(f10(a904,f913(a904,a904),x103902),a317))),f319(f319(f9(x103902,f913(x103902,f913(x103902,x103902)),f913(x103902,f913(x103902,a904))),f319(f319(f10(f913(f913(x103902,x103902),f913(x103902,a904)),f913(f913(x103902,f913(x103902,x103902)),f913(x103902,f913(x103902,a904))),x103902),f10(f913(x103902,x103902),f913(x103902,a904),x103902)),f319(f319(f10(f913(x103902,a904),f913(f913(x103902,x103902),f913(x103902,a904)),x103902),f10(x103902,a904,x103902)),a316))),f230(x103902)))))),f319(f319(f9(x103902,f913(x103902,a904),f913(x103902,a904)),f319(f319(f10(f913(a904,a904),f913(f913(x103902,a904),f913(x103902,a904)),x103902),f10(a904,a904,x103902)),f319(f319(f10(a904,f913(a904,a904),x103902),a317),f319(f319(f9(x103902,f913(x103902,a904),a904),f321(x103902)),x103903)))),f319(f319(f9(x103902,f913(x103902,a904),a904),f321(x103902)),x103901))))))),f319(f319(f230(x103902),f13(x103902,f180(x103902),x103903)),f13(x103902,f180(x103902),x103901)))
% 22.40/22.32 [7310]~P126(x73103)+E(x73101,x73102)+~E(f319(f319(f236(x73103),x73101),x73104),f319(f319(f236(x73103),x73102),x73104))+~P1(f319(f319(f225(x73103),f2(x73103)),x73102))+~P1(f319(f319(f225(x73103),f2(x73103)),x73101))+~P1(f319(f319(f226(a906),f2(a906)),x73104))
% 22.40/22.32 [9226]~P1(f319(x92262,x92263))+~P1(f319(x92261,x92264))+E(f229(a906,x92261),f319(a104,f229(a906,x92262)))+P1(f319(x92262,f815(x92263,x92262,x92264,x92261)))+P1(f319(x92261,f2(a906)))+P1(f319(x92261,f319(a104,f815(x92263,x92262,x92264,x92261))))
% 22.40/22.32 [9495]~P1(f319(x94952,x94953))+~P1(f319(x94951,x94954))+E(f229(a906,x94951),f319(a104,f229(a906,x94952)))+~P1(f319(x94952,f815(x94953,x94952,x94954,x94951)))+P1(f319(x94951,f2(a906)))+~P1(f319(x94951,f319(a104,f815(x94953,x94952,x94954,x94951))))
% 22.40/22.32 [7573]~P4(x75732)+E(x75731,f181(f913(x75732,a904)))+~P1(f319(f55(x75732),x75731))+~P1(f319(f319(f321(x75732),x75734),x75731))+P1(f319(f319(f225(x75732),x75733),x75734))+~P1(f319(f319(f225(x75732),x75733),f319(f57(x75732,f230(x75732)),x75731)))
% 22.40/22.32 [7574]~P107(x75742)+E(x75741,f181(f913(x75742,a904)))+~P1(f319(f55(x75742),x75741))+~P1(f319(f319(f321(x75742),x75744),x75741))+P1(f319(f319(f225(x75742),x75743),x75744))+~P1(f319(f319(f225(x75742),x75743),f319(f57(x75742,f94(x75742)),x75741)))
% 22.40/22.32 [7575]~P4(x75752)+E(x75751,f181(f913(x75752,a904)))+~P1(f319(f55(x75752),x75751))+~P1(f319(f319(f321(x75752),x75754),x75751))+P1(f319(f319(f226(x75752),x75753),x75754))+~P1(f319(f319(f226(x75752),x75753),f319(f57(x75752,f230(x75752)),x75751)))
% 22.40/22.32 [7480]E(x74801,f2(a1))+E(f319(f319(f30(a1),x74802),x74801),x74803)+~P1(f319(f319(f225(a1),x74804),f2(a1)))+~E(x74802,f319(f319(f74(a1),f319(f319(f75(a1),x74801),x74803)),x74804))+P1(f319(f319(f226(a1),f2(a1)),x74801))+~P1(f319(f319(f226(a1),x74801),x74804))
% 22.40/22.32 [7496]E(f39(a1,x74962,x74961),x74963)+E(x74961,f2(a1))+~P1(f319(f319(f225(a1),x74963),f2(a1)))+~E(x74962,f319(f319(f74(a1),f319(f319(f75(a1),x74961),x74964)),x74963))+P1(f319(f319(f226(a1),f2(a1)),x74961))+~P1(f319(f319(f226(a1),x74961),x74963))
% 22.40/22.32 [7611]E(x76111,f2(a1))+E(f319(f319(f30(a1),x76112),x76111),x76113)+~E(x76112,f319(f319(f74(a1),f319(f319(f75(a1),x76111),x76113)),x76114))+~P1(f319(f319(f225(a1),f2(a1)),x76114))+~P1(f319(f319(f226(a1),f2(a1)),x76111))+~P1(f319(f319(f226(a1),x76114),x76111))
% 22.40/22.32 [7632]E(f39(a1,x76322,x76321),x76323)+E(x76321,f2(a1))+~E(x76322,f319(f319(f74(a1),f319(f319(f75(a1),x76321),x76324)),x76323))+~P1(f319(f319(f225(a1),f2(a1)),x76323))+~P1(f319(f319(f226(a1),f2(a1)),x76321))+~P1(f319(f319(f226(a1),x76323),x76321))
% 22.40/22.32 [7770]~P4(x77702)+E(x77701,f181(f913(x77702,a904)))+~P1(f319(f55(x77702),x77701))+~P1(f319(f319(f321(x77702),x77704),x77701))+~P1(f319(f319(f225(x77702),x77704),x77703))+P1(f319(f319(f225(x77702),f319(f57(x77702,f230(x77702)),x77701)),x77703))
% 22.40/22.32 [7771]~P4(x77712)+E(x77711,f181(f913(x77712,a904)))+~P1(f319(f55(x77712),x77711))+~P1(f319(f319(f226(x77712),x77714),x77713))+~P1(f319(f319(f321(x77712),x77714),x77711))+P1(f319(f319(f226(x77712),f319(f57(x77712,f230(x77712)),x77711)),x77713))
% 22.40/22.32 [8327]~P1(f319(f319(f225(a1),x83274),f2(a1)))+~E(x83271,f319(f319(f74(a1),f319(f319(f75(a1),x83272),x83273)),x83274))+~P1(f319(f319(f225(a1),f2(a1)),x83274))+~P1(f319(f319(f226(a1),x83274),x83272))+~P1(f319(f319(f226(a1),x83272),x83274))+P1(f319(f43(x83271,x83272),f319(f319(f244(a1,a1),x83273),x83274)))
% 22.40/22.32 [8491]~P111(x84911)+P1(f319(f319(f226(f913(x84911,a904)),f295(x84911,x84912,x84913)),f295(x84911,x84914,x84915)))+~P1(f319(f319(f225(x84911),x84914),x84912))+~P1(f319(f319(f225(x84911),x84914),x84915))+~P1(f319(f319(f225(x84911),x84913),x84915))+~P1(f319(f319(f226(x84911),x84913),x84915))
% 22.40/22.32 [8492]~P111(x84921)+P1(f319(f319(f226(f913(x84921,a904)),f295(x84921,x84922,x84923)),f295(x84921,x84924,x84925)))+~P1(f319(f319(f225(x84921),x84923),x84925))+~P1(f319(f319(f225(x84921),x84924),x84925))+~P1(f319(f319(f225(x84921),x84924),x84922))+~P1(f319(f319(f226(x84921),x84924),x84922))
% 22.40/22.32 [9353]P60(x93532,x93533,x93534,x93531)+E(x93531,f181(f913(x93532,a904)))+~P1(f319(f55(x93532),x93534))+~P1(f319(f55(x93532),x93531))+~P1(f319(f319(x93533,f523(x93531,x93534,x93533,x93532)),x93535))+~P1(f319(f319(f321(x93532),x93535),x93531))
% 22.40/22.32 [9354]P60(x93542,x93543,x93544,x93541)+E(x93541,f181(f913(x93542,a904)))+~P1(f319(f55(x93542),x93544))+~P1(f319(f55(x93542),x93541))+~P1(f319(f319(x93543,f787(x93543,x93541,x93544,x93542)),x93545))+~P1(f319(f319(f321(x93542),x93545),x93541))
% 22.40/22.32 [9355]P60(x93552,x93553,x93554,x93551)+E(x93551,f181(f913(x93552,a904)))+~P1(f319(f55(x93552),x93554))+~P1(f319(f55(x93552),x93551))+~P1(f319(f319(x93553,f788(x93551,x93554,x93553,x93552)),x93555))+~P1(f319(f319(f321(x93552),x93555),x93551))
% 22.40/22.32 [9511]~E(x95113,x95115)+~P76(x95111)+~P82(x95111)+~P41(x95113)+E(f319(f319(f8(a1,x95111),x95112),x95113),f319(f319(f8(a1,x95111),x95114),x95115))+P1(f319(f319(f225(a1),f2(a1)),f525(x95112,x95114,x95113,x95115,x95111)))
% 22.40/22.32 [9512]~E(x95123,x95125)+~P76(x95121)+~P82(x95121)+~P41(x95123)+E(f319(f319(f11(a1,x95121),x95122),x95123),f319(f319(f11(a1,x95121),x95124),x95125))+P1(f319(f319(f225(a1),f2(a1)),f503(x95122,x95124,x95123,x95125,x95121)))
% 22.40/22.32 [9691]~E(x96915,x96913)+~P76(x96911)+~P82(x96911)+~P41(x96915)+~E(f319(x96912,f525(x96914,x96912,x96915,x96913,x96911)),f319(x96914,f525(x96914,x96912,x96915,x96913,x96911)))+E(f319(f319(f8(a1,x96911),x96912),x96913),f319(f319(f8(a1,x96911),x96914),x96915))
% 22.40/22.32 [9692]~E(x96925,x96923)+~P76(x96921)+~P82(x96921)+~P41(x96925)+~E(f319(x96922,f503(x96924,x96922,x96925,x96923,x96921)),f319(x96924,f503(x96924,x96922,x96925,x96923,x96921)))+E(f319(f319(f11(a1,x96921),x96922),x96923),f319(f319(f11(a1,x96921),x96924),x96925))
% 22.40/22.32 [9794]~P65(x97943)+E(f319(x97941,x97942),f2(x97943))+~E(f319(f319(f8(x97944,x97943),x97941),x97945),f2(x97943))+~P1(f319(f55(x97944),x97945))+P1(f319(f319(f321(x97944),f505(x97942,x97941,x97945,x97944,x97943)),x97945))+~P1(f319(f319(f321(x97944),x97942),x97945))
% 22.40/22.32 [9937]~P65(x99373)+E(f319(x99371,x99372),f2(x99373))+~E(f319(f319(f8(x99374,x99373),x99371),x99375),f2(x99373))+~P1(f319(f55(x99374),x99375))+~P1(f319(f319(f321(x99374),x99372),x99375))+~P1(f319(f319(f225(x99373),f2(x99373)),f319(x99371,f505(x99372,x99371,x99375,x99374,x99373))))
% 22.40/22.32 [8412]~P137(x84121)+~P1(f319(f319(f225(x84121),x84123),x84125))+~P1(f319(f319(f225(x84121),x84122),x84124))+~P1(f319(f319(f225(x84121),f2(x84121)),x84123))+~P1(f319(f319(f225(x84121),f2(x84121)),x84124))+P1(f319(f319(f225(x84121),f319(f319(f75(x84121),x84122),x84123)),f319(f319(f75(x84121),x84124),x84125)))
% 22.40/22.32 [8413]~P137(x84131)+~P1(f319(f319(f225(x84131),x84133),x84135))+~P1(f319(f319(f225(x84131),x84132),x84134))+~P1(f319(f319(f225(x84131),f2(x84131)),x84133))+~P1(f319(f319(f225(x84131),f2(x84131)),x84132))+P1(f319(f319(f225(x84131),f319(f319(f75(x84131),x84132),x84133)),f319(f319(f75(x84131),x84134),x84135)))
% 22.40/22.32 [8414]~P75(x84141)+~P1(f319(f319(f226(x84141),f2(x84141)),x84145))+~P1(f319(f319(f225(x84141),x84145),x84143))+~P1(f319(f319(f225(x84141),x84142),x84144))+~P1(f319(f319(f225(x84141),f2(x84141)),x84142))+P1(f319(f319(f225(x84141),f319(f319(f282(x84141),x84142),x84143)),f319(f319(f282(x84141),x84144),x84145)))
% 22.40/22.32 [8415]~P131(x84151)+~P1(f319(f319(f225(x84151),x84153),x84155))+~P1(f319(f319(f225(x84151),f2(x84151)),x84152))+~P1(f319(f319(f226(x84151),x84152),x84154))+~P1(f319(f319(f226(x84151),f2(x84151)),x84153))+P1(f319(f319(f226(x84151),f319(f319(f75(x84151),x84152),x84153)),f319(f319(f75(x84151),x84154),x84155)))
% 22.40/22.32 [8416]~P131(x84161)+~P1(f319(f319(f225(x84161),x84162),x84164))+~P1(f319(f319(f225(x84161),f2(x84161)),x84163))+~P1(f319(f319(f226(x84161),x84163),x84165))+~P1(f319(f319(f226(x84161),f2(x84161)),x84162))+P1(f319(f319(f226(x84161),f319(f319(f75(x84161),x84162),x84163)),f319(f319(f75(x84161),x84164),x84165)))
% 22.40/22.32 [8417]~P131(x84171)+~P1(f319(f319(f225(x84171),f2(x84171)),x84173))+~P1(f319(f319(f225(x84171),f2(x84171)),x84172))+~P1(f319(f319(f226(x84171),x84173),x84175))+~P1(f319(f319(f226(x84171),x84172),x84174))+P1(f319(f319(f226(x84171),f319(f319(f75(x84171),x84172),x84173)),f319(f319(f75(x84171),x84174),x84175)))
% 22.40/22.32 [8418]~P131(x84181)+~P1(f319(f319(f225(x84181),f2(x84181)),x84183))+~P1(f319(f319(f226(x84181),x84183),x84185))+~P1(f319(f319(f226(x84181),x84182),x84184))+~P1(f319(f319(f226(x84181),f2(x84181)),x84184))+P1(f319(f319(f226(x84181),f319(f319(f75(x84181),x84182),x84183)),f319(f319(f75(x84181),x84184),x84185)))
% 22.40/22.32 [8419]~P75(x84191)+~P1(f319(f319(f225(x84191),x84195),x84193))+~P1(f319(f319(f225(x84191),f2(x84191)),x84192))+~P1(f319(f319(f226(x84191),x84192),x84194))+~P1(f319(f319(f226(x84191),f2(x84191)),x84195))+P1(f319(f319(f226(x84191),f319(f319(f282(x84191),x84192),x84193)),f319(f319(f282(x84191),x84194),x84195)))
% 22.40/22.32 [8420]~P75(x84201)+~P1(f319(f319(f225(x84201),x84202),x84204))+~P1(f319(f319(f226(x84201),x84205),x84203))+~P1(f319(f319(f226(x84201),f2(x84201)),x84205))+~P1(f319(f319(f226(x84201),f2(x84201)),x84202))+P1(f319(f319(f226(x84201),f319(f319(f282(x84201),x84202),x84203)),f319(f319(f282(x84201),x84204),x84205)))
% 22.40/22.32 [9836]~P76(x98365)+~P89(x98365)+E(x98361,f181(f913(x98362,a904)))+~P1(f319(f55(x98362),x98361))+P1(f319(f319(f321(x98362),f882(x98363,x98364,x98361,x98362,x98365)),x98361))+P1(f319(f319(f226(x98365),f319(f319(f8(x98362,x98365),x98364),x98361)),f319(f319(f8(x98362,x98365),x98363),x98361)))
% 22.40/22.32 [9960]~P76(x99601)+~P91(x99601)+~P1(f319(f55(x99602),x99605))+~P1(f319(f319(f225(x99601),f2(x99601)),f319(x99603,f355(x99603,x99604,x99605,x99602,x99601))))+P1(f319(f319(f225(x99601),f319(f319(f8(x99602,x99601),x99603),x99604)),f319(f319(f8(x99602,x99601),x99603),x99605)))+~P1(f319(f319(f225(f913(x99602,a904)),x99604),x99605))
% 22.40/22.32 [10096]~P76(x100963)+~P89(x100963)+E(x100961,f181(f913(x100962,a904)))+~P1(f319(f55(x100962),x100961))+~P1(f319(f319(f226(x100963),f319(x100964,f882(x100965,x100964,x100961,x100962,x100963))),f319(x100965,f882(x100965,x100964,x100961,x100962,x100963))))+P1(f319(f319(f226(x100963),f319(f319(f8(x100962,x100963),x100964),x100961)),f319(f319(f8(x100962,x100963),x100965),x100961)))
% 22.40/22.32 [7168]~P18(x71682,x71685,x71684)+E(x71681,f181(f913(x71682,a904)))+E(x71683,f181(f913(x71682,a904)))+~P1(f319(f55(x71682),x71681))+~P1(f319(f55(x71682),x71683))+E(f319(x71684,f319(f319(f93(f913(x71682,a904)),x71683),x71681)),f319(f319(x71685,f319(x71684,x71683)),f319(x71684,x71681)))
% 22.40/22.32 [7737]~P148(x77371,x77374,x77373)+P1(f319(x77371,x77372))+~P1(f319(f319(f226(a1),x77374),f2(a1)))+~P1(f319(f319(f225(a1),x77375),f2(a1)))+~E(x77373,f319(f319(f74(a1),f319(f319(f75(a1),x77374),x77372)),x77375))+~P1(f319(f319(f226(a1),x77374),x77375))
% 22.40/22.32 [7738]~P147(x77381,x77384,x77383)+P1(f319(x77381,x77382))+~P1(f319(f319(f226(a1),x77384),f2(a1)))+~P1(f319(f319(f225(a1),x77382),f2(a1)))+~E(x77383,f319(f319(f74(a1),f319(f319(f75(a1),x77384),x77385)),x77382))+~P1(f319(f319(f226(a1),x77384),x77382))
% 22.40/22.32 [7780]~P148(x77801,x77804,x77803)+P1(f319(x77801,x77802))+~E(x77803,f319(f319(f74(a1),f319(f319(f75(a1),x77804),x77802)),x77805))+~P1(f319(f319(f225(a1),f2(a1)),x77805))+~P1(f319(f319(f226(a1),f2(a1)),x77804))+~P1(f319(f319(f226(a1),x77805),x77804))
% 22.40/22.32 [7781]~P147(x77811,x77814,x77813)+P1(f319(x77811,x77812))+~E(x77813,f319(f319(f74(a1),f319(f319(f75(a1),x77814),x77815)),x77812))+~P1(f319(f319(f225(a1),f2(a1)),x77812))+~P1(f319(f319(f226(a1),f2(a1)),x77814))+~P1(f319(f319(f226(a1),x77812),x77814))
% 22.40/22.32 [8702]P1(f319(f319(x87021,x87022),x87023))+~P1(f319(f319(x87021,f319(f319(f30(a1),x87024),x87025)),f39(a1,x87024,x87025)))+~P1(f319(f319(f226(a1),x87025),f2(a1)))+~P1(f319(f319(f225(a1),x87023),f2(a1)))+~E(x87024,f319(f319(f74(a1),f319(f319(f75(a1),x87025),x87022)),x87023))+~P1(f319(f319(f226(a1),x87025),x87023))
% 22.40/22.32 [8711]P1(f319(f319(x87111,x87112),x87113))+~P1(f319(f319(x87111,f319(f319(f30(a1),x87114),x87115)),f39(a1,x87114,x87115)))+~E(x87114,f319(f319(f74(a1),f319(f319(f75(a1),x87115),x87112)),x87113))+~P1(f319(f319(f225(a1),f2(a1)),x87113))+~P1(f319(f319(f226(a1),f2(a1)),x87115))+~P1(f319(f319(f226(a1),x87113),x87115))
% 22.40/22.32 [8972]E(x89721,x89722)+~P57(x89723,x89725,x89724)+~P1(f319(f319(f321(x89723),x89722),x89725))+~P1(f319(f319(f321(x89723),x89721),x89725))+P1(f319(f319(f321(f912(x89723,x89723)),f319(f319(f244(x89723,x89723),x89721),x89722)),x89724))+P1(f319(f319(f321(f912(x89723,x89723)),f319(f319(f244(x89723,x89723),x89722),x89721)),x89724))
% 22.40/22.32 [9810]~P111(x98101)+~P111(x98102)+~P40(x98102,x98101,x98103)+~P1(f319(f319(f225(x98102),x98105),f497(x98104,x98103,x98102,x98101,x98105)))+E(f229(x98101,f319(f319(f9(x98101,f913(x98101,a904),a904),f321(x98101)),f319(f302(x98102,x98101,x98103),x98104))),f319(x98103,f229(x98102,f319(f319(f9(x98102,f913(x98102,a904),a904),f321(x98102)),x98104))))+~P1(f319(f319(f321(x98102),x98105),x98104))
% 22.40/22.32 [9864]~P76(x98645)+~P91(x98645)+~P1(f319(f55(x98641),x98644))+P1(f319(f319(f225(x98645),f319(f319(f8(x98641,x98645),x98642),x98643)),f319(f319(f8(x98641,x98645),x98642),x98644)))+~P1(f319(f319(f225(f913(x98641,a904)),x98643),x98644))+P1(f319(f319(f321(x98641),f355(x98642,x98643,x98644,x98641,x98645)),f319(f319(f3(f913(x98641,a904)),x98644),x98643)))
% 22.40/22.32 [9880]~P111(x98801)+~P111(x98802)+~P40(x98802,x98801,x98803)+E(f229(x98801,f319(f319(f9(x98801,f913(x98801,a904),a904),f321(x98801)),f319(f302(x98802,x98801,x98803),x98804))),f319(x98803,f229(x98802,f319(f319(f9(x98802,f913(x98802,a904),a904),f321(x98802)),x98804))))+~P1(f319(f319(f321(x98802),x98805),x98804))+P1(f319(f319(f321(x98802),f497(x98804,x98803,x98802,x98801,x98805)),x98804))
% 22.40/22.32 [9968]E(x99681,f181(f913(x99682,a904)))+~P1(f319(f55(x99682),x99683))+~P1(f319(f55(x99682),x99681))+P1(f319(f319(f321(f912(f913(x99682,a904),f913(x99682,a904))),f319(f319(f244(f913(x99682,a904),f913(x99682,a904)),x99683),x99681)),f311(x99682,x99684)))+~P1(f319(f319(f321(x99682),x99685),x99681))+~P1(f319(f319(f321(f912(x99682,x99682)),f319(f319(f244(x99682,x99682),f527(x99684,x99681,x99683,x99682)),x99685)),x99684))
% 22.40/22.32 [9969]E(x99691,f181(f913(x99692,a904)))+~P1(f319(f55(x99692),x99693))+~P1(f319(f55(x99692),x99691))+P1(f319(f319(f321(f912(f913(x99692,a904),f913(x99692,a904))),f319(f319(f244(f913(x99692,a904),f913(x99692,a904)),x99693),x99691)),f311(x99692,x99694)))+~P1(f319(f319(f321(x99692),x99695),x99691))+~P1(f319(f319(f321(f912(x99692,x99692)),f319(f319(f244(x99692,x99692),f596(x99694,x99691,x99693,x99692)),x99695)),x99694))
% 22.40/22.32 [10100]~P65(x101001)+~E(f319(f319(f8(x101005,x101001),x101002),x101006),x101004)+~P1(f319(f55(x101005),x101006))+P1(f319(f319(f321(x101005),f506(x101003,x101004,x101002,x101006,x101005,x101001)),x101006))+P1(f319(f319(f225(x101001),f319(x101002,x101003)),x101004))+~P1(f319(f319(f321(x101005),x101003),x101006))
% 22.40/22.32 [10142]~P65(x101421)+~E(f319(f319(f8(x101425,x101421),x101422),x101426),x101424)+~P1(f319(f55(x101425),x101426))+~P1(f319(f319(f321(x101425),x101423),x101426))+~P1(f319(f319(f225(x101421),f2(x101421)),f319(x101422,f506(x101423,x101424,x101422,x101426,x101425,x101421))))+P1(f319(f319(f225(x101421),f319(x101422,x101423)),x101424))
% 22.40/22.32 [10311]~E(x103115,x103118)+~E(x103114,x103117)+~P3(x103111)+~P76(x103112)+E(f319(f319(f8(x103111,x103112),x103113),f319(f294(x103111,x103114),x103115)),f319(f319(f8(x103111,x103112),x103116),f319(f294(x103111,x103117),x103118)))+P1(f319(f319(f225(x103111),x103114),f896(x103113,x103116,x103115,x103118,x103114,x103117,x103111,x103112)))
% 22.40/22.32 [10334]~E(x103347,x103344)+~E(x103348,x103345)+~P3(x103341)+~P76(x103342)+~E(f319(x103343,f896(x103346,x103343,x103348,x103345,x103347,x103344,x103341,x103342)),f319(x103346,f896(x103346,x103343,x103348,x103345,x103347,x103344,x103341,x103342)))+E(f319(f319(f8(x103341,x103342),x103343),f319(f294(x103341,x103344),x103345)),f319(f319(f8(x103341,x103342),x103346),f319(f294(x103341,x103347),x103348)))
% 22.40/22.32 [10343]~E(x103434,x103437)+~E(x103435,x103438)+~P3(x103431)+~P76(x103432)+E(f319(f319(f8(x103431,x103432),x103433),f319(f294(x103431,x103434),x103435)),f319(f319(f8(x103431,x103432),x103436),f319(f294(x103431,x103437),x103438)))+P1(f319(f319(f226(x103431),f896(x103433,x103436,x103435,x103438,x103434,x103437,x103431,x103432)),x103435))
% 22.40/22.32 [9975]~P8(x99755,x99759,x99756)+~P8(x99751,x997510,x99753)+~P12(x99751,x99755,f913(x99752,a904),x99753,x99756,x99758)+~P1(f319(f319(f321(x99755),x99757),x99759))+~P1(f319(f319(f321(x99751),x99754),x997510))+E(f319(f319(f33(x99751,f913(x99752,a904)),f319(f277(x99751,x99751,x99753),f319(f319(f301(x99751),x99754),f181(f913(x99751,a904))))),f319(f319(f10(f913(x99755,f913(x99752,a904)),f913(x99752,a904),x99751),f319(f33(x99755,f913(x99752,a904)),f319(f277(x99755,x99755,x99756),f319(f319(f301(x99755),x99757),f181(f913(x99755,a904)))))),x99758)),f319(f319(x99758,x99754),x99757))
% 22.40/22.32 [5697]~P4(x56973)+~P13(x56973,x56972)+~P13(x56973,x56971)+E(x56971,x56972)+~E(f319(f164(x56973),x56971),f319(f164(x56973),x56972))+~P1(f319(f129(x56973),x56972))+~P1(f319(f129(x56973),x56971))
% 22.40/22.32 [5027]~P129(x50272)+~P130(x50272)+~P144(x50272)+~P116(x50272)+~E(x50273,f2(x50272))+E(x50271,f2(a906))+E(f319(f319(f236(x50272),x50273),x50271),f2(x50272))
% 22.40/22.32 [9221]E(x92211,f2(a906))+~E(x92212,f319(f319(f74(a906),f319(f319(f75(a906),f319(f243(a906,a906),x92213)),x92211)),f319(f248(a906,a906),x92213)))+P1(f319(f42(x92212,x92211),x92213))+~P1(f319(f319(f225(a906),f319(f248(a906,a906),x92213)),f2(a906)))+~P1(f319(f319(f225(a906),f2(a906)),f319(f248(a906,a906),x92213)))+~P1(f319(f319(f226(a906),x92211),f319(f248(a906,a906),x92213)))+~P1(f319(f319(f226(a906),f319(f248(a906,a906),x92213)),x92211))
% 22.40/22.32 [9235]~E(f319(f243(a906,a906),x92353),f2(a906))+~E(x92351,f319(f319(f74(a906),f319(f319(f75(a906),f319(f243(a906,a906),x92353)),x92352)),f319(f248(a906,a906),x92353)))+P1(f319(f42(x92351,x92352),x92353))+~P1(f319(f319(f225(a906),f319(f248(a906,a906),x92353)),f2(a906)))+~P1(f319(f319(f225(a906),f2(a906)),f319(f248(a906,a906),x92353)))+~P1(f319(f319(f226(a906),x92352),f319(f248(a906,a906),x92353)))+~P1(f319(f319(f226(a906),f319(f248(a906,a906),x92353)),x92352))
% 22.40/22.32 [8082]~P77(x80822)+E(x80821,f181(f913(x80822,a904)))+E(x80823,f181(f913(x80822,a904)))+~P1(f319(f55(x80822),x80821))+~P1(f319(f55(x80822),x80823))+~E(f319(f319(f94(f913(x80822,a904)),x80823),x80821),f181(f913(x80822,a904)))+E(f319(f319(f75(x80822),f319(f57(x80822,f75(x80822)),x80823)),f319(f57(x80822,f75(x80822)),x80821)),f319(f57(x80822,f75(x80822)),f319(f319(f93(f913(x80822,a904)),x80823),x80821)))
% 22.40/22.32 [7874]E(x78741,f2(a1))+E(f319(f319(f30(a1),x78742),x78741),x78743)+~P1(f319(f319(f225(a1),x78744),f2(a1)))+~E(x78742,f319(f319(f74(a1),f319(f319(f75(a1),x78741),x78743)),x78744))+~P1(f319(f319(f225(a1),f2(a1)),x78744))+~P1(f319(f319(f226(a1),x78744),x78741))+~P1(f319(f319(f226(a1),x78741),x78744))
% 22.40/22.32 [7882]E(f39(a1,x78822,x78821),x78823)+E(x78821,f2(a1))+~P1(f319(f319(f225(a1),x78823),f2(a1)))+~E(x78822,f319(f319(f74(a1),f319(f319(f75(a1),x78821),x78824)),x78823))+~P1(f319(f319(f225(a1),f2(a1)),x78823))+~P1(f319(f319(f226(a1),x78823),x78821))+~P1(f319(f319(f226(a1),x78821),x78823))
% 22.40/22.32 [7789]~P19(x77892,x77895,x77894)+E(x77891,f181(f913(x77892,a904)))+E(x77893,f181(f913(x77892,a904)))+~P1(f319(f55(x77892),x77891))+~P1(f319(f55(x77892),x77893))+~E(f319(f319(f94(f913(x77892,a904)),x77893),x77891),f181(f913(x77892,a904)))+E(f319(x77894,f319(f319(f93(f913(x77892,a904)),x77893),x77891)),f319(f319(x77895,f319(x77894,x77893)),f319(x77894,x77891)))
% 22.40/22.32 [9479]~P25(x94793,x94791,x94795,x94794)+~P25(x94791,x94793,x94796,x94792)+E(f319(f29(x94791),x94792),f319(f29(x94793),x94794))+~P1(f319(f55(x94793),x94794))+~P1(f319(f55(x94791),x94792))+~P1(f319(f319(f225(f913(x94793,a904)),f319(f302(x94791,x94793,x94796),x94792)),x94794))+~P1(f319(f319(f225(f913(x94791,a904)),f319(f302(x94793,x94791,x94795),x94794)),x94792))
% 22.40/22.32 [9427]~P1(f319(f319(f226(a1),f319(f319(f74(a1),f319(f319(f75(a1),x94275),x94271)),x94276)),f2(a1)))+~E(f319(f319(f74(a1),f319(f319(f75(a1),x94273),x94272)),x94274),f319(f319(f74(a1),f319(f319(f75(a1),x94275),x94271)),x94276))+~P1(f319(f319(f225(a1),f2(a1)),x94276))+~P1(f319(f319(f226(a1),f2(a1)),x94275))+~P1(f319(f319(f225(a1),x94275),x94273))+~P1(f319(f319(f226(a1),x94274),x94273))+P1(f319(f319(f225(a1),x94271),x94272))
% 22.40/22.32 [9177]~E(f319(f319(f74(a1),f319(f319(f75(a1),x91773),x91771)),x91774),f319(f319(f74(a1),f319(f319(f75(a1),x91775),x91772)),x91776))+~P1(f319(f319(f225(a1),f2(a1)),x91774))+~P1(f319(f319(f226(a1),f2(a1)),x91775))+~P1(f319(f319(f225(a1),x91775),x91773))+~P1(f319(f319(f226(a1),x91776),x91775))+P1(f319(f319(f225(a1),x91771),x91772))+~P1(f319(f319(f225(a1),f2(a1)),f319(f319(f74(a1),f319(f319(f75(a1),x91775),x91772)),x91776)))
% 22.40/22.32 [9359]~P133(x93591)+~E(f319(f319(f74(x93591),x93592),x93594),f72(x93591))+~P1(f319(f319(f225(x93591),x93595),x93596))+~P1(f319(f319(f225(x93591),x93593),x93596))+~P1(f319(f319(f225(x93591),f2(x93591)),x93594))+~P1(f319(f319(f225(x93591),f2(x93591)),x93592))+P1(f319(f319(f225(x93591),f319(f319(f74(x93591),f319(f319(f75(x93591),x93592),x93593)),f319(f319(f75(x93591),x93594),x93595))),x93596))
% 22.40/22.32 [9360]~P134(x93601)+~E(f319(f319(f74(x93601),x93602),x93604),f72(x93601))+~P1(f319(f319(f225(x93601),f2(x93601)),x93604))+~P1(f319(f319(f225(x93601),f2(x93601)),x93602))+~P1(f319(f319(f226(x93601),x93605),x93606))+~P1(f319(f319(f226(x93601),x93603),x93606))+P1(f319(f319(f226(x93601),f319(f319(f74(x93601),f319(f319(f75(x93601),x93602),x93603)),f319(f319(f75(x93601),x93604),x93605))),x93606))
% 22.40/22.32 [10186]~P8(x101867,x101866,x101865)+E(x101861,x101862)+~P11(x101867,f913(x101864,a904),x101865,x101863)+E(f319(x101863,f517(x101861,x101862,x101863,x101864,x101865,x101866,x101867)),f319(x101863,f518(x101861,x101862,x101863,x101864,x101865,x101866,x101867)))+~E(f319(f319(f33(x101867,f913(x101864,a904)),x101861),x101863),f319(f319(f33(x101867,f913(x101864,a904)),x101862),x101863))+~P1(f319(f319(f321(f913(x101867,a904)),x101862),f319(f319(f54(x101867),x101866),x101865)))+~P1(f319(f319(f321(f913(x101867,a904)),x101861),f319(f319(f54(x101867),x101866),x101865)))
% 22.40/22.32 [10244]~P8(x102443,x102447,x102446)+E(x102441,x102442)+~P11(x102443,f913(x102445,a904),x102446,x102444)+~E(f319(f319(f33(x102443,f913(x102445,a904)),x102441),x102444),f319(f319(f33(x102443,f913(x102445,a904)),x102442),x102444))+P1(f319(f319(f321(x102443),f518(x102441,x102442,x102444,x102445,x102446,x102447,x102443)),x102447))+~P1(f319(f319(f321(f913(x102443,a904)),x102442),f319(f319(f54(x102443),x102447),x102446)))+~P1(f319(f319(f321(f913(x102443,a904)),x102441),f319(f319(f54(x102443),x102447),x102446)))
% 22.40/22.32 [10245]~P8(x102453,x102457,x102456)+E(x102451,x102452)+~P11(x102453,f913(x102455,a904),x102456,x102454)+~E(f319(f319(f33(x102453,f913(x102455,a904)),x102451),x102454),f319(f319(f33(x102453,f913(x102455,a904)),x102452),x102454))+P1(f319(f319(f321(x102453),f517(x102451,x102452,x102454,x102455,x102456,x102457,x102453)),x102457))+~P1(f319(f319(f321(f913(x102453,a904)),x102452),f319(f319(f54(x102453),x102457),x102456)))+~P1(f319(f319(f321(f913(x102453,a904)),x102451),f319(f319(f54(x102453),x102457),x102456)))
% 22.40/22.32 [10364]E(x103641,x103642)+~P8(x103643,x103646,x103647)+~P11(x103643,f913(x103644,a904),x103647,x103645)+~E(f319(f319(f33(x103643,f913(x103644,a904)),x103641),x103645),f319(f319(f33(x103643,f913(x103644,a904)),x103642),x103645))+~P1(f319(f319(f321(f912(x103643,x103643)),f319(f319(f244(x103643,x103643),f518(x103641,x103642,x103645,x103644,x103647,x103646,x103643)),f517(x103641,x103642,x103645,x103644,x103647,x103646,x103643))),x103647))+~P1(f319(f319(f321(f913(x103643,a904)),x103642),f319(f319(f54(x103643),x103646),x103647)))+~P1(f319(f319(f321(f913(x103643,a904)),x103641),f319(f319(f54(x103643),x103646),x103647)))
% 22.40/22.32 [9176]~P8(x91761,x91767,x91764)+~E(x91765,x91766)+~P1(f319(f319(f321(x91761),x91763),x91766))+~P1(f319(f319(f321(x91761),x91762),x91765))+~P1(f319(f319(f321(f913(x91761,a904)),x91766),f319(f319(f54(x91761),x91767),x91764)))+~P1(f319(f319(f321(f913(x91761,a904)),x91765),f319(f319(f54(x91761),x91767),x91764)))+P1(f319(f319(f321(f912(x91761,x91761)),f319(f319(f244(x91761,x91761),x91762),x91763)),x91764))
% 22.40/22.32 [9318]E(x93181,x93182)+~P8(x93183,x93184,x93185)+~P1(f319(f319(f321(x93183),x93186),x93182))+~P1(f319(f319(f321(x93183),x93187),x93181))+~P1(f319(f319(f321(f913(x93183,a904)),x93182),f319(f319(f54(x93183),x93184),x93185)))+~P1(f319(f319(f321(f913(x93183,a904)),x93181),f319(f319(f54(x93183),x93184),x93185)))+~P1(f319(f319(f321(f912(x93183,x93183)),f319(f319(f244(x93183,x93183),x93187),x93186)),x93185))
% 22.40/22.32 [10396]~P8(x103969,x103968,x103967)+~P8(x103961,x1039611,x1039610)+~P12(x103961,x103969,f913(x103966,a904),x1039610,x103967,x103965)+P1(f319(f319(f321(x103961),f520(x103962,x103963,x103964,x103965,x103966,x103967,x103968,x103969,x1039610,x1039611,x103961)),x1039611))+~P1(f319(f319(f321(f913(x103969,a904)),x103963),f319(f319(f54(x103969),x103968),x103967)))+~P1(f319(f319(f321(f913(x103961,a904)),x103964),f319(f319(f54(x103961),x1039611),x1039610)))+P1(f319(f319(f321(f913(x103966,a904)),f319(f319(f33(x103961,f913(x103966,a904)),x103964),f319(f319(f10(f913(x103969,f913(x103966,a904)),f913(x103966,a904),x103961),f319(f33(x103969,f913(x103966,a904)),x103963)),x103965))),x103962))
% 22.40/22.32 [10397]~P8(x1039711,x1039710,x103979)+~P8(x103971,x103978,x103977)+~P12(x1039711,x103971,f913(x103976,a904),x103979,x103977,x103975)+P1(f319(f319(f321(x103971),f521(x103972,x103973,x103974,x103975,x103976,x103977,x103978,x103971,x103979,x1039710,x1039711)),x103978))+~P1(f319(f319(f321(f913(x1039711,a904)),x103974),f319(f319(f54(x1039711),x1039710),x103979)))+~P1(f319(f319(f321(f913(x103971,a904)),x103973),f319(f319(f54(x103971),x103978),x103977)))+P1(f319(f319(f321(f913(x103976,a904)),f319(f319(f33(x1039711,f913(x103976,a904)),x103974),f319(f319(f10(f913(x103971,f913(x103976,a904)),f913(x103976,a904),x1039711),f319(f33(x103971,f913(x103976,a904)),x103973)),x103975))),x103972))
% 22.40/22.32 [10398]~P8(x103982,x103988,x103989)+~P8(x103984,x1039810,x1039811)+~P12(x103982,x103984,f913(x103981,a904),x103989,x1039811,x103986)+~P1(f319(f319(f321(f913(x103982,a904)),x103983),f319(f319(f54(x103982),x103988),x103989)))+~P1(f319(f319(f321(f913(x103984,a904)),x103985),f319(f319(f54(x103984),x1039810),x1039811)))+~P1(f319(f319(f321(f913(x103981,a904)),f319(f319(x103986,f520(x103987,x103985,x103983,x103986,x103981,x1039811,x1039810,x103984,x103989,x103988,x103982)),f521(x103987,x103985,x103983,x103986,x103981,x1039811,x1039810,x103984,x103989,x103988,x103982))),x103987))+P1(f319(f319(f321(f913(x103981,a904)),f319(f319(f33(x103982,f913(x103981,a904)),x103983),f319(f319(f10(f913(x103984,f913(x103981,a904)),f913(x103981,a904),x103982),f319(f33(x103984,f913(x103981,a904)),x103985)),x103986))),x103987))
% 22.40/22.32 [9206]E(x92061,x92062)+~P4(x92064)+~P25(x92063,x92064,x92065,f319(f319(f93(f913(x92063,a904)),f319(f164(x92063),x92061)),f319(f164(x92063),x92062)))+~E(f319(f164(x92063),x92061),f319(f164(x92063),x92062))+~P13(x92064,f319(f319(f146(x92063,x92064),x92065),x92062))+~P13(x92064,f319(f319(f146(x92063,x92064),x92065),x92061))+~P1(f319(f129(x92064),f319(f319(f146(x92063,x92064),x92065),x92062)))+~P1(f319(f129(x92064),f319(f319(f146(x92063,x92064),x92065),x92061)))
% 22.40/22.32 %EqnAxiom
% 22.40/22.32 [1]E(x11,x11)
% 22.40/22.32 [2]E(x22,x21)+~E(x21,x22)
% 22.40/22.32 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 22.40/22.32 [4]~E(x41,x42)+E(f2(x41),f2(x42))
% 22.40/22.32 [5]~E(x51,x52)+E(f3(x51),f3(x52))
% 22.40/22.32 [6]~E(x61,x62)+E(f92(x61),f92(x62))
% 22.40/22.32 [7]~E(x71,x72)+E(f93(x71),f93(x72))
% 22.40/22.32 [8]~E(x81,x82)+E(f180(x81),f180(x82))
% 22.40/22.32 [9]~E(x91,x92)+E(f94(x91),f94(x92))
% 22.40/22.32 [10]~E(x101,x102)+E(f230(x101),f230(x102))
% 22.40/22.32 [11]~E(x111,x112)+E(f181(x111),f181(x112))
% 22.40/22.32 [12]~E(x121,x122)+E(f319(x121,x123),f319(x122,x123))
% 22.40/22.32 [13]~E(x131,x132)+E(f319(x133,x131),f319(x133,x132))
% 22.40/22.32 [14]~E(x141,x142)+E(f95(x141),f95(x142))
% 22.40/22.32 [15]~E(x151,x152)+E(f25(x151),f25(x152))
% 22.40/22.32 [16]~E(x161,x162)+E(f78(x161),f78(x162))
% 22.40/22.32 [17]~E(x171,x172)+E(f172(x171),f172(x172))
% 22.40/22.32 [18]~E(x181,x182)+E(f102(x181),f102(x182))
% 22.40/22.32 [19]~E(x191,x192)+E(f907(x191),f907(x192))
% 22.40/22.32 [20]~E(x201,x202)+E(f72(x201),f72(x202))
% 22.40/22.32 [21]~E(x211,x212)+E(f521(x211,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112),f521(x212,x213,x214,x215,x216,x217,x218,x219,x2110,x2111,x2112))
% 22.40/22.32 [22]~E(x221,x222)+E(f521(x223,x221,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f521(x223,x222,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212))
% 22.40/22.32 [23]~E(x231,x232)+E(f521(x233,x234,x231,x235,x236,x237,x238,x239,x2310,x2311,x2312),f521(x233,x234,x232,x235,x236,x237,x238,x239,x2310,x2311,x2312))
% 22.40/22.32 [24]~E(x241,x242)+E(f521(x243,x244,x245,x241,x246,x247,x248,x249,x2410,x2411,x2412),f521(x243,x244,x245,x242,x246,x247,x248,x249,x2410,x2411,x2412))
% 22.40/22.32 [25]~E(x251,x252)+E(f521(x253,x254,x255,x256,x251,x257,x258,x259,x2510,x2511,x2512),f521(x253,x254,x255,x256,x252,x257,x258,x259,x2510,x2511,x2512))
% 22.40/22.32 [26]~E(x261,x262)+E(f521(x263,x264,x265,x266,x267,x261,x268,x269,x2610,x2611,x2612),f521(x263,x264,x265,x266,x267,x262,x268,x269,x2610,x2611,x2612))
% 22.40/22.32 [27]~E(x271,x272)+E(f521(x273,x274,x275,x276,x277,x278,x271,x279,x2710,x2711,x2712),f521(x273,x274,x275,x276,x277,x278,x272,x279,x2710,x2711,x2712))
% 22.40/22.32 [28]~E(x281,x282)+E(f521(x283,x284,x285,x286,x287,x288,x289,x281,x2810,x2811,x2812),f521(x283,x284,x285,x286,x287,x288,x289,x282,x2810,x2811,x2812))
% 22.40/22.32 [29]~E(x291,x292)+E(f521(x293,x294,x295,x296,x297,x298,x299,x2910,x291,x2911,x2912),f521(x293,x294,x295,x296,x297,x298,x299,x2910,x292,x2911,x2912))
% 22.40/22.32 [30]~E(x301,x302)+E(f521(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x301,x3012),f521(x303,x304,x305,x306,x307,x308,x309,x3010,x3011,x302,x3012))
% 22.40/22.32 [31]~E(x311,x312)+E(f521(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x311),f521(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x3112,x312))
% 22.40/22.32 [32]~E(x321,x322)+E(f776(x321,x323,x324,x325,x326,x327,x328),f776(x322,x323,x324,x325,x326,x327,x328))
% 22.40/22.32 [33]~E(x331,x332)+E(f776(x333,x331,x334,x335,x336,x337,x338),f776(x333,x332,x334,x335,x336,x337,x338))
% 22.40/22.32 [34]~E(x341,x342)+E(f776(x343,x344,x341,x345,x346,x347,x348),f776(x343,x344,x342,x345,x346,x347,x348))
% 22.40/22.32 [35]~E(x351,x352)+E(f776(x353,x354,x355,x351,x356,x357,x358),f776(x353,x354,x355,x352,x356,x357,x358))
% 22.40/22.32 [36]~E(x361,x362)+E(f776(x363,x364,x365,x366,x361,x367,x368),f776(x363,x364,x365,x366,x362,x367,x368))
% 22.40/22.32 [37]~E(x371,x372)+E(f776(x373,x374,x375,x376,x377,x371,x378),f776(x373,x374,x375,x376,x377,x372,x378))
% 22.40/22.32 [38]~E(x381,x382)+E(f776(x383,x384,x385,x386,x387,x388,x381),f776(x383,x384,x385,x386,x387,x388,x382))
% 22.40/22.32 [39]~E(x391,x392)+E(f6(x391),f6(x392))
% 22.40/22.32 [40]~E(x401,x402)+E(f520(x401,x403,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012),f520(x402,x403,x404,x405,x406,x407,x408,x409,x4010,x4011,x4012))
% 22.40/22.32 [41]~E(x411,x412)+E(f520(x413,x411,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112),f520(x413,x412,x414,x415,x416,x417,x418,x419,x4110,x4111,x4112))
% 22.40/22.32 [42]~E(x421,x422)+E(f520(x423,x424,x421,x425,x426,x427,x428,x429,x4210,x4211,x4212),f520(x423,x424,x422,x425,x426,x427,x428,x429,x4210,x4211,x4212))
% 22.40/22.32 [43]~E(x431,x432)+E(f520(x433,x434,x435,x431,x436,x437,x438,x439,x4310,x4311,x4312),f520(x433,x434,x435,x432,x436,x437,x438,x439,x4310,x4311,x4312))
% 22.40/22.32 [44]~E(x441,x442)+E(f520(x443,x444,x445,x446,x441,x447,x448,x449,x4410,x4411,x4412),f520(x443,x444,x445,x446,x442,x447,x448,x449,x4410,x4411,x4412))
% 22.40/22.32 [45]~E(x451,x452)+E(f520(x453,x454,x455,x456,x457,x451,x458,x459,x4510,x4511,x4512),f520(x453,x454,x455,x456,x457,x452,x458,x459,x4510,x4511,x4512))
% 22.40/22.32 [46]~E(x461,x462)+E(f520(x463,x464,x465,x466,x467,x468,x461,x469,x4610,x4611,x4612),f520(x463,x464,x465,x466,x467,x468,x462,x469,x4610,x4611,x4612))
% 22.40/22.32 [47]~E(x471,x472)+E(f520(x473,x474,x475,x476,x477,x478,x479,x471,x4710,x4711,x4712),f520(x473,x474,x475,x476,x477,x478,x479,x472,x4710,x4711,x4712))
% 22.40/22.32 [48]~E(x481,x482)+E(f520(x483,x484,x485,x486,x487,x488,x489,x4810,x481,x4811,x4812),f520(x483,x484,x485,x486,x487,x488,x489,x4810,x482,x4811,x4812))
% 22.40/22.32 [49]~E(x491,x492)+E(f520(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x491,x4912),f520(x493,x494,x495,x496,x497,x498,x499,x4910,x4911,x492,x4912))
% 22.40/22.32 [50]~E(x501,x502)+E(f520(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x5012,x501),f520(x503,x504,x505,x506,x507,x508,x509,x5010,x5011,x5012,x502))
% 22.40/22.32 [51]~E(x511,x512)+E(f321(x511),f321(x512))
% 22.40/22.32 [52]~E(x521,x522)+E(f103(x521),f103(x522))
% 22.40/22.32 [53]~E(x531,x532)+E(f913(x531,x533),f913(x532,x533))
% 22.40/22.32 [54]~E(x541,x542)+E(f913(x543,x541),f913(x543,x542))
% 22.40/22.32 [55]~E(x551,x552)+E(f905(x551),f905(x552))
% 22.40/22.32 [56]~E(x561,x562)+E(f910(x561),f910(x562))
% 22.40/22.32 [57]~E(x571,x572)+E(f164(x571),f164(x572))
% 22.40/22.32 [58]~E(x581,x582)+E(f908(x581),f908(x582))
% 22.40/22.32 [59]~E(x591,x592)+E(f73(x591),f73(x592))
% 22.40/22.32 [60]~E(x601,x602)+E(f171(x601,x603),f171(x602,x603))
% 22.40/22.32 [61]~E(x611,x612)+E(f171(x613,x611),f171(x613,x612))
% 22.40/22.32 [62]~E(x621,x622)+E(f96(x621),f96(x622))
% 22.40/22.32 [63]~E(x631,x632)+E(f143(x631),f143(x632))
% 22.40/22.32 [64]~E(x641,x642)+E(f182(x641),f182(x642))
% 22.40/22.32 [65]~E(x651,x652)+E(f912(x651,x653),f912(x652,x653))
% 22.40/22.32 [66]~E(x661,x662)+E(f912(x663,x661),f912(x663,x662))
% 22.40/22.32 [67]~E(x671,x672)+E(f226(x671),f226(x672))
% 22.40/22.32 [68]~E(x681,x682)+E(f74(x681),f74(x682))
% 22.40/22.32 [69]~E(x691,x692)+E(f225(x691),f225(x692))
% 22.40/22.32 [70]~E(x701,x702)+E(f246(x701,x703),f246(x702,x703))
% 22.40/22.32 [71]~E(x711,x712)+E(f246(x713,x711),f246(x713,x712))
% 22.40/22.32 [72]~E(x721,x722)+E(f148(x721,x723,x724,x725),f148(x722,x723,x724,x725))
% 22.40/22.32 [73]~E(x731,x732)+E(f148(x733,x731,x734,x735),f148(x733,x732,x734,x735))
% 22.40/22.32 [74]~E(x741,x742)+E(f148(x743,x744,x741,x745),f148(x743,x744,x742,x745))
% 22.40/22.32 [75]~E(x751,x752)+E(f148(x753,x754,x755,x751),f148(x753,x754,x755,x752))
% 22.40/22.32 [76]~E(x761,x762)+E(f301(x761),f301(x762))
% 22.40/22.32 [77]~E(x771,x772)+E(f667(x771,x773,x774),f667(x772,x773,x774))
% 22.40/22.32 [78]~E(x781,x782)+E(f667(x783,x781,x784),f667(x783,x782,x784))
% 22.40/22.32 [79]~E(x791,x792)+E(f667(x793,x794,x791),f667(x793,x794,x792))
% 22.40/22.32 [80]~E(x801,x802)+E(f105(x801),f105(x802))
% 22.40/22.32 [81]~E(x811,x812)+E(f531(x811),f531(x812))
% 22.40/22.32 [82]~E(x821,x822)+E(f15(x821,x823),f15(x822,x823))
% 22.40/22.32 [83]~E(x831,x832)+E(f15(x833,x831),f15(x833,x832))
% 22.40/22.32 [84]~E(x841,x842)+E(f8(x841,x843),f8(x842,x843))
% 22.40/22.32 [85]~E(x851,x852)+E(f8(x853,x851),f8(x853,x852))
% 22.40/22.32 [86]~E(x861,x862)+E(f130(x861),f130(x862))
% 22.40/22.32 [87]~E(x871,x872)+E(f54(x871),f54(x872))
% 22.40/22.32 [88]~E(x881,x882)+E(f9(x881,x883,x884),f9(x882,x883,x884))
% 22.40/22.32 [89]~E(x891,x892)+E(f9(x893,x891,x894),f9(x893,x892,x894))
% 22.40/22.32 [90]~E(x901,x902)+E(f9(x903,x904,x901),f9(x903,x904,x902))
% 22.40/22.32 [91]~E(x911,x912)+E(f409(x911,x913,x914,x915),f409(x912,x913,x914,x915))
% 22.40/22.32 [92]~E(x921,x922)+E(f409(x923,x921,x924,x925),f409(x923,x922,x924,x925))
% 22.40/22.32 [93]~E(x931,x932)+E(f409(x933,x934,x931,x935),f409(x933,x934,x932,x935))
% 22.40/22.32 [94]~E(x941,x942)+E(f409(x943,x944,x945,x941),f409(x943,x944,x945,x942))
% 22.40/22.32 [95]~E(x951,x952)+E(f55(x951),f55(x952))
% 22.40/22.32 [96]~E(x961,x962)+E(f243(x961,x963),f243(x962,x963))
% 22.40/22.32 [97]~E(x971,x972)+E(f243(x973,x971),f243(x973,x972))
% 22.40/22.32 [98]~E(x981,x982)+E(f131(x981,x983),f131(x982,x983))
% 22.40/22.32 [99]~E(x991,x992)+E(f131(x993,x991),f131(x993,x992))
% 22.40/22.32 [100]~E(x1001,x1002)+E(f18(x1001,x1003),f18(x1002,x1003))
% 22.40/22.32 [101]~E(x1011,x1012)+E(f18(x1013,x1011),f18(x1013,x1012))
% 22.40/22.32 [102]~E(x1021,x1022)+E(f40(x1021,x1023),f40(x1022,x1023))
% 22.40/22.32 [103]~E(x1031,x1032)+E(f40(x1033,x1031),f40(x1033,x1032))
% 22.40/22.32 [104]~E(x1041,x1042)+E(f747(x1041,x1043,x1044),f747(x1042,x1043,x1044))
% 22.40/22.32 [105]~E(x1051,x1052)+E(f747(x1053,x1051,x1054),f747(x1053,x1052,x1054))
% 22.40/22.32 [106]~E(x1061,x1062)+E(f747(x1063,x1064,x1061),f747(x1063,x1064,x1062))
% 22.40/22.32 [107]~E(x1071,x1072)+E(f75(x1071),f75(x1072))
% 22.40/22.32 [108]~E(x1081,x1082)+E(f279(x1081),f279(x1082))
% 22.40/22.32 [109]~E(x1091,x1092)+E(f288(x1091,x1093,x1094,x1095),f288(x1092,x1093,x1094,x1095))
% 22.40/22.32 [110]~E(x1101,x1102)+E(f288(x1103,x1101,x1104,x1105),f288(x1103,x1102,x1104,x1105))
% 22.40/22.32 [111]~E(x1111,x1112)+E(f288(x1113,x1114,x1111,x1115),f288(x1113,x1114,x1112,x1115))
% 22.40/22.32 [112]~E(x1121,x1122)+E(f288(x1123,x1124,x1125,x1121),f288(x1123,x1124,x1125,x1122))
% 22.40/22.32 [113]~E(x1131,x1132)+E(f58(x1131,x1133,x1134),f58(x1132,x1133,x1134))
% 22.40/22.32 [114]~E(x1141,x1142)+E(f58(x1143,x1141,x1144),f58(x1143,x1142,x1144))
% 22.40/22.32 [115]~E(x1151,x1152)+E(f58(x1153,x1154,x1151),f58(x1153,x1154,x1152))
% 22.40/22.32 [116]~E(x1161,x1162)+E(f757(x1161,x1163,x1164),f757(x1162,x1163,x1164))
% 22.40/22.32 [117]~E(x1171,x1172)+E(f757(x1173,x1171,x1174),f757(x1173,x1172,x1174))
% 22.40/22.32 [118]~E(x1181,x1182)+E(f757(x1183,x1184,x1181),f757(x1183,x1184,x1182))
% 22.40/22.32 [119]~E(x1191,x1192)+E(f146(x1191,x1193),f146(x1192,x1193))
% 22.40/22.32 [120]~E(x1201,x1202)+E(f146(x1203,x1201),f146(x1203,x1202))
% 22.40/22.32 [121]~E(x1211,x1212)+E(f42(x1211,x1213),f42(x1212,x1213))
% 22.40/22.32 [122]~E(x1221,x1222)+E(f42(x1223,x1221),f42(x1223,x1222))
% 22.40/22.32 [123]~E(x1231,x1232)+E(f66(x1231,x1233,x1234,x1235),f66(x1232,x1233,x1234,x1235))
% 22.40/22.32 [124]~E(x1241,x1242)+E(f66(x1243,x1241,x1244,x1245),f66(x1243,x1242,x1244,x1245))
% 22.40/22.32 [125]~E(x1251,x1252)+E(f66(x1253,x1254,x1251,x1255),f66(x1253,x1254,x1252,x1255))
% 22.40/22.32 [126]~E(x1261,x1262)+E(f66(x1263,x1264,x1265,x1261),f66(x1263,x1264,x1265,x1262))
% 22.40/22.32 [127]~E(x1271,x1272)+E(f902(x1271,x1273,x1274,x1275),f902(x1272,x1273,x1274,x1275))
% 22.40/22.32 [128]~E(x1281,x1282)+E(f902(x1283,x1281,x1284,x1285),f902(x1283,x1282,x1284,x1285))
% 22.40/22.32 [129]~E(x1291,x1292)+E(f902(x1293,x1294,x1291,x1295),f902(x1293,x1294,x1292,x1295))
% 22.40/22.32 [130]~E(x1301,x1302)+E(f902(x1303,x1304,x1305,x1301),f902(x1303,x1304,x1305,x1302))
% 22.40/22.32 [131]~E(x1311,x1312)+E(f69(x1311),f69(x1312))
% 22.40/22.32 [132]~E(x1321,x1322)+E(f334(x1321,x1323,x1324),f334(x1322,x1323,x1324))
% 22.40/22.32 [133]~E(x1331,x1332)+E(f334(x1333,x1331,x1334),f334(x1333,x1332,x1334))
% 22.40/22.32 [134]~E(x1341,x1342)+E(f334(x1343,x1344,x1341),f334(x1343,x1344,x1342))
% 22.40/22.32 [135]~E(x1351,x1352)+E(f302(x1351,x1353,x1354),f302(x1352,x1353,x1354))
% 22.40/22.32 [136]~E(x1361,x1362)+E(f302(x1363,x1361,x1364),f302(x1363,x1362,x1364))
% 22.40/22.32 [137]~E(x1371,x1372)+E(f302(x1373,x1374,x1371),f302(x1373,x1374,x1372))
% 22.40/22.32 [138]~E(x1381,x1382)+E(f30(x1381),f30(x1382))
% 22.40/22.32 [139]~E(x1391,x1392)+E(f528(x1391,x1393),f528(x1392,x1393))
% 22.40/22.32 [140]~E(x1401,x1402)+E(f528(x1403,x1401),f528(x1403,x1402))
% 22.40/22.32 [141]~E(x1411,x1412)+E(f88(x1411,x1413),f88(x1412,x1413))
% 22.40/22.32 [142]~E(x1421,x1422)+E(f88(x1423,x1421),f88(x1423,x1422))
% 22.40/22.32 [143]~E(x1431,x1432)+E(f98(x1431),f98(x1432))
% 22.40/22.32 [144]~E(x1441,x1442)+E(f100(x1441),f100(x1442))
% 22.40/22.32 [145]~E(x1451,x1452)+E(f320(x1451),f320(x1452))
% 22.40/22.32 [146]~E(x1461,x1462)+E(f254(x1461),f254(x1462))
% 22.40/22.32 [147]~E(x1471,x1472)+E(f572(x1471),f572(x1472))
% 22.40/22.32 [148]~E(x1481,x1482)+E(f47(x1481,x1483),f47(x1482,x1483))
% 22.40/22.32 [149]~E(x1491,x1492)+E(f47(x1493,x1491),f47(x1493,x1492))
% 22.40/22.32 [150]~E(x1501,x1502)+E(f282(x1501),f282(x1502))
% 22.40/22.32 [151]~E(x1511,x1512)+E(f233(x1511,x1513),f233(x1512,x1513))
% 22.40/22.32 [152]~E(x1521,x1522)+E(f233(x1523,x1521),f233(x1523,x1522))
% 22.40/22.32 [153]~E(x1531,x1532)+E(f741(x1531,x1533,x1534),f741(x1532,x1533,x1534))
% 22.40/22.32 [154]~E(x1541,x1542)+E(f741(x1543,x1541,x1544),f741(x1543,x1542,x1544))
% 22.40/22.32 [155]~E(x1551,x1552)+E(f741(x1553,x1554,x1551),f741(x1553,x1554,x1552))
% 22.40/22.32 [156]~E(x1561,x1562)+E(f29(x1561),f29(x1562))
% 22.40/22.32 [157]~E(x1571,x1572)+E(f244(x1571,x1573),f244(x1572,x1573))
% 22.40/22.32 [158]~E(x1581,x1582)+E(f244(x1583,x1581),f244(x1583,x1582))
% 22.40/22.32 [159]~E(x1591,x1592)+E(f20(x1591,x1593,x1594),f20(x1592,x1593,x1594))
% 22.40/22.32 [160]~E(x1601,x1602)+E(f20(x1603,x1601,x1604),f20(x1603,x1602,x1604))
% 22.40/22.32 [161]~E(x1611,x1612)+E(f20(x1613,x1614,x1611),f20(x1613,x1614,x1612))
% 22.40/22.32 [162]~E(x1621,x1622)+E(f7(x1621),f7(x1622))
% 22.40/22.32 [163]~E(x1631,x1632)+E(f151(x1631,x1633),f151(x1632,x1633))
% 22.40/22.32 [164]~E(x1641,x1642)+E(f151(x1643,x1641),f151(x1643,x1642))
% 22.40/22.32 [165]~E(x1651,x1652)+E(f87(x1651,x1653),f87(x1652,x1653))
% 22.40/22.32 [166]~E(x1661,x1662)+E(f87(x1663,x1661),f87(x1663,x1662))
% 22.40/22.32 [167]~E(x1671,x1672)+E(f604(x1671,x1673,x1674),f604(x1672,x1673,x1674))
% 22.40/22.32 [168]~E(x1681,x1682)+E(f604(x1683,x1681,x1684),f604(x1683,x1682,x1684))
% 22.40/22.32 [169]~E(x1691,x1692)+E(f604(x1693,x1694,x1691),f604(x1693,x1694,x1692))
% 22.40/22.32 [170]~E(x1701,x1702)+E(f10(x1701,x1703,x1704),f10(x1702,x1703,x1704))
% 22.40/22.32 [171]~E(x1711,x1712)+E(f10(x1713,x1711,x1714),f10(x1713,x1712,x1714))
% 22.40/22.32 [172]~E(x1721,x1722)+E(f10(x1723,x1724,x1721),f10(x1723,x1724,x1722))
% 22.40/22.32 [173]~E(x1731,x1732)+E(f354(x1731,x1733),f354(x1732,x1733))
% 22.40/22.32 [174]~E(x1741,x1742)+E(f354(x1743,x1741),f354(x1743,x1742))
% 22.40/22.32 [175]~E(x1751,x1752)+E(f530(x1751),f530(x1752))
% 22.40/22.32 [176]~E(x1761,x1762)+E(f134(x1761,x1763,x1764,x1765),f134(x1762,x1763,x1764,x1765))
% 22.40/22.32 [177]~E(x1771,x1772)+E(f134(x1773,x1771,x1774,x1775),f134(x1773,x1772,x1774,x1775))
% 22.40/22.32 [178]~E(x1781,x1782)+E(f134(x1783,x1784,x1781,x1785),f134(x1783,x1784,x1782,x1785))
% 22.40/22.32 [179]~E(x1791,x1792)+E(f134(x1793,x1794,x1795,x1791),f134(x1793,x1794,x1795,x1792))
% 22.40/22.32 [180]~E(x1801,x1802)+E(f447(x1801,x1803,x1804,x1805),f447(x1802,x1803,x1804,x1805))
% 22.40/22.32 [181]~E(x1811,x1812)+E(f447(x1813,x1811,x1814,x1815),f447(x1813,x1812,x1814,x1815))
% 22.40/22.32 [182]~E(x1821,x1822)+E(f447(x1823,x1824,x1821,x1825),f447(x1823,x1824,x1822,x1825))
% 22.40/22.32 [183]~E(x1831,x1832)+E(f447(x1833,x1834,x1835,x1831),f447(x1833,x1834,x1835,x1832))
% 22.40/22.32 [184]~E(x1841,x1842)+E(f850(x1841,x1843,x1844),f850(x1842,x1843,x1844))
% 22.40/22.32 [185]~E(x1851,x1852)+E(f850(x1853,x1851,x1854),f850(x1853,x1852,x1854))
% 22.40/22.32 [186]~E(x1861,x1862)+E(f850(x1863,x1864,x1861),f850(x1863,x1864,x1862))
% 22.40/22.32 [187]~E(x1871,x1872)+E(f854(x1871,x1873,x1874),f854(x1872,x1873,x1874))
% 22.40/22.32 [188]~E(x1881,x1882)+E(f854(x1883,x1881,x1884),f854(x1883,x1882,x1884))
% 22.40/22.32 [189]~E(x1891,x1892)+E(f854(x1893,x1894,x1891),f854(x1893,x1894,x1892))
% 22.40/22.32 [190]~E(x1901,x1902)+E(f852(x1901,x1903,x1904),f852(x1902,x1903,x1904))
% 22.40/22.32 [191]~E(x1911,x1912)+E(f852(x1913,x1911,x1914),f852(x1913,x1912,x1914))
% 22.40/22.32 [192]~E(x1921,x1922)+E(f852(x1923,x1924,x1921),f852(x1923,x1924,x1922))
% 22.40/22.32 [193]~E(x1931,x1932)+E(f157(x1931),f157(x1932))
% 22.40/22.32 [194]~E(x1941,x1942)+E(f723(x1941,x1943,x1944,x1945,x1946,x1947,x1948,x1949),f723(x1942,x1943,x1944,x1945,x1946,x1947,x1948,x1949))
% 22.40/22.32 [195]~E(x1951,x1952)+E(f723(x1953,x1951,x1954,x1955,x1956,x1957,x1958,x1959),f723(x1953,x1952,x1954,x1955,x1956,x1957,x1958,x1959))
% 22.40/22.32 [196]~E(x1961,x1962)+E(f723(x1963,x1964,x1961,x1965,x1966,x1967,x1968,x1969),f723(x1963,x1964,x1962,x1965,x1966,x1967,x1968,x1969))
% 22.40/22.32 [197]~E(x1971,x1972)+E(f723(x1973,x1974,x1975,x1971,x1976,x1977,x1978,x1979),f723(x1973,x1974,x1975,x1972,x1976,x1977,x1978,x1979))
% 22.40/22.32 [198]~E(x1981,x1982)+E(f723(x1983,x1984,x1985,x1986,x1981,x1987,x1988,x1989),f723(x1983,x1984,x1985,x1986,x1982,x1987,x1988,x1989))
% 22.40/22.32 [199]~E(x1991,x1992)+E(f723(x1993,x1994,x1995,x1996,x1997,x1991,x1998,x1999),f723(x1993,x1994,x1995,x1996,x1997,x1992,x1998,x1999))
% 22.40/22.32 [200]~E(x2001,x2002)+E(f723(x2003,x2004,x2005,x2006,x2007,x2008,x2001,x2009),f723(x2003,x2004,x2005,x2006,x2007,x2008,x2002,x2009))
% 22.40/22.32 [201]~E(x2011,x2012)+E(f723(x2013,x2014,x2015,x2016,x2017,x2018,x2019,x2011),f723(x2013,x2014,x2015,x2016,x2017,x2018,x2019,x2012))
% 22.40/22.32 [202]~E(x2021,x2022)+E(f126(x2021),f126(x2022))
% 22.40/22.32 [203]~E(x2031,x2032)+E(f277(x2031,x2033,x2034),f277(x2032,x2033,x2034))
% 22.40/22.32 [204]~E(x2041,x2042)+E(f277(x2043,x2041,x2044),f277(x2043,x2042,x2044))
% 22.40/22.32 [205]~E(x2051,x2052)+E(f277(x2053,x2054,x2051),f277(x2053,x2054,x2052))
% 22.40/22.32 [206]~E(x2061,x2062)+E(f307(x2061,x2063),f307(x2062,x2063))
% 22.40/22.32 [207]~E(x2071,x2072)+E(f307(x2073,x2071),f307(x2073,x2072))
% 22.40/22.32 [208]~E(x2081,x2082)+E(f152(x2081,x2083),f152(x2082,x2083))
% 22.40/22.32 [209]~E(x2091,x2092)+E(f152(x2093,x2091),f152(x2093,x2092))
% 22.40/22.32 [210]~E(x2101,x2102)+E(f50(x2101),f50(x2102))
% 22.40/22.32 [211]~E(x2111,x2112)+E(f31(x2111,x2113),f31(x2112,x2113))
% 22.40/22.32 [212]~E(x2121,x2122)+E(f31(x2123,x2121),f31(x2123,x2122))
% 22.40/22.32 [213]~E(x2131,x2132)+E(f268(x2131,x2133,x2134,x2135),f268(x2132,x2133,x2134,x2135))
% 22.40/22.32 [214]~E(x2141,x2142)+E(f268(x2143,x2141,x2144,x2145),f268(x2143,x2142,x2144,x2145))
% 22.40/22.32 [215]~E(x2151,x2152)+E(f268(x2153,x2154,x2151,x2155),f268(x2153,x2154,x2152,x2155))
% 22.40/22.32 [216]~E(x2161,x2162)+E(f268(x2163,x2164,x2165,x2161),f268(x2163,x2164,x2165,x2162))
% 22.40/22.32 [217]~E(x2171,x2172)+E(f835(x2171,x2173,x2174,x2175,x2176,x2177,x2178,x2179),f835(x2172,x2173,x2174,x2175,x2176,x2177,x2178,x2179))
% 22.40/22.32 [218]~E(x2181,x2182)+E(f835(x2183,x2181,x2184,x2185,x2186,x2187,x2188,x2189),f835(x2183,x2182,x2184,x2185,x2186,x2187,x2188,x2189))
% 22.40/22.32 [219]~E(x2191,x2192)+E(f835(x2193,x2194,x2191,x2195,x2196,x2197,x2198,x2199),f835(x2193,x2194,x2192,x2195,x2196,x2197,x2198,x2199))
% 22.40/22.32 [220]~E(x2201,x2202)+E(f835(x2203,x2204,x2205,x2201,x2206,x2207,x2208,x2209),f835(x2203,x2204,x2205,x2202,x2206,x2207,x2208,x2209))
% 22.40/22.32 [221]~E(x2211,x2212)+E(f835(x2213,x2214,x2215,x2216,x2211,x2217,x2218,x2219),f835(x2213,x2214,x2215,x2216,x2212,x2217,x2218,x2219))
% 22.40/22.32 [222]~E(x2221,x2222)+E(f835(x2223,x2224,x2225,x2226,x2227,x2221,x2228,x2229),f835(x2223,x2224,x2225,x2226,x2227,x2222,x2228,x2229))
% 22.40/22.32 [223]~E(x2231,x2232)+E(f835(x2233,x2234,x2235,x2236,x2237,x2238,x2231,x2239),f835(x2233,x2234,x2235,x2236,x2237,x2238,x2232,x2239))
% 22.40/22.32 [224]~E(x2241,x2242)+E(f835(x2243,x2244,x2245,x2246,x2247,x2248,x2249,x2241),f835(x2243,x2244,x2245,x2246,x2247,x2248,x2249,x2242))
% 22.40/22.32 [225]~E(x2251,x2252)+E(f142(x2251,x2253,x2254,x2255),f142(x2252,x2253,x2254,x2255))
% 22.40/22.32 [226]~E(x2261,x2262)+E(f142(x2263,x2261,x2264,x2265),f142(x2263,x2262,x2264,x2265))
% 22.40/22.32 [227]~E(x2271,x2272)+E(f142(x2273,x2274,x2271,x2275),f142(x2273,x2274,x2272,x2275))
% 22.40/22.32 [228]~E(x2281,x2282)+E(f142(x2283,x2284,x2285,x2281),f142(x2283,x2284,x2285,x2282))
% 22.40/22.32 [229]~E(x2291,x2292)+E(f234(x2291),f234(x2292))
% 22.40/22.32 [230]~E(x2301,x2302)+E(f145(x2301,x2303),f145(x2302,x2303))
% 22.40/22.32 [231]~E(x2311,x2312)+E(f145(x2313,x2311),f145(x2313,x2312))
% 22.40/22.32 [232]~E(x2321,x2322)+E(f297(x2321,x2323,x2324),f297(x2322,x2323,x2324))
% 22.40/22.32 [233]~E(x2331,x2332)+E(f297(x2333,x2331,x2334),f297(x2333,x2332,x2334))
% 22.40/22.32 [234]~E(x2341,x2342)+E(f297(x2343,x2344,x2341),f297(x2343,x2344,x2342))
% 22.40/22.32 [235]~E(x2351,x2352)+E(f807(x2351,x2353),f807(x2352,x2353))
% 22.40/22.32 [236]~E(x2361,x2362)+E(f807(x2363,x2361),f807(x2363,x2362))
% 22.40/22.32 [237]~E(x2371,x2372)+E(f136(x2371,x2373),f136(x2372,x2373))
% 22.40/22.32 [238]~E(x2381,x2382)+E(f136(x2383,x2381),f136(x2383,x2382))
% 22.40/22.32 [239]~E(x2391,x2392)+E(f33(x2391,x2393),f33(x2392,x2393))
% 22.40/22.32 [240]~E(x2401,x2402)+E(f33(x2403,x2401),f33(x2403,x2402))
% 22.40/22.32 [241]~E(x2411,x2412)+E(f14(x2411,x2413,x2414),f14(x2412,x2413,x2414))
% 22.40/22.32 [242]~E(x2421,x2422)+E(f14(x2423,x2421,x2424),f14(x2423,x2422,x2424))
% 22.40/22.32 [243]~E(x2431,x2432)+E(f14(x2433,x2434,x2431),f14(x2433,x2434,x2432))
% 22.40/22.32 [244]~E(x2441,x2442)+E(f13(x2441,x2443,x2444),f13(x2442,x2443,x2444))
% 22.40/22.32 [245]~E(x2451,x2452)+E(f13(x2453,x2451,x2454),f13(x2453,x2452,x2454))
% 22.40/22.32 [246]~E(x2461,x2462)+E(f13(x2463,x2464,x2461),f13(x2463,x2464,x2462))
% 22.40/22.32 [247]~E(x2471,x2472)+E(f59(x2471,x2473,x2474),f59(x2472,x2473,x2474))
% 22.40/22.32 [248]~E(x2481,x2482)+E(f59(x2483,x2481,x2484),f59(x2483,x2482,x2484))
% 22.40/22.32 [249]~E(x2491,x2492)+E(f59(x2493,x2494,x2491),f59(x2493,x2494,x2492))
% 22.40/22.32 [250]~E(x2501,x2502)+E(f175(x2501,x2503),f175(x2502,x2503))
% 22.40/22.32 [251]~E(x2511,x2512)+E(f175(x2513,x2511),f175(x2513,x2512))
% 22.40/22.32 [252]~E(x2521,x2522)+E(f248(x2521,x2523),f248(x2522,x2523))
% 22.40/22.32 [253]~E(x2531,x2532)+E(f248(x2533,x2531),f248(x2533,x2532))
% 22.40/22.32 [254]~E(x2541,x2542)+E(f840(x2541,x2543,x2544),f840(x2542,x2543,x2544))
% 22.40/22.32 [255]~E(x2551,x2552)+E(f840(x2553,x2551,x2554),f840(x2553,x2552,x2554))
% 22.40/22.32 [256]~E(x2561,x2562)+E(f840(x2563,x2564,x2561),f840(x2563,x2564,x2562))
% 22.40/22.32 [257]~E(x2571,x2572)+E(f51(x2571),f51(x2572))
% 22.40/22.32 [258]~E(x2581,x2582)+E(f686(x2581,x2583,x2584,x2585,x2586),f686(x2582,x2583,x2584,x2585,x2586))
% 22.40/22.32 [259]~E(x2591,x2592)+E(f686(x2593,x2591,x2594,x2595,x2596),f686(x2593,x2592,x2594,x2595,x2596))
% 22.40/22.32 [260]~E(x2601,x2602)+E(f686(x2603,x2604,x2601,x2605,x2606),f686(x2603,x2604,x2602,x2605,x2606))
% 22.40/22.32 [261]~E(x2611,x2612)+E(f686(x2613,x2614,x2615,x2611,x2616),f686(x2613,x2614,x2615,x2612,x2616))
% 22.40/22.32 [262]~E(x2621,x2622)+E(f686(x2623,x2624,x2625,x2626,x2621),f686(x2623,x2624,x2625,x2626,x2622))
% 22.40/22.32 [263]~E(x2631,x2632)+E(f106(x2631,x2633),f106(x2632,x2633))
% 22.40/22.32 [264]~E(x2641,x2642)+E(f106(x2643,x2641),f106(x2643,x2642))
% 22.40/22.32 [265]~E(x2651,x2652)+E(f156(x2651),f156(x2652))
% 22.40/22.32 [266]~E(x2661,x2662)+E(f57(x2661,x2663),f57(x2662,x2663))
% 22.40/22.32 [267]~E(x2671,x2672)+E(f57(x2673,x2671),f57(x2673,x2672))
% 22.40/22.32 [268]~E(x2681,x2682)+E(f144(x2681,x2683),f144(x2682,x2683))
% 22.40/22.32 [269]~E(x2691,x2692)+E(f144(x2693,x2691),f144(x2693,x2692))
% 22.40/22.32 [270]~E(x2701,x2702)+E(f224(x2701,x2703,x2704,x2705),f224(x2702,x2703,x2704,x2705))
% 22.40/22.32 [271]~E(x2711,x2712)+E(f224(x2713,x2711,x2714,x2715),f224(x2713,x2712,x2714,x2715))
% 22.40/22.32 [272]~E(x2721,x2722)+E(f224(x2723,x2724,x2721,x2725),f224(x2723,x2724,x2722,x2725))
% 22.40/22.32 [273]~E(x2731,x2732)+E(f224(x2733,x2734,x2735,x2731),f224(x2733,x2734,x2735,x2732))
% 22.40/22.32 [274]~E(x2741,x2742)+E(f184(x2741),f184(x2742))
% 22.40/22.32 [275]~E(x2751,x2752)+E(f295(x2751,x2753,x2754),f295(x2752,x2753,x2754))
% 22.40/22.32 [276]~E(x2761,x2762)+E(f295(x2763,x2761,x2764),f295(x2763,x2762,x2764))
% 22.40/22.32 [277]~E(x2771,x2772)+E(f295(x2773,x2774,x2771),f295(x2773,x2774,x2772))
% 22.40/22.32 [278]~E(x2781,x2782)+E(f107(x2781),f107(x2782))
% 22.40/22.32 [279]~E(x2791,x2792)+E(f299(x2791,x2793),f299(x2792,x2793))
% 22.40/22.32 [280]~E(x2801,x2802)+E(f299(x2803,x2801),f299(x2803,x2802))
% 22.40/22.32 [281]~E(x2811,x2812)+E(f914(x2811,x2813),f914(x2812,x2813))
% 22.40/22.32 [282]~E(x2821,x2822)+E(f914(x2823,x2821),f914(x2823,x2822))
% 22.40/22.32 [283]~E(x2831,x2832)+E(f911(x2831,x2833),f911(x2832,x2833))
% 22.40/22.32 [284]~E(x2841,x2842)+E(f911(x2843,x2841),f911(x2843,x2842))
% 22.40/22.32 [285]~E(x2851,x2852)+E(f159(x2851),f159(x2852))
% 22.40/22.32 [286]~E(x2861,x2862)+E(f236(x2861),f236(x2862))
% 22.40/22.32 [287]~E(x2871,x2872)+E(f85(x2871,x2873,x2874,x2875),f85(x2872,x2873,x2874,x2875))
% 22.40/22.32 [288]~E(x2881,x2882)+E(f85(x2883,x2881,x2884,x2885),f85(x2883,x2882,x2884,x2885))
% 22.40/22.32 [289]~E(x2891,x2892)+E(f85(x2893,x2894,x2891,x2895),f85(x2893,x2894,x2892,x2895))
% 22.40/22.32 [290]~E(x2901,x2902)+E(f85(x2903,x2904,x2905,x2901),f85(x2903,x2904,x2905,x2902))
% 22.40/22.32 [291]~E(x2911,x2912)+E(f160(x2911),f160(x2912))
% 22.40/22.32 [292]~E(x2921,x2922)+E(f163(x2921),f163(x2922))
% 22.40/22.32 [293]~E(x2931,x2932)+E(f169(x2931,x2933,x2934),f169(x2932,x2933,x2934))
% 22.40/22.32 [294]~E(x2941,x2942)+E(f169(x2943,x2941,x2944),f169(x2943,x2942,x2944))
% 22.40/22.32 [295]~E(x2951,x2952)+E(f169(x2953,x2954,x2951),f169(x2953,x2954,x2952))
% 22.40/22.32 [296]~E(x2961,x2962)+E(f12(x2961,x2963),f12(x2962,x2963))
% 22.40/22.32 [297]~E(x2971,x2972)+E(f12(x2973,x2971),f12(x2973,x2972))
% 22.40/22.32 [298]~E(x2981,x2982)+E(f855(x2981,x2983,x2984),f855(x2982,x2983,x2984))
% 22.40/22.32 [299]~E(x2991,x2992)+E(f855(x2993,x2991,x2994),f855(x2993,x2992,x2994))
% 22.40/22.32 [300]~E(x3001,x3002)+E(f855(x3003,x3004,x3001),f855(x3003,x3004,x3002))
% 22.40/22.32 [301]~E(x3011,x3012)+E(f86(x3011),f86(x3012))
% 22.40/22.32 [302]~E(x3021,x3022)+E(f17(x3021,x3023),f17(x3022,x3023))
% 22.40/22.32 [303]~E(x3031,x3032)+E(f17(x3033,x3031),f17(x3033,x3032))
% 22.40/22.32 [304]~E(x3041,x3042)+E(f139(x3041,x3043),f139(x3042,x3043))
% 22.40/22.32 [305]~E(x3051,x3052)+E(f139(x3053,x3051),f139(x3053,x3052))
% 22.40/22.32 [306]~E(x3061,x3062)+E(f39(x3061,x3063,x3064),f39(x3062,x3063,x3064))
% 22.40/22.32 [307]~E(x3071,x3072)+E(f39(x3073,x3071,x3074),f39(x3073,x3072,x3074))
% 22.40/22.32 [308]~E(x3081,x3082)+E(f39(x3083,x3084,x3081),f39(x3083,x3084,x3082))
% 22.40/22.32 [309]~E(x3091,x3092)+E(f276(x3091,x3093),f276(x3092,x3093))
% 22.40/22.32 [310]~E(x3101,x3102)+E(f276(x3103,x3101),f276(x3103,x3102))
% 22.40/22.32 [311]~E(x3111,x3112)+E(f255(x3111,x3113),f255(x3112,x3113))
% 22.40/22.32 [312]~E(x3121,x3122)+E(f255(x3123,x3121),f255(x3123,x3122))
% 22.40/22.32 [313]~E(x3131,x3132)+E(f280(x3131,x3133),f280(x3132,x3133))
% 22.40/22.32 [314]~E(x3141,x3142)+E(f280(x3143,x3141),f280(x3143,x3142))
% 22.40/22.32 [315]~E(x3151,x3152)+E(f664(x3151,x3153,x3154),f664(x3152,x3153,x3154))
% 22.40/22.32 [316]~E(x3161,x3162)+E(f664(x3163,x3161,x3164),f664(x3163,x3162,x3164))
% 22.40/22.32 [317]~E(x3171,x3172)+E(f664(x3173,x3174,x3171),f664(x3173,x3174,x3172))
% 22.40/22.32 [318]~E(x3181,x3182)+E(f381(x3181,x3183,x3184,x3185,x3186,x3187),f381(x3182,x3183,x3184,x3185,x3186,x3187))
% 22.40/22.32 [319]~E(x3191,x3192)+E(f381(x3193,x3191,x3194,x3195,x3196,x3197),f381(x3193,x3192,x3194,x3195,x3196,x3197))
% 22.40/22.32 [320]~E(x3201,x3202)+E(f381(x3203,x3204,x3201,x3205,x3206,x3207),f381(x3203,x3204,x3202,x3205,x3206,x3207))
% 22.40/22.32 [321]~E(x3211,x3212)+E(f381(x3213,x3214,x3215,x3211,x3216,x3217),f381(x3213,x3214,x3215,x3212,x3216,x3217))
% 22.40/22.32 [322]~E(x3221,x3222)+E(f381(x3223,x3224,x3225,x3226,x3221,x3227),f381(x3223,x3224,x3225,x3226,x3222,x3227))
% 22.40/22.32 [323]~E(x3231,x3232)+E(f381(x3233,x3234,x3235,x3236,x3237,x3231),f381(x3233,x3234,x3235,x3236,x3237,x3232))
% 22.40/22.32 [324]~E(x3241,x3242)+E(f310(x3241,x3243),f310(x3242,x3243))
% 22.40/22.32 [325]~E(x3251,x3252)+E(f310(x3253,x3251),f310(x3253,x3252))
% 22.40/22.32 [326]~E(x3261,x3262)+E(f828(x3261,x3263,x3264,x3265,x3266),f828(x3262,x3263,x3264,x3265,x3266))
% 22.40/22.32 [327]~E(x3271,x3272)+E(f828(x3273,x3271,x3274,x3275,x3276),f828(x3273,x3272,x3274,x3275,x3276))
% 22.40/22.32 [328]~E(x3281,x3282)+E(f828(x3283,x3284,x3281,x3285,x3286),f828(x3283,x3284,x3282,x3285,x3286))
% 22.40/22.32 [329]~E(x3291,x3292)+E(f828(x3293,x3294,x3295,x3291,x3296),f828(x3293,x3294,x3295,x3292,x3296))
% 22.40/22.32 [330]~E(x3301,x3302)+E(f828(x3303,x3304,x3305,x3306,x3301),f828(x3303,x3304,x3305,x3306,x3302))
% 22.40/22.32 [331]~E(x3311,x3312)+E(f311(x3311,x3313),f311(x3312,x3313))
% 22.40/22.32 [332]~E(x3321,x3322)+E(f311(x3323,x3321),f311(x3323,x3322))
% 22.40/22.32 [333]~E(x3331,x3332)+E(f153(x3331,x3333),f153(x3332,x3333))
% 22.40/22.32 [334]~E(x3341,x3342)+E(f153(x3343,x3341),f153(x3343,x3342))
% 22.40/22.32 [335]~E(x3351,x3352)+E(f575(x3351,x3353),f575(x3352,x3353))
% 22.40/22.32 [336]~E(x3361,x3362)+E(f575(x3363,x3361),f575(x3363,x3362))
% 22.40/22.32 [337]~E(x3371,x3372)+E(f623(x3371,x3373,x3374,x3375,x3376),f623(x3372,x3373,x3374,x3375,x3376))
% 22.40/22.32 [338]~E(x3381,x3382)+E(f623(x3383,x3381,x3384,x3385,x3386),f623(x3383,x3382,x3384,x3385,x3386))
% 22.40/22.32 [339]~E(x3391,x3392)+E(f623(x3393,x3394,x3391,x3395,x3396),f623(x3393,x3394,x3392,x3395,x3396))
% 22.40/22.32 [340]~E(x3401,x3402)+E(f623(x3403,x3404,x3405,x3401,x3406),f623(x3403,x3404,x3405,x3402,x3406))
% 22.40/22.32 [341]~E(x3411,x3412)+E(f623(x3413,x3414,x3415,x3416,x3411),f623(x3413,x3414,x3415,x3416,x3412))
% 22.40/22.32 [342]~E(x3421,x3422)+E(f250(x3421,x3423,x3424,x3425,x3426,x3427),f250(x3422,x3423,x3424,x3425,x3426,x3427))
% 22.40/22.32 [343]~E(x3431,x3432)+E(f250(x3433,x3431,x3434,x3435,x3436,x3437),f250(x3433,x3432,x3434,x3435,x3436,x3437))
% 22.40/22.32 [344]~E(x3441,x3442)+E(f250(x3443,x3444,x3441,x3445,x3446,x3447),f250(x3443,x3444,x3442,x3445,x3446,x3447))
% 22.40/22.32 [345]~E(x3451,x3452)+E(f250(x3453,x3454,x3455,x3451,x3456,x3457),f250(x3453,x3454,x3455,x3452,x3456,x3457))
% 22.40/22.32 [346]~E(x3461,x3462)+E(f250(x3463,x3464,x3465,x3466,x3461,x3467),f250(x3463,x3464,x3465,x3466,x3462,x3467))
% 22.40/22.32 [347]~E(x3471,x3472)+E(f250(x3473,x3474,x3475,x3476,x3477,x3471),f250(x3473,x3474,x3475,x3476,x3477,x3472))
% 22.40/22.32 [348]~E(x3481,x3482)+E(f503(x3481,x3483,x3484,x3485,x3486),f503(x3482,x3483,x3484,x3485,x3486))
% 22.40/22.32 [349]~E(x3491,x3492)+E(f503(x3493,x3491,x3494,x3495,x3496),f503(x3493,x3492,x3494,x3495,x3496))
% 22.40/22.32 [350]~E(x3501,x3502)+E(f503(x3503,x3504,x3501,x3505,x3506),f503(x3503,x3504,x3502,x3505,x3506))
% 22.40/22.32 [351]~E(x3511,x3512)+E(f503(x3513,x3514,x3515,x3511,x3516),f503(x3513,x3514,x3515,x3512,x3516))
% 22.40/22.32 [352]~E(x3521,x3522)+E(f503(x3523,x3524,x3525,x3526,x3521),f503(x3523,x3524,x3525,x3526,x3522))
% 22.40/22.32 [353]~E(x3531,x3532)+E(f785(x3531,x3533,x3534),f785(x3532,x3533,x3534))
% 22.40/22.32 [354]~E(x3541,x3542)+E(f785(x3543,x3541,x3544),f785(x3543,x3542,x3544))
% 22.40/22.32 [355]~E(x3551,x3552)+E(f785(x3553,x3554,x3551),f785(x3553,x3554,x3552))
% 22.40/22.32 [356]~E(x3561,x3562)+E(f249(x3561,x3563,x3564),f249(x3562,x3563,x3564))
% 22.40/22.32 [357]~E(x3571,x3572)+E(f249(x3573,x3571,x3574),f249(x3573,x3572,x3574))
% 22.40/22.32 [358]~E(x3581,x3582)+E(f249(x3583,x3584,x3581),f249(x3583,x3584,x3582))
% 22.40/22.32 [359]~E(x3591,x3592)+E(f648(x3591,x3593,x3594,x3595),f648(x3592,x3593,x3594,x3595))
% 22.40/22.32 [360]~E(x3601,x3602)+E(f648(x3603,x3601,x3604,x3605),f648(x3603,x3602,x3604,x3605))
% 22.40/22.32 [361]~E(x3611,x3612)+E(f648(x3613,x3614,x3611,x3615),f648(x3613,x3614,x3612,x3615))
% 22.40/22.32 [362]~E(x3621,x3622)+E(f648(x3623,x3624,x3625,x3621),f648(x3623,x3624,x3625,x3622))
% 22.40/22.32 [363]~E(x3631,x3632)+E(f11(x3631,x3633),f11(x3632,x3633))
% 22.40/22.32 [364]~E(x3641,x3642)+E(f11(x3643,x3641),f11(x3643,x3642))
% 22.40/22.32 [365]~E(x3651,x3652)+E(f457(x3651,x3653,x3654,x3655),f457(x3652,x3653,x3654,x3655))
% 22.40/22.32 [366]~E(x3661,x3662)+E(f457(x3663,x3661,x3664,x3665),f457(x3663,x3662,x3664,x3665))
% 22.40/22.32 [367]~E(x3671,x3672)+E(f457(x3673,x3674,x3671,x3675),f457(x3673,x3674,x3672,x3675))
% 22.40/22.32 [368]~E(x3681,x3682)+E(f457(x3683,x3684,x3685,x3681),f457(x3683,x3684,x3685,x3682))
% 22.40/22.32 [369]~E(x3691,x3692)+E(f440(x3691,x3693,x3694),f440(x3692,x3693,x3694))
% 22.40/22.32 [370]~E(x3701,x3702)+E(f440(x3703,x3701,x3704),f440(x3703,x3702,x3704))
% 22.40/22.32 [371]~E(x3711,x3712)+E(f440(x3713,x3714,x3711),f440(x3713,x3714,x3712))
% 22.40/22.32 [372]~E(x3721,x3722)+E(f646(x3721,x3723,x3724,x3725),f646(x3722,x3723,x3724,x3725))
% 22.40/22.32 [373]~E(x3731,x3732)+E(f646(x3733,x3731,x3734,x3735),f646(x3733,x3732,x3734,x3735))
% 22.40/22.32 [374]~E(x3741,x3742)+E(f646(x3743,x3744,x3741,x3745),f646(x3743,x3744,x3742,x3745))
% 22.40/22.32 [375]~E(x3751,x3752)+E(f646(x3753,x3754,x3755,x3751),f646(x3753,x3754,x3755,x3752))
% 22.40/22.32 [376]~E(x3761,x3762)+E(f278(x3761,x3763),f278(x3762,x3763))
% 22.40/22.32 [377]~E(x3771,x3772)+E(f278(x3773,x3771),f278(x3773,x3772))
% 22.40/22.32 [378]~E(x3781,x3782)+E(f129(x3781),f129(x3782))
% 22.40/22.32 [379]~E(x3791,x3792)+E(f111(x3791),f111(x3792))
% 22.40/22.32 [380]~E(x3801,x3802)+E(f112(x3801,x3803),f112(x3802,x3803))
% 22.40/22.32 [381]~E(x3811,x3812)+E(f112(x3813,x3811),f112(x3813,x3812))
% 22.40/22.32 [382]~E(x3821,x3822)+E(f666(x3821,x3823),f666(x3822,x3823))
% 22.40/22.32 [383]~E(x3831,x3832)+E(f666(x3833,x3831),f666(x3833,x3832))
% 22.40/22.32 [384]~E(x3841,x3842)+E(f308(x3841,x3843),f308(x3842,x3843))
% 22.40/22.32 [385]~E(x3851,x3852)+E(f308(x3853,x3851),f308(x3853,x3852))
% 22.40/22.32 [386]~E(x3861,x3862)+E(f709(x3861,x3863,x3864),f709(x3862,x3863,x3864))
% 22.40/22.32 [387]~E(x3871,x3872)+E(f709(x3873,x3871,x3874),f709(x3873,x3872,x3874))
% 22.40/22.32 [388]~E(x3881,x3882)+E(f709(x3883,x3884,x3881),f709(x3883,x3884,x3882))
% 22.40/22.32 [389]~E(x3891,x3892)+E(f305(x3891,x3893,x3894,x3895),f305(x3892,x3893,x3894,x3895))
% 22.40/22.32 [390]~E(x3901,x3902)+E(f305(x3903,x3901,x3904,x3905),f305(x3903,x3902,x3904,x3905))
% 22.40/22.32 [391]~E(x3911,x3912)+E(f305(x3913,x3914,x3911,x3915),f305(x3913,x3914,x3912,x3915))
% 22.40/22.32 [392]~E(x3921,x3922)+E(f305(x3923,x3924,x3925,x3921),f305(x3923,x3924,x3925,x3922))
% 22.40/22.32 [393]~E(x3931,x3932)+E(f79(x3931,x3933),f79(x3932,x3933))
% 22.40/22.32 [394]~E(x3941,x3942)+E(f79(x3943,x3941),f79(x3943,x3942))
% 22.40/22.32 [395]~E(x3951,x3952)+E(f621(x3951,x3953,x3954,x3955,x3956),f621(x3952,x3953,x3954,x3955,x3956))
% 22.40/22.32 [396]~E(x3961,x3962)+E(f621(x3963,x3961,x3964,x3965,x3966),f621(x3963,x3962,x3964,x3965,x3966))
% 22.40/22.32 [397]~E(x3971,x3972)+E(f621(x3973,x3974,x3971,x3975,x3976),f621(x3973,x3974,x3972,x3975,x3976))
% 22.40/22.32 [398]~E(x3981,x3982)+E(f621(x3983,x3984,x3985,x3981,x3986),f621(x3983,x3984,x3985,x3982,x3986))
% 22.40/22.32 [399]~E(x3991,x3992)+E(f621(x3993,x3994,x3995,x3996,x3991),f621(x3993,x3994,x3995,x3996,x3992))
% 22.40/22.32 [400]~E(x4001,x4002)+E(f84(x4001,x4003),f84(x4002,x4003))
% 22.40/22.32 [401]~E(x4011,x4012)+E(f84(x4013,x4011),f84(x4013,x4012))
% 22.40/22.32 [402]~E(x4021,x4022)+E(f170(x4021,x4023),f170(x4022,x4023))
% 22.40/22.32 [403]~E(x4031,x4032)+E(f170(x4033,x4031),f170(x4033,x4032))
% 22.40/22.32 [404]~E(x4041,x4042)+E(f851(x4041,x4043,x4044),f851(x4042,x4043,x4044))
% 22.40/22.32 [405]~E(x4051,x4052)+E(f851(x4053,x4051,x4054),f851(x4053,x4052,x4054))
% 22.40/22.32 [406]~E(x4061,x4062)+E(f851(x4063,x4064,x4061),f851(x4063,x4064,x4062))
% 22.40/22.32 [407]~E(x4071,x4072)+E(f82(x4071,x4073),f82(x4072,x4073))
% 22.40/22.32 [408]~E(x4081,x4082)+E(f82(x4083,x4081),f82(x4083,x4082))
% 22.40/22.32 [409]~E(x4091,x4092)+E(f173(x4091,x4093),f173(x4092,x4093))
% 22.40/22.32 [410]~E(x4101,x4102)+E(f173(x4103,x4101),f173(x4103,x4102))
% 22.40/22.32 [411]~E(x4111,x4112)+E(f862(x4111,x4113,x4114),f862(x4112,x4113,x4114))
% 22.40/22.32 [412]~E(x4121,x4122)+E(f862(x4123,x4121,x4124),f862(x4123,x4122,x4124))
% 22.40/22.32 [413]~E(x4131,x4132)+E(f862(x4133,x4134,x4131),f862(x4133,x4134,x4132))
% 22.40/22.32 [414]~E(x4141,x4142)+E(f251(x4141,x4143,x4144,x4145),f251(x4142,x4143,x4144,x4145))
% 22.40/22.32 [415]~E(x4151,x4152)+E(f251(x4153,x4151,x4154,x4155),f251(x4153,x4152,x4154,x4155))
% 22.40/22.32 [416]~E(x4161,x4162)+E(f251(x4163,x4164,x4161,x4165),f251(x4163,x4164,x4162,x4165))
% 22.40/22.32 [417]~E(x4171,x4172)+E(f251(x4173,x4174,x4175,x4171),f251(x4173,x4174,x4175,x4172))
% 22.40/22.32 [418]~E(x4181,x4182)+E(f749(x4181,x4183,x4184),f749(x4182,x4183,x4184))
% 22.40/22.32 [419]~E(x4191,x4192)+E(f749(x4193,x4191,x4194),f749(x4193,x4192,x4194))
% 22.40/22.32 [420]~E(x4201,x4202)+E(f749(x4203,x4204,x4201),f749(x4203,x4204,x4202))
% 22.40/22.32 [421]~E(x4211,x4212)+E(f274(x4211),f274(x4212))
% 22.40/22.32 [422]~E(x4221,x4222)+E(f384(x4221,x4223,x4224),f384(x4222,x4223,x4224))
% 22.40/22.32 [423]~E(x4231,x4232)+E(f384(x4233,x4231,x4234),f384(x4233,x4232,x4234))
% 22.40/22.32 [424]~E(x4241,x4242)+E(f384(x4243,x4244,x4241),f384(x4243,x4244,x4242))
% 22.40/22.32 [425]~E(x4251,x4252)+E(f595(x4251,x4253,x4254,x4255),f595(x4252,x4253,x4254,x4255))
% 22.40/22.32 [426]~E(x4261,x4262)+E(f595(x4263,x4261,x4264,x4265),f595(x4263,x4262,x4264,x4265))
% 22.40/22.32 [427]~E(x4271,x4272)+E(f595(x4273,x4274,x4271,x4275),f595(x4273,x4274,x4272,x4275))
% 22.40/22.32 [428]~E(x4281,x4282)+E(f595(x4283,x4284,x4285,x4281),f595(x4283,x4284,x4285,x4282))
% 22.40/22.32 [429]~E(x4291,x4292)+E(f294(x4291,x4293),f294(x4292,x4293))
% 22.40/22.32 [430]~E(x4301,x4302)+E(f294(x4303,x4301),f294(x4303,x4302))
% 22.40/22.32 [431]~E(x4311,x4312)+E(f722(x4311,x4313),f722(x4312,x4313))
% 22.40/22.32 [432]~E(x4321,x4322)+E(f722(x4323,x4321),f722(x4323,x4322))
% 22.40/22.32 [433]~E(x4331,x4332)+E(f495(x4331,x4333,x4334),f495(x4332,x4333,x4334))
% 22.40/22.32 [434]~E(x4341,x4342)+E(f495(x4343,x4341,x4344),f495(x4343,x4342,x4344))
% 22.40/22.32 [435]~E(x4351,x4352)+E(f495(x4353,x4354,x4351),f495(x4353,x4354,x4352))
% 22.40/22.32 [436]~E(x4361,x4362)+E(f397(x4361,x4363),f397(x4362,x4363))
% 22.40/22.32 [437]~E(x4371,x4372)+E(f397(x4373,x4371),f397(x4373,x4372))
% 22.40/22.32 [438]~E(x4381,x4382)+E(f769(x4381,x4383,x4384,x4385),f769(x4382,x4383,x4384,x4385))
% 22.40/22.32 [439]~E(x4391,x4392)+E(f769(x4393,x4391,x4394,x4395),f769(x4393,x4392,x4394,x4395))
% 22.40/22.32 [440]~E(x4401,x4402)+E(f769(x4403,x4404,x4401,x4405),f769(x4403,x4404,x4402,x4405))
% 22.40/22.32 [441]~E(x4411,x4412)+E(f769(x4413,x4414,x4415,x4411),f769(x4413,x4414,x4415,x4412))
% 22.40/22.32 [442]~E(x4421,x4422)+E(f565(x4421,x4423),f565(x4422,x4423))
% 22.40/22.32 [443]~E(x4431,x4432)+E(f565(x4433,x4431),f565(x4433,x4432))
% 22.40/22.32 [444]~E(x4441,x4442)+E(f860(x4441,x4443,x4444),f860(x4442,x4443,x4444))
% 22.40/22.32 [445]~E(x4451,x4452)+E(f860(x4453,x4451,x4454),f860(x4453,x4452,x4454))
% 22.40/22.32 [446]~E(x4461,x4462)+E(f860(x4463,x4464,x4461),f860(x4463,x4464,x4462))
% 22.40/22.32 [447]~E(x4471,x4472)+E(f43(x4471,x4473),f43(x4472,x4473))
% 22.40/22.32 [448]~E(x4481,x4482)+E(f43(x4483,x4481),f43(x4483,x4482))
% 22.40/22.32 [449]~E(x4491,x4492)+E(f403(x4491,x4493,x4494),f403(x4492,x4493,x4494))
% 22.40/22.32 [450]~E(x4501,x4502)+E(f403(x4503,x4501,x4504),f403(x4503,x4502,x4504))
% 22.40/22.32 [451]~E(x4511,x4512)+E(f403(x4513,x4514,x4511),f403(x4513,x4514,x4512))
% 22.40/22.32 [452]~E(x4521,x4522)+E(f788(x4521,x4523,x4524,x4525),f788(x4522,x4523,x4524,x4525))
% 22.40/22.32 [453]~E(x4531,x4532)+E(f788(x4533,x4531,x4534,x4535),f788(x4533,x4532,x4534,x4535))
% 22.40/22.32 [454]~E(x4541,x4542)+E(f788(x4543,x4544,x4541,x4545),f788(x4543,x4544,x4542,x4545))
% 22.40/22.32 [455]~E(x4551,x4552)+E(f788(x4553,x4554,x4555,x4551),f788(x4553,x4554,x4555,x4552))
% 22.40/22.32 [456]~E(x4561,x4562)+E(f76(x4561,x4563),f76(x4562,x4563))
% 22.40/22.32 [457]~E(x4571,x4572)+E(f76(x4573,x4571),f76(x4573,x4572))
% 22.40/22.32 [458]~E(x4581,x4582)+E(f34(x4581,x4583),f34(x4582,x4583))
% 22.40/22.32 [459]~E(x4591,x4592)+E(f34(x4593,x4591),f34(x4593,x4592))
% 22.40/22.32 [460]~E(x4601,x4602)+E(f275(x4601),f275(x4602))
% 22.40/22.32 [461]~E(x4611,x4612)+E(f205(x4611),f205(x4612))
% 22.40/22.32 [462]~E(x4621,x4622)+E(f300(x4621),f300(x4622))
% 22.40/22.32 [463]~E(x4631,x4632)+E(f853(x4631,x4633,x4634),f853(x4632,x4633,x4634))
% 22.40/22.32 [464]~E(x4641,x4642)+E(f853(x4643,x4641,x4644),f853(x4643,x4642,x4644))
% 22.40/22.32 [465]~E(x4651,x4652)+E(f853(x4653,x4654,x4651),f853(x4653,x4654,x4652))
% 22.40/22.32 [466]~E(x4661,x4662)+E(f216(x4661,x4663,x4664,x4665,x4666),f216(x4662,x4663,x4664,x4665,x4666))
% 22.40/22.32 [467]~E(x4671,x4672)+E(f216(x4673,x4671,x4674,x4675,x4676),f216(x4673,x4672,x4674,x4675,x4676))
% 22.40/22.32 [468]~E(x4681,x4682)+E(f216(x4683,x4684,x4681,x4685,x4686),f216(x4683,x4684,x4682,x4685,x4686))
% 22.40/22.32 [469]~E(x4691,x4692)+E(f216(x4693,x4694,x4695,x4691,x4696),f216(x4693,x4694,x4695,x4692,x4696))
% 22.40/22.32 [470]~E(x4701,x4702)+E(f216(x4703,x4704,x4705,x4706,x4701),f216(x4703,x4704,x4705,x4706,x4702))
% 22.40/22.32 [471]~E(x4711,x4712)+E(f458(x4711,x4713,x4714,x4715),f458(x4712,x4713,x4714,x4715))
% 22.40/22.32 [472]~E(x4721,x4722)+E(f458(x4723,x4721,x4724,x4725),f458(x4723,x4722,x4724,x4725))
% 22.40/22.32 [473]~E(x4731,x4732)+E(f458(x4733,x4734,x4731,x4735),f458(x4733,x4734,x4732,x4735))
% 22.40/22.32 [474]~E(x4741,x4742)+E(f458(x4743,x4744,x4745,x4741),f458(x4743,x4744,x4745,x4742))
% 22.40/22.32 [475]~E(x4751,x4752)+E(f306(x4751),f306(x4752))
% 22.40/22.32 [476]~E(x4761,x4762)+E(f522(x4761,x4763,x4764),f522(x4762,x4763,x4764))
% 22.40/22.32 [477]~E(x4771,x4772)+E(f522(x4773,x4771,x4774),f522(x4773,x4772,x4774))
% 22.40/22.32 [478]~E(x4781,x4782)+E(f522(x4783,x4784,x4781),f522(x4783,x4784,x4782))
% 22.40/22.32 [479]~E(x4791,x4792)+E(f256(x4791,x4793),f256(x4792,x4793))
% 22.40/22.32 [480]~E(x4801,x4802)+E(f256(x4803,x4801),f256(x4803,x4802))
% 22.40/22.32 [481]~E(x4811,x4812)+E(f784(x4811,x4813,x4814,x4815),f784(x4812,x4813,x4814,x4815))
% 22.40/22.32 [482]~E(x4821,x4822)+E(f784(x4823,x4821,x4824,x4825),f784(x4823,x4822,x4824,x4825))
% 22.40/22.32 [483]~E(x4831,x4832)+E(f784(x4833,x4834,x4831,x4835),f784(x4833,x4834,x4832,x4835))
% 22.40/22.32 [484]~E(x4841,x4842)+E(f784(x4843,x4844,x4845,x4841),f784(x4843,x4844,x4845,x4842))
% 22.40/22.32 [485]~E(x4851,x4852)+E(f80(x4851),f80(x4852))
% 22.40/22.32 [486]~E(x4861,x4862)+E(f149(x4861,x4863),f149(x4862,x4863))
% 22.40/22.32 [487]~E(x4871,x4872)+E(f149(x4873,x4871),f149(x4873,x4872))
% 22.40/22.32 [488]~E(x4881,x4882)+E(f49(x4881,x4883,x4884),f49(x4882,x4883,x4884))
% 22.40/22.32 [489]~E(x4891,x4892)+E(f49(x4893,x4891,x4894),f49(x4893,x4892,x4894))
% 22.40/22.32 [490]~E(x4901,x4902)+E(f49(x4903,x4904,x4901),f49(x4903,x4904,x4902))
% 22.40/22.32 [491]~E(x4911,x4912)+E(f140(x4911,x4913,x4914),f140(x4912,x4913,x4914))
% 22.40/22.32 [492]~E(x4921,x4922)+E(f140(x4923,x4921,x4924),f140(x4923,x4922,x4924))
% 22.40/22.32 [493]~E(x4931,x4932)+E(f140(x4933,x4934,x4931),f140(x4933,x4934,x4932))
% 22.40/22.32 [494]~E(x4941,x4942)+E(f62(x4941,x4943,x4944),f62(x4942,x4943,x4944))
% 22.40/22.32 [495]~E(x4951,x4952)+E(f62(x4953,x4951,x4954),f62(x4953,x4952,x4954))
% 22.40/22.32 [496]~E(x4961,x4962)+E(f62(x4963,x4964,x4961),f62(x4963,x4964,x4962))
% 22.40/22.32 [497]~E(x4971,x4972)+E(f247(x4971,x4973,x4974,x4975),f247(x4972,x4973,x4974,x4975))
% 22.40/22.32 [498]~E(x4981,x4982)+E(f247(x4983,x4981,x4984,x4985),f247(x4983,x4982,x4984,x4985))
% 22.40/22.32 [499]~E(x4991,x4992)+E(f247(x4993,x4994,x4991,x4995),f247(x4993,x4994,x4992,x4995))
% 22.40/22.32 [500]~E(x5001,x5002)+E(f247(x5003,x5004,x5005,x5001),f247(x5003,x5004,x5005,x5002))
% 22.40/22.32 [501]~E(x5011,x5012)+E(f639(x5011,x5013,x5014,x5015,x5016,x5017),f639(x5012,x5013,x5014,x5015,x5016,x5017))
% 22.40/22.32 [502]~E(x5021,x5022)+E(f639(x5023,x5021,x5024,x5025,x5026,x5027),f639(x5023,x5022,x5024,x5025,x5026,x5027))
% 22.40/22.32 [503]~E(x5031,x5032)+E(f639(x5033,x5034,x5031,x5035,x5036,x5037),f639(x5033,x5034,x5032,x5035,x5036,x5037))
% 22.40/22.32 [504]~E(x5041,x5042)+E(f639(x5043,x5044,x5045,x5041,x5046,x5047),f639(x5043,x5044,x5045,x5042,x5046,x5047))
% 22.40/22.32 [505]~E(x5051,x5052)+E(f639(x5053,x5054,x5055,x5056,x5051,x5057),f639(x5053,x5054,x5055,x5056,x5052,x5057))
% 22.40/22.32 [506]~E(x5061,x5062)+E(f639(x5063,x5064,x5065,x5066,x5067,x5061),f639(x5063,x5064,x5065,x5066,x5067,x5062))
% 22.40/22.32 [507]~E(x5071,x5072)+E(f68(x5071,x5073,x5074,x5075,x5076),f68(x5072,x5073,x5074,x5075,x5076))
% 22.40/22.32 [508]~E(x5081,x5082)+E(f68(x5083,x5081,x5084,x5085,x5086),f68(x5083,x5082,x5084,x5085,x5086))
% 22.40/22.32 [509]~E(x5091,x5092)+E(f68(x5093,x5094,x5091,x5095,x5096),f68(x5093,x5094,x5092,x5095,x5096))
% 22.40/22.32 [510]~E(x5101,x5102)+E(f68(x5103,x5104,x5105,x5101,x5106),f68(x5103,x5104,x5105,x5102,x5106))
% 22.40/22.32 [511]~E(x5111,x5112)+E(f68(x5113,x5114,x5115,x5116,x5111),f68(x5113,x5114,x5115,x5116,x5112))
% 22.40/22.32 [512]~E(x5121,x5122)+E(f881(x5121,x5123,x5124),f881(x5122,x5123,x5124))
% 22.40/22.32 [513]~E(x5131,x5132)+E(f881(x5133,x5131,x5134),f881(x5133,x5132,x5134))
% 22.40/22.32 [514]~E(x5141,x5142)+E(f881(x5143,x5144,x5141),f881(x5143,x5144,x5142))
% 22.40/22.32 [515]~E(x5151,x5152)+E(f407(x5151,x5153,x5154,x5155),f407(x5152,x5153,x5154,x5155))
% 22.40/22.32 [516]~E(x5161,x5162)+E(f407(x5163,x5161,x5164,x5165),f407(x5163,x5162,x5164,x5165))
% 22.40/22.32 [517]~E(x5171,x5172)+E(f407(x5173,x5174,x5171,x5175),f407(x5173,x5174,x5172,x5175))
% 22.40/22.32 [518]~E(x5181,x5182)+E(f407(x5183,x5184,x5185,x5181),f407(x5183,x5184,x5185,x5182))
% 22.40/22.32 [519]~E(x5191,x5192)+E(f229(x5191,x5193),f229(x5192,x5193))
% 22.40/22.32 [520]~E(x5201,x5202)+E(f229(x5203,x5201),f229(x5203,x5202))
% 22.40/22.32 [521]~E(x5211,x5212)+E(f465(x5211,x5213),f465(x5212,x5213))
% 22.40/22.32 [522]~E(x5221,x5222)+E(f465(x5223,x5221),f465(x5223,x5222))
% 22.40/22.32 [523]~E(x5231,x5232)+E(f371(x5231,x5233,x5234,x5235,x5236,x5237,x5238),f371(x5232,x5233,x5234,x5235,x5236,x5237,x5238))
% 22.40/22.32 [524]~E(x5241,x5242)+E(f371(x5243,x5241,x5244,x5245,x5246,x5247,x5248),f371(x5243,x5242,x5244,x5245,x5246,x5247,x5248))
% 22.40/22.32 [525]~E(x5251,x5252)+E(f371(x5253,x5254,x5251,x5255,x5256,x5257,x5258),f371(x5253,x5254,x5252,x5255,x5256,x5257,x5258))
% 22.40/22.32 [526]~E(x5261,x5262)+E(f371(x5263,x5264,x5265,x5261,x5266,x5267,x5268),f371(x5263,x5264,x5265,x5262,x5266,x5267,x5268))
% 22.40/22.32 [527]~E(x5271,x5272)+E(f371(x5273,x5274,x5275,x5276,x5271,x5277,x5278),f371(x5273,x5274,x5275,x5276,x5272,x5277,x5278))
% 22.40/22.32 [528]~E(x5281,x5282)+E(f371(x5283,x5284,x5285,x5286,x5287,x5281,x5288),f371(x5283,x5284,x5285,x5286,x5287,x5282,x5288))
% 22.40/22.32 [529]~E(x5291,x5292)+E(f371(x5293,x5294,x5295,x5296,x5297,x5298,x5291),f371(x5293,x5294,x5295,x5296,x5297,x5298,x5292))
% 22.40/22.32 [530]~E(x5301,x5302)+E(f768(x5301,x5303,x5304,x5305),f768(x5302,x5303,x5304,x5305))
% 22.40/22.32 [531]~E(x5311,x5312)+E(f768(x5313,x5311,x5314,x5315),f768(x5313,x5312,x5314,x5315))
% 22.40/22.32 [532]~E(x5321,x5322)+E(f768(x5323,x5324,x5321,x5325),f768(x5323,x5324,x5322,x5325))
% 22.40/22.32 [533]~E(x5331,x5332)+E(f768(x5333,x5334,x5335,x5331),f768(x5333,x5334,x5335,x5332))
% 22.40/22.32 [534]~E(x5341,x5342)+E(f829(x5341,x5343,x5344,x5345,x5346,x5347),f829(x5342,x5343,x5344,x5345,x5346,x5347))
% 22.40/22.32 [535]~E(x5351,x5352)+E(f829(x5353,x5351,x5354,x5355,x5356,x5357),f829(x5353,x5352,x5354,x5355,x5356,x5357))
% 22.40/22.32 [536]~E(x5361,x5362)+E(f829(x5363,x5364,x5361,x5365,x5366,x5367),f829(x5363,x5364,x5362,x5365,x5366,x5367))
% 22.40/22.32 [537]~E(x5371,x5372)+E(f829(x5373,x5374,x5375,x5371,x5376,x5377),f829(x5373,x5374,x5375,x5372,x5376,x5377))
% 22.40/22.32 [538]~E(x5381,x5382)+E(f829(x5383,x5384,x5385,x5386,x5381,x5387),f829(x5383,x5384,x5385,x5386,x5382,x5387))
% 22.40/22.32 [539]~E(x5391,x5392)+E(f829(x5393,x5394,x5395,x5396,x5397,x5391),f829(x5393,x5394,x5395,x5396,x5397,x5392))
% 22.40/22.32 [540]~E(x5401,x5402)+E(f228(x5401,x5403),f228(x5402,x5403))
% 22.40/22.32 [541]~E(x5411,x5412)+E(f228(x5413,x5411),f228(x5413,x5412))
% 22.40/22.32 [542]~E(x5421,x5422)+E(f242(x5421,x5423,x5424),f242(x5422,x5423,x5424))
% 22.40/22.32 [543]~E(x5431,x5432)+E(f242(x5433,x5431,x5434),f242(x5433,x5432,x5434))
% 22.40/22.32 [544]~E(x5441,x5442)+E(f242(x5443,x5444,x5441),f242(x5443,x5444,x5442))
% 22.40/22.32 [545]~E(x5451,x5452)+E(f580(x5451,x5453,x5454),f580(x5452,x5453,x5454))
% 22.40/22.32 [546]~E(x5461,x5462)+E(f580(x5463,x5461,x5464),f580(x5463,x5462,x5464))
% 22.40/22.32 [547]~E(x5471,x5472)+E(f580(x5473,x5474,x5471),f580(x5473,x5474,x5472))
% 22.40/22.32 [548]~E(x5481,x5482)+E(f167(x5481),f167(x5482))
% 22.40/22.32 [549]~E(x5491,x5492)+E(f716(x5491,x5493),f716(x5492,x5493))
% 22.40/22.32 [550]~E(x5501,x5502)+E(f716(x5503,x5501),f716(x5503,x5502))
% 22.40/22.32 [551]~E(x5511,x5512)+E(f770(x5511,x5513,x5514,x5515),f770(x5512,x5513,x5514,x5515))
% 22.40/22.32 [552]~E(x5521,x5522)+E(f770(x5523,x5521,x5524,x5525),f770(x5523,x5522,x5524,x5525))
% 22.40/22.32 [553]~E(x5531,x5532)+E(f770(x5533,x5534,x5531,x5535),f770(x5533,x5534,x5532,x5535))
% 22.40/22.32 [554]~E(x5541,x5542)+E(f770(x5543,x5544,x5545,x5541),f770(x5543,x5544,x5545,x5542))
% 22.40/22.32 [555]~E(x5551,x5552)+E(f445(x5551,x5553,x5554),f445(x5552,x5553,x5554))
% 22.40/22.32 [556]~E(x5561,x5562)+E(f445(x5563,x5561,x5564),f445(x5563,x5562,x5564))
% 22.40/22.32 [557]~E(x5571,x5572)+E(f445(x5573,x5574,x5571),f445(x5573,x5574,x5572))
% 22.40/22.32 [558]~E(x5581,x5582)+E(f713(x5581,x5583,x5584,x5585),f713(x5582,x5583,x5584,x5585))
% 22.40/22.32 [559]~E(x5591,x5592)+E(f713(x5593,x5591,x5594,x5595),f713(x5593,x5592,x5594,x5595))
% 22.40/22.32 [560]~E(x5601,x5602)+E(f713(x5603,x5604,x5601,x5605),f713(x5603,x5604,x5602,x5605))
% 22.40/22.32 [561]~E(x5611,x5612)+E(f713(x5613,x5614,x5615,x5611),f713(x5613,x5614,x5615,x5612))
% 22.40/22.32 [562]~E(x5621,x5622)+E(f208(x5621,x5623),f208(x5622,x5623))
% 22.40/22.32 [563]~E(x5631,x5632)+E(f208(x5633,x5631),f208(x5633,x5632))
% 22.40/22.32 [564]~E(x5641,x5642)+E(f117(x5641,x5643),f117(x5642,x5643))
% 22.40/22.32 [565]~E(x5651,x5652)+E(f117(x5653,x5651),f117(x5653,x5652))
% 22.40/22.32 [566]~E(x5661,x5662)+E(f16(x5661,x5663),f16(x5662,x5663))
% 22.40/22.32 [567]~E(x5671,x5672)+E(f16(x5673,x5671),f16(x5673,x5672))
% 22.40/22.32 [568]~E(x5681,x5682)+E(f510(x5681),f510(x5682))
% 22.40/22.32 [569]~E(x5691,x5692)+E(f372(x5691,x5693),f372(x5692,x5693))
% 22.40/22.32 [570]~E(x5701,x5702)+E(f372(x5703,x5701),f372(x5703,x5702))
% 22.40/22.32 [571]~E(x5711,x5712)+E(f674(x5711,x5713,x5714,x5715,x5716),f674(x5712,x5713,x5714,x5715,x5716))
% 22.40/22.32 [572]~E(x5721,x5722)+E(f674(x5723,x5721,x5724,x5725,x5726),f674(x5723,x5722,x5724,x5725,x5726))
% 22.40/22.32 [573]~E(x5731,x5732)+E(f674(x5733,x5734,x5731,x5735,x5736),f674(x5733,x5734,x5732,x5735,x5736))
% 22.40/22.32 [574]~E(x5741,x5742)+E(f674(x5743,x5744,x5745,x5741,x5746),f674(x5743,x5744,x5745,x5742,x5746))
% 22.40/22.32 [575]~E(x5751,x5752)+E(f674(x5753,x5754,x5755,x5756,x5751),f674(x5753,x5754,x5755,x5756,x5752))
% 22.40/22.32 [576]~E(x5761,x5762)+E(f456(x5761,x5763,x5764,x5765),f456(x5762,x5763,x5764,x5765))
% 22.40/22.32 [577]~E(x5771,x5772)+E(f456(x5773,x5771,x5774,x5775),f456(x5773,x5772,x5774,x5775))
% 22.40/22.32 [578]~E(x5781,x5782)+E(f456(x5783,x5784,x5781,x5785),f456(x5783,x5784,x5782,x5785))
% 22.40/22.32 [579]~E(x5791,x5792)+E(f456(x5793,x5794,x5795,x5791),f456(x5793,x5794,x5795,x5792))
% 22.40/22.32 [580]~E(x5801,x5802)+E(f535(x5801,x5803,x5804),f535(x5802,x5803,x5804))
% 22.40/22.32 [581]~E(x5811,x5812)+E(f535(x5813,x5811,x5814),f535(x5813,x5812,x5814))
% 22.40/22.32 [582]~E(x5821,x5822)+E(f535(x5823,x5824,x5821),f535(x5823,x5824,x5822))
% 22.40/22.32 [583]~E(x5831,x5832)+E(f60(x5831,x5833,x5834,x5835,x5836),f60(x5832,x5833,x5834,x5835,x5836))
% 22.40/22.32 [584]~E(x5841,x5842)+E(f60(x5843,x5841,x5844,x5845,x5846),f60(x5843,x5842,x5844,x5845,x5846))
% 22.40/22.32 [585]~E(x5851,x5852)+E(f60(x5853,x5854,x5851,x5855,x5856),f60(x5853,x5854,x5852,x5855,x5856))
% 22.40/22.32 [586]~E(x5861,x5862)+E(f60(x5863,x5864,x5865,x5861,x5866),f60(x5863,x5864,x5865,x5862,x5866))
% 22.40/22.32 [587]~E(x5871,x5872)+E(f60(x5873,x5874,x5875,x5876,x5871),f60(x5873,x5874,x5875,x5876,x5872))
% 22.40/22.32 [588]~E(x5881,x5882)+E(f191(x5881,x5883,x5884,x5885),f191(x5882,x5883,x5884,x5885))
% 22.40/22.32 [589]~E(x5891,x5892)+E(f191(x5893,x5891,x5894,x5895),f191(x5893,x5892,x5894,x5895))
% 22.40/22.32 [590]~E(x5901,x5902)+E(f191(x5903,x5904,x5901,x5905),f191(x5903,x5904,x5902,x5905))
% 22.40/22.32 [591]~E(x5911,x5912)+E(f191(x5913,x5914,x5915,x5911),f191(x5913,x5914,x5915,x5912))
% 22.40/22.32 [592]~E(x5921,x5922)+E(f577(x5921,x5923),f577(x5922,x5923))
% 22.40/22.32 [593]~E(x5931,x5932)+E(f577(x5933,x5931),f577(x5933,x5932))
% 22.40/22.32 [594]~E(x5941,x5942)+E(f281(x5941,x5943,x5944),f281(x5942,x5943,x5944))
% 22.40/22.32 [595]~E(x5951,x5952)+E(f281(x5953,x5951,x5954),f281(x5953,x5952,x5954))
% 22.40/22.32 [596]~E(x5961,x5962)+E(f281(x5963,x5964,x5961),f281(x5963,x5964,x5962))
% 22.40/22.32 [597]~E(x5971,x5972)+E(f415(x5971,x5973,x5974,x5975),f415(x5972,x5973,x5974,x5975))
% 22.40/22.32 [598]~E(x5981,x5982)+E(f415(x5983,x5981,x5984,x5985),f415(x5983,x5982,x5984,x5985))
% 22.40/22.32 [599]~E(x5991,x5992)+E(f415(x5993,x5994,x5991,x5995),f415(x5993,x5994,x5992,x5995))
% 22.40/22.32 [600]~E(x6001,x6002)+E(f415(x6003,x6004,x6005,x6001),f415(x6003,x6004,x6005,x6002))
% 22.40/22.32 [601]~E(x6011,x6012)+E(f821(x6011,x6013,x6014,x6015),f821(x6012,x6013,x6014,x6015))
% 22.40/22.32 [602]~E(x6021,x6022)+E(f821(x6023,x6021,x6024,x6025),f821(x6023,x6022,x6024,x6025))
% 22.40/22.32 [603]~E(x6031,x6032)+E(f821(x6033,x6034,x6031,x6035),f821(x6033,x6034,x6032,x6035))
% 22.40/22.32 [604]~E(x6041,x6042)+E(f821(x6043,x6044,x6045,x6041),f821(x6043,x6044,x6045,x6042))
% 22.40/22.32 [605]~E(x6051,x6052)+E(f128(x6051,x6053),f128(x6052,x6053))
% 22.40/22.32 [606]~E(x6061,x6062)+E(f128(x6063,x6061),f128(x6063,x6062))
% 22.40/22.32 [607]~E(x6071,x6072)+E(f245(x6071,x6073,x6074,x6075,x6076),f245(x6072,x6073,x6074,x6075,x6076))
% 22.40/22.32 [608]~E(x6081,x6082)+E(f245(x6083,x6081,x6084,x6085,x6086),f245(x6083,x6082,x6084,x6085,x6086))
% 22.40/22.32 [609]~E(x6091,x6092)+E(f245(x6093,x6094,x6091,x6095,x6096),f245(x6093,x6094,x6092,x6095,x6096))
% 22.40/22.32 [610]~E(x6101,x6102)+E(f245(x6103,x6104,x6105,x6101,x6106),f245(x6103,x6104,x6105,x6102,x6106))
% 22.40/22.32 [611]~E(x6111,x6112)+E(f245(x6113,x6114,x6115,x6116,x6111),f245(x6113,x6114,x6115,x6116,x6112))
% 22.40/22.32 [612]~E(x6121,x6122)+E(f141(x6121,x6123,x6124,x6125,x6126),f141(x6122,x6123,x6124,x6125,x6126))
% 22.40/22.32 [613]~E(x6131,x6132)+E(f141(x6133,x6131,x6134,x6135,x6136),f141(x6133,x6132,x6134,x6135,x6136))
% 22.40/22.32 [614]~E(x6141,x6142)+E(f141(x6143,x6144,x6141,x6145,x6146),f141(x6143,x6144,x6142,x6145,x6146))
% 22.40/22.32 [615]~E(x6151,x6152)+E(f141(x6153,x6154,x6155,x6151,x6156),f141(x6153,x6154,x6155,x6152,x6156))
% 22.40/22.32 [616]~E(x6161,x6162)+E(f141(x6163,x6164,x6165,x6166,x6161),f141(x6163,x6164,x6165,x6166,x6162))
% 22.40/22.32 [617]~E(x6171,x6172)+E(f303(x6171,x6173,x6174),f303(x6172,x6173,x6174))
% 22.40/22.32 [618]~E(x6181,x6182)+E(f303(x6183,x6181,x6184),f303(x6183,x6182,x6184))
% 22.40/22.32 [619]~E(x6191,x6192)+E(f303(x6193,x6194,x6191),f303(x6193,x6194,x6192))
% 22.40/22.32 [620]~E(x6201,x6202)+E(f690(x6201,x6203,x6204,x6205,x6206),f690(x6202,x6203,x6204,x6205,x6206))
% 22.40/22.32 [621]~E(x6211,x6212)+E(f690(x6213,x6211,x6214,x6215,x6216),f690(x6213,x6212,x6214,x6215,x6216))
% 22.40/22.32 [622]~E(x6221,x6222)+E(f690(x6223,x6224,x6221,x6225,x6226),f690(x6223,x6224,x6222,x6225,x6226))
% 22.40/22.32 [623]~E(x6231,x6232)+E(f690(x6233,x6234,x6235,x6231,x6236),f690(x6233,x6234,x6235,x6232,x6236))
% 22.40/22.32 [624]~E(x6241,x6242)+E(f690(x6243,x6244,x6245,x6246,x6241),f690(x6243,x6244,x6245,x6246,x6242))
% 22.40/22.32 [625]~E(x6251,x6252)+E(f262(x6251,x6253),f262(x6252,x6253))
% 22.40/22.32 [626]~E(x6261,x6262)+E(f262(x6263,x6261),f262(x6263,x6262))
% 22.40/22.32 [627]~E(x6271,x6272)+E(f387(x6271,x6273,x6274),f387(x6272,x6273,x6274))
% 22.40/22.32 [628]~E(x6281,x6282)+E(f387(x6283,x6281,x6284),f387(x6283,x6282,x6284))
% 22.40/22.32 [629]~E(x6291,x6292)+E(f387(x6293,x6294,x6291),f387(x6293,x6294,x6292))
% 22.40/22.32 [630]~E(x6301,x6302)+E(f412(x6301,x6303,x6304,x6305),f412(x6302,x6303,x6304,x6305))
% 22.40/22.32 [631]~E(x6311,x6312)+E(f412(x6313,x6311,x6314,x6315),f412(x6313,x6312,x6314,x6315))
% 22.40/22.32 [632]~E(x6321,x6322)+E(f412(x6323,x6324,x6321,x6325),f412(x6323,x6324,x6322,x6325))
% 22.40/22.32 [633]~E(x6331,x6332)+E(f412(x6333,x6334,x6335,x6331),f412(x6333,x6334,x6335,x6332))
% 22.40/22.32 [634]~E(x6341,x6342)+E(f455(x6341,x6343,x6344),f455(x6342,x6343,x6344))
% 22.40/22.32 [635]~E(x6351,x6352)+E(f455(x6353,x6351,x6354),f455(x6353,x6352,x6354))
% 22.40/22.32 [636]~E(x6361,x6362)+E(f455(x6363,x6364,x6361),f455(x6363,x6364,x6362))
% 22.40/22.32 [637]~E(x6371,x6372)+E(f161(x6371,x6373,x6374),f161(x6372,x6373,x6374))
% 22.40/22.32 [638]~E(x6381,x6382)+E(f161(x6383,x6381,x6384),f161(x6383,x6382,x6384))
% 22.40/22.32 [639]~E(x6391,x6392)+E(f161(x6393,x6394,x6391),f161(x6393,x6394,x6392))
% 22.40/22.32 [640]~E(x6401,x6402)+E(f895(x6401,x6403,x6404,x6405),f895(x6402,x6403,x6404,x6405))
% 22.40/22.32 [641]~E(x6411,x6412)+E(f895(x6413,x6411,x6414,x6415),f895(x6413,x6412,x6414,x6415))
% 22.40/22.32 [642]~E(x6421,x6422)+E(f895(x6423,x6424,x6421,x6425),f895(x6423,x6424,x6422,x6425))
% 22.40/22.32 [643]~E(x6431,x6432)+E(f895(x6433,x6434,x6435,x6431),f895(x6433,x6434,x6435,x6432))
% 22.40/22.32 [644]~E(x6441,x6442)+E(f657(x6441,x6443),f657(x6442,x6443))
% 22.40/22.32 [645]~E(x6451,x6452)+E(f657(x6453,x6451),f657(x6453,x6452))
% 22.40/22.32 [646]~E(x6461,x6462)+E(f804(x6461,x6463,x6464,x6465,x6466,x6467),f804(x6462,x6463,x6464,x6465,x6466,x6467))
% 22.40/22.32 [647]~E(x6471,x6472)+E(f804(x6473,x6471,x6474,x6475,x6476,x6477),f804(x6473,x6472,x6474,x6475,x6476,x6477))
% 22.40/22.32 [648]~E(x6481,x6482)+E(f804(x6483,x6484,x6481,x6485,x6486,x6487),f804(x6483,x6484,x6482,x6485,x6486,x6487))
% 22.40/22.32 [649]~E(x6491,x6492)+E(f804(x6493,x6494,x6495,x6491,x6496,x6497),f804(x6493,x6494,x6495,x6492,x6496,x6497))
% 22.40/22.32 [650]~E(x6501,x6502)+E(f804(x6503,x6504,x6505,x6506,x6501,x6507),f804(x6503,x6504,x6505,x6506,x6502,x6507))
% 22.40/22.32 [651]~E(x6511,x6512)+E(f804(x6513,x6514,x6515,x6516,x6517,x6511),f804(x6513,x6514,x6515,x6516,x6517,x6512))
% 22.40/22.32 [652]~E(x6521,x6522)+E(f464(x6521,x6523,x6524,x6525),f464(x6522,x6523,x6524,x6525))
% 22.40/22.32 [653]~E(x6531,x6532)+E(f464(x6533,x6531,x6534,x6535),f464(x6533,x6532,x6534,x6535))
% 22.40/22.32 [654]~E(x6541,x6542)+E(f464(x6543,x6544,x6541,x6545),f464(x6543,x6544,x6542,x6545))
% 22.40/22.32 [655]~E(x6551,x6552)+E(f464(x6553,x6554,x6555,x6551),f464(x6553,x6554,x6555,x6552))
% 22.40/22.32 [656]~E(x6561,x6562)+E(f461(x6561,x6563,x6564,x6565),f461(x6562,x6563,x6564,x6565))
% 22.40/22.32 [657]~E(x6571,x6572)+E(f461(x6573,x6571,x6574,x6575),f461(x6573,x6572,x6574,x6575))
% 22.40/22.32 [658]~E(x6581,x6582)+E(f461(x6583,x6584,x6581,x6585),f461(x6583,x6584,x6582,x6585))
% 22.40/22.32 [659]~E(x6591,x6592)+E(f461(x6593,x6594,x6595,x6591),f461(x6593,x6594,x6595,x6592))
% 22.40/22.32 [660]~E(x6601,x6602)+E(f643(x6601,x6603,x6604,x6605,x6606),f643(x6602,x6603,x6604,x6605,x6606))
% 22.40/22.32 [661]~E(x6611,x6612)+E(f643(x6613,x6611,x6614,x6615,x6616),f643(x6613,x6612,x6614,x6615,x6616))
% 22.40/22.32 [662]~E(x6621,x6622)+E(f643(x6623,x6624,x6621,x6625,x6626),f643(x6623,x6624,x6622,x6625,x6626))
% 22.40/22.32 [663]~E(x6631,x6632)+E(f643(x6633,x6634,x6635,x6631,x6636),f643(x6633,x6634,x6635,x6632,x6636))
% 22.40/22.32 [664]~E(x6641,x6642)+E(f643(x6643,x6644,x6645,x6646,x6641),f643(x6643,x6644,x6645,x6646,x6642))
% 22.40/22.32 [665]~E(x6651,x6652)+E(f506(x6651,x6653,x6654,x6655,x6656,x6657),f506(x6652,x6653,x6654,x6655,x6656,x6657))
% 22.40/22.32 [666]~E(x6661,x6662)+E(f506(x6663,x6661,x6664,x6665,x6666,x6667),f506(x6663,x6662,x6664,x6665,x6666,x6667))
% 22.40/22.32 [667]~E(x6671,x6672)+E(f506(x6673,x6674,x6671,x6675,x6676,x6677),f506(x6673,x6674,x6672,x6675,x6676,x6677))
% 22.40/22.32 [668]~E(x6681,x6682)+E(f506(x6683,x6684,x6685,x6681,x6686,x6687),f506(x6683,x6684,x6685,x6682,x6686,x6687))
% 22.40/22.32 [669]~E(x6691,x6692)+E(f506(x6693,x6694,x6695,x6696,x6691,x6697),f506(x6693,x6694,x6695,x6696,x6692,x6697))
% 22.40/22.32 [670]~E(x6701,x6702)+E(f506(x6703,x6704,x6705,x6706,x6707,x6701),f506(x6703,x6704,x6705,x6706,x6707,x6702))
% 22.40/22.32 [671]~E(x6711,x6712)+E(f637(x6711,x6713,x6714),f637(x6712,x6713,x6714))
% 22.40/22.32 [672]~E(x6721,x6722)+E(f637(x6723,x6721,x6724),f637(x6723,x6722,x6724))
% 22.40/22.32 [673]~E(x6731,x6732)+E(f637(x6733,x6734,x6731),f637(x6733,x6734,x6732))
% 22.40/22.32 [674]~E(x6741,x6742)+E(f773(x6741),f773(x6742))
% 22.40/22.32 [675]~E(x6751,x6752)+E(f731(x6751,x6753,x6754,x6755),f731(x6752,x6753,x6754,x6755))
% 22.40/22.32 [676]~E(x6761,x6762)+E(f731(x6763,x6761,x6764,x6765),f731(x6763,x6762,x6764,x6765))
% 22.40/22.32 [677]~E(x6771,x6772)+E(f731(x6773,x6774,x6771,x6775),f731(x6773,x6774,x6772,x6775))
% 22.40/22.32 [678]~E(x6781,x6782)+E(f731(x6783,x6784,x6785,x6781),f731(x6783,x6784,x6785,x6782))
% 22.40/22.32 [679]~E(x6791,x6792)+E(f260(x6791,x6793),f260(x6792,x6793))
% 22.40/22.32 [680]~E(x6801,x6802)+E(f260(x6803,x6801),f260(x6803,x6802))
% 22.40/22.32 [681]~E(x6811,x6812)+E(f869(x6811,x6813,x6814,x6815),f869(x6812,x6813,x6814,x6815))
% 22.40/22.32 [682]~E(x6821,x6822)+E(f869(x6823,x6821,x6824,x6825),f869(x6823,x6822,x6824,x6825))
% 22.40/22.32 [683]~E(x6831,x6832)+E(f869(x6833,x6834,x6831,x6835),f869(x6833,x6834,x6832,x6835))
% 22.40/22.32 [684]~E(x6841,x6842)+E(f869(x6843,x6844,x6845,x6841),f869(x6843,x6844,x6845,x6842))
% 22.40/22.32 [685]~E(x6851,x6852)+E(f698(x6851,x6853),f698(x6852,x6853))
% 22.40/22.32 [686]~E(x6861,x6862)+E(f698(x6863,x6861),f698(x6863,x6862))
% 22.40/22.32 [687]~E(x6871,x6872)+E(f581(x6871,x6873,x6874),f581(x6872,x6873,x6874))
% 22.40/22.32 [688]~E(x6881,x6882)+E(f581(x6883,x6881,x6884),f581(x6883,x6882,x6884))
% 22.40/22.32 [689]~E(x6891,x6892)+E(f581(x6893,x6894,x6891),f581(x6893,x6894,x6892))
% 22.40/22.32 [690]~E(x6901,x6902)+E(f367(x6901,x6903,x6904,x6905,x6906),f367(x6902,x6903,x6904,x6905,x6906))
% 22.40/22.32 [691]~E(x6911,x6912)+E(f367(x6913,x6911,x6914,x6915,x6916),f367(x6913,x6912,x6914,x6915,x6916))
% 22.40/22.32 [692]~E(x6921,x6922)+E(f367(x6923,x6924,x6921,x6925,x6926),f367(x6923,x6924,x6922,x6925,x6926))
% 22.40/22.32 [693]~E(x6931,x6932)+E(f367(x6933,x6934,x6935,x6931,x6936),f367(x6933,x6934,x6935,x6932,x6936))
% 22.40/22.32 [694]~E(x6941,x6942)+E(f367(x6943,x6944,x6945,x6946,x6941),f367(x6943,x6944,x6945,x6946,x6942))
% 22.40/22.32 [695]~E(x6951,x6952)+E(f150(x6951,x6953),f150(x6952,x6953))
% 22.40/22.32 [696]~E(x6961,x6962)+E(f150(x6963,x6961),f150(x6963,x6962))
% 22.40/22.32 [697]~E(x6971,x6972)+E(f873(x6971,x6973,x6974,x6975,x6976),f873(x6972,x6973,x6974,x6975,x6976))
% 22.40/22.32 [698]~E(x6981,x6982)+E(f873(x6983,x6981,x6984,x6985,x6986),f873(x6983,x6982,x6984,x6985,x6986))
% 22.40/22.32 [699]~E(x6991,x6992)+E(f873(x6993,x6994,x6991,x6995,x6996),f873(x6993,x6994,x6992,x6995,x6996))
% 22.40/22.32 [700]~E(x7001,x7002)+E(f873(x7003,x7004,x7005,x7001,x7006),f873(x7003,x7004,x7005,x7002,x7006))
% 22.40/22.32 [701]~E(x7011,x7012)+E(f873(x7013,x7014,x7015,x7016,x7011),f873(x7013,x7014,x7015,x7016,x7012))
% 22.40/22.32 [702]~E(x7021,x7022)+E(f553(x7021,x7023,x7024,x7025,x7026,x7027),f553(x7022,x7023,x7024,x7025,x7026,x7027))
% 22.40/22.32 [703]~E(x7031,x7032)+E(f553(x7033,x7031,x7034,x7035,x7036,x7037),f553(x7033,x7032,x7034,x7035,x7036,x7037))
% 22.40/22.32 [704]~E(x7041,x7042)+E(f553(x7043,x7044,x7041,x7045,x7046,x7047),f553(x7043,x7044,x7042,x7045,x7046,x7047))
% 22.40/22.32 [705]~E(x7051,x7052)+E(f553(x7053,x7054,x7055,x7051,x7056,x7057),f553(x7053,x7054,x7055,x7052,x7056,x7057))
% 22.40/22.32 [706]~E(x7061,x7062)+E(f553(x7063,x7064,x7065,x7066,x7061,x7067),f553(x7063,x7064,x7065,x7066,x7062,x7067))
% 22.40/22.32 [707]~E(x7071,x7072)+E(f553(x7073,x7074,x7075,x7076,x7077,x7071),f553(x7073,x7074,x7075,x7076,x7077,x7072))
% 22.40/22.32 [708]~E(x7081,x7082)+E(f269(x7081,x7083,x7084,x7085),f269(x7082,x7083,x7084,x7085))
% 22.40/22.32 [709]~E(x7091,x7092)+E(f269(x7093,x7091,x7094,x7095),f269(x7093,x7092,x7094,x7095))
% 22.40/22.32 [710]~E(x7101,x7102)+E(f269(x7103,x7104,x7101,x7105),f269(x7103,x7104,x7102,x7105))
% 22.40/22.32 [711]~E(x7111,x7112)+E(f269(x7113,x7114,x7115,x7111),f269(x7113,x7114,x7115,x7112))
% 22.40/22.32 [712]~E(x7121,x7122)+E(f375(x7121,x7123,x7124,x7125),f375(x7122,x7123,x7124,x7125))
% 22.40/22.32 [713]~E(x7131,x7132)+E(f375(x7133,x7131,x7134,x7135),f375(x7133,x7132,x7134,x7135))
% 22.40/22.32 [714]~E(x7141,x7142)+E(f375(x7143,x7144,x7141,x7145),f375(x7143,x7144,x7142,x7145))
% 22.40/22.32 [715]~E(x7151,x7152)+E(f375(x7153,x7154,x7155,x7151),f375(x7153,x7154,x7155,x7152))
% 22.40/22.32 [716]~E(x7161,x7162)+E(f235(x7161,x7163,x7164),f235(x7162,x7163,x7164))
% 22.40/22.32 [717]~E(x7171,x7172)+E(f235(x7173,x7171,x7174),f235(x7173,x7172,x7174))
% 22.40/22.32 [718]~E(x7181,x7182)+E(f235(x7183,x7184,x7181),f235(x7183,x7184,x7182))
% 22.40/22.32 [719]~E(x7191,x7192)+E(f490(x7191,x7193,x7194),f490(x7192,x7193,x7194))
% 22.40/22.32 [720]~E(x7201,x7202)+E(f490(x7203,x7201,x7204),f490(x7203,x7202,x7204))
% 22.40/22.32 [721]~E(x7211,x7212)+E(f490(x7213,x7214,x7211),f490(x7213,x7214,x7212))
% 22.40/22.32 [722]~E(x7221,x7222)+E(f859(x7221,x7223,x7224),f859(x7222,x7223,x7224))
% 22.40/22.32 [723]~E(x7231,x7232)+E(f859(x7233,x7231,x7234),f859(x7233,x7232,x7234))
% 22.40/22.32 [724]~E(x7241,x7242)+E(f859(x7243,x7244,x7241),f859(x7243,x7244,x7242))
% 22.40/22.32 [725]~E(x7251,x7252)+E(f844(x7251,x7253,x7254,x7255,x7256,x7257),f844(x7252,x7253,x7254,x7255,x7256,x7257))
% 22.40/22.32 [726]~E(x7261,x7262)+E(f844(x7263,x7261,x7264,x7265,x7266,x7267),f844(x7263,x7262,x7264,x7265,x7266,x7267))
% 22.40/22.32 [727]~E(x7271,x7272)+E(f844(x7273,x7274,x7271,x7275,x7276,x7277),f844(x7273,x7274,x7272,x7275,x7276,x7277))
% 22.40/22.32 [728]~E(x7281,x7282)+E(f844(x7283,x7284,x7285,x7281,x7286,x7287),f844(x7283,x7284,x7285,x7282,x7286,x7287))
% 22.40/22.32 [729]~E(x7291,x7292)+E(f844(x7293,x7294,x7295,x7296,x7291,x7297),f844(x7293,x7294,x7295,x7296,x7292,x7297))
% 22.40/22.32 [730]~E(x7301,x7302)+E(f844(x7303,x7304,x7305,x7306,x7307,x7301),f844(x7303,x7304,x7305,x7306,x7307,x7302))
% 22.40/22.32 [731]~E(x7311,x7312)+E(f796(x7311),f796(x7312))
% 22.40/22.32 [732]~E(x7321,x7322)+E(f293(x7321),f293(x7322))
% 22.40/22.32 [733]~E(x7331,x7332)+E(f539(x7331,x7333,x7334,x7335,x7336),f539(x7332,x7333,x7334,x7335,x7336))
% 22.40/22.32 [734]~E(x7341,x7342)+E(f539(x7343,x7341,x7344,x7345,x7346),f539(x7343,x7342,x7344,x7345,x7346))
% 22.40/22.32 [735]~E(x7351,x7352)+E(f539(x7353,x7354,x7351,x7355,x7356),f539(x7353,x7354,x7352,x7355,x7356))
% 22.40/22.32 [736]~E(x7361,x7362)+E(f539(x7363,x7364,x7365,x7361,x7366),f539(x7363,x7364,x7365,x7362,x7366))
% 22.40/22.32 [737]~E(x7371,x7372)+E(f539(x7373,x7374,x7375,x7376,x7371),f539(x7373,x7374,x7375,x7376,x7372))
% 22.40/22.32 [738]~E(x7381,x7382)+E(f137(x7381,x7383),f137(x7382,x7383))
% 22.40/22.32 [739]~E(x7391,x7392)+E(f137(x7393,x7391),f137(x7393,x7392))
% 22.40/22.32 [740]~E(x7401,x7402)+E(f806(x7401,x7403,x7404,x7405,x7406,x7407),f806(x7402,x7403,x7404,x7405,x7406,x7407))
% 22.40/22.32 [741]~E(x7411,x7412)+E(f806(x7413,x7411,x7414,x7415,x7416,x7417),f806(x7413,x7412,x7414,x7415,x7416,x7417))
% 22.40/22.32 [742]~E(x7421,x7422)+E(f806(x7423,x7424,x7421,x7425,x7426,x7427),f806(x7423,x7424,x7422,x7425,x7426,x7427))
% 22.40/22.32 [743]~E(x7431,x7432)+E(f806(x7433,x7434,x7435,x7431,x7436,x7437),f806(x7433,x7434,x7435,x7432,x7436,x7437))
% 22.40/22.32 [744]~E(x7441,x7442)+E(f806(x7443,x7444,x7445,x7446,x7441,x7447),f806(x7443,x7444,x7445,x7446,x7442,x7447))
% 22.40/22.32 [745]~E(x7451,x7452)+E(f806(x7453,x7454,x7455,x7456,x7457,x7451),f806(x7453,x7454,x7455,x7456,x7457,x7452))
% 22.40/22.32 [746]~E(x7461,x7462)+E(f892(x7461,x7463,x7464),f892(x7462,x7463,x7464))
% 22.40/22.32 [747]~E(x7471,x7472)+E(f892(x7473,x7471,x7474),f892(x7473,x7472,x7474))
% 22.40/22.32 [748]~E(x7481,x7482)+E(f892(x7483,x7484,x7481),f892(x7483,x7484,x7482))
% 22.40/22.32 [749]~E(x7491,x7492)+E(f32(x7491,x7493),f32(x7492,x7493))
% 22.40/22.32 [750]~E(x7501,x7502)+E(f32(x7503,x7501),f32(x7503,x7502))
% 22.40/22.32 [751]~E(x7511,x7512)+E(f593(x7511,x7513),f593(x7512,x7513))
% 22.40/22.32 [752]~E(x7521,x7522)+E(f593(x7523,x7521),f593(x7523,x7522))
% 22.40/22.32 [753]~E(x7531,x7532)+E(f436(x7531,x7533,x7534),f436(x7532,x7533,x7534))
% 22.40/22.32 [754]~E(x7541,x7542)+E(f436(x7543,x7541,x7544),f436(x7543,x7542,x7544))
% 22.40/22.32 [755]~E(x7551,x7552)+E(f436(x7553,x7554,x7551),f436(x7553,x7554,x7552))
% 22.40/22.32 [756]~E(x7561,x7562)+E(f518(x7561,x7563,x7564,x7565,x7566,x7567,x7568),f518(x7562,x7563,x7564,x7565,x7566,x7567,x7568))
% 22.40/22.32 [757]~E(x7571,x7572)+E(f518(x7573,x7571,x7574,x7575,x7576,x7577,x7578),f518(x7573,x7572,x7574,x7575,x7576,x7577,x7578))
% 22.40/22.32 [758]~E(x7581,x7582)+E(f518(x7583,x7584,x7581,x7585,x7586,x7587,x7588),f518(x7583,x7584,x7582,x7585,x7586,x7587,x7588))
% 22.40/22.32 [759]~E(x7591,x7592)+E(f518(x7593,x7594,x7595,x7591,x7596,x7597,x7598),f518(x7593,x7594,x7595,x7592,x7596,x7597,x7598))
% 22.40/22.32 [760]~E(x7601,x7602)+E(f518(x7603,x7604,x7605,x7606,x7601,x7607,x7608),f518(x7603,x7604,x7605,x7606,x7602,x7607,x7608))
% 22.40/22.32 [761]~E(x7611,x7612)+E(f518(x7613,x7614,x7615,x7616,x7617,x7611,x7618),f518(x7613,x7614,x7615,x7616,x7617,x7612,x7618))
% 22.40/22.32 [762]~E(x7621,x7622)+E(f518(x7623,x7624,x7625,x7626,x7627,x7628,x7621),f518(x7623,x7624,x7625,x7626,x7627,x7628,x7622))
% 22.40/22.32 [763]~E(x7631,x7632)+E(f400(x7631,x7633),f400(x7632,x7633))
% 22.40/22.32 [764]~E(x7641,x7642)+E(f400(x7643,x7641),f400(x7643,x7642))
% 22.40/22.32 [765]~E(x7651,x7652)+E(f454(x7651,x7653,x7654),f454(x7652,x7653,x7654))
% 22.40/22.32 [766]~E(x7661,x7662)+E(f454(x7663,x7661,x7664),f454(x7663,x7662,x7664))
% 22.40/22.32 [767]~E(x7671,x7672)+E(f454(x7673,x7674,x7671),f454(x7673,x7674,x7672))
% 22.40/22.32 [768]~E(x7681,x7682)+E(f197(x7681),f197(x7682))
% 22.40/22.32 [769]~E(x7691,x7692)+E(f211(x7691,x7693),f211(x7692,x7693))
% 22.40/22.32 [770]~E(x7701,x7702)+E(f211(x7703,x7701),f211(x7703,x7702))
% 22.40/22.32 [771]~E(x7711,x7712)+E(f44(x7711,x7713),f44(x7712,x7713))
% 22.40/22.32 [772]~E(x7721,x7722)+E(f44(x7723,x7721),f44(x7723,x7722))
% 22.40/22.32 [773]~E(x7731,x7732)+E(f688(x7731,x7733,x7734),f688(x7732,x7733,x7734))
% 22.40/22.32 [774]~E(x7741,x7742)+E(f688(x7743,x7741,x7744),f688(x7743,x7742,x7744))
% 22.40/22.32 [775]~E(x7751,x7752)+E(f688(x7753,x7754,x7751),f688(x7753,x7754,x7752))
% 22.40/22.32 [776]~E(x7761,x7762)+E(f352(x7761),f352(x7762))
% 22.40/22.32 [777]~E(x7771,x7772)+E(f857(x7771,x7773,x7774),f857(x7772,x7773,x7774))
% 22.40/22.32 [778]~E(x7781,x7782)+E(f857(x7783,x7781,x7784),f857(x7783,x7782,x7784))
% 22.40/22.32 [779]~E(x7791,x7792)+E(f857(x7793,x7794,x7791),f857(x7793,x7794,x7792))
% 22.40/22.32 [780]~E(x7801,x7802)+E(f177(x7801,x7803,x7804,x7805),f177(x7802,x7803,x7804,x7805))
% 22.40/22.32 [781]~E(x7811,x7812)+E(f177(x7813,x7811,x7814,x7815),f177(x7813,x7812,x7814,x7815))
% 22.40/22.32 [782]~E(x7821,x7822)+E(f177(x7823,x7824,x7821,x7825),f177(x7823,x7824,x7822,x7825))
% 22.40/22.32 [783]~E(x7831,x7832)+E(f177(x7833,x7834,x7835,x7831),f177(x7833,x7834,x7835,x7832))
% 22.40/22.32 [784]~E(x7841,x7842)+E(f870(x7841,x7843,x7844,x7845),f870(x7842,x7843,x7844,x7845))
% 22.40/22.32 [785]~E(x7851,x7852)+E(f870(x7853,x7851,x7854,x7855),f870(x7853,x7852,x7854,x7855))
% 22.40/22.32 [786]~E(x7861,x7862)+E(f870(x7863,x7864,x7861,x7865),f870(x7863,x7864,x7862,x7865))
% 22.40/22.32 [787]~E(x7871,x7872)+E(f870(x7873,x7874,x7875,x7871),f870(x7873,x7874,x7875,x7872))
% 22.40/22.32 [788]~E(x7881,x7882)+E(f579(x7881,x7883,x7884),f579(x7882,x7883,x7884))
% 22.40/22.32 [789]~E(x7891,x7892)+E(f579(x7893,x7891,x7894),f579(x7893,x7892,x7894))
% 22.40/22.32 [790]~E(x7901,x7902)+E(f579(x7903,x7904,x7901),f579(x7903,x7904,x7902))
% 22.40/22.32 [791]~E(x7911,x7912)+E(f37(x7911),f37(x7912))
% 22.40/22.32 [792]~E(x7921,x7922)+E(f658(x7921,x7923),f658(x7922,x7923))
% 22.40/22.32 [793]~E(x7931,x7932)+E(f658(x7933,x7931),f658(x7933,x7932))
% 22.40/22.32 [794]~E(x7941,x7942)+E(f872(x7941,x7943,x7944,x7945,x7946),f872(x7942,x7943,x7944,x7945,x7946))
% 22.40/22.32 [795]~E(x7951,x7952)+E(f872(x7953,x7951,x7954,x7955,x7956),f872(x7953,x7952,x7954,x7955,x7956))
% 22.40/22.32 [796]~E(x7961,x7962)+E(f872(x7963,x7964,x7961,x7965,x7966),f872(x7963,x7964,x7962,x7965,x7966))
% 22.40/22.32 [797]~E(x7971,x7972)+E(f872(x7973,x7974,x7975,x7971,x7976),f872(x7973,x7974,x7975,x7972,x7976))
% 22.40/22.32 [798]~E(x7981,x7982)+E(f872(x7983,x7984,x7985,x7986,x7981),f872(x7983,x7984,x7985,x7986,x7982))
% 22.40/22.32 [799]~E(x7991,x7992)+E(f298(x7991,x7993,x7994),f298(x7992,x7993,x7994))
% 22.40/22.32 [800]~E(x8001,x8002)+E(f298(x8003,x8001,x8004),f298(x8003,x8002,x8004))
% 22.40/22.32 [801]~E(x8011,x8012)+E(f298(x8013,x8014,x8011),f298(x8013,x8014,x8012))
% 22.40/22.32 [802]~E(x8021,x8022)+E(f711(x8021,x8023),f711(x8022,x8023))
% 22.40/22.32 [803]~E(x8031,x8032)+E(f711(x8033,x8031),f711(x8033,x8032))
% 22.40/22.32 [804]~E(x8041,x8042)+E(f717(x8041,x8043),f717(x8042,x8043))
% 22.40/22.32 [805]~E(x8051,x8052)+E(f717(x8053,x8051),f717(x8053,x8052))
% 22.40/22.32 [806]~E(x8061,x8062)+E(f878(x8061,x8063,x8064),f878(x8062,x8063,x8064))
% 22.40/22.32 [807]~E(x8071,x8072)+E(f878(x8073,x8071,x8074),f878(x8073,x8072,x8074))
% 22.40/22.32 [808]~E(x8081,x8082)+E(f878(x8083,x8084,x8081),f878(x8083,x8084,x8082))
% 22.40/22.32 [809]~E(x8091,x8092)+E(f147(x8091,x8093,x8094),f147(x8092,x8093,x8094))
% 22.40/22.32 [810]~E(x8101,x8102)+E(f147(x8103,x8101,x8104),f147(x8103,x8102,x8104))
% 22.40/22.32 [811]~E(x8111,x8112)+E(f147(x8113,x8114,x8111),f147(x8113,x8114,x8112))
% 22.40/22.32 [812]~E(x8121,x8122)+E(f842(x8121,x8123,x8124,x8125,x8126,x8127),f842(x8122,x8123,x8124,x8125,x8126,x8127))
% 22.40/22.32 [813]~E(x8131,x8132)+E(f842(x8133,x8131,x8134,x8135,x8136,x8137),f842(x8133,x8132,x8134,x8135,x8136,x8137))
% 22.40/22.32 [814]~E(x8141,x8142)+E(f842(x8143,x8144,x8141,x8145,x8146,x8147),f842(x8143,x8144,x8142,x8145,x8146,x8147))
% 22.40/22.32 [815]~E(x8151,x8152)+E(f842(x8153,x8154,x8155,x8151,x8156,x8157),f842(x8153,x8154,x8155,x8152,x8156,x8157))
% 22.40/22.32 [816]~E(x8161,x8162)+E(f842(x8163,x8164,x8165,x8166,x8161,x8167),f842(x8163,x8164,x8165,x8166,x8162,x8167))
% 22.40/22.32 [817]~E(x8171,x8172)+E(f842(x8173,x8174,x8175,x8176,x8177,x8171),f842(x8173,x8174,x8175,x8176,x8177,x8172))
% 22.40/22.32 [818]~E(x8181,x8182)+E(f896(x8181,x8183,x8184,x8185,x8186,x8187,x8188,x8189),f896(x8182,x8183,x8184,x8185,x8186,x8187,x8188,x8189))
% 22.40/22.32 [819]~E(x8191,x8192)+E(f896(x8193,x8191,x8194,x8195,x8196,x8197,x8198,x8199),f896(x8193,x8192,x8194,x8195,x8196,x8197,x8198,x8199))
% 22.40/22.32 [820]~E(x8201,x8202)+E(f896(x8203,x8204,x8201,x8205,x8206,x8207,x8208,x8209),f896(x8203,x8204,x8202,x8205,x8206,x8207,x8208,x8209))
% 22.40/22.32 [821]~E(x8211,x8212)+E(f896(x8213,x8214,x8215,x8211,x8216,x8217,x8218,x8219),f896(x8213,x8214,x8215,x8212,x8216,x8217,x8218,x8219))
% 22.40/22.32 [822]~E(x8221,x8222)+E(f896(x8223,x8224,x8225,x8226,x8221,x8227,x8228,x8229),f896(x8223,x8224,x8225,x8226,x8222,x8227,x8228,x8229))
% 22.40/22.32 [823]~E(x8231,x8232)+E(f896(x8233,x8234,x8235,x8236,x8237,x8231,x8238,x8239),f896(x8233,x8234,x8235,x8236,x8237,x8232,x8238,x8239))
% 22.40/22.32 [824]~E(x8241,x8242)+E(f896(x8243,x8244,x8245,x8246,x8247,x8248,x8241,x8249),f896(x8243,x8244,x8245,x8246,x8247,x8248,x8242,x8249))
% 22.40/22.32 [825]~E(x8251,x8252)+E(f896(x8253,x8254,x8255,x8256,x8257,x8258,x8259,x8251),f896(x8253,x8254,x8255,x8256,x8257,x8258,x8259,x8252))
% 22.40/22.32 [826]~E(x8261,x8262)+E(f556(x8261,x8263,x8264,x8265),f556(x8262,x8263,x8264,x8265))
% 22.40/22.32 [827]~E(x8271,x8272)+E(f556(x8273,x8271,x8274,x8275),f556(x8273,x8272,x8274,x8275))
% 22.40/22.32 [828]~E(x8281,x8282)+E(f556(x8283,x8284,x8281,x8285),f556(x8283,x8284,x8282,x8285))
% 22.40/22.32 [829]~E(x8291,x8292)+E(f556(x8293,x8294,x8295,x8291),f556(x8293,x8294,x8295,x8292))
% 22.40/22.32 [830]~E(x8301,x8302)+E(f624(x8301,x8303,x8304,x8305,x8306),f624(x8302,x8303,x8304,x8305,x8306))
% 22.40/22.32 [831]~E(x8311,x8312)+E(f624(x8313,x8311,x8314,x8315,x8316),f624(x8313,x8312,x8314,x8315,x8316))
% 22.40/22.32 [832]~E(x8321,x8322)+E(f624(x8323,x8324,x8321,x8325,x8326),f624(x8323,x8324,x8322,x8325,x8326))
% 22.40/22.32 [833]~E(x8331,x8332)+E(f624(x8333,x8334,x8335,x8331,x8336),f624(x8333,x8334,x8335,x8332,x8336))
% 22.40/22.32 [834]~E(x8341,x8342)+E(f624(x8343,x8344,x8345,x8346,x8341),f624(x8343,x8344,x8345,x8346,x8342))
% 22.40/22.32 [835]~E(x8351,x8352)+E(f885(x8351,x8353),f885(x8352,x8353))
% 22.40/22.32 [836]~E(x8361,x8362)+E(f885(x8363,x8361),f885(x8363,x8362))
% 22.40/22.32 [837]~E(x8371,x8372)+E(f877(x8371,x8373,x8374),f877(x8372,x8373,x8374))
% 22.40/22.32 [838]~E(x8381,x8382)+E(f877(x8383,x8381,x8384),f877(x8383,x8382,x8384))
% 22.40/22.32 [839]~E(x8391,x8392)+E(f877(x8393,x8394,x8391),f877(x8393,x8394,x8392))
% 22.40/22.32 [840]~E(x8401,x8402)+E(f273(x8401),f273(x8402))
% 22.40/22.32 [841]~E(x8411,x8412)+E(f625(x8411,x8413,x8414,x8415,x8416),f625(x8412,x8413,x8414,x8415,x8416))
% 22.40/22.32 [842]~E(x8421,x8422)+E(f625(x8423,x8421,x8424,x8425,x8426),f625(x8423,x8422,x8424,x8425,x8426))
% 22.40/22.32 [843]~E(x8431,x8432)+E(f625(x8433,x8434,x8431,x8435,x8436),f625(x8433,x8434,x8432,x8435,x8436))
% 22.40/22.32 [844]~E(x8441,x8442)+E(f625(x8443,x8444,x8445,x8441,x8446),f625(x8443,x8444,x8445,x8442,x8446))
% 22.40/22.32 [845]~E(x8451,x8452)+E(f625(x8453,x8454,x8455,x8456,x8451),f625(x8453,x8454,x8455,x8456,x8452))
% 22.40/22.32 [846]~E(x8461,x8462)+E(f702(x8461,x8463,x8464),f702(x8462,x8463,x8464))
% 22.40/22.32 [847]~E(x8471,x8472)+E(f702(x8473,x8471,x8474),f702(x8473,x8472,x8474))
% 22.40/22.32 [848]~E(x8481,x8482)+E(f702(x8483,x8484,x8481),f702(x8483,x8484,x8482))
% 22.40/22.32 [849]~E(x8491,x8492)+E(f386(x8491,x8493,x8494,x8495),f386(x8492,x8493,x8494,x8495))
% 22.40/22.32 [850]~E(x8501,x8502)+E(f386(x8503,x8501,x8504,x8505),f386(x8503,x8502,x8504,x8505))
% 22.40/22.32 [851]~E(x8511,x8512)+E(f386(x8513,x8514,x8511,x8515),f386(x8513,x8514,x8512,x8515))
% 22.40/22.32 [852]~E(x8521,x8522)+E(f386(x8523,x8524,x8525,x8521),f386(x8523,x8524,x8525,x8522))
% 22.40/22.32 [853]~E(x8531,x8532)+E(f897(x8531,x8533,x8534,x8535,x8536,x8537,x8538),f897(x8532,x8533,x8534,x8535,x8536,x8537,x8538))
% 22.40/22.32 [854]~E(x8541,x8542)+E(f897(x8543,x8541,x8544,x8545,x8546,x8547,x8548),f897(x8543,x8542,x8544,x8545,x8546,x8547,x8548))
% 22.40/22.32 [855]~E(x8551,x8552)+E(f897(x8553,x8554,x8551,x8555,x8556,x8557,x8558),f897(x8553,x8554,x8552,x8555,x8556,x8557,x8558))
% 22.40/22.32 [856]~E(x8561,x8562)+E(f897(x8563,x8564,x8565,x8561,x8566,x8567,x8568),f897(x8563,x8564,x8565,x8562,x8566,x8567,x8568))
% 22.40/22.32 [857]~E(x8571,x8572)+E(f897(x8573,x8574,x8575,x8576,x8571,x8577,x8578),f897(x8573,x8574,x8575,x8576,x8572,x8577,x8578))
% 22.40/22.32 [858]~E(x8581,x8582)+E(f897(x8583,x8584,x8585,x8586,x8587,x8581,x8588),f897(x8583,x8584,x8585,x8586,x8587,x8582,x8588))
% 22.40/22.32 [859]~E(x8591,x8592)+E(f897(x8593,x8594,x8595,x8596,x8597,x8598,x8591),f897(x8593,x8594,x8595,x8596,x8597,x8598,x8592))
% 22.40/22.32 [860]~E(x8601,x8602)+E(f418(x8601,x8603,x8604,x8605,x8606),f418(x8602,x8603,x8604,x8605,x8606))
% 22.40/22.32 [861]~E(x8611,x8612)+E(f418(x8613,x8611,x8614,x8615,x8616),f418(x8613,x8612,x8614,x8615,x8616))
% 22.40/22.32 [862]~E(x8621,x8622)+E(f418(x8623,x8624,x8621,x8625,x8626),f418(x8623,x8624,x8622,x8625,x8626))
% 22.40/22.32 [863]~E(x8631,x8632)+E(f418(x8633,x8634,x8635,x8631,x8636),f418(x8633,x8634,x8635,x8632,x8636))
% 22.40/22.32 [864]~E(x8641,x8642)+E(f418(x8643,x8644,x8645,x8646,x8641),f418(x8643,x8644,x8645,x8646,x8642))
% 22.40/22.32 [865]~E(x8651,x8652)+E(f720(x8651,x8653),f720(x8652,x8653))
% 22.40/22.32 [866]~E(x8661,x8662)+E(f720(x8663,x8661),f720(x8663,x8662))
% 22.40/22.32 [867]~E(x8671,x8672)+E(f166(x8671,x8673,x8674),f166(x8672,x8673,x8674))
% 22.40/22.32 [868]~E(x8681,x8682)+E(f166(x8683,x8681,x8684),f166(x8683,x8682,x8684))
% 22.40/22.32 [869]~E(x8691,x8692)+E(f166(x8693,x8694,x8691),f166(x8693,x8694,x8692))
% 22.40/22.32 [870]~E(x8701,x8702)+E(f56(x8701,x8703,x8704),f56(x8702,x8703,x8704))
% 22.40/22.32 [871]~E(x8711,x8712)+E(f56(x8713,x8711,x8714),f56(x8713,x8712,x8714))
% 22.40/22.32 [872]~E(x8721,x8722)+E(f56(x8723,x8724,x8721),f56(x8723,x8724,x8722))
% 22.40/22.32 [873]~E(x8731,x8732)+E(f41(x8731,x8733),f41(x8732,x8733))
% 22.40/22.32 [874]~E(x8741,x8742)+E(f41(x8743,x8741),f41(x8743,x8742))
% 22.40/22.32 [875]~E(x8751,x8752)+E(f576(x8751,x8753),f576(x8752,x8753))
% 22.40/22.32 [876]~E(x8761,x8762)+E(f576(x8763,x8761),f576(x8763,x8762))
% 22.40/22.32 [877]~E(x8771,x8772)+E(f162(x8771,x8773,x8774),f162(x8772,x8773,x8774))
% 22.40/22.32 [878]~E(x8781,x8782)+E(f162(x8783,x8781,x8784),f162(x8783,x8782,x8784))
% 22.40/22.32 [879]~E(x8791,x8792)+E(f162(x8793,x8794,x8791),f162(x8793,x8794,x8792))
% 22.40/22.32 [880]~E(x8801,x8802)+E(f670(x8801,x8803,x8804,x8805,x8806),f670(x8802,x8803,x8804,x8805,x8806))
% 22.40/22.32 [881]~E(x8811,x8812)+E(f670(x8813,x8811,x8814,x8815,x8816),f670(x8813,x8812,x8814,x8815,x8816))
% 22.40/22.32 [882]~E(x8821,x8822)+E(f670(x8823,x8824,x8821,x8825,x8826),f670(x8823,x8824,x8822,x8825,x8826))
% 22.40/22.32 [883]~E(x8831,x8832)+E(f670(x8833,x8834,x8835,x8831,x8836),f670(x8833,x8834,x8835,x8832,x8836))
% 22.40/22.32 [884]~E(x8841,x8842)+E(f670(x8843,x8844,x8845,x8846,x8841),f670(x8843,x8844,x8845,x8846,x8842))
% 22.40/22.32 [885]~E(x8851,x8852)+E(f289(x8851,x8853,x8854,x8855,x8856),f289(x8852,x8853,x8854,x8855,x8856))
% 22.40/22.32 [886]~E(x8861,x8862)+E(f289(x8863,x8861,x8864,x8865,x8866),f289(x8863,x8862,x8864,x8865,x8866))
% 22.40/22.32 [887]~E(x8871,x8872)+E(f289(x8873,x8874,x8871,x8875,x8876),f289(x8873,x8874,x8872,x8875,x8876))
% 22.40/22.32 [888]~E(x8881,x8882)+E(f289(x8883,x8884,x8885,x8881,x8886),f289(x8883,x8884,x8885,x8882,x8886))
% 22.40/22.32 [889]~E(x8891,x8892)+E(f289(x8893,x8894,x8895,x8896,x8891),f289(x8893,x8894,x8895,x8896,x8892))
% 22.40/22.32 [890]~E(x8901,x8902)+E(f567(x8901,x8903,x8904),f567(x8902,x8903,x8904))
% 22.40/22.32 [891]~E(x8911,x8912)+E(f567(x8913,x8911,x8914),f567(x8913,x8912,x8914))
% 22.40/22.32 [892]~E(x8921,x8922)+E(f567(x8923,x8924,x8921),f567(x8923,x8924,x8922))
% 22.40/22.32 [893]~E(x8931,x8932)+E(f647(x8931,x8933),f647(x8932,x8933))
% 22.40/22.32 [894]~E(x8941,x8942)+E(f647(x8943,x8941),f647(x8943,x8942))
% 22.40/22.32 [895]~E(x8951,x8952)+E(f185(x8951,x8953),f185(x8952,x8953))
% 22.40/22.32 [896]~E(x8961,x8962)+E(f185(x8963,x8961),f185(x8963,x8962))
% 22.40/22.32 [897]~E(x8971,x8972)+E(f343(x8971,x8973),f343(x8972,x8973))
% 22.40/22.32 [898]~E(x8981,x8982)+E(f343(x8983,x8981),f343(x8983,x8982))
% 22.40/22.32 [899]~E(x8991,x8992)+E(f113(x8991,x8993),f113(x8992,x8993))
% 22.40/22.32 [900]~E(x9001,x9002)+E(f113(x9003,x9001),f113(x9003,x9002))
% 22.40/22.32 [901]~E(x9011,x9012)+E(f638(x9011,x9013),f638(x9012,x9013))
% 22.40/22.32 [902]~E(x9021,x9022)+E(f638(x9023,x9021),f638(x9023,x9022))
% 22.40/22.32 [903]~E(x9031,x9032)+E(f846(x9031,x9033,x9034,x9035,x9036,x9037,x9038),f846(x9032,x9033,x9034,x9035,x9036,x9037,x9038))
% 22.40/22.32 [904]~E(x9041,x9042)+E(f846(x9043,x9041,x9044,x9045,x9046,x9047,x9048),f846(x9043,x9042,x9044,x9045,x9046,x9047,x9048))
% 22.40/22.32 [905]~E(x9051,x9052)+E(f846(x9053,x9054,x9051,x9055,x9056,x9057,x9058),f846(x9053,x9054,x9052,x9055,x9056,x9057,x9058))
% 22.40/22.32 [906]~E(x9061,x9062)+E(f846(x9063,x9064,x9065,x9061,x9066,x9067,x9068),f846(x9063,x9064,x9065,x9062,x9066,x9067,x9068))
% 22.40/22.32 [907]~E(x9071,x9072)+E(f846(x9073,x9074,x9075,x9076,x9071,x9077,x9078),f846(x9073,x9074,x9075,x9076,x9072,x9077,x9078))
% 22.40/22.32 [908]~E(x9081,x9082)+E(f846(x9083,x9084,x9085,x9086,x9087,x9081,x9088),f846(x9083,x9084,x9085,x9086,x9087,x9082,x9088))
% 22.40/22.32 [909]~E(x9091,x9092)+E(f846(x9093,x9094,x9095,x9096,x9097,x9098,x9091),f846(x9093,x9094,x9095,x9096,x9097,x9098,x9092))
% 22.40/22.32 [910]~E(x9101,x9102)+E(f474(x9101,x9103,x9104,x9105,x9106),f474(x9102,x9103,x9104,x9105,x9106))
% 22.40/22.32 [911]~E(x9111,x9112)+E(f474(x9113,x9111,x9114,x9115,x9116),f474(x9113,x9112,x9114,x9115,x9116))
% 22.40/22.32 [912]~E(x9121,x9122)+E(f474(x9123,x9124,x9121,x9125,x9126),f474(x9123,x9124,x9122,x9125,x9126))
% 22.40/22.32 [913]~E(x9131,x9132)+E(f474(x9133,x9134,x9135,x9131,x9136),f474(x9133,x9134,x9135,x9132,x9136))
% 22.40/22.32 [914]~E(x9141,x9142)+E(f474(x9143,x9144,x9145,x9146,x9141),f474(x9143,x9144,x9145,x9146,x9142))
% 22.40/22.32 [915]~E(x9151,x9152)+E(f805(x9151,x9153,x9154,x9155,x9156,x9157),f805(x9152,x9153,x9154,x9155,x9156,x9157))
% 22.40/22.32 [916]~E(x9161,x9162)+E(f805(x9163,x9161,x9164,x9165,x9166,x9167),f805(x9163,x9162,x9164,x9165,x9166,x9167))
% 22.40/22.32 [917]~E(x9171,x9172)+E(f805(x9173,x9174,x9171,x9175,x9176,x9177),f805(x9173,x9174,x9172,x9175,x9176,x9177))
% 22.40/22.32 [918]~E(x9181,x9182)+E(f805(x9183,x9184,x9185,x9181,x9186,x9187),f805(x9183,x9184,x9185,x9182,x9186,x9187))
% 22.40/22.32 [919]~E(x9191,x9192)+E(f805(x9193,x9194,x9195,x9196,x9191,x9197),f805(x9193,x9194,x9195,x9196,x9192,x9197))
% 22.40/22.32 [920]~E(x9201,x9202)+E(f805(x9203,x9204,x9205,x9206,x9207,x9201),f805(x9203,x9204,x9205,x9206,x9207,x9202))
% 22.40/22.32 [921]~E(x9211,x9212)+E(f564(x9211,x9213,x9214,x9215),f564(x9212,x9213,x9214,x9215))
% 22.40/22.32 [922]~E(x9221,x9222)+E(f564(x9223,x9221,x9224,x9225),f564(x9223,x9222,x9224,x9225))
% 22.40/22.32 [923]~E(x9231,x9232)+E(f564(x9233,x9234,x9231,x9235),f564(x9233,x9234,x9232,x9235))
% 22.40/22.32 [924]~E(x9241,x9242)+E(f564(x9243,x9244,x9245,x9241),f564(x9243,x9244,x9245,x9242))
% 22.40/22.32 [925]~E(x9251,x9252)+E(f480(x9251,x9253,x9254),f480(x9252,x9253,x9254))
% 22.40/22.32 [926]~E(x9261,x9262)+E(f480(x9263,x9261,x9264),f480(x9263,x9262,x9264))
% 22.40/22.32 [927]~E(x9271,x9272)+E(f480(x9273,x9274,x9271),f480(x9273,x9274,x9272))
% 22.40/22.32 [928]~E(x9281,x9282)+E(f220(x9281,x9283),f220(x9282,x9283))
% 22.40/22.32 [929]~E(x9291,x9292)+E(f220(x9293,x9291),f220(x9293,x9292))
% 22.40/22.32 [930]~E(x9301,x9302)+E(f374(x9301,x9303,x9304),f374(x9302,x9303,x9304))
% 22.40/22.32 [931]~E(x9311,x9312)+E(f374(x9313,x9311,x9314),f374(x9313,x9312,x9314))
% 22.40/22.32 [932]~E(x9321,x9322)+E(f374(x9323,x9324,x9321),f374(x9323,x9324,x9322))
% 22.40/22.32 [933]~E(x9331,x9332)+E(f267(x9331,x9333),f267(x9332,x9333))
% 22.40/22.32 [934]~E(x9341,x9342)+E(f267(x9343,x9341),f267(x9343,x9342))
% 22.40/22.32 [935]~E(x9351,x9352)+E(f774(x9351,x9353,x9354),f774(x9352,x9353,x9354))
% 22.40/22.32 [936]~E(x9361,x9362)+E(f774(x9363,x9361,x9364),f774(x9363,x9362,x9364))
% 22.40/22.32 [937]~E(x9371,x9372)+E(f774(x9373,x9374,x9371),f774(x9373,x9374,x9372))
% 22.40/22.32 [938]~E(x9381,x9382)+E(f668(x9381,x9383,x9384,x9385),f668(x9382,x9383,x9384,x9385))
% 22.40/22.32 [939]~E(x9391,x9392)+E(f668(x9393,x9391,x9394,x9395),f668(x9393,x9392,x9394,x9395))
% 22.40/22.32 [940]~E(x9401,x9402)+E(f668(x9403,x9404,x9401,x9405),f668(x9403,x9404,x9402,x9405))
% 22.40/22.32 [941]~E(x9411,x9412)+E(f668(x9413,x9414,x9415,x9411),f668(x9413,x9414,x9415,x9412))
% 22.40/22.32 [942]~E(x9421,x9422)+E(f695(x9421,x9423,x9424),f695(x9422,x9423,x9424))
% 22.40/22.32 [943]~E(x9431,x9432)+E(f695(x9433,x9431,x9434),f695(x9433,x9432,x9434))
% 22.40/22.32 [944]~E(x9441,x9442)+E(f695(x9443,x9444,x9441),f695(x9443,x9444,x9442))
% 22.40/22.32 [945]~E(x9451,x9452)+E(f486(x9451,x9453,x9454),f486(x9452,x9453,x9454))
% 22.40/22.32 [946]~E(x9461,x9462)+E(f486(x9463,x9461,x9464),f486(x9463,x9462,x9464))
% 22.40/22.32 [947]~E(x9471,x9472)+E(f486(x9473,x9474,x9471),f486(x9473,x9474,x9472))
% 22.40/22.32 [948]~E(x9481,x9482)+E(f563(x9481,x9483,x9484,x9485),f563(x9482,x9483,x9484,x9485))
% 22.40/22.32 [949]~E(x9491,x9492)+E(f563(x9493,x9491,x9494,x9495),f563(x9493,x9492,x9494,x9495))
% 22.40/22.32 [950]~E(x9501,x9502)+E(f563(x9503,x9504,x9501,x9505),f563(x9503,x9504,x9502,x9505))
% 22.40/22.32 [951]~E(x9511,x9512)+E(f563(x9513,x9514,x9515,x9511),f563(x9513,x9514,x9515,x9512))
% 22.40/22.32 [952]~E(x9521,x9522)+E(f431(x9521),f431(x9522))
% 22.40/22.32 [953]~E(x9531,x9532)+E(f893(x9531,x9533,x9534),f893(x9532,x9533,x9534))
% 22.40/22.32 [954]~E(x9541,x9542)+E(f893(x9543,x9541,x9544),f893(x9543,x9542,x9544))
% 22.40/22.32 [955]~E(x9551,x9552)+E(f893(x9553,x9554,x9551),f893(x9553,x9554,x9552))
% 22.40/22.32 [956]~E(x9561,x9562)+E(f694(x9561,x9563,x9564),f694(x9562,x9563,x9564))
% 22.40/22.32 [957]~E(x9571,x9572)+E(f694(x9573,x9571,x9574),f694(x9573,x9572,x9574))
% 22.40/22.32 [958]~E(x9581,x9582)+E(f694(x9583,x9584,x9581),f694(x9583,x9584,x9582))
% 22.40/22.32 [959]~E(x9591,x9592)+E(f834(x9591,x9593,x9594,x9595,x9596,x9597,x9598,x9599),f834(x9592,x9593,x9594,x9595,x9596,x9597,x9598,x9599))
% 22.40/22.32 [960]~E(x9601,x9602)+E(f834(x9603,x9601,x9604,x9605,x9606,x9607,x9608,x9609),f834(x9603,x9602,x9604,x9605,x9606,x9607,x9608,x9609))
% 22.40/22.32 [961]~E(x9611,x9612)+E(f834(x9613,x9614,x9611,x9615,x9616,x9617,x9618,x9619),f834(x9613,x9614,x9612,x9615,x9616,x9617,x9618,x9619))
% 22.40/22.32 [962]~E(x9621,x9622)+E(f834(x9623,x9624,x9625,x9621,x9626,x9627,x9628,x9629),f834(x9623,x9624,x9625,x9622,x9626,x9627,x9628,x9629))
% 22.40/22.32 [963]~E(x9631,x9632)+E(f834(x9633,x9634,x9635,x9636,x9631,x9637,x9638,x9639),f834(x9633,x9634,x9635,x9636,x9632,x9637,x9638,x9639))
% 22.40/22.32 [964]~E(x9641,x9642)+E(f834(x9643,x9644,x9645,x9646,x9647,x9641,x9648,x9649),f834(x9643,x9644,x9645,x9646,x9647,x9642,x9648,x9649))
% 22.40/22.32 [965]~E(x9651,x9652)+E(f834(x9653,x9654,x9655,x9656,x9657,x9658,x9651,x9659),f834(x9653,x9654,x9655,x9656,x9657,x9658,x9652,x9659))
% 22.40/22.32 [966]~E(x9661,x9662)+E(f834(x9663,x9664,x9665,x9666,x9667,x9668,x9669,x9661),f834(x9663,x9664,x9665,x9666,x9667,x9668,x9669,x9662))
% 22.40/22.32 [967]~E(x9671,x9672)+E(f737(x9671,x9673,x9674,x9675,x9676),f737(x9672,x9673,x9674,x9675,x9676))
% 22.40/22.32 [968]~E(x9681,x9682)+E(f737(x9683,x9681,x9684,x9685,x9686),f737(x9683,x9682,x9684,x9685,x9686))
% 22.40/22.32 [969]~E(x9691,x9692)+E(f737(x9693,x9694,x9691,x9695,x9696),f737(x9693,x9694,x9692,x9695,x9696))
% 22.40/22.32 [970]~E(x9701,x9702)+E(f737(x9703,x9704,x9705,x9701,x9706),f737(x9703,x9704,x9705,x9702,x9706))
% 22.40/22.32 [971]~E(x9711,x9712)+E(f737(x9713,x9714,x9715,x9716,x9711),f737(x9713,x9714,x9715,x9716,x9712))
% 22.40/22.32 [972]~E(x9721,x9722)+E(f899(x9721,x9723,x9724),f899(x9722,x9723,x9724))
% 22.40/22.32 [973]~E(x9731,x9732)+E(f899(x9733,x9731,x9734),f899(x9733,x9732,x9734))
% 22.40/22.32 [974]~E(x9741,x9742)+E(f899(x9743,x9744,x9741),f899(x9743,x9744,x9742))
% 22.40/22.32 [975]~E(x9751,x9752)+E(f120(x9751,x9753),f120(x9752,x9753))
% 22.40/22.32 [976]~E(x9761,x9762)+E(f120(x9763,x9761),f120(x9763,x9762))
% 22.40/22.32 [977]~E(x9771,x9772)+E(f476(x9771,x9773,x9774,x9775,x9776),f476(x9772,x9773,x9774,x9775,x9776))
% 22.40/22.32 [978]~E(x9781,x9782)+E(f476(x9783,x9781,x9784,x9785,x9786),f476(x9783,x9782,x9784,x9785,x9786))
% 22.40/22.32 [979]~E(x9791,x9792)+E(f476(x9793,x9794,x9791,x9795,x9796),f476(x9793,x9794,x9792,x9795,x9796))
% 22.40/22.32 [980]~E(x9801,x9802)+E(f476(x9803,x9804,x9805,x9801,x9806),f476(x9803,x9804,x9805,x9802,x9806))
% 22.40/22.32 [981]~E(x9811,x9812)+E(f476(x9813,x9814,x9815,x9816,x9811),f476(x9813,x9814,x9815,x9816,x9812))
% 22.40/22.32 [982]~E(x9821,x9822)+E(f649(x9821,x9823,x9824),f649(x9822,x9823,x9824))
% 22.40/22.32 [983]~E(x9831,x9832)+E(f649(x9833,x9831,x9834),f649(x9833,x9832,x9834))
% 22.40/22.32 [984]~E(x9841,x9842)+E(f649(x9843,x9844,x9841),f649(x9843,x9844,x9842))
% 22.40/22.32 [985]~E(x9851,x9852)+E(f708(x9851,x9853,x9854),f708(x9852,x9853,x9854))
% 22.40/22.32 [986]~E(x9861,x9862)+E(f708(x9863,x9861,x9864),f708(x9863,x9862,x9864))
% 22.40/22.32 [987]~E(x9871,x9872)+E(f708(x9873,x9874,x9871),f708(x9873,x9874,x9872))
% 22.40/22.32 [988]~E(x9881,x9882)+E(f21(x9881,x9883,x9884,x9885),f21(x9882,x9883,x9884,x9885))
% 22.40/22.32 [989]~E(x9891,x9892)+E(f21(x9893,x9891,x9894,x9895),f21(x9893,x9892,x9894,x9895))
% 22.40/22.32 [990]~E(x9901,x9902)+E(f21(x9903,x9904,x9901,x9905),f21(x9903,x9904,x9902,x9905))
% 22.40/22.32 [991]~E(x9911,x9912)+E(f21(x9913,x9914,x9915,x9911),f21(x9913,x9914,x9915,x9912))
% 22.40/22.32 [992]~E(x9921,x9922)+E(f326(x9921,x9923),f326(x9922,x9923))
% 22.40/22.32 [993]~E(x9931,x9932)+E(f326(x9933,x9931),f326(x9933,x9932))
% 22.40/22.32 [994]~E(x9941,x9942)+E(f585(x9941,x9943,x9944,x9945,x9946,x9947),f585(x9942,x9943,x9944,x9945,x9946,x9947))
% 22.40/22.32 [995]~E(x9951,x9952)+E(f585(x9953,x9951,x9954,x9955,x9956,x9957),f585(x9953,x9952,x9954,x9955,x9956,x9957))
% 22.40/22.32 [996]~E(x9961,x9962)+E(f585(x9963,x9964,x9961,x9965,x9966,x9967),f585(x9963,x9964,x9962,x9965,x9966,x9967))
% 22.40/22.32 [997]~E(x9971,x9972)+E(f585(x9973,x9974,x9975,x9971,x9976,x9977),f585(x9973,x9974,x9975,x9972,x9976,x9977))
% 22.40/22.32 [998]~E(x9981,x9982)+E(f585(x9983,x9984,x9985,x9986,x9981,x9987),f585(x9983,x9984,x9985,x9986,x9982,x9987))
% 22.40/22.32 [999]~E(x9991,x9992)+E(f585(x9993,x9994,x9995,x9996,x9997,x9991),f585(x9993,x9994,x9995,x9996,x9997,x9992))
% 22.40/22.32 [1000]~E(x10001,x10002)+E(f814(x10001,x10003,x10004,x10005),f814(x10002,x10003,x10004,x10005))
% 22.40/22.32 [1001]~E(x10011,x10012)+E(f814(x10013,x10011,x10014,x10015),f814(x10013,x10012,x10014,x10015))
% 22.40/22.32 [1002]~E(x10021,x10022)+E(f814(x10023,x10024,x10021,x10025),f814(x10023,x10024,x10022,x10025))
% 22.40/22.32 [1003]~E(x10031,x10032)+E(f814(x10033,x10034,x10035,x10031),f814(x10033,x10034,x10035,x10032))
% 22.40/22.32 [1004]~E(x10041,x10042)+E(f285(x10041,x10043,x10044),f285(x10042,x10043,x10044))
% 22.40/22.32 [1005]~E(x10051,x10052)+E(f285(x10053,x10051,x10054),f285(x10053,x10052,x10054))
% 22.40/22.32 [1006]~E(x10061,x10062)+E(f285(x10063,x10064,x10061),f285(x10063,x10064,x10062))
% 22.40/22.32 [1007]~E(x10071,x10072)+E(f696(x10071,x10073),f696(x10072,x10073))
% 22.40/22.32 [1008]~E(x10081,x10082)+E(f696(x10083,x10081),f696(x10083,x10082))
% 22.40/22.32 [1009]~E(x10091,x10092)+E(f591(x10091,x10093,x10094),f591(x10092,x10093,x10094))
% 22.40/22.32 [1010]~E(x10101,x10102)+E(f591(x10103,x10101,x10104),f591(x10103,x10102,x10104))
% 22.40/22.32 [1011]~E(x10111,x10112)+E(f591(x10113,x10114,x10111),f591(x10113,x10114,x10112))
% 22.40/22.32 [1012]~E(x10121,x10122)+E(f71(x10121,x10123,x10124,x10125),f71(x10122,x10123,x10124,x10125))
% 22.40/22.32 [1013]~E(x10131,x10132)+E(f71(x10133,x10131,x10134,x10135),f71(x10133,x10132,x10134,x10135))
% 22.40/22.32 [1014]~E(x10141,x10142)+E(f71(x10143,x10144,x10141,x10145),f71(x10143,x10144,x10142,x10145))
% 22.40/22.32 [1015]~E(x10151,x10152)+E(f71(x10153,x10154,x10155,x10151),f71(x10153,x10154,x10155,x10152))
% 22.40/22.32 [1016]~E(x10161,x10162)+E(f679(x10161,x10163,x10164,x10165,x10166),f679(x10162,x10163,x10164,x10165,x10166))
% 22.40/22.32 [1017]~E(x10171,x10172)+E(f679(x10173,x10171,x10174,x10175,x10176),f679(x10173,x10172,x10174,x10175,x10176))
% 22.40/22.32 [1018]~E(x10181,x10182)+E(f679(x10183,x10184,x10181,x10185,x10186),f679(x10183,x10184,x10182,x10185,x10186))
% 22.40/22.32 [1019]~E(x10191,x10192)+E(f679(x10193,x10194,x10195,x10191,x10196),f679(x10193,x10194,x10195,x10192,x10196))
% 22.40/22.32 [1020]~E(x10201,x10202)+E(f679(x10203,x10204,x10205,x10206,x10201),f679(x10203,x10204,x10205,x10206,x10202))
% 22.40/22.32 [1021]~E(x10211,x10212)+E(f258(x10211,x10213),f258(x10212,x10213))
% 22.40/22.32 [1022]~E(x10221,x10222)+E(f258(x10223,x10221),f258(x10223,x10222))
% 22.40/22.32 [1023]~E(x10231,x10232)+E(f373(x10231,x10233,x10234),f373(x10232,x10233,x10234))
% 22.40/22.32 [1024]~E(x10241,x10242)+E(f373(x10243,x10241,x10244),f373(x10243,x10242,x10244))
% 22.40/22.32 [1025]~E(x10251,x10252)+E(f373(x10253,x10254,x10251),f373(x10253,x10254,x10252))
% 22.40/22.32 [1026]~E(x10261,x10262)+E(f70(x10261,x10263,x10264,x10265,x10266),f70(x10262,x10263,x10264,x10265,x10266))
% 22.40/22.32 [1027]~E(x10271,x10272)+E(f70(x10273,x10271,x10274,x10275,x10276),f70(x10273,x10272,x10274,x10275,x10276))
% 22.40/22.32 [1028]~E(x10281,x10282)+E(f70(x10283,x10284,x10281,x10285,x10286),f70(x10283,x10284,x10282,x10285,x10286))
% 22.40/22.32 [1029]~E(x10291,x10292)+E(f70(x10293,x10294,x10295,x10291,x10296),f70(x10293,x10294,x10295,x10292,x10296))
% 22.40/22.32 [1030]~E(x10301,x10302)+E(f70(x10303,x10304,x10305,x10306,x10301),f70(x10303,x10304,x10305,x10306,x10302))
% 22.40/22.32 [1031]~E(x10311,x10312)+E(f36(x10311),f36(x10312))
% 22.40/22.32 [1032]~E(x10321,x10322)+E(f617(x10321,x10323,x10324,x10325,x10326),f617(x10322,x10323,x10324,x10325,x10326))
% 22.40/22.32 [1033]~E(x10331,x10332)+E(f617(x10333,x10331,x10334,x10335,x10336),f617(x10333,x10332,x10334,x10335,x10336))
% 22.40/22.32 [1034]~E(x10341,x10342)+E(f617(x10343,x10344,x10341,x10345,x10346),f617(x10343,x10344,x10342,x10345,x10346))
% 22.40/22.32 [1035]~E(x10351,x10352)+E(f617(x10353,x10354,x10355,x10351,x10356),f617(x10353,x10354,x10355,x10352,x10356))
% 22.40/22.32 [1036]~E(x10361,x10362)+E(f617(x10363,x10364,x10365,x10366,x10361),f617(x10363,x10364,x10365,x10366,x10362))
% 22.40/22.32 [1037]~E(x10371,x10372)+E(f831(x10371,x10373,x10374,x10375,x10376,x10377,x10378,x10379),f831(x10372,x10373,x10374,x10375,x10376,x10377,x10378,x10379))
% 22.40/22.32 [1038]~E(x10381,x10382)+E(f831(x10383,x10381,x10384,x10385,x10386,x10387,x10388,x10389),f831(x10383,x10382,x10384,x10385,x10386,x10387,x10388,x10389))
% 22.40/22.32 [1039]~E(x10391,x10392)+E(f831(x10393,x10394,x10391,x10395,x10396,x10397,x10398,x10399),f831(x10393,x10394,x10392,x10395,x10396,x10397,x10398,x10399))
% 22.40/22.32 [1040]~E(x10401,x10402)+E(f831(x10403,x10404,x10405,x10401,x10406,x10407,x10408,x10409),f831(x10403,x10404,x10405,x10402,x10406,x10407,x10408,x10409))
% 22.40/22.32 [1041]~E(x10411,x10412)+E(f831(x10413,x10414,x10415,x10416,x10411,x10417,x10418,x10419),f831(x10413,x10414,x10415,x10416,x10412,x10417,x10418,x10419))
% 22.40/22.32 [1042]~E(x10421,x10422)+E(f831(x10423,x10424,x10425,x10426,x10427,x10421,x10428,x10429),f831(x10423,x10424,x10425,x10426,x10427,x10422,x10428,x10429))
% 22.40/22.32 [1043]~E(x10431,x10432)+E(f831(x10433,x10434,x10435,x10436,x10437,x10438,x10431,x10439),f831(x10433,x10434,x10435,x10436,x10437,x10438,x10432,x10439))
% 22.40/22.32 [1044]~E(x10441,x10442)+E(f831(x10443,x10444,x10445,x10446,x10447,x10448,x10449,x10441),f831(x10443,x10444,x10445,x10446,x10447,x10448,x10449,x10442))
% 22.40/22.32 [1045]~E(x10451,x10452)+E(f493(x10451,x10453,x10454),f493(x10452,x10453,x10454))
% 22.40/22.32 [1046]~E(x10461,x10462)+E(f493(x10463,x10461,x10464),f493(x10463,x10462,x10464))
% 22.40/22.32 [1047]~E(x10471,x10472)+E(f493(x10473,x10474,x10471),f493(x10473,x10474,x10472))
% 22.40/22.32 [1048]~E(x10481,x10482)+E(f721(x10481,x10483),f721(x10482,x10483))
% 22.40/22.32 [1049]~E(x10491,x10492)+E(f721(x10493,x10491),f721(x10493,x10492))
% 22.40/22.32 [1050]~E(x10501,x10502)+E(f178(x10501),f178(x10502))
% 22.40/22.32 [1051]~E(x10511,x10512)+E(f725(x10511,x10513,x10514,x10515),f725(x10512,x10513,x10514,x10515))
% 22.40/22.32 [1052]~E(x10521,x10522)+E(f725(x10523,x10521,x10524,x10525),f725(x10523,x10522,x10524,x10525))
% 22.40/22.32 [1053]~E(x10531,x10532)+E(f725(x10533,x10534,x10531,x10535),f725(x10533,x10534,x10532,x10535))
% 22.40/22.32 [1054]~E(x10541,x10542)+E(f725(x10543,x10544,x10545,x10541),f725(x10543,x10544,x10545,x10542))
% 22.40/22.32 [1055]~E(x10551,x10552)+E(f744(x10551,x10553,x10554),f744(x10552,x10553,x10554))
% 22.40/22.32 [1056]~E(x10561,x10562)+E(f744(x10563,x10561,x10564),f744(x10563,x10562,x10564))
% 22.40/22.32 [1057]~E(x10571,x10572)+E(f744(x10573,x10574,x10571),f744(x10573,x10574,x10572))
% 22.40/22.32 [1058]~E(x10581,x10582)+E(f650(x10581,x10583,x10584),f650(x10582,x10583,x10584))
% 22.40/22.32 [1059]~E(x10591,x10592)+E(f650(x10593,x10591,x10594),f650(x10593,x10592,x10594))
% 22.40/22.32 [1060]~E(x10601,x10602)+E(f650(x10603,x10604,x10601),f650(x10603,x10604,x10602))
% 22.40/22.32 [1061]~E(x10611,x10612)+E(f369(x10611,x10613,x10614),f369(x10612,x10613,x10614))
% 22.40/22.32 [1062]~E(x10621,x10622)+E(f369(x10623,x10621,x10624),f369(x10623,x10622,x10624))
% 22.40/22.32 [1063]~E(x10631,x10632)+E(f369(x10633,x10634,x10631),f369(x10633,x10634,x10632))
% 22.40/22.32 [1064]~E(x10641,x10642)+E(f874(x10641,x10643,x10644,x10645,x10646,x10647,x10648),f874(x10642,x10643,x10644,x10645,x10646,x10647,x10648))
% 22.40/22.32 [1065]~E(x10651,x10652)+E(f874(x10653,x10651,x10654,x10655,x10656,x10657,x10658),f874(x10653,x10652,x10654,x10655,x10656,x10657,x10658))
% 22.40/22.32 [1066]~E(x10661,x10662)+E(f874(x10663,x10664,x10661,x10665,x10666,x10667,x10668),f874(x10663,x10664,x10662,x10665,x10666,x10667,x10668))
% 22.40/22.32 [1067]~E(x10671,x10672)+E(f874(x10673,x10674,x10675,x10671,x10676,x10677,x10678),f874(x10673,x10674,x10675,x10672,x10676,x10677,x10678))
% 22.40/22.32 [1068]~E(x10681,x10682)+E(f874(x10683,x10684,x10685,x10686,x10681,x10687,x10688),f874(x10683,x10684,x10685,x10686,x10682,x10687,x10688))
% 22.40/22.32 [1069]~E(x10691,x10692)+E(f874(x10693,x10694,x10695,x10696,x10697,x10691,x10698),f874(x10693,x10694,x10695,x10696,x10697,x10692,x10698))
% 22.40/22.32 [1070]~E(x10701,x10702)+E(f874(x10703,x10704,x10705,x10706,x10707,x10708,x10701),f874(x10703,x10704,x10705,x10706,x10707,x10708,x10702))
% 22.40/22.32 [1071]~E(x10711,x10712)+E(f693(x10711,x10713),f693(x10712,x10713))
% 22.40/22.32 [1072]~E(x10721,x10722)+E(f693(x10723,x10721),f693(x10723,x10722))
% 22.40/22.32 [1073]~E(x10731,x10732)+E(f697(x10731,x10733),f697(x10732,x10733))
% 22.40/22.32 [1074]~E(x10741,x10742)+E(f697(x10743,x10741),f697(x10743,x10742))
% 22.40/22.32 [1075]~E(x10751,x10752)+E(f634(x10751,x10753,x10754,x10755,x10756),f634(x10752,x10753,x10754,x10755,x10756))
% 22.40/22.32 [1076]~E(x10761,x10762)+E(f634(x10763,x10761,x10764,x10765,x10766),f634(x10763,x10762,x10764,x10765,x10766))
% 22.40/22.32 [1077]~E(x10771,x10772)+E(f634(x10773,x10774,x10771,x10775,x10776),f634(x10773,x10774,x10772,x10775,x10776))
% 22.40/22.32 [1078]~E(x10781,x10782)+E(f634(x10783,x10784,x10785,x10781,x10786),f634(x10783,x10784,x10785,x10782,x10786))
% 22.40/22.32 [1079]~E(x10791,x10792)+E(f634(x10793,x10794,x10795,x10796,x10791),f634(x10793,x10794,x10795,x10796,x10792))
% 22.40/22.32 [1080]~E(x10801,x10802)+E(f296(x10801),f296(x10802))
% 22.40/22.32 [1081]~E(x10811,x10812)+E(f815(x10811,x10813,x10814,x10815),f815(x10812,x10813,x10814,x10815))
% 22.40/22.32 [1082]~E(x10821,x10822)+E(f815(x10823,x10821,x10824,x10825),f815(x10823,x10822,x10824,x10825))
% 22.40/22.32 [1083]~E(x10831,x10832)+E(f815(x10833,x10834,x10831,x10835),f815(x10833,x10834,x10832,x10835))
% 22.40/22.32 [1084]~E(x10841,x10842)+E(f815(x10843,x10844,x10845,x10841),f815(x10843,x10844,x10845,x10842))
% 22.40/22.32 [1085]~E(x10851,x10852)+E(f286(x10851,x10853,x10854),f286(x10852,x10853,x10854))
% 22.40/22.32 [1086]~E(x10861,x10862)+E(f286(x10863,x10861,x10864),f286(x10863,x10862,x10864))
% 22.40/22.32 [1087]~E(x10871,x10872)+E(f286(x10873,x10874,x10871),f286(x10873,x10874,x10872))
% 22.40/22.32 [1088]~E(x10881,x10882)+E(f557(x10881,x10883,x10884,x10885,x10886),f557(x10882,x10883,x10884,x10885,x10886))
% 22.40/22.32 [1089]~E(x10891,x10892)+E(f557(x10893,x10891,x10894,x10895,x10896),f557(x10893,x10892,x10894,x10895,x10896))
% 22.40/22.32 [1090]~E(x10901,x10902)+E(f557(x10903,x10904,x10901,x10905,x10906),f557(x10903,x10904,x10902,x10905,x10906))
% 22.40/22.32 [1091]~E(x10911,x10912)+E(f557(x10913,x10914,x10915,x10911,x10916),f557(x10913,x10914,x10915,x10912,x10916))
% 22.40/22.32 [1092]~E(x10921,x10922)+E(f557(x10923,x10924,x10925,x10926,x10921),f557(x10923,x10924,x10925,x10926,x10922))
% 22.40/22.32 [1093]~E(x10931,x10932)+E(f329(x10931,x10933),f329(x10932,x10933))
% 22.40/22.32 [1094]~E(x10941,x10942)+E(f329(x10943,x10941),f329(x10943,x10942))
% 22.40/22.32 [1095]~E(x10951,x10952)+E(f265(x10951,x10953,x10954,x10955),f265(x10952,x10953,x10954,x10955))
% 22.40/22.32 [1096]~E(x10961,x10962)+E(f265(x10963,x10961,x10964,x10965),f265(x10963,x10962,x10964,x10965))
% 22.40/22.32 [1097]~E(x10971,x10972)+E(f265(x10973,x10974,x10971,x10975),f265(x10973,x10974,x10972,x10975))
% 22.40/22.32 [1098]~E(x10981,x10982)+E(f265(x10983,x10984,x10985,x10981),f265(x10983,x10984,x10985,x10982))
% 22.40/22.32 [1099]~E(x10991,x10992)+E(f680(x10991,x10993),f680(x10992,x10993))
% 22.40/22.32 [1100]~E(x11001,x11002)+E(f680(x11003,x11001),f680(x11003,x11002))
% 22.40/22.32 [1101]~E(x11011,x11012)+E(f715(x11011,x11013,x11014,x11015),f715(x11012,x11013,x11014,x11015))
% 22.40/22.32 [1102]~E(x11021,x11022)+E(f715(x11023,x11021,x11024,x11025),f715(x11023,x11022,x11024,x11025))
% 22.40/22.32 [1103]~E(x11031,x11032)+E(f715(x11033,x11034,x11031,x11035),f715(x11033,x11034,x11032,x11035))
% 22.40/22.32 [1104]~E(x11041,x11042)+E(f715(x11043,x11044,x11045,x11041),f715(x11043,x11044,x11045,x11042))
% 22.40/22.32 [1105]~E(x11051,x11052)+E(f38(x11051),f38(x11052))
% 22.40/22.32 [1106]~E(x11061,x11062)+E(f603(x11061,x11063,x11064,x11065),f603(x11062,x11063,x11064,x11065))
% 22.40/22.32 [1107]~E(x11071,x11072)+E(f603(x11073,x11071,x11074,x11075),f603(x11073,x11072,x11074,x11075))
% 22.40/22.32 [1108]~E(x11081,x11082)+E(f603(x11083,x11084,x11081,x11085),f603(x11083,x11084,x11082,x11085))
% 22.40/22.32 [1109]~E(x11091,x11092)+E(f603(x11093,x11094,x11095,x11091),f603(x11093,x11094,x11095,x11092))
% 22.40/22.32 [1110]~E(x11101,x11102)+E(f176(x11101,x11103,x11104),f176(x11102,x11103,x11104))
% 22.40/22.32 [1111]~E(x11111,x11112)+E(f176(x11113,x11111,x11114),f176(x11113,x11112,x11114))
% 22.40/22.32 [1112]~E(x11121,x11122)+E(f176(x11123,x11124,x11121),f176(x11123,x11124,x11122))
% 22.40/22.32 [1113]~E(x11131,x11132)+E(f241(x11131,x11133,x11134),f241(x11132,x11133,x11134))
% 22.40/22.32 [1114]~E(x11141,x11142)+E(f241(x11143,x11141,x11144),f241(x11143,x11142,x11144))
% 22.40/22.32 [1115]~E(x11151,x11152)+E(f241(x11153,x11154,x11151),f241(x11153,x11154,x11152))
% 22.40/22.32 [1116]~E(x11161,x11162)+E(f483(x11161,x11163,x11164),f483(x11162,x11163,x11164))
% 22.40/22.32 [1117]~E(x11171,x11172)+E(f483(x11173,x11171,x11174),f483(x11173,x11172,x11174))
% 22.40/22.32 [1118]~E(x11181,x11182)+E(f483(x11183,x11184,x11181),f483(x11183,x11184,x11182))
% 22.40/22.32 [1119]~E(x11191,x11192)+E(f856(x11191,x11193,x11194),f856(x11192,x11193,x11194))
% 22.40/22.32 [1120]~E(x11201,x11202)+E(f856(x11203,x11201,x11204),f856(x11203,x11202,x11204))
% 22.40/22.32 [1121]~E(x11211,x11212)+E(f856(x11213,x11214,x11211),f856(x11213,x11214,x11212))
% 22.40/22.32 [1122]~E(x11221,x11222)+E(f124(x11221,x11223),f124(x11222,x11223))
% 22.40/22.32 [1123]~E(x11231,x11232)+E(f124(x11233,x11231),f124(x11233,x11232))
% 22.40/22.32 [1124]~E(x11241,x11242)+E(f168(x11241,x11243,x11244),f168(x11242,x11243,x11244))
% 22.40/22.32 [1125]~E(x11251,x11252)+E(f168(x11253,x11251,x11254),f168(x11253,x11252,x11254))
% 22.40/22.32 [1126]~E(x11261,x11262)+E(f168(x11263,x11264,x11261),f168(x11263,x11264,x11262))
% 22.40/22.32 [1127]~E(x11271,x11272)+E(f81(x11271),f81(x11272))
% 22.40/22.32 [1128]~E(x11281,x11282)+E(f192(x11281,x11283),f192(x11282,x11283))
% 22.40/22.32 [1129]~E(x11291,x11292)+E(f192(x11293,x11291),f192(x11293,x11292))
% 22.40/22.32 [1130]~E(x11301,x11302)+E(f115(x11301),f115(x11302))
% 22.40/22.32 [1131]~E(x11311,x11312)+E(f422(x11311),f422(x11312))
% 22.40/22.32 [1132]~E(x11321,x11322)+E(f53(x11321,x11323,x11324,x11325),f53(x11322,x11323,x11324,x11325))
% 22.40/22.32 [1133]~E(x11331,x11332)+E(f53(x11333,x11331,x11334,x11335),f53(x11333,x11332,x11334,x11335))
% 22.40/22.32 [1134]~E(x11341,x11342)+E(f53(x11343,x11344,x11341,x11345),f53(x11343,x11344,x11342,x11345))
% 22.40/22.32 [1135]~E(x11351,x11352)+E(f53(x11353,x11354,x11355,x11351),f53(x11353,x11354,x11355,x11352))
% 22.40/22.32 [1136]~E(x11361,x11362)+E(f598(x11361,x11363,x11364,x11365,x11366),f598(x11362,x11363,x11364,x11365,x11366))
% 22.40/22.32 [1137]~E(x11371,x11372)+E(f598(x11373,x11371,x11374,x11375,x11376),f598(x11373,x11372,x11374,x11375,x11376))
% 22.40/22.32 [1138]~E(x11381,x11382)+E(f598(x11383,x11384,x11381,x11385,x11386),f598(x11383,x11384,x11382,x11385,x11386))
% 22.40/22.32 [1139]~E(x11391,x11392)+E(f598(x11393,x11394,x11395,x11391,x11396),f598(x11393,x11394,x11395,x11392,x11396))
% 22.40/22.32 [1140]~E(x11401,x11402)+E(f598(x11403,x11404,x11405,x11406,x11401),f598(x11403,x11404,x11405,x11406,x11402))
% 22.40/22.32 [1141]~E(x11411,x11412)+E(f541(x11411,x11413,x11414,x11415,x11416,x11417,x11418,x11419),f541(x11412,x11413,x11414,x11415,x11416,x11417,x11418,x11419))
% 22.40/22.32 [1142]~E(x11421,x11422)+E(f541(x11423,x11421,x11424,x11425,x11426,x11427,x11428,x11429),f541(x11423,x11422,x11424,x11425,x11426,x11427,x11428,x11429))
% 22.40/22.32 [1143]~E(x11431,x11432)+E(f541(x11433,x11434,x11431,x11435,x11436,x11437,x11438,x11439),f541(x11433,x11434,x11432,x11435,x11436,x11437,x11438,x11439))
% 22.40/22.32 [1144]~E(x11441,x11442)+E(f541(x11443,x11444,x11445,x11441,x11446,x11447,x11448,x11449),f541(x11443,x11444,x11445,x11442,x11446,x11447,x11448,x11449))
% 22.40/22.32 [1145]~E(x11451,x11452)+E(f541(x11453,x11454,x11455,x11456,x11451,x11457,x11458,x11459),f541(x11453,x11454,x11455,x11456,x11452,x11457,x11458,x11459))
% 22.40/22.32 [1146]~E(x11461,x11462)+E(f541(x11463,x11464,x11465,x11466,x11467,x11461,x11468,x11469),f541(x11463,x11464,x11465,x11466,x11467,x11462,x11468,x11469))
% 22.40/22.32 [1147]~E(x11471,x11472)+E(f541(x11473,x11474,x11475,x11476,x11477,x11478,x11471,x11479),f541(x11473,x11474,x11475,x11476,x11477,x11478,x11472,x11479))
% 22.40/22.32 [1148]~E(x11481,x11482)+E(f541(x11483,x11484,x11485,x11486,x11487,x11488,x11489,x11481),f541(x11483,x11484,x11485,x11486,x11487,x11488,x11489,x11482))
% 22.40/22.32 [1149]~E(x11491,x11492)+E(f599(x11491,x11493,x11494,x11495,x11496),f599(x11492,x11493,x11494,x11495,x11496))
% 22.40/22.32 [1150]~E(x11501,x11502)+E(f599(x11503,x11501,x11504,x11505,x11506),f599(x11503,x11502,x11504,x11505,x11506))
% 22.40/22.32 [1151]~E(x11511,x11512)+E(f599(x11513,x11514,x11511,x11515,x11516),f599(x11513,x11514,x11512,x11515,x11516))
% 22.40/22.32 [1152]~E(x11521,x11522)+E(f599(x11523,x11524,x11525,x11521,x11526),f599(x11523,x11524,x11525,x11522,x11526))
% 22.40/22.32 [1153]~E(x11531,x11532)+E(f599(x11533,x11534,x11535,x11536,x11531),f599(x11533,x11534,x11535,x11536,x11532))
% 22.40/22.32 [1154]~E(x11541,x11542)+E(f473(x11541,x11543,x11544,x11545,x11546),f473(x11542,x11543,x11544,x11545,x11546))
% 22.40/22.32 [1155]~E(x11551,x11552)+E(f473(x11553,x11551,x11554,x11555,x11556),f473(x11553,x11552,x11554,x11555,x11556))
% 22.40/22.32 [1156]~E(x11561,x11562)+E(f473(x11563,x11564,x11561,x11565,x11566),f473(x11563,x11564,x11562,x11565,x11566))
% 22.40/22.32 [1157]~E(x11571,x11572)+E(f473(x11573,x11574,x11575,x11571,x11576),f473(x11573,x11574,x11575,x11572,x11576))
% 22.40/22.32 [1158]~E(x11581,x11582)+E(f473(x11583,x11584,x11585,x11586,x11581),f473(x11583,x11584,x11585,x11586,x11582))
% 22.40/22.32 [1159]~E(x11591,x11592)+E(f127(x11591),f127(x11592))
% 22.40/22.32 [1160]~E(x11601,x11602)+E(f213(x11601,x11603,x11604,x11605),f213(x11602,x11603,x11604,x11605))
% 22.40/22.32 [1161]~E(x11611,x11612)+E(f213(x11613,x11611,x11614,x11615),f213(x11613,x11612,x11614,x11615))
% 22.40/22.32 [1162]~E(x11621,x11622)+E(f213(x11623,x11624,x11621,x11625),f213(x11623,x11624,x11622,x11625))
% 22.40/22.32 [1163]~E(x11631,x11632)+E(f213(x11633,x11634,x11635,x11631),f213(x11633,x11634,x11635,x11632))
% 22.40/22.32 [1164]~E(x11641,x11642)+E(f121(x11641),f121(x11642))
% 22.40/22.32 [1165]~E(x11651,x11652)+E(f662(x11651,x11653),f662(x11652,x11653))
% 22.40/22.32 [1166]~E(x11661,x11662)+E(f662(x11663,x11661),f662(x11663,x11662))
% 22.40/22.32 [1167]~E(x11671,x11672)+E(f223(x11671,x11673,x11674),f223(x11672,x11673,x11674))
% 22.40/22.32 [1168]~E(x11681,x11682)+E(f223(x11683,x11681,x11684),f223(x11683,x11682,x11684))
% 22.40/22.32 [1169]~E(x11691,x11692)+E(f223(x11693,x11694,x11691),f223(x11693,x11694,x11692))
% 22.40/22.32 [1170]~E(x11701,x11702)+E(f777(x11701,x11703,x11704,x11705,x11706,x11707,x11708),f777(x11702,x11703,x11704,x11705,x11706,x11707,x11708))
% 22.40/22.32 [1171]~E(x11711,x11712)+E(f777(x11713,x11711,x11714,x11715,x11716,x11717,x11718),f777(x11713,x11712,x11714,x11715,x11716,x11717,x11718))
% 22.40/22.32 [1172]~E(x11721,x11722)+E(f777(x11723,x11724,x11721,x11725,x11726,x11727,x11728),f777(x11723,x11724,x11722,x11725,x11726,x11727,x11728))
% 22.40/22.32 [1173]~E(x11731,x11732)+E(f777(x11733,x11734,x11735,x11731,x11736,x11737,x11738),f777(x11733,x11734,x11735,x11732,x11736,x11737,x11738))
% 22.40/22.32 [1174]~E(x11741,x11742)+E(f777(x11743,x11744,x11745,x11746,x11741,x11747,x11748),f777(x11743,x11744,x11745,x11746,x11742,x11747,x11748))
% 22.40/22.32 [1175]~E(x11751,x11752)+E(f777(x11753,x11754,x11755,x11756,x11757,x11751,x11758),f777(x11753,x11754,x11755,x11756,x11757,x11752,x11758))
% 22.40/22.32 [1176]~E(x11761,x11762)+E(f777(x11763,x11764,x11765,x11766,x11767,x11768,x11761),f777(x11763,x11764,x11765,x11766,x11767,x11768,x11762))
% 22.40/22.32 [1177]~E(x11771,x11772)+E(f685(x11771,x11773,x11774,x11775,x11776),f685(x11772,x11773,x11774,x11775,x11776))
% 22.40/22.32 [1178]~E(x11781,x11782)+E(f685(x11783,x11781,x11784,x11785,x11786),f685(x11783,x11782,x11784,x11785,x11786))
% 22.40/22.32 [1179]~E(x11791,x11792)+E(f685(x11793,x11794,x11791,x11795,x11796),f685(x11793,x11794,x11792,x11795,x11796))
% 22.40/22.32 [1180]~E(x11801,x11802)+E(f685(x11803,x11804,x11805,x11801,x11806),f685(x11803,x11804,x11805,x11802,x11806))
% 22.40/22.32 [1181]~E(x11811,x11812)+E(f685(x11813,x11814,x11815,x11816,x11811),f685(x11813,x11814,x11815,x11816,x11812))
% 22.40/22.32 [1182]~E(x11821,x11822)+E(f118(x11821,x11823,x11824),f118(x11822,x11823,x11824))
% 22.40/22.32 [1183]~E(x11831,x11832)+E(f118(x11833,x11831,x11834),f118(x11833,x11832,x11834))
% 22.40/22.32 [1184]~E(x11841,x11842)+E(f118(x11843,x11844,x11841),f118(x11843,x11844,x11842))
% 22.40/22.32 [1185]~E(x11851,x11852)+E(f587(x11851,x11853,x11854),f587(x11852,x11853,x11854))
% 22.40/22.32 [1186]~E(x11861,x11862)+E(f587(x11863,x11861,x11864),f587(x11863,x11862,x11864))
% 22.40/22.32 [1187]~E(x11871,x11872)+E(f587(x11873,x11874,x11871),f587(x11873,x11874,x11872))
% 22.40/22.32 [1188]~E(x11881,x11882)+E(f158(x11881,x11883,x11884),f158(x11882,x11883,x11884))
% 22.40/22.32 [1189]~E(x11891,x11892)+E(f158(x11893,x11891,x11894),f158(x11893,x11892,x11894))
% 22.40/22.32 [1190]~E(x11901,x11902)+E(f158(x11903,x11904,x11901),f158(x11903,x11904,x11902))
% 22.40/22.32 [1191]~E(x11911,x11912)+E(f618(x11911,x11913,x11914,x11915,x11916),f618(x11912,x11913,x11914,x11915,x11916))
% 22.40/22.32 [1192]~E(x11921,x11922)+E(f618(x11923,x11921,x11924,x11925,x11926),f618(x11923,x11922,x11924,x11925,x11926))
% 22.40/22.32 [1193]~E(x11931,x11932)+E(f618(x11933,x11934,x11931,x11935,x11936),f618(x11933,x11934,x11932,x11935,x11936))
% 22.40/22.32 [1194]~E(x11941,x11942)+E(f618(x11943,x11944,x11945,x11941,x11946),f618(x11943,x11944,x11945,x11942,x11946))
% 22.40/22.32 [1195]~E(x11951,x11952)+E(f618(x11953,x11954,x11955,x11956,x11951),f618(x11953,x11954,x11955,x11956,x11952))
% 22.40/22.32 [1196]~E(x11961,x11962)+E(f651(x11961,x11963,x11964,x11965),f651(x11962,x11963,x11964,x11965))
% 22.40/22.32 [1197]~E(x11971,x11972)+E(f651(x11973,x11971,x11974,x11975),f651(x11973,x11972,x11974,x11975))
% 22.40/22.32 [1198]~E(x11981,x11982)+E(f651(x11983,x11984,x11981,x11985),f651(x11983,x11984,x11982,x11985))
% 22.40/22.32 [1199]~E(x11991,x11992)+E(f651(x11993,x11994,x11995,x11991),f651(x11993,x11994,x11995,x11992))
% 22.40/22.32 [1200]~E(x12001,x12002)+E(f858(x12001,x12003,x12004),f858(x12002,x12003,x12004))
% 22.40/22.32 [1201]~E(x12011,x12012)+E(f858(x12013,x12011,x12014),f858(x12013,x12012,x12014))
% 22.40/22.32 [1202]~E(x12021,x12022)+E(f858(x12023,x12024,x12021),f858(x12023,x12024,x12022))
% 22.40/22.32 [1203]~E(x12031,x12032)+E(f356(x12031,x12033,x12034,x12035,x12036),f356(x12032,x12033,x12034,x12035,x12036))
% 22.40/22.32 [1204]~E(x12041,x12042)+E(f356(x12043,x12041,x12044,x12045,x12046),f356(x12043,x12042,x12044,x12045,x12046))
% 22.40/22.32 [1205]~E(x12051,x12052)+E(f356(x12053,x12054,x12051,x12055,x12056),f356(x12053,x12054,x12052,x12055,x12056))
% 22.40/22.32 [1206]~E(x12061,x12062)+E(f356(x12063,x12064,x12065,x12061,x12066),f356(x12063,x12064,x12065,x12062,x12066))
% 22.40/22.32 [1207]~E(x12071,x12072)+E(f356(x12073,x12074,x12075,x12076,x12071),f356(x12073,x12074,x12075,x12076,x12072))
% 22.40/22.32 [1208]~E(x12081,x12082)+E(f809(x12081,x12083,x12084),f809(x12082,x12083,x12084))
% 22.40/22.32 [1209]~E(x12091,x12092)+E(f809(x12093,x12091,x12094),f809(x12093,x12092,x12094))
% 22.40/22.32 [1210]~E(x12101,x12102)+E(f809(x12103,x12104,x12101),f809(x12103,x12104,x12102))
% 22.40/22.32 [1211]~E(x12111,x12112)+E(f479(x12111,x12113,x12114),f479(x12112,x12113,x12114))
% 22.40/22.32 [1212]~E(x12121,x12122)+E(f479(x12123,x12121,x12124),f479(x12123,x12122,x12124))
% 22.40/22.32 [1213]~E(x12131,x12132)+E(f479(x12133,x12134,x12131),f479(x12133,x12134,x12132))
% 22.40/22.32 [1214]~E(x12141,x12142)+E(f838(x12141,x12143,x12144,x12145,x12146,x12147,x12148,x12149),f838(x12142,x12143,x12144,x12145,x12146,x12147,x12148,x12149))
% 22.40/22.32 [1215]~E(x12151,x12152)+E(f838(x12153,x12151,x12154,x12155,x12156,x12157,x12158,x12159),f838(x12153,x12152,x12154,x12155,x12156,x12157,x12158,x12159))
% 22.40/22.32 [1216]~E(x12161,x12162)+E(f838(x12163,x12164,x12161,x12165,x12166,x12167,x12168,x12169),f838(x12163,x12164,x12162,x12165,x12166,x12167,x12168,x12169))
% 22.40/22.32 [1217]~E(x12171,x12172)+E(f838(x12173,x12174,x12175,x12171,x12176,x12177,x12178,x12179),f838(x12173,x12174,x12175,x12172,x12176,x12177,x12178,x12179))
% 22.40/22.32 [1218]~E(x12181,x12182)+E(f838(x12183,x12184,x12185,x12186,x12181,x12187,x12188,x12189),f838(x12183,x12184,x12185,x12186,x12182,x12187,x12188,x12189))
% 22.40/22.32 [1219]~E(x12191,x12192)+E(f838(x12193,x12194,x12195,x12196,x12197,x12191,x12198,x12199),f838(x12193,x12194,x12195,x12196,x12197,x12192,x12198,x12199))
% 22.40/22.32 [1220]~E(x12201,x12202)+E(f838(x12203,x12204,x12205,x12206,x12207,x12208,x12201,x12209),f838(x12203,x12204,x12205,x12206,x12207,x12208,x12202,x12209))
% 22.40/22.32 [1221]~E(x12211,x12212)+E(f838(x12213,x12214,x12215,x12216,x12217,x12218,x12219,x12211),f838(x12213,x12214,x12215,x12216,x12217,x12218,x12219,x12212))
% 22.40/22.32 [1222]~E(x12221,x12222)+E(f430(x12221,x12223),f430(x12222,x12223))
% 22.40/22.32 [1223]~E(x12231,x12232)+E(f430(x12233,x12231),f430(x12233,x12232))
% 22.40/22.32 [1224]~E(x12241,x12242)+E(f165(x12241,x12243,x12244),f165(x12242,x12243,x12244))
% 22.40/22.32 [1225]~E(x12251,x12252)+E(f165(x12253,x12251,x12254),f165(x12253,x12252,x12254))
% 22.40/22.32 [1226]~E(x12261,x12262)+E(f165(x12263,x12264,x12261),f165(x12263,x12264,x12262))
% 22.40/22.32 [1227]~E(x12271,x12272)+E(f437(x12271,x12273),f437(x12272,x12273))
% 22.40/22.32 [1228]~E(x12281,x12282)+E(f437(x12283,x12281),f437(x12283,x12282))
% 22.40/22.32 [1229]~E(x12291,x12292)+E(f800(x12291,x12293,x12294),f800(x12292,x12293,x12294))
% 22.40/22.32 [1230]~E(x12301,x12302)+E(f800(x12303,x12301,x12304),f800(x12303,x12302,x12304))
% 22.40/22.32 [1231]~E(x12311,x12312)+E(f800(x12313,x12314,x12311),f800(x12313,x12314,x12312))
% 22.40/22.32 [1232]~E(x12321,x12322)+E(f67(x12321,x12323),f67(x12322,x12323))
% 22.40/22.32 [1233]~E(x12331,x12332)+E(f67(x12333,x12331),f67(x12333,x12332))
% 22.40/22.32 [1234]~E(x12341,x12342)+E(f108(x12341,x12343,x12344),f108(x12342,x12343,x12344))
% 22.40/22.32 [1235]~E(x12351,x12352)+E(f108(x12353,x12351,x12354),f108(x12353,x12352,x12354))
% 22.40/22.32 [1236]~E(x12361,x12362)+E(f108(x12363,x12364,x12361),f108(x12363,x12364,x12362))
% 22.40/22.32 [1237]~E(x12371,x12372)+E(f794(x12371,x12373),f794(x12372,x12373))
% 22.40/22.32 [1238]~E(x12381,x12382)+E(f794(x12383,x12381),f794(x12383,x12382))
% 22.40/22.32 [1239]~E(x12391,x12392)+E(f841(x12391,x12393,x12394,x12395,x12396,x12397),f841(x12392,x12393,x12394,x12395,x12396,x12397))
% 22.40/22.32 [1240]~E(x12401,x12402)+E(f841(x12403,x12401,x12404,x12405,x12406,x12407),f841(x12403,x12402,x12404,x12405,x12406,x12407))
% 22.40/22.32 [1241]~E(x12411,x12412)+E(f841(x12413,x12414,x12411,x12415,x12416,x12417),f841(x12413,x12414,x12412,x12415,x12416,x12417))
% 22.40/22.32 [1242]~E(x12421,x12422)+E(f841(x12423,x12424,x12425,x12421,x12426,x12427),f841(x12423,x12424,x12425,x12422,x12426,x12427))
% 22.40/22.32 [1243]~E(x12431,x12432)+E(f841(x12433,x12434,x12435,x12436,x12431,x12437),f841(x12433,x12434,x12435,x12436,x12432,x12437))
% 22.40/22.32 [1244]~E(x12441,x12442)+E(f841(x12443,x12444,x12445,x12446,x12447,x12441),f841(x12443,x12444,x12445,x12446,x12447,x12442))
% 22.40/22.32 [1245]~E(x12451,x12452)+E(f353(x12451,x12453,x12454),f353(x12452,x12453,x12454))
% 22.40/22.32 [1246]~E(x12461,x12462)+E(f353(x12463,x12461,x12464),f353(x12463,x12462,x12464))
% 22.40/22.32 [1247]~E(x12471,x12472)+E(f353(x12473,x12474,x12471),f353(x12473,x12474,x12472))
% 22.40/22.32 [1248]~E(x12481,x12482)+E(f763(x12481,x12483,x12484),f763(x12482,x12483,x12484))
% 22.40/22.32 [1249]~E(x12491,x12492)+E(f763(x12493,x12491,x12494),f763(x12493,x12492,x12494))
% 22.40/22.32 [1250]~E(x12501,x12502)+E(f763(x12503,x12504,x12501),f763(x12503,x12504,x12502))
% 22.40/22.32 [1251]~E(x12511,x12512)+E(f633(x12511,x12513),f633(x12512,x12513))
% 22.40/22.32 [1252]~E(x12521,x12522)+E(f633(x12523,x12521),f633(x12523,x12522))
% 22.40/22.32 [1253]~E(x12531,x12532)+E(f401(x12531,x12533),f401(x12532,x12533))
% 22.40/22.32 [1254]~E(x12541,x12542)+E(f401(x12543,x12541),f401(x12543,x12542))
% 22.40/22.32 [1255]~E(x12551,x12552)+E(f837(x12551,x12553,x12554,x12555,x12556,x12557,x12558,x12559),f837(x12552,x12553,x12554,x12555,x12556,x12557,x12558,x12559))
% 22.40/22.32 [1256]~E(x12561,x12562)+E(f837(x12563,x12561,x12564,x12565,x12566,x12567,x12568,x12569),f837(x12563,x12562,x12564,x12565,x12566,x12567,x12568,x12569))
% 22.40/22.32 [1257]~E(x12571,x12572)+E(f837(x12573,x12574,x12571,x12575,x12576,x12577,x12578,x12579),f837(x12573,x12574,x12572,x12575,x12576,x12577,x12578,x12579))
% 22.40/22.32 [1258]~E(x12581,x12582)+E(f837(x12583,x12584,x12585,x12581,x12586,x12587,x12588,x12589),f837(x12583,x12584,x12585,x12582,x12586,x12587,x12588,x12589))
% 22.40/22.32 [1259]~E(x12591,x12592)+E(f837(x12593,x12594,x12595,x12596,x12591,x12597,x12598,x12599),f837(x12593,x12594,x12595,x12596,x12592,x12597,x12598,x12599))
% 22.40/22.32 [1260]~E(x12601,x12602)+E(f837(x12603,x12604,x12605,x12606,x12607,x12601,x12608,x12609),f837(x12603,x12604,x12605,x12606,x12607,x12602,x12608,x12609))
% 22.40/22.32 [1261]~E(x12611,x12612)+E(f837(x12613,x12614,x12615,x12616,x12617,x12618,x12611,x12619),f837(x12613,x12614,x12615,x12616,x12617,x12618,x12612,x12619))
% 22.40/22.32 [1262]~E(x12621,x12622)+E(f837(x12623,x12624,x12625,x12626,x12627,x12628,x12629,x12621),f837(x12623,x12624,x12625,x12626,x12627,x12628,x12629,x12622))
% 22.40/22.32 [1263]~E(x12631,x12632)+E(f378(x12631,x12633,x12634,x12635),f378(x12632,x12633,x12634,x12635))
% 22.40/22.32 [1264]~E(x12641,x12642)+E(f378(x12643,x12641,x12644,x12645),f378(x12643,x12642,x12644,x12645))
% 22.40/22.32 [1265]~E(x12651,x12652)+E(f378(x12653,x12654,x12651,x12655),f378(x12653,x12654,x12652,x12655))
% 22.40/22.32 [1266]~E(x12661,x12662)+E(f378(x12663,x12664,x12665,x12661),f378(x12663,x12664,x12665,x12662))
% 22.40/22.32 [1267]~E(x12671,x12672)+E(f616(x12671,x12673,x12674),f616(x12672,x12673,x12674))
% 22.40/22.32 [1268]~E(x12681,x12682)+E(f616(x12683,x12681,x12684),f616(x12683,x12682,x12684))
% 22.40/22.32 [1269]~E(x12691,x12692)+E(f616(x12693,x12694,x12691),f616(x12693,x12694,x12692))
% 22.40/22.32 [1270]~E(x12701,x12702)+E(f290(x12701,x12703,x12704),f290(x12702,x12703,x12704))
% 22.40/22.32 [1271]~E(x12711,x12712)+E(f290(x12713,x12711,x12714),f290(x12713,x12712,x12714))
% 22.40/22.32 [1272]~E(x12721,x12722)+E(f290(x12723,x12724,x12721),f290(x12723,x12724,x12722))
% 22.40/22.32 [1273]~E(x12731,x12732)+E(f189(x12731,x12733,x12734,x12735),f189(x12732,x12733,x12734,x12735))
% 22.40/22.32 [1274]~E(x12741,x12742)+E(f189(x12743,x12741,x12744,x12745),f189(x12743,x12742,x12744,x12745))
% 22.40/22.32 [1275]~E(x12751,x12752)+E(f189(x12753,x12754,x12751,x12755),f189(x12753,x12754,x12752,x12755))
% 22.40/22.32 [1276]~E(x12761,x12762)+E(f189(x12763,x12764,x12765,x12761),f189(x12763,x12764,x12765,x12762))
% 22.40/22.32 [1277]~E(x12771,x12772)+E(f732(x12771,x12773,x12774,x12775,x12776),f732(x12772,x12773,x12774,x12775,x12776))
% 22.40/22.32 [1278]~E(x12781,x12782)+E(f732(x12783,x12781,x12784,x12785,x12786),f732(x12783,x12782,x12784,x12785,x12786))
% 22.40/22.32 [1279]~E(x12791,x12792)+E(f732(x12793,x12794,x12791,x12795,x12796),f732(x12793,x12794,x12792,x12795,x12796))
% 22.40/22.32 [1280]~E(x12801,x12802)+E(f732(x12803,x12804,x12805,x12801,x12806),f732(x12803,x12804,x12805,x12802,x12806))
% 22.40/22.32 [1281]~E(x12811,x12812)+E(f732(x12813,x12814,x12815,x12816,x12811),f732(x12813,x12814,x12815,x12816,x12812))
% 22.40/22.32 [1282]~E(x12821,x12822)+E(f514(x12821),f514(x12822))
% 22.40/22.32 [1283]~E(x12831,x12832)+E(f819(x12831,x12833,x12834),f819(x12832,x12833,x12834))
% 22.40/22.32 [1284]~E(x12841,x12842)+E(f819(x12843,x12841,x12844),f819(x12843,x12842,x12844))
% 22.40/22.32 [1285]~E(x12851,x12852)+E(f819(x12853,x12854,x12851),f819(x12853,x12854,x12852))
% 22.40/22.32 [1286]~E(x12861,x12862)+E(f772(x12861,x12863,x12864,x12865),f772(x12862,x12863,x12864,x12865))
% 22.40/22.32 [1287]~E(x12871,x12872)+E(f772(x12873,x12871,x12874,x12875),f772(x12873,x12872,x12874,x12875))
% 22.40/22.32 [1288]~E(x12881,x12882)+E(f772(x12883,x12884,x12881,x12885),f772(x12883,x12884,x12882,x12885))
% 22.40/22.32 [1289]~E(x12891,x12892)+E(f772(x12893,x12894,x12895,x12891),f772(x12893,x12894,x12895,x12892))
% 22.40/22.32 [1290]~E(x12901,x12902)+E(f652(x12901,x12903,x12904),f652(x12902,x12903,x12904))
% 22.40/22.32 [1291]~E(x12911,x12912)+E(f652(x12913,x12911,x12914),f652(x12913,x12912,x12914))
% 22.40/22.32 [1292]~E(x12921,x12922)+E(f652(x12923,x12924,x12921),f652(x12923,x12924,x12922))
% 22.40/22.32 [1293]~E(x12931,x12932)+E(f110(x12931,x12933,x12934),f110(x12932,x12933,x12934))
% 22.40/22.32 [1294]~E(x12941,x12942)+E(f110(x12943,x12941,x12944),f110(x12943,x12942,x12944))
% 22.40/22.32 [1295]~E(x12951,x12952)+E(f110(x12953,x12954,x12951),f110(x12953,x12954,x12952))
% 22.40/22.32 [1296]~E(x12961,x12962)+E(f586(x12961,x12963,x12964),f586(x12962,x12963,x12964))
% 22.40/22.32 [1297]~E(x12971,x12972)+E(f586(x12973,x12971,x12974),f586(x12973,x12972,x12974))
% 22.40/22.32 [1298]~E(x12981,x12982)+E(f586(x12983,x12984,x12981),f586(x12983,x12984,x12982))
% 22.40/22.32 [1299]~E(x12991,x12992)+E(f133(x12991),f133(x12992))
% 22.40/22.32 [1300]~E(x13001,x13002)+E(f359(x13001,x13003,x13004,x13005,x13006),f359(x13002,x13003,x13004,x13005,x13006))
% 22.40/22.32 [1301]~E(x13011,x13012)+E(f359(x13013,x13011,x13014,x13015,x13016),f359(x13013,x13012,x13014,x13015,x13016))
% 22.40/22.32 [1302]~E(x13021,x13022)+E(f359(x13023,x13024,x13021,x13025,x13026),f359(x13023,x13024,x13022,x13025,x13026))
% 22.40/22.32 [1303]~E(x13031,x13032)+E(f359(x13033,x13034,x13035,x13031,x13036),f359(x13033,x13034,x13035,x13032,x13036))
% 22.40/22.32 [1304]~E(x13041,x13042)+E(f359(x13043,x13044,x13045,x13046,x13041),f359(x13043,x13044,x13045,x13046,x13042))
% 22.40/22.32 [1305]~E(x13051,x13052)+E(f485(x13051,x13053,x13054),f485(x13052,x13053,x13054))
% 22.40/22.32 [1306]~E(x13061,x13062)+E(f485(x13063,x13061,x13064),f485(x13063,x13062,x13064))
% 22.40/22.32 [1307]~E(x13071,x13072)+E(f485(x13073,x13074,x13071),f485(x13073,x13074,x13072))
% 22.40/22.32 [1308]~E(x13081,x13082)+E(f758(x13081,x13083,x13084,x13085),f758(x13082,x13083,x13084,x13085))
% 22.40/22.32 [1309]~E(x13091,x13092)+E(f758(x13093,x13091,x13094,x13095),f758(x13093,x13092,x13094,x13095))
% 22.40/22.32 [1310]~E(x13101,x13102)+E(f758(x13103,x13104,x13101,x13105),f758(x13103,x13104,x13102,x13105))
% 22.40/22.32 [1311]~E(x13111,x13112)+E(f758(x13113,x13114,x13115,x13111),f758(x13113,x13114,x13115,x13112))
% 22.40/22.32 [1312]~E(x13121,x13122)+E(f425(x13121),f425(x13122))
% 22.40/22.32 [1313]~E(x13131,x13132)+E(f370(x13131,x13133,x13134,x13135),f370(x13132,x13133,x13134,x13135))
% 22.40/22.32 [1314]~E(x13141,x13142)+E(f370(x13143,x13141,x13144,x13145),f370(x13143,x13142,x13144,x13145))
% 22.40/22.32 [1315]~E(x13151,x13152)+E(f370(x13153,x13154,x13151,x13155),f370(x13153,x13154,x13152,x13155))
% 22.40/22.32 [1316]~E(x13161,x13162)+E(f370(x13163,x13164,x13165,x13161),f370(x13163,x13164,x13165,x13162))
% 22.40/22.32 [1317]~E(x13171,x13172)+E(f792(x13171,x13173),f792(x13172,x13173))
% 22.40/22.32 [1318]~E(x13181,x13182)+E(f792(x13183,x13181),f792(x13183,x13182))
% 22.40/22.32 [1319]~E(x13191,x13192)+E(f868(x13191,x13193,x13194,x13195),f868(x13192,x13193,x13194,x13195))
% 22.40/22.32 [1320]~E(x13201,x13202)+E(f868(x13203,x13201,x13204,x13205),f868(x13203,x13202,x13204,x13205))
% 22.40/22.32 [1321]~E(x13211,x13212)+E(f868(x13213,x13214,x13211,x13215),f868(x13213,x13214,x13212,x13215))
% 22.40/22.32 [1322]~E(x13221,x13222)+E(f868(x13223,x13224,x13225,x13221),f868(x13223,x13224,x13225,x13222))
% 22.40/22.32 [1323]~E(x13231,x13232)+E(f524(x13231,x13233,x13234),f524(x13232,x13233,x13234))
% 22.40/22.32 [1324]~E(x13241,x13242)+E(f524(x13243,x13241,x13244),f524(x13243,x13242,x13244))
% 22.40/22.32 [1325]~E(x13251,x13252)+E(f524(x13253,x13254,x13251),f524(x13253,x13254,x13252))
% 22.40/22.32 [1326]~E(x13261,x13262)+E(f901(x13261,x13263,x13264,x13265,x13266),f901(x13262,x13263,x13264,x13265,x13266))
% 22.40/22.32 [1327]~E(x13271,x13272)+E(f901(x13273,x13271,x13274,x13275,x13276),f901(x13273,x13272,x13274,x13275,x13276))
% 22.40/22.32 [1328]~E(x13281,x13282)+E(f901(x13283,x13284,x13281,x13285,x13286),f901(x13283,x13284,x13282,x13285,x13286))
% 22.40/22.32 [1329]~E(x13291,x13292)+E(f901(x13293,x13294,x13295,x13291,x13296),f901(x13293,x13294,x13295,x13292,x13296))
% 22.40/22.32 [1330]~E(x13301,x13302)+E(f901(x13303,x13304,x13305,x13306,x13301),f901(x13303,x13304,x13305,x13306,x13302))
% 22.40/22.32 [1331]~E(x13311,x13312)+E(f408(x13311,x13313,x13314,x13315),f408(x13312,x13313,x13314,x13315))
% 22.40/22.32 [1332]~E(x13321,x13322)+E(f408(x13323,x13321,x13324,x13325),f408(x13323,x13322,x13324,x13325))
% 22.40/22.32 [1333]~E(x13331,x13332)+E(f408(x13333,x13334,x13331,x13335),f408(x13333,x13334,x13332,x13335))
% 22.40/22.32 [1334]~E(x13341,x13342)+E(f408(x13343,x13344,x13345,x13341),f408(x13343,x13344,x13345,x13342))
% 22.40/22.32 [1335]~E(x13351,x13352)+E(f116(x13351),f116(x13352))
% 22.40/22.32 [1336]~E(x13361,x13362)+E(f335(x13361,x13363,x13364),f335(x13362,x13363,x13364))
% 22.40/22.32 [1337]~E(x13371,x13372)+E(f335(x13373,x13371,x13374),f335(x13373,x13372,x13374))
% 22.40/22.32 [1338]~E(x13381,x13382)+E(f335(x13383,x13384,x13381),f335(x13383,x13384,x13382))
% 22.40/22.32 [1339]~E(x13391,x13392)+E(f240(x13391,x13393),f240(x13392,x13393))
% 22.40/22.32 [1340]~E(x13401,x13402)+E(f240(x13403,x13401),f240(x13403,x13402))
% 22.40/22.32 [1341]~E(x13411,x13412)+E(f767(x13411,x13413,x13414,x13415),f767(x13412,x13413,x13414,x13415))
% 22.40/22.32 [1342]~E(x13421,x13422)+E(f767(x13423,x13421,x13424,x13425),f767(x13423,x13422,x13424,x13425))
% 22.40/22.32 [1343]~E(x13431,x13432)+E(f767(x13433,x13434,x13431,x13435),f767(x13433,x13434,x13432,x13435))
% 22.40/22.32 [1344]~E(x13441,x13442)+E(f767(x13443,x13444,x13445,x13441),f767(x13443,x13444,x13445,x13442))
% 22.40/22.32 [1345]~E(x13451,x13452)+E(f719(x13451,x13453,x13454,x13455),f719(x13452,x13453,x13454,x13455))
% 22.40/22.32 [1346]~E(x13461,x13462)+E(f719(x13463,x13461,x13464,x13465),f719(x13463,x13462,x13464,x13465))
% 22.40/22.32 [1347]~E(x13471,x13472)+E(f719(x13473,x13474,x13471,x13475),f719(x13473,x13474,x13472,x13475))
% 22.40/22.32 [1348]~E(x13481,x13482)+E(f719(x13483,x13484,x13485,x13481),f719(x13483,x13484,x13485,x13482))
% 22.40/22.32 [1349]~E(x13491,x13492)+E(f393(x13491,x13493,x13494,x13495),f393(x13492,x13493,x13494,x13495))
% 22.40/22.32 [1350]~E(x13501,x13502)+E(f393(x13503,x13501,x13504,x13505),f393(x13503,x13502,x13504,x13505))
% 22.40/22.32 [1351]~E(x13511,x13512)+E(f393(x13513,x13514,x13511,x13515),f393(x13513,x13514,x13512,x13515))
% 22.40/22.32 [1352]~E(x13521,x13522)+E(f393(x13523,x13524,x13525,x13521),f393(x13523,x13524,x13525,x13522))
% 22.40/22.32 [1353]~E(x13531,x13532)+E(f611(x13531,x13533,x13534),f611(x13532,x13533,x13534))
% 22.40/22.32 [1354]~E(x13541,x13542)+E(f611(x13543,x13541,x13544),f611(x13543,x13542,x13544))
% 22.40/22.32 [1355]~E(x13551,x13552)+E(f611(x13553,x13554,x13551),f611(x13553,x13554,x13552))
% 22.40/22.32 [1356]~E(x13561,x13562)+E(f491(x13561,x13563),f491(x13562,x13563))
% 22.40/22.32 [1357]~E(x13571,x13572)+E(f491(x13573,x13571),f491(x13573,x13572))
% 22.40/22.32 [1358]~E(x13581,x13582)+E(f867(x13581,x13583,x13584),f867(x13582,x13583,x13584))
% 22.40/22.32 [1359]~E(x13591,x13592)+E(f867(x13593,x13591,x13594),f867(x13593,x13592,x13594))
% 22.40/22.32 [1360]~E(x13601,x13602)+E(f867(x13603,x13604,x13601),f867(x13603,x13604,x13602))
% 22.40/22.32 [1361]~E(x13611,x13612)+E(f203(x13611,x13613,x13614,x13615),f203(x13612,x13613,x13614,x13615))
% 22.40/22.32 [1362]~E(x13621,x13622)+E(f203(x13623,x13621,x13624,x13625),f203(x13623,x13622,x13624,x13625))
% 22.40/22.32 [1363]~E(x13631,x13632)+E(f203(x13633,x13634,x13631,x13635),f203(x13633,x13634,x13632,x13635))
% 22.40/22.32 [1364]~E(x13641,x13642)+E(f203(x13643,x13644,x13645,x13641),f203(x13643,x13644,x13645,x13642))
% 22.40/22.32 [1365]~E(x13651,x13652)+E(f871(x13651,x13653,x13654,x13655),f871(x13652,x13653,x13654,x13655))
% 22.40/22.32 [1366]~E(x13661,x13662)+E(f871(x13663,x13661,x13664,x13665),f871(x13663,x13662,x13664,x13665))
% 22.40/22.32 [1367]~E(x13671,x13672)+E(f871(x13673,x13674,x13671,x13675),f871(x13673,x13674,x13672,x13675))
% 22.40/22.32 [1368]~E(x13681,x13682)+E(f871(x13683,x13684,x13685,x13681),f871(x13683,x13684,x13685,x13682))
% 22.40/22.32 [1369]~E(x13691,x13692)+E(f612(x13691,x13693),f612(x13692,x13693))
% 22.40/22.32 [1370]~E(x13701,x13702)+E(f612(x13703,x13701),f612(x13703,x13702))
% 22.40/22.32 [1371]~E(x13711,x13712)+E(f584(x13711,x13713,x13714,x13715,x13716,x13717),f584(x13712,x13713,x13714,x13715,x13716,x13717))
% 22.40/22.32 [1372]~E(x13721,x13722)+E(f584(x13723,x13721,x13724,x13725,x13726,x13727),f584(x13723,x13722,x13724,x13725,x13726,x13727))
% 22.40/22.32 [1373]~E(x13731,x13732)+E(f584(x13733,x13734,x13731,x13735,x13736,x13737),f584(x13733,x13734,x13732,x13735,x13736,x13737))
% 22.40/22.32 [1374]~E(x13741,x13742)+E(f584(x13743,x13744,x13745,x13741,x13746,x13747),f584(x13743,x13744,x13745,x13742,x13746,x13747))
% 22.40/22.32 [1375]~E(x13751,x13752)+E(f584(x13753,x13754,x13755,x13756,x13751,x13757),f584(x13753,x13754,x13755,x13756,x13752,x13757))
% 22.40/22.32 [1376]~E(x13761,x13762)+E(f584(x13763,x13764,x13765,x13766,x13767,x13761),f584(x13763,x13764,x13765,x13766,x13767,x13762))
% 22.40/22.32 [1377]~E(x13771,x13772)+E(f548(x13771,x13773,x13774),f548(x13772,x13773,x13774))
% 22.40/22.32 [1378]~E(x13781,x13782)+E(f548(x13783,x13781,x13784),f548(x13783,x13782,x13784))
% 22.40/22.32 [1379]~E(x13791,x13792)+E(f548(x13793,x13794,x13791),f548(x13793,x13794,x13792))
% 22.40/22.32 [1380]~E(x13801,x13802)+E(f459(x13801,x13803,x13804),f459(x13802,x13803,x13804))
% 22.40/22.32 [1381]~E(x13811,x13812)+E(f459(x13813,x13811,x13814),f459(x13813,x13812,x13814))
% 22.40/22.32 [1382]~E(x13821,x13822)+E(f459(x13823,x13824,x13821),f459(x13823,x13824,x13822))
% 22.40/22.32 [1383]~E(x13831,x13832)+E(f596(x13831,x13833,x13834,x13835),f596(x13832,x13833,x13834,x13835))
% 22.40/22.32 [1384]~E(x13841,x13842)+E(f596(x13843,x13841,x13844,x13845),f596(x13843,x13842,x13844,x13845))
% 22.40/22.32 [1385]~E(x13851,x13852)+E(f596(x13853,x13854,x13851,x13855),f596(x13853,x13854,x13852,x13855))
% 22.40/22.32 [1386]~E(x13861,x13862)+E(f596(x13863,x13864,x13865,x13861),f596(x13863,x13864,x13865,x13862))
% 22.40/22.32 [1387]~E(x13871,x13872)+E(f891(x13871,x13873,x13874,x13875),f891(x13872,x13873,x13874,x13875))
% 22.40/22.32 [1388]~E(x13881,x13882)+E(f891(x13883,x13881,x13884,x13885),f891(x13883,x13882,x13884,x13885))
% 22.40/22.32 [1389]~E(x13891,x13892)+E(f891(x13893,x13894,x13891,x13895),f891(x13893,x13894,x13892,x13895))
% 22.40/22.32 [1390]~E(x13901,x13902)+E(f891(x13903,x13904,x13905,x13901),f891(x13903,x13904,x13905,x13902))
% 22.40/22.32 [1391]~E(x13911,x13912)+E(f582(x13911,x13913,x13914,x13915,x13916,x13917),f582(x13912,x13913,x13914,x13915,x13916,x13917))
% 22.40/22.32 [1392]~E(x13921,x13922)+E(f582(x13923,x13921,x13924,x13925,x13926,x13927),f582(x13923,x13922,x13924,x13925,x13926,x13927))
% 22.40/22.32 [1393]~E(x13931,x13932)+E(f582(x13933,x13934,x13931,x13935,x13936,x13937),f582(x13933,x13934,x13932,x13935,x13936,x13937))
% 22.40/22.32 [1394]~E(x13941,x13942)+E(f582(x13943,x13944,x13945,x13941,x13946,x13947),f582(x13943,x13944,x13945,x13942,x13946,x13947))
% 22.40/22.32 [1395]~E(x13951,x13952)+E(f582(x13953,x13954,x13955,x13956,x13951,x13957),f582(x13953,x13954,x13955,x13956,x13952,x13957))
% 22.40/22.32 [1396]~E(x13961,x13962)+E(f582(x13963,x13964,x13965,x13966,x13967,x13961),f582(x13963,x13964,x13965,x13966,x13967,x13962))
% 22.40/22.32 [1397]~E(x13971,x13972)+E(f187(x13971,x13973),f187(x13972,x13973))
% 22.40/22.32 [1398]~E(x13981,x13982)+E(f187(x13983,x13981),f187(x13983,x13982))
% 22.40/22.32 [1399]~E(x13991,x13992)+E(f484(x13991,x13993,x13994),f484(x13992,x13993,x13994))
% 22.40/22.32 [1400]~E(x14001,x14002)+E(f484(x14003,x14001,x14004),f484(x14003,x14002,x14004))
% 22.40/22.32 [1401]~E(x14011,x14012)+E(f484(x14013,x14014,x14011),f484(x14013,x14014,x14012))
% 22.40/22.32 [1402]~E(x14021,x14022)+E(f312(x14021,x14023,x14024,x14025),f312(x14022,x14023,x14024,x14025))
% 22.40/22.32 [1403]~E(x14031,x14032)+E(f312(x14033,x14031,x14034,x14035),f312(x14033,x14032,x14034,x14035))
% 22.40/22.32 [1404]~E(x14041,x14042)+E(f312(x14043,x14044,x14041,x14045),f312(x14043,x14044,x14042,x14045))
% 22.40/22.32 [1405]~E(x14051,x14052)+E(f312(x14053,x14054,x14055,x14051),f312(x14053,x14054,x14055,x14052))
% 22.40/22.32 [1406]~E(x14061,x14062)+E(f761(x14061,x14063,x14064,x14065),f761(x14062,x14063,x14064,x14065))
% 22.40/22.32 [1407]~E(x14071,x14072)+E(f761(x14073,x14071,x14074,x14075),f761(x14073,x14072,x14074,x14075))
% 22.40/22.32 [1408]~E(x14081,x14082)+E(f761(x14083,x14084,x14081,x14085),f761(x14083,x14084,x14082,x14085))
% 22.40/22.32 [1409]~E(x14091,x14092)+E(f761(x14093,x14094,x14095,x14091),f761(x14093,x14094,x14095,x14092))
% 22.40/22.32 [1410]~E(x14101,x14102)+E(f385(x14101,x14103,x14104,x14105),f385(x14102,x14103,x14104,x14105))
% 22.40/22.32 [1411]~E(x14111,x14112)+E(f385(x14113,x14111,x14114,x14115),f385(x14113,x14112,x14114,x14115))
% 22.40/22.32 [1412]~E(x14121,x14122)+E(f385(x14123,x14124,x14121,x14125),f385(x14123,x14124,x14122,x14125))
% 22.40/22.32 [1413]~E(x14131,x14132)+E(f385(x14133,x14134,x14135,x14131),f385(x14133,x14134,x14135,x14132))
% 22.40/22.32 [1414]~E(x14141,x14142)+E(f434(x14141,x14143),f434(x14142,x14143))
% 22.40/22.32 [1415]~E(x14151,x14152)+E(f434(x14153,x14151),f434(x14153,x14152))
% 22.40/22.32 [1416]~E(x14161,x14162)+E(f261(x14161,x14163),f261(x14162,x14163))
% 22.40/22.32 [1417]~E(x14171,x14172)+E(f261(x14173,x14171),f261(x14173,x14172))
% 22.40/22.32 [1418]~E(x14181,x14182)+E(f714(x14181,x14183,x14184,x14185),f714(x14182,x14183,x14184,x14185))
% 22.40/22.32 [1419]~E(x14191,x14192)+E(f714(x14193,x14191,x14194,x14195),f714(x14193,x14192,x14194,x14195))
% 22.40/22.32 [1420]~E(x14201,x14202)+E(f714(x14203,x14204,x14201,x14205),f714(x14203,x14204,x14202,x14205))
% 22.40/22.32 [1421]~E(x14211,x14212)+E(f714(x14213,x14214,x14215,x14211),f714(x14213,x14214,x14215,x14212))
% 22.40/22.32 [1422]~E(x14221,x14222)+E(f798(x14221),f798(x14222))
% 22.40/22.32 [1423]~E(x14231,x14232)+E(f791(x14231),f791(x14232))
% 22.40/22.32 [1424]~E(x14241,x14242)+E(f344(x14241,x14243),f344(x14242,x14243))
% 22.40/22.32 [1425]~E(x14251,x14252)+E(f344(x14253,x14251),f344(x14253,x14252))
% 22.40/22.32 [1426]~E(x14261,x14262)+E(f663(x14261,x14263,x14264),f663(x14262,x14263,x14264))
% 22.40/22.32 [1427]~E(x14271,x14272)+E(f663(x14273,x14271,x14274),f663(x14273,x14272,x14274))
% 22.40/22.32 [1428]~E(x14281,x14282)+E(f663(x14283,x14284,x14281),f663(x14283,x14284,x14282))
% 22.40/22.32 [1429]~E(x14291,x14292)+E(f376(x14291,x14293,x14294),f376(x14292,x14293,x14294))
% 22.40/22.32 [1430]~E(x14301,x14302)+E(f376(x14303,x14301,x14304),f376(x14303,x14302,x14304))
% 22.40/22.32 [1431]~E(x14311,x14312)+E(f376(x14313,x14314,x14311),f376(x14313,x14314,x14312))
% 22.40/22.32 [1432]~E(x14321,x14322)+E(f390(x14321,x14323,x14324,x14325),f390(x14322,x14323,x14324,x14325))
% 22.40/22.32 [1433]~E(x14331,x14332)+E(f390(x14333,x14331,x14334,x14335),f390(x14333,x14332,x14334,x14335))
% 22.40/22.32 [1434]~E(x14341,x14342)+E(f390(x14343,x14344,x14341,x14345),f390(x14343,x14344,x14342,x14345))
% 22.40/22.32 [1435]~E(x14351,x14352)+E(f390(x14353,x14354,x14355,x14351),f390(x14353,x14354,x14355,x14352))
% 22.40/22.32 [1436]~E(x14361,x14362)+E(f515(x14361),f515(x14362))
% 22.40/22.32 [1437]~E(x14371,x14372)+E(f825(x14371,x14373,x14374),f825(x14372,x14373,x14374))
% 22.40/22.32 [1438]~E(x14381,x14382)+E(f825(x14383,x14381,x14384),f825(x14383,x14382,x14384))
% 22.40/22.32 [1439]~E(x14391,x14392)+E(f825(x14393,x14394,x14391),f825(x14393,x14394,x14392))
% 22.40/22.32 [1440]~E(x14401,x14402)+E(f813(x14401,x14403),f813(x14402,x14403))
% 22.40/22.32 [1441]~E(x14411,x14412)+E(f813(x14413,x14411),f813(x14413,x14412))
% 22.40/22.32 [1442]~E(x14421,x14422)+E(f341(x14421,x14423,x14424,x14425),f341(x14422,x14423,x14424,x14425))
% 22.40/22.32 [1443]~E(x14431,x14432)+E(f341(x14433,x14431,x14434,x14435),f341(x14433,x14432,x14434,x14435))
% 22.40/22.32 [1444]~E(x14441,x14442)+E(f341(x14443,x14444,x14441,x14445),f341(x14443,x14444,x14442,x14445))
% 22.40/22.32 [1445]~E(x14451,x14452)+E(f341(x14453,x14454,x14455,x14451),f341(x14453,x14454,x14455,x14452))
% 22.40/22.32 [1446]~E(x14461,x14462)+E(f345(x14461,x14463,x14464),f345(x14462,x14463,x14464))
% 22.40/22.32 [1447]~E(x14471,x14472)+E(f345(x14473,x14471,x14474),f345(x14473,x14472,x14474))
% 22.40/22.32 [1448]~E(x14481,x14482)+E(f345(x14483,x14484,x14481),f345(x14483,x14484,x14482))
% 22.40/22.32 [1449]~E(x14491,x14492)+E(f699(x14491,x14493),f699(x14492,x14493))
% 22.40/22.32 [1450]~E(x14501,x14502)+E(f699(x14503,x14501),f699(x14503,x14502))
% 22.40/22.32 [1451]~E(x14511,x14512)+E(f237(x14511,x14513,x14514),f237(x14512,x14513,x14514))
% 22.40/22.32 [1452]~E(x14521,x14522)+E(f237(x14523,x14521,x14524),f237(x14523,x14522,x14524))
% 22.40/22.32 [1453]~E(x14531,x14532)+E(f237(x14533,x14534,x14531),f237(x14533,x14534,x14532))
% 22.40/22.32 [1454]~E(x14541,x14542)+E(f270(x14541),f270(x14542))
% 22.40/22.32 [1455]~E(x14551,x14552)+E(f822(x14551,x14553,x14554,x14555),f822(x14552,x14553,x14554,x14555))
% 22.40/22.32 [1456]~E(x14561,x14562)+E(f822(x14563,x14561,x14564,x14565),f822(x14563,x14562,x14564,x14565))
% 22.40/22.32 [1457]~E(x14571,x14572)+E(f822(x14573,x14574,x14571,x14575),f822(x14573,x14574,x14572,x14575))
% 22.40/22.32 [1458]~E(x14581,x14582)+E(f822(x14583,x14584,x14585,x14581),f822(x14583,x14584,x14585,x14582))
% 22.40/22.32 [1459]~E(x14591,x14592)+E(f511(x14591,x14593,x14594,x14595),f511(x14592,x14593,x14594,x14595))
% 22.40/22.32 [1460]~E(x14601,x14602)+E(f511(x14603,x14601,x14604,x14605),f511(x14603,x14602,x14604,x14605))
% 22.40/22.32 [1461]~E(x14611,x14612)+E(f511(x14613,x14614,x14611,x14615),f511(x14613,x14614,x14612,x14615))
% 22.40/22.32 [1462]~E(x14621,x14622)+E(f511(x14623,x14624,x14625,x14621),f511(x14623,x14624,x14625,x14622))
% 22.40/22.32 [1463]~E(x14631,x14632)+E(f836(x14631,x14633,x14634,x14635,x14636,x14637,x14638,x14639),f836(x14632,x14633,x14634,x14635,x14636,x14637,x14638,x14639))
% 22.40/22.32 [1464]~E(x14641,x14642)+E(f836(x14643,x14641,x14644,x14645,x14646,x14647,x14648,x14649),f836(x14643,x14642,x14644,x14645,x14646,x14647,x14648,x14649))
% 22.40/22.32 [1465]~E(x14651,x14652)+E(f836(x14653,x14654,x14651,x14655,x14656,x14657,x14658,x14659),f836(x14653,x14654,x14652,x14655,x14656,x14657,x14658,x14659))
% 22.40/22.32 [1466]~E(x14661,x14662)+E(f836(x14663,x14664,x14665,x14661,x14666,x14667,x14668,x14669),f836(x14663,x14664,x14665,x14662,x14666,x14667,x14668,x14669))
% 22.40/22.32 [1467]~E(x14671,x14672)+E(f836(x14673,x14674,x14675,x14676,x14671,x14677,x14678,x14679),f836(x14673,x14674,x14675,x14676,x14672,x14677,x14678,x14679))
% 22.40/22.32 [1468]~E(x14681,x14682)+E(f836(x14683,x14684,x14685,x14686,x14687,x14681,x14688,x14689),f836(x14683,x14684,x14685,x14686,x14687,x14682,x14688,x14689))
% 22.40/22.32 [1469]~E(x14691,x14692)+E(f836(x14693,x14694,x14695,x14696,x14697,x14698,x14691,x14699),f836(x14693,x14694,x14695,x14696,x14697,x14698,x14692,x14699))
% 22.40/22.32 [1470]~E(x14701,x14702)+E(f836(x14703,x14704,x14705,x14706,x14707,x14708,x14709,x14701),f836(x14703,x14704,x14705,x14706,x14707,x14708,x14709,x14702))
% 22.40/22.32 [1471]~E(x14711,x14712)+E(f426(x14711,x14713,x14714),f426(x14712,x14713,x14714))
% 22.40/22.32 [1472]~E(x14721,x14722)+E(f426(x14723,x14721,x14724),f426(x14723,x14722,x14724))
% 22.40/22.32 [1473]~E(x14731,x14732)+E(f426(x14733,x14734,x14731),f426(x14733,x14734,x14732))
% 22.40/22.32 [1474]~E(x14741,x14742)+E(f336(x14741,x14743,x14744,x14745),f336(x14742,x14743,x14744,x14745))
% 22.40/22.32 [1475]~E(x14751,x14752)+E(f336(x14753,x14751,x14754,x14755),f336(x14753,x14752,x14754,x14755))
% 22.40/22.32 [1476]~E(x14761,x14762)+E(f336(x14763,x14764,x14761,x14765),f336(x14763,x14764,x14762,x14765))
% 22.40/22.32 [1477]~E(x14771,x14772)+E(f336(x14773,x14774,x14775,x14771),f336(x14773,x14774,x14775,x14772))
% 22.40/22.32 [1478]~E(x14781,x14782)+E(f762(x14781,x14783,x14784),f762(x14782,x14783,x14784))
% 22.40/22.32 [1479]~E(x14791,x14792)+E(f762(x14793,x14791,x14794),f762(x14793,x14792,x14794))
% 22.40/22.32 [1480]~E(x14801,x14802)+E(f762(x14803,x14804,x14801),f762(x14803,x14804,x14802))
% 22.40/22.32 [1481]~E(x14811,x14812)+E(f636(x14811,x14813),f636(x14812,x14813))
% 22.40/22.32 [1482]~E(x14821,x14822)+E(f636(x14823,x14821),f636(x14823,x14822))
% 22.40/22.32 [1483]~E(x14831,x14832)+E(f644(x14831,x14833,x14834,x14835,x14836),f644(x14832,x14833,x14834,x14835,x14836))
% 22.40/22.32 [1484]~E(x14841,x14842)+E(f644(x14843,x14841,x14844,x14845,x14846),f644(x14843,x14842,x14844,x14845,x14846))
% 22.40/22.32 [1485]~E(x14851,x14852)+E(f644(x14853,x14854,x14851,x14855,x14856),f644(x14853,x14854,x14852,x14855,x14856))
% 22.40/22.32 [1486]~E(x14861,x14862)+E(f644(x14863,x14864,x14865,x14861,x14866),f644(x14863,x14864,x14865,x14862,x14866))
% 22.40/22.32 [1487]~E(x14871,x14872)+E(f644(x14873,x14874,x14875,x14876,x14871),f644(x14873,x14874,x14875,x14876,x14872))
% 22.40/22.32 [1488]~E(x14881,x14882)+E(f610(x14881,x14883,x14884),f610(x14882,x14883,x14884))
% 22.40/22.32 [1489]~E(x14891,x14892)+E(f610(x14893,x14891,x14894),f610(x14893,x14892,x14894))
% 22.40/22.32 [1490]~E(x14901,x14902)+E(f610(x14903,x14904,x14901),f610(x14903,x14904,x14902))
% 22.40/22.32 [1491]~E(x14911,x14912)+E(f420(x14911,x14913,x14914,x14915,x14916,x14917,x14918),f420(x14912,x14913,x14914,x14915,x14916,x14917,x14918))
% 22.40/22.32 [1492]~E(x14921,x14922)+E(f420(x14923,x14921,x14924,x14925,x14926,x14927,x14928),f420(x14923,x14922,x14924,x14925,x14926,x14927,x14928))
% 22.40/22.32 [1493]~E(x14931,x14932)+E(f420(x14933,x14934,x14931,x14935,x14936,x14937,x14938),f420(x14933,x14934,x14932,x14935,x14936,x14937,x14938))
% 22.40/22.32 [1494]~E(x14941,x14942)+E(f420(x14943,x14944,x14945,x14941,x14946,x14947,x14948),f420(x14943,x14944,x14945,x14942,x14946,x14947,x14948))
% 22.40/22.32 [1495]~E(x14951,x14952)+E(f420(x14953,x14954,x14955,x14956,x14951,x14957,x14958),f420(x14953,x14954,x14955,x14956,x14952,x14957,x14958))
% 22.40/22.32 [1496]~E(x14961,x14962)+E(f420(x14963,x14964,x14965,x14966,x14967,x14961,x14968),f420(x14963,x14964,x14965,x14966,x14967,x14962,x14968))
% 22.40/22.32 [1497]~E(x14971,x14972)+E(f420(x14973,x14974,x14975,x14976,x14977,x14978,x14971),f420(x14973,x14974,x14975,x14976,x14977,x14978,x14972))
% 22.40/22.32 [1498]~E(x14981,x14982)+E(f330(x14981,x14983),f330(x14982,x14983))
% 22.40/22.32 [1499]~E(x14991,x14992)+E(f330(x14993,x14991),f330(x14993,x14992))
% 22.40/22.32 [1500]~E(x15001,x15002)+E(f122(x15001,x15003,x15004,x15005),f122(x15002,x15003,x15004,x15005))
% 22.40/22.32 [1501]~E(x15011,x15012)+E(f122(x15013,x15011,x15014,x15015),f122(x15013,x15012,x15014,x15015))
% 22.40/22.32 [1502]~E(x15021,x15022)+E(f122(x15023,x15024,x15021,x15025),f122(x15023,x15024,x15022,x15025))
% 22.40/22.32 [1503]~E(x15031,x15032)+E(f122(x15033,x15034,x15035,x15031),f122(x15033,x15034,x15035,x15032))
% 22.40/22.32 [1504]~E(x15041,x15042)+E(f453(x15041,x15043,x15044),f453(x15042,x15043,x15044))
% 22.40/22.32 [1505]~E(x15051,x15052)+E(f453(x15053,x15051,x15054),f453(x15053,x15052,x15054))
% 22.40/22.32 [1506]~E(x15061,x15062)+E(f453(x15063,x15064,x15061),f453(x15063,x15064,x15062))
% 22.40/22.32 [1507]~E(x15071,x15072)+E(f215(x15071,x15073,x15074),f215(x15072,x15073,x15074))
% 22.40/22.32 [1508]~E(x15081,x15082)+E(f215(x15083,x15081,x15084),f215(x15083,x15082,x15084))
% 22.40/22.32 [1509]~E(x15091,x15092)+E(f215(x15093,x15094,x15091),f215(x15093,x15094,x15092))
% 22.40/22.32 [1510]~E(x15101,x15102)+E(f537(x15101,x15103,x15104,x15105,x15106,x15107),f537(x15102,x15103,x15104,x15105,x15106,x15107))
% 22.40/22.32 [1511]~E(x15111,x15112)+E(f537(x15113,x15111,x15114,x15115,x15116,x15117),f537(x15113,x15112,x15114,x15115,x15116,x15117))
% 22.40/22.32 [1512]~E(x15121,x15122)+E(f537(x15123,x15124,x15121,x15125,x15126,x15127),f537(x15123,x15124,x15122,x15125,x15126,x15127))
% 22.40/22.32 [1513]~E(x15131,x15132)+E(f537(x15133,x15134,x15135,x15131,x15136,x15137),f537(x15133,x15134,x15135,x15132,x15136,x15137))
% 22.40/22.32 [1514]~E(x15141,x15142)+E(f537(x15143,x15144,x15145,x15146,x15141,x15147),f537(x15143,x15144,x15145,x15146,x15142,x15147))
% 22.40/22.32 [1515]~E(x15151,x15152)+E(f537(x15153,x15154,x15155,x15156,x15157,x15151),f537(x15153,x15154,x15155,x15156,x15157,x15152))
% 22.40/22.32 [1516]~E(x15161,x15162)+E(f325(x15161),f325(x15162))
% 22.40/22.32 [1517]~E(x15171,x15172)+E(f743(x15171,x15173,x15174,x15175),f743(x15172,x15173,x15174,x15175))
% 22.40/22.32 [1518]~E(x15181,x15182)+E(f743(x15183,x15181,x15184,x15185),f743(x15183,x15182,x15184,x15185))
% 22.40/22.32 [1519]~E(x15191,x15192)+E(f743(x15193,x15194,x15191,x15195),f743(x15193,x15194,x15192,x15195))
% 22.40/22.32 [1520]~E(x15201,x15202)+E(f743(x15203,x15204,x15205,x15201),f743(x15203,x15204,x15205,x15202))
% 22.40/22.32 [1521]~E(x15211,x15212)+E(f705(x15211,x15213,x15214),f705(x15212,x15213,x15214))
% 22.40/22.32 [1522]~E(x15221,x15222)+E(f705(x15223,x15221,x15224),f705(x15223,x15222,x15224))
% 22.40/22.32 [1523]~E(x15231,x15232)+E(f705(x15233,x15234,x15231),f705(x15233,x15234,x15232))
% 22.40/22.32 [1524]~E(x15241,x15242)+E(f379(x15241,x15243,x15244,x15245),f379(x15242,x15243,x15244,x15245))
% 22.40/22.32 [1525]~E(x15251,x15252)+E(f379(x15253,x15251,x15254,x15255),f379(x15253,x15252,x15254,x15255))
% 22.40/22.32 [1526]~E(x15261,x15262)+E(f379(x15263,x15264,x15261,x15265),f379(x15263,x15264,x15262,x15265))
% 22.40/22.32 [1527]~E(x15271,x15272)+E(f379(x15273,x15274,x15275,x15271),f379(x15273,x15274,x15275,x15272))
% 22.40/22.32 [1528]~E(x15281,x15282)+E(f291(x15281,x15283,x15284,x15285),f291(x15282,x15283,x15284,x15285))
% 22.40/22.32 [1529]~E(x15291,x15292)+E(f291(x15293,x15291,x15294,x15295),f291(x15293,x15292,x15294,x15295))
% 22.40/22.32 [1530]~E(x15301,x15302)+E(f291(x15303,x15304,x15301,x15305),f291(x15303,x15304,x15302,x15305))
% 22.40/22.32 [1531]~E(x15311,x15312)+E(f291(x15313,x15314,x15315,x15311),f291(x15313,x15314,x15315,x15312))
% 22.40/22.32 [1532]~E(x15321,x15322)+E(f135(x15321,x15323),f135(x15322,x15323))
% 22.40/22.32 [1533]~E(x15331,x15332)+E(f135(x15333,x15331),f135(x15333,x15332))
% 22.40/22.32 [1534]~E(x15341,x15342)+E(f429(x15341,x15343,x15344),f429(x15342,x15343,x15344))
% 22.40/22.32 [1535]~E(x15351,x15352)+E(f429(x15353,x15351,x15354),f429(x15353,x15352,x15354))
% 22.40/22.32 [1536]~E(x15361,x15362)+E(f429(x15363,x15364,x15361),f429(x15363,x15364,x15362))
% 22.40/22.32 [1537]~E(x15371,x15372)+E(f601(x15371,x15373,x15374,x15375,x15376,x15377),f601(x15372,x15373,x15374,x15375,x15376,x15377))
% 22.40/22.32 [1538]~E(x15381,x15382)+E(f601(x15383,x15381,x15384,x15385,x15386,x15387),f601(x15383,x15382,x15384,x15385,x15386,x15387))
% 22.40/22.32 [1539]~E(x15391,x15392)+E(f601(x15393,x15394,x15391,x15395,x15396,x15397),f601(x15393,x15394,x15392,x15395,x15396,x15397))
% 22.40/22.32 [1540]~E(x15401,x15402)+E(f601(x15403,x15404,x15405,x15401,x15406,x15407),f601(x15403,x15404,x15405,x15402,x15406,x15407))
% 22.40/22.32 [1541]~E(x15411,x15412)+E(f601(x15413,x15414,x15415,x15416,x15411,x15417),f601(x15413,x15414,x15415,x15416,x15412,x15417))
% 22.40/22.32 [1542]~E(x15421,x15422)+E(f601(x15423,x15424,x15425,x15426,x15427,x15421),f601(x15423,x15424,x15425,x15426,x15427,x15422))
% 22.40/22.32 [1543]~E(x15431,x15432)+E(f227(x15431,x15433),f227(x15432,x15433))
% 22.40/22.32 [1544]~E(x15441,x15442)+E(f227(x15443,x15441),f227(x15443,x15442))
% 22.40/22.32 [1545]~E(x15451,x15452)+E(f198(x15451,x15453,x15454,x15455),f198(x15452,x15453,x15454,x15455))
% 22.40/22.32 [1546]~E(x15461,x15462)+E(f198(x15463,x15461,x15464,x15465),f198(x15463,x15462,x15464,x15465))
% 22.40/22.32 [1547]~E(x15471,x15472)+E(f198(x15473,x15474,x15471,x15475),f198(x15473,x15474,x15472,x15475))
% 22.40/22.32 [1548]~E(x15481,x15482)+E(f198(x15483,x15484,x15485,x15481),f198(x15483,x15484,x15485,x15482))
% 22.40/22.32 [1549]~E(x15491,x15492)+E(f677(x15491,x15493,x15494,x15495),f677(x15492,x15493,x15494,x15495))
% 22.40/22.32 [1550]~E(x15501,x15502)+E(f677(x15503,x15501,x15504,x15505),f677(x15503,x15502,x15504,x15505))
% 22.40/22.32 [1551]~E(x15511,x15512)+E(f677(x15513,x15514,x15511,x15515),f677(x15513,x15514,x15512,x15515))
% 22.40/22.32 [1552]~E(x15521,x15522)+E(f677(x15523,x15524,x15525,x15521),f677(x15523,x15524,x15525,x15522))
% 22.40/22.32 [1553]~E(x15531,x15532)+E(f468(x15531,x15533,x15534,x15535,x15536),f468(x15532,x15533,x15534,x15535,x15536))
% 22.40/22.32 [1554]~E(x15541,x15542)+E(f468(x15543,x15541,x15544,x15545,x15546),f468(x15543,x15542,x15544,x15545,x15546))
% 22.40/22.32 [1555]~E(x15551,x15552)+E(f468(x15553,x15554,x15551,x15555,x15556),f468(x15553,x15554,x15552,x15555,x15556))
% 22.40/22.32 [1556]~E(x15561,x15562)+E(f468(x15563,x15564,x15565,x15561,x15566),f468(x15563,x15564,x15565,x15562,x15566))
% 22.40/22.32 [1557]~E(x15571,x15572)+E(f468(x15573,x15574,x15575,x15576,x15571),f468(x15573,x15574,x15575,x15576,x15572))
% 22.40/22.32 [1558]~E(x15581,x15582)+E(f402(x15581,x15583),f402(x15582,x15583))
% 22.40/22.32 [1559]~E(x15591,x15592)+E(f402(x15593,x15591),f402(x15593,x15592))
% 22.40/22.32 [1560]~E(x15601,x15602)+E(f656(x15601,x15603,x15604,x15605),f656(x15602,x15603,x15604,x15605))
% 22.40/22.32 [1561]~E(x15611,x15612)+E(f656(x15613,x15611,x15614,x15615),f656(x15613,x15612,x15614,x15615))
% 22.40/22.32 [1562]~E(x15621,x15622)+E(f656(x15623,x15624,x15621,x15625),f656(x15623,x15624,x15622,x15625))
% 22.40/22.32 [1563]~E(x15631,x15632)+E(f656(x15633,x15634,x15635,x15631),f656(x15633,x15634,x15635,x15632))
% 22.40/22.32 [1564]~E(x15641,x15642)+E(f797(x15641),f797(x15642))
% 22.40/22.32 [1565]~E(x15651,x15652)+E(f654(x15651,x15653,x15654,x15655),f654(x15652,x15653,x15654,x15655))
% 22.40/22.32 [1566]~E(x15661,x15662)+E(f654(x15663,x15661,x15664,x15665),f654(x15663,x15662,x15664,x15665))
% 22.40/22.32 [1567]~E(x15671,x15672)+E(f654(x15673,x15674,x15671,x15675),f654(x15673,x15674,x15672,x15675))
% 22.40/22.32 [1568]~E(x15681,x15682)+E(f654(x15683,x15684,x15685,x15681),f654(x15683,x15684,x15685,x15682))
% 22.40/22.32 [1569]~E(x15691,x15692)+E(f432(x15691),f432(x15692))
% 22.40/22.32 [1570]~E(x15701,x15702)+E(f682(x15701,x15703,x15704),f682(x15702,x15703,x15704))
% 22.40/22.32 [1571]~E(x15711,x15712)+E(f682(x15713,x15711,x15714),f682(x15713,x15712,x15714))
% 22.40/22.32 [1572]~E(x15721,x15722)+E(f682(x15723,x15724,x15721),f682(x15723,x15724,x15722))
% 22.40/22.32 [1573]~E(x15731,x15732)+E(f620(x15731,x15733,x15734,x15735,x15736),f620(x15732,x15733,x15734,x15735,x15736))
% 22.40/22.32 [1574]~E(x15741,x15742)+E(f620(x15743,x15741,x15744,x15745,x15746),f620(x15743,x15742,x15744,x15745,x15746))
% 22.40/22.32 [1575]~E(x15751,x15752)+E(f620(x15753,x15754,x15751,x15755,x15756),f620(x15753,x15754,x15752,x15755,x15756))
% 22.40/22.32 [1576]~E(x15761,x15762)+E(f620(x15763,x15764,x15765,x15761,x15766),f620(x15763,x15764,x15765,x15762,x15766))
% 22.40/22.32 [1577]~E(x15771,x15772)+E(f620(x15773,x15774,x15775,x15776,x15771),f620(x15773,x15774,x15775,x15776,x15772))
% 22.40/22.32 [1578]~E(x15781,x15782)+E(f900(x15781,x15783,x15784,x15785,x15786),f900(x15782,x15783,x15784,x15785,x15786))
% 22.40/22.32 [1579]~E(x15791,x15792)+E(f900(x15793,x15791,x15794,x15795,x15796),f900(x15793,x15792,x15794,x15795,x15796))
% 22.40/22.32 [1580]~E(x15801,x15802)+E(f900(x15803,x15804,x15801,x15805,x15806),f900(x15803,x15804,x15802,x15805,x15806))
% 22.40/22.32 [1581]~E(x15811,x15812)+E(f900(x15813,x15814,x15815,x15811,x15816),f900(x15813,x15814,x15815,x15812,x15816))
% 22.40/22.32 [1582]~E(x15821,x15822)+E(f900(x15823,x15824,x15825,x15826,x15821),f900(x15823,x15824,x15825,x15826,x15822))
% 22.40/22.32 [1583]~E(x15831,x15832)+E(f672(x15831,x15833),f672(x15832,x15833))
% 22.40/22.32 [1584]~E(x15841,x15842)+E(f672(x15843,x15841),f672(x15843,x15842))
% 22.40/22.32 [1585]~E(x15851,x15852)+E(f778(x15851,x15853),f778(x15852,x15853))
% 22.40/22.32 [1586]~E(x15861,x15862)+E(f778(x15863,x15861),f778(x15863,x15862))
% 22.40/22.32 [1587]~E(x15871,x15872)+E(f626(x15871,x15873,x15874,x15875),f626(x15872,x15873,x15874,x15875))
% 22.40/22.32 [1588]~E(x15881,x15882)+E(f626(x15883,x15881,x15884,x15885),f626(x15883,x15882,x15884,x15885))
% 22.40/22.32 [1589]~E(x15891,x15892)+E(f626(x15893,x15894,x15891,x15895),f626(x15893,x15894,x15892,x15895))
% 22.40/22.32 [1590]~E(x15901,x15902)+E(f626(x15903,x15904,x15905,x15901),f626(x15903,x15904,x15905,x15902))
% 22.40/22.32 [1591]~E(x15911,x15912)+E(f201(x15911),f201(x15912))
% 22.40/22.32 [1592]~E(x15921,x15922)+E(f202(x15921,x15923,x15924,x15925),f202(x15922,x15923,x15924,x15925))
% 22.40/22.32 [1593]~E(x15931,x15932)+E(f202(x15933,x15931,x15934,x15935),f202(x15933,x15932,x15934,x15935))
% 22.40/22.32 [1594]~E(x15941,x15942)+E(f202(x15943,x15944,x15941,x15945),f202(x15943,x15944,x15942,x15945))
% 22.40/22.32 [1595]~E(x15951,x15952)+E(f202(x15953,x15954,x15955,x15951),f202(x15953,x15954,x15955,x15952))
% 22.40/22.32 [1596]~E(x15961,x15962)+E(f392(x15961,x15963,x15964,x15965),f392(x15962,x15963,x15964,x15965))
% 22.40/22.32 [1597]~E(x15971,x15972)+E(f392(x15973,x15971,x15974,x15975),f392(x15973,x15972,x15974,x15975))
% 22.40/22.32 [1598]~E(x15981,x15982)+E(f392(x15983,x15984,x15981,x15985),f392(x15983,x15984,x15982,x15985))
% 22.40/22.32 [1599]~E(x15991,x15992)+E(f392(x15993,x15994,x15995,x15991),f392(x15993,x15994,x15995,x15992))
% 22.40/22.32 [1600]~E(x16001,x16002)+E(f728(x16001,x16003),f728(x16002,x16003))
% 22.40/22.32 [1601]~E(x16011,x16012)+E(f728(x16013,x16011),f728(x16013,x16012))
% 22.40/22.32 [1602]~E(x16021,x16022)+E(f355(x16021,x16023,x16024,x16025,x16026),f355(x16022,x16023,x16024,x16025,x16026))
% 22.40/22.32 [1603]~E(x16031,x16032)+E(f355(x16033,x16031,x16034,x16035,x16036),f355(x16033,x16032,x16034,x16035,x16036))
% 22.40/22.32 [1604]~E(x16041,x16042)+E(f355(x16043,x16044,x16041,x16045,x16046),f355(x16043,x16044,x16042,x16045,x16046))
% 22.40/22.32 [1605]~E(x16051,x16052)+E(f355(x16053,x16054,x16055,x16051,x16056),f355(x16053,x16054,x16055,x16052,x16056))
% 22.40/22.32 [1606]~E(x16061,x16062)+E(f355(x16063,x16064,x16065,x16066,x16061),f355(x16063,x16064,x16065,x16066,x16062))
% 22.40/22.32 [1607]~E(x16071,x16072)+E(f546(x16071,x16073),f546(x16072,x16073))
% 22.40/22.32 [1608]~E(x16081,x16082)+E(f546(x16083,x16081),f546(x16083,x16082))
% 22.40/22.32 [1609]~E(x16091,x16092)+E(f765(x16091,x16093,x16094,x16095),f765(x16092,x16093,x16094,x16095))
% 22.40/22.32 [1610]~E(x16101,x16102)+E(f765(x16103,x16101,x16104,x16105),f765(x16103,x16102,x16104,x16105))
% 22.40/22.32 [1611]~E(x16111,x16112)+E(f765(x16113,x16114,x16111,x16115),f765(x16113,x16114,x16112,x16115))
% 22.40/22.32 [1612]~E(x16121,x16122)+E(f765(x16123,x16124,x16125,x16121),f765(x16123,x16124,x16125,x16122))
% 22.40/22.32 [1613]~E(x16131,x16132)+E(f890(x16131,x16133,x16134),f890(x16132,x16133,x16134))
% 22.40/22.32 [1614]~E(x16141,x16142)+E(f890(x16143,x16141,x16144),f890(x16143,x16142,x16144))
% 22.40/22.32 [1615]~E(x16151,x16152)+E(f890(x16153,x16154,x16151),f890(x16153,x16154,x16152))
% 22.40/22.32 [1616]~E(x16161,x16162)+E(f183(x16161,x16163,x16164,x16165),f183(x16162,x16163,x16164,x16165))
% 22.40/22.32 [1617]~E(x16171,x16172)+E(f183(x16173,x16171,x16174,x16175),f183(x16173,x16172,x16174,x16175))
% 22.40/22.32 [1618]~E(x16181,x16182)+E(f183(x16183,x16184,x16181,x16185),f183(x16183,x16184,x16182,x16185))
% 22.40/22.32 [1619]~E(x16191,x16192)+E(f183(x16193,x16194,x16195,x16191),f183(x16193,x16194,x16195,x16192))
% 22.40/22.32 [1620]~E(x16201,x16202)+E(f754(x16201,x16203,x16204),f754(x16202,x16203,x16204))
% 22.40/22.32 [1621]~E(x16211,x16212)+E(f754(x16213,x16211,x16214),f754(x16213,x16212,x16214))
% 22.40/22.32 [1622]~E(x16221,x16222)+E(f754(x16223,x16224,x16221),f754(x16223,x16224,x16222))
% 22.40/22.32 [1623]~E(x16231,x16232)+E(f477(x16231,x16233,x16234,x16235,x16236,x16237,x16238),f477(x16232,x16233,x16234,x16235,x16236,x16237,x16238))
% 22.40/22.32 [1624]~E(x16241,x16242)+E(f477(x16243,x16241,x16244,x16245,x16246,x16247,x16248),f477(x16243,x16242,x16244,x16245,x16246,x16247,x16248))
% 22.40/22.32 [1625]~E(x16251,x16252)+E(f477(x16253,x16254,x16251,x16255,x16256,x16257,x16258),f477(x16253,x16254,x16252,x16255,x16256,x16257,x16258))
% 22.40/22.32 [1626]~E(x16261,x16262)+E(f477(x16263,x16264,x16265,x16261,x16266,x16267,x16268),f477(x16263,x16264,x16265,x16262,x16266,x16267,x16268))
% 22.40/22.32 [1627]~E(x16271,x16272)+E(f477(x16273,x16274,x16275,x16276,x16271,x16277,x16278),f477(x16273,x16274,x16275,x16276,x16272,x16277,x16278))
% 22.40/22.32 [1628]~E(x16281,x16282)+E(f477(x16283,x16284,x16285,x16286,x16287,x16281,x16288),f477(x16283,x16284,x16285,x16286,x16287,x16282,x16288))
% 22.40/22.32 [1629]~E(x16291,x16292)+E(f477(x16293,x16294,x16295,x16296,x16297,x16298,x16291),f477(x16293,x16294,x16295,x16296,x16297,x16298,x16292))
% 22.40/22.32 [1630]~E(x16301,x16302)+E(f448(x16301,x16303,x16304,x16305,x16306),f448(x16302,x16303,x16304,x16305,x16306))
% 22.40/22.32 [1631]~E(x16311,x16312)+E(f448(x16313,x16311,x16314,x16315,x16316),f448(x16313,x16312,x16314,x16315,x16316))
% 22.40/22.32 [1632]~E(x16321,x16322)+E(f448(x16323,x16324,x16321,x16325,x16326),f448(x16323,x16324,x16322,x16325,x16326))
% 22.40/22.32 [1633]~E(x16331,x16332)+E(f448(x16333,x16334,x16335,x16331,x16336),f448(x16333,x16334,x16335,x16332,x16336))
% 22.40/22.32 [1634]~E(x16341,x16342)+E(f448(x16343,x16344,x16345,x16346,x16341),f448(x16343,x16344,x16345,x16346,x16342))
% 22.40/22.32 [1635]~E(x16351,x16352)+E(f526(x16351,x16353,x16354,x16355,x16356),f526(x16352,x16353,x16354,x16355,x16356))
% 22.40/22.32 [1636]~E(x16361,x16362)+E(f526(x16363,x16361,x16364,x16365,x16366),f526(x16363,x16362,x16364,x16365,x16366))
% 22.40/22.32 [1637]~E(x16371,x16372)+E(f526(x16373,x16374,x16371,x16375,x16376),f526(x16373,x16374,x16372,x16375,x16376))
% 22.40/22.32 [1638]~E(x16381,x16382)+E(f526(x16383,x16384,x16385,x16381,x16386),f526(x16383,x16384,x16385,x16382,x16386))
% 22.40/22.32 [1639]~E(x16391,x16392)+E(f526(x16393,x16394,x16395,x16396,x16391),f526(x16393,x16394,x16395,x16396,x16392))
% 22.40/22.32 [1640]~E(x16401,x16402)+E(f478(x16401,x16403,x16404,x16405,x16406,x16407,x16408),f478(x16402,x16403,x16404,x16405,x16406,x16407,x16408))
% 22.40/22.32 [1641]~E(x16411,x16412)+E(f478(x16413,x16411,x16414,x16415,x16416,x16417,x16418),f478(x16413,x16412,x16414,x16415,x16416,x16417,x16418))
% 22.40/22.32 [1642]~E(x16421,x16422)+E(f478(x16423,x16424,x16421,x16425,x16426,x16427,x16428),f478(x16423,x16424,x16422,x16425,x16426,x16427,x16428))
% 22.40/22.32 [1643]~E(x16431,x16432)+E(f478(x16433,x16434,x16435,x16431,x16436,x16437,x16438),f478(x16433,x16434,x16435,x16432,x16436,x16437,x16438))
% 22.40/22.32 [1644]~E(x16441,x16442)+E(f478(x16443,x16444,x16445,x16446,x16441,x16447,x16448),f478(x16443,x16444,x16445,x16446,x16442,x16447,x16448))
% 22.40/22.32 [1645]~E(x16451,x16452)+E(f478(x16453,x16454,x16455,x16456,x16457,x16451,x16458),f478(x16453,x16454,x16455,x16456,x16457,x16452,x16458))
% 22.40/22.32 [1646]~E(x16461,x16462)+E(f478(x16463,x16464,x16465,x16466,x16467,x16468,x16461),f478(x16463,x16464,x16465,x16466,x16467,x16468,x16462))
% 22.40/22.32 [1647]~E(x16471,x16472)+E(f439(x16471,x16473,x16474),f439(x16472,x16473,x16474))
% 22.40/22.32 [1648]~E(x16481,x16482)+E(f439(x16483,x16481,x16484),f439(x16483,x16482,x16484))
% 22.40/22.32 [1649]~E(x16491,x16492)+E(f439(x16493,x16494,x16491),f439(x16493,x16494,x16492))
% 22.40/22.32 [1650]~E(x16501,x16502)+E(f438(x16501,x16503),f438(x16502,x16503))
% 22.40/22.32 [1651]~E(x16511,x16512)+E(f438(x16513,x16511),f438(x16513,x16512))
% 22.40/22.32 [1652]~E(x16521,x16522)+E(f830(x16521,x16523,x16524,x16525,x16526,x16527,x16528,x16529),f830(x16522,x16523,x16524,x16525,x16526,x16527,x16528,x16529))
% 22.40/22.32 [1653]~E(x16531,x16532)+E(f830(x16533,x16531,x16534,x16535,x16536,x16537,x16538,x16539),f830(x16533,x16532,x16534,x16535,x16536,x16537,x16538,x16539))
% 22.40/22.32 [1654]~E(x16541,x16542)+E(f830(x16543,x16544,x16541,x16545,x16546,x16547,x16548,x16549),f830(x16543,x16544,x16542,x16545,x16546,x16547,x16548,x16549))
% 22.40/22.32 [1655]~E(x16551,x16552)+E(f830(x16553,x16554,x16555,x16551,x16556,x16557,x16558,x16559),f830(x16553,x16554,x16555,x16552,x16556,x16557,x16558,x16559))
% 22.40/22.32 [1656]~E(x16561,x16562)+E(f830(x16563,x16564,x16565,x16566,x16561,x16567,x16568,x16569),f830(x16563,x16564,x16565,x16566,x16562,x16567,x16568,x16569))
% 22.40/22.32 [1657]~E(x16571,x16572)+E(f830(x16573,x16574,x16575,x16576,x16577,x16571,x16578,x16579),f830(x16573,x16574,x16575,x16576,x16577,x16572,x16578,x16579))
% 22.40/22.32 [1658]~E(x16581,x16582)+E(f830(x16583,x16584,x16585,x16586,x16587,x16588,x16581,x16589),f830(x16583,x16584,x16585,x16586,x16587,x16588,x16582,x16589))
% 22.40/22.32 [1659]~E(x16591,x16592)+E(f830(x16593,x16594,x16595,x16596,x16597,x16598,x16599,x16591),f830(x16593,x16594,x16595,x16596,x16597,x16598,x16599,x16592))
% 22.40/22.32 [1660]~E(x16601,x16602)+E(f740(x16601,x16603),f740(x16602,x16603))
% 22.40/22.32 [1661]~E(x16611,x16612)+E(f740(x16613,x16611),f740(x16613,x16612))
% 22.40/22.32 [1662]~E(x16621,x16622)+E(f342(x16621,x16623),f342(x16622,x16623))
% 22.40/22.32 [1663]~E(x16631,x16632)+E(f342(x16633,x16631),f342(x16633,x16632))
% 22.40/22.32 [1664]~E(x16641,x16642)+E(f61(x16641,x16643,x16644),f61(x16642,x16643,x16644))
% 22.40/22.32 [1665]~E(x16651,x16652)+E(f61(x16653,x16651,x16654),f61(x16653,x16652,x16654))
% 22.40/22.32 [1666]~E(x16661,x16662)+E(f61(x16663,x16664,x16661),f61(x16663,x16664,x16662))
% 22.40/22.32 [1667]~E(x16671,x16672)+E(f727(x16671,x16673,x16674,x16675,x16676),f727(x16672,x16673,x16674,x16675,x16676))
% 22.40/22.32 [1668]~E(x16681,x16682)+E(f727(x16683,x16681,x16684,x16685,x16686),f727(x16683,x16682,x16684,x16685,x16686))
% 22.40/22.32 [1669]~E(x16691,x16692)+E(f727(x16693,x16694,x16691,x16695,x16696),f727(x16693,x16694,x16692,x16695,x16696))
% 22.40/22.32 [1670]~E(x16701,x16702)+E(f727(x16703,x16704,x16705,x16701,x16706),f727(x16703,x16704,x16705,x16702,x16706))
% 22.40/22.32 [1671]~E(x16711,x16712)+E(f727(x16713,x16714,x16715,x16716,x16711),f727(x16713,x16714,x16715,x16716,x16712))
% 22.40/22.32 [1672]~E(x16721,x16722)+E(f463(x16721,x16723,x16724,x16725),f463(x16722,x16723,x16724,x16725))
% 22.40/22.32 [1673]~E(x16731,x16732)+E(f463(x16733,x16731,x16734,x16735),f463(x16733,x16732,x16734,x16735))
% 22.40/22.32 [1674]~E(x16741,x16742)+E(f463(x16743,x16744,x16741,x16745),f463(x16743,x16744,x16742,x16745))
% 22.40/22.32 [1675]~E(x16751,x16752)+E(f463(x16753,x16754,x16755,x16751),f463(x16753,x16754,x16755,x16752))
% 22.40/22.32 [1676]~E(x16761,x16762)+E(f411(x16761,x16763,x16764,x16765),f411(x16762,x16763,x16764,x16765))
% 22.40/22.32 [1677]~E(x16771,x16772)+E(f411(x16773,x16771,x16774,x16775),f411(x16773,x16772,x16774,x16775))
% 22.40/22.32 [1678]~E(x16781,x16782)+E(f411(x16783,x16784,x16781,x16785),f411(x16783,x16784,x16782,x16785))
% 22.40/22.32 [1679]~E(x16791,x16792)+E(f411(x16793,x16794,x16795,x16791),f411(x16793,x16794,x16795,x16792))
% 22.40/22.32 [1680]~E(x16801,x16802)+E(f824(x16801,x16803,x16804),f824(x16802,x16803,x16804))
% 22.40/22.32 [1681]~E(x16811,x16812)+E(f824(x16813,x16811,x16814),f824(x16813,x16812,x16814))
% 22.40/22.32 [1682]~E(x16821,x16822)+E(f824(x16823,x16824,x16821),f824(x16823,x16824,x16822))
% 22.40/22.32 [1683]~E(x16831,x16832)+E(f864(x16831,x16833,x16834),f864(x16832,x16833,x16834))
% 22.40/22.32 [1684]~E(x16841,x16842)+E(f864(x16843,x16841,x16844),f864(x16843,x16842,x16844))
% 22.40/22.32 [1685]~E(x16851,x16852)+E(f864(x16853,x16854,x16851),f864(x16853,x16854,x16852))
% 22.40/22.32 [1686]~E(x16861,x16862)+E(f362(x16861,x16863,x16864),f362(x16862,x16863,x16864))
% 22.40/22.32 [1687]~E(x16871,x16872)+E(f362(x16873,x16871,x16874),f362(x16873,x16872,x16874))
% 22.40/22.32 [1688]~E(x16881,x16882)+E(f362(x16883,x16884,x16881),f362(x16883,x16884,x16882))
% 22.40/22.32 [1689]~E(x16891,x16892)+E(f424(x16891),f424(x16892))
% 22.40/22.32 [1690]~E(x16901,x16902)+E(f574(x16901,x16903),f574(x16902,x16903))
% 22.40/22.32 [1691]~E(x16911,x16912)+E(f574(x16913,x16911),f574(x16913,x16912))
% 22.40/22.32 [1692]~E(x16921,x16922)+E(f475(x16921,x16923,x16924,x16925,x16926),f475(x16922,x16923,x16924,x16925,x16926))
% 22.40/22.32 [1693]~E(x16931,x16932)+E(f475(x16933,x16931,x16934,x16935,x16936),f475(x16933,x16932,x16934,x16935,x16936))
% 22.40/22.32 [1694]~E(x16941,x16942)+E(f475(x16943,x16944,x16941,x16945,x16946),f475(x16943,x16944,x16942,x16945,x16946))
% 22.40/22.32 [1695]~E(x16951,x16952)+E(f475(x16953,x16954,x16955,x16951,x16956),f475(x16953,x16954,x16955,x16952,x16956))
% 22.40/22.32 [1696]~E(x16961,x16962)+E(f475(x16963,x16964,x16965,x16966,x16961),f475(x16963,x16964,x16965,x16966,x16962))
% 22.40/22.32 [1697]~E(x16971,x16972)+E(f569(x16971,x16973,x16974,x16975),f569(x16972,x16973,x16974,x16975))
% 22.40/22.32 [1698]~E(x16981,x16982)+E(f569(x16983,x16981,x16984,x16985),f569(x16983,x16982,x16984,x16985))
% 22.40/22.32 [1699]~E(x16991,x16992)+E(f569(x16993,x16994,x16991,x16995),f569(x16993,x16994,x16992,x16995))
% 22.40/22.32 [1700]~E(x17001,x17002)+E(f569(x17003,x17004,x17005,x17001),f569(x17003,x17004,x17005,x17002))
% 22.40/22.32 [1701]~E(x17011,x17012)+E(f395(x17011,x17013,x17014),f395(x17012,x17013,x17014))
% 22.40/22.32 [1702]~E(x17021,x17022)+E(f395(x17023,x17021,x17024),f395(x17023,x17022,x17024))
% 22.40/22.32 [1703]~E(x17031,x17032)+E(f395(x17033,x17034,x17031),f395(x17033,x17034,x17032))
% 22.40/22.32 [1704]~E(x17041,x17042)+E(f550(x17041,x17043,x17044,x17045),f550(x17042,x17043,x17044,x17045))
% 22.40/22.32 [1705]~E(x17051,x17052)+E(f550(x17053,x17051,x17054,x17055),f550(x17053,x17052,x17054,x17055))
% 22.40/22.32 [1706]~E(x17061,x17062)+E(f550(x17063,x17064,x17061,x17065),f550(x17063,x17064,x17062,x17065))
% 22.40/22.32 [1707]~E(x17071,x17072)+E(f550(x17073,x17074,x17075,x17071),f550(x17073,x17074,x17075,x17072))
% 22.40/22.32 [1708]~E(x17081,x17082)+E(f218(x17081,x17083,x17084,x17085,x17086),f218(x17082,x17083,x17084,x17085,x17086))
% 22.40/22.32 [1709]~E(x17091,x17092)+E(f218(x17093,x17091,x17094,x17095,x17096),f218(x17093,x17092,x17094,x17095,x17096))
% 22.40/22.32 [1710]~E(x17101,x17102)+E(f218(x17103,x17104,x17101,x17105,x17106),f218(x17103,x17104,x17102,x17105,x17106))
% 22.40/22.32 [1711]~E(x17111,x17112)+E(f218(x17113,x17114,x17115,x17111,x17116),f218(x17113,x17114,x17115,x17112,x17116))
% 22.40/22.32 [1712]~E(x17121,x17122)+E(f218(x17123,x17124,x17125,x17126,x17121),f218(x17123,x17124,x17125,x17126,x17122))
% 22.40/22.32 [1713]~E(x17131,x17132)+E(f573(x17131),f573(x17132))
% 22.40/22.32 [1714]~E(x17141,x17142)+E(f700(x17141,x17143),f700(x17142,x17143))
% 22.40/22.32 [1715]~E(x17151,x17152)+E(f700(x17153,x17151),f700(x17153,x17152))
% 22.40/22.32 [1716]~E(x17161,x17162)+E(f481(x17161,x17163,x17164),f481(x17162,x17163,x17164))
% 22.40/22.32 [1717]~E(x17171,x17172)+E(f481(x17173,x17171,x17174),f481(x17173,x17172,x17174))
% 22.40/22.32 [1718]~E(x17181,x17182)+E(f481(x17183,x17184,x17181),f481(x17183,x17184,x17182))
% 22.40/22.32 [1719]~E(x17191,x17192)+E(f469(x17191,x17193,x17194,x17195,x17196),f469(x17192,x17193,x17194,x17195,x17196))
% 22.40/22.32 [1720]~E(x17201,x17202)+E(f469(x17203,x17201,x17204,x17205,x17206),f469(x17203,x17202,x17204,x17205,x17206))
% 22.40/22.32 [1721]~E(x17211,x17212)+E(f469(x17213,x17214,x17211,x17215,x17216),f469(x17213,x17214,x17212,x17215,x17216))
% 22.40/22.32 [1722]~E(x17221,x17222)+E(f469(x17223,x17224,x17225,x17221,x17226),f469(x17223,x17224,x17225,x17222,x17226))
% 22.40/22.32 [1723]~E(x17231,x17232)+E(f469(x17233,x17234,x17235,x17236,x17231),f469(x17233,x17234,x17235,x17236,x17232))
% 22.40/22.32 [1724]~E(x17241,x17242)+E(f608(x17241,x17243,x17244),f608(x17242,x17243,x17244))
% 22.40/22.32 [1725]~E(x17251,x17252)+E(f608(x17253,x17251,x17254),f608(x17253,x17252,x17254))
% 22.40/22.32 [1726]~E(x17261,x17262)+E(f608(x17263,x17264,x17261),f608(x17263,x17264,x17262))
% 22.40/22.32 [1727]~E(x17271,x17272)+E(f635(x17271,x17273,x17274,x17275),f635(x17272,x17273,x17274,x17275))
% 22.40/22.32 [1728]~E(x17281,x17282)+E(f635(x17283,x17281,x17284,x17285),f635(x17283,x17282,x17284,x17285))
% 22.40/22.32 [1729]~E(x17291,x17292)+E(f635(x17293,x17294,x17291,x17295),f635(x17293,x17294,x17292,x17295))
% 22.40/22.32 [1730]~E(x17301,x17302)+E(f635(x17303,x17304,x17305,x17301),f635(x17303,x17304,x17305,x17302))
% 22.40/22.32 [1731]~E(x17311,x17312)+E(f337(x17311,x17313,x17314,x17315),f337(x17312,x17313,x17314,x17315))
% 22.40/22.32 [1732]~E(x17321,x17322)+E(f337(x17323,x17321,x17324,x17325),f337(x17323,x17322,x17324,x17325))
% 22.40/22.32 [1733]~E(x17331,x17332)+E(f337(x17333,x17334,x17331,x17335),f337(x17333,x17334,x17332,x17335))
% 22.40/22.32 [1734]~E(x17341,x17342)+E(f337(x17343,x17344,x17345,x17341),f337(x17343,x17344,x17345,x17342))
% 22.40/22.32 [1735]~E(x17351,x17352)+E(f389(x17351,x17353,x17354,x17355),f389(x17352,x17353,x17354,x17355))
% 22.40/22.32 [1736]~E(x17361,x17362)+E(f389(x17363,x17361,x17364,x17365),f389(x17363,x17362,x17364,x17365))
% 22.40/22.32 [1737]~E(x17371,x17372)+E(f389(x17373,x17374,x17371,x17375),f389(x17373,x17374,x17372,x17375))
% 22.40/22.32 [1738]~E(x17381,x17382)+E(f389(x17383,x17384,x17385,x17381),f389(x17383,x17384,x17385,x17382))
% 22.40/22.32 [1739]~E(x17391,x17392)+E(f839(x17391,x17393,x17394,x17395,x17396,x17397,x17398,x17399),f839(x17392,x17393,x17394,x17395,x17396,x17397,x17398,x17399))
% 22.40/22.32 [1740]~E(x17401,x17402)+E(f839(x17403,x17401,x17404,x17405,x17406,x17407,x17408,x17409),f839(x17403,x17402,x17404,x17405,x17406,x17407,x17408,x17409))
% 22.40/22.32 [1741]~E(x17411,x17412)+E(f839(x17413,x17414,x17411,x17415,x17416,x17417,x17418,x17419),f839(x17413,x17414,x17412,x17415,x17416,x17417,x17418,x17419))
% 22.40/22.32 [1742]~E(x17421,x17422)+E(f839(x17423,x17424,x17425,x17421,x17426,x17427,x17428,x17429),f839(x17423,x17424,x17425,x17422,x17426,x17427,x17428,x17429))
% 22.40/22.32 [1743]~E(x17431,x17432)+E(f839(x17433,x17434,x17435,x17436,x17431,x17437,x17438,x17439),f839(x17433,x17434,x17435,x17436,x17432,x17437,x17438,x17439))
% 22.40/22.32 [1744]~E(x17441,x17442)+E(f839(x17443,x17444,x17445,x17446,x17447,x17441,x17448,x17449),f839(x17443,x17444,x17445,x17446,x17447,x17442,x17448,x17449))
% 22.40/22.32 [1745]~E(x17451,x17452)+E(f839(x17453,x17454,x17455,x17456,x17457,x17458,x17451,x17459),f839(x17453,x17454,x17455,x17456,x17457,x17458,x17452,x17459))
% 22.40/22.32 [1746]~E(x17461,x17462)+E(f839(x17463,x17464,x17465,x17466,x17467,x17468,x17469,x17461),f839(x17463,x17464,x17465,x17466,x17467,x17468,x17469,x17462))
% 22.40/22.32 [1747]~E(x17471,x17472)+E(f190(x17471,x17473,x17474,x17475),f190(x17472,x17473,x17474,x17475))
% 22.40/22.32 [1748]~E(x17481,x17482)+E(f190(x17483,x17481,x17484,x17485),f190(x17483,x17482,x17484,x17485))
% 22.40/22.32 [1749]~E(x17491,x17492)+E(f190(x17493,x17494,x17491,x17495),f190(x17493,x17494,x17492,x17495))
% 22.40/22.32 [1750]~E(x17501,x17502)+E(f190(x17503,x17504,x17505,x17501),f190(x17503,x17504,x17505,x17502))
% 22.40/22.32 [1751]~E(x17511,x17512)+E(f883(x17511,x17513,x17514,x17515),f883(x17512,x17513,x17514,x17515))
% 22.40/22.32 [1752]~E(x17521,x17522)+E(f883(x17523,x17521,x17524,x17525),f883(x17523,x17522,x17524,x17525))
% 22.40/22.32 [1753]~E(x17531,x17532)+E(f883(x17533,x17534,x17531,x17535),f883(x17533,x17534,x17532,x17535))
% 22.40/22.32 [1754]~E(x17541,x17542)+E(f883(x17543,x17544,x17545,x17541),f883(x17543,x17544,x17545,x17542))
% 22.40/22.32 [1755]~E(x17551,x17552)+E(f673(x17551,x17553,x17554,x17555,x17556),f673(x17552,x17553,x17554,x17555,x17556))
% 22.40/22.32 [1756]~E(x17561,x17562)+E(f673(x17563,x17561,x17564,x17565,x17566),f673(x17563,x17562,x17564,x17565,x17566))
% 22.40/22.32 [1757]~E(x17571,x17572)+E(f673(x17573,x17574,x17571,x17575,x17576),f673(x17573,x17574,x17572,x17575,x17576))
% 22.40/22.32 [1758]~E(x17581,x17582)+E(f673(x17583,x17584,x17585,x17581,x17586),f673(x17583,x17584,x17585,x17582,x17586))
% 22.40/22.32 [1759]~E(x17591,x17592)+E(f673(x17593,x17594,x17595,x17596,x17591),f673(x17593,x17594,x17595,x17596,x17592))
% 22.40/22.32 [1760]~E(x17601,x17602)+E(f361(x17601,x17603,x17604),f361(x17602,x17603,x17604))
% 22.40/22.32 [1761]~E(x17611,x17612)+E(f361(x17613,x17611,x17614),f361(x17613,x17612,x17614))
% 22.40/22.32 [1762]~E(x17621,x17622)+E(f361(x17623,x17624,x17621),f361(x17623,x17624,x17622))
% 22.40/22.32 [1763]~E(x17631,x17632)+E(f866(x17631,x17633,x17634),f866(x17632,x17633,x17634))
% 22.40/22.32 [1764]~E(x17641,x17642)+E(f866(x17643,x17641,x17644),f866(x17643,x17642,x17644))
% 22.40/22.32 [1765]~E(x17651,x17652)+E(f866(x17653,x17654,x17651),f866(x17653,x17654,x17652))
% 22.40/22.32 [1766]~E(x17661,x17662)+E(f48(x17661,x17663),f48(x17662,x17663))
% 22.40/22.32 [1767]~E(x17671,x17672)+E(f48(x17673,x17671),f48(x17673,x17672))
% 22.40/22.32 [1768]~E(x17681,x17682)+E(f861(x17681,x17683,x17684),f861(x17682,x17683,x17684))
% 22.40/22.32 [1769]~E(x17691,x17692)+E(f861(x17693,x17691,x17694),f861(x17693,x17692,x17694))
% 22.40/22.32 [1770]~E(x17701,x17702)+E(f861(x17703,x17704,x17701),f861(x17703,x17704,x17702))
% 22.40/22.32 [1771]~E(x17711,x17712)+E(f724(x17711,x17713),f724(x17712,x17713))
% 22.40/22.32 [1772]~E(x17721,x17722)+E(f724(x17723,x17721),f724(x17723,x17722))
% 22.40/22.32 [1773]~E(x17731,x17732)+E(f338(x17731,x17733),f338(x17732,x17733))
% 22.40/22.32 [1774]~E(x17741,x17742)+E(f338(x17743,x17741),f338(x17743,x17742))
% 22.40/22.32 [1775]~E(x17751,x17752)+E(f209(x17751,x17753),f209(x17752,x17753))
% 22.40/22.32 [1776]~E(x17761,x17762)+E(f209(x17763,x17761),f209(x17763,x17762))
% 22.40/22.32 [1777]~E(x17771,x17772)+E(f594(x17771,x17773,x17774),f594(x17772,x17773,x17774))
% 22.40/22.32 [1778]~E(x17781,x17782)+E(f594(x17783,x17781,x17784),f594(x17783,x17782,x17784))
% 22.40/22.32 [1779]~E(x17791,x17792)+E(f594(x17793,x17794,x17791),f594(x17793,x17794,x17792))
% 22.40/22.32 [1780]~E(x17801,x17802)+E(f327(x17801,x17803,x17804),f327(x17802,x17803,x17804))
% 22.40/22.32 [1781]~E(x17811,x17812)+E(f327(x17813,x17811,x17814),f327(x17813,x17812,x17814))
% 22.40/22.32 [1782]~E(x17821,x17822)+E(f327(x17823,x17824,x17821),f327(x17823,x17824,x17822))
% 22.40/22.32 [1783]~E(x17831,x17832)+E(f504(x17831,x17833,x17834),f504(x17832,x17833,x17834))
% 22.40/22.32 [1784]~E(x17841,x17842)+E(f504(x17843,x17841,x17844),f504(x17843,x17842,x17844))
% 22.40/22.32 [1785]~E(x17851,x17852)+E(f504(x17853,x17854,x17851),f504(x17853,x17854,x17852))
% 22.40/22.32 [1786]~E(x17861,x17862)+E(f848(x17861,x17863),f848(x17862,x17863))
% 22.40/22.32 [1787]~E(x17871,x17872)+E(f848(x17873,x17871),f848(x17873,x17872))
% 22.40/22.32 [1788]~E(x17881,x17882)+E(f365(x17881,x17883,x17884,x17885,x17886),f365(x17882,x17883,x17884,x17885,x17886))
% 22.40/22.32 [1789]~E(x17891,x17892)+E(f365(x17893,x17891,x17894,x17895,x17896),f365(x17893,x17892,x17894,x17895,x17896))
% 22.40/22.32 [1790]~E(x17901,x17902)+E(f365(x17903,x17904,x17901,x17905,x17906),f365(x17903,x17904,x17902,x17905,x17906))
% 22.40/22.32 [1791]~E(x17911,x17912)+E(f365(x17913,x17914,x17915,x17911,x17916),f365(x17913,x17914,x17915,x17912,x17916))
% 22.40/22.32 [1792]~E(x17921,x17922)+E(f365(x17923,x17924,x17925,x17926,x17921),f365(x17923,x17924,x17925,x17926,x17922))
% 22.40/22.32 [1793]~E(x17931,x17932)+E(f380(x17931,x17933,x17934,x17935),f380(x17932,x17933,x17934,x17935))
% 22.40/22.32 [1794]~E(x17941,x17942)+E(f380(x17943,x17941,x17944,x17945),f380(x17943,x17942,x17944,x17945))
% 22.40/22.32 [1795]~E(x17951,x17952)+E(f380(x17953,x17954,x17951,x17955),f380(x17953,x17954,x17952,x17955))
% 22.40/22.32 [1796]~E(x17961,x17962)+E(f380(x17963,x17964,x17965,x17961),f380(x17963,x17964,x17965,x17962))
% 22.40/22.32 [1797]~E(x17971,x17972)+E(f898(x17971,x17973,x17974,x17975),f898(x17972,x17973,x17974,x17975))
% 22.40/22.32 [1798]~E(x17981,x17982)+E(f898(x17983,x17981,x17984,x17985),f898(x17983,x17982,x17984,x17985))
% 22.40/22.32 [1799]~E(x17991,x17992)+E(f898(x17993,x17994,x17991,x17995),f898(x17993,x17994,x17992,x17995))
% 22.40/22.32 [1800]~E(x18001,x18002)+E(f898(x18003,x18004,x18005,x18001),f898(x18003,x18004,x18005,x18002))
% 22.40/22.32 [1801]~E(x18011,x18012)+E(f492(x18011,x18013,x18014),f492(x18012,x18013,x18014))
% 22.40/22.32 [1802]~E(x18021,x18022)+E(f492(x18023,x18021,x18024),f492(x18023,x18022,x18024))
% 22.40/22.32 [1803]~E(x18031,x18032)+E(f492(x18033,x18034,x18031),f492(x18033,x18034,x18032))
% 22.40/22.32 [1804]~E(x18041,x18042)+E(f707(x18041,x18043),f707(x18042,x18043))
% 22.40/22.32 [1805]~E(x18051,x18052)+E(f707(x18053,x18051),f707(x18053,x18052))
% 22.40/22.32 [1806]~E(x18061,x18062)+E(f568(x18061,x18063,x18064),f568(x18062,x18063,x18064))
% 22.40/22.32 [1807]~E(x18071,x18072)+E(f568(x18073,x18071,x18074),f568(x18073,x18072,x18074))
% 22.40/22.32 [1808]~E(x18081,x18082)+E(f568(x18083,x18084,x18081),f568(x18083,x18084,x18082))
% 22.40/22.32 [1809]~E(x18091,x18092)+E(f272(x18091,x18093,x18094,x18095),f272(x18092,x18093,x18094,x18095))
% 22.40/22.32 [1810]~E(x18101,x18102)+E(f272(x18103,x18101,x18104,x18105),f272(x18103,x18102,x18104,x18105))
% 22.40/22.32 [1811]~E(x18111,x18112)+E(f272(x18113,x18114,x18111,x18115),f272(x18113,x18114,x18112,x18115))
% 22.40/22.32 [1812]~E(x18121,x18122)+E(f272(x18123,x18124,x18125,x18121),f272(x18123,x18124,x18125,x18122))
% 22.40/22.32 [1813]~E(x18131,x18132)+E(f764(x18131,x18133,x18134,x18135,x18136),f764(x18132,x18133,x18134,x18135,x18136))
% 22.40/22.32 [1814]~E(x18141,x18142)+E(f764(x18143,x18141,x18144,x18145,x18146),f764(x18143,x18142,x18144,x18145,x18146))
% 22.40/22.32 [1815]~E(x18151,x18152)+E(f764(x18153,x18154,x18151,x18155,x18156),f764(x18153,x18154,x18152,x18155,x18156))
% 22.40/22.32 [1816]~E(x18161,x18162)+E(f764(x18163,x18164,x18165,x18161,x18166),f764(x18163,x18164,x18165,x18162,x18166))
% 22.40/22.32 [1817]~E(x18171,x18172)+E(f764(x18173,x18174,x18175,x18176,x18171),f764(x18173,x18174,x18175,x18176,x18172))
% 22.40/22.32 [1818]~E(x18181,x18182)+E(f339(x18181,x18183),f339(x18182,x18183))
% 22.40/22.32 [1819]~E(x18191,x18192)+E(f339(x18193,x18191),f339(x18193,x18192))
% 22.40/22.32 [1820]~E(x18201,x18202)+E(f894(x18201,x18203),f894(x18202,x18203))
% 22.40/22.32 [1821]~E(x18211,x18212)+E(f894(x18213,x18211),f894(x18213,x18212))
% 22.40/22.32 [1822]~E(x18221,x18222)+E(f132(x18221,x18223,x18224),f132(x18222,x18223,x18224))
% 22.40/22.32 [1823]~E(x18231,x18232)+E(f132(x18233,x18231,x18234),f132(x18233,x18232,x18234))
% 22.40/22.32 [1824]~E(x18241,x18242)+E(f132(x18243,x18244,x18241),f132(x18243,x18244,x18242))
% 22.40/22.32 [1825]~E(x18251,x18252)+E(f441(x18251,x18253,x18254),f441(x18252,x18253,x18254))
% 22.40/22.32 [1826]~E(x18261,x18262)+E(f441(x18263,x18261,x18264),f441(x18263,x18262,x18264))
% 22.40/22.32 [1827]~E(x18271,x18272)+E(f441(x18273,x18274,x18271),f441(x18273,x18274,x18272))
% 22.40/22.32 [1828]~E(x18281,x18282)+E(f35(x18281),f35(x18282))
% 22.40/22.32 [1829]~E(x18291,x18292)+E(f659(x18291,x18293,x18294,x18295),f659(x18292,x18293,x18294,x18295))
% 22.40/22.32 [1830]~E(x18301,x18302)+E(f659(x18303,x18301,x18304,x18305),f659(x18303,x18302,x18304,x18305))
% 22.40/22.32 [1831]~E(x18311,x18312)+E(f659(x18313,x18314,x18311,x18315),f659(x18313,x18314,x18312,x18315))
% 22.40/22.32 [1832]~E(x18321,x18322)+E(f659(x18323,x18324,x18325,x18321),f659(x18323,x18324,x18325,x18322))
% 22.40/22.32 [1833]~E(x18331,x18332)+E(f525(x18331,x18333,x18334,x18335,x18336),f525(x18332,x18333,x18334,x18335,x18336))
% 22.40/22.32 [1834]~E(x18341,x18342)+E(f525(x18343,x18341,x18344,x18345,x18346),f525(x18343,x18342,x18344,x18345,x18346))
% 22.40/22.32 [1835]~E(x18351,x18352)+E(f525(x18353,x18354,x18351,x18355,x18356),f525(x18353,x18354,x18352,x18355,x18356))
% 22.40/22.32 [1836]~E(x18361,x18362)+E(f525(x18363,x18364,x18365,x18361,x18366),f525(x18363,x18364,x18365,x18362,x18366))
% 22.40/22.32 [1837]~E(x18371,x18372)+E(f525(x18373,x18374,x18375,x18376,x18371),f525(x18373,x18374,x18375,x18376,x18372))
% 22.40/22.32 [1838]~E(x18381,x18382)+E(f832(x18381,x18383,x18384,x18385,x18386,x18387,x18388),f832(x18382,x18383,x18384,x18385,x18386,x18387,x18388))
% 22.40/22.32 [1839]~E(x18391,x18392)+E(f832(x18393,x18391,x18394,x18395,x18396,x18397,x18398),f832(x18393,x18392,x18394,x18395,x18396,x18397,x18398))
% 22.40/22.32 [1840]~E(x18401,x18402)+E(f832(x18403,x18404,x18401,x18405,x18406,x18407,x18408),f832(x18403,x18404,x18402,x18405,x18406,x18407,x18408))
% 22.40/22.32 [1841]~E(x18411,x18412)+E(f832(x18413,x18414,x18415,x18411,x18416,x18417,x18418),f832(x18413,x18414,x18415,x18412,x18416,x18417,x18418))
% 22.40/22.32 [1842]~E(x18421,x18422)+E(f832(x18423,x18424,x18425,x18426,x18421,x18427,x18428),f832(x18423,x18424,x18425,x18426,x18422,x18427,x18428))
% 22.40/22.32 [1843]~E(x18431,x18432)+E(f832(x18433,x18434,x18435,x18436,x18437,x18431,x18438),f832(x18433,x18434,x18435,x18436,x18437,x18432,x18438))
% 22.40/22.32 [1844]~E(x18441,x18442)+E(f832(x18443,x18444,x18445,x18446,x18447,x18448,x18441),f832(x18443,x18444,x18445,x18446,x18447,x18448,x18442))
% 22.40/22.32 [1845]~E(x18451,x18452)+E(f207(x18451,x18453),f207(x18452,x18453))
% 22.40/22.32 [1846]~E(x18461,x18462)+E(f207(x18463,x18461),f207(x18463,x18462))
% 22.40/22.32 [1847]~E(x18471,x18472)+E(f428(x18471,x18473,x18474),f428(x18472,x18473,x18474))
% 22.40/22.32 [1848]~E(x18481,x18482)+E(f428(x18483,x18481,x18484),f428(x18483,x18482,x18484))
% 22.40/22.32 [1849]~E(x18491,x18492)+E(f428(x18493,x18494,x18491),f428(x18493,x18494,x18492))
% 22.40/22.32 [1850]~E(x18501,x18502)+E(f570(x18501,x18503,x18504,x18505,x18506),f570(x18502,x18503,x18504,x18505,x18506))
% 22.40/22.32 [1851]~E(x18511,x18512)+E(f570(x18513,x18511,x18514,x18515,x18516),f570(x18513,x18512,x18514,x18515,x18516))
% 22.40/22.32 [1852]~E(x18521,x18522)+E(f570(x18523,x18524,x18521,x18525,x18526),f570(x18523,x18524,x18522,x18525,x18526))
% 22.40/22.32 [1853]~E(x18531,x18532)+E(f570(x18533,x18534,x18535,x18531,x18536),f570(x18533,x18534,x18535,x18532,x18536))
% 22.40/22.32 [1854]~E(x18541,x18542)+E(f570(x18543,x18544,x18545,x18546,x18541),f570(x18543,x18544,x18545,x18546,x18542))
% 22.40/22.32 [1855]~E(x18551,x18552)+E(f194(x18551),f194(x18552))
% 22.40/22.32 [1856]~E(x18561,x18562)+E(f488(x18561,x18563,x18564),f488(x18562,x18563,x18564))
% 22.40/22.32 [1857]~E(x18571,x18572)+E(f488(x18573,x18571,x18574),f488(x18573,x18572,x18574))
% 22.40/22.32 [1858]~E(x18581,x18582)+E(f488(x18583,x18584,x18581),f488(x18583,x18584,x18582))
% 22.40/22.32 [1859]~E(x18591,x18592)+E(f497(x18591,x18593,x18594,x18595,x18596),f497(x18592,x18593,x18594,x18595,x18596))
% 22.40/22.32 [1860]~E(x18601,x18602)+E(f497(x18603,x18601,x18604,x18605,x18606),f497(x18603,x18602,x18604,x18605,x18606))
% 22.40/22.32 [1861]~E(x18611,x18612)+E(f497(x18613,x18614,x18611,x18615,x18616),f497(x18613,x18614,x18612,x18615,x18616))
% 22.40/22.32 [1862]~E(x18621,x18622)+E(f497(x18623,x18624,x18625,x18621,x18626),f497(x18623,x18624,x18625,x18622,x18626))
% 22.40/22.32 [1863]~E(x18631,x18632)+E(f497(x18633,x18634,x18635,x18636,x18631),f497(x18633,x18634,x18635,x18636,x18632))
% 22.40/22.32 [1864]~E(x18641,x18642)+E(f882(x18641,x18643,x18644,x18645,x18646),f882(x18642,x18643,x18644,x18645,x18646))
% 22.40/22.32 [1865]~E(x18651,x18652)+E(f882(x18653,x18651,x18654,x18655,x18656),f882(x18653,x18652,x18654,x18655,x18656))
% 22.40/22.32 [1866]~E(x18661,x18662)+E(f882(x18663,x18664,x18661,x18665,x18666),f882(x18663,x18664,x18662,x18665,x18666))
% 22.40/22.32 [1867]~E(x18671,x18672)+E(f882(x18673,x18674,x18675,x18671,x18676),f882(x18673,x18674,x18675,x18672,x18676))
% 22.40/22.32 [1868]~E(x18681,x18682)+E(f882(x18683,x18684,x18685,x18686,x18681),f882(x18683,x18684,x18685,x18686,x18682))
% 22.40/22.32 [1869]~E(x18691,x18692)+E(f195(x18691,x18693),f195(x18692,x18693))
% 22.40/22.32 [1870]~E(x18701,x18702)+E(f195(x18703,x18701),f195(x18703,x18702))
% 22.40/22.32 [1871]~E(x18711,x18712)+E(f382(x18711,x18713,x18714,x18715),f382(x18712,x18713,x18714,x18715))
% 22.40/22.32 [1872]~E(x18721,x18722)+E(f382(x18723,x18721,x18724,x18725),f382(x18723,x18722,x18724,x18725))
% 22.40/22.32 [1873]~E(x18731,x18732)+E(f382(x18733,x18734,x18731,x18735),f382(x18733,x18734,x18732,x18735))
% 22.40/22.32 [1874]~E(x18741,x18742)+E(f382(x18743,x18744,x18745,x18741),f382(x18743,x18744,x18745,x18742))
% 22.40/22.32 [1875]~E(x18751,x18752)+E(f119(x18751,x18753,x18754,x18755,x18756),f119(x18752,x18753,x18754,x18755,x18756))
% 22.40/22.32 [1876]~E(x18761,x18762)+E(f119(x18763,x18761,x18764,x18765,x18766),f119(x18763,x18762,x18764,x18765,x18766))
% 22.40/22.32 [1877]~E(x18771,x18772)+E(f119(x18773,x18774,x18771,x18775,x18776),f119(x18773,x18774,x18772,x18775,x18776))
% 22.40/22.32 [1878]~E(x18781,x18782)+E(f119(x18783,x18784,x18785,x18781,x18786),f119(x18783,x18784,x18785,x18782,x18786))
% 22.40/22.32 [1879]~E(x18791,x18792)+E(f119(x18793,x18794,x18795,x18796,x18791),f119(x18793,x18794,x18795,x18796,x18792))
% 22.40/22.32 [1880]~E(x18801,x18802)+E(f781(x18801,x18803),f781(x18802,x18803))
% 22.40/22.32 [1881]~E(x18811,x18812)+E(f781(x18813,x18811),f781(x18813,x18812))
% 22.40/22.32 [1882]~E(x18821,x18822)+E(f417(x18821,x18823,x18824,x18825),f417(x18822,x18823,x18824,x18825))
% 22.40/22.32 [1883]~E(x18831,x18832)+E(f417(x18833,x18831,x18834,x18835),f417(x18833,x18832,x18834,x18835))
% 22.40/22.32 [1884]~E(x18841,x18842)+E(f417(x18843,x18844,x18841,x18845),f417(x18843,x18844,x18842,x18845))
% 22.40/22.32 [1885]~E(x18851,x18852)+E(f417(x18853,x18854,x18855,x18851),f417(x18853,x18854,x18855,x18852))
% 22.40/22.32 [1886]~E(x18861,x18862)+E(f348(x18861,x18863,x18864,x18865),f348(x18862,x18863,x18864,x18865))
% 22.40/22.32 [1887]~E(x18871,x18872)+E(f348(x18873,x18871,x18874,x18875),f348(x18873,x18872,x18874,x18875))
% 22.40/22.32 [1888]~E(x18881,x18882)+E(f348(x18883,x18884,x18881,x18885),f348(x18883,x18884,x18882,x18885))
% 22.40/22.32 [1889]~E(x18891,x18892)+E(f348(x18893,x18894,x18895,x18891),f348(x18893,x18894,x18895,x18892))
% 22.40/22.32 [1890]~E(x18901,x18902)+E(f669(x18901,x18903,x18904),f669(x18902,x18903,x18904))
% 22.40/22.32 [1891]~E(x18911,x18912)+E(f669(x18913,x18911,x18914),f669(x18913,x18912,x18914))
% 22.40/22.32 [1892]~E(x18921,x18922)+E(f669(x18923,x18924,x18921),f669(x18923,x18924,x18922))
% 22.40/22.32 [1893]~E(x18931,x18932)+E(f252(x18931,x18933,x18934,x18935,x18936),f252(x18932,x18933,x18934,x18935,x18936))
% 22.40/22.32 [1894]~E(x18941,x18942)+E(f252(x18943,x18941,x18944,x18945,x18946),f252(x18943,x18942,x18944,x18945,x18946))
% 22.40/22.32 [1895]~E(x18951,x18952)+E(f252(x18953,x18954,x18951,x18955,x18956),f252(x18953,x18954,x18952,x18955,x18956))
% 22.40/22.32 [1896]~E(x18961,x18962)+E(f252(x18963,x18964,x18965,x18961,x18966),f252(x18963,x18964,x18965,x18962,x18966))
% 22.40/22.32 [1897]~E(x18971,x18972)+E(f252(x18973,x18974,x18975,x18976,x18971),f252(x18973,x18974,x18975,x18976,x18972))
% 22.40/22.32 [1898]~E(x18981,x18982)+E(f435(x18981,x18983),f435(x18982,x18983))
% 22.40/22.32 [1899]~E(x18991,x18992)+E(f435(x18993,x18991),f435(x18993,x18992))
% 22.40/22.32 [1900]~E(x19001,x19002)+E(f516(x19001,x19003,x19004),f516(x19002,x19003,x19004))
% 22.40/22.32 [1901]~E(x19011,x19012)+E(f516(x19013,x19011,x19014),f516(x19013,x19012,x19014))
% 22.40/22.32 [1902]~E(x19021,x19022)+E(f516(x19023,x19024,x19021),f516(x19023,x19024,x19022))
% 22.40/22.32 [1903]~E(x19031,x19032)+E(f360(x19031,x19033,x19034,x19035,x19036),f360(x19032,x19033,x19034,x19035,x19036))
% 22.40/22.32 [1904]~E(x19041,x19042)+E(f360(x19043,x19041,x19044,x19045,x19046),f360(x19043,x19042,x19044,x19045,x19046))
% 22.40/22.32 [1905]~E(x19051,x19052)+E(f360(x19053,x19054,x19051,x19055,x19056),f360(x19053,x19054,x19052,x19055,x19056))
% 22.40/22.32 [1906]~E(x19061,x19062)+E(f360(x19063,x19064,x19065,x19061,x19066),f360(x19063,x19064,x19065,x19062,x19066))
% 22.40/22.32 [1907]~E(x19071,x19072)+E(f360(x19073,x19074,x19075,x19076,x19071),f360(x19073,x19074,x19075,x19076,x19072))
% 22.40/22.32 [1908]~E(x19081,x19082)+E(f671(x19081,x19083,x19084,x19085,x19086),f671(x19082,x19083,x19084,x19085,x19086))
% 22.40/22.32 [1909]~E(x19091,x19092)+E(f671(x19093,x19091,x19094,x19095,x19096),f671(x19093,x19092,x19094,x19095,x19096))
% 22.40/22.32 [1910]~E(x19101,x19102)+E(f671(x19103,x19104,x19101,x19105,x19106),f671(x19103,x19104,x19102,x19105,x19106))
% 22.40/22.32 [1911]~E(x19111,x19112)+E(f671(x19113,x19114,x19115,x19111,x19116),f671(x19113,x19114,x19115,x19112,x19116))
% 22.40/22.32 [1912]~E(x19121,x19122)+E(f671(x19123,x19124,x19125,x19126,x19121),f671(x19123,x19124,x19125,x19126,x19122))
% 22.40/22.32 [1913]~E(x19131,x19132)+E(f783(x19131,x19133),f783(x19132,x19133))
% 22.40/22.32 [1914]~E(x19141,x19142)+E(f783(x19143,x19141),f783(x19143,x19142))
% 22.40/22.32 [1915]~E(x19151,x19152)+E(f405(x19151,x19153,x19154),f405(x19152,x19153,x19154))
% 22.40/22.32 [1916]~E(x19161,x19162)+E(f405(x19163,x19161,x19164),f405(x19163,x19162,x19164))
% 22.40/22.32 [1917]~E(x19171,x19172)+E(f405(x19173,x19174,x19171),f405(x19173,x19174,x19172))
% 22.40/22.32 [1918]~E(x19181,x19182)+E(f292(x19181,x19183,x19184,x19185,x19186),f292(x19182,x19183,x19184,x19185,x19186))
% 22.40/22.32 [1919]~E(x19191,x19192)+E(f292(x19193,x19191,x19194,x19195,x19196),f292(x19193,x19192,x19194,x19195,x19196))
% 22.40/22.32 [1920]~E(x19201,x19202)+E(f292(x19203,x19204,x19201,x19205,x19206),f292(x19203,x19204,x19202,x19205,x19206))
% 22.40/22.32 [1921]~E(x19211,x19212)+E(f292(x19213,x19214,x19215,x19211,x19216),f292(x19213,x19214,x19215,x19212,x19216))
% 22.40/22.32 [1922]~E(x19221,x19222)+E(f292(x19223,x19224,x19225,x19226,x19221),f292(x19223,x19224,x19225,x19226,x19222))
% 22.40/22.32 [1923]~E(x19231,x19232)+E(f324(x19231),f324(x19232))
% 22.40/22.32 [1924]~E(x19241,x19242)+E(f613(x19241,x19243,x19244,x19245),f613(x19242,x19243,x19244,x19245))
% 22.40/22.32 [1925]~E(x19251,x19252)+E(f613(x19253,x19251,x19254,x19255),f613(x19253,x19252,x19254,x19255))
% 22.40/22.32 [1926]~E(x19261,x19262)+E(f613(x19263,x19264,x19261,x19265),f613(x19263,x19264,x19262,x19265))
% 22.40/22.32 [1927]~E(x19271,x19272)+E(f613(x19273,x19274,x19275,x19271),f613(x19273,x19274,x19275,x19272))
% 22.40/22.32 [1928]~E(x19281,x19282)+E(f351(x19281,x19283,x19284,x19285,x19286),f351(x19282,x19283,x19284,x19285,x19286))
% 22.40/22.32 [1929]~E(x19291,x19292)+E(f351(x19293,x19291,x19294,x19295,x19296),f351(x19293,x19292,x19294,x19295,x19296))
% 22.40/22.32 [1930]~E(x19301,x19302)+E(f351(x19303,x19304,x19301,x19305,x19306),f351(x19303,x19304,x19302,x19305,x19306))
% 22.40/22.32 [1931]~E(x19311,x19312)+E(f351(x19313,x19314,x19315,x19311,x19316),f351(x19313,x19314,x19315,x19312,x19316))
% 22.40/22.32 [1932]~E(x19321,x19322)+E(f351(x19323,x19324,x19325,x19326,x19321),f351(x19323,x19324,x19325,x19326,x19322))
% 22.40/22.32 [1933]~E(x19331,x19332)+E(f467(x19331,x19333,x19334,x19335,x19336),f467(x19332,x19333,x19334,x19335,x19336))
% 22.40/22.32 [1934]~E(x19341,x19342)+E(f467(x19343,x19341,x19344,x19345,x19346),f467(x19343,x19342,x19344,x19345,x19346))
% 22.40/22.32 [1935]~E(x19351,x19352)+E(f467(x19353,x19354,x19351,x19355,x19356),f467(x19353,x19354,x19352,x19355,x19356))
% 22.40/22.32 [1936]~E(x19361,x19362)+E(f467(x19363,x19364,x19365,x19361,x19366),f467(x19363,x19364,x19365,x19362,x19366))
% 22.40/22.32 [1937]~E(x19371,x19372)+E(f467(x19373,x19374,x19375,x19376,x19371),f467(x19373,x19374,x19375,x19376,x19372))
% 22.40/22.32 [1938]~E(x19381,x19382)+E(f501(x19381,x19383,x19384,x19385,x19386,x19387),f501(x19382,x19383,x19384,x19385,x19386,x19387))
% 22.40/22.32 [1939]~E(x19391,x19392)+E(f501(x19393,x19391,x19394,x19395,x19396,x19397),f501(x19393,x19392,x19394,x19395,x19396,x19397))
% 22.40/22.32 [1940]~E(x19401,x19402)+E(f501(x19403,x19404,x19401,x19405,x19406,x19407),f501(x19403,x19404,x19402,x19405,x19406,x19407))
% 22.40/22.32 [1941]~E(x19411,x19412)+E(f501(x19413,x19414,x19415,x19411,x19416,x19417),f501(x19413,x19414,x19415,x19412,x19416,x19417))
% 22.40/22.32 [1942]~E(x19421,x19422)+E(f501(x19423,x19424,x19425,x19426,x19421,x19427),f501(x19423,x19424,x19425,x19426,x19422,x19427))
% 22.40/22.32 [1943]~E(x19431,x19432)+E(f501(x19433,x19434,x19435,x19436,x19437,x19431),f501(x19433,x19434,x19435,x19436,x19437,x19432))
% 22.40/22.32 [1944]~E(x19441,x19442)+E(f284(x19441,x19443),f284(x19442,x19443))
% 22.40/22.32 [1945]~E(x19451,x19452)+E(f284(x19453,x19451),f284(x19453,x19452))
% 22.40/22.32 [1946]~E(x19461,x19462)+E(f257(x19461,x19463,x19464),f257(x19462,x19463,x19464))
% 22.40/22.32 [1947]~E(x19471,x19472)+E(f257(x19473,x19471,x19474),f257(x19473,x19472,x19474))
% 22.40/22.32 [1948]~E(x19481,x19482)+E(f257(x19483,x19484,x19481),f257(x19483,x19484,x19482))
% 22.40/22.32 [1949]~E(x19491,x19492)+E(f826(x19491,x19493,x19494,x19495),f826(x19492,x19493,x19494,x19495))
% 22.40/22.32 [1950]~E(x19501,x19502)+E(f826(x19503,x19501,x19504,x19505),f826(x19503,x19502,x19504,x19505))
% 22.40/22.32 [1951]~E(x19511,x19512)+E(f826(x19513,x19514,x19511,x19515),f826(x19513,x19514,x19512,x19515))
% 22.40/22.32 [1952]~E(x19521,x19522)+E(f826(x19523,x19524,x19525,x19521),f826(x19523,x19524,x19525,x19522))
% 22.40/22.32 [1953]~E(x19531,x19532)+E(f154(x19531,x19533),f154(x19532,x19533))
% 22.40/22.32 [1954]~E(x19541,x19542)+E(f154(x19543,x19541),f154(x19543,x19542))
% 22.40/22.32 [1955]~E(x19551,x19552)+E(f547(x19551,x19553),f547(x19552,x19553))
% 22.40/22.32 [1956]~E(x19561,x19562)+E(f547(x19563,x19561),f547(x19563,x19562))
% 22.40/22.32 [1957]~E(x19571,x19572)+E(f551(x19571,x19573,x19574,x19575),f551(x19572,x19573,x19574,x19575))
% 22.40/22.32 [1958]~E(x19581,x19582)+E(f551(x19583,x19581,x19584,x19585),f551(x19583,x19582,x19584,x19585))
% 22.40/22.32 [1959]~E(x19591,x19592)+E(f551(x19593,x19594,x19591,x19595),f551(x19593,x19594,x19592,x19595))
% 22.40/22.32 [1960]~E(x19601,x19602)+E(f551(x19603,x19604,x19605,x19601),f551(x19603,x19604,x19605,x19602))
% 22.40/22.32 [1961]~E(x19611,x19612)+E(f499(x19611,x19613,x19614,x19615),f499(x19612,x19613,x19614,x19615))
% 22.40/22.32 [1962]~E(x19621,x19622)+E(f499(x19623,x19621,x19624,x19625),f499(x19623,x19622,x19624,x19625))
% 22.40/22.32 [1963]~E(x19631,x19632)+E(f499(x19633,x19634,x19631,x19635),f499(x19633,x19634,x19632,x19635))
% 22.40/22.32 [1964]~E(x19641,x19642)+E(f499(x19643,x19644,x19645,x19641),f499(x19643,x19644,x19645,x19642))
% 22.40/22.32 [1965]~E(x19651,x19652)+E(f583(x19651,x19653,x19654,x19655,x19656,x19657),f583(x19652,x19653,x19654,x19655,x19656,x19657))
% 22.40/22.32 [1966]~E(x19661,x19662)+E(f583(x19663,x19661,x19664,x19665,x19666,x19667),f583(x19663,x19662,x19664,x19665,x19666,x19667))
% 22.40/22.32 [1967]~E(x19671,x19672)+E(f583(x19673,x19674,x19671,x19675,x19676,x19677),f583(x19673,x19674,x19672,x19675,x19676,x19677))
% 22.40/22.32 [1968]~E(x19681,x19682)+E(f583(x19683,x19684,x19685,x19681,x19686,x19687),f583(x19683,x19684,x19685,x19682,x19686,x19687))
% 22.40/22.32 [1969]~E(x19691,x19692)+E(f583(x19693,x19694,x19695,x19696,x19691,x19697),f583(x19693,x19694,x19695,x19696,x19692,x19697))
% 22.40/22.32 [1970]~E(x19701,x19702)+E(f583(x19703,x19704,x19705,x19706,x19707,x19701),f583(x19703,x19704,x19705,x19706,x19707,x19702))
% 22.40/22.32 [1971]~E(x19711,x19712)+E(f629(x19711,x19713,x19714,x19715,x19716),f629(x19712,x19713,x19714,x19715,x19716))
% 22.40/22.32 [1972]~E(x19721,x19722)+E(f629(x19723,x19721,x19724,x19725,x19726),f629(x19723,x19722,x19724,x19725,x19726))
% 22.40/22.32 [1973]~E(x19731,x19732)+E(f629(x19733,x19734,x19731,x19735,x19736),f629(x19733,x19734,x19732,x19735,x19736))
% 22.40/22.32 [1974]~E(x19741,x19742)+E(f629(x19743,x19744,x19745,x19741,x19746),f629(x19743,x19744,x19745,x19742,x19746))
% 22.40/22.32 [1975]~E(x19751,x19752)+E(f629(x19753,x19754,x19755,x19756,x19751),f629(x19753,x19754,x19755,x19756,x19752))
% 22.40/22.32 [1976]~E(x19761,x19762)+E(f517(x19761,x19763,x19764,x19765,x19766,x19767,x19768),f517(x19762,x19763,x19764,x19765,x19766,x19767,x19768))
% 22.40/22.32 [1977]~E(x19771,x19772)+E(f517(x19773,x19771,x19774,x19775,x19776,x19777,x19778),f517(x19773,x19772,x19774,x19775,x19776,x19777,x19778))
% 22.40/22.32 [1978]~E(x19781,x19782)+E(f517(x19783,x19784,x19781,x19785,x19786,x19787,x19788),f517(x19783,x19784,x19782,x19785,x19786,x19787,x19788))
% 22.40/22.32 [1979]~E(x19791,x19792)+E(f517(x19793,x19794,x19795,x19791,x19796,x19797,x19798),f517(x19793,x19794,x19795,x19792,x19796,x19797,x19798))
% 22.40/22.32 [1980]~E(x19801,x19802)+E(f517(x19803,x19804,x19805,x19806,x19801,x19807,x19808),f517(x19803,x19804,x19805,x19806,x19802,x19807,x19808))
% 22.40/22.32 [1981]~E(x19811,x19812)+E(f517(x19813,x19814,x19815,x19816,x19817,x19811,x19818),f517(x19813,x19814,x19815,x19816,x19817,x19812,x19818))
% 22.40/22.32 [1982]~E(x19821,x19822)+E(f517(x19823,x19824,x19825,x19826,x19827,x19828,x19821),f517(x19823,x19824,x19825,x19826,x19827,x19828,x19822))
% 22.40/22.32 [1983]~E(x19831,x19832)+E(f799(x19831,x19833),f799(x19832,x19833))
% 22.40/22.32 [1984]~E(x19841,x19842)+E(f799(x19843,x19841),f799(x19843,x19842))
% 22.40/22.32 [1985]~E(x19851,x19852)+E(f471(x19851,x19853,x19854,x19855,x19856),f471(x19852,x19853,x19854,x19855,x19856))
% 22.40/22.32 [1986]~E(x19861,x19862)+E(f471(x19863,x19861,x19864,x19865,x19866),f471(x19863,x19862,x19864,x19865,x19866))
% 22.40/22.32 [1987]~E(x19871,x19872)+E(f471(x19873,x19874,x19871,x19875,x19876),f471(x19873,x19874,x19872,x19875,x19876))
% 22.40/22.32 [1988]~E(x19881,x19882)+E(f471(x19883,x19884,x19885,x19881,x19886),f471(x19883,x19884,x19885,x19882,x19886))
% 22.40/22.32 [1989]~E(x19891,x19892)+E(f471(x19893,x19894,x19895,x19896,x19891),f471(x19893,x19894,x19895,x19896,x19892))
% 22.40/22.32 [1990]~E(x19901,x19902)+E(f533(x19901,x19903,x19904,x19905,x19906,x19907),f533(x19902,x19903,x19904,x19905,x19906,x19907))
% 22.40/22.32 [1991]~E(x19911,x19912)+E(f533(x19913,x19911,x19914,x19915,x19916,x19917),f533(x19913,x19912,x19914,x19915,x19916,x19917))
% 22.40/22.32 [1992]~E(x19921,x19922)+E(f533(x19923,x19924,x19921,x19925,x19926,x19927),f533(x19923,x19924,x19922,x19925,x19926,x19927))
% 22.40/22.32 [1993]~E(x19931,x19932)+E(f533(x19933,x19934,x19935,x19931,x19936,x19937),f533(x19933,x19934,x19935,x19932,x19936,x19937))
% 22.40/22.32 [1994]~E(x19941,x19942)+E(f533(x19943,x19944,x19945,x19946,x19941,x19947),f533(x19943,x19944,x19945,x19946,x19942,x19947))
% 22.40/22.32 [1995]~E(x19951,x19952)+E(f533(x19953,x19954,x19955,x19956,x19957,x19951),f533(x19953,x19954,x19955,x19956,x19957,x19952))
% 22.40/22.32 [1996]~E(x19961,x19962)+E(f328(x19961),f328(x19962))
% 22.40/22.32 [1997]~E(x19971,x19972)+E(f222(x19971,x19973,x19974,x19975),f222(x19972,x19973,x19974,x19975))
% 22.40/22.32 [1998]~E(x19981,x19982)+E(f222(x19983,x19981,x19984,x19985),f222(x19983,x19982,x19984,x19985))
% 22.40/22.32 [1999]~E(x19991,x19992)+E(f222(x19993,x19994,x19991,x19995),f222(x19993,x19994,x19992,x19995))
% 22.40/22.32 [2000]~E(x20001,x20002)+E(f222(x20003,x20004,x20005,x20001),f222(x20003,x20004,x20005,x20002))
% 22.40/22.32 [2001]~E(x20011,x20012)+E(f200(x20011,x20013,x20014,x20015,x20016,x20017,x20018),f200(x20012,x20013,x20014,x20015,x20016,x20017,x20018))
% 22.40/22.32 [2002]~E(x20021,x20022)+E(f200(x20023,x20021,x20024,x20025,x20026,x20027,x20028),f200(x20023,x20022,x20024,x20025,x20026,x20027,x20028))
% 22.40/22.32 [2003]~E(x20031,x20032)+E(f200(x20033,x20034,x20031,x20035,x20036,x20037,x20038),f200(x20033,x20034,x20032,x20035,x20036,x20037,x20038))
% 22.40/22.32 [2004]~E(x20041,x20042)+E(f200(x20043,x20044,x20045,x20041,x20046,x20047,x20048),f200(x20043,x20044,x20045,x20042,x20046,x20047,x20048))
% 22.40/22.32 [2005]~E(x20051,x20052)+E(f200(x20053,x20054,x20055,x20056,x20051,x20057,x20058),f200(x20053,x20054,x20055,x20056,x20052,x20057,x20058))
% 22.40/22.32 [2006]~E(x20061,x20062)+E(f200(x20063,x20064,x20065,x20066,x20067,x20061,x20068),f200(x20063,x20064,x20065,x20066,x20067,x20062,x20068))
% 22.40/22.32 [2007]~E(x20071,x20072)+E(f200(x20073,x20074,x20075,x20076,x20077,x20078,x20071),f200(x20073,x20074,x20075,x20076,x20077,x20078,x20072))
% 22.40/22.32 [2008]~E(x20081,x20082)+E(f661(x20081,x20083,x20084,x20085),f661(x20082,x20083,x20084,x20085))
% 22.40/22.32 [2009]~E(x20091,x20092)+E(f661(x20093,x20091,x20094,x20095),f661(x20093,x20092,x20094,x20095))
% 22.40/22.32 [2010]~E(x20101,x20102)+E(f661(x20103,x20104,x20101,x20105),f661(x20103,x20104,x20102,x20105))
% 22.40/22.32 [2011]~E(x20111,x20112)+E(f661(x20113,x20114,x20115,x20111),f661(x20113,x20114,x20115,x20112))
% 22.40/22.32 [2012]~E(x20121,x20122)+E(f684(x20121,x20123,x20124),f684(x20122,x20123,x20124))
% 22.40/22.32 [2013]~E(x20131,x20132)+E(f684(x20133,x20131,x20134),f684(x20133,x20132,x20134))
% 22.40/22.32 [2014]~E(x20141,x20142)+E(f684(x20143,x20144,x20141),f684(x20143,x20144,x20142))
% 22.40/22.32 [2015]~E(x20151,x20152)+E(f313(x20151,x20153,x20154),f313(x20152,x20153,x20154))
% 22.40/22.32 [2016]~E(x20161,x20162)+E(f313(x20163,x20161,x20164),f313(x20163,x20162,x20164))
% 22.40/22.32 [2017]~E(x20171,x20172)+E(f313(x20173,x20174,x20171),f313(x20173,x20174,x20172))
% 22.40/22.32 [2018]~E(x20181,x20182)+E(f109(x20181,x20183,x20184),f109(x20182,x20183,x20184))
% 22.40/22.32 [2019]~E(x20191,x20192)+E(f109(x20193,x20191,x20194),f109(x20193,x20192,x20194))
% 22.40/22.32 [2020]~E(x20201,x20202)+E(f109(x20203,x20204,x20201),f109(x20203,x20204,x20202))
% 22.40/22.32 [2021]~E(x20211,x20212)+E(f588(x20211,x20213),f588(x20212,x20213))
% 22.40/22.32 [2022]~E(x20221,x20222)+E(f588(x20223,x20221),f588(x20223,x20222))
% 22.40/22.32 [2023]~E(x20231,x20232)+E(f155(x20231,x20233,x20234,x20235),f155(x20232,x20233,x20234,x20235))
% 22.40/22.32 [2024]~E(x20241,x20242)+E(f155(x20243,x20241,x20244,x20245),f155(x20243,x20242,x20244,x20245))
% 22.40/22.32 [2025]~E(x20251,x20252)+E(f155(x20253,x20254,x20251,x20255),f155(x20253,x20254,x20252,x20255))
% 22.40/22.32 [2026]~E(x20261,x20262)+E(f155(x20263,x20264,x20265,x20261),f155(x20263,x20264,x20265,x20262))
% 22.40/22.32 [2027]~E(x20271,x20272)+E(f614(x20271,x20273),f614(x20272,x20273))
% 22.40/22.32 [2028]~E(x20281,x20282)+E(f614(x20283,x20281),f614(x20283,x20282))
% 22.40/22.32 [2029]~E(x20291,x20292)+E(f349(x20291,x20293,x20294,x20295,x20296),f349(x20292,x20293,x20294,x20295,x20296))
% 22.40/22.32 [2030]~E(x20301,x20302)+E(f349(x20303,x20301,x20304,x20305,x20306),f349(x20303,x20302,x20304,x20305,x20306))
% 22.40/22.32 [2031]~E(x20311,x20312)+E(f349(x20313,x20314,x20311,x20315,x20316),f349(x20313,x20314,x20312,x20315,x20316))
% 22.40/22.32 [2032]~E(x20321,x20322)+E(f349(x20323,x20324,x20325,x20321,x20326),f349(x20323,x20324,x20325,x20322,x20326))
% 22.40/22.32 [2033]~E(x20331,x20332)+E(f349(x20333,x20334,x20335,x20336,x20331),f349(x20333,x20334,x20335,x20336,x20332))
% 22.40/22.32 [2034]~E(x20341,x20342)+E(f414(x20341,x20343,x20344,x20345),f414(x20342,x20343,x20344,x20345))
% 22.40/22.32 [2035]~E(x20351,x20352)+E(f414(x20353,x20351,x20354,x20355),f414(x20353,x20352,x20354,x20355))
% 22.40/22.32 [2036]~E(x20361,x20362)+E(f414(x20363,x20364,x20361,x20365),f414(x20363,x20364,x20362,x20365))
% 22.40/22.32 [2037]~E(x20371,x20372)+E(f414(x20373,x20374,x20375,x20371),f414(x20373,x20374,x20375,x20372))
% 22.40/22.32 [2038]~E(x20381,x20382)+E(f193(x20381),f193(x20382))
% 22.40/22.32 [2039]~E(x20391,x20392)+E(f264(x20391,x20393),f264(x20392,x20393))
% 22.40/22.32 [2040]~E(x20401,x20402)+E(f264(x20403,x20401),f264(x20403,x20402))
% 22.40/22.32 [2041]~E(x20411,x20412)+E(f398(x20411,x20413,x20414,x20415),f398(x20412,x20413,x20414,x20415))
% 22.40/22.32 [2042]~E(x20421,x20422)+E(f398(x20423,x20421,x20424,x20425),f398(x20423,x20422,x20424,x20425))
% 22.40/22.32 [2043]~E(x20431,x20432)+E(f398(x20433,x20434,x20431,x20435),f398(x20433,x20434,x20432,x20435))
% 22.40/22.32 [2044]~E(x20441,x20442)+E(f398(x20443,x20444,x20445,x20441),f398(x20443,x20444,x20445,x20442))
% 22.40/22.32 [2045]~E(x20451,x20452)+E(f283(x20451,x20453),f283(x20452,x20453))
% 22.40/22.32 [2046]~E(x20461,x20462)+E(f283(x20463,x20461),f283(x20463,x20462))
% 22.40/22.32 [2047]~E(x20471,x20472)+E(f571(x20471,x20473,x20474,x20475),f571(x20472,x20473,x20474,x20475))
% 22.40/22.32 [2048]~E(x20481,x20482)+E(f571(x20483,x20481,x20484,x20485),f571(x20483,x20482,x20484,x20485))
% 22.40/22.32 [2049]~E(x20491,x20492)+E(f571(x20493,x20494,x20491,x20495),f571(x20493,x20494,x20492,x20495))
% 22.40/22.32 [2050]~E(x20501,x20502)+E(f571(x20503,x20504,x20505,x20501),f571(x20503,x20504,x20505,x20502))
% 22.40/22.32 [2051]~E(x20511,x20512)+E(f363(x20511,x20513,x20514,x20515,x20516),f363(x20512,x20513,x20514,x20515,x20516))
% 22.40/22.32 [2052]~E(x20521,x20522)+E(f363(x20523,x20521,x20524,x20525,x20526),f363(x20523,x20522,x20524,x20525,x20526))
% 22.40/22.32 [2053]~E(x20531,x20532)+E(f363(x20533,x20534,x20531,x20535,x20536),f363(x20533,x20534,x20532,x20535,x20536))
% 22.40/22.32 [2054]~E(x20541,x20542)+E(f363(x20543,x20544,x20545,x20541,x20546),f363(x20543,x20544,x20545,x20542,x20546))
% 22.40/22.32 [2055]~E(x20551,x20552)+E(f363(x20553,x20554,x20555,x20556,x20551),f363(x20553,x20554,x20555,x20556,x20552))
% 22.40/22.32 [2056]~E(x20561,x20562)+E(f500(x20561,x20563,x20564,x20565,x20566,x20567),f500(x20562,x20563,x20564,x20565,x20566,x20567))
% 22.40/22.32 [2057]~E(x20571,x20572)+E(f500(x20573,x20571,x20574,x20575,x20576,x20577),f500(x20573,x20572,x20574,x20575,x20576,x20577))
% 22.40/22.32 [2058]~E(x20581,x20582)+E(f500(x20583,x20584,x20581,x20585,x20586,x20587),f500(x20583,x20584,x20582,x20585,x20586,x20587))
% 22.40/22.32 [2059]~E(x20591,x20592)+E(f500(x20593,x20594,x20595,x20591,x20596,x20597),f500(x20593,x20594,x20595,x20592,x20596,x20597))
% 22.40/22.32 [2060]~E(x20601,x20602)+E(f500(x20603,x20604,x20605,x20606,x20601,x20607),f500(x20603,x20604,x20605,x20606,x20602,x20607))
% 22.40/22.32 [2061]~E(x20611,x20612)+E(f500(x20613,x20614,x20615,x20616,x20617,x20611),f500(x20613,x20614,x20615,x20616,x20617,x20612))
% 22.40/22.32 [2062]~E(x20621,x20622)+E(f451(x20621,x20623,x20624),f451(x20622,x20623,x20624))
% 22.40/22.32 [2063]~E(x20631,x20632)+E(f451(x20633,x20631,x20634),f451(x20633,x20632,x20634))
% 22.40/22.32 [2064]~E(x20641,x20642)+E(f451(x20643,x20644,x20641),f451(x20643,x20644,x20642))
% 22.40/22.32 [2065]~E(x20651,x20652)+E(f114(x20651,x20653,x20654,x20655),f114(x20652,x20653,x20654,x20655))
% 22.40/22.32 [2066]~E(x20661,x20662)+E(f114(x20663,x20661,x20664,x20665),f114(x20663,x20662,x20664,x20665))
% 22.40/22.32 [2067]~E(x20671,x20672)+E(f114(x20673,x20674,x20671,x20675),f114(x20673,x20674,x20672,x20675))
% 22.40/22.32 [2068]~E(x20681,x20682)+E(f114(x20683,x20684,x20685,x20681),f114(x20683,x20684,x20685,x20682))
% 22.40/22.32 [2069]~E(x20691,x20692)+E(f416(x20691,x20693,x20694,x20695),f416(x20692,x20693,x20694,x20695))
% 22.40/22.32 [2070]~E(x20701,x20702)+E(f416(x20703,x20701,x20704,x20705),f416(x20703,x20702,x20704,x20705))
% 22.40/22.32 [2071]~E(x20711,x20712)+E(f416(x20713,x20714,x20711,x20715),f416(x20713,x20714,x20712,x20715))
% 22.40/22.32 [2072]~E(x20721,x20722)+E(f416(x20723,x20724,x20725,x20721),f416(x20723,x20724,x20725,x20722))
% 22.40/22.32 [2073]~E(x20731,x20732)+E(f779(x20731,x20733,x20734,x20735,x20736,x20737,x20738),f779(x20732,x20733,x20734,x20735,x20736,x20737,x20738))
% 22.40/22.32 [2074]~E(x20741,x20742)+E(f779(x20743,x20741,x20744,x20745,x20746,x20747,x20748),f779(x20743,x20742,x20744,x20745,x20746,x20747,x20748))
% 22.40/22.32 [2075]~E(x20751,x20752)+E(f779(x20753,x20754,x20751,x20755,x20756,x20757,x20758),f779(x20753,x20754,x20752,x20755,x20756,x20757,x20758))
% 22.40/22.32 [2076]~E(x20761,x20762)+E(f779(x20763,x20764,x20765,x20761,x20766,x20767,x20768),f779(x20763,x20764,x20765,x20762,x20766,x20767,x20768))
% 22.40/22.32 [2077]~E(x20771,x20772)+E(f779(x20773,x20774,x20775,x20776,x20771,x20777,x20778),f779(x20773,x20774,x20775,x20776,x20772,x20777,x20778))
% 22.40/22.32 [2078]~E(x20781,x20782)+E(f779(x20783,x20784,x20785,x20786,x20787,x20781,x20788),f779(x20783,x20784,x20785,x20786,x20787,x20782,x20788))
% 22.40/22.32 [2079]~E(x20791,x20792)+E(f779(x20793,x20794,x20795,x20796,x20797,x20798,x20791),f779(x20793,x20794,x20795,x20796,x20797,x20798,x20792))
% 22.40/22.32 [2080]~E(x20801,x20802)+E(f641(x20801,x20803,x20804,x20805,x20806,x20807),f641(x20802,x20803,x20804,x20805,x20806,x20807))
% 22.40/22.32 [2081]~E(x20811,x20812)+E(f641(x20813,x20811,x20814,x20815,x20816,x20817),f641(x20813,x20812,x20814,x20815,x20816,x20817))
% 22.40/22.32 [2082]~E(x20821,x20822)+E(f641(x20823,x20824,x20821,x20825,x20826,x20827),f641(x20823,x20824,x20822,x20825,x20826,x20827))
% 22.40/22.32 [2083]~E(x20831,x20832)+E(f641(x20833,x20834,x20835,x20831,x20836,x20837),f641(x20833,x20834,x20835,x20832,x20836,x20837))
% 22.40/22.32 [2084]~E(x20841,x20842)+E(f641(x20843,x20844,x20845,x20846,x20841,x20847),f641(x20843,x20844,x20845,x20846,x20842,x20847))
% 22.40/22.32 [2085]~E(x20851,x20852)+E(f641(x20853,x20854,x20855,x20856,x20857,x20851),f641(x20853,x20854,x20855,x20856,x20857,x20852))
% 22.40/22.32 [2086]~E(x20861,x20862)+E(f607(x20861,x20863,x20864,x20865,x20866),f607(x20862,x20863,x20864,x20865,x20866))
% 22.40/22.32 [2087]~E(x20871,x20872)+E(f607(x20873,x20871,x20874,x20875,x20876),f607(x20873,x20872,x20874,x20875,x20876))
% 22.40/22.32 [2088]~E(x20881,x20882)+E(f607(x20883,x20884,x20881,x20885,x20886),f607(x20883,x20884,x20882,x20885,x20886))
% 22.40/22.32 [2089]~E(x20891,x20892)+E(f607(x20893,x20894,x20895,x20891,x20896),f607(x20893,x20894,x20895,x20892,x20896))
% 22.40/22.32 [2090]~E(x20901,x20902)+E(f607(x20903,x20904,x20905,x20906,x20901),f607(x20903,x20904,x20905,x20906,x20902))
% 22.40/22.32 [2091]~E(x20911,x20912)+E(f812(x20911,x20913),f812(x20912,x20913))
% 22.40/22.32 [2092]~E(x20921,x20922)+E(f812(x20923,x20921),f812(x20923,x20922))
% 22.40/22.32 [2093]~E(x20931,x20932)+E(f450(x20931,x20933,x20934),f450(x20932,x20933,x20934))
% 22.40/22.32 [2094]~E(x20941,x20942)+E(f450(x20943,x20941,x20944),f450(x20943,x20942,x20944))
% 22.40/22.32 [2095]~E(x20951,x20952)+E(f450(x20953,x20954,x20951),f450(x20953,x20954,x20952))
% 22.40/22.32 [2096]~E(x20961,x20962)+E(f703(x20961,x20963,x20964),f703(x20962,x20963,x20964))
% 22.40/22.32 [2097]~E(x20971,x20972)+E(f703(x20973,x20971,x20974),f703(x20973,x20972,x20974))
% 22.40/22.32 [2098]~E(x20981,x20982)+E(f703(x20983,x20984,x20981),f703(x20983,x20984,x20982))
% 22.40/22.32 [2099]~E(x20991,x20992)+E(f750(x20991,x20993,x20994),f750(x20992,x20993,x20994))
% 22.40/22.32 [2100]~E(x21001,x21002)+E(f750(x21003,x21001,x21004),f750(x21003,x21002,x21004))
% 22.40/22.32 [2101]~E(x21011,x21012)+E(f750(x21013,x21014,x21011),f750(x21013,x21014,x21012))
% 22.40/22.32 [2102]~E(x21021,x21022)+E(f427(x21021,x21023,x21024),f427(x21022,x21023,x21024))
% 22.40/22.32 [2103]~E(x21031,x21032)+E(f427(x21033,x21031,x21034),f427(x21033,x21032,x21034))
% 22.40/22.32 [2104]~E(x21041,x21042)+E(f427(x21043,x21044,x21041),f427(x21043,x21044,x21042))
% 22.40/22.32 [2105]~E(x21051,x21052)+E(f880(x21051,x21053,x21054),f880(x21052,x21053,x21054))
% 22.40/22.32 [2106]~E(x21061,x21062)+E(f880(x21063,x21061,x21064),f880(x21063,x21062,x21064))
% 22.40/22.32 [2107]~E(x21071,x21072)+E(f880(x21073,x21074,x21071),f880(x21073,x21074,x21072))
% 22.40/22.32 [2108]~E(x21081,x21082)+E(f653(x21081,x21083,x21084),f653(x21082,x21083,x21084))
% 22.40/22.32 [2109]~E(x21091,x21092)+E(f653(x21093,x21091,x21094),f653(x21093,x21092,x21094))
% 22.40/22.32 [2110]~E(x21101,x21102)+E(f653(x21103,x21104,x21101),f653(x21103,x21104,x21102))
% 22.40/22.32 [2111]~E(x21111,x21112)+E(f645(x21111,x21113,x21114,x21115,x21116),f645(x21112,x21113,x21114,x21115,x21116))
% 22.40/22.32 [2112]~E(x21121,x21122)+E(f645(x21123,x21121,x21124,x21125,x21126),f645(x21123,x21122,x21124,x21125,x21126))
% 22.40/22.32 [2113]~E(x21131,x21132)+E(f645(x21133,x21134,x21131,x21135,x21136),f645(x21133,x21134,x21132,x21135,x21136))
% 22.40/22.32 [2114]~E(x21141,x21142)+E(f645(x21143,x21144,x21145,x21141,x21146),f645(x21143,x21144,x21145,x21142,x21146))
% 22.40/22.32 [2115]~E(x21151,x21152)+E(f645(x21153,x21154,x21155,x21156,x21151),f645(x21153,x21154,x21155,x21156,x21152))
% 22.40/22.32 [2116]~E(x21161,x21162)+E(f536(x21161,x21163,x21164,x21165),f536(x21162,x21163,x21164,x21165))
% 22.40/22.32 [2117]~E(x21171,x21172)+E(f536(x21173,x21171,x21174,x21175),f536(x21173,x21172,x21174,x21175))
% 22.40/22.32 [2118]~E(x21181,x21182)+E(f536(x21183,x21184,x21181,x21185),f536(x21183,x21184,x21182,x21185))
% 22.40/22.32 [2119]~E(x21191,x21192)+E(f536(x21193,x21194,x21195,x21191),f536(x21193,x21194,x21195,x21192))
% 22.40/22.32 [2120]~E(x21201,x21202)+E(f676(x21201,x21203,x21204,x21205),f676(x21202,x21203,x21204,x21205))
% 22.40/22.32 [2121]~E(x21211,x21212)+E(f676(x21213,x21211,x21214,x21215),f676(x21213,x21212,x21214,x21215))
% 22.40/22.32 [2122]~E(x21221,x21222)+E(f676(x21223,x21224,x21221,x21225),f676(x21223,x21224,x21222,x21225))
% 22.40/22.32 [2123]~E(x21231,x21232)+E(f676(x21233,x21234,x21235,x21231),f676(x21233,x21234,x21235,x21232))
% 22.40/22.32 [2124]~E(x21241,x21242)+E(f701(x21241,x21243,x21244),f701(x21242,x21243,x21244))
% 22.40/22.32 [2125]~E(x21251,x21252)+E(f701(x21253,x21251,x21254),f701(x21253,x21252,x21254))
% 22.40/22.32 [2126]~E(x21261,x21262)+E(f701(x21263,x21264,x21261),f701(x21263,x21264,x21262))
% 22.40/22.32 [2127]~E(x21271,x21272)+E(f507(x21271,x21273,x21274,x21275,x21276,x21277,x21278,x21279),f507(x21272,x21273,x21274,x21275,x21276,x21277,x21278,x21279))
% 22.40/22.32 [2128]~E(x21281,x21282)+E(f507(x21283,x21281,x21284,x21285,x21286,x21287,x21288,x21289),f507(x21283,x21282,x21284,x21285,x21286,x21287,x21288,x21289))
% 22.40/22.32 [2129]~E(x21291,x21292)+E(f507(x21293,x21294,x21291,x21295,x21296,x21297,x21298,x21299),f507(x21293,x21294,x21292,x21295,x21296,x21297,x21298,x21299))
% 22.40/22.32 [2130]~E(x21301,x21302)+E(f507(x21303,x21304,x21305,x21301,x21306,x21307,x21308,x21309),f507(x21303,x21304,x21305,x21302,x21306,x21307,x21308,x21309))
% 22.40/22.32 [2131]~E(x21311,x21312)+E(f507(x21313,x21314,x21315,x21316,x21311,x21317,x21318,x21319),f507(x21313,x21314,x21315,x21316,x21312,x21317,x21318,x21319))
% 22.40/22.32 [2132]~E(x21321,x21322)+E(f507(x21323,x21324,x21325,x21326,x21327,x21321,x21328,x21329),f507(x21323,x21324,x21325,x21326,x21327,x21322,x21328,x21329))
% 22.40/22.32 [2133]~E(x21331,x21332)+E(f507(x21333,x21334,x21335,x21336,x21337,x21338,x21331,x21339),f507(x21333,x21334,x21335,x21336,x21337,x21338,x21332,x21339))
% 22.40/22.32 [2134]~E(x21341,x21342)+E(f507(x21343,x21344,x21345,x21346,x21347,x21348,x21349,x21341),f507(x21343,x21344,x21345,x21346,x21347,x21348,x21349,x21342))
% 22.40/22.32 [2135]~E(x21351,x21352)+E(f219(x21351,x21353,x21354,x21355,x21356),f219(x21352,x21353,x21354,x21355,x21356))
% 22.40/22.32 [2136]~E(x21361,x21362)+E(f219(x21363,x21361,x21364,x21365,x21366),f219(x21363,x21362,x21364,x21365,x21366))
% 22.40/22.32 [2137]~E(x21371,x21372)+E(f219(x21373,x21374,x21371,x21375,x21376),f219(x21373,x21374,x21372,x21375,x21376))
% 22.40/22.32 [2138]~E(x21381,x21382)+E(f219(x21383,x21384,x21385,x21381,x21386),f219(x21383,x21384,x21385,x21382,x21386))
% 22.40/22.32 [2139]~E(x21391,x21392)+E(f219(x21393,x21394,x21395,x21396,x21391),f219(x21393,x21394,x21395,x21396,x21392))
% 22.40/22.32 [2140]~E(x21401,x21402)+E(f692(x21401,x21403,x21404,x21405,x21406),f692(x21402,x21403,x21404,x21405,x21406))
% 22.40/22.32 [2141]~E(x21411,x21412)+E(f692(x21413,x21411,x21414,x21415,x21416),f692(x21413,x21412,x21414,x21415,x21416))
% 22.40/22.32 [2142]~E(x21421,x21422)+E(f692(x21423,x21424,x21421,x21425,x21426),f692(x21423,x21424,x21422,x21425,x21426))
% 22.40/22.32 [2143]~E(x21431,x21432)+E(f692(x21433,x21434,x21435,x21431,x21436),f692(x21433,x21434,x21435,x21432,x21436))
% 22.40/22.32 [2144]~E(x21441,x21442)+E(f692(x21443,x21444,x21445,x21446,x21441),f692(x21443,x21444,x21445,x21446,x21442))
% 22.40/22.32 [2145]~E(x21451,x21452)+E(f304(x21451,x21453),f304(x21452,x21453))
% 22.40/22.32 [2146]~E(x21461,x21462)+E(f304(x21463,x21461),f304(x21463,x21462))
% 22.40/22.32 [2147]~E(x21471,x21472)+E(f188(x21471,x21473,x21474,x21475),f188(x21472,x21473,x21474,x21475))
% 22.40/22.32 [2148]~E(x21481,x21482)+E(f188(x21483,x21481,x21484,x21485),f188(x21483,x21482,x21484,x21485))
% 22.40/22.32 [2149]~E(x21491,x21492)+E(f188(x21493,x21494,x21491,x21495),f188(x21493,x21494,x21492,x21495))
% 22.40/22.32 [2150]~E(x21501,x21502)+E(f188(x21503,x21504,x21505,x21501),f188(x21503,x21504,x21505,x21502))
% 22.40/22.32 [2151]~E(x21511,x21512)+E(f358(x21511,x21513,x21514,x21515,x21516),f358(x21512,x21513,x21514,x21515,x21516))
% 22.40/22.32 [2152]~E(x21521,x21522)+E(f358(x21523,x21521,x21524,x21525,x21526),f358(x21523,x21522,x21524,x21525,x21526))
% 22.40/22.32 [2153]~E(x21531,x21532)+E(f358(x21533,x21534,x21531,x21535,x21536),f358(x21533,x21534,x21532,x21535,x21536))
% 22.40/22.32 [2154]~E(x21541,x21542)+E(f358(x21543,x21544,x21545,x21541,x21546),f358(x21543,x21544,x21545,x21542,x21546))
% 22.40/22.32 [2155]~E(x21551,x21552)+E(f358(x21553,x21554,x21555,x21556,x21551),f358(x21553,x21554,x21555,x21556,x21552))
% 22.40/22.32 [2156]~E(x21561,x21562)+E(f394(x21561,x21563,x21564),f394(x21562,x21563,x21564))
% 22.40/22.32 [2157]~E(x21571,x21572)+E(f394(x21573,x21571,x21574),f394(x21573,x21572,x21574))
% 22.40/22.32 [2158]~E(x21581,x21582)+E(f394(x21583,x21584,x21581),f394(x21583,x21584,x21582))
% 22.40/22.32 [2159]~E(x21591,x21592)+E(f706(x21591,x21593,x21594),f706(x21592,x21593,x21594))
% 22.40/22.32 [2160]~E(x21601,x21602)+E(f706(x21603,x21601,x21604),f706(x21603,x21602,x21604))
% 22.40/22.32 [2161]~E(x21611,x21612)+E(f706(x21613,x21614,x21611),f706(x21613,x21614,x21612))
% 22.40/22.32 [2162]~E(x21621,x21622)+E(f552(x21621,x21623,x21624,x21625,x21626,x21627),f552(x21622,x21623,x21624,x21625,x21626,x21627))
% 22.40/22.32 [2163]~E(x21631,x21632)+E(f552(x21633,x21631,x21634,x21635,x21636,x21637),f552(x21633,x21632,x21634,x21635,x21636,x21637))
% 22.40/22.32 [2164]~E(x21641,x21642)+E(f552(x21643,x21644,x21641,x21645,x21646,x21647),f552(x21643,x21644,x21642,x21645,x21646,x21647))
% 22.40/22.32 [2165]~E(x21651,x21652)+E(f552(x21653,x21654,x21655,x21651,x21656,x21657),f552(x21653,x21654,x21655,x21652,x21656,x21657))
% 22.40/22.32 [2166]~E(x21661,x21662)+E(f552(x21663,x21664,x21665,x21666,x21661,x21667),f552(x21663,x21664,x21665,x21666,x21662,x21667))
% 22.40/22.32 [2167]~E(x21671,x21672)+E(f552(x21673,x21674,x21675,x21676,x21677,x21671),f552(x21673,x21674,x21675,x21676,x21677,x21672))
% 22.40/22.32 [2168]~E(x21681,x21682)+E(f560(x21681,x21683,x21684),f560(x21682,x21683,x21684))
% 22.40/22.32 [2169]~E(x21691,x21692)+E(f560(x21693,x21691,x21694),f560(x21693,x21692,x21694))
% 22.40/22.32 [2170]~E(x21701,x21702)+E(f560(x21703,x21704,x21701),f560(x21703,x21704,x21702))
% 22.40/22.32 [2171]~E(x21711,x21712)+E(f863(x21711,x21713,x21714),f863(x21712,x21713,x21714))
% 22.40/22.32 [2172]~E(x21721,x21722)+E(f863(x21723,x21721,x21724),f863(x21723,x21722,x21724))
% 22.40/22.32 [2173]~E(x21731,x21732)+E(f863(x21733,x21734,x21731),f863(x21733,x21734,x21732))
% 22.40/22.32 [2174]~E(x21741,x21742)+E(f628(x21741,x21743,x21744,x21745,x21746),f628(x21742,x21743,x21744,x21745,x21746))
% 22.40/22.32 [2175]~E(x21751,x21752)+E(f628(x21753,x21751,x21754,x21755,x21756),f628(x21753,x21752,x21754,x21755,x21756))
% 22.40/22.32 [2176]~E(x21761,x21762)+E(f628(x21763,x21764,x21761,x21765,x21766),f628(x21763,x21764,x21762,x21765,x21766))
% 22.40/22.32 [2177]~E(x21771,x21772)+E(f628(x21773,x21774,x21775,x21771,x21776),f628(x21773,x21774,x21775,x21772,x21776))
% 22.40/22.32 [2178]~E(x21781,x21782)+E(f628(x21783,x21784,x21785,x21786,x21781),f628(x21783,x21784,x21785,x21786,x21782))
% 22.40/22.32 [2179]~E(x21791,x21792)+E(f755(x21791,x21793,x21794),f755(x21792,x21793,x21794))
% 22.40/22.32 [2180]~E(x21801,x21802)+E(f755(x21803,x21801,x21804),f755(x21803,x21802,x21804))
% 22.40/22.32 [2181]~E(x21811,x21812)+E(f755(x21813,x21814,x21811),f755(x21813,x21814,x21812))
% 22.40/22.32 [2182]~E(x21821,x21822)+E(f795(x21821,x21823),f795(x21822,x21823))
% 22.40/22.32 [2183]~E(x21831,x21832)+E(f795(x21833,x21831),f795(x21833,x21832))
% 22.40/22.32 [2184]~E(x21841,x21842)+E(f753(x21841,x21843,x21844),f753(x21842,x21843,x21844))
% 22.40/22.32 [2185]~E(x21851,x21852)+E(f753(x21853,x21851,x21854),f753(x21853,x21852,x21854))
% 22.40/22.32 [2186]~E(x21861,x21862)+E(f753(x21863,x21864,x21861),f753(x21863,x21864,x21862))
% 22.40/22.32 [2187]~E(x21871,x21872)+E(f443(x21871),f443(x21872))
% 22.40/22.32 [2188]~E(x21881,x21882)+E(f590(x21881,x21883,x21884,x21885,x21886,x21887),f590(x21882,x21883,x21884,x21885,x21886,x21887))
% 22.40/22.32 [2189]~E(x21891,x21892)+E(f590(x21893,x21891,x21894,x21895,x21896,x21897),f590(x21893,x21892,x21894,x21895,x21896,x21897))
% 22.40/22.32 [2190]~E(x21901,x21902)+E(f590(x21903,x21904,x21901,x21905,x21906,x21907),f590(x21903,x21904,x21902,x21905,x21906,x21907))
% 22.40/22.32 [2191]~E(x21911,x21912)+E(f590(x21913,x21914,x21915,x21911,x21916,x21917),f590(x21913,x21914,x21915,x21912,x21916,x21917))
% 22.40/22.32 [2192]~E(x21921,x21922)+E(f590(x21923,x21924,x21925,x21926,x21921,x21927),f590(x21923,x21924,x21925,x21926,x21922,x21927))
% 22.40/22.32 [2193]~E(x21931,x21932)+E(f590(x21933,x21934,x21935,x21936,x21937,x21931),f590(x21933,x21934,x21935,x21936,x21937,x21932))
% 22.40/22.32 [2194]~E(x21941,x21942)+E(f738(x21941,x21943,x21944,x21945,x21946,x21947,x21948),f738(x21942,x21943,x21944,x21945,x21946,x21947,x21948))
% 22.40/22.32 [2195]~E(x21951,x21952)+E(f738(x21953,x21951,x21954,x21955,x21956,x21957,x21958),f738(x21953,x21952,x21954,x21955,x21956,x21957,x21958))
% 22.40/22.32 [2196]~E(x21961,x21962)+E(f738(x21963,x21964,x21961,x21965,x21966,x21967,x21968),f738(x21963,x21964,x21962,x21965,x21966,x21967,x21968))
% 22.40/22.32 [2197]~E(x21971,x21972)+E(f738(x21973,x21974,x21975,x21971,x21976,x21977,x21978),f738(x21973,x21974,x21975,x21972,x21976,x21977,x21978))
% 22.40/22.32 [2198]~E(x21981,x21982)+E(f738(x21983,x21984,x21985,x21986,x21981,x21987,x21988),f738(x21983,x21984,x21985,x21986,x21982,x21987,x21988))
% 22.40/22.32 [2199]~E(x21991,x21992)+E(f738(x21993,x21994,x21995,x21996,x21997,x21991,x21998),f738(x21993,x21994,x21995,x21996,x21997,x21992,x21998))
% 22.40/22.32 [2200]~E(x22001,x22002)+E(f738(x22003,x22004,x22005,x22006,x22007,x22008,x22001),f738(x22003,x22004,x22005,x22006,x22007,x22008,x22002))
% 22.40/22.32 [2201]~E(x22011,x22012)+E(f383(x22011,x22013,x22014),f383(x22012,x22013,x22014))
% 22.40/22.32 [2202]~E(x22021,x22022)+E(f383(x22023,x22021,x22024),f383(x22023,x22022,x22024))
% 22.40/22.32 [2203]~E(x22031,x22032)+E(f383(x22033,x22034,x22031),f383(x22033,x22034,x22032))
% 22.40/22.32 [2204]~E(x22041,x22042)+E(f505(x22041,x22043,x22044,x22045,x22046),f505(x22042,x22043,x22044,x22045,x22046))
% 22.40/22.32 [2205]~E(x22051,x22052)+E(f505(x22053,x22051,x22054,x22055,x22056),f505(x22053,x22052,x22054,x22055,x22056))
% 22.40/22.32 [2206]~E(x22061,x22062)+E(f505(x22063,x22064,x22061,x22065,x22066),f505(x22063,x22064,x22062,x22065,x22066))
% 22.40/22.32 [2207]~E(x22071,x22072)+E(f505(x22073,x22074,x22075,x22071,x22076),f505(x22073,x22074,x22075,x22072,x22076))
% 22.40/22.32 [2208]~E(x22081,x22082)+E(f505(x22083,x22084,x22085,x22086,x22081),f505(x22083,x22084,x22085,x22086,x22082))
% 22.40/22.32 [2209]~E(x22091,x22092)+E(f660(x22091,x22093,x22094,x22095),f660(x22092,x22093,x22094,x22095))
% 22.40/22.32 [2210]~E(x22101,x22102)+E(f660(x22103,x22101,x22104,x22105),f660(x22103,x22102,x22104,x22105))
% 22.40/22.32 [2211]~E(x22111,x22112)+E(f660(x22113,x22114,x22111,x22115),f660(x22113,x22114,x22112,x22115))
% 22.40/22.32 [2212]~E(x22121,x22122)+E(f660(x22123,x22124,x22125,x22121),f660(x22123,x22124,x22125,x22122))
% 22.40/22.32 [2213]~E(x22131,x22132)+E(f508(x22131,x22133,x22134,x22135,x22136),f508(x22132,x22133,x22134,x22135,x22136))
% 22.40/22.32 [2214]~E(x22141,x22142)+E(f508(x22143,x22141,x22144,x22145,x22146),f508(x22143,x22142,x22144,x22145,x22146))
% 22.40/22.32 [2215]~E(x22151,x22152)+E(f508(x22153,x22154,x22151,x22155,x22156),f508(x22153,x22154,x22152,x22155,x22156))
% 22.40/22.32 [2216]~E(x22161,x22162)+E(f508(x22163,x22164,x22165,x22161,x22166),f508(x22163,x22164,x22165,x22162,x22166))
% 22.40/22.32 [2217]~E(x22171,x22172)+E(f508(x22173,x22174,x22175,x22176,x22171),f508(x22173,x22174,x22175,x22176,x22172))
% 22.40/22.32 [2218]~E(x22181,x22182)+E(f691(x22181,x22183,x22184,x22185,x22186),f691(x22182,x22183,x22184,x22185,x22186))
% 22.40/22.32 [2219]~E(x22191,x22192)+E(f691(x22193,x22191,x22194,x22195,x22196),f691(x22193,x22192,x22194,x22195,x22196))
% 22.40/22.32 [2220]~E(x22201,x22202)+E(f691(x22203,x22204,x22201,x22205,x22206),f691(x22203,x22204,x22202,x22205,x22206))
% 22.40/22.32 [2221]~E(x22211,x22212)+E(f691(x22213,x22214,x22215,x22211,x22216),f691(x22213,x22214,x22215,x22212,x22216))
% 22.40/22.32 [2222]~E(x22221,x22222)+E(f691(x22223,x22224,x22225,x22226,x22221),f691(x22223,x22224,x22225,x22226,x22222))
% 22.40/22.32 [2223]~E(x22231,x22232)+E(f421(x22231,x22233,x22234),f421(x22232,x22233,x22234))
% 22.40/22.32 [2224]~E(x22241,x22242)+E(f421(x22243,x22241,x22244),f421(x22243,x22242,x22244))
% 22.40/22.32 [2225]~E(x22251,x22252)+E(f421(x22253,x22254,x22251),f421(x22253,x22254,x22252))
% 22.40/22.32 [2226]~E(x22261,x22262)+E(f687(x22261,x22263),f687(x22262,x22263))
% 22.40/22.32 [2227]~E(x22271,x22272)+E(f687(x22273,x22271),f687(x22273,x22272))
% 22.40/22.32 [2228]~E(x22281,x22282)+E(f597(x22281,x22283,x22284,x22285,x22286),f597(x22282,x22283,x22284,x22285,x22286))
% 22.40/22.32 [2229]~E(x22291,x22292)+E(f597(x22293,x22291,x22294,x22295,x22296),f597(x22293,x22292,x22294,x22295,x22296))
% 22.40/22.32 [2230]~E(x22301,x22302)+E(f597(x22303,x22304,x22301,x22305,x22306),f597(x22303,x22304,x22302,x22305,x22306))
% 22.40/22.32 [2231]~E(x22311,x22312)+E(f597(x22313,x22314,x22315,x22311,x22316),f597(x22313,x22314,x22315,x22312,x22316))
% 22.40/22.32 [2232]~E(x22321,x22322)+E(f597(x22323,x22324,x22325,x22326,x22321),f597(x22323,x22324,x22325,x22326,x22322))
% 22.40/22.32 [2233]~E(x22331,x22332)+E(f470(x22331,x22333,x22334,x22335,x22336),f470(x22332,x22333,x22334,x22335,x22336))
% 22.40/22.32 [2234]~E(x22341,x22342)+E(f470(x22343,x22341,x22344,x22345,x22346),f470(x22343,x22342,x22344,x22345,x22346))
% 22.40/22.32 [2235]~E(x22351,x22352)+E(f470(x22353,x22354,x22351,x22355,x22356),f470(x22353,x22354,x22352,x22355,x22356))
% 22.40/22.32 [2236]~E(x22361,x22362)+E(f470(x22363,x22364,x22365,x22361,x22366),f470(x22363,x22364,x22365,x22362,x22366))
% 22.40/22.32 [2237]~E(x22371,x22372)+E(f470(x22373,x22374,x22375,x22376,x22371),f470(x22373,x22374,x22375,x22376,x22372))
% 22.40/22.32 [2238]~E(x22381,x22382)+E(f472(x22381,x22383,x22384,x22385,x22386),f472(x22382,x22383,x22384,x22385,x22386))
% 22.40/22.32 [2239]~E(x22391,x22392)+E(f472(x22393,x22391,x22394,x22395,x22396),f472(x22393,x22392,x22394,x22395,x22396))
% 22.40/22.32 [2240]~E(x22401,x22402)+E(f472(x22403,x22404,x22401,x22405,x22406),f472(x22403,x22404,x22402,x22405,x22406))
% 22.40/22.32 [2241]~E(x22411,x22412)+E(f472(x22413,x22414,x22415,x22411,x22416),f472(x22413,x22414,x22415,x22412,x22416))
% 22.40/22.32 [2242]~E(x22421,x22422)+E(f472(x22423,x22424,x22425,x22426,x22421),f472(x22423,x22424,x22425,x22426,x22422))
% 22.40/22.32 [2243]~E(x22431,x22432)+E(f631(x22431,x22433,x22434,x22435),f631(x22432,x22433,x22434,x22435))
% 22.40/22.32 [2244]~E(x22441,x22442)+E(f631(x22443,x22441,x22444,x22445),f631(x22443,x22442,x22444,x22445))
% 22.40/22.32 [2245]~E(x22451,x22452)+E(f631(x22453,x22454,x22451,x22455),f631(x22453,x22454,x22452,x22455))
% 22.40/22.32 [2246]~E(x22461,x22462)+E(f631(x22463,x22464,x22465,x22461),f631(x22463,x22464,x22465,x22462))
% 22.40/22.32 [2247]~E(x22471,x22472)+E(f287(x22471,x22473,x22474),f287(x22472,x22473,x22474))
% 22.40/22.32 [2248]~E(x22481,x22482)+E(f287(x22483,x22481,x22484),f287(x22483,x22482,x22484))
% 22.40/22.32 [2249]~E(x22491,x22492)+E(f287(x22493,x22494,x22491),f287(x22493,x22494,x22492))
% 22.40/22.32 [2250]~E(x22501,x22502)+E(f802(x22501,x22503),f802(x22502,x22503))
% 22.40/22.32 [2251]~E(x22511,x22512)+E(f802(x22513,x22511),f802(x22513,x22512))
% 22.40/22.32 [2252]~E(x22521,x22522)+E(f787(x22521,x22523,x22524,x22525),f787(x22522,x22523,x22524,x22525))
% 22.40/22.32 [2253]~E(x22531,x22532)+E(f787(x22533,x22531,x22534,x22535),f787(x22533,x22532,x22534,x22535))
% 22.40/22.32 [2254]~E(x22541,x22542)+E(f787(x22543,x22544,x22541,x22545),f787(x22543,x22544,x22542,x22545))
% 22.40/22.32 [2255]~E(x22551,x22552)+E(f787(x22553,x22554,x22555,x22551),f787(x22553,x22554,x22555,x22552))
% 22.40/22.32 [2256]~E(x22561,x22562)+E(f519(x22561,x22563,x22564,x22565,x22566,x22567,x22568),f519(x22562,x22563,x22564,x22565,x22566,x22567,x22568))
% 22.40/22.32 [2257]~E(x22571,x22572)+E(f519(x22573,x22571,x22574,x22575,x22576,x22577,x22578),f519(x22573,x22572,x22574,x22575,x22576,x22577,x22578))
% 22.40/22.32 [2258]~E(x22581,x22582)+E(f519(x22583,x22584,x22581,x22585,x22586,x22587,x22588),f519(x22583,x22584,x22582,x22585,x22586,x22587,x22588))
% 22.40/22.32 [2259]~E(x22591,x22592)+E(f519(x22593,x22594,x22595,x22591,x22596,x22597,x22598),f519(x22593,x22594,x22595,x22592,x22596,x22597,x22598))
% 22.40/22.32 [2260]~E(x22601,x22602)+E(f519(x22603,x22604,x22605,x22606,x22601,x22607,x22608),f519(x22603,x22604,x22605,x22606,x22602,x22607,x22608))
% 22.40/22.32 [2261]~E(x22611,x22612)+E(f519(x22613,x22614,x22615,x22616,x22617,x22611,x22618),f519(x22613,x22614,x22615,x22616,x22617,x22612,x22618))
% 22.40/22.32 [2262]~E(x22621,x22622)+E(f519(x22623,x22624,x22625,x22626,x22627,x22628,x22621),f519(x22623,x22624,x22625,x22626,x22627,x22628,x22622))
% 22.40/22.32 [2263]~E(x22631,x22632)+E(f509(x22631),f509(x22632))
% 22.40/22.32 [2264]~E(x22641,x22642)+E(f350(x22641,x22643,x22644,x22645,x22646),f350(x22642,x22643,x22644,x22645,x22646))
% 22.40/22.32 [2265]~E(x22651,x22652)+E(f350(x22653,x22651,x22654,x22655,x22656),f350(x22653,x22652,x22654,x22655,x22656))
% 22.40/22.32 [2266]~E(x22661,x22662)+E(f350(x22663,x22664,x22661,x22665,x22666),f350(x22663,x22664,x22662,x22665,x22666))
% 22.40/22.32 [2267]~E(x22671,x22672)+E(f350(x22673,x22674,x22675,x22671,x22676),f350(x22673,x22674,x22675,x22672,x22676))
% 22.40/22.32 [2268]~E(x22681,x22682)+E(f350(x22683,x22684,x22685,x22686,x22681),f350(x22683,x22684,x22685,x22686,x22682))
% 22.40/22.32 [2269]~E(x22691,x22692)+E(f538(x22691,x22693,x22694,x22695,x22696,x22697),f538(x22692,x22693,x22694,x22695,x22696,x22697))
% 22.40/22.32 [2270]~E(x22701,x22702)+E(f538(x22703,x22701,x22704,x22705,x22706,x22707),f538(x22703,x22702,x22704,x22705,x22706,x22707))
% 22.40/22.32 [2271]~E(x22711,x22712)+E(f538(x22713,x22714,x22711,x22715,x22716,x22717),f538(x22713,x22714,x22712,x22715,x22716,x22717))
% 22.40/22.32 [2272]~E(x22721,x22722)+E(f538(x22723,x22724,x22725,x22721,x22726,x22727),f538(x22723,x22724,x22725,x22722,x22726,x22727))
% 22.40/22.32 [2273]~E(x22731,x22732)+E(f538(x22733,x22734,x22735,x22736,x22731,x22737),f538(x22733,x22734,x22735,x22736,x22732,x22737))
% 22.40/22.32 [2274]~E(x22741,x22742)+E(f538(x22743,x22744,x22745,x22746,x22747,x22741),f538(x22743,x22744,x22745,x22746,x22747,x22742))
% 22.40/22.32 [2275]~E(x22751,x22752)+E(f406(x22751,x22753,x22754,x22755),f406(x22752,x22753,x22754,x22755))
% 22.40/22.32 [2276]~E(x22761,x22762)+E(f406(x22763,x22761,x22764,x22765),f406(x22763,x22762,x22764,x22765))
% 22.40/22.32 [2277]~E(x22771,x22772)+E(f406(x22773,x22774,x22771,x22775),f406(x22773,x22774,x22772,x22775))
% 22.40/22.32 [2278]~E(x22781,x22782)+E(f406(x22783,x22784,x22785,x22781),f406(x22783,x22784,x22785,x22782))
% 22.40/22.32 [2279]~E(x22791,x22792)+E(f766(x22791,x22793,x22794),f766(x22792,x22793,x22794))
% 22.40/22.32 [2280]~E(x22801,x22802)+E(f766(x22803,x22801,x22804),f766(x22803,x22802,x22804))
% 22.40/22.32 [2281]~E(x22811,x22812)+E(f766(x22813,x22814,x22811),f766(x22813,x22814,x22812))
% 22.40/22.32 [2282]~E(x22821,x22822)+E(f331(x22821,x22823,x22824),f331(x22822,x22823,x22824))
% 22.40/22.32 [2283]~E(x22831,x22832)+E(f331(x22833,x22831,x22834),f331(x22833,x22832,x22834))
% 22.40/22.32 [2284]~E(x22841,x22842)+E(f331(x22843,x22844,x22841),f331(x22843,x22844,x22842))
% 22.40/22.32 [2285]~E(x22851,x22852)+E(f827(x22851,x22853,x22854),f827(x22852,x22853,x22854))
% 22.40/22.32 [2286]~E(x22861,x22862)+E(f827(x22863,x22861,x22864),f827(x22863,x22862,x22864))
% 22.40/22.32 [2287]~E(x22871,x22872)+E(f827(x22873,x22874,x22871),f827(x22873,x22874,x22872))
% 22.40/22.32 [2288]~E(x22881,x22882)+E(f549(x22881,x22883,x22884,x22885,x22886),f549(x22882,x22883,x22884,x22885,x22886))
% 22.40/22.32 [2289]~E(x22891,x22892)+E(f549(x22893,x22891,x22894,x22895,x22896),f549(x22893,x22892,x22894,x22895,x22896))
% 22.40/22.32 [2290]~E(x22901,x22902)+E(f549(x22903,x22904,x22901,x22905,x22906),f549(x22903,x22904,x22902,x22905,x22906))
% 22.40/22.32 [2291]~E(x22911,x22912)+E(f549(x22913,x22914,x22915,x22911,x22916),f549(x22913,x22914,x22915,x22912,x22916))
% 22.40/22.32 [2292]~E(x22921,x22922)+E(f549(x22923,x22924,x22925,x22926,x22921),f549(x22923,x22924,x22925,x22926,x22922))
% 22.40/22.32 [2293]~E(x22931,x22932)+E(f364(x22931,x22933,x22934),f364(x22932,x22933,x22934))
% 22.40/22.32 [2294]~E(x22941,x22942)+E(f364(x22943,x22941,x22944),f364(x22943,x22942,x22944))
% 22.40/22.32 [2295]~E(x22951,x22952)+E(f364(x22953,x22954,x22951),f364(x22953,x22954,x22952))
% 22.40/22.32 [2296]~E(x22961,x22962)+E(f446(x22961,x22963,x22964),f446(x22962,x22963,x22964))
% 22.40/22.32 [2297]~E(x22971,x22972)+E(f446(x22973,x22971,x22974),f446(x22973,x22972,x22974))
% 22.40/22.32 [2298]~E(x22981,x22982)+E(f446(x22983,x22984,x22981),f446(x22983,x22984,x22982))
% 22.40/22.32 [2299]~E(x22991,x22992)+E(f746(x22991,x22993,x22994),f746(x22992,x22993,x22994))
% 22.40/22.32 [2300]~E(x23001,x23002)+E(f746(x23003,x23001,x23004),f746(x23003,x23002,x23004))
% 22.40/22.32 [2301]~E(x23011,x23012)+E(f746(x23013,x23014,x23011),f746(x23013,x23014,x23012))
% 22.40/22.32 [2302]~E(x23021,x23022)+E(f759(x23021,x23023,x23024,x23025),f759(x23022,x23023,x23024,x23025))
% 22.40/22.32 [2303]~E(x23031,x23032)+E(f759(x23033,x23031,x23034,x23035),f759(x23033,x23032,x23034,x23035))
% 22.40/22.32 [2304]~E(x23041,x23042)+E(f759(x23043,x23044,x23041,x23045),f759(x23043,x23044,x23042,x23045))
% 22.40/22.32 [2305]~E(x23051,x23052)+E(f759(x23053,x23054,x23055,x23051),f759(x23053,x23054,x23055,x23052))
% 22.40/22.32 [2306]~E(x23061,x23062)+E(f780(x23061,x23063,x23064,x23065,x23066,x23067,x23068),f780(x23062,x23063,x23064,x23065,x23066,x23067,x23068))
% 22.40/22.32 [2307]~E(x23071,x23072)+E(f780(x23073,x23071,x23074,x23075,x23076,x23077,x23078),f780(x23073,x23072,x23074,x23075,x23076,x23077,x23078))
% 22.40/22.32 [2308]~E(x23081,x23082)+E(f780(x23083,x23084,x23081,x23085,x23086,x23087,x23088),f780(x23083,x23084,x23082,x23085,x23086,x23087,x23088))
% 22.40/22.32 [2309]~E(x23091,x23092)+E(f780(x23093,x23094,x23095,x23091,x23096,x23097,x23098),f780(x23093,x23094,x23095,x23092,x23096,x23097,x23098))
% 22.40/22.32 [2310]~E(x23101,x23102)+E(f780(x23103,x23104,x23105,x23106,x23101,x23107,x23108),f780(x23103,x23104,x23105,x23106,x23102,x23107,x23108))
% 22.40/22.32 [2311]~E(x23111,x23112)+E(f780(x23113,x23114,x23115,x23116,x23117,x23111,x23118),f780(x23113,x23114,x23115,x23116,x23117,x23112,x23118))
% 22.40/22.32 [2312]~E(x23121,x23122)+E(f780(x23123,x23124,x23125,x23126,x23127,x23128,x23121),f780(x23123,x23124,x23125,x23126,x23127,x23128,x23122))
% 22.40/22.32 [2313]~E(x23131,x23132)+E(f847(x23131,x23133),f847(x23132,x23133))
% 22.40/22.32 [2314]~E(x23141,x23142)+E(f847(x23143,x23141),f847(x23143,x23142))
% 22.40/22.32 [2315]~E(x23151,x23152)+E(f803(x23151,x23153,x23154,x23155,x23156),f803(x23152,x23153,x23154,x23155,x23156))
% 22.40/22.32 [2316]~E(x23161,x23162)+E(f803(x23163,x23161,x23164,x23165,x23166),f803(x23163,x23162,x23164,x23165,x23166))
% 22.40/22.32 [2317]~E(x23171,x23172)+E(f803(x23173,x23174,x23171,x23175,x23176),f803(x23173,x23174,x23172,x23175,x23176))
% 22.40/22.32 [2318]~E(x23181,x23182)+E(f803(x23183,x23184,x23185,x23181,x23186),f803(x23183,x23184,x23185,x23182,x23186))
% 22.40/22.32 [2319]~E(x23191,x23192)+E(f803(x23193,x23194,x23195,x23196,x23191),f803(x23193,x23194,x23195,x23196,x23192))
% 22.40/22.32 [2320]~E(x23201,x23202)+E(f391(x23201,x23203,x23204,x23205),f391(x23202,x23203,x23204,x23205))
% 22.40/22.32 [2321]~E(x23211,x23212)+E(f391(x23213,x23211,x23214,x23215),f391(x23213,x23212,x23214,x23215))
% 22.40/22.32 [2322]~E(x23221,x23222)+E(f391(x23223,x23224,x23221,x23225),f391(x23223,x23224,x23222,x23225))
% 22.40/22.32 [2323]~E(x23231,x23232)+E(f391(x23233,x23234,x23235,x23231),f391(x23233,x23234,x23235,x23232))
% 22.40/22.32 [2324]~E(x23241,x23242)+E(f782(x23241,x23243),f782(x23242,x23243))
% 22.40/22.32 [2325]~E(x23251,x23252)+E(f782(x23253,x23251),f782(x23253,x23252))
% 22.40/22.32 [2326]~E(x23261,x23262)+E(f559(x23261,x23263),f559(x23262,x23263))
% 22.40/22.32 [2327]~E(x23271,x23272)+E(f559(x23273,x23271),f559(x23273,x23272))
% 22.40/22.32 [2328]~E(x23281,x23282)+E(f739(x23281,x23283,x23284,x23285,x23286,x23287,x23288),f739(x23282,x23283,x23284,x23285,x23286,x23287,x23288))
% 22.40/22.32 [2329]~E(x23291,x23292)+E(f739(x23293,x23291,x23294,x23295,x23296,x23297,x23298),f739(x23293,x23292,x23294,x23295,x23296,x23297,x23298))
% 22.40/22.32 [2330]~E(x23301,x23302)+E(f739(x23303,x23304,x23301,x23305,x23306,x23307,x23308),f739(x23303,x23304,x23302,x23305,x23306,x23307,x23308))
% 22.40/22.32 [2331]~E(x23311,x23312)+E(f739(x23313,x23314,x23315,x23311,x23316,x23317,x23318),f739(x23313,x23314,x23315,x23312,x23316,x23317,x23318))
% 22.40/22.32 [2332]~E(x23321,x23322)+E(f739(x23323,x23324,x23325,x23326,x23321,x23327,x23328),f739(x23323,x23324,x23325,x23326,x23322,x23327,x23328))
% 22.40/22.32 [2333]~E(x23331,x23332)+E(f739(x23333,x23334,x23335,x23336,x23337,x23331,x23338),f739(x23333,x23334,x23335,x23336,x23337,x23332,x23338))
% 22.40/22.32 [2334]~E(x23341,x23342)+E(f739(x23343,x23344,x23345,x23346,x23347,x23348,x23341),f739(x23343,x23344,x23345,x23346,x23347,x23348,x23342))
% 22.40/22.32 [2335]~E(x23351,x23352)+E(f487(x23351,x23353,x23354,x23355),f487(x23352,x23353,x23354,x23355))
% 22.40/22.32 [2336]~E(x23361,x23362)+E(f487(x23363,x23361,x23364,x23365),f487(x23363,x23362,x23364,x23365))
% 22.40/22.32 [2337]~E(x23371,x23372)+E(f487(x23373,x23374,x23371,x23375),f487(x23373,x23374,x23372,x23375))
% 22.40/22.32 [2338]~E(x23381,x23382)+E(f487(x23383,x23384,x23385,x23381),f487(x23383,x23384,x23385,x23382))
% 22.40/22.32 [2339]~E(x23391,x23392)+E(f790(x23391,x23393),f790(x23392,x23393))
% 22.40/22.32 [2340]~E(x23401,x23402)+E(f790(x23403,x23401),f790(x23403,x23402))
% 22.40/22.32 [2341]~E(x23411,x23412)+E(f818(x23411,x23413,x23414,x23415,x23416),f818(x23412,x23413,x23414,x23415,x23416))
% 22.40/22.32 [2342]~E(x23421,x23422)+E(f818(x23423,x23421,x23424,x23425,x23426),f818(x23423,x23422,x23424,x23425,x23426))
% 22.40/22.32 [2343]~E(x23431,x23432)+E(f818(x23433,x23434,x23431,x23435,x23436),f818(x23433,x23434,x23432,x23435,x23436))
% 22.40/22.32 [2344]~E(x23441,x23442)+E(f818(x23443,x23444,x23445,x23441,x23446),f818(x23443,x23444,x23445,x23442,x23446))
% 22.40/22.32 [2345]~E(x23451,x23452)+E(f818(x23453,x23454,x23455,x23456,x23451),f818(x23453,x23454,x23455,x23456,x23452))
% 22.40/22.32 [2346]~E(x23461,x23462)+E(f347(x23461,x23463,x23464),f347(x23462,x23463,x23464))
% 22.40/22.32 [2347]~E(x23471,x23472)+E(f347(x23473,x23471,x23474),f347(x23473,x23472,x23474))
% 22.40/22.32 [2348]~E(x23481,x23482)+E(f347(x23483,x23484,x23481),f347(x23483,x23484,x23482))
% 22.40/22.32 [2349]~E(x23491,x23492)+E(f729(x23491,x23493,x23494),f729(x23492,x23493,x23494))
% 22.40/22.32 [2350]~E(x23501,x23502)+E(f729(x23503,x23501,x23504),f729(x23503,x23502,x23504))
% 22.40/22.32 [2351]~E(x23511,x23512)+E(f729(x23513,x23514,x23511),f729(x23513,x23514,x23512))
% 22.40/22.32 [2352]~E(x23521,x23522)+E(f466(x23521,x23523,x23524,x23525),f466(x23522,x23523,x23524,x23525))
% 22.40/22.32 [2353]~E(x23531,x23532)+E(f466(x23533,x23531,x23534,x23535),f466(x23533,x23532,x23534,x23535))
% 22.40/22.32 [2354]~E(x23541,x23542)+E(f466(x23543,x23544,x23541,x23545),f466(x23543,x23544,x23542,x23545))
% 22.40/22.32 [2355]~E(x23551,x23552)+E(f466(x23553,x23554,x23555,x23551),f466(x23553,x23554,x23555,x23552))
% 22.40/22.32 [2356]~E(x23561,x23562)+E(f810(x23561,x23563,x23564),f810(x23562,x23563,x23564))
% 22.40/22.32 [2357]~E(x23571,x23572)+E(f810(x23573,x23571,x23574),f810(x23573,x23572,x23574))
% 22.40/22.32 [2358]~E(x23581,x23582)+E(f810(x23583,x23584,x23581),f810(x23583,x23584,x23582))
% 22.40/22.32 [2359]~E(x23591,x23592)+E(f502(x23591,x23593,x23594,x23595,x23596,x23597,x23598,x23599),f502(x23592,x23593,x23594,x23595,x23596,x23597,x23598,x23599))
% 22.40/22.32 [2360]~E(x23601,x23602)+E(f502(x23603,x23601,x23604,x23605,x23606,x23607,x23608,x23609),f502(x23603,x23602,x23604,x23605,x23606,x23607,x23608,x23609))
% 22.40/22.32 [2361]~E(x23611,x23612)+E(f502(x23613,x23614,x23611,x23615,x23616,x23617,x23618,x23619),f502(x23613,x23614,x23612,x23615,x23616,x23617,x23618,x23619))
% 22.40/22.32 [2362]~E(x23621,x23622)+E(f502(x23623,x23624,x23625,x23621,x23626,x23627,x23628,x23629),f502(x23623,x23624,x23625,x23622,x23626,x23627,x23628,x23629))
% 22.40/22.32 [2363]~E(x23631,x23632)+E(f502(x23633,x23634,x23635,x23636,x23631,x23637,x23638,x23639),f502(x23633,x23634,x23635,x23636,x23632,x23637,x23638,x23639))
% 22.40/22.32 [2364]~E(x23641,x23642)+E(f502(x23643,x23644,x23645,x23646,x23647,x23641,x23648,x23649),f502(x23643,x23644,x23645,x23646,x23647,x23642,x23648,x23649))
% 22.40/22.32 [2365]~E(x23651,x23652)+E(f502(x23653,x23654,x23655,x23656,x23657,x23658,x23651,x23659),f502(x23653,x23654,x23655,x23656,x23657,x23658,x23652,x23659))
% 22.40/22.32 [2366]~E(x23661,x23662)+E(f502(x23663,x23664,x23665,x23666,x23667,x23668,x23669,x23661),f502(x23663,x23664,x23665,x23666,x23667,x23668,x23669,x23662))
% 22.40/22.32 [2367]~E(x23671,x23672)+E(f357(x23671,x23673,x23674,x23675,x23676),f357(x23672,x23673,x23674,x23675,x23676))
% 22.40/22.32 [2368]~E(x23681,x23682)+E(f357(x23683,x23681,x23684,x23685,x23686),f357(x23683,x23682,x23684,x23685,x23686))
% 22.40/22.32 [2369]~E(x23691,x23692)+E(f357(x23693,x23694,x23691,x23695,x23696),f357(x23693,x23694,x23692,x23695,x23696))
% 22.40/22.32 [2370]~E(x23701,x23702)+E(f357(x23703,x23704,x23705,x23701,x23706),f357(x23703,x23704,x23705,x23702,x23706))
% 22.40/22.32 [2371]~E(x23711,x23712)+E(f357(x23713,x23714,x23715,x23716,x23711),f357(x23713,x23714,x23715,x23716,x23712))
% 22.40/22.32 [2372]~E(x23721,x23722)+E(f562(x23721,x23723,x23724,x23725),f562(x23722,x23723,x23724,x23725))
% 22.40/22.32 [2373]~E(x23731,x23732)+E(f562(x23733,x23731,x23734,x23735),f562(x23733,x23732,x23734,x23735))
% 22.40/22.32 [2374]~E(x23741,x23742)+E(f562(x23743,x23744,x23741,x23745),f562(x23743,x23744,x23742,x23745))
% 22.40/22.32 [2375]~E(x23751,x23752)+E(f562(x23753,x23754,x23755,x23751),f562(x23753,x23754,x23755,x23752))
% 22.40/22.32 [2376]~E(x23761,x23762)+E(f642(x23761,x23763,x23764,x23765,x23766),f642(x23762,x23763,x23764,x23765,x23766))
% 22.40/22.32 [2377]~E(x23771,x23772)+E(f642(x23773,x23771,x23774,x23775,x23776),f642(x23773,x23772,x23774,x23775,x23776))
% 22.40/22.32 [2378]~E(x23781,x23782)+E(f642(x23783,x23784,x23781,x23785,x23786),f642(x23783,x23784,x23782,x23785,x23786))
% 22.40/22.32 [2379]~E(x23791,x23792)+E(f642(x23793,x23794,x23795,x23791,x23796),f642(x23793,x23794,x23795,x23792,x23796))
% 22.40/22.32 [2380]~E(x23801,x23802)+E(f642(x23803,x23804,x23805,x23806,x23801),f642(x23803,x23804,x23805,x23806,x23802))
% 22.40/22.32 [2381]~E(x23811,x23812)+E(f259(x23811),f259(x23812))
% 22.40/22.32 [2382]~E(x23821,x23822)+E(f756(x23821,x23823,x23824),f756(x23822,x23823,x23824))
% 22.40/22.32 [2383]~E(x23831,x23832)+E(f756(x23833,x23831,x23834),f756(x23833,x23832,x23834))
% 22.40/22.32 [2384]~E(x23841,x23842)+E(f756(x23843,x23844,x23841),f756(x23843,x23844,x23842))
% 22.40/22.32 [2385]~E(x23851,x23852)+E(f346(x23851,x23853),f346(x23852,x23853))
% 22.40/22.33 [2386]~E(x23861,x23862)+E(f346(x23863,x23861),f346(x23863,x23862))
% 22.40/22.33 [2387]~E(x23871,x23872)+E(f833(x23871,x23873,x23874,x23875,x23876,x23877,x23878),f833(x23872,x23873,x23874,x23875,x23876,x23877,x23878))
% 22.40/22.33 [2388]~E(x23881,x23882)+E(f833(x23883,x23881,x23884,x23885,x23886,x23887,x23888),f833(x23883,x23882,x23884,x23885,x23886,x23887,x23888))
% 22.40/22.33 [2389]~E(x23891,x23892)+E(f833(x23893,x23894,x23891,x23895,x23896,x23897,x23898),f833(x23893,x23894,x23892,x23895,x23896,x23897,x23898))
% 22.40/22.33 [2390]~E(x23901,x23902)+E(f833(x23903,x23904,x23905,x23901,x23906,x23907,x23908),f833(x23903,x23904,x23905,x23902,x23906,x23907,x23908))
% 22.40/22.33 [2391]~E(x23911,x23912)+E(f833(x23913,x23914,x23915,x23916,x23911,x23917,x23918),f833(x23913,x23914,x23915,x23916,x23912,x23917,x23918))
% 22.40/22.33 [2392]~E(x23921,x23922)+E(f833(x23923,x23924,x23925,x23926,x23927,x23921,x23928),f833(x23923,x23924,x23925,x23926,x23927,x23922,x23928))
% 22.40/22.33 [2393]~E(x23931,x23932)+E(f833(x23933,x23934,x23935,x23936,x23937,x23938,x23931),f833(x23933,x23934,x23935,x23936,x23937,x23938,x23932))
% 22.40/22.33 [2394]~E(x23941,x23942)+E(f735(x23941,x23943,x23944,x23945,x23946),f735(x23942,x23943,x23944,x23945,x23946))
% 22.40/22.33 [2395]~E(x23951,x23952)+E(f735(x23953,x23951,x23954,x23955,x23956),f735(x23953,x23952,x23954,x23955,x23956))
% 22.40/22.33 [2396]~E(x23961,x23962)+E(f735(x23963,x23964,x23961,x23965,x23966),f735(x23963,x23964,x23962,x23965,x23966))
% 22.40/22.33 [2397]~E(x23971,x23972)+E(f735(x23973,x23974,x23975,x23971,x23976),f735(x23973,x23974,x23975,x23972,x23976))
% 22.40/22.33 [2398]~E(x23981,x23982)+E(f735(x23983,x23984,x23985,x23986,x23981),f735(x23983,x23984,x23985,x23986,x23982))
% 22.40/22.33 [2399]~E(x23991,x23992)+E(f404(x23991,x23993,x23994),f404(x23992,x23993,x23994))
% 22.40/22.33 [2400]~E(x24001,x24002)+E(f404(x24003,x24001,x24004),f404(x24003,x24002,x24004))
% 22.40/22.33 [2401]~E(x24011,x24012)+E(f404(x24013,x24014,x24011),f404(x24013,x24014,x24012))
% 22.40/22.33 [2402]~E(x24021,x24022)+E(f609(x24021,x24023,x24024),f609(x24022,x24023,x24024))
% 22.40/22.33 [2403]~E(x24031,x24032)+E(f609(x24033,x24031,x24034),f609(x24033,x24032,x24034))
% 22.40/22.33 [2404]~E(x24041,x24042)+E(f609(x24043,x24044,x24041),f609(x24043,x24044,x24042))
% 22.40/22.33 [2405]~E(x24051,x24052)+E(f366(x24051,x24053,x24054,x24055,x24056),f366(x24052,x24053,x24054,x24055,x24056))
% 22.40/22.33 [2406]~E(x24061,x24062)+E(f366(x24063,x24061,x24064,x24065,x24066),f366(x24063,x24062,x24064,x24065,x24066))
% 22.40/22.33 [2407]~E(x24071,x24072)+E(f366(x24073,x24074,x24071,x24075,x24076),f366(x24073,x24074,x24072,x24075,x24076))
% 22.40/22.33 [2408]~E(x24081,x24082)+E(f366(x24083,x24084,x24085,x24081,x24086),f366(x24083,x24084,x24085,x24082,x24086))
% 22.40/22.33 [2409]~E(x24091,x24092)+E(f366(x24093,x24094,x24095,x24096,x24091),f366(x24093,x24094,x24095,x24096,x24092))
% 22.40/22.33 [2410]~E(x24101,x24102)+E(f820(x24101,x24103,x24104,x24105),f820(x24102,x24103,x24104,x24105))
% 22.40/22.33 [2411]~E(x24111,x24112)+E(f820(x24113,x24111,x24114,x24115),f820(x24113,x24112,x24114,x24115))
% 22.40/22.33 [2412]~E(x24121,x24122)+E(f820(x24123,x24124,x24121,x24125),f820(x24123,x24124,x24122,x24125))
% 22.40/22.33 [2413]~E(x24131,x24132)+E(f820(x24133,x24134,x24135,x24131),f820(x24133,x24134,x24135,x24132))
% 22.40/22.33 [2414]~E(x24141,x24142)+E(f496(x24141,x24143,x24144),f496(x24142,x24143,x24144))
% 22.40/22.33 [2415]~E(x24151,x24152)+E(f496(x24153,x24151,x24154),f496(x24153,x24152,x24154))
% 22.40/22.33 [2416]~E(x24161,x24162)+E(f496(x24163,x24164,x24161),f496(x24163,x24164,x24162))
% 22.40/22.33 [2417]~E(x24171,x24172)+E(f513(x24171,x24173,x24174,x24175,x24176),f513(x24172,x24173,x24174,x24175,x24176))
% 22.40/22.33 [2418]~E(x24181,x24182)+E(f513(x24183,x24181,x24184,x24185,x24186),f513(x24183,x24182,x24184,x24185,x24186))
% 22.40/22.33 [2419]~E(x24191,x24192)+E(f513(x24193,x24194,x24191,x24195,x24196),f513(x24193,x24194,x24192,x24195,x24196))
% 22.40/22.33 [2420]~E(x24201,x24202)+E(f513(x24203,x24204,x24205,x24201,x24206),f513(x24203,x24204,x24205,x24202,x24206))
% 22.40/22.33 [2421]~E(x24211,x24212)+E(f513(x24213,x24214,x24215,x24216,x24211),f513(x24213,x24214,x24215,x24216,x24212))
% 22.40/22.33 [2422]~E(x24221,x24222)+E(f622(x24221,x24223,x24224,x24225,x24226),f622(x24222,x24223,x24224,x24225,x24226))
% 22.40/22.33 [2423]~E(x24231,x24232)+E(f622(x24233,x24231,x24234,x24235,x24236),f622(x24233,x24232,x24234,x24235,x24236))
% 22.40/22.33 [2424]~E(x24241,x24242)+E(f622(x24243,x24244,x24241,x24245,x24246),f622(x24243,x24244,x24242,x24245,x24246))
% 22.40/22.33 [2425]~E(x24251,x24252)+E(f622(x24253,x24254,x24255,x24251,x24256),f622(x24253,x24254,x24255,x24252,x24256))
% 22.40/22.33 [2426]~E(x24261,x24262)+E(f622(x24263,x24264,x24265,x24266,x24261),f622(x24263,x24264,x24265,x24266,x24262))
% 22.40/22.33 [2427]~E(x24271,x24272)+E(f630(x24271,x24273,x24274,x24275,x24276),f630(x24272,x24273,x24274,x24275,x24276))
% 22.40/22.33 [2428]~E(x24281,x24282)+E(f630(x24283,x24281,x24284,x24285,x24286),f630(x24283,x24282,x24284,x24285,x24286))
% 22.40/22.33 [2429]~E(x24291,x24292)+E(f630(x24293,x24294,x24291,x24295,x24296),f630(x24293,x24294,x24292,x24295,x24296))
% 22.40/22.33 [2430]~E(x24301,x24302)+E(f630(x24303,x24304,x24305,x24301,x24306),f630(x24303,x24304,x24305,x24302,x24306))
% 22.40/22.33 [2431]~E(x24311,x24312)+E(f630(x24313,x24314,x24315,x24316,x24311),f630(x24313,x24314,x24315,x24316,x24312))
% 22.40/22.33 [2432]~E(x24321,x24322)+E(f875(x24321,x24323,x24324),f875(x24322,x24323,x24324))
% 22.40/22.33 [2433]~E(x24331,x24332)+E(f875(x24333,x24331,x24334),f875(x24333,x24332,x24334))
% 22.40/22.33 [2434]~E(x24341,x24342)+E(f875(x24343,x24344,x24341),f875(x24343,x24344,x24342))
% 22.40/22.33 [2435]~E(x24351,x24352)+E(f396(x24351,x24353,x24354),f396(x24352,x24353,x24354))
% 22.40/22.33 [2436]~E(x24361,x24362)+E(f396(x24363,x24361,x24364),f396(x24363,x24362,x24364))
% 22.40/22.33 [2437]~E(x24371,x24372)+E(f396(x24373,x24374,x24371),f396(x24373,x24374,x24372))
% 22.40/22.33 [2438]~E(x24381,x24382)+E(f843(x24381,x24383,x24384,x24385,x24386,x24387),f843(x24382,x24383,x24384,x24385,x24386,x24387))
% 22.40/22.33 [2439]~E(x24391,x24392)+E(f843(x24393,x24391,x24394,x24395,x24396,x24397),f843(x24393,x24392,x24394,x24395,x24396,x24397))
% 22.40/22.33 [2440]~E(x24401,x24402)+E(f843(x24403,x24404,x24401,x24405,x24406,x24407),f843(x24403,x24404,x24402,x24405,x24406,x24407))
% 22.40/22.33 [2441]~E(x24411,x24412)+E(f843(x24413,x24414,x24415,x24411,x24416,x24417),f843(x24413,x24414,x24415,x24412,x24416,x24417))
% 22.40/22.33 [2442]~E(x24421,x24422)+E(f843(x24423,x24424,x24425,x24426,x24421,x24427),f843(x24423,x24424,x24425,x24426,x24422,x24427))
% 22.40/22.33 [2443]~E(x24431,x24432)+E(f843(x24433,x24434,x24435,x24436,x24437,x24431),f843(x24433,x24434,x24435,x24436,x24437,x24432))
% 22.40/22.33 [2444]~E(x24441,x24442)+E(f534(x24441,x24443,x24444),f534(x24442,x24443,x24444))
% 22.40/22.33 [2445]~E(x24451,x24452)+E(f534(x24453,x24451,x24454),f534(x24453,x24452,x24454))
% 22.40/22.33 [2446]~E(x24461,x24462)+E(f534(x24463,x24464,x24461),f534(x24463,x24464,x24462))
% 22.40/22.33 [2447]~E(x24471,x24472)+E(f760(x24471,x24473),f760(x24472,x24473))
% 22.40/22.33 [2448]~E(x24481,x24482)+E(f760(x24483,x24481),f760(x24483,x24482))
% 22.40/22.33 [2449]~E(x24491,x24492)+E(f606(x24491,x24493,x24494),f606(x24492,x24493,x24494))
% 22.40/22.33 [2450]~E(x24501,x24502)+E(f606(x24503,x24501,x24504),f606(x24503,x24502,x24504))
% 22.40/22.33 [2451]~E(x24511,x24512)+E(f606(x24513,x24514,x24511),f606(x24513,x24514,x24512))
% 22.40/22.33 [2452]~E(x24521,x24522)+E(f640(x24521,x24523,x24524,x24525,x24526,x24527),f640(x24522,x24523,x24524,x24525,x24526,x24527))
% 22.40/22.33 [2453]~E(x24531,x24532)+E(f640(x24533,x24531,x24534,x24535,x24536,x24537),f640(x24533,x24532,x24534,x24535,x24536,x24537))
% 22.40/22.33 [2454]~E(x24541,x24542)+E(f640(x24543,x24544,x24541,x24545,x24546,x24547),f640(x24543,x24544,x24542,x24545,x24546,x24547))
% 22.40/22.33 [2455]~E(x24551,x24552)+E(f640(x24553,x24554,x24555,x24551,x24556,x24557),f640(x24553,x24554,x24555,x24552,x24556,x24557))
% 22.40/22.33 [2456]~E(x24561,x24562)+E(f640(x24563,x24564,x24565,x24566,x24561,x24567),f640(x24563,x24564,x24565,x24566,x24562,x24567))
% 22.40/22.33 [2457]~E(x24571,x24572)+E(f640(x24573,x24574,x24575,x24576,x24577,x24571),f640(x24573,x24574,x24575,x24576,x24577,x24572))
% 22.40/22.33 [2458]~E(x24581,x24582)+E(f489(x24581,x24583,x24584),f489(x24582,x24583,x24584))
% 22.40/22.33 [2459]~E(x24591,x24592)+E(f489(x24593,x24591,x24594),f489(x24593,x24592,x24594))
% 22.40/22.33 [2460]~E(x24601,x24602)+E(f489(x24603,x24604,x24601),f489(x24603,x24604,x24602))
% 22.40/22.33 [2461]~E(x24611,x24612)+E(f340(x24611,x24613),f340(x24612,x24613))
% 22.40/22.33 [2462]~E(x24621,x24622)+E(f340(x24623,x24621),f340(x24623,x24622))
% 22.40/22.33 [2463]~E(x24631,x24632)+E(f704(x24631,x24633,x24634),f704(x24632,x24633,x24634))
% 22.40/22.33 [2464]~E(x24641,x24642)+E(f704(x24643,x24641,x24644),f704(x24643,x24642,x24644))
% 22.40/22.33 [2465]~E(x24651,x24652)+E(f704(x24653,x24654,x24651),f704(x24653,x24654,x24652))
% 22.40/22.33 [2466]~E(x24661,x24662)+E(f775(x24661,x24663),f775(x24662,x24663))
% 22.40/22.33 [2467]~E(x24671,x24672)+E(f775(x24673,x24671),f775(x24673,x24672))
% 22.40/22.33 [2468]~E(x24681,x24682)+E(f462(x24681,x24683,x24684,x24685),f462(x24682,x24683,x24684,x24685))
% 22.40/22.33 [2469]~E(x24691,x24692)+E(f462(x24693,x24691,x24694,x24695),f462(x24693,x24692,x24694,x24695))
% 22.40/22.33 [2470]~E(x24701,x24702)+E(f462(x24703,x24704,x24701,x24705),f462(x24703,x24704,x24702,x24705))
% 22.40/22.33 [2471]~E(x24711,x24712)+E(f462(x24713,x24714,x24715,x24711),f462(x24713,x24714,x24715,x24712))
% 22.40/22.33 [2472]~E(x24721,x24722)+E(f771(x24721,x24723),f771(x24722,x24723))
% 22.40/22.33 [2473]~E(x24731,x24732)+E(f771(x24733,x24731),f771(x24733,x24732))
% 22.40/22.33 [2474]~E(x24741,x24742)+E(f592(x24741,x24743),f592(x24742,x24743))
% 22.40/22.33 [2475]~E(x24751,x24752)+E(f592(x24753,x24751),f592(x24753,x24752))
% 22.40/22.33 [2476]~E(x24761,x24762)+E(f271(x24761,x24763,x24764,x24765),f271(x24762,x24763,x24764,x24765))
% 22.40/22.33 [2477]~E(x24771,x24772)+E(f271(x24773,x24771,x24774,x24775),f271(x24773,x24772,x24774,x24775))
% 22.40/22.33 [2478]~E(x24781,x24782)+E(f271(x24783,x24784,x24781,x24785),f271(x24783,x24784,x24782,x24785))
% 22.40/22.33 [2479]~E(x24791,x24792)+E(f271(x24793,x24794,x24795,x24791),f271(x24793,x24794,x24795,x24792))
% 22.40/22.33 [2480]~E(x24801,x24802)+E(f332(x24801,x24803,x24804),f332(x24802,x24803,x24804))
% 22.40/22.33 [2481]~E(x24811,x24812)+E(f332(x24813,x24811,x24814),f332(x24813,x24812,x24814))
% 22.40/22.33 [2482]~E(x24821,x24822)+E(f332(x24823,x24824,x24821),f332(x24823,x24824,x24822))
% 22.40/22.33 [2483]~E(x24831,x24832)+E(f748(x24831,x24833,x24834),f748(x24832,x24833,x24834))
% 22.40/22.33 [2484]~E(x24841,x24842)+E(f748(x24843,x24841,x24844),f748(x24843,x24842,x24844))
% 22.40/22.33 [2485]~E(x24851,x24852)+E(f748(x24853,x24854,x24851),f748(x24853,x24854,x24852))
% 22.40/22.33 [2486]~E(x24861,x24862)+E(f665(x24861,x24863,x24864),f665(x24862,x24863,x24864))
% 22.40/22.33 [2487]~E(x24871,x24872)+E(f665(x24873,x24871,x24874),f665(x24873,x24872,x24874))
% 22.40/22.33 [2488]~E(x24881,x24882)+E(f665(x24883,x24884,x24881),f665(x24883,x24884,x24882))
% 22.40/22.33 [2489]~E(x24891,x24892)+E(f558(x24891,x24893),f558(x24892,x24893))
% 22.40/22.33 [2490]~E(x24901,x24902)+E(f558(x24903,x24901),f558(x24903,x24902))
% 22.40/22.33 [2491]~E(x24911,x24912)+E(f745(x24911,x24913,x24914),f745(x24912,x24913,x24914))
% 22.40/22.33 [2492]~E(x24921,x24922)+E(f745(x24923,x24921,x24924),f745(x24923,x24922,x24924))
% 22.40/22.33 [2493]~E(x24931,x24932)+E(f745(x24933,x24934,x24931),f745(x24933,x24934,x24932))
% 22.40/22.33 [2494]~E(x24941,x24942)+E(f681(x24941,x24943,x24944),f681(x24942,x24943,x24944))
% 22.40/22.33 [2495]~E(x24951,x24952)+E(f681(x24953,x24951,x24954),f681(x24953,x24952,x24954))
% 22.40/22.33 [2496]~E(x24961,x24962)+E(f681(x24963,x24964,x24961),f681(x24963,x24964,x24962))
% 22.40/22.33 [2497]~E(x24971,x24972)+E(f19(x24971,x24973,x24974,x24975),f19(x24972,x24973,x24974,x24975))
% 22.40/22.33 [2498]~E(x24981,x24982)+E(f19(x24983,x24981,x24984,x24985),f19(x24983,x24982,x24984,x24985))
% 22.40/22.33 [2499]~E(x24991,x24992)+E(f19(x24993,x24994,x24991,x24995),f19(x24993,x24994,x24992,x24995))
% 22.40/22.33 [2500]~E(x25001,x25002)+E(f19(x25003,x25004,x25005,x25001),f19(x25003,x25004,x25005,x25002))
% 22.40/22.33 [2501]~E(x25011,x25012)+E(f388(x25011,x25013,x25014,x25015),f388(x25012,x25013,x25014,x25015))
% 22.40/22.33 [2502]~E(x25021,x25022)+E(f388(x25023,x25021,x25024,x25025),f388(x25023,x25022,x25024,x25025))
% 22.40/22.33 [2503]~E(x25031,x25032)+E(f388(x25033,x25034,x25031,x25035),f388(x25033,x25034,x25032,x25035))
% 22.40/22.33 [2504]~E(x25041,x25042)+E(f388(x25043,x25044,x25045,x25041),f388(x25043,x25044,x25045,x25042))
% 22.40/22.33 [2505]~E(x25051,x25052)+E(f333(x25051,x25053,x25054),f333(x25052,x25053,x25054))
% 22.40/22.33 [2506]~E(x25061,x25062)+E(f333(x25063,x25061,x25064),f333(x25063,x25062,x25064))
% 22.40/22.33 [2507]~E(x25071,x25072)+E(f333(x25073,x25074,x25071),f333(x25073,x25074,x25072))
% 22.40/22.33 [2508]~E(x25081,x25082)+E(f433(x25081),f433(x25082))
% 22.40/22.33 [2509]~E(x25091,x25092)+E(f751(x25091,x25093),f751(x25092,x25093))
% 22.40/22.33 [2510]~E(x25101,x25102)+E(f751(x25103,x25101),f751(x25103,x25102))
% 22.40/22.33 [2511]~E(x25111,x25112)+E(f368(x25111,x25113,x25114,x25115,x25116),f368(x25112,x25113,x25114,x25115,x25116))
% 22.40/22.33 [2512]~E(x25121,x25122)+E(f368(x25123,x25121,x25124,x25125,x25126),f368(x25123,x25122,x25124,x25125,x25126))
% 22.40/22.33 [2513]~E(x25131,x25132)+E(f368(x25133,x25134,x25131,x25135,x25136),f368(x25133,x25134,x25132,x25135,x25136))
% 22.40/22.33 [2514]~E(x25141,x25142)+E(f368(x25143,x25144,x25145,x25141,x25146),f368(x25143,x25144,x25145,x25142,x25146))
% 22.40/22.33 [2515]~E(x25151,x25152)+E(f368(x25153,x25154,x25155,x25156,x25151),f368(x25153,x25154,x25155,x25156,x25152))
% 22.40/22.33 [2516]~E(x25161,x25162)+E(f221(x25161,x25163,x25164),f221(x25162,x25163,x25164))
% 22.40/22.33 [2517]~E(x25171,x25172)+E(f221(x25173,x25171,x25174),f221(x25173,x25172,x25174))
% 22.40/22.33 [2518]~E(x25181,x25182)+E(f221(x25183,x25184,x25181),f221(x25183,x25184,x25182))
% 22.40/22.33 [2519]~E(x25191,x25192)+E(f578(x25191,x25193,x25194,x25195),f578(x25192,x25193,x25194,x25195))
% 22.40/22.33 [2520]~E(x25201,x25202)+E(f578(x25203,x25201,x25204,x25205),f578(x25203,x25202,x25204,x25205))
% 22.40/22.33 [2521]~E(x25211,x25212)+E(f578(x25213,x25214,x25211,x25215),f578(x25213,x25214,x25212,x25215))
% 22.40/22.33 [2522]~E(x25221,x25222)+E(f578(x25223,x25224,x25225,x25221),f578(x25223,x25224,x25225,x25222))
% 22.40/22.33 [2523]~E(x25231,x25232)+E(f675(x25231,x25233,x25234,x25235),f675(x25232,x25233,x25234,x25235))
% 22.40/22.33 [2524]~E(x25241,x25242)+E(f675(x25243,x25241,x25244,x25245),f675(x25243,x25242,x25244,x25245))
% 22.40/22.33 [2525]~E(x25251,x25252)+E(f675(x25253,x25254,x25251,x25255),f675(x25253,x25254,x25252,x25255))
% 22.40/22.33 [2526]~E(x25261,x25262)+E(f675(x25263,x25264,x25265,x25261),f675(x25263,x25264,x25265,x25262))
% 22.40/22.33 [2527]~E(x25271,x25272)+E(f793(x25271,x25273),f793(x25272,x25273))
% 22.40/22.33 [2528]~E(x25281,x25282)+E(f793(x25283,x25281),f793(x25283,x25282))
% 22.40/22.33 [2529]~E(x25291,x25292)+E(f734(x25291,x25293,x25294,x25295,x25296),f734(x25292,x25293,x25294,x25295,x25296))
% 22.40/22.33 [2530]~E(x25301,x25302)+E(f734(x25303,x25301,x25304,x25305,x25306),f734(x25303,x25302,x25304,x25305,x25306))
% 22.40/22.33 [2531]~E(x25311,x25312)+E(f734(x25313,x25314,x25311,x25315,x25316),f734(x25313,x25314,x25312,x25315,x25316))
% 22.40/22.33 [2532]~E(x25321,x25322)+E(f734(x25323,x25324,x25325,x25321,x25326),f734(x25323,x25324,x25325,x25322,x25326))
% 22.40/22.33 [2533]~E(x25331,x25332)+E(f734(x25333,x25334,x25335,x25336,x25331),f734(x25333,x25334,x25335,x25336,x25332))
% 22.40/22.33 [2534]~E(x25341,x25342)+E(f811(x25341,x25343),f811(x25342,x25343))
% 22.40/22.33 [2535]~E(x25351,x25352)+E(f811(x25353,x25351),f811(x25353,x25352))
% 22.40/22.33 [2536]~E(x25361,x25362)+E(f689(x25361,x25363,x25364,x25365),f689(x25362,x25363,x25364,x25365))
% 22.40/22.33 [2537]~E(x25371,x25372)+E(f689(x25373,x25371,x25374,x25375),f689(x25373,x25372,x25374,x25375))
% 22.40/22.33 [2538]~E(x25381,x25382)+E(f689(x25383,x25384,x25381,x25385),f689(x25383,x25384,x25382,x25385))
% 22.40/22.33 [2539]~E(x25391,x25392)+E(f689(x25393,x25394,x25395,x25391),f689(x25393,x25394,x25395,x25392))
% 22.40/22.33 [2540]~E(x25401,x25402)+E(f442(x25401,x25403,x25404),f442(x25402,x25403,x25404))
% 22.40/22.33 [2541]~E(x25411,x25412)+E(f442(x25413,x25411,x25414),f442(x25413,x25412,x25414))
% 22.40/22.33 [2542]~E(x25421,x25422)+E(f442(x25423,x25424,x25421),f442(x25423,x25424,x25422))
% 22.40/22.33 [2543]~E(x25431,x25432)+E(f627(x25431,x25433,x25434,x25435),f627(x25432,x25433,x25434,x25435))
% 22.40/22.33 [2544]~E(x25441,x25442)+E(f627(x25443,x25441,x25444,x25445),f627(x25443,x25442,x25444,x25445))
% 22.40/22.33 [2545]~E(x25451,x25452)+E(f627(x25453,x25454,x25451,x25455),f627(x25453,x25454,x25452,x25455))
% 22.40/22.33 [2546]~E(x25461,x25462)+E(f627(x25463,x25464,x25465,x25461),f627(x25463,x25464,x25465,x25462))
% 22.40/22.33 [2547]~E(x25471,x25472)+E(f123(x25471,x25473,x25474,x25475),f123(x25472,x25473,x25474,x25475))
% 22.40/22.33 [2548]~E(x25481,x25482)+E(f123(x25483,x25481,x25484,x25485),f123(x25483,x25482,x25484,x25485))
% 22.40/22.33 [2549]~E(x25491,x25492)+E(f123(x25493,x25494,x25491,x25495),f123(x25493,x25494,x25492,x25495))
% 22.40/22.33 [2550]~E(x25501,x25502)+E(f123(x25503,x25504,x25505,x25501),f123(x25503,x25504,x25505,x25502))
% 22.40/22.33 [2551]~E(x25511,x25512)+E(f619(x25511,x25513,x25514,x25515,x25516),f619(x25512,x25513,x25514,x25515,x25516))
% 22.40/22.33 [2552]~E(x25521,x25522)+E(f619(x25523,x25521,x25524,x25525,x25526),f619(x25523,x25522,x25524,x25525,x25526))
% 22.40/22.33 [2553]~E(x25531,x25532)+E(f619(x25533,x25534,x25531,x25535,x25536),f619(x25533,x25534,x25532,x25535,x25536))
% 22.40/22.33 [2554]~E(x25541,x25542)+E(f619(x25543,x25544,x25545,x25541,x25546),f619(x25543,x25544,x25545,x25542,x25546))
% 22.40/22.33 [2555]~E(x25551,x25552)+E(f619(x25553,x25554,x25555,x25556,x25551),f619(x25553,x25554,x25555,x25556,x25552))
% 22.40/22.33 [2556]~E(x25561,x25562)+E(f523(x25561,x25563,x25564,x25565),f523(x25562,x25563,x25564,x25565))
% 22.40/22.33 [2557]~E(x25571,x25572)+E(f523(x25573,x25571,x25574,x25575),f523(x25573,x25572,x25574,x25575))
% 22.40/22.33 [2558]~E(x25581,x25582)+E(f523(x25583,x25584,x25581,x25585),f523(x25583,x25584,x25582,x25585))
% 22.40/22.33 [2559]~E(x25591,x25592)+E(f523(x25593,x25594,x25595,x25591),f523(x25593,x25594,x25595,x25592))
% 22.40/22.33 [2560]~E(x25601,x25602)+E(f886(x25601),f886(x25602))
% 22.40/22.33 [2561]~E(x25611,x25612)+E(f444(x25611),f444(x25612))
% 22.40/22.33 [2562]~E(x25621,x25622)+E(f712(x25621,x25623,x25624),f712(x25622,x25623,x25624))
% 22.40/22.33 [2563]~E(x25631,x25632)+E(f712(x25633,x25631,x25634),f712(x25633,x25632,x25634))
% 22.40/22.33 [2564]~E(x25641,x25642)+E(f712(x25643,x25644,x25641),f712(x25643,x25644,x25642))
% 22.40/22.33 [2565]~E(x25651,x25652)+E(f736(x25651,x25653),f736(x25652,x25653))
% 22.40/22.33 [2566]~E(x25661,x25662)+E(f736(x25663,x25661),f736(x25663,x25662))
% 22.40/22.33 [2567]~E(x25671,x25672)+E(f742(x25671,x25673,x25674),f742(x25672,x25673,x25674))
% 22.40/22.33 [2568]~E(x25681,x25682)+E(f742(x25683,x25681,x25684),f742(x25683,x25682,x25684))
% 22.40/22.33 [2569]~E(x25691,x25692)+E(f742(x25693,x25694,x25691),f742(x25693,x25694,x25692))
% 22.40/22.33 [2570]~E(x25701,x25702)+E(f602(x25701,x25703,x25704,x25705,x25706,x25707),f602(x25702,x25703,x25704,x25705,x25706,x25707))
% 22.40/22.33 [2571]~E(x25711,x25712)+E(f602(x25713,x25711,x25714,x25715,x25716,x25717),f602(x25713,x25712,x25714,x25715,x25716,x25717))
% 22.40/22.33 [2572]~E(x25721,x25722)+E(f602(x25723,x25724,x25721,x25725,x25726,x25727),f602(x25723,x25724,x25722,x25725,x25726,x25727))
% 22.40/22.33 [2573]~E(x25731,x25732)+E(f602(x25733,x25734,x25735,x25731,x25736,x25737),f602(x25733,x25734,x25735,x25732,x25736,x25737))
% 22.40/22.33 [2574]~E(x25741,x25742)+E(f602(x25743,x25744,x25745,x25746,x25741,x25747),f602(x25743,x25744,x25745,x25746,x25742,x25747))
% 22.40/22.33 [2575]~E(x25751,x25752)+E(f602(x25753,x25754,x25755,x25756,x25757,x25751),f602(x25753,x25754,x25755,x25756,x25757,x25752))
% 22.40/22.33 [2576]~E(x25761,x25762)+E(f399(x25761,x25763,x25764,x25765),f399(x25762,x25763,x25764,x25765))
% 22.40/22.33 [2577]~E(x25771,x25772)+E(f399(x25773,x25771,x25774,x25775),f399(x25773,x25772,x25774,x25775))
% 22.40/22.33 [2578]~E(x25781,x25782)+E(f399(x25783,x25784,x25781,x25785),f399(x25783,x25784,x25782,x25785))
% 22.40/22.33 [2579]~E(x25791,x25792)+E(f399(x25793,x25794,x25795,x25791),f399(x25793,x25794,x25795,x25792))
% 22.40/22.33 [2580]~E(x25801,x25802)+E(f879(x25801,x25803,x25804),f879(x25802,x25803,x25804))
% 22.40/22.33 [2581]~E(x25811,x25812)+E(f879(x25813,x25811,x25814),f879(x25813,x25812,x25814))
% 22.40/22.33 [2582]~E(x25821,x25822)+E(f879(x25823,x25824,x25821),f879(x25823,x25824,x25822))
% 22.40/22.33 [2583]~E(x25831,x25832)+E(f710(x25831,x25833,x25834,x25835,x25836),f710(x25832,x25833,x25834,x25835,x25836))
% 22.40/22.33 [2584]~E(x25841,x25842)+E(f710(x25843,x25841,x25844,x25845,x25846),f710(x25843,x25842,x25844,x25845,x25846))
% 22.40/22.33 [2585]~E(x25851,x25852)+E(f710(x25853,x25854,x25851,x25855,x25856),f710(x25853,x25854,x25852,x25855,x25856))
% 22.40/22.33 [2586]~E(x25861,x25862)+E(f710(x25863,x25864,x25865,x25861,x25866),f710(x25863,x25864,x25865,x25862,x25866))
% 22.40/22.33 [2587]~E(x25871,x25872)+E(f710(x25873,x25874,x25875,x25876,x25871),f710(x25873,x25874,x25875,x25876,x25872))
% 22.40/22.33 [2588]~E(x25881,x25882)+E(f655(x25881,x25883),f655(x25882,x25883))
% 22.40/22.33 [2589]~E(x25891,x25892)+E(f655(x25893,x25891),f655(x25893,x25892))
% 22.40/22.33 [2590]~E(x25901,x25902)+E(f449(x25901,x25903,x25904),f449(x25902,x25903,x25904))
% 22.40/22.33 [2591]~E(x25911,x25912)+E(f449(x25913,x25911,x25914),f449(x25913,x25912,x25914))
% 22.40/22.33 [2592]~E(x25921,x25922)+E(f449(x25923,x25924,x25921),f449(x25923,x25924,x25922))
% 22.40/22.33 [2593]~E(x25931,x25932)+E(f632(x25931,x25933,x25934,x25935),f632(x25932,x25933,x25934,x25935))
% 22.40/22.33 [2594]~E(x25941,x25942)+E(f632(x25943,x25941,x25944,x25945),f632(x25943,x25942,x25944,x25945))
% 22.40/22.33 [2595]~E(x25951,x25952)+E(f632(x25953,x25954,x25951,x25955),f632(x25953,x25954,x25952,x25955))
% 22.40/22.33 [2596]~E(x25961,x25962)+E(f632(x25963,x25964,x25965,x25961),f632(x25963,x25964,x25965,x25962))
% 22.40/22.33 [2597]~E(x25971,x25972)+E(f423(x25971),f423(x25972))
% 22.40/22.33 [2598]~E(x25981,x25982)+E(f845(x25981,x25983,x25984),f845(x25982,x25983,x25984))
% 22.40/22.33 [2599]~E(x25991,x25992)+E(f845(x25993,x25991,x25994),f845(x25993,x25992,x25994))
% 22.40/22.33 [2600]~E(x26001,x26002)+E(f845(x26003,x26004,x26001),f845(x26003,x26004,x26002))
% 22.40/22.33 [2601]~E(x26011,x26012)+E(f323(x26011,x26013,x26014,x26015),f323(x26012,x26013,x26014,x26015))
% 22.40/22.33 [2602]~E(x26021,x26022)+E(f323(x26023,x26021,x26024,x26025),f323(x26023,x26022,x26024,x26025))
% 22.40/22.33 [2603]~E(x26031,x26032)+E(f323(x26033,x26034,x26031,x26035),f323(x26033,x26034,x26032,x26035))
% 22.40/22.33 [2604]~E(x26041,x26042)+E(f323(x26043,x26044,x26045,x26041),f323(x26043,x26044,x26045,x26042))
% 22.40/22.33 [2605]~E(x26051,x26052)+E(f239(x26051,x26053,x26054),f239(x26052,x26053,x26054))
% 22.40/22.33 [2606]~E(x26061,x26062)+E(f239(x26063,x26061,x26064),f239(x26063,x26062,x26064))
% 22.40/22.33 [2607]~E(x26071,x26072)+E(f239(x26073,x26074,x26071),f239(x26073,x26074,x26072))
% 22.40/22.33 [2608]~E(x26081,x26082)+E(f527(x26081,x26083,x26084,x26085),f527(x26082,x26083,x26084,x26085))
% 22.40/22.33 [2609]~E(x26091,x26092)+E(f527(x26093,x26091,x26094,x26095),f527(x26093,x26092,x26094,x26095))
% 22.40/22.33 [2610]~E(x26101,x26102)+E(f527(x26103,x26104,x26101,x26105),f527(x26103,x26104,x26102,x26105))
% 22.40/22.33 [2611]~E(x26111,x26112)+E(f527(x26113,x26114,x26115,x26111),f527(x26113,x26114,x26115,x26112))
% 22.40/22.33 [2612]~E(x26121,x26122)+E(f865(x26121,x26123,x26124),f865(x26122,x26123,x26124))
% 22.40/22.33 [2613]~E(x26131,x26132)+E(f865(x26133,x26131,x26134),f865(x26133,x26132,x26134))
% 22.40/22.33 [2614]~E(x26141,x26142)+E(f865(x26143,x26144,x26141),f865(x26143,x26144,x26142))
% 22.40/22.33 [2615]~E(x26151,x26152)+E(f554(x26151,x26153,x26154,x26155),f554(x26152,x26153,x26154,x26155))
% 22.40/22.33 [2616]~E(x26161,x26162)+E(f554(x26163,x26161,x26164,x26165),f554(x26163,x26162,x26164,x26165))
% 22.40/22.33 [2617]~E(x26171,x26172)+E(f554(x26173,x26174,x26171,x26175),f554(x26173,x26174,x26172,x26175))
% 22.40/22.33 [2618]~E(x26181,x26182)+E(f554(x26183,x26184,x26185,x26181),f554(x26183,x26184,x26185,x26182))
% 22.40/22.33 [2619]~E(x26191,x26192)+E(f789(x26191,x26193,x26194,x26195,x26196),f789(x26192,x26193,x26194,x26195,x26196))
% 22.40/22.33 [2620]~E(x26201,x26202)+E(f789(x26203,x26201,x26204,x26205,x26206),f789(x26203,x26202,x26204,x26205,x26206))
% 22.40/22.33 [2621]~E(x26211,x26212)+E(f789(x26213,x26214,x26211,x26215,x26216),f789(x26213,x26214,x26212,x26215,x26216))
% 22.40/22.33 [2622]~E(x26221,x26222)+E(f789(x26223,x26224,x26225,x26221,x26226),f789(x26223,x26224,x26225,x26222,x26226))
% 22.40/22.33 [2623]~E(x26231,x26232)+E(f789(x26233,x26234,x26235,x26236,x26231),f789(x26233,x26234,x26235,x26236,x26232))
% 22.40/22.33 [2624]~E(x26241,x26242)+E(f263(x26241,x26243,x26244,x26245),f263(x26242,x26243,x26244,x26245))
% 22.40/22.33 [2625]~E(x26251,x26252)+E(f263(x26253,x26251,x26254,x26255),f263(x26253,x26252,x26254,x26255))
% 22.40/22.33 [2626]~E(x26261,x26262)+E(f263(x26263,x26264,x26261,x26265),f263(x26263,x26264,x26262,x26265))
% 22.40/22.33 [2627]~E(x26271,x26272)+E(f263(x26273,x26274,x26275,x26271),f263(x26273,x26274,x26275,x26272))
% 22.40/22.33 [2628]~E(x26281,x26282)+E(f452(x26281,x26283,x26284),f452(x26282,x26283,x26284))
% 22.40/22.33 [2629]~E(x26291,x26292)+E(f452(x26293,x26291,x26294),f452(x26293,x26292,x26294))
% 22.40/22.33 [2630]~E(x26301,x26302)+E(f452(x26303,x26304,x26301),f452(x26303,x26304,x26302))
% 22.40/22.33 [2631]~E(x26311,x26312)+E(f543(x26311,x26313),f543(x26312,x26313))
% 22.40/22.33 [2632]~E(x26321,x26322)+E(f543(x26323,x26321),f543(x26323,x26322))
% 22.40/22.33 [2633]~E(x26331,x26332)+E(f413(x26331,x26333,x26334,x26335),f413(x26332,x26333,x26334,x26335))
% 22.40/22.33 [2634]~E(x26341,x26342)+E(f413(x26343,x26341,x26344,x26345),f413(x26343,x26342,x26344,x26345))
% 22.40/22.33 [2635]~E(x26351,x26352)+E(f413(x26353,x26354,x26351,x26355),f413(x26353,x26354,x26352,x26355))
% 22.40/22.33 [2636]~E(x26361,x26362)+E(f413(x26363,x26364,x26365,x26361),f413(x26363,x26364,x26365,x26362))
% 22.40/22.33 [2637]~E(x26371,x26372)+E(f532(x26371,x26373,x26374,x26375),f532(x26372,x26373,x26374,x26375))
% 22.40/22.33 [2638]~E(x26381,x26382)+E(f532(x26383,x26381,x26384,x26385),f532(x26383,x26382,x26384,x26385))
% 22.40/22.33 [2639]~E(x26391,x26392)+E(f532(x26393,x26394,x26391,x26395),f532(x26393,x26394,x26392,x26395))
% 22.40/22.33 [2640]~E(x26401,x26402)+E(f532(x26403,x26404,x26405,x26401),f532(x26403,x26404,x26405,x26402))
% 22.40/22.33 [2641]~E(x26411,x26412)+E(f377(x26411,x26413,x26414),f377(x26412,x26413,x26414))
% 22.40/22.33 [2642]~E(x26421,x26422)+E(f377(x26423,x26421,x26424),f377(x26423,x26422,x26424))
% 22.40/22.33 [2643]~E(x26431,x26432)+E(f377(x26433,x26434,x26431),f377(x26433,x26434,x26432))
% 22.40/22.33 [2644]~E(x26441,x26442)+E(f817(x26441,x26443,x26444,x26445,x26446,x26447),f817(x26442,x26443,x26444,x26445,x26446,x26447))
% 22.40/22.33 [2645]~E(x26451,x26452)+E(f817(x26453,x26451,x26454,x26455,x26456,x26457),f817(x26453,x26452,x26454,x26455,x26456,x26457))
% 22.40/22.33 [2646]~E(x26461,x26462)+E(f817(x26463,x26464,x26461,x26465,x26466,x26467),f817(x26463,x26464,x26462,x26465,x26466,x26467))
% 22.40/22.33 [2647]~E(x26471,x26472)+E(f817(x26473,x26474,x26475,x26471,x26476,x26477),f817(x26473,x26474,x26475,x26472,x26476,x26477))
% 22.40/22.33 [2648]~E(x26481,x26482)+E(f817(x26483,x26484,x26485,x26486,x26481,x26487),f817(x26483,x26484,x26485,x26486,x26482,x26487))
% 22.40/22.33 [2649]~E(x26491,x26492)+E(f817(x26493,x26494,x26495,x26496,x26497,x26491),f817(x26493,x26494,x26495,x26496,x26497,x26492))
% 22.40/22.33 [2650]~E(x26501,x26502)+E(f718(x26501,x26503),f718(x26502,x26503))
% 22.40/22.33 [2651]~E(x26511,x26512)+E(f718(x26513,x26511),f718(x26513,x26512))
% 22.40/22.33 [2652]~E(x26521,x26522)+E(f204(x26521,x26523,x26524,x26525,x26526,x26527,x26528),f204(x26522,x26523,x26524,x26525,x26526,x26527,x26528))
% 22.40/22.33 [2653]~E(x26531,x26532)+E(f204(x26533,x26531,x26534,x26535,x26536,x26537,x26538),f204(x26533,x26532,x26534,x26535,x26536,x26537,x26538))
% 22.40/22.33 [2654]~E(x26541,x26542)+E(f204(x26543,x26544,x26541,x26545,x26546,x26547,x26548),f204(x26543,x26544,x26542,x26545,x26546,x26547,x26548))
% 22.40/22.33 [2655]~E(x26551,x26552)+E(f204(x26553,x26554,x26555,x26551,x26556,x26557,x26558),f204(x26553,x26554,x26555,x26552,x26556,x26557,x26558))
% 22.40/22.33 [2656]~E(x26561,x26562)+E(f204(x26563,x26564,x26565,x26566,x26561,x26567,x26568),f204(x26563,x26564,x26565,x26566,x26562,x26567,x26568))
% 22.40/22.33 [2657]~E(x26571,x26572)+E(f204(x26573,x26574,x26575,x26576,x26577,x26571,x26578),f204(x26573,x26574,x26575,x26576,x26577,x26572,x26578))
% 22.40/22.33 [2658]~E(x26581,x26582)+E(f204(x26583,x26584,x26585,x26586,x26587,x26588,x26581),f204(x26583,x26584,x26585,x26586,x26587,x26588,x26582))
% 22.40/22.33 [2659]~E(x26591,x26592)+E(f733(x26591,x26593,x26594,x26595,x26596),f733(x26592,x26593,x26594,x26595,x26596))
% 22.40/22.33 [2660]~E(x26601,x26602)+E(f733(x26603,x26601,x26604,x26605,x26606),f733(x26603,x26602,x26604,x26605,x26606))
% 22.40/22.33 [2661]~E(x26611,x26612)+E(f733(x26613,x26614,x26611,x26615,x26616),f733(x26613,x26614,x26612,x26615,x26616))
% 22.40/22.33 [2662]~E(x26621,x26622)+E(f733(x26623,x26624,x26625,x26621,x26626),f733(x26623,x26624,x26625,x26622,x26626))
% 22.40/22.33 [2663]~E(x26631,x26632)+E(f733(x26633,x26634,x26635,x26636,x26631),f733(x26633,x26634,x26635,x26636,x26632))
% 22.40/22.33 [2664]~E(x26641,x26642)+E(f238(x26641,x26643,x26644,x26645,x26646,x26647),f238(x26642,x26643,x26644,x26645,x26646,x26647))
% 22.40/22.33 [2665]~E(x26651,x26652)+E(f238(x26653,x26651,x26654,x26655,x26656,x26657),f238(x26653,x26652,x26654,x26655,x26656,x26657))
% 22.40/22.33 [2666]~E(x26661,x26662)+E(f238(x26663,x26664,x26661,x26665,x26666,x26667),f238(x26663,x26664,x26662,x26665,x26666,x26667))
% 22.40/22.33 [2667]~E(x26671,x26672)+E(f238(x26673,x26674,x26675,x26671,x26676,x26677),f238(x26673,x26674,x26675,x26672,x26676,x26677))
% 22.40/22.33 [2668]~E(x26681,x26682)+E(f238(x26683,x26684,x26685,x26686,x26681,x26687),f238(x26683,x26684,x26685,x26686,x26682,x26687))
% 22.40/22.33 [2669]~E(x26691,x26692)+E(f238(x26693,x26694,x26695,x26696,x26697,x26691),f238(x26693,x26694,x26695,x26696,x26697,x26692))
% 22.40/22.33 [2670]~E(x26701,x26702)+E(f726(x26701,x26703,x26704,x26705),f726(x26702,x26703,x26704,x26705))
% 22.40/22.33 [2671]~E(x26711,x26712)+E(f726(x26713,x26711,x26714,x26715),f726(x26713,x26712,x26714,x26715))
% 22.40/22.33 [2672]~E(x26721,x26722)+E(f726(x26723,x26724,x26721,x26725),f726(x26723,x26724,x26722,x26725))
% 22.40/22.33 [2673]~E(x26731,x26732)+E(f726(x26733,x26734,x26735,x26731),f726(x26733,x26734,x26735,x26732))
% 22.40/22.33 [2674]~E(x26741,x26742)+E(f529(x26741,x26743,x26744,x26745,x26746,x26747),f529(x26742,x26743,x26744,x26745,x26746,x26747))
% 22.40/22.33 [2675]~E(x26751,x26752)+E(f529(x26753,x26751,x26754,x26755,x26756,x26757),f529(x26753,x26752,x26754,x26755,x26756,x26757))
% 22.40/22.33 [2676]~E(x26761,x26762)+E(f529(x26763,x26764,x26761,x26765,x26766,x26767),f529(x26763,x26764,x26762,x26765,x26766,x26767))
% 22.40/22.33 [2677]~E(x26771,x26772)+E(f529(x26773,x26774,x26775,x26771,x26776,x26777),f529(x26773,x26774,x26775,x26772,x26776,x26777))
% 22.40/22.33 [2678]~E(x26781,x26782)+E(f529(x26783,x26784,x26785,x26786,x26781,x26787),f529(x26783,x26784,x26785,x26786,x26782,x26787))
% 22.40/22.33 [2679]~E(x26791,x26792)+E(f529(x26793,x26794,x26795,x26796,x26797,x26791),f529(x26793,x26794,x26795,x26796,x26797,x26792))
% 22.40/22.33 [2680]~E(x26801,x26802)+E(f196(x26801,x26803,x26804),f196(x26802,x26803,x26804))
% 22.40/22.33 [2681]~E(x26811,x26812)+E(f196(x26813,x26811,x26814),f196(x26813,x26812,x26814))
% 22.40/22.33 [2682]~E(x26821,x26822)+E(f196(x26823,x26824,x26821),f196(x26823,x26824,x26822))
% 22.40/22.33 [2683]~E(x26831,x26832)+E(f589(x26831,x26833,x26834),f589(x26832,x26833,x26834))
% 22.40/22.33 [2684]~E(x26841,x26842)+E(f589(x26843,x26841,x26844),f589(x26843,x26842,x26844))
% 22.40/22.33 [2685]~E(x26851,x26852)+E(f589(x26853,x26854,x26851),f589(x26853,x26854,x26852))
% 22.40/22.33 [2686]~E(x26861,x26862)+E(f419(x26861,x26863,x26864,x26865,x26866,x26867,x26868),f419(x26862,x26863,x26864,x26865,x26866,x26867,x26868))
% 22.40/22.33 [2687]~E(x26871,x26872)+E(f419(x26873,x26871,x26874,x26875,x26876,x26877,x26878),f419(x26873,x26872,x26874,x26875,x26876,x26877,x26878))
% 22.40/22.33 [2688]~E(x26881,x26882)+E(f419(x26883,x26884,x26881,x26885,x26886,x26887,x26888),f419(x26883,x26884,x26882,x26885,x26886,x26887,x26888))
% 22.40/22.33 [2689]~E(x26891,x26892)+E(f419(x26893,x26894,x26895,x26891,x26896,x26897,x26898),f419(x26893,x26894,x26895,x26892,x26896,x26897,x26898))
% 22.40/22.33 [2690]~E(x26901,x26902)+E(f419(x26903,x26904,x26905,x26906,x26901,x26907,x26908),f419(x26903,x26904,x26905,x26906,x26902,x26907,x26908))
% 22.40/22.33 [2691]~E(x26911,x26912)+E(f419(x26913,x26914,x26915,x26916,x26917,x26911,x26918),f419(x26913,x26914,x26915,x26916,x26917,x26912,x26918))
% 22.40/22.33 [2692]~E(x26921,x26922)+E(f419(x26923,x26924,x26925,x26926,x26927,x26928,x26921),f419(x26923,x26924,x26925,x26926,x26927,x26928,x26922))
% 22.40/22.33 [2693]~E(x26931,x26932)+E(f266(x26931,x26933,x26934),f266(x26932,x26933,x26934))
% 22.40/22.33 [2694]~E(x26941,x26942)+E(f266(x26943,x26941,x26944),f266(x26943,x26942,x26944))
% 22.40/22.33 [2695]~E(x26951,x26952)+E(f266(x26953,x26954,x26951),f266(x26953,x26954,x26952))
% 22.40/22.33 [2696]~E(x26961,x26962)+E(f605(x26961,x26963),f605(x26962,x26963))
% 22.40/22.33 [2697]~E(x26971,x26972)+E(f605(x26973,x26971),f605(x26973,x26972))
% 22.40/22.33 [2698]~E(x26981,x26982)+E(f494(x26981,x26983,x26984,x26985),f494(x26982,x26983,x26984,x26985))
% 22.40/22.33 [2699]~E(x26991,x26992)+E(f494(x26993,x26991,x26994,x26995),f494(x26993,x26992,x26994,x26995))
% 22.40/22.33 [2700]~E(x27001,x27002)+E(f494(x27003,x27004,x27001,x27005),f494(x27003,x27004,x27002,x27005))
% 22.40/22.33 [2701]~E(x27011,x27012)+E(f494(x27013,x27014,x27015,x27011),f494(x27013,x27014,x27015,x27012))
% 22.40/22.33 [2702]~E(x27021,x27022)+E(f545(x27021,x27023),f545(x27022,x27023))
% 22.40/22.33 [2703]~E(x27031,x27032)+E(f545(x27033,x27031),f545(x27033,x27032))
% 22.40/22.33 [2704]~E(x27041,x27042)+E(f542(x27041,x27043,x27044,x27045,x27046,x27047,x27048,x27049),f542(x27042,x27043,x27044,x27045,x27046,x27047,x27048,x27049))
% 22.40/22.33 [2705]~E(x27051,x27052)+E(f542(x27053,x27051,x27054,x27055,x27056,x27057,x27058,x27059),f542(x27053,x27052,x27054,x27055,x27056,x27057,x27058,x27059))
% 22.40/22.33 [2706]~E(x27061,x27062)+E(f542(x27063,x27064,x27061,x27065,x27066,x27067,x27068,x27069),f542(x27063,x27064,x27062,x27065,x27066,x27067,x27068,x27069))
% 22.40/22.33 [2707]~E(x27071,x27072)+E(f542(x27073,x27074,x27075,x27071,x27076,x27077,x27078,x27079),f542(x27073,x27074,x27075,x27072,x27076,x27077,x27078,x27079))
% 22.40/22.33 [2708]~E(x27081,x27082)+E(f542(x27083,x27084,x27085,x27086,x27081,x27087,x27088,x27089),f542(x27083,x27084,x27085,x27086,x27082,x27087,x27088,x27089))
% 22.40/22.33 [2709]~E(x27091,x27092)+E(f542(x27093,x27094,x27095,x27096,x27097,x27091,x27098,x27099),f542(x27093,x27094,x27095,x27096,x27097,x27092,x27098,x27099))
% 22.40/22.33 [2710]~E(x27101,x27102)+E(f542(x27103,x27104,x27105,x27106,x27107,x27108,x27101,x27109),f542(x27103,x27104,x27105,x27106,x27107,x27108,x27102,x27109))
% 22.40/22.33 [2711]~E(x27111,x27112)+E(f542(x27113,x27114,x27115,x27116,x27117,x27118,x27119,x27111),f542(x27113,x27114,x27115,x27116,x27117,x27118,x27119,x27112))
% 22.40/22.33 [2712]~E(x27121,x27122)+E(f823(x27121,x27123,x27124),f823(x27122,x27123,x27124))
% 22.40/22.33 [2713]~E(x27131,x27132)+E(f823(x27133,x27131,x27134),f823(x27133,x27132,x27134))
% 22.40/22.33 [2714]~E(x27141,x27142)+E(f823(x27143,x27144,x27141),f823(x27143,x27144,x27142))
% 22.40/22.33 [2715]~E(x27151,x27152)+E(f512(x27151,x27153,x27154),f512(x27152,x27153,x27154))
% 22.40/22.33 [2716]~E(x27161,x27162)+E(f512(x27163,x27161,x27164),f512(x27163,x27162,x27164))
% 22.40/22.33 [2717]~E(x27171,x27172)+E(f512(x27173,x27174,x27171),f512(x27173,x27174,x27172))
% 22.40/22.33 [2718]~E(x27181,x27182)+E(f884(x27181,x27183,x27184,x27185,x27186,x27187,x27188,x27189),f884(x27182,x27183,x27184,x27185,x27186,x27187,x27188,x27189))
% 22.40/22.33 [2719]~E(x27191,x27192)+E(f884(x27193,x27191,x27194,x27195,x27196,x27197,x27198,x27199),f884(x27193,x27192,x27194,x27195,x27196,x27197,x27198,x27199))
% 22.40/22.33 [2720]~E(x27201,x27202)+E(f884(x27203,x27204,x27201,x27205,x27206,x27207,x27208,x27209),f884(x27203,x27204,x27202,x27205,x27206,x27207,x27208,x27209))
% 22.40/22.33 [2721]~E(x27211,x27212)+E(f884(x27213,x27214,x27215,x27211,x27216,x27217,x27218,x27219),f884(x27213,x27214,x27215,x27212,x27216,x27217,x27218,x27219))
% 22.40/22.33 [2722]~E(x27221,x27222)+E(f884(x27223,x27224,x27225,x27226,x27221,x27227,x27228,x27229),f884(x27223,x27224,x27225,x27226,x27222,x27227,x27228,x27229))
% 22.40/22.33 [2723]~E(x27231,x27232)+E(f884(x27233,x27234,x27235,x27236,x27237,x27231,x27238,x27239),f884(x27233,x27234,x27235,x27236,x27237,x27232,x27238,x27239))
% 22.40/22.33 [2724]~E(x27241,x27242)+E(f884(x27243,x27244,x27245,x27246,x27247,x27248,x27241,x27249),f884(x27243,x27244,x27245,x27246,x27247,x27248,x27242,x27249))
% 22.40/22.33 [2725]~E(x27251,x27252)+E(f884(x27253,x27254,x27255,x27256,x27257,x27258,x27259,x27251),f884(x27253,x27254,x27255,x27256,x27257,x27258,x27259,x27252))
% 22.40/22.33 [2726]~E(x27261,x27262)+E(f253(x27261,x27263,x27264,x27265,x27266),f253(x27262,x27263,x27264,x27265,x27266))
% 22.40/22.33 [2727]~E(x27271,x27272)+E(f253(x27273,x27271,x27274,x27275,x27276),f253(x27273,x27272,x27274,x27275,x27276))
% 22.40/22.33 [2728]~E(x27281,x27282)+E(f253(x27283,x27284,x27281,x27285,x27286),f253(x27283,x27284,x27282,x27285,x27286))
% 22.40/22.33 [2729]~E(x27291,x27292)+E(f253(x27293,x27294,x27295,x27291,x27296),f253(x27293,x27294,x27295,x27292,x27296))
% 22.40/22.33 [2730]~E(x27301,x27302)+E(f253(x27303,x27304,x27305,x27306,x27301),f253(x27303,x27304,x27305,x27306,x27302))
% 22.40/22.33 [2731]~E(x27311,x27312)+E(f801(x27311,x27313),f801(x27312,x27313))
% 22.40/22.33 [2732]~E(x27321,x27322)+E(f801(x27323,x27321),f801(x27323,x27322))
% 22.40/22.33 [2733]~E(x27331,x27332)+E(f561(x27331,x27333,x27334,x27335),f561(x27332,x27333,x27334,x27335))
% 22.40/22.33 [2734]~E(x27341,x27342)+E(f561(x27343,x27341,x27344,x27345),f561(x27343,x27342,x27344,x27345))
% 22.40/22.33 [2735]~E(x27351,x27352)+E(f561(x27353,x27354,x27351,x27355),f561(x27353,x27354,x27352,x27355))
% 22.40/22.33 [2736]~E(x27361,x27362)+E(f561(x27363,x27364,x27365,x27361),f561(x27363,x27364,x27365,x27362))
% 22.40/22.33 [2737]~E(x27371,x27372)+E(f544(x27371,x27373),f544(x27372,x27373))
% 22.40/22.33 [2738]~E(x27381,x27382)+E(f544(x27383,x27381),f544(x27383,x27382))
% 22.40/22.33 [2739]~E(x27391,x27392)+E(f540(x27391,x27393,x27394,x27395,x27396),f540(x27392,x27393,x27394,x27395,x27396))
% 22.40/22.33 [2740]~E(x27401,x27402)+E(f540(x27403,x27401,x27404,x27405,x27406),f540(x27403,x27402,x27404,x27405,x27406))
% 22.40/22.33 [2741]~E(x27411,x27412)+E(f540(x27413,x27414,x27411,x27415,x27416),f540(x27413,x27414,x27412,x27415,x27416))
% 22.40/22.33 [2742]~E(x27421,x27422)+E(f540(x27423,x27424,x27425,x27421,x27426),f540(x27423,x27424,x27425,x27422,x27426))
% 22.40/22.33 [2743]~E(x27431,x27432)+E(f540(x27433,x27434,x27435,x27436,x27431),f540(x27433,x27434,x27435,x27436,x27432))
% 22.40/22.33 [2744]~E(x27441,x27442)+E(f498(x27441,x27443,x27444),f498(x27442,x27443,x27444))
% 22.40/22.33 [2745]~E(x27451,x27452)+E(f498(x27453,x27451,x27454),f498(x27453,x27452,x27454))
% 22.40/22.33 [2746]~E(x27461,x27462)+E(f498(x27463,x27464,x27461),f498(x27463,x27464,x27462))
% 22.40/22.33 [2747]~E(x27471,x27472)+E(f566(x27471,x27473,x27474),f566(x27472,x27473,x27474))
% 22.40/22.33 [2748]~E(x27481,x27482)+E(f566(x27483,x27481,x27484),f566(x27483,x27482,x27484))
% 22.40/22.33 [2749]~E(x27491,x27492)+E(f566(x27493,x27494,x27491),f566(x27493,x27494,x27492))
% 22.40/22.33 [2750]~E(x27501,x27502)+E(f683(x27501,x27503,x27504),f683(x27502,x27503,x27504))
% 22.40/22.33 [2751]~E(x27511,x27512)+E(f683(x27513,x27511,x27514),f683(x27513,x27512,x27514))
% 22.40/22.33 [2752]~E(x27521,x27522)+E(f683(x27523,x27524,x27521),f683(x27523,x27524,x27522))
% 22.40/22.33 [2753]~E(x27531,x27532)+E(f678(x27531,x27533,x27534,x27535),f678(x27532,x27533,x27534,x27535))
% 22.40/22.33 [2754]~E(x27541,x27542)+E(f678(x27543,x27541,x27544,x27545),f678(x27543,x27542,x27544,x27545))
% 22.40/22.33 [2755]~E(x27551,x27552)+E(f678(x27553,x27554,x27551,x27555),f678(x27553,x27554,x27552,x27555))
% 22.40/22.33 [2756]~E(x27561,x27562)+E(f678(x27563,x27564,x27565,x27561),f678(x27563,x27564,x27565,x27562))
% 22.40/22.33 [2757]~E(x27571,x27572)+E(f888(x27571,x27573),f888(x27572,x27573))
% 22.40/22.33 [2758]~E(x27581,x27582)+E(f888(x27583,x27581),f888(x27583,x27582))
% 22.40/22.33 [2759]~E(x27591,x27592)+E(f138(x27591,x27593),f138(x27592,x27593))
% 22.40/22.33 [2760]~E(x27601,x27602)+E(f138(x27603,x27601),f138(x27603,x27602))
% 22.40/22.33 [2761]~E(x27611,x27612)+E(f887(x27611,x27613),f887(x27612,x27613))
% 22.40/22.33 [2762]~E(x27621,x27622)+E(f887(x27623,x27621),f887(x27623,x27622))
% 22.40/22.33 [2763]~E(x27631,x27632)+E(f23(x27631,x27633),f23(x27632,x27633))
% 22.40/22.33 [2764]~E(x27641,x27642)+E(f23(x27643,x27641),f23(x27643,x27642))
% 22.40/22.33 [2765]~E(x27651,x27652)+E(f482(x27651,x27653,x27654,x27655),f482(x27652,x27653,x27654,x27655))
% 22.40/22.33 [2766]~E(x27661,x27662)+E(f482(x27663,x27661,x27664,x27665),f482(x27663,x27662,x27664,x27665))
% 22.40/22.33 [2767]~E(x27671,x27672)+E(f482(x27673,x27674,x27671,x27675),f482(x27673,x27674,x27672,x27675))
% 22.40/22.33 [2768]~E(x27681,x27682)+E(f482(x27683,x27684,x27685,x27681),f482(x27683,x27684,x27685,x27682))
% 22.40/22.33 [2769]~E(x27691,x27692)+E(f816(x27691,x27693),f816(x27692,x27693))
% 22.40/22.33 [2770]~E(x27701,x27702)+E(f816(x27703,x27701),f816(x27703,x27702))
% 22.40/22.33 [2771]~E(x27711,x27712)+E(f786(x27711,x27713,x27714),f786(x27712,x27713,x27714))
% 22.40/22.33 [2772]~E(x27721,x27722)+E(f786(x27723,x27721,x27724),f786(x27723,x27722,x27724))
% 22.40/22.33 [2773]~E(x27731,x27732)+E(f786(x27733,x27734,x27731),f786(x27733,x27734,x27732))
% 22.40/22.33 [2774]~E(x27741,x27742)+E(f889(x27741,x27743),f889(x27742,x27743))
% 22.40/22.33 [2775]~E(x27751,x27752)+E(f889(x27753,x27751),f889(x27753,x27752))
% 22.40/22.33 [2776]~E(x27761,x27762)+E(f199(x27761,x27763,x27764,x27765),f199(x27762,x27763,x27764,x27765))
% 22.40/22.33 [2777]~E(x27771,x27772)+E(f199(x27773,x27771,x27774,x27775),f199(x27773,x27772,x27774,x27775))
% 22.40/22.33 [2778]~E(x27781,x27782)+E(f199(x27783,x27784,x27781,x27785),f199(x27783,x27784,x27782,x27785))
% 22.40/22.33 [2779]~E(x27791,x27792)+E(f199(x27793,x27794,x27795,x27791),f199(x27793,x27794,x27795,x27792))
% 22.40/22.33 [2780]~E(x27801,x27802)+E(f615(x27801,x27803,x27804),f615(x27802,x27803,x27804))
% 22.40/22.33 [2781]~E(x27811,x27812)+E(f615(x27813,x27811,x27814),f615(x27813,x27812,x27814))
% 22.40/22.33 [2782]~E(x27821,x27822)+E(f615(x27823,x27824,x27821),f615(x27823,x27824,x27822))
% 22.40/22.33 [2783]~E(x27831,x27832)+E(f876(x27831,x27833,x27834),f876(x27832,x27833,x27834))
% 22.40/22.33 [2784]~E(x27841,x27842)+E(f876(x27843,x27841,x27844),f876(x27843,x27842,x27844))
% 22.40/22.33 [2785]~E(x27851,x27852)+E(f876(x27853,x27854,x27851),f876(x27853,x27854,x27852))
% 22.40/22.33 [2786]~E(x27861,x27862)+E(f460(x27861,x27863,x27864),f460(x27862,x27863,x27864))
% 22.40/22.33 [2787]~E(x27871,x27872)+E(f460(x27873,x27871,x27874),f460(x27873,x27872,x27874))
% 22.40/22.33 [2788]~E(x27881,x27882)+E(f460(x27883,x27884,x27881),f460(x27883,x27884,x27882))
% 22.40/22.33 [2789]~E(x27891,x27892)+E(f730(x27891,x27893),f730(x27892,x27893))
% 22.40/22.33 [2790]~E(x27901,x27902)+E(f730(x27903,x27901),f730(x27903,x27902))
% 22.40/22.33 [2791]~E(x27911,x27912)+E(f410(x27911,x27913,x27914,x27915),f410(x27912,x27913,x27914,x27915))
% 22.40/22.33 [2792]~E(x27921,x27922)+E(f410(x27923,x27921,x27924,x27925),f410(x27923,x27922,x27924,x27925))
% 22.40/22.33 [2793]~E(x27931,x27932)+E(f410(x27933,x27934,x27931,x27935),f410(x27933,x27934,x27932,x27935))
% 22.40/22.33 [2794]~E(x27941,x27942)+E(f410(x27943,x27944,x27945,x27941),f410(x27943,x27944,x27945,x27942))
% 22.40/22.33 [2795]~E(x27951,x27952)+E(f600(x27951,x27953,x27954),f600(x27952,x27953,x27954))
% 22.40/22.33 [2796]~E(x27961,x27962)+E(f600(x27963,x27961,x27964),f600(x27963,x27962,x27964))
% 22.40/22.33 [2797]~E(x27971,x27972)+E(f600(x27973,x27974,x27971),f600(x27973,x27974,x27972))
% 22.40/22.33 [2798]~E(x27981,x27982)+E(f555(x27981,x27983,x27984,x27985),f555(x27982,x27983,x27984,x27985))
% 22.40/22.33 [2799]~E(x27991,x27992)+E(f555(x27993,x27991,x27994,x27995),f555(x27993,x27992,x27994,x27995))
% 22.40/22.33 [2800]~E(x28001,x28002)+E(f555(x28003,x28004,x28001,x28005),f555(x28003,x28004,x28002,x28005))
% 22.40/22.33 [2801]~E(x28011,x28012)+E(f555(x28013,x28014,x28015,x28011),f555(x28013,x28014,x28015,x28012))
% 22.40/22.33 [2802]~E(x28021,x28022)+E(f752(x28021,x28023,x28024),f752(x28022,x28023,x28024))
% 22.40/22.33 [2803]~E(x28031,x28032)+E(f752(x28033,x28031,x28034),f752(x28033,x28032,x28034))
% 22.40/22.33 [2804]~E(x28041,x28042)+E(f752(x28043,x28044,x28041),f752(x28043,x28044,x28042))
% 22.40/22.33 [2805]~E(x28051,x28052)+E(f849(x28051),f849(x28052))
% 22.40/22.33 [2806]~E(x28061,x28062)+E(f217(x28061,x28063,x28064,x28065,x28066),f217(x28062,x28063,x28064,x28065,x28066))
% 22.40/22.33 [2807]~E(x28071,x28072)+E(f217(x28073,x28071,x28074,x28075,x28076),f217(x28073,x28072,x28074,x28075,x28076))
% 22.40/22.33 [2808]~E(x28081,x28082)+E(f217(x28083,x28084,x28081,x28085,x28086),f217(x28083,x28084,x28082,x28085,x28086))
% 22.40/22.33 [2809]~E(x28091,x28092)+E(f217(x28093,x28094,x28095,x28091,x28096),f217(x28093,x28094,x28095,x28092,x28096))
% 22.40/22.33 [2810]~E(x28101,x28102)+E(f217(x28103,x28104,x28105,x28106,x28101),f217(x28103,x28104,x28105,x28106,x28102))
% 22.40/22.33 [2811]~P1(x28111)+P1(x28112)+~E(x28111,x28112)
% 22.40/22.33 [2812]~P2(x28121)+P2(x28122)+~E(x28121,x28122)
% 22.40/22.33 [2813]~P77(x28131)+P77(x28132)+~E(x28131,x28132)
% 22.40/22.33 [2814]~P98(x28141)+P98(x28142)+~E(x28141,x28142)
% 22.40/22.33 [2815]P28(x28152,x28153)+~E(x28151,x28152)+~P28(x28151,x28153)
% 22.40/22.33 [2816]P28(x28163,x28162)+~E(x28161,x28162)+~P28(x28163,x28161)
% 22.40/22.33 [2817]~P3(x28171)+P3(x28172)+~E(x28171,x28172)
% 22.40/22.33 [2818]~P97(x28181)+P97(x28182)+~E(x28181,x28182)
% 22.40/22.33 [2819]P148(x28192,x28193,x28194)+~E(x28191,x28192)+~P148(x28191,x28193,x28194)
% 22.40/22.33 [2820]P148(x28203,x28202,x28204)+~E(x28201,x28202)+~P148(x28203,x28201,x28204)
% 22.40/22.33 [2821]P148(x28213,x28214,x28212)+~E(x28211,x28212)+~P148(x28213,x28214,x28211)
% 22.40/22.33 [2822]P147(x28222,x28223,x28224)+~E(x28221,x28222)+~P147(x28221,x28223,x28224)
% 22.40/22.33 [2823]P147(x28233,x28232,x28234)+~E(x28231,x28232)+~P147(x28233,x28231,x28234)
% 22.40/22.33 [2824]P147(x28243,x28244,x28242)+~E(x28241,x28242)+~P147(x28243,x28244,x28241)
% 22.40/22.33 [2825]~P4(x28251)+P4(x28252)+~E(x28251,x28252)
% 22.40/22.33 [2826]~P126(x28261)+P126(x28262)+~E(x28261,x28262)
% 22.40/22.33 [2827]P49(x28272,x28273)+~E(x28271,x28272)+~P49(x28271,x28273)
% 22.40/22.33 [2828]P49(x28283,x28282)+~E(x28281,x28282)+~P49(x28283,x28281)
% 22.40/22.33 [2829]~P111(x28291)+P111(x28292)+~E(x28291,x28292)
% 22.40/22.33 [2830]P25(x28302,x28303,x28304,x28305)+~E(x28301,x28302)+~P25(x28301,x28303,x28304,x28305)
% 22.40/22.33 [2831]P25(x28313,x28312,x28314,x28315)+~E(x28311,x28312)+~P25(x28313,x28311,x28314,x28315)
% 22.40/22.33 [2832]P25(x28323,x28324,x28322,x28325)+~E(x28321,x28322)+~P25(x28323,x28324,x28321,x28325)
% 22.40/22.33 [2833]P25(x28333,x28334,x28335,x28332)+~E(x28331,x28332)+~P25(x28333,x28334,x28335,x28331)
% 22.40/22.33 [2834]~P101(x28341)+P101(x28342)+~E(x28341,x28342)
% 22.40/22.33 [2835]~P65(x28351)+P65(x28352)+~E(x28351,x28352)
% 22.40/22.33 [2836]~P5(x28361)+P5(x28362)+~E(x28361,x28362)
% 22.40/22.33 [2837]~P112(x28371)+P112(x28372)+~E(x28371,x28372)
% 22.40/22.33 [2838]~P62(x28381)+P62(x28382)+~E(x28381,x28382)
% 22.40/22.33 [2839]~P82(x28391)+P82(x28392)+~E(x28391,x28392)
% 22.40/22.33 [2840]~P63(x28401)+P63(x28402)+~E(x28401,x28402)
% 22.40/22.33 [2841]~P64(x28411)+P64(x28412)+~E(x28411,x28412)
% 22.40/22.33 [2842]~P93(x28421)+P93(x28422)+~E(x28421,x28422)
% 22.40/22.33 [2843]~P69(x28431)+P69(x28432)+~E(x28431,x28432)
% 22.40/22.33 [2844]P54(x28442,x28443,x28444)+~E(x28441,x28442)+~P54(x28441,x28443,x28444)
% 22.40/22.33 [2845]P54(x28453,x28452,x28454)+~E(x28451,x28452)+~P54(x28453,x28451,x28454)
% 22.40/22.33 [2846]P54(x28463,x28464,x28462)+~E(x28461,x28462)+~P54(x28463,x28464,x28461)
% 22.40/22.33 [2847]~P74(x28471)+P74(x28472)+~E(x28471,x28472)
% 22.40/22.33 [2848]P26(x28482,x28483,x28484,x28485,x28486)+~E(x28481,x28482)+~P26(x28481,x28483,x28484,x28485,x28486)
% 22.40/22.33 [2849]P26(x28493,x28492,x28494,x28495,x28496)+~E(x28491,x28492)+~P26(x28493,x28491,x28494,x28495,x28496)
% 22.40/22.33 [2850]P26(x28503,x28504,x28502,x28505,x28506)+~E(x28501,x28502)+~P26(x28503,x28504,x28501,x28505,x28506)
% 22.40/22.33 [2851]P26(x28513,x28514,x28515,x28512,x28516)+~E(x28511,x28512)+~P26(x28513,x28514,x28515,x28511,x28516)
% 22.40/22.33 [2852]P26(x28523,x28524,x28525,x28526,x28522)+~E(x28521,x28522)+~P26(x28523,x28524,x28525,x28526,x28521)
% 22.40/22.33 [2853]~P102(x28531)+P102(x28532)+~E(x28531,x28532)
% 22.40/22.33 [2854]~P113(x28541)+P113(x28542)+~E(x28541,x28542)
% 22.40/22.33 [2855]~P92(x28551)+P92(x28552)+~E(x28551,x28552)
% 22.40/22.33 [2856]~P106(x28561)+P106(x28562)+~E(x28561,x28562)
% 22.40/22.33 [2857]P59(x28572,x28573)+~E(x28571,x28572)+~P59(x28571,x28573)
% 22.40/22.33 [2858]P59(x28583,x28582)+~E(x28581,x28582)+~P59(x28583,x28581)
% 22.40/22.33 [2859]P58(x28592,x28593,x28594,x28595,x28596)+~E(x28591,x28592)+~P58(x28591,x28593,x28594,x28595,x28596)
% 22.40/22.33 [2860]P58(x28603,x28602,x28604,x28605,x28606)+~E(x28601,x28602)+~P58(x28603,x28601,x28604,x28605,x28606)
% 22.40/22.33 [2861]P58(x28613,x28614,x28612,x28615,x28616)+~E(x28611,x28612)+~P58(x28613,x28614,x28611,x28615,x28616)
% 22.40/22.33 [2862]P58(x28623,x28624,x28625,x28622,x28626)+~E(x28621,x28622)+~P58(x28623,x28624,x28625,x28621,x28626)
% 22.40/22.33 [2863]P58(x28633,x28634,x28635,x28636,x28632)+~E(x28631,x28632)+~P58(x28633,x28634,x28635,x28636,x28631)
% 22.40/22.33 [2864]~P107(x28641)+P107(x28642)+~E(x28641,x28642)
% 22.40/22.33 [2865]P60(x28652,x28653,x28654,x28655)+~E(x28651,x28652)+~P60(x28651,x28653,x28654,x28655)
% 22.40/22.33 [2866]P60(x28663,x28662,x28664,x28665)+~E(x28661,x28662)+~P60(x28663,x28661,x28664,x28665)
% 22.40/22.33 [2867]P60(x28673,x28674,x28672,x28675)+~E(x28671,x28672)+~P60(x28673,x28674,x28671,x28675)
% 22.40/22.33 [2868]P60(x28683,x28684,x28685,x28682)+~E(x28681,x28682)+~P60(x28683,x28684,x28685,x28681)
% 22.40/22.33 [2869]~P41(x28691)+P41(x28692)+~E(x28691,x28692)
% 22.40/22.33 [2870]~P103(x28701)+P103(x28702)+~E(x28701,x28702)
% 22.40/22.33 [2871]~P105(x28711)+P105(x28712)+~E(x28711,x28712)
% 22.40/22.33 [2872]~P66(x28721)+P66(x28722)+~E(x28721,x28722)
% 22.40/22.33 [2873]P33(x28732,x28733,x28734)+~E(x28731,x28732)+~P33(x28731,x28733,x28734)
% 22.40/22.33 [2874]P33(x28743,x28742,x28744)+~E(x28741,x28742)+~P33(x28743,x28741,x28744)
% 22.40/22.33 [2875]P33(x28753,x28754,x28752)+~E(x28751,x28752)+~P33(x28753,x28754,x28751)
% 22.40/22.33 [2876]~P83(x28761)+P83(x28762)+~E(x28761,x28762)
% 22.40/22.33 [2877]~P84(x28771)+P84(x28772)+~E(x28771,x28772)
% 22.40/22.33 [2878]~P127(x28781)+P127(x28782)+~E(x28781,x28782)
% 22.40/22.33 [2879]~P99(x28791)+P99(x28792)+~E(x28791,x28792)
% 22.40/22.33 [2880]P31(x28802,x28803,x28804)+~E(x28801,x28802)+~P31(x28801,x28803,x28804)
% 22.40/22.33 [2881]P31(x28813,x28812,x28814)+~E(x28811,x28812)+~P31(x28813,x28811,x28814)
% 22.40/22.33 [2882]P31(x28823,x28824,x28822)+~E(x28821,x28822)+~P31(x28823,x28824,x28821)
% 22.40/22.33 [2883]~P67(x28831)+P67(x28832)+~E(x28831,x28832)
% 22.40/22.33 [2884]~P68(x28841)+P68(x28842)+~E(x28841,x28842)
% 22.40/22.33 [2885]P17(x28852,x28853,x28854)+~E(x28851,x28852)+~P17(x28851,x28853,x28854)
% 22.40/22.33 [2886]P17(x28863,x28862,x28864)+~E(x28861,x28862)+~P17(x28863,x28861,x28864)
% 22.40/22.33 [2887]P17(x28873,x28874,x28872)+~E(x28871,x28872)+~P17(x28873,x28874,x28871)
% 22.40/22.33 [2888]~P124(x28881)+P124(x28882)+~E(x28881,x28882)
% 22.40/22.33 [2889]~P76(x28891)+P76(x28892)+~E(x28891,x28892)
% 22.40/22.33 [2890]P13(x28902,x28903)+~E(x28901,x28902)+~P13(x28901,x28903)
% 22.40/22.33 [2891]P13(x28913,x28912)+~E(x28911,x28912)+~P13(x28913,x28911)
% 22.40/22.33 [2892]P16(x28922,x28923)+~E(x28921,x28922)+~P16(x28921,x28923)
% 22.40/22.33 [2893]P16(x28933,x28932)+~E(x28931,x28932)+~P16(x28933,x28931)
% 22.40/22.33 [2894]~P89(x28941)+P89(x28942)+~E(x28941,x28942)
% 22.40/22.33 [2895]P11(x28952,x28953,x28954,x28955)+~E(x28951,x28952)+~P11(x28951,x28953,x28954,x28955)
% 22.40/22.33 [2896]P11(x28963,x28962,x28964,x28965)+~E(x28961,x28962)+~P11(x28963,x28961,x28964,x28965)
% 22.40/22.33 [2897]P11(x28973,x28974,x28972,x28975)+~E(x28971,x28972)+~P11(x28973,x28974,x28971,x28975)
% 22.40/22.33 [2898]P11(x28983,x28984,x28985,x28982)+~E(x28981,x28982)+~P11(x28983,x28984,x28985,x28981)
% 22.40/22.33 [2899]~P125(x28991)+P125(x28992)+~E(x28991,x28992)
% 22.40/22.33 [2900]P7(x29002,x29003)+~E(x29001,x29002)+~P7(x29001,x29003)
% 22.40/22.33 [2901]P7(x29013,x29012)+~E(x29011,x29012)+~P7(x29013,x29011)
% 22.40/22.33 [2902]P37(x29022,x29023)+~E(x29021,x29022)+~P37(x29021,x29023)
% 22.40/22.33 [2903]P37(x29033,x29032)+~E(x29031,x29032)+~P37(x29033,x29031)
% 22.40/22.33 [2904]~P119(x29041)+P119(x29042)+~E(x29041,x29042)
% 22.40/22.33 [2905]~P78(x29051)+P78(x29052)+~E(x29051,x29052)
% 22.40/22.33 [2906]P39(x29062,x29063)+~E(x29061,x29062)+~P39(x29061,x29063)
% 22.40/22.33 [2907]P39(x29073,x29072)+~E(x29071,x29072)+~P39(x29073,x29071)
% 22.40/22.33 [2908]P38(x29082,x29083)+~E(x29081,x29082)+~P38(x29081,x29083)
% 22.40/22.33 [2909]P38(x29093,x29092)+~E(x29091,x29092)+~P38(x29093,x29091)
% 22.40/22.33 [2910]~P79(x29101)+P79(x29102)+~E(x29101,x29102)
% 22.40/22.33 [2911]~P120(x29111)+P120(x29112)+~E(x29111,x29112)
% 22.40/22.33 [2912]~P115(x29121)+P115(x29122)+~E(x29121,x29122)
% 22.40/22.33 [2913]~P80(x29131)+P80(x29132)+~E(x29131,x29132)
% 22.40/22.33 [2914]P53(x29142,x29143)+~E(x29141,x29142)+~P53(x29141,x29143)
% 22.40/22.33 [2915]P53(x29153,x29152)+~E(x29151,x29152)+~P53(x29153,x29151)
% 22.40/22.33 [2916]P61(x29162,x29163)+~E(x29161,x29162)+~P61(x29161,x29163)
% 22.40/22.33 [2917]P61(x29173,x29172)+~E(x29171,x29172)+~P61(x29173,x29171)
% 22.40/22.33 [2918]~P114(x29181)+P114(x29182)+~E(x29181,x29182)
% 22.40/22.33 [2919]~P117(x29191)+P117(x29192)+~E(x29191,x29192)
% 22.40/22.33 [2920]~P90(x29201)+P90(x29202)+~E(x29201,x29202)
% 22.40/22.33 [2921]~P139(x29211)+P139(x29212)+~E(x29211,x29212)
% 22.40/22.33 [2922]~P141(x29221)+P141(x29222)+~E(x29221,x29222)
% 22.40/22.33 [2923]~P146(x29231)+P146(x29232)+~E(x29231,x29232)
% 22.40/22.33 [2924]P57(x29242,x29243,x29244)+~E(x29241,x29242)+~P57(x29241,x29243,x29244)
% 22.40/22.33 [2925]P57(x29253,x29252,x29254)+~E(x29251,x29252)+~P57(x29253,x29251,x29254)
% 22.40/22.33 [2926]P57(x29263,x29264,x29262)+~E(x29261,x29262)+~P57(x29263,x29264,x29261)
% 22.40/22.33 [2927]P43(x29272,x29273,x29274,x29275,x29276,x29277)+~E(x29271,x29272)+~P43(x29271,x29273,x29274,x29275,x29276,x29277)
% 22.40/22.33 [2928]P43(x29283,x29282,x29284,x29285,x29286,x29287)+~E(x29281,x29282)+~P43(x29283,x29281,x29284,x29285,x29286,x29287)
% 22.40/22.33 [2929]P43(x29293,x29294,x29292,x29295,x29296,x29297)+~E(x29291,x29292)+~P43(x29293,x29294,x29291,x29295,x29296,x29297)
% 22.40/22.33 [2930]P43(x29303,x29304,x29305,x29302,x29306,x29307)+~E(x29301,x29302)+~P43(x29303,x29304,x29305,x29301,x29306,x29307)
% 22.40/22.33 [2931]P43(x29313,x29314,x29315,x29316,x29312,x29317)+~E(x29311,x29312)+~P43(x29313,x29314,x29315,x29316,x29311,x29317)
% 22.40/22.33 [2932]P43(x29323,x29324,x29325,x29326,x29327,x29322)+~E(x29321,x29322)+~P43(x29323,x29324,x29325,x29326,x29327,x29321)
% 22.40/22.33 [2933]P19(x29332,x29333,x29334)+~E(x29331,x29332)+~P19(x29331,x29333,x29334)
% 22.40/22.33 [2934]P19(x29343,x29342,x29344)+~E(x29341,x29342)+~P19(x29343,x29341,x29344)
% 22.40/22.33 [2935]P19(x29353,x29354,x29352)+~E(x29351,x29352)+~P19(x29353,x29354,x29351)
% 22.40/22.33 [2936]~P72(x29361)+P72(x29362)+~E(x29361,x29362)
% 22.40/22.33 [2937]~P91(x29371)+P91(x29372)+~E(x29371,x29372)
% 22.40/22.33 [2938]~P140(x29381)+P140(x29382)+~E(x29381,x29382)
% 22.40/22.33 [2939]P51(x29392,x29393)+~E(x29391,x29392)+~P51(x29391,x29393)
% 22.40/22.33 [2940]P51(x29403,x29402)+~E(x29401,x29402)+~P51(x29403,x29401)
% 22.40/22.33 [2941]~P118(x29411)+P118(x29412)+~E(x29411,x29412)
% 22.40/22.33 [2942]P40(x29422,x29423,x29424)+~E(x29421,x29422)+~P40(x29421,x29423,x29424)
% 22.40/22.33 [2943]P40(x29433,x29432,x29434)+~E(x29431,x29432)+~P40(x29433,x29431,x29434)
% 22.40/22.33 [2944]P40(x29443,x29444,x29442)+~E(x29441,x29442)+~P40(x29443,x29444,x29441)
% 22.40/22.33 [2945]P30(x29452,x29453,x29454)+~E(x29451,x29452)+~P30(x29451,x29453,x29454)
% 22.40/22.33 [2946]P30(x29463,x29462,x29464)+~E(x29461,x29462)+~P30(x29463,x29461,x29464)
% 22.40/22.33 [2947]P30(x29473,x29474,x29472)+~E(x29471,x29472)+~P30(x29473,x29474,x29471)
% 22.40/22.33 [2948]P50(x29482,x29483,x29484)+~E(x29481,x29482)+~P50(x29481,x29483,x29484)
% 22.40/22.33 [2949]P50(x29493,x29492,x29494)+~E(x29491,x29492)+~P50(x29493,x29491,x29494)
% 22.40/22.33 [2950]P50(x29503,x29504,x29502)+~E(x29501,x29502)+~P50(x29503,x29504,x29501)
% 22.40/22.33 [2951]~P45(x29511)+P45(x29512)+~E(x29511,x29512)
% 22.40/22.33 [2952]~P143(x29521)+P143(x29522)+~E(x29521,x29522)
% 22.40/22.33 [2953]P34(x29532,x29533,x29534,x29535,x29536)+~E(x29531,x29532)+~P34(x29531,x29533,x29534,x29535,x29536)
% 22.40/22.33 [2954]P34(x29543,x29542,x29544,x29545,x29546)+~E(x29541,x29542)+~P34(x29543,x29541,x29544,x29545,x29546)
% 22.40/22.33 [2955]P34(x29553,x29554,x29552,x29555,x29556)+~E(x29551,x29552)+~P34(x29553,x29554,x29551,x29555,x29556)
% 22.40/22.33 [2956]P34(x29563,x29564,x29565,x29562,x29566)+~E(x29561,x29562)+~P34(x29563,x29564,x29565,x29561,x29566)
% 22.40/22.33 [2957]P34(x29573,x29574,x29575,x29576,x29572)+~E(x29571,x29572)+~P34(x29573,x29574,x29575,x29576,x29571)
% 22.40/22.33 [2958]~P87(x29581)+P87(x29582)+~E(x29581,x29582)
% 22.40/22.33 [2959]~P100(x29591)+P100(x29592)+~E(x29591,x29592)
% 22.40/22.33 [2960]P18(x29602,x29603,x29604)+~E(x29601,x29602)+~P18(x29601,x29603,x29604)
% 22.40/22.33 [2961]P18(x29613,x29612,x29614)+~E(x29611,x29612)+~P18(x29613,x29611,x29614)
% 22.40/22.33 [2962]P18(x29623,x29624,x29622)+~E(x29621,x29622)+~P18(x29623,x29624,x29621)
% 22.40/22.33 [2963]~P86(x29631)+P86(x29632)+~E(x29631,x29632)
% 22.40/22.33 [2964]~P75(x29641)+P75(x29642)+~E(x29641,x29642)
% 22.40/22.33 [2965]P15(x29652,x29653,x29654)+~E(x29651,x29652)+~P15(x29651,x29653,x29654)
% 22.40/22.33 [2966]P15(x29663,x29662,x29664)+~E(x29661,x29662)+~P15(x29663,x29661,x29664)
% 22.40/22.33 [2967]P15(x29673,x29674,x29672)+~E(x29671,x29672)+~P15(x29673,x29674,x29671)
% 22.40/22.33 [2968]~P121(x29681)+P121(x29682)+~E(x29681,x29682)
% 22.40/22.33 [2969]~P130(x29691)+P130(x29692)+~E(x29691,x29692)
% 22.40/22.33 [2970]P56(x29702,x29703,x29704)+~E(x29701,x29702)+~P56(x29701,x29703,x29704)
% 22.40/22.33 [2971]P56(x29713,x29712,x29714)+~E(x29711,x29712)+~P56(x29713,x29711,x29714)
% 22.40/22.33 [2972]P56(x29723,x29724,x29722)+~E(x29721,x29722)+~P56(x29723,x29724,x29721)
% 22.40/22.33 [2973]~P6(x29731)+P6(x29732)+~E(x29731,x29732)
% 22.40/22.33 [2974]~P36(x29741)+P36(x29742)+~E(x29741,x29742)
% 22.40/22.33 [2975]P47(x29752,x29753,x29754)+~E(x29751,x29752)+~P47(x29751,x29753,x29754)
% 22.40/22.33 [2976]P47(x29763,x29762,x29764)+~E(x29761,x29762)+~P47(x29763,x29761,x29764)
% 22.40/22.33 [2977]P47(x29773,x29774,x29772)+~E(x29771,x29772)+~P47(x29773,x29774,x29771)
% 22.40/22.33 [2978]P22(x29782,x29783,x29784,x29785,x29786)+~E(x29781,x29782)+~P22(x29781,x29783,x29784,x29785,x29786)
% 22.40/22.33 [2979]P22(x29793,x29792,x29794,x29795,x29796)+~E(x29791,x29792)+~P22(x29793,x29791,x29794,x29795,x29796)
% 22.40/22.33 [2980]P22(x29803,x29804,x29802,x29805,x29806)+~E(x29801,x29802)+~P22(x29803,x29804,x29801,x29805,x29806)
% 22.40/22.33 [2981]P22(x29813,x29814,x29815,x29812,x29816)+~E(x29811,x29812)+~P22(x29813,x29814,x29815,x29811,x29816)
% 22.40/22.33 [2982]P22(x29823,x29824,x29825,x29826,x29822)+~E(x29821,x29822)+~P22(x29823,x29824,x29825,x29826,x29821)
% 22.40/22.33 [2983]~P96(x29831)+P96(x29832)+~E(x29831,x29832)
% 22.40/22.33 [2984]~P104(x29841)+P104(x29842)+~E(x29841,x29842)
% 22.40/22.33 [2985]P8(x29852,x29853,x29854)+~E(x29851,x29852)+~P8(x29851,x29853,x29854)
% 22.40/22.33 [2986]P8(x29863,x29862,x29864)+~E(x29861,x29862)+~P8(x29863,x29861,x29864)
% 22.40/22.33 [2987]P8(x29873,x29874,x29872)+~E(x29871,x29872)+~P8(x29873,x29874,x29871)
% 22.40/22.33 [2988]~P88(x29881)+P88(x29882)+~E(x29881,x29882)
% 22.40/22.33 [2989]~P145(x29891)+P145(x29892)+~E(x29891,x29892)
% 22.40/22.33 [2990]P14(x29902,x29903,x29904)+~E(x29901,x29902)+~P14(x29901,x29903,x29904)
% 22.40/22.33 [2991]P14(x29913,x29912,x29914)+~E(x29911,x29912)+~P14(x29913,x29911,x29914)
% 22.40/22.33 [2992]P14(x29923,x29924,x29922)+~E(x29921,x29922)+~P14(x29923,x29924,x29921)
% 22.40/22.33 [2993]~P129(x29931)+P129(x29932)+~E(x29931,x29932)
% 22.40/22.33 [2994]~P73(x29941)+P73(x29942)+~E(x29941,x29942)
% 22.40/22.33 [2995]~P71(x29951)+P71(x29952)+~E(x29951,x29952)
% 22.40/22.33 [2996]~P142(x29961)+P142(x29962)+~E(x29961,x29962)
% 22.40/22.33 [2997]~P109(x29971)+P109(x29972)+~E(x29971,x29972)
% 22.40/22.33 [2998]P24(x29982,x29983,x29984,x29985,x29986,x29987)+~E(x29981,x29982)+~P24(x29981,x29983,x29984,x29985,x29986,x29987)
% 22.40/22.33 [2999]P24(x29993,x29992,x29994,x29995,x29996,x29997)+~E(x29991,x29992)+~P24(x29993,x29991,x29994,x29995,x29996,x29997)
% 22.40/22.33 [3000]P24(x30003,x30004,x30002,x30005,x30006,x30007)+~E(x30001,x30002)+~P24(x30003,x30004,x30001,x30005,x30006,x30007)
% 22.40/22.33 [3001]P24(x30013,x30014,x30015,x30012,x30016,x30017)+~E(x30011,x30012)+~P24(x30013,x30014,x30015,x30011,x30016,x30017)
% 22.40/22.33 [3002]P24(x30023,x30024,x30025,x30026,x30022,x30027)+~E(x30021,x30022)+~P24(x30023,x30024,x30025,x30026,x30021,x30027)
% 22.40/22.33 [3003]P24(x30033,x30034,x30035,x30036,x30037,x30032)+~E(x30031,x30032)+~P24(x30033,x30034,x30035,x30036,x30037,x30031)
% 22.40/22.33 [3004]~P131(x30041)+P131(x30042)+~E(x30041,x30042)
% 22.40/22.33 [3005]~P144(x30051)+P144(x30052)+~E(x30051,x30052)
% 22.40/22.33 [3006]~P135(x30061)+P135(x30062)+~E(x30061,x30062)
% 22.40/22.33 [3007]P12(x30072,x30073,x30074,x30075,x30076,x30077)+~E(x30071,x30072)+~P12(x30071,x30073,x30074,x30075,x30076,x30077)
% 22.40/22.33 [3008]P12(x30083,x30082,x30084,x30085,x30086,x30087)+~E(x30081,x30082)+~P12(x30083,x30081,x30084,x30085,x30086,x30087)
% 22.40/22.33 [3009]P12(x30093,x30094,x30092,x30095,x30096,x30097)+~E(x30091,x30092)+~P12(x30093,x30094,x30091,x30095,x30096,x30097)
% 22.40/22.33 [3010]P12(x30103,x30104,x30105,x30102,x30106,x30107)+~E(x30101,x30102)+~P12(x30103,x30104,x30105,x30101,x30106,x30107)
% 22.40/22.33 [3011]P12(x30113,x30114,x30115,x30116,x30112,x30117)+~E(x30111,x30112)+~P12(x30113,x30114,x30115,x30116,x30111,x30117)
% 22.40/22.33 [3012]P12(x30123,x30124,x30125,x30126,x30127,x30122)+~E(x30121,x30122)+~P12(x30123,x30124,x30125,x30126,x30127,x30121)
% 22.40/22.33 [3013]P10(x30132,x30133,x30134,x30135,x30136)+~E(x30131,x30132)+~P10(x30131,x30133,x30134,x30135,x30136)
% 22.40/22.33 [3014]P10(x30143,x30142,x30144,x30145,x30146)+~E(x30141,x30142)+~P10(x30143,x30141,x30144,x30145,x30146)
% 22.40/22.33 [3015]P10(x30153,x30154,x30152,x30155,x30156)+~E(x30151,x30152)+~P10(x30153,x30154,x30151,x30155,x30156)
% 22.40/22.33 [3016]P10(x30163,x30164,x30165,x30162,x30166)+~E(x30161,x30162)+~P10(x30163,x30164,x30165,x30161,x30166)
% 22.40/22.33 [3017]P10(x30173,x30174,x30175,x30176,x30172)+~E(x30171,x30172)+~P10(x30173,x30174,x30175,x30176,x30171)
% 22.40/22.33 [3018]~P128(x30181)+P128(x30182)+~E(x30181,x30182)
% 22.40/22.33 [3019]P46(x30192,x30193)+~E(x30191,x30192)+~P46(x30191,x30193)
% 22.56/22.33 [3020]P46(x30203,x30202)+~E(x30201,x30202)+~P46(x30203,x30201)
% 22.56/22.33 [3021]P23(x30212,x30213,x30214,x30215,x30216,x30217)+~E(x30211,x30212)+~P23(x30211,x30213,x30214,x30215,x30216,x30217)
% 22.56/22.33 [3022]P23(x30223,x30222,x30224,x30225,x30226,x30227)+~E(x30221,x30222)+~P23(x30223,x30221,x30224,x30225,x30226,x30227)
% 22.56/22.33 [3023]P23(x30233,x30234,x30232,x30235,x30236,x30237)+~E(x30231,x30232)+~P23(x30233,x30234,x30231,x30235,x30236,x30237)
% 22.56/22.33 [3024]P23(x30243,x30244,x30245,x30242,x30246,x30247)+~E(x30241,x30242)+~P23(x30243,x30244,x30245,x30241,x30246,x30247)
% 22.56/22.33 [3025]P23(x30253,x30254,x30255,x30256,x30252,x30257)+~E(x30251,x30252)+~P23(x30253,x30254,x30255,x30256,x30251,x30257)
% 22.56/22.33 [3026]P23(x30263,x30264,x30265,x30266,x30267,x30262)+~E(x30261,x30262)+~P23(x30263,x30264,x30265,x30266,x30267,x30261)
% 22.56/22.33 [3027]P52(x30272,x30273)+~E(x30271,x30272)+~P52(x30271,x30273)
% 22.56/22.33 [3028]P52(x30283,x30282)+~E(x30281,x30282)+~P52(x30283,x30281)
% 22.56/22.33 [3029]P21(x30292,x30293,x30294,x30295)+~E(x30291,x30292)+~P21(x30291,x30293,x30294,x30295)
% 22.56/22.33 [3030]P21(x30303,x30302,x30304,x30305)+~E(x30301,x30302)+~P21(x30303,x30301,x30304,x30305)
% 22.56/22.33 [3031]P21(x30313,x30314,x30312,x30315)+~E(x30311,x30312)+~P21(x30313,x30314,x30311,x30315)
% 22.56/22.33 [3032]P21(x30323,x30324,x30325,x30322)+~E(x30321,x30322)+~P21(x30323,x30324,x30325,x30321)
% 22.56/22.33 [3033]~P70(x30331)+P70(x30332)+~E(x30331,x30332)
% 22.56/22.33 [3034]P27(x30342,x30343)+~E(x30341,x30342)+~P27(x30341,x30343)
% 22.56/22.33 [3035]P27(x30353,x30352)+~E(x30351,x30352)+~P27(x30353,x30351)
% 22.56/22.33 [3036]~P137(x30361)+P137(x30362)+~E(x30361,x30362)
% 22.56/22.33 [3037]~P138(x30371)+P138(x30372)+~E(x30371,x30372)
% 22.56/22.33 [3038]P32(x30382,x30383,x30384,x30385)+~E(x30381,x30382)+~P32(x30381,x30383,x30384,x30385)
% 22.56/22.33 [3039]P32(x30393,x30392,x30394,x30395)+~E(x30391,x30392)+~P32(x30393,x30391,x30394,x30395)
% 22.56/22.33 [3040]P32(x30403,x30404,x30402,x30405)+~E(x30401,x30402)+~P32(x30403,x30404,x30401,x30405)
% 22.56/22.33 [3041]P32(x30413,x30414,x30415,x30412)+~E(x30411,x30412)+~P32(x30413,x30414,x30415,x30411)
% 22.56/22.33 [3042]~P136(x30421)+P136(x30422)+~E(x30421,x30422)
% 22.56/22.33 [3043]~P122(x30431)+P122(x30432)+~E(x30431,x30432)
% 22.56/22.33 [3044]P48(x30442,x30443,x30444)+~E(x30441,x30442)+~P48(x30441,x30443,x30444)
% 22.56/22.33 [3045]P48(x30453,x30452,x30454)+~E(x30451,x30452)+~P48(x30453,x30451,x30454)
% 22.56/22.33 [3046]P48(x30463,x30464,x30462)+~E(x30461,x30462)+~P48(x30463,x30464,x30461)
% 22.56/22.33 [3047]P20(x30472,x30473,x30474,x30475)+~E(x30471,x30472)+~P20(x30471,x30473,x30474,x30475)
% 22.56/22.33 [3048]P20(x30483,x30482,x30484,x30485)+~E(x30481,x30482)+~P20(x30483,x30481,x30484,x30485)
% 22.56/22.33 [3049]P20(x30493,x30494,x30492,x30495)+~E(x30491,x30492)+~P20(x30493,x30494,x30491,x30495)
% 22.56/22.33 [3050]P20(x30503,x30504,x30505,x30502)+~E(x30501,x30502)+~P20(x30503,x30504,x30505,x30501)
% 22.56/22.33 [3051]P35(x30512,x30513,x30514)+~E(x30511,x30512)+~P35(x30511,x30513,x30514)
% 22.56/22.33 [3052]P35(x30523,x30522,x30524)+~E(x30521,x30522)+~P35(x30523,x30521,x30524)
% 22.56/22.33 [3053]P35(x30533,x30534,x30532)+~E(x30531,x30532)+~P35(x30533,x30534,x30531)
% 22.56/22.33 [3054]P44(x30542,x30543)+~E(x30541,x30542)+~P44(x30541,x30543)
% 22.56/22.33 [3055]P44(x30553,x30552)+~E(x30551,x30552)+~P44(x30553,x30551)
% 22.56/22.33 [3056]P9(x30562,x30563,x30564)+~E(x30561,x30562)+~P9(x30561,x30563,x30564)
% 22.56/22.33 [3057]P9(x30573,x30572,x30574)+~E(x30571,x30572)+~P9(x30573,x30571,x30574)
% 22.56/22.33 [3058]P9(x30583,x30584,x30582)+~E(x30581,x30582)+~P9(x30583,x30584,x30581)
% 22.56/22.33 [3059]~P116(x30591)+P116(x30592)+~E(x30591,x30592)
% 22.56/22.33 [3060]~P134(x30601)+P134(x30602)+~E(x30601,x30602)
% 22.56/22.33 [3061]~P132(x30611)+P132(x30612)+~E(x30611,x30612)
% 22.56/22.33 [3062]~P110(x30621)+P110(x30622)+~E(x30621,x30622)
% 22.56/22.33 [3063]P29(x30632,x30633,x30634)+~E(x30631,x30632)+~P29(x30631,x30633,x30634)
% 22.56/22.33 [3064]P29(x30643,x30642,x30644)+~E(x30641,x30642)+~P29(x30643,x30641,x30644)
% 22.56/22.33 [3065]P29(x30653,x30654,x30652)+~E(x30651,x30652)+~P29(x30653,x30654,x30651)
% 22.56/22.33 [3066]~P133(x30661)+P133(x30662)+~E(x30661,x30662)
% 22.56/22.33 [3067]~P85(x30671)+P85(x30672)+~E(x30671,x30672)
% 22.56/22.33 [3068]~P95(x30681)+P95(x30682)+~E(x30681,x30682)
% 22.56/22.33 [3069]~P94(x30691)+P94(x30692)+~E(x30691,x30692)
% 22.56/22.33 [3070]~P108(x30701)+P108(x30702)+~E(x30701,x30702)
% 22.56/22.33 [3071]~P81(x30711)+P81(x30712)+~E(x30711,x30712)
% 22.56/22.33 [3072]P42(x30722,x30723,x30724,x30725)+~E(x30721,x30722)+~P42(x30721,x30723,x30724,x30725)
% 22.56/22.33 [3073]P42(x30733,x30732,x30734,x30735)+~E(x30731,x30732)+~P42(x30733,x30731,x30734,x30735)
% 22.56/22.33 [3074]P42(x30743,x30744,x30742,x30745)+~E(x30741,x30742)+~P42(x30743,x30744,x30741,x30745)
% 22.56/22.33 [3075]P42(x30753,x30754,x30755,x30752)+~E(x30751,x30752)+~P42(x30753,x30754,x30755,x30751)
% 22.56/22.33 [3076]~P123(x30761)+P123(x30762)+~E(x30761,x30762)
% 22.56/22.33 [3077]P55(x30772,x30773)+~E(x30771,x30772)+~P55(x30771,x30773)
% 22.56/22.33 [3078]P55(x30783,x30782)+~E(x30781,x30782)+~P55(x30783,x30781)
% 22.56/22.33
% 22.56/22.33 %-------------------------------------------
% 22.56/22.34 cnf(10402,plain,
% 22.56/22.34 (~E(f319(a104,x104021),x104021)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(10412,plain,
% 22.56/22.34 (~E(f319(a104,x104121),x104121)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(10425,plain,
% 22.56/22.34 (~E(f319(a104,x104251),x104251)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(10430,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x104301),f105(x104301)),x104302))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10433,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x104331),f105(x104331)),x104332))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10436,plain,
% 22.56/22.34 (~E(f319(a104,x104361),x104361)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(10439,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x104391),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(10442,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x104421),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(10459,plain,
% 22.56/22.34 (~P1(f319(f319(f225(a906),f319(a104,x104591)),x104591))),
% 22.56/22.34 inference(rename_variables,[],[4654])).
% 22.56/22.34 cnf(10462,plain,
% 22.56/22.34 (~E(f319(f319(f143(x104621),x104622),x104623),x104623)),
% 22.56/22.34 inference(rename_variables,[],[4626])).
% 22.56/22.34 cnf(10468,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x104681),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(10471,plain,
% 22.56/22.34 (E(f319(f276(x104711,x104711),f255(x104711,x104712)),x104712)),
% 22.56/22.34 inference(rename_variables,[],[3431])).
% 22.56/22.34 cnf(10474,plain,
% 22.56/22.34 (E(f319(f276(x104741,x104741),f255(x104741,x104742)),x104742)),
% 22.56/22.34 inference(rename_variables,[],[3431])).
% 22.56/22.34 cnf(10479,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x104791),x104791))),
% 22.56/22.34 inference(rename_variables,[],[4646])).
% 22.56/22.34 cnf(10484,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),f319(f319(f74(a906),x104841),x104842)),x104842))),
% 22.56/22.34 inference(rename_variables,[],[4666])).
% 22.56/22.34 cnf(10487,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),f319(f319(f74(a906),x104871),x104872)),x104872))),
% 22.56/22.34 inference(rename_variables,[],[4666])).
% 22.56/22.34 cnf(10505,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x105051),x105051))),
% 22.56/22.34 inference(rename_variables,[],[4646])).
% 22.56/22.34 cnf(10508,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),f39(a906,x105081,x105082)),x105081))),
% 22.56/22.34 inference(rename_variables,[],[3915])).
% 22.56/22.34 cnf(10529,plain,
% 22.56/22.34 (E(f319(f29(a906),f319(f274(a906),x105291)),x105291)),
% 22.56/22.34 inference(rename_variables,[],[3366])).
% 22.56/22.34 cnf(10537,plain,
% 22.56/22.34 (~E(f319(a104,x105371),x105371)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(10540,plain,
% 22.56/22.34 (~E(f319(a104,x105401),x105401)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(10543,plain,
% 22.56/22.34 (~E(f319(a104,x105431),x105431)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(10548,plain,
% 22.56/22.34 (P1(f319(f319(f226(a906),x105481),f319(a104,x105481)))),
% 22.56/22.34 inference(rename_variables,[],[3537])).
% 22.56/22.34 cnf(10557,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x105571),x105571))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(10564,plain,
% 22.56/22.34 (E(f319(f276(x105641,x105641),f255(x105641,x105642)),x105642)),
% 22.56/22.34 inference(rename_variables,[],[3431])).
% 22.56/22.34 cnf(10567,plain,
% 22.56/22.34 (E(f319(f276(x105671,x105671),f255(x105671,x105672)),x105672)),
% 22.56/22.34 inference(rename_variables,[],[3431])).
% 22.56/22.34 cnf(10584,plain,
% 22.56/22.34 (P1(f319(f319(f225(a1),x105841),x105841))),
% 22.56/22.34 inference(rename_variables,[],[3471])).
% 22.56/22.34 cnf(10589,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x105891),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(10592,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x105921,a904)),x105922),f234(f913(x105921,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3844])).
% 22.56/22.34 cnf(10597,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x105971),f105(x105971)),x105972))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10626,plain,
% 22.56/22.34 (~E(f319(f319(f143(x106261),x106262),x106263),x106263)),
% 22.56/22.34 inference(rename_variables,[],[4626])).
% 22.56/22.34 cnf(10629,plain,
% 22.56/22.34 (~E(f319(a104,x106291),f2(a906))),
% 22.56/22.34 inference(rename_variables,[],[4620])).
% 22.56/22.34 cnf(10640,plain,
% 22.56/22.34 (P1(f319(f319(f225(a1),x106401),x106401))),
% 22.56/22.34 inference(rename_variables,[],[3471])).
% 22.56/22.34 cnf(10645,plain,
% 22.56/22.34 (~E(f319(a104,x106451),x106451)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(10648,plain,
% 22.56/22.34 (~P1(f319(f319(f181(f913(x106481,f913(x106482,a904))),x106483),x106484))),
% 22.56/22.34 inference(rename_variables,[],[4669])).
% 22.56/22.34 cnf(10655,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x106551),x106551))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(10668,plain,
% 22.56/22.34 (P1(f319(f319(f226(a906),x106681),f319(a104,x106681)))),
% 22.56/22.34 inference(rename_variables,[],[3537])).
% 22.56/22.34 cnf(10689,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x106891,a904)),x106892),f234(f913(x106891,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3844])).
% 22.56/22.34 cnf(10692,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x106921),f105(x106921)),x106922))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10711,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x107111),f105(x107111)),x107112))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10718,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x107181),f105(x107181)),x107182))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10729,plain,
% 22.56/22.34 (~E(f319(a104,x107291),f2(a906))),
% 22.56/22.34 inference(rename_variables,[],[4620])).
% 22.56/22.34 cnf(10734,plain,
% 22.56/22.34 (P1(f319(f319(f321(x107341),x107342),f234(f913(x107341,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3619])).
% 22.56/22.34 cnf(10741,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x107411),f105(x107411)),x107412))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10746,plain,
% 22.56/22.34 (P1(f319(f319(f226(a906),x107461),f319(a104,x107461)))),
% 22.56/22.34 inference(rename_variables,[],[3537])).
% 22.56/22.34 cnf(10749,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x107491),f105(x107491)),x107492))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10752,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x107521),f105(x107521)),x107522))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10755,plain,
% 22.56/22.34 (~P1(f319(f56(x107551,x107552,f181(f913(x107551,a904))),x107553))),
% 22.56/22.34 inference(rename_variables,[],[4665])).
% 22.56/22.34 cnf(10758,plain,
% 22.56/22.34 (~P1(f319(f56(x107581,x107582,f181(f913(x107581,a904))),x107583))),
% 22.56/22.34 inference(rename_variables,[],[4665])).
% 22.56/22.34 cnf(10764,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x107641),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(10769,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x107691),f105(x107691)),x107692))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10780,plain,
% 22.56/22.34 (~E(f319(a104,x107801),x107801)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(10805,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x108051),x108051))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(10808,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x108081),f319(f319(f75(a906),x108081),x108081)))),
% 22.56/22.34 inference(rename_variables,[],[3727])).
% 22.56/22.34 cnf(10811,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x108111),f319(f319(f75(a906),x108111),x108111)))),
% 22.56/22.34 inference(rename_variables,[],[3727])).
% 22.56/22.34 cnf(10814,plain,
% 22.56/22.34 (P1(f319(f319(f226(a906),x108141),f319(a104,f319(f319(f74(a906),x108142),x108141))))),
% 22.56/22.34 inference(rename_variables,[],[3904])).
% 22.56/22.34 cnf(10819,plain,
% 22.56/22.34 (P1(f319(f319(f226(a906),x108191),f319(a104,x108191)))),
% 22.56/22.34 inference(rename_variables,[],[3537])).
% 22.56/22.34 cnf(10822,plain,
% 22.56/22.34 (P1(f319(f319(f226(a906),x108221),f319(a104,x108221)))),
% 22.56/22.34 inference(rename_variables,[],[3537])).
% 22.56/22.34 cnf(10825,plain,
% 22.56/22.34 (P1(f319(f319(f321(x108251),x108252),f234(f913(x108251,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3619])).
% 22.56/22.34 cnf(10844,plain,
% 22.56/22.34 (~P1(f319(f319(f225(a906),f319(a104,x108441)),x108441))),
% 22.56/22.34 inference(rename_variables,[],[4654])).
% 22.56/22.34 cnf(10847,plain,
% 22.56/22.34 (~P1(f319(f319(f225(a906),f319(a104,x108471)),x108471))),
% 22.56/22.34 inference(rename_variables,[],[4654])).
% 22.56/22.34 cnf(10850,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),f319(f319(f74(a906),x108501),x108502)),x108502))),
% 22.56/22.34 inference(rename_variables,[],[4666])).
% 22.56/22.34 cnf(10853,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),f319(f319(f74(a906),x108531),x108532)),x108532))),
% 22.56/22.34 inference(rename_variables,[],[4666])).
% 22.56/22.34 cnf(10856,plain,
% 22.56/22.34 (P1(f319(f234(f913(x108561,a904)),x108562))),
% 22.56/22.34 inference(rename_variables,[],[3530])).
% 22.56/22.34 cnf(10859,plain,
% 22.56/22.34 (E(f319(f29(a906),f319(f274(a906),x108591)),x108591)),
% 22.56/22.34 inference(rename_variables,[],[3366])).
% 22.56/22.34 cnf(10862,plain,
% 22.56/22.34 (P1(f319(f319(f226(a906),x108621),f319(a104,x108621)))),
% 22.56/22.34 inference(rename_variables,[],[3537])).
% 22.56/22.34 cnf(10869,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x108691),x108691))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(10874,plain,
% 22.56/22.34 (P1(f319(f319(f225(a1),x108741),x108741))),
% 22.56/22.34 inference(rename_variables,[],[3471])).
% 22.56/22.34 cnf(10883,plain,
% 22.56/22.34 (E(f319(f276(x108831,x108831),f255(x108831,x108832)),x108832)),
% 22.56/22.34 inference(rename_variables,[],[3431])).
% 22.56/22.34 cnf(10886,plain,
% 22.56/22.34 (P1(f319(f234(f913(x108861,a904)),x108862))),
% 22.56/22.34 inference(rename_variables,[],[3530])).
% 22.56/22.34 cnf(10889,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),f2(a906)),x108891))),
% 22.56/22.34 inference(rename_variables,[],[3491])).
% 22.56/22.34 cnf(10892,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x108921,a904)),f181(f913(x108921,a904))),x108922))),
% 22.56/22.34 inference(rename_variables,[],[3903])).
% 22.56/22.34 cnf(10895,plain,
% 22.56/22.34 (P1(f319(f234(f913(x108951,a904)),x108952))),
% 22.56/22.34 inference(rename_variables,[],[3530])).
% 22.56/22.34 cnf(10898,plain,
% 22.56/22.34 (P1(f319(f234(f913(x108981,a904)),x108982))),
% 22.56/22.34 inference(rename_variables,[],[3530])).
% 22.56/22.34 cnf(10901,plain,
% 22.56/22.34 (P1(f319(f234(f913(x109011,a904)),x109012))),
% 22.56/22.34 inference(rename_variables,[],[3530])).
% 22.56/22.34 cnf(10904,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x109041),f319(f319(f75(a906),x109041),x109041)))),
% 22.56/22.34 inference(rename_variables,[],[3727])).
% 22.56/22.34 cnf(10944,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x109441),x109441))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(10955,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x109551),f105(x109551)),x109552))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(10962,plain,
% 22.56/22.34 (P1(f319(f319(f226(a906),x109621),f319(a104,x109621)))),
% 22.56/22.34 inference(rename_variables,[],[3537])).
% 22.56/22.34 cnf(10965,plain,
% 22.56/22.34 (P1(f319(f319(f225(a1),x109651),x109651))),
% 22.56/22.34 inference(rename_variables,[],[3471])).
% 22.56/22.34 cnf(10970,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x109701),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(10983,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x109831),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(10986,plain,
% 22.56/22.34 (~P1(f319(f319(f226(f913(x109861,a904)),x109862),f181(f913(x109861,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4663])).
% 22.56/22.34 cnf(10989,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x109891),x109891))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(10992,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x109921),x109921))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(11007,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x110071),x110071))),
% 22.56/22.34 inference(rename_variables,[],[4646])).
% 22.56/22.34 cnf(11016,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x110161),x110162),f181(f913(x110161,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11023,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x110231),x110231))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(11037,plain,
% 22.56/22.34 (E(f319(f302(x110371,x110371,f7(x110371)),x110372),x110372)),
% 22.56/22.34 inference(rename_variables,[],[3526])).
% 22.56/22.34 cnf(11042,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),f2(a906)),x110421))),
% 22.56/22.34 inference(rename_variables,[],[3491])).
% 22.56/22.34 cnf(11045,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x110451),x110451))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(11048,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x110481),x110481))),
% 22.56/22.34 inference(rename_variables,[],[4646])).
% 22.56/22.34 cnf(11068,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x110681),f319(f319(f75(a906),x110681),x110681)))),
% 22.56/22.34 inference(rename_variables,[],[3727])).
% 22.56/22.34 cnf(11081,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x110811),x110811))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(11084,plain,
% 22.56/22.34 (P1(f319(f319(f225(a1),x110841),x110841))),
% 22.56/22.34 inference(rename_variables,[],[3471])).
% 22.56/22.34 cnf(11087,plain,
% 22.56/22.34 (~E(f319(a104,x110871),x110871)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11092,plain,
% 22.56/22.34 (P1(f319(f319(f321(x110921),x110922),f234(f913(x110921,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3619])).
% 22.56/22.34 cnf(11097,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x110971),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(11119,plain,
% 22.56/22.34 (P1(f319(f319(f225(a906),x111191),x111191))),
% 22.56/22.34 inference(rename_variables,[],[3470])).
% 22.56/22.34 cnf(11128,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x111281),x111282),f181(f913(x111281,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11136,plain,
% 22.56/22.34 (P1(f319(f319(f321(x111361),x111362),f234(f913(x111361,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3619])).
% 22.56/22.34 cnf(11139,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x111391),f907(x111391))),f319(f319(f244(f907(x111391),f907(x111391)),x111392),f105(x111391))),f137(x111391,x111393)))),
% 22.56/22.34 inference(rename_variables,[],[4675])).
% 22.56/22.34 cnf(11149,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x111491),x111492),f181(f913(x111491,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11152,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x111521),x111522),f181(f913(x111521,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11155,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x111551,a904)),x111552),f319(f319(f301(x111551),x111553),x111552)))),
% 22.56/22.34 inference(rename_variables,[],[3901])).
% 22.56/22.34 cnf(11161,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x111611,a904)),x111612),f319(f319(f301(x111611),x111613),x111612)))),
% 22.56/22.34 inference(rename_variables,[],[3901])).
% 22.56/22.34 cnf(11190,plain,
% 22.56/22.34 (~E(f319(a104,x111901),f2(a906))),
% 22.56/22.34 inference(rename_variables,[],[4620])).
% 22.56/22.34 cnf(11193,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x111931),f105(x111931)),x111932))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(11206,plain,
% 22.56/22.34 (P1(f319(f319(f226(a906),x112061),f319(a104,x112061)))),
% 22.56/22.34 inference(rename_variables,[],[3537])).
% 22.56/22.34 cnf(11216,plain,
% 22.56/22.34 (~E(f319(f302(x112161,f913(x112161,a904),x112162),x112163),f319(f300(x112161),x112163))),
% 22.56/22.34 inference(rename_variables,[],[4655])).
% 22.56/22.34 cnf(11219,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x112191),x112192),f181(f913(x112191,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11222,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x112221),x112222),f181(f913(x112221,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11225,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(x112251,x112251)),f319(f319(f244(x112251,x112251),x112252),x112253)),f145(x112251,f105(f913(x112251,a906)))))),
% 22.56/22.34 inference(rename_variables,[],[4674])).
% 22.56/22.34 cnf(11228,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(x112281,x112281)),f319(f319(f244(x112281,x112281),x112282),x112283)),f145(x112281,f105(f913(x112281,a906)))))),
% 22.56/22.34 inference(rename_variables,[],[4674])).
% 22.56/22.34 cnf(11233,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x112331),x112332),f181(f913(x112331,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11236,plain,
% 22.56/22.34 (P1(f319(f319(f321(f912(x112361,x112361)),f319(f319(f244(x112361,x112361),x112362),x112362)),f299(x112361,x112363)))),
% 22.56/22.34 inference(rename_variables,[],[4089])).
% 22.56/22.34 cnf(11242,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x112421,a904)),x112422),f234(f913(x112421,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3844])).
% 22.56/22.34 cnf(11258,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x112581,a904)),f181(f913(x112581,a904))),x112582))),
% 22.56/22.34 inference(rename_variables,[],[3903])).
% 22.56/22.34 cnf(11269,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x112691),f907(x112691))),f319(f319(f244(f907(x112691),f907(x112691)),x112692),f105(x112691))),f139(x112691,x112693)))),
% 22.56/22.34 inference(rename_variables,[],[4676])).
% 22.56/22.34 cnf(11280,plain,
% 22.56/22.34 (~E(f319(a104,x112801),x112801)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11283,plain,
% 22.56/22.34 (~E(f319(a104,x112831),x112831)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11295,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x112951,a904)),x112952),x112952))),
% 22.56/22.34 inference(rename_variables,[],[3759])).
% 22.56/22.34 cnf(11302,plain,
% 22.56/22.34 (~E(f319(a104,x113021),x113021)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11305,plain,
% 22.56/22.34 (~E(f319(a104,x113051),x113051)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11315,plain,
% 22.56/22.34 (~E(f319(f302(x113151,f913(x113151,a904),x113152),x113153),f319(f300(x113151),x113153))),
% 22.56/22.34 inference(rename_variables,[],[4655])).
% 22.56/22.34 cnf(11320,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x113201,a904)),x113202),f234(f913(x113201,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3844])).
% 22.56/22.34 cnf(11336,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x113361),x113362),f181(f913(x113361,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11339,plain,
% 22.56/22.34 (~P1(f319(f319(f225(a906),f319(a104,x113391)),x113391))),
% 22.56/22.34 inference(rename_variables,[],[4654])).
% 22.56/22.34 cnf(11346,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x113461),x113462),f181(f913(x113461,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11355,plain,
% 22.56/22.34 (~P1(f319(f319(f225(a906),f319(a104,x113551)),x113551))),
% 22.56/22.34 inference(rename_variables,[],[4654])).
% 22.56/22.34 cnf(11358,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x113581),x113582),f181(f913(x113581,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11371,plain,
% 22.56/22.34 (P1(f319(f319(f321(f912(x113711,x113711)),f319(f319(f244(x113711,x113711),x113712),x113712)),f299(x113711,x113713)))),
% 22.56/22.34 inference(rename_variables,[],[4089])).
% 22.56/22.34 cnf(11374,plain,
% 22.56/22.34 (P1(f319(f319(f321(x113741),x113742),f234(f913(x113741,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3619])).
% 22.56/22.34 cnf(11377,plain,
% 22.56/22.34 (P1(f319(f319(f321(x113771),x113772),f234(f913(x113771,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3619])).
% 22.56/22.34 cnf(11384,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x113841),f907(x113841))),f319(f319(f244(f907(x113841),f907(x113841)),x113842),f105(x113841))),f137(x113841,x113843)))),
% 22.56/22.34 inference(rename_variables,[],[4675])).
% 22.56/22.34 cnf(11387,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x113871),f907(x113871))),f319(f319(f244(f907(x113871),f907(x113871)),x113872),f105(x113871))),f139(x113871,x113873)))),
% 22.56/22.34 inference(rename_variables,[],[4676])).
% 22.56/22.34 cnf(11390,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x113901),f907(x113901))),f319(f319(f244(f907(x113901),f907(x113901)),x113902),f105(x113901))),f149(x113901,x113903)))),
% 22.56/22.34 inference(rename_variables,[],[4677])).
% 22.56/22.34 cnf(11395,plain,
% 22.56/22.34 (~P1(f319(f319(f226(f913(x113951,a904)),x113952),f181(f913(x113951,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4663])).
% 22.56/22.34 cnf(11398,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x113981),x113982),f181(f913(x113981,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11403,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x114031,a904)),x114032),f234(f913(x114031,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3844])).
% 22.56/22.34 cnf(11410,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x114101),f105(x114101)),x114102))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(11415,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x114151),x114152),f181(f913(x114151,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11418,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(x114181,x114181)),f319(f319(f244(x114181,x114181),x114182),x114183)),f145(x114181,f105(f913(x114181,a906)))))),
% 22.56/22.34 inference(rename_variables,[],[4674])).
% 22.56/22.34 cnf(11424,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x114241),x114242),f181(f913(x114241,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11427,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x114271,a904)),f181(f913(x114271,a904))),x114272))),
% 22.56/22.34 inference(rename_variables,[],[3903])).
% 22.56/22.34 cnf(11430,plain,
% 22.56/22.34 (P1(f319(f319(f321(f912(x114301,x114301)),f319(f319(f244(x114301,x114301),x114302),x114302)),f299(x114301,x114303)))),
% 22.56/22.34 inference(rename_variables,[],[4089])).
% 22.56/22.34 cnf(11448,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x114481),f907(x114481))),f319(f319(f244(f907(x114481),f907(x114481)),f105(x114481)),x114482)),f137(x114481,x114483)))),
% 22.56/22.34 inference(rename_variables,[],[4678])).
% 22.56/22.34 cnf(11456,plain,
% 22.56/22.34 (P1(f319(f319(f321(x114561),x114562),f234(f913(x114561,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3619])).
% 22.56/22.34 cnf(11461,plain,
% 22.56/22.34 (P1(f319(f319(f225(f913(x114611,a904)),f181(f913(x114611,a904))),x114612))),
% 22.56/22.34 inference(rename_variables,[],[3903])).
% 22.56/22.34 cnf(11464,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x114641),x114642),f181(f913(x114641,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11493,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x114931),f907(x114931))),f319(f319(f244(f907(x114931),f907(x114931)),x114932),f105(x114931))),f137(x114931,x114933)))),
% 22.56/22.34 inference(rename_variables,[],[4675])).
% 22.56/22.34 cnf(11496,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x114961),f907(x114961))),f319(f319(f244(f907(x114961),f907(x114961)),x114962),f105(x114961))),f139(x114961,x114963)))),
% 22.56/22.34 inference(rename_variables,[],[4676])).
% 22.56/22.34 cnf(11499,plain,
% 22.56/22.34 (~E(f319(f319(f143(x114991),x114992),x114993),x114993)),
% 22.56/22.34 inference(rename_variables,[],[4626])).
% 22.56/22.34 cnf(11502,plain,
% 22.56/22.34 (~E(f319(a104,x115021),x115021)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11505,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x115051),x115052),f181(f913(x115051,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11510,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x115101),x115102),f181(f913(x115101,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11513,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x115131),x115132),f181(f913(x115131,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11516,plain,
% 22.56/22.34 (P1(f319(f319(f321(f912(f907(x115161),f907(x115161))),f319(f319(f244(f907(x115161),f907(x115161)),x115162),x115162)),f150(x115161,f299(x115161,x115163))))),
% 22.56/22.34 inference(rename_variables,[],[4218])).
% 22.56/22.34 cnf(11519,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x115191),f907(x115191))),f319(f319(f244(f907(x115191),f907(x115191)),x115192),f105(x115191))),f137(x115191,x115193)))),
% 22.56/22.34 inference(rename_variables,[],[4675])).
% 22.56/22.34 cnf(11529,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(x115291,x115291)),f319(f319(f244(x115291,x115291),x115292),x115293)),f145(x115291,f105(f913(x115291,a906)))))),
% 22.56/22.34 inference(rename_variables,[],[4674])).
% 22.56/22.34 cnf(11532,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x115321),x115322),f181(f913(x115321,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11535,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x115351),x115352),f181(f913(x115351,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11538,plain,
% 22.56/22.34 (P1(f319(f319(f321(x115381),x115382),f234(f913(x115381,a904))))),
% 22.56/22.34 inference(rename_variables,[],[3619])).
% 22.56/22.34 cnf(11541,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x115411),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(11546,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(x115461,x115461)),f319(f319(f244(x115461,x115461),x115462),x115463)),f145(x115461,f105(f913(x115461,a906)))))),
% 22.56/22.34 inference(rename_variables,[],[4674])).
% 22.56/22.34 cnf(11549,plain,
% 22.56/22.34 (~E(f319(f302(x115491,f913(x115491,a904),x115492),x115493),f319(f300(x115491),x115493))),
% 22.56/22.34 inference(rename_variables,[],[4655])).
% 22.56/22.34 cnf(11552,plain,
% 22.56/22.34 (~E(f319(f302(x115521,f913(x115521,a904),x115522),x115523),f319(f300(x115521),x115523))),
% 22.56/22.34 inference(rename_variables,[],[4655])).
% 22.56/22.34 cnf(11557,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x115571),f907(x115571))),f319(f319(f244(f907(x115571),f907(x115571)),x115572),f105(x115571))),f137(x115571,x115573)))),
% 22.56/22.34 inference(rename_variables,[],[4675])).
% 22.56/22.34 cnf(11563,plain,
% 22.56/22.34 (~P1(f319(f319(f321(f912(f907(x115631),f907(x115631))),f319(f319(f244(f907(x115631),f907(x115631)),x115632),f105(x115631))),f137(x115631,x115633)))),
% 22.56/22.34 inference(rename_variables,[],[4675])).
% 22.56/22.34 cnf(11566,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x115661),x115662),f181(f913(x115661,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11571,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x115711),x115712),f181(f913(x115711,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11574,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x115741),x115742),f181(f913(x115741,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11577,plain,
% 22.56/22.34 (~P1(f319(f319(f321(x115771),x115772),f181(f913(x115771,a904))))),
% 22.56/22.34 inference(rename_variables,[],[4657])).
% 22.56/22.34 cnf(11594,plain,
% 22.56/22.34 (E(f106(x115941,f105(x115941)),f105(x115941))),
% 22.56/22.34 inference(rename_variables,[],[3316])).
% 22.56/22.34 cnf(11597,plain,
% 22.56/22.34 (~E(f319(a104,x115971),x115971)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11604,plain,
% 22.56/22.34 (~E(f319(a104,x116041),x116041)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11609,plain,
% 22.56/22.34 (E(f319(f276(x116091,x116091),f255(x116091,x116092)),x116092)),
% 22.56/22.34 inference(rename_variables,[],[3431])).
% 22.56/22.34 cnf(11612,plain,
% 22.56/22.34 (E(f319(f276(x116121,x116121),f255(x116121,x116122)),x116122)),
% 22.56/22.34 inference(rename_variables,[],[3431])).
% 22.56/22.34 cnf(11618,plain,
% 22.56/22.34 (~E(f319(a104,x116181),x116181)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11630,plain,
% 22.56/22.34 (E(f319(f319(f3(a906),f2(a906)),x116301),f2(a906))),
% 22.56/22.34 inference(rename_variables,[],[3388])).
% 22.56/22.34 cnf(11633,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a906),x116331),f2(a906)))),
% 22.56/22.34 inference(rename_variables,[],[4650])).
% 22.56/22.34 cnf(11640,plain,
% 22.56/22.34 (E(f319(f319(f74(a1),f319(f319(f75(a1),x116401),f319(f319(f30(a1),x116402),x116401))),f39(a1,x116402,x116401)),x116402)),
% 22.56/22.34 inference(rename_variables,[],[4006])).
% 22.56/22.34 cnf(11664,plain,
% 22.56/22.34 (~E(f319(a104,x116641),x116641)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11667,plain,
% 22.56/22.34 (~E(f319(a104,x116671),x116671)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11689,plain,
% 22.56/22.34 (~E(f319(a104,x116891),x116891)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11699,plain,
% 22.56/22.34 (~P1(f319(f319(f164(x116991),f105(x116991)),x116992))),
% 22.56/22.34 inference(rename_variables,[],[4653])).
% 22.56/22.34 cnf(11706,plain,
% 22.56/22.34 (~E(f319(a104,x117061),x117061)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11721,plain,
% 22.56/22.34 (~E(f319(a104,x117211),x117211)),
% 22.56/22.34 inference(rename_variables,[],[4614])).
% 22.56/22.34 cnf(11732,plain,
% 22.56/22.34 (E(f319(f276(x117321,x117321),f255(x117321,x117322)),x117322)),
% 22.56/22.34 inference(rename_variables,[],[3431])).
% 22.56/22.34 cnf(11748,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a1),f319(f92(a1),x117481)),f2(a1)))),
% 22.56/22.34 inference(rename_variables,[],[4659])).
% 22.56/22.34 cnf(11771,plain,
% 22.56/22.34 (E(f319(f276(x117711,x117711),f255(x117711,x117712)),x117712)),
% 22.56/22.34 inference(rename_variables,[],[3431])).
% 22.56/22.34 cnf(11779,plain,
% 22.56/22.34 (~P1(f319(f319(f226(a1),f319(f92(a1),x117791)),f2(a1)))),
% 22.56/22.34 inference(rename_variables,[],[4659])).
% 22.56/22.34 cnf(11795,plain,
% 22.56/22.34 ($false),
% 22.56/22.34 inference(scs_inference,[],[3792,3701,4614,10402,10412,10425,10436,10537,10540,10543,10645,10780,11087,11280,11283,11302,11305,11502,11597,11604,11618,11664,11667,11689,11706,11721,3391,4620,10629,10729,11190,4624,3085,3091,3095,3096,3098,3107,3113,3116,3120,3121,3122,3131,3143,3167,3168,3169,3223,3239,3240,3248,3256,3361,3362,3268,4612,3316,11594,3431,10471,10474,10564,10567,10883,11609,11612,11732,11771,3408,3917,3306,4006,11640,3371,3302,3329,3325,3312,3313,3930,3526,11037,3401,4086,4626,10462,10626,11499,4655,11216,11315,11549,11552,3573,3365,3366,10529,10859,3284,3388,11630,4225,4089,11236,11371,11430,4675,11139,11384,11493,11519,11557,11563,4676,11269,11387,11496,4677,11390,4678,11448,4679,3386,3662,3826,3763,3972,3537,10548,10668,10746,10819,10822,10862,10962,11206,3906,3454,3549,4650,10439,10442,10468,10589,10764,10970,10983,11097,11541,11633,4659,11748,11779,3893,3672,4035,3497,3499,3473,4647,4622,3655,4662,4218,11516,3785,4653,10430,10433,10597,10692,10711,10718,10741,10749,10752,10769,10955,11193,11410,11699,4189,4144,3827,4177,3844,10592,10689,11242,11320,11403,4663,10986,11395,3470,10557,10655,10805,10869,10944,10989,10992,11023,11045,11081,11119,3471,10584,10640,10874,10965,11084,4646,10479,10505,11007,11048,3619,10734,10825,11092,11136,11374,11377,11456,11538,4657,11016,11128,11149,11152,11219,11222,11233,11336,11346,11358,11398,11415,11424,11464,11505,11510,11513,11532,11535,11566,11571,11574,11577,3530,10856,10886,10895,10898,10901,3569,3562,3976,3915,10508,4654,10459,10844,10847,11339,11355,3491,10889,11042,4651,3984,4638,4641,3447,3451,4640,4639,4673,4362,4665,10755,10758,4674,11225,11228,11418,11529,11546,4053,3901,11155,11161,3759,11295,3903,10892,11258,11427,11461,3620,3727,10808,10811,10904,11068,4668,4669,10648,4315,4230,3938,4666,10484,10487,10850,10853,3904,10814,4163,4686,4712,4767,4771,4793,4808,4815,4817,4853,4858,4887,4893,4977,5003,5004,5019,5070,5071,5093,5094,5108,5112,5137,5143,5159,5163,5164,5165,5170,5171,5196,5222,5224,5225,5235,5248,5284,5285,5293,5302,5306,5308,5322,5324,5330,5335,5336,5349,5355,5358,5359,5363,5390,5405,5414,5416,5417,5420,5421,5422,5432,5434,5440,5441,5442,5448,5452,5453,5454,5462,5466,5467,5472,5485,5493,5506,5508,5516,5518,5519,5522,5526,5553,5567,5568,5583,5593,5615,5621,5645,5646,5649,5668,5676,5677,5682,5683,5693,5695,5710,5714,5723,5724,5726,5727,5743,5748,5758,5759,5770,5777,5791,5795,5798,5804,5805,5806,5809,5814,5850,5851,5854,5856,5858,5860,5861,5862,5864,5866,5868,5873,5880,5895,5909,5915,5916,5923,5934,5935,5942,5947,5949,5954,5962,5998,6011,6020,6023,6032,6035,6036,6037,6038,6039,6043,6048,6058,6064,6082,6085,6094,6123,6138,6162,6179,6180,6183,6197,6199,6201,6203,6218,6219,6222,6224,6227,6228,6245,6253,6254,6255,6259,6261,6293,6294,6300,6303,6310,6314,6348,6350,6352,6354,6363,6365,6368,6374,6376,6381,6384,6392,6400,6402,6403,6408,6430,6431,6432,6433,6434,6436,6442,6445,6480,6481,6484,6485,6486,6488,6489,6490,6491,6500,6535,6536,6545,6566,6567,6588,6590,6602,6603,6609,6635,6637,6653,6692,6694,6695,6753,6776,6823,6844,6853,6854,6855,6856,6875,6876,6883,6890,6893,6895,6897,6898,6899,6901,6915,6926,6927,6928,6939,6992,7003,7005,7027,7028,7063,7070,7078,7108,7137,7193,7221,7276,7297,7305,7308,7368,7378,7437,7439,7447,7456,7457,7458,7475,7479,7481,7527,7537,7540,7555,7602,7604,7607,7649,7650,7668,7733,7751,7775,7798,7809,7823,7834,7845,7846,7873,7875,7877,7889,7925,7939,7964,7987,8019,8047,8079,8117,8133,8135,8151,8152,8218,8230,8296,8319,8337,8364,8403,8404,8422,8459,8461,8463,8469,8484,8488,8503,8524,8532,8534,8545,8550,8554,8555,8556,8557,8558,8559,8580,8592,8593,8610,8611,8620,8621,8622,8623,8624,8642,8643,8644,8655,8668,8670,8681,8686,8688,8690,8691,8692,8699,8704,8712,8715,8733,8734,8743,8744,8752,8766,8779,8782,8802,8824,8827,8828,8835,8845,8846,8847,8867,8879,8889,8890,8891,8894,8917,8918,8931,8983,8989,8996,8998,9014,9017,9029,9030,9031,9041,9106,9137,9138,9139,9154,9167,9173,9195,9196,9275,9309,9315,9325,9326,9327,9335,9364,9380,9384,9388,9414,9415,9442,9509,9514,9517,9545,9546,9547,9571,9572,9586,9607,9613,9633,9663,9684,9693,9694,9695,9696,9710,9712,9717,9754,9755,9761,9762,9813,9814,9825,9826,9851,9870,9872,9873,9882,9891,9905,9934,9965,9967,9971,10016,10050,10051,10052,10060,10061,10066,10080,10163,10261,10262,10263,10264,10361,10386,2,12,13,4699,4700,4718,4760,4761,4763,4786,4788,4789,4797,4842,4844,4892,5020,5021,5035,5059,5115,5116,5122,5123,5125,5127,5136,5139,5140,5148,5161,5162,5168,5189,5190,5211,5216,5217,5218,5219,5223,5231,5234,5241,5242,5243,5299,5304,5305,5310,5316,5346,5356,5361,5371,5388,5389,5396,5397,5399,5410,5428,5430,5431,5438,5445,5446,5458,5459,5460,5461,5463,5464,5468,5469,5470,5471,5502,5503,5504,5512,5513,5514,5515,5559,5564,5566,5592]),
% 22.56/22.34 ['proof']).
% 22.56/22.34 % SZS output end Proof
% 22.56/22.34 % Total time :8.130000s
%------------------------------------------------------------------------------